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1 // vim: filetype=c:tabstop=4:ai:expandtab
2 // SPDX-License-Identifier: ICU
3 // scspell-id: c39f59d7-f62c-11ec-ba31-80ee73e9b8e7
4 /* ------------------------------------------------------------------- */
5 /* Decimal Number arithmetic module */
6 /* ------------------------------------------------------------------- */
7 /* */
8 /* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */
9 /* */
10 /* This software is made available under the terms of the ICU License. */
11 /* */
12 /* The description and User's Guide ("The decNumber C Library") for */
13 /* this software is called decNumber.pdf. This document is available, */
14 /* together with arithmetic and format specifications, testcases, and */
15 /* Web links, on the General Decimal Arithmetic page. */
16 /* */
17 /* Please send comments, suggestions, and corrections to the author: */
18 /* mfc@uk.ibm.com */
19 /* Mike Cowlishaw, IBM Fellow */
20 /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
21 /* */
22 /* ------------------------------------------------------------------- */
23 /* */
24 /* This module comprises the routines for arbitrary-precision General */
25 /* Decimal Arithmetic as defined in the specification which may be */
26 /* found on the General Decimal Arithmetic pages. It implements both */
27 /* the full ('extended') arithmetic and the simpler ('subset') */
28 /* arithmetic. */
29 /* */
30 /* Usage notes: */
31 /* */
32 /* 1. The decNumber format which this library uses is optimized for */
33 /* efficient processing of relatively short numbers; in particular */
34 /* it allows the use of fixed sized structures and minimizes copy */
35 /* and move operations. It does, however, support arbitrary */
36 /* precision (up to 999,999,999 digits) and arbitrary exponent */
37 /* range (Emax in the range 0 through 999,999,999 and Emin in the */
38 /* range -999,999,999 through 0). Mathematical functions (for */
39 /* example decNumberExp) as identified below are restricted more */
40 /* tightly: digits, emax, and -emin in the context must be <= */
41 /* DEC_MAX_MATH (999999), and their operand(s) must be within */
42 /* these bounds. */
43 /* */
44 /* 2. Logical functions are further restricted; their operands must */
45 /* be finite, positive, have an exponent of zero, and all digits */
46 /* must be either 0 or 1. The result will only contain digits */
47 /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
48 /* */
49 /* 3. Operands to operator functions are never modified unless they */
50 /* are also specified to be the result number (which is always */
51 /* permitted). Other than that case, operands must not overlap. */
52 /* */
53 /* 4. Error handling: the type of the error is ORed into the status */
54 /* flags in the current context (decContext structure). The SIGFPE */
55 /* signal is then raised if the corresponding trap-enabler flag in */
56 /* the decContext is set (is 1). */
57 /* */
58 /* It is the responsibility of the caller to clear the status flags */
59 /* as required. */
60 /* */
61 /* The result of any routine which returns a number will always be */
62 /* a valid number (which may be a special value, such as an */
63 /* Infinity or NaN). */
64 /* */
65 /* 5. The decNumber format is not an exchangeable concrete */
66 /* representation as it comprises fields which may be machine- */
67 /* dependent (packed or unpacked, or special length, for example). */
68 /* Canonical conversions to and from strings are provided; other */
69 /* conversions are available in separate modules. */
70 /* */
71 /* 6. Subset arithmetic is available only if DECSUBSET is set to 1. */
72 /* */
73 /* ------------------------------------------------------------------- */
74 /* */
75 /* Implementation notes for maintenance of this module: */
76 /* */
77 /* 1. Storage leak protection: Routines which use malloc are not */
78 /* permitted to use return for fastpath or error exits (i.e., they */
79 /* follow strict structured programming conventions). Instead they */
80 /* have a do{}while(0); construct surrounding the code which is */
81 /* protected -- break may be used to exit this. Other routines can */
82 /* safely use the return statement inline. */
83 /* */
84 /* 2. All loops use the for(;;) construct. Any do construct does not */
85 /* loop; it is for allocation protection as just described. */
86 /* */
87 /* 3. Setting status in the context must always be the very last */
88 /* action in a routine, as non-0 status may raise a trap and hence */
89 /* the call to set status may not return (if the handler uses long */
90 /* jump). Therefore all cleanup must be done first. In general, */
91 /* to achieve this status is accumulated and is only applied just */
92 /* before return by calling decContextSetStatus (via decStatus). */
93 /* */
94 /* Routines which allocate storage cannot, in general, use the 'top */
95 /* level' routines which could cause a non-returning transfer of */
96 /* control. The decXxxxOp routines are safe (do not call decStatus */
97 /* even if traps are set in the context) and should be used instead */
98 /* (they are also a little faster). */
99 /* */
100 /* 4. Exponent checking is minimized by allowing the exponent to grow */
101 /* outside its limits during calculations, provided that the */
102 /* decFinalize function is called later. Multiplication and */
103 /* division, and intermediate calculations in exponentiation, */
104 /* require more careful checks because of the risk of 31-bit */
105 /* overflow (the most negative valid exponent is -1999999997, for a */
106 /* 999999999-digit number with adjusted exponent of -999999999). */
107 /* */
108 /* 5. Rounding is deferred until finalization of results, with any */
109 /* 'off to the right' data being represented as a single digit */
110 /* residue (in the range -1 through 9). This avoids any double- */
111 /* rounding when more than one shortening takes place (for example */
112 /* when a result is subnormal). */
113 /* */
114 /* 6. The digits count is allowed to rise to a multiple of DECDPUN */
115 /* during many operations, so whole Units are handled and exact */
116 /* accounting of digits is not needed. The correct digits value is */
117 /* found by decGetDigits, which accounts for leading zeros. This */
118 /* must be called before any rounding if the number of digits is */
119 /* not known exactly. */
120 /* */
121 /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
122 /* numbers up to four digits, using appropriate constants. This is */
123 /* not useful for longer numbers because overflow of 32 bits would */
124 /* lead to 4 multiplies, which is almost as expensive as a divide */
125 /* (unless a floating-point or 64-bit multiply is assumed to be */
126 /* available). */
127 /* */
128 /* 8. Unusual abbreviations that may be used in the commentary: */
129 /* lhs -- left hand side (operand, of an operation) */
130 /* lsd -- least significant digit (of coefficient) */
131 /* lsu -- least significant Unit (of coefficient) */
132 /* msd -- most significant digit (of coefficient) */
133 /* msi -- most significant item (in an array) */
134 /* msu -- most significant Unit (of coefficient) */
135 /* rhs -- right hand side (operand, of an operation) */
136 /* +ve -- positive */
137 /* -ve -- negative */
138 /* ** -- raise to the power */
139 /* */
140 /* ------------------------------------------------------------------- */
141
142 #include <string.h> // for strcpy
143 #include <stdlib.h> // for malloc, free, etc.
144 #include <ctype.h> // for lower
145 #include "decNumber.h" // base number library
146 #include "decNumberLocal.h" // decNumber local types, etc.
147
148 #if defined(FREE)
149 # undef FREE
150 #endif /* if defined(FREE) */
151 #define FREE(p) do \
152 { \
153 free((p)); \
154 (p) = NULL; \
155 } while(0)
156
157 /* Constants */
158 // Public lookup table used by the D2U macro
159 const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
160
161 #define powers DECPOWERS // old internal name
162
163 // Local constants
164 #define DIVIDE 0x80 // Divide operators
165 #define REMAINDER 0x40 // ..
166 #define DIVIDEINT 0x20 // ..
167 #define REMNEAR 0x10 // ..
168 #define COMPARE 0x01 // Compare operators
169 #define COMPMAX 0x02 // ..
170 #define COMPMIN 0x03 // ..
171 #define COMPTOTAL 0x04 // ..
172 #define COMPNAN 0x05 // .. [NaN processing]
173 #define COMPSIG 0x06 // .. [signaling COMPARE]
174 #define COMPMAXMAG 0x07 // ..
175 #define COMPMINMAG 0x08 // ..
176
177 #define DEC_sNaN 0x40000000 // local status: sNaN signal
178 #define BADINT (Int)0x80000000 // most-negative Int; error indicator
179 // Next two indicate an integer >= 10**6, and its parity (bottom bit)
180 #define BIGEVEN (Int)0x80000002
181 #define BIGODD (Int)0x80000003
182
183 static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing
184
185 /* Granularity-dependent code */
186 #if DECDPUN<=4
187 # define eInt Int // extended integer
188 # define ueInt uInt // unsigned extended integer
189 // Constant multipliers for divide-by-power-of five using reciprocal
190 // multiply, after removing powers of 2 by shifting, and final shift
191 // of 17 [we only need up to **4]
192 static const uInt multies[]={131073, 26215, 5243, 1049, 210};
193 // QUOT10 -- macro to return the quotient of unit u divided by 10**n
194 # define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
195 #else
196 // For DECDPUN>4 non-ANSI-89 64-bit types are needed.
197 # if !DECUSE64
198 # error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
199 # endif
200 # define eInt Long // extended integer
201 # define ueInt uLong // unsigned extended integer
202 #endif
203
204 /* Local routines */
205 static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
206 decContext *, uByte, uInt *);
207 static Flag decBiStr(const char *, const char *, const char *);
208 static uInt decCheckMath(const decNumber *, decContext *, uInt *);
209 static void decApplyRound(decNumber *, decContext *, Int, uInt *);
210 static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
211 static decNumber * decCompareOp(decNumber *, const decNumber *,
212 const decNumber *, decContext *,
213 Flag, uInt *);
214 static void decCopyFit(decNumber *, const decNumber *, decContext *,
215 Int *, uInt *);
216 static decNumber * decDecap(decNumber *, Int);
217 static decNumber * decDivideOp(decNumber *, const decNumber *,
218 const decNumber *, decContext *, Flag, uInt *);
219 static decNumber * decExpOp(decNumber *, const decNumber *,
220 decContext *, uInt *);
221 static void decFinalize(decNumber *, decContext *, Int *, uInt *);
222 static Int decGetDigits(Unit *, Int);
223 static Int decGetInt(const decNumber *);
224 static decNumber * decLnOp(decNumber *, const decNumber *,
225 decContext *, uInt *);
226 static decNumber * decMultiplyOp(decNumber *, const decNumber *,
227 const decNumber *, decContext *,
228 uInt *);
229 static decNumber * decNaNs(decNumber *, const decNumber *,
230 const decNumber *, decContext *, uInt *);
231 static decNumber * decQuantizeOp(decNumber *, const decNumber *,
232 const decNumber *, decContext *, Flag,
233 uInt *);
234 static void decReverse(Unit *, Unit *);
235 static void decSetCoeff(decNumber *, decContext *, const Unit *,
236 Int, Int *, uInt *);
237 static void decSetMaxValue(decNumber *, decContext *);
238 static void decSetOverflow(decNumber *, decContext *, uInt *);
239 static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
240 static Int decShiftToLeast(Unit *, Int, Int);
241 static Int decShiftToMost(Unit *, Int, Int);
242 static void decStatus(decNumber *, uInt, decContext *);
243 static void decToString(const decNumber *, char[], Flag);
244 static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
245 static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
246 Unit *, Int);
247 static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
248
249 #if !DECSUBSET
250 /* decFinish == decFinalize when no subset arithmetic needed */
251 # define decFinish(a,b,c,d) decFinalize(a,b,c,d)
252 #else
253 static void decFinish(decNumber *, decContext *, Int *, uInt *);
254 static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
255 #endif
256
257 /* Local macros */
258 // masked special-values bits
259 #define SPECIALARG (rhs->bits & DECSPECIAL)
260 #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
261
262 /* ================================================================== */
263 /* Conversions */
264 /* ================================================================== */
265
266 /* ------------------------------------------------------------------ */
267 /* from-int32 -- conversion from Int or uInt */
268 /* */
269 /* dn is the decNumber to receive the integer */
270 /* in or uin is the integer to be converted */
271 /* returns dn */
272 /* */
273 /* No error is possible. */
274 /* ------------------------------------------------------------------ */
275 decNumber * decNumberFromInt32(decNumber *dn, Int in) {
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276 uInt unsig;
277 if (in>=0) unsig=in;
278 else { // negative (possibly BADINT)
279 if (in==BADINT) unsig=(uInt)1073741824*2; // special case
280 else unsig=-in; // invert
281 }
282 // in is now positive
283 decNumberFromUInt32(dn, unsig);
284 if (in<0) dn->bits=DECNEG; // sign needed
285 return dn;
286 } // decNumberFromInt32
287
288 decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
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289 Unit *up; // work pointer
290 decNumberZero(dn); // clean
291 if (uin==0) return dn; // [or decGetDigits bad call]
292 for (up=dn->lsu; uin>0; up++) {
293 *up=(Unit)(uin%(DECDPUNMAX+1));
294 uin=uin/(DECDPUNMAX+1);
295 }
296 dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
297 return dn;
298 } // decNumberFromUInt32
299
300 /* ------------------------------------------------------------------ */
301 /* to-int32 -- conversion to Int or uInt */
302 /* */
303 /* dn is the decNumber to convert */
304 /* set is the context for reporting errors */
305 /* returns the converted decNumber, or 0 if Invalid is set */
306 /* */
307 /* Invalid is set if the decNumber does not have exponent==0 or if */
308 /* it is a NaN, Infinite, or out-of-range. */
309 /* ------------------------------------------------------------------ */
310 Int decNumberToInt32(const decNumber *dn, decContext *set) {
/* */
311 // special or too many digits, or bad exponent
312 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad
313 else { // is a finite integer with 10 or fewer digits
314 Int d; // work
315 const Unit *up; // ..
316 uInt hi=0, lo; // ..
317 up=dn->lsu; // -> lsu
318 lo=*up; // get 1 to 9 digits
319 #if DECDPUN>1 // split to higher
320 hi=lo/10;
321 lo=lo%10;
322 #endif
323 up++;
324 // collect remaining Units, if any, into hi
325 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
326 // now low has the lsd, hi the remainder
327 if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range?
328 // most-negative is a reprieve
329 if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
330 // bad -- drop through
331 }
332 else { // in-range always
333 Int i=X10(hi)+lo;
334 if (dn->bits&DECNEG) return -i;
335 return i;
336 }
337 } // integer
338 (void)decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
339 return 0;
340 } // decNumberToInt32
341
342 uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
/* */
343 // special or too many digits, or bad exponent, or negative (<0)
344 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
345 || (dn->bits&DECNEG && !ISZERO(dn))); // bad
346 else { // is a finite integer with 10 or fewer digits
347 Int d; // work
348 const Unit *up; // ..
349 uInt hi=0, lo; // ..
350 up=dn->lsu; // -> lsu
351 lo=*up; // get 1 to 9 digits
352 #if DECDPUN>1 // split to higher
353 hi=lo/10;
354 lo=lo%10;
355 #endif
356 up++;
357 // collect remaining Units, if any, into hi
358 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
359
360 // now low has the lsd, hi the remainder
361 if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve
362 else return X10(hi)+lo;
363 } // integer
364 (void)decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
365 return 0;
366 } // decNumberToUInt32
367
368 /* ------------------------------------------------------------------ */
369 /* to-scientific-string -- conversion to numeric string */
370 /* to-engineering-string -- conversion to numeric string */
371 /* */
372 /* decNumberToString(dn, string); */
373 /* decNumberToEngString(dn, string); */
374 /* */
375 /* dn is the decNumber to convert */
376 /* string is the string where the result will be laid out */
377 /* */
378 /* string must be at least dn->digits+14 characters long */
379 /* */
380 /* No error is possible, and no status can be set. */
381 /* ------------------------------------------------------------------ */
382 char * decNumberToString(const decNumber *dn, char *string){
/* */
383 decToString(dn, string, 0);
384 return string;
385 } // DecNumberToString
386
387 char * decNumberToEngString(const decNumber *dn, char *string){
/* */
388 decToString(dn, string, 1);
389 return string;
390 } // DecNumberToEngString
391
392 /* ------------------------------------------------------------------ */
393 /* to-number -- conversion from numeric string */
394 /* */
395 /* decNumberFromString -- convert string to decNumber */
396 /* dn -- the number structure to fill */
397 /* chars[] -- the string to convert ('\0' terminated) */
398 /* set -- the context used for processing any error, */
399 /* determining the maximum precision available */
400 /* (set.digits), determining the maximum and minimum */
401 /* exponent (set.emax and set.emin), determining if */
402 /* extended values are allowed, and checking the */
403 /* rounding mode if overflow occurs or rounding is */
404 /* needed. */
405 /* */
406 /* The length of the coefficient and the size of the exponent are */
407 /* checked by this routine, so the correct error (Underflow or */
408 /* Overflow) can be reported or rounding applied, as necessary. */
409 /* */
410 /* If bad syntax is detected, the result will be a quiet NaN. */
411 /* ------------------------------------------------------------------ */
412 decNumber * decNumberFromString(decNumber *dn, const char chars[],
/* */
413 decContext *set) {
414 Int exponent=0; // working exponent [assume 0]
415 uByte bits=0; // working flags [assume +ve]
416 Unit *res; // where result will be built
417 Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary
418 // [+9 allows for ln() constants]
419 Unit *allocres=NULL; // -> allocated result, iff allocated
420 Int d=0; // count of digits found in decimal part
421 const char *dotchar=NULL; // where dot was found
422 const char *cfirst=chars; // -> first character of decimal part
423 const char *last=NULL; // -> last digit of decimal part
424 const char *c; // work
425 Unit *up; // ..
426 #if DECDPUN>1
427 Int cut, out; // ..
428 #endif
429 Int residue; // rounding residue
430 uInt status=0; // error code
431
432 do { // status & malloc protection
433 for (c=chars;; c++) { // -> input character
434 if (*c>='0' && *c<='9') { // test for Arabic digit
435 last=c;
436 d++; // count of real digits
437 continue; // still in decimal part
438 }
439 if (*c=='.' && dotchar==NULL) { // first '.'
440 dotchar=c; // record offset into decimal part
441 if (c==cfirst) cfirst++; // first digit must follow
442 continue;}
443 if (c==chars) { // first in string...
444 if (*c=='-') { // valid - sign
445 cfirst++;
446 bits=DECNEG;
447 continue;}
448 if (*c=='+') { // valid + sign
449 cfirst++;
450 continue;}
451 }
452 // *c is not a digit, or a valid +, -, or '.'
453 break;
454 } // c
455
456 if (last==NULL) { // no digits yet
457 status=DEC_Conversion_syntax;// assume the worst
458 if (*c=='\0') break; // and no more to come...
459 #if DECSUBSET
460 // if subset then infinities and NaNs are not allowed
461 if (!set->extended) break; // hopeless
462 #endif
463 // Infinities and NaNs are possible, here
464 if (dotchar!=NULL) break; // .. unless had a dot
465 decNumberZero(dn); // be optimistic
466 if (decBiStr(c, "infinity", "INFINITY")
467 || decBiStr(c, "inf", "INF")) {
468 dn->bits=bits | DECINF;
469 status=0; // is OK
470 break; // all done
471 }
472 // a NaN expected
473 // 2003.09.10 NaNs are now permitted to have a sign
474 dn->bits=bits | DECNAN; // assume simple NaN
475 if (*c=='s' || *c=='S') { // looks like an sNaN
476 c++;
477 dn->bits=bits | DECSNAN;
478 }
479 if (*c!='n' && *c!='N') break; // check caseless "NaN"
480 c++;
481 if (*c!='a' && *c!='A') break; // ..
482 c++;
483 if (*c!='n' && *c!='N') break; // ..
484 c++;
485 // now either nothing, or nnnn payload, expected
486 // -> start of integer and skip leading 0s [including plain 0]
487 for (cfirst=c; *cfirst=='0';) cfirst++;
488 if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s
489 status=0; // it's good
490 break; // ..
491 }
492 // something other than 0s; setup last and d as usual [no dots]
493 for (c=cfirst;; c++, d++) {
494 if (*c<'0' || *c>'9') break; // test for Arabic digit
495 last=c;
496 }
497 if (*c!='\0') break; // not all digits
498 if (d>set->digits-1) {
499 // [NB: payload in a decNumber can be full length unless
500 // clamped, in which case can only be digits-1]
501 if (set->clamp) break;
502 if (d>set->digits) break;
503 } // too many digits?
504 // good; drop through to convert the integer to coefficient
505 status=0; // syntax is OK
506 bits=dn->bits; // for copy-back
507 } // last==NULL
508
509 else if (*c!='\0') { // more to process...
510 // had some digits; exponent is only valid sequence now
511 Flag nege; // 1=negative exponent
512 const char *firstexp; // -> first significant exponent digit
513 status=DEC_Conversion_syntax;// assume the worst
514 if (*c!='e' && *c!='E') break;
515 /* Found 'e' or 'E' -- now process explicit exponent */
516 // 1998.07.11: sign no longer required
517 nege=0;
518 c++; // to (possible) sign
519 if (*c=='-') {nege=1; c++;}
520 else if (*c=='+') c++;
521 if (*c=='\0') break;
522
523 for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros
524 firstexp=c; // save exponent digit place
525 for (; ;c++) {
526 if (*c<'0' || *c>'9') break; // not a digit
527 exponent=X10(exponent)+(Int)*c-(Int)'0';
528 } // c
529 // if not now on a '\0', *c must not be a digit
530 if (*c!='\0') break;
531
532 // (this next test must be after the syntax checks)
533 // if it was too long the exponent may have wrapped, so check
534 // carefully and set it to a certain overflow if wrap possible
535 if (c>=firstexp+9+1) {
536 if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
537 // [up to 1999999999 is OK, for example 1E-1000000998]
538 }
539 if (nege) exponent=-exponent; // was negative
540 status=0; // is OK
541 } // stuff after digits
542
543 // Here when whole string has been inspected; syntax is good
544 // cfirst->first digit (never dot), last->last digit (ditto)
545
546 // strip leading zeros/dot [leave final 0 if all 0's]
547 if (*cfirst=='0') { // [cfirst has stepped over .]
548 for (c=cfirst; c<last; c++, cfirst++) {
549 if (*c=='.') continue; // ignore dots
550 if (*c!='0') break; // non-zero found
551 d--; // 0 stripped
552 } // c
553 #if DECSUBSET
554 // make a rapid exit for easy zeros if !extended
555 if (*cfirst=='0' && !set->extended) {
556 decNumberZero(dn); // clean result
557 break; // [could be return]
558 }
559 #endif
560 } // at least one leading 0
561
562 // Handle decimal point...
563 if (dotchar!=NULL && dotchar<last) // non-trailing '.' found?
564 exponent-=(last-dotchar); // adjust exponent
565 // [we can now ignore the .]
566
567 // OK, the digits string is good. Assemble in the decNumber, or in
568 // a temporary units array if rounding is needed
569 if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber
570 else { // rounding needed
571 Int needbytes=D2U(d)*sizeof(Unit);// bytes needed
572 res=resbuff; // assume use local buffer
573 if (needbytes>(Int)sizeof(resbuff)) { // too big for local
574 allocres=(Unit *)malloc(needbytes);
575 if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
576 res=allocres;
577 }
578 }
579 // res now -> number lsu, buffer, or allocated storage for Unit array
580
581 // Place the coefficient into the selected Unit array
582 // [this is often 70% of the cost of this function when DECDPUN>1]
583 #if DECDPUN>1
584 out=0; // accumulator
585 up=res+D2U(d)-1; // -> msu
586 cut=d-(up-res)*DECDPUN; // digits in top unit
587 for (c=cfirst;; c++) { // along the digits
588 if (*c=='.') continue; // ignore '.' [don't decrement cut]
589 out=X10(out)+(Int)*c-(Int)'0';
590 if (c==last) break; // done [never get to trailing '.']
591 cut--;
592 if (cut>0) continue; // more for this unit
593 *up=(Unit)out; // write unit
594 up--; // prepare for unit below..
595 cut=DECDPUN; // ..
596 out=0; // ..
597 } // c
598 *up=(Unit)out; // write lsu
599
600 #else
601 // DECDPUN==1
602 up=res; // -> lsu
603 for (c=last; c>=cfirst; c--) { // over each character, from least
604 if (*c=='.') continue; // ignore . [don't step up]
605 *up=(Unit)((Int)*c-(Int)'0');
606 up++;
607 } // c
608 #endif
609
610 dn->bits=bits;
611 dn->exponent=exponent;
612 dn->digits=d;
613
614 // if not in number (too long) shorten into the number
615 if (d>set->digits) {
616 residue=0;
617 decSetCoeff(dn, set, res, d, &residue, &status);
618 // always check for overflow or subnormal and round as needed
619 decFinalize(dn, set, &residue, &status);
620 }
621 else { // no rounding, but may still have overflow or subnormal
622 // [these tests are just for performance; finalize repeats them]
623 if ((dn->exponent-1<set->emin-dn->digits)
624 || (dn->exponent-1>set->emax-set->digits)) {
625 residue=0;
626 decFinalize(dn, set, &residue, &status);
627 }
628 }
629 // decNumberShow(dn);
630 } while(0); // [for break]
631
632 if (allocres!=NULL) FREE(allocres); // drop any storage used
633 if (status!=0) decStatus(dn, status, set);
634 return dn;
635 } /* decNumberFromString */
636
637 /* ================================================================== */
638 /* Operators */
639 /* ================================================================== */
640
641 /* ------------------------------------------------------------------ */
642 /* decNumberAbs -- absolute value operator */
643 /* */
644 /* This computes C = abs(A) */
645 /* */
646 /* res is C, the result. C may be A */
647 /* rhs is A */
648 /* set is the context */
649 /* */
650 /* See also decNumberCopyAbs for a quiet bitwise version of this. */
651 /* C must have space for set->digits digits. */
652 /* ------------------------------------------------------------------ */
653 /* This has the same effect as decNumberPlus unless A is negative, */
654 /* in which case it has the same effect as decNumberMinus. */
655 /* ------------------------------------------------------------------ */
656 decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
/* */
657 decContext *set) {
658 decNumber dzero; // for 0
659 uInt status=0; // accumulator
660
661 decNumberZero(&dzero); // set 0
662 dzero.exponent=rhs->exponent; // [no coefficient expansion]
663 decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
664 if (status!=0) decStatus(res, status, set);
665 return res;
666 } // decNumberAbs
667
668 /* ------------------------------------------------------------------ */
669 /* decNumberAdd -- add two Numbers */
670 /* */
671 /* This computes C = A + B */
672 /* */
673 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
674 /* lhs is A */
675 /* rhs is B */
676 /* set is the context */
677 /* */
678 /* C must have space for set->digits digits. */
679 /* ------------------------------------------------------------------ */
680 /* This just calls the routine shared with Subtract */
681 decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
/* */
682 const decNumber *rhs, decContext *set) {
683 uInt status=0; // accumulator
684 decAddOp(res, lhs, rhs, set, 0, &status);
685 if (status!=0) decStatus(res, status, set);
686 return res;
687 } // decNumberAdd
688
689 /* ------------------------------------------------------------------ */
690 /* decNumberAnd -- AND two Numbers, digitwise */
691 /* */
692 /* This computes C = A & B */
693 /* */
694 /* res is C, the result. C may be A and/or B (e.g., X=X&X) */
695 /* lhs is A */
696 /* rhs is B */
697 /* set is the context (used for result length and error report) */
698 /* */
699 /* C must have space for set->digits digits. */
700 /* */
701 /* Logical function restrictions apply (see above); a NaN is */
702 /* returned with Invalid_operation if a restriction is violated. */
703 /* ------------------------------------------------------------------ */
704 decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
/* */
705 const decNumber *rhs, decContext *set) {
706 const Unit *ua, *ub; // -> operands
707 const Unit *msua, *msub; // -> operand msus
708 Unit *uc, *msuc; // -> result and its msu
709 Int msudigs; // digits in res msu
710
711 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
712 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
713 decStatus(res, DEC_Invalid_operation, set);
714 return res;
715 }
716
717 // operands are valid
718 ua=lhs->lsu; // bottom-up
719 ub=rhs->lsu; // ..
720 uc=res->lsu; // ..
721 msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
722 msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
723 msuc=uc+D2U(set->digits)-1; // -> msu of result
724 msudigs=MSUDIGITS(set->digits); // [faster than remainder]
725 for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
726 Unit a, b; // extract units
727 if (ua>msua) a=0;
728 else a=*ua;
729 if (ub>msub) b=0;
730 else b=*ub;
731 *uc=0; // can now write back
732 if (a|b) { // maybe 1 bits to examine
733 Int i, j;
734 *uc=0; //-V1048 // can now write back
735 // This loop could be unrolled and/or use BIN2BCD tables
736 for (i=0; i<DECDPUN; i++) {
737 if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND
738 j=a%10;
739 a=a/10;
740 j|=b%10;
741 b=b/10;
742 if (j>1) {
743 decStatus(res, DEC_Invalid_operation, set);
744 return res;
745 }
746 if (uc==msuc && i==msudigs-1) break; // just did final digit
747 } // each digit
748 } // both OK
749 } // each unit
750 // [here uc-1 is the msu of the result]
751 res->digits=decGetDigits(res->lsu, uc-res->lsu);
752 res->exponent=0; // integer
753 res->bits=0; // sign=0
754 return res; // [no status to set]
755 } // decNumberAnd
756
757 /* ------------------------------------------------------------------ */
758 /* decNumberCompare -- compare two Numbers */
759 /* */
760 /* This computes C = A ? B */
761 /* */
762 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
763 /* lhs is A */
764 /* rhs is B */
765 /* set is the context */
766 /* */
767 /* C must have space for one digit (or NaN). */
768 /* ------------------------------------------------------------------ */
769 decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
/* */
770 const decNumber *rhs, decContext *set) {
771 uInt status=0; // accumulator
772 decCompareOp(res, lhs, rhs, set, COMPARE, &status);
773 if (status!=0) decStatus(res, status, set);
774 return res;
775 } // decNumberCompare
776
777 /* ------------------------------------------------------------------ */
778 /* decNumberCompareSignal -- compare, signalling on all NaNs */
779 /* */
780 /* This computes C = A ? B */
781 /* */
782 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
783 /* lhs is A */
784 /* rhs is B */
785 /* set is the context */
786 /* */
787 /* C must have space for one digit (or NaN). */
788 /* ------------------------------------------------------------------ */
789 decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
/* */
790 const decNumber *rhs, decContext *set) {
791 uInt status=0; // accumulator
792 decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
793 if (status!=0) decStatus(res, status, set);
794 return res;
795 } // decNumberCompareSignal
796
797 /* ------------------------------------------------------------------ */
798 /* decNumberCompareTotal -- compare two Numbers, using total ordering */
799 /* */
800 /* This computes C = A ? B, under total ordering */
801 /* */
802 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
803 /* lhs is A */
804 /* rhs is B */
805 /* set is the context */
806 /* */
807 /* C must have space for one digit; the result will always be one of */
808 /* -1, 0, or 1. */
809 /* ------------------------------------------------------------------ */
810 decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
/* */
811 const decNumber *rhs, decContext *set) {
812 uInt status=0; // accumulator
813 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
814 if (status!=0) decStatus(res, status, set);
815 return res;
816 } // decNumberCompareTotal
817
818 /* ------------------------------------------------------------------ */
819 /* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
820 /* */
821 /* This computes C = |A| ? |B|, under total ordering */
822 /* */
823 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
824 /* lhs is A */
825 /* rhs is B */
826 /* set is the context */
827 /* */
828 /* C must have space for one digit; the result will always be one of */
829 /* -1, 0, or 1. */
830 /* ------------------------------------------------------------------ */
831 decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
/* */
832 const decNumber *rhs, decContext *set) {
833 uInt status=0; // accumulator
834 uInt needbytes; // for space calculations
835 decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0
836 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
837 decNumber bufb[D2N(DECBUFFER+1)];
838 decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
839 decNumber *a, *b; // temporary pointers
840
841 do { // protect allocated storage
842 // if either is negative, take a copy and absolute
843 if (decNumberIsNegative(lhs)) { // lhs<0
844 a=bufa;
845 needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
846 if (needbytes>sizeof(bufa)) { // need malloc space
847 allocbufa=(decNumber *)malloc(needbytes);
848 if (allocbufa==NULL) { // hopeless -- abandon
849 status|=DEC_Insufficient_storage;
850 break;}
851 a=allocbufa; // use the allocated space
852 }
853 decNumberCopy(a, lhs); // copy content
854 a->bits&=~DECNEG; // .. and clear the sign
855 lhs=a; // use copy from here on
856 }
857 if (decNumberIsNegative(rhs)) { // rhs<0
858 b=bufb;
859 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
860 if (needbytes>sizeof(bufb)) { // need malloc space
861 allocbufb=(decNumber *)malloc(needbytes);
862 if (allocbufb==NULL) { // hopeless -- abandon
863 status|=DEC_Insufficient_storage;
864 break;}
865 b=allocbufb; // use the allocated space
866 }
867 decNumberCopy(b, rhs); // copy content
868 b->bits&=~DECNEG; // .. and clear the sign
869 rhs=b; // use copy from here on
870 }
871 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
872 } while(0); // end protected
873
874 if (allocbufa!=NULL) FREE(allocbufa); // drop any storage used
875 if (allocbufb!=NULL) FREE(allocbufb); // ..
876 if (status!=0) decStatus(res, status, set);
877 return res;
878 } // decNumberCompareTotalMag
879
880 /* ------------------------------------------------------------------ */
881 /* decNumberDivide -- divide one number by another */
882 /* */
883 /* This computes C = A / B */
884 /* */
885 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */
886 /* lhs is A */
887 /* rhs is B */
888 /* set is the context */
889 /* */
890 /* C must have space for set->digits digits. */
891 /* ------------------------------------------------------------------ */
892 decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
/* */
893 const decNumber *rhs, decContext *set) {
894 uInt status=0; // accumulator
895 decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
896 if (status!=0) decStatus(res, status, set);
897 return res;
898 } // decNumberDivide
899
900 /* ------------------------------------------------------------------ */
901 /* decNumberDivideInteger -- divide and return integer quotient */
902 /* */
903 /* This computes C = A # B, where # is the integer divide operator */
904 /* */
905 /* res is C, the result. C may be A and/or B (e.g., X=X#X) */
906 /* lhs is A */
907 /* rhs is B */
908 /* set is the context */
909 /* */
910 /* C must have space for set->digits digits. */
911 /* ------------------------------------------------------------------ */
912 decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
/* */
913 const decNumber *rhs, decContext *set) {
914 uInt status=0; // accumulator
915 decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
916 if (status!=0) decStatus(res, status, set);
917 return res;
918 } // decNumberDivideInteger
919
920 /* ------------------------------------------------------------------ */
921 /* decNumberExp -- exponentiation */
922 /* */
923 /* This computes C = exp(A) */
924 /* */
925 /* res is C, the result. C may be A */
926 /* rhs is A */
927 /* set is the context; note that rounding mode has no effect */
928 /* */
929 /* C must have space for set->digits digits. */
930 /* */
931 /* Mathematical function restrictions apply (see above); a NaN is */
932 /* returned with Invalid_operation if a restriction is violated. */
933 /* */
934 /* Finite results will always be full precision and Inexact, except */
935 /* when A is a zero or -Infinity (giving 1 or 0 respectively). */
936 /* */
937 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
938 /* almost always be correctly rounded, but may be up to 1 ulp in */
939 /* error in rare cases. */
940 /* ------------------------------------------------------------------ */
941 /* This is a wrapper for decExpOp which can handle the slightly wider */
942 /* (double) range needed by Ln (which has to be able to calculate */
943 /* exp(-a) where a can be the tiniest number (Ntiny). */
944 /* ------------------------------------------------------------------ */
945 decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
/* */
946 decContext *set) {
947 uInt status=0; // accumulator
948 #if DECSUBSET
949 decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
950 #endif
951
952 // Check restrictions; these restrictions ensure that if h=8 (see
953 // decExpOp) then the result will either overflow or underflow to 0.
954 // Other math functions restrict the input range, too, for inverses.
955 // If not violated then carry out the operation.
956 if (!decCheckMath(rhs, set, &status)) do { // protect allocation
957 #if DECSUBSET
958 if (!set->extended) {
959 // reduce operand and set lostDigits status, as needed
960 if (rhs->digits>set->digits) {
961 allocrhs=decRoundOperand(rhs, set, &status);
962 if (allocrhs==NULL) break;
963 rhs=allocrhs;
964 }
965 }
966 #endif
967 decExpOp(res, rhs, set, &status);
968 } while(0); // end protected
969
970 #if DECSUBSET
971 if (allocrhs !=NULL) FREE(allocrhs); // drop any storage used
972 #endif
973 // apply significant status
974 if (status!=0) decStatus(res, status, set);
975 return res;
976 } // decNumberExp
977
978 /* ------------------------------------------------------------------ */
979 /* decNumberFMA -- fused multiply add */
980 /* */
981 /* This computes D = (A * B) + C with only one rounding */
982 /* */
983 /* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
984 /* lhs is A */
985 /* rhs is B */
986 /* fhs is C [far hand side] */
987 /* set is the context */
988 /* */
989 /* Mathematical function restrictions apply (see above); a NaN is */
990 /* returned with Invalid_operation if a restriction is violated. */
991 /* */
992 /* C must have space for set->digits digits. */
993 /* ------------------------------------------------------------------ */
994 decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
/* */
995 const decNumber *rhs, const decNumber *fhs,
996 decContext *set) {
997 uInt status=0; // accumulator
998 decContext dcmul; // context for the multiplication
999 uInt needbytes; // for space calculations
1000 decNumber bufa[D2N(DECBUFFER*2+1)];
1001 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
1002 decNumber *acc; // accumulator pointer
1003 decNumber dzero; // work
1004
1005 do { // protect allocated storage
1006 #if DECSUBSET
1007 if (!set->extended) { // [undefined if subset]
1008 status|=DEC_Invalid_operation;
1009 break;}
1010 #endif
1011 // Check math restrictions [these ensure no overflow or underflow]
1012 if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
1013 || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
1014 || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
1015 // set up context for multiply
1016 dcmul=*set;
1017 dcmul.digits=lhs->digits+rhs->digits; // just enough
1018 // [The above may be an over-estimate for subset arithmetic, but that's OK]
1019 dcmul.emax=DEC_MAX_EMAX; // effectively unbounded ..
1020 dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions]
1021 // set up decNumber space to receive the result of the multiply
1022 acc=bufa; // may fit
1023 needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
1024 if (needbytes>sizeof(bufa)) { // need malloc space
1025 allocbufa=(decNumber *)malloc(needbytes);
1026 if (allocbufa==NULL) { // hopeless -- abandon
1027 status|=DEC_Insufficient_storage;
1028 break;}
1029 acc=allocbufa; // use the allocated space
1030 }
1031 // multiply with extended range and necessary precision
1032 decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
1033 // Only Invalid operation (from sNaN or Inf * 0) is possible in
1034 // status; if either is seen than ignore fhs (in case it is
1035 // another sNaN) and set acc to NaN unless we had an sNaN
1036 // [decMultiplyOp leaves that to caller]
1037 // Note sNaN has to go through addOp to shorten payload if
1038 // necessary
1039 if ((status&DEC_Invalid_operation)!=0) {
1040 if (!(status&DEC_sNaN)) { // but be true invalid
1041 decNumberZero(res); // acc not yet set
1042 res->bits=DECNAN;
1043 break;
1044 }
1045 decNumberZero(&dzero); // make 0 (any non-NaN would do)
1046 fhs=&dzero; // use that
1047 }
1048 // add the third operand and result -> res, and all is done
1049 decAddOp(res, acc, fhs, set, 0, &status);
1050 } while(0); // end protected
1051
1052 if (allocbufa!=NULL) FREE(allocbufa); // drop any storage used
1053 if (status!=0) decStatus(res, status, set);
1054 return res;
1055 } // decNumberFMA
1056
1057 /* ------------------------------------------------------------------ */
1058 /* decNumberInvert -- invert a Number, digitwise */
1059 /* */
1060 /* This computes C = ~A */
1061 /* */
1062 /* res is C, the result. C may be A (e.g., X=~X) */
1063 /* rhs is A */
1064 /* set is the context (used for result length and error report) */
1065 /* */
1066 /* C must have space for set->digits digits. */
1067 /* */
1068 /* Logical function restrictions apply (see above); a NaN is */
1069 /* returned with Invalid_operation if a restriction is violated. */
1070 /* ------------------------------------------------------------------ */
1071 decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
/* */
1072 decContext *set) {
1073 const Unit *ua, *msua; // -> operand and its msu
1074 Unit *uc, *msuc; // -> result and its msu
1075 Int msudigs; // digits in res msu
1076
1077 if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
1078 decStatus(res, DEC_Invalid_operation, set);
1079 return res;
1080 }
1081 // operand is valid
1082 ua=rhs->lsu; // bottom-up
1083 uc=res->lsu; // ..
1084 msua=ua+D2U(rhs->digits)-1; // -> msu of rhs
1085 msuc=uc+D2U(set->digits)-1; // -> msu of result
1086 msudigs=MSUDIGITS(set->digits); // [faster than remainder]
1087 for (; uc<=msuc; ua++, uc++) { // Unit loop
1088 Unit a; // extract unit
1089 Int i, j; // work
1090 if (ua>msua) a=0;
1091 else a=*ua;
1092 *uc=0; // can now write back
1093 // always need to examine all bits in rhs
1094 // This loop could be unrolled and/or use BIN2BCD tables
1095 for (i=0; i<DECDPUN; i++) {
1096 if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT
1097 j=a%10;
1098 a=a/10;
1099 if (j>1) {
1100 decStatus(res, DEC_Invalid_operation, set);
1101 return res;
1102 }
1103 if (uc==msuc && i==msudigs-1) break; // just did final digit
1104 } // each digit
1105 } // each unit
1106 // [here uc-1 is the msu of the result]
1107 res->digits=decGetDigits(res->lsu, uc-res->lsu);
1108 res->exponent=0; // integer
1109 res->bits=0; // sign=0
1110 return res; // [no status to set]
1111 } // decNumberInvert
1112
1113 /* ------------------------------------------------------------------ */
1114 /* decNumberLn -- natural logarithm */
1115 /* */
1116 /* This computes C = ln(A) */
1117 /* */
1118 /* res is C, the result. C may be A */
1119 /* rhs is A */
1120 /* set is the context; note that rounding mode has no effect */
1121 /* */
1122 /* C must have space for set->digits digits. */
1123 /* */
1124 /* Notable cases: */
1125 /* A<0 -> Invalid */
1126 /* A=0 -> -Infinity (Exact) */
1127 /* A=+Infinity -> +Infinity (Exact) */
1128 /* A=1 exactly -> 0 (Exact) */
1129 /* */
1130 /* Mathematical function restrictions apply (see above); a NaN is */
1131 /* returned with Invalid_operation if a restriction is violated. */
1132 /* */
1133 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
1134 /* almost always be correctly rounded, but may be up to 1 ulp in */
1135 /* error in rare cases. */
1136 /* ------------------------------------------------------------------ */
1137 /* This is a wrapper for decLnOp which can handle the slightly wider */
1138 /* (+11) range needed by Ln, Log10, etc. (which may have to be able */
1139 /* to calculate at p+e+2). */
1140 /* ------------------------------------------------------------------ */
1141 decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
/* */
1142 decContext *set) {
1143 uInt status=0; // accumulator
1144 #if DECSUBSET
1145 decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
1146 #endif
1147
1148 // Check restrictions; this is a math function; if not violated
1149 // then carry out the operation.
1150 if (!decCheckMath(rhs, set, &status)) do { // protect allocation
1151 #if DECSUBSET
1152 if (!set->extended) {
1153 // reduce operand and set lostDigits status, as needed
1154 if (rhs->digits>set->digits) {
1155 allocrhs=decRoundOperand(rhs, set, &status);
1156 if (allocrhs==NULL) break;
1157 rhs=allocrhs;
1158 }
1159 // special check in subset for rhs=0
1160 if (ISZERO(rhs)) { // +/- zeros -> error
1161 status|=DEC_Invalid_operation;
1162 break;}
1163 } // extended=0
1164 #endif
1165 decLnOp(res, rhs, set, &status);
1166 } while(0); // end protected
1167
1168 #if DECSUBSET
1169 if (allocrhs !=NULL) FREE(allocrhs); // drop any storage used
1170 #endif
1171 // apply significant status
1172 if (status!=0) decStatus(res, status, set);
1173 return res;
1174 } // decNumberLn
1175
1176 /* ------------------------------------------------------------------ */
1177 /* decNumberLogB - get adjusted exponent, by 754 rules */
1178 /* */
1179 /* This computes C = adjustedexponent(A) */
1180 /* */
1181 /* res is C, the result. C may be A */
1182 /* rhs is A */
1183 /* set is the context, used only for digits and status */
1184 /* */
1185 /* For an unrounded result, digits may need to be 10 (A might have */
1186 /* 10**9 digits and an exponent of +999999999, or one digit and an */
1187 /* exponent of -1999999999). */
1188 /* */
1189 /* This returns the adjusted exponent of A after (in theory) padding */
1190 /* with zeros on the right to set->digits digits while keeping the */
1191 /* same value. The exponent is not limited by emin/emax. */
1192 /* */
1193 /* Notable cases: */
1194 /* A<0 -> Use |A| */
1195 /* A=0 -> -Infinity (Division by zero) */
1196 /* A=Infinite -> +Infinity (Exact) */
1197 /* A=1 exactly -> 0 (Exact) */
1198 /* NaNs are propagated as usual */
1199 /* ------------------------------------------------------------------ */
1200 decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
/* */
1201 decContext *set) {
1202 uInt status=0; // accumulator
1203
1204 // NaNs as usual; Infinities return +Infinity; 0->oops
1205 if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
1206 else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
1207 else if (decNumberIsZero(rhs)) {
1208 decNumberZero(res); // prepare for Infinity
1209 res->bits=DECNEG|DECINF; // -Infinity
1210 status|=DEC_Division_by_zero; // as per 754
1211 }
1212 else { // finite non-zero
1213 Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
1214 if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out
1215 else {
1216 decNumber buft[D2N(10)]; // temporary number
1217 decNumber *t=buft; // ..
1218 decNumberFromInt32(t, ae); // lay it out
1219 decNumberPlus(res, t, set); // round as necessary
1220 }
1221 }
1222
1223 if (status!=0) decStatus(res, status, set);
1224 return res;
1225 } // decNumberLogB
1226
1227 /* ------------------------------------------------------------------ */
1228 /* decNumberLog10 -- logarithm in base 10 */
1229 /* */
1230 /* This computes C = log10(A) */
1231 /* */
1232 /* res is C, the result. C may be A */
1233 /* rhs is A */
1234 /* set is the context; note that rounding mode has no effect */
1235 /* */
1236 /* C must have space for set->digits digits. */
1237 /* */
1238 /* Notable cases: */
1239 /* A<0 -> Invalid */
1240 /* A=0 -> -Infinity (Exact) */
1241 /* A=+Infinity -> +Infinity (Exact) */
1242 /* A=10**n (if n is an integer) -> n (Exact) */
1243 /* */
1244 /* Mathematical function restrictions apply (see above); a NaN is */
1245 /* returned with Invalid_operation if a restriction is violated. */
1246 /* */
1247 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
1248 /* almost always be correctly rounded, but may be up to 1 ulp in */
1249 /* error in rare cases. */
1250 /* ------------------------------------------------------------------ */
1251 /* This calculates ln(A)/ln(10) using appropriate precision. For */
1252 /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
1253 /* requested digits and t is the number of digits in the exponent */
1254 /* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
1255 /* fastpath in decLnOp. The final division is done to the requested */
1256 /* precision. */
1257 /* ------------------------------------------------------------------ */
1258 decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
/* */
1259 decContext *set) {
1260 uInt status=0, ignore=0; // status accumulators
1261 uInt needbytes; // for space calculations
1262 Int p; // working precision
1263 Int t; // digits in exponent of A
1264
1265 // buffers for a and b working decimals
1266 // (adjustment calculator, same size)
1267 decNumber bufa[D2N(DECBUFFER+2)];
1268 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
1269 decNumber *a=bufa; // temporary a
1270 decNumber bufb[D2N(DECBUFFER+2)];
1271 decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
1272 decNumber *b=bufb; // temporary b
1273 decNumber bufw[D2N(10)]; // working 2-10 digit number
1274 decNumber *w=bufw; // ..
1275 #if DECSUBSET
1276 decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
1277 #endif
1278
1279 decContext aset; // working context
1280
1281 // Handle payloads that exceed the context precision.
1282 if (rhs->bits&(DECNAN|DECSNAN)) {
1283 decNumberPlus(res, rhs, set);
1284 return res;
1285 }
1286
1287 // Check restrictions; this is a math function; if not violated
1288 // then carry out the operation.
1289 if (!decCheckMath(rhs, set, &status)) do { // protect malloc
1290 #if DECSUBSET
1291 if (!set->extended) {
1292 // reduce operand and set lostDigits status, as needed
1293 if (rhs->digits>set->digits) {
1294 allocrhs=decRoundOperand(rhs, set, &status);
1295 if (allocrhs==NULL) break;
1296 rhs=allocrhs;
1297 }
1298 // special check in subset for rhs=0
1299 if (ISZERO(rhs)) { // +/- zeros -> error
1300 status|=DEC_Invalid_operation;
1301 break;}
1302 } // extended=0
1303 #endif
1304
1305 decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
1306
1307 // handle exact powers of 10; only check if +ve finite
1308 if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
1309 Int residue=0; // (no residue)
1310 uInt copystat=0; // clean status
1311
1312 // round to a single digit...
1313 aset.digits=1;
1314 decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten
1315 // if exact and the digit is 1, rhs is a power of 10
1316 if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
1317 // the exponent, conveniently, is the power of 10; making
1318 // this the result needs a little care as it might not fit,
1319 // so first convert it into the working number, and then move
1320 // to res
1321 decNumberFromInt32(w, w->exponent);
1322 residue=0;
1323 decCopyFit(res, w, set, &residue, &status); // copy & round
1324 decFinish(res, set, &residue, &status); // cleanup/set flags
1325 break;
1326 } // not a power of 10
1327 } // not a candidate for exact
1328
1329 // simplify the information-content calculation to use 'total
1330 // number of digits in a, including exponent' as compared to the
1331 // requested digits, as increasing this will only rarely cost an
1332 // iteration in ln(a) anyway
1333 t=6; // it can never be >6
1334
1335 // allocate space when needed...
1336 p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
1337 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
1338 if (needbytes>sizeof(bufa)) { // need malloc space
1339 allocbufa=(decNumber *)malloc(needbytes);
1340 if (allocbufa==NULL) { // hopeless -- abandon
1341 status|=DEC_Insufficient_storage;
1342 break;}
1343 a=allocbufa; // use the allocated space
1344 }
1345 aset.digits=p; // as calculated
1346 aset.emax=DEC_MAX_MATH; // usual bounds
1347 aset.emin=-DEC_MAX_MATH; // ..
1348 aset.clamp=0; // and no concrete format
1349 decLnOp(a, rhs, &aset, &status); // a=ln(rhs)
1350
1351 // skip the division if the result so far is infinite, NaN, or
1352 // zero, or there was an error; note NaN from sNaN needs copy
1353 if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
1354 if (a->bits&DECSPECIAL || ISZERO(a)) {
1355 decNumberCopy(res, a); // [will fit]
1356 break;}
1357
1358 // for ln(10) an extra 3 digits of precision are needed
1359 p=set->digits+3;
1360 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
1361 if (needbytes>sizeof(bufb)) { // need malloc space
1362 allocbufb=(decNumber *)malloc(needbytes);
1363 if (allocbufb==NULL) { // hopeless -- abandon
1364 status|=DEC_Insufficient_storage;
1365 break;}
1366 b=allocbufb; // use the allocated space
1367 }
1368 decNumberZero(w); // set up 10...
1369 #if DECDPUN==1
1370 w->lsu[1]=1; w->lsu[0]=0; // ..
1371 #else
1372 w->lsu[0]=10; // ..
1373 #endif
1374 w->digits=2; // ..
1375
1376 aset.digits=p;
1377 decLnOp(b, w, &aset, &ignore); // b=ln(10)
1378
1379 aset.digits=set->digits; // for final divide
1380 decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result
1381 } while(0); // [for break]
1382
1383 if (allocbufa!=NULL) FREE(allocbufa); // drop any storage used
1384 if (allocbufb!=NULL) FREE(allocbufb); // ..
1385 #if DECSUBSET
1386 if (allocrhs !=NULL) FREE(allocrhs); // ..
1387 #endif
1388 // apply significant status
1389 if (status!=0) decStatus(res, status, set);
1390 return res;
1391 } // decNumberLog10
1392
1393 /* ------------------------------------------------------------------ */
1394 /* decNumberMax -- compare two Numbers and return the maximum */
1395 /* */
1396 /* This computes C = A ? B, returning the maximum by 754 rules */
1397 /* */
1398 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
1399 /* lhs is A */
1400 /* rhs is B */
1401 /* set is the context */
1402 /* */
1403 /* C must have space for set->digits digits. */
1404 /* ------------------------------------------------------------------ */
1405 decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
/* */
1406 const decNumber *rhs, decContext *set) {
1407 uInt status=0; // accumulator
1408 decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
1409 if (status!=0) decStatus(res, status, set);
1410 return res;
1411 } // decNumberMax
1412
1413 /* ------------------------------------------------------------------ */
1414 /* decNumberMaxMag -- compare and return the maximum by magnitude */
1415 /* */
1416 /* This computes C = A ? B, returning the maximum by 754 rules */
1417 /* */
1418 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
1419 /* lhs is A */
1420 /* rhs is B */
1421 /* set is the context */
1422 /* */
1423 /* C must have space for set->digits digits. */
1424 /* ------------------------------------------------------------------ */
1425 decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
/* */
1426 const decNumber *rhs, decContext *set) {
1427 uInt status=0; // accumulator
1428 decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
1429 if (status!=0) decStatus(res, status, set);
1430 return res;
1431 } // decNumberMaxMag
1432
1433 /* ------------------------------------------------------------------ */
1434 /* decNumberMin -- compare two Numbers and return the minimum */
1435 /* */
1436 /* This computes C = A ? B, returning the minimum by 754 rules */
1437 /* */
1438 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
1439 /* lhs is A */
1440 /* rhs is B */
1441 /* set is the context */
1442 /* */
1443 /* C must have space for set->digits digits. */
1444 /* ------------------------------------------------------------------ */
1445 decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
/* */
1446 const decNumber *rhs, decContext *set) {
1447 uInt status=0; // accumulator
1448 decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
1449 if (status!=0) decStatus(res, status, set);
1450 return res;
1451 } // decNumberMin
1452
1453 /* ------------------------------------------------------------------ */
1454 /* decNumberMinMag -- compare and return the minimum by magnitude */
1455 /* */
1456 /* This computes C = A ? B, returning the minimum by 754 rules */
1457 /* */
1458 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
1459 /* lhs is A */
1460 /* rhs is B */
1461 /* set is the context */
1462 /* */
1463 /* C must have space for set->digits digits. */
1464 /* ------------------------------------------------------------------ */
1465 decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
/* */
1466 const decNumber *rhs, decContext *set) {
1467 uInt status=0; // accumulator
1468 decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
1469 if (status!=0) decStatus(res, status, set);
1470 return res;
1471 } // decNumberMinMag
1472
1473 /* ------------------------------------------------------------------ */
1474 /* decNumberMinus -- prefix minus operator */
1475 /* */
1476 /* This computes C = 0 - A */
1477 /* */
1478 /* res is C, the result. C may be A */
1479 /* rhs is A */
1480 /* set is the context */
1481 /* */
1482 /* See also decNumberCopyNegate for a quiet bitwise version of this. */
1483 /* C must have space for set->digits digits. */
1484 /* ------------------------------------------------------------------ */
1485 /* Simply use AddOp for the subtract, which will do the necessary. */
1486 /* ------------------------------------------------------------------ */
1487 decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
/* */
1488 decContext *set) {
1489 decNumber dzero;
1490 uInt status=0; // accumulator
1491
1492 decNumberZero(&dzero); // make 0
1493 dzero.exponent=rhs->exponent; // [no coefficient expansion]
1494 decAddOp(res, &dzero, rhs, set, DECNEG, &status);
1495 if (status!=0) decStatus(res, status, set);
1496 return res;
1497 } // decNumberMinus
1498
1499 /* ------------------------------------------------------------------ */
1500 /* decNumberNextMinus -- next towards -Infinity */
1501 /* */
1502 /* This computes C = A - infinitesimal, rounded towards -Infinity */
1503 /* */
1504 /* res is C, the result. C may be A */
1505 /* rhs is A */
1506 /* set is the context */
1507 /* */
1508 /* This is a generalization of 754 NextDown. */
1509 /* ------------------------------------------------------------------ */
1510 decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
/* */
1511 decContext *set) {
1512 decNumber dtiny; // constant
1513 decContext workset=*set; // work
1514 uInt status=0; // accumulator
1515
1516 // +Infinity is the special case
1517 if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
1518 decSetMaxValue(res, set); // is +ve
1519 // there is no status to set
1520 return res;
1521 }
1522 // Apply the context. If the result is inexact, we are done.
1523 workset.round=DEC_ROUND_FLOOR;
1524 workset.status=0;
1525 decNumberPlus(res, rhs, &workset);
1526 if (workset.status&(DEC_Inexact|DEC_NaNs)) {
1527 set->status |= (workset.status&DEC_NaNs);
1528 return res;
1529 }
1530 // Applying the context was exact. Subtract tiny quantity and round.
1531 decNumberZero(&dtiny); // start with 0
1532 dtiny.lsu[0]=1;
1533 dtiny.exponent=set->emin-set->digits;
1534 decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
1535 status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
1536 if (status!=0) decStatus(res, status, set);
1537 return res;
1538 } // decNumberNextMinus
1539
1540 /* ------------------------------------------------------------------ */
1541 /* decNumberNextPlus -- next towards +Infinity */
1542 /* */
1543 /* This computes C = A + infinitesimal, rounded towards +Infinity */
1544 /* */
1545 /* res is C, the result. C may be A */
1546 /* rhs is A */
1547 /* set is the context */
1548 /* */
1549 /* This is a generalization of 754 NextUp. */
1550 /* ------------------------------------------------------------------ */
1551 decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
/* */
1552 decContext *set) {
1553 decNumber dtiny; // constant
1554 decContext workset=*set; // work
1555 uInt status=0; // accumulator
1556
1557 // -Infinity is the special case
1558 if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
1559 decSetMaxValue(res, set);
1560 res->bits=DECNEG; // negative
1561 // there is no status to set
1562 return res;
1563 }
1564 // Apply the context. If the result is inexact, we are done.
1565 workset.round=DEC_ROUND_CEILING;
1566 workset.status=0;
1567 decNumberPlus(res, rhs, &workset);
1568 if (workset.status&(DEC_Inexact|DEC_NaNs)) {
1569 set->status |= (workset.status&DEC_NaNs);
1570 return res;
1571 }
1572 // Applying the context was exact. Add tiny quantity and round.
1573 decNumberZero(&dtiny); // start with 0
1574 dtiny.lsu[0]=1;
1575 dtiny.exponent=set->emin-set->digits;
1576 decAddOp(res, rhs, &dtiny, &workset, 0, &status);
1577 status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
1578 if (status!=0) decStatus(res, status, set);
1579 return res;
1580 } // decNumberNextPlus
1581
1582 /* ------------------------------------------------------------------ */
1583 /* decNumberNextToward -- next towards rhs */
1584 /* */
1585 /* This computes C = A +/- infinitesimal, rounded towards */
1586 /* +/-Infinity in the direction of B, as per 754-1985 nextafter */
1587 /* modified during revision but dropped from 754-2008. */
1588 /* */
1589 /* res is C, the result. C may be A or B. */
1590 /* lhs is A */
1591 /* rhs is B */
1592 /* set is the context */
1593 /* */
1594 /* This is a generalization of 754-1985 NextAfter. */
1595 /* ------------------------------------------------------------------ */
1596 decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
/* */
1597 const decNumber *rhs, decContext *set) {
1598 decNumber dtiny; // constant
1599 decContext workset=*set; // work
1600 Int result; // ..
1601 uInt status=0; // accumulator
1602
1603 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
1604 decNaNs(res, lhs, rhs, set, &status);
1605 }
1606 else { // Is numeric, so no chance of sNaN Invalid, etc.
1607 result=decCompare(lhs, rhs, 0); // sign matters
1608 if (result==BADINT) status|=DEC_Insufficient_storage; // rare
1609 else { // valid compare
1610 if (result==0) decNumberCopySign(res, lhs, rhs); // easy
1611 else { // differ: need NextPlus or NextMinus
1612 uByte sub; // add or subtract
1613 if (result<0) { // lhs<rhs, do nextplus
1614 // -Infinity is the special case
1615 if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
1616 decSetMaxValue(res, set);
1617 res->bits=DECNEG; // negative
1618 return res; // there is no status to set
1619 }
1620 workset.round=DEC_ROUND_CEILING;
1621 sub=0; // add, please
1622 } // plus
1623 else { // lhs>rhs, do nextminus
1624 // +Infinity is the special case
1625 if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
1626 decSetMaxValue(res, set);
1627 return res; // there is no status to set
1628 }
1629 workset.round=DEC_ROUND_FLOOR;
1630 sub=DECNEG; // subtract, please
1631 } // minus
1632 decNumberZero(&dtiny); // start with 0
1633 dtiny.lsu[0]=1; // make number that is ..
1634 dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
1635 decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or -
1636 // turn off exceptions if the result is a normal number
1637 // (including Nmin), otherwise let all status through
1638 if (decNumberIsNormal(res, set)) status=0;
1639 } // unequal
1640 } // compare OK
1641 } // numeric
1642 if (status!=0) decStatus(res, status, set);
1643 return res;
1644 } // decNumberNextToward
1645
1646 /* ------------------------------------------------------------------ */
1647 /* decNumberOr -- OR two Numbers, digitwise */
1648 /* */
1649 /* This computes C = A | B */
1650 /* */
1651 /* res is C, the result. C may be A and/or B (e.g., X=X|X) */
1652 /* lhs is A */
1653 /* rhs is B */
1654 /* set is the context (used for result length and error report) */
1655 /* */
1656 /* C must have space for set->digits digits. */
1657 /* */
1658 /* Logical function restrictions apply (see above); a NaN is */
1659 /* returned with Invalid_operation if a restriction is violated. */
1660 /* ------------------------------------------------------------------ */
1661 decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
/* */
1662 const decNumber *rhs, decContext *set) {
1663 const Unit *ua, *ub; // -> operands
1664 const Unit *msua, *msub; // -> operand msus
1665 Unit *uc, *msuc; // -> result and its msu
1666 Int msudigs; // digits in res msu
1667
1668 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
1669 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
1670 decStatus(res, DEC_Invalid_operation, set);
1671 return res;
1672 }
1673 // operands are valid
1674 ua=lhs->lsu; // bottom-up
1675 ub=rhs->lsu; // ..
1676 uc=res->lsu; // ..
1677 msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
1678 msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
1679 msuc=uc+D2U(set->digits)-1; // -> msu of result
1680 msudigs=MSUDIGITS(set->digits); // [faster than remainder]
1681 for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
1682 Unit a, b; // extract units
1683 if (ua>msua) a=0;
1684 else a=*ua;
1685 if (ub>msub) b=0;
1686 else b=*ub;
1687 *uc=0; // can now write back
1688 if (a|b) { // maybe 1 bits to examine
1689 Int i, j;
1690 // This loop could be unrolled and/or use BIN2BCD tables
1691 for (i=0; i<DECDPUN; i++) {
1692 if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR
1693 j=a%10;
1694 a=a/10;
1695 j|=b%10;
1696 b=b/10;
1697 if (j>1) {
1698 decStatus(res, DEC_Invalid_operation, set);
1699 return res;
1700 }
1701 if (uc==msuc && i==msudigs-1) break; // just did final digit
1702 } // each digit
1703 } // non-zero
1704 } // each unit
1705 // [here uc-1 is the msu of the result]
1706 res->digits=decGetDigits(res->lsu, uc-res->lsu);
1707 res->exponent=0; // integer
1708 res->bits=0; // sign=0
1709 return res; // [no status to set]
1710 } // decNumberOr
1711
1712 /* ------------------------------------------------------------------ */
1713 /* decNumberPlus -- prefix plus operator */
1714 /* */
1715 /* This computes C = 0 + A */
1716 /* */
1717 /* res is C, the result. C may be A */
1718 /* rhs is A */
1719 /* set is the context */
1720 /* */
1721 /* See also decNumberCopy for a quiet bitwise version of this. */
1722 /* C must have space for set->digits digits. */
1723 /* ------------------------------------------------------------------ */
1724 /* This simply uses AddOp; Add will take fast path after preparing A. */
1725 /* Performance is a concern here, as this routine is often used to */
1726 /* check operands and apply rounding and overflow/underflow testing. */
1727 /* ------------------------------------------------------------------ */
1728 decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
/* */
1729 decContext *set) {
1730 decNumber dzero;
1731 uInt status=0; // accumulator
1732
1733 decNumberZero(&dzero); // make 0
1734 dzero.exponent=rhs->exponent; // [no coefficient expansion]
1735 decAddOp(res, &dzero, rhs, set, 0, &status);
1736 if (status!=0) decStatus(res, status, set);
1737 return res;
1738 } // decNumberPlus
1739
1740 /* ------------------------------------------------------------------ */
1741 /* decNumberMultiply -- multiply two Numbers */
1742 /* */
1743 /* This computes C = A x B */
1744 /* */
1745 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
1746 /* lhs is A */
1747 /* rhs is B */
1748 /* set is the context */
1749 /* */
1750 /* C must have space for set->digits digits. */
1751 /* ------------------------------------------------------------------ */
1752 decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
/* */
1753 const decNumber *rhs, decContext *set) {
1754 uInt status=0; // accumulator
1755 decMultiplyOp(res, lhs, rhs, set, &status);
1756 if (status!=0) decStatus(res, status, set);
1757 return res;
1758 } // decNumberMultiply
1759
1760 /* ------------------------------------------------------------------ */
1761 /* decNumberPower -- raise a number to a power */
1762 /* */
1763 /* This computes C = A ** B */
1764 /* */
1765 /* res is C, the result. C may be A and/or B (e.g., X=X**X) */
1766 /* lhs is A */
1767 /* rhs is B */
1768 /* set is the context */
1769 /* */
1770 /* C must have space for set->digits digits. */
1771 /* */
1772 /* Mathematical function restrictions apply (see above); a NaN is */
1773 /* returned with Invalid_operation if a restriction is violated. */
1774 /* */
1775 /* However, if 1999999997<=B<=999999999 and B is an integer then the */
1776 /* restrictions on A and the context are relaxed to the usual bounds, */
1777 /* for compatibility with the earlier (integer power only) version */
1778 /* of this function. */
1779 /* */
1780 /* When B is an integer, the result may be exact, even if rounded. */
1781 /* */
1782 /* The final result is rounded according to the context; it will */
1783 /* almost always be correctly rounded, but may be up to 1 ulp in */
1784 /* error in rare cases. */
1785 /* ------------------------------------------------------------------ */
1786 decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
/* */
1787 const decNumber *rhs, decContext *set) {
1788 #if DECSUBSET
1789 decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
1790 decNumber *allocrhs=NULL; // .., rhs
1791 #endif
1792 decNumber *allocdac=NULL; // -> allocated acc buffer, iff used
1793 decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used
1794 Int reqdigits=set->digits; // requested DIGITS
1795 Int n; // rhs in binary
1796 Flag rhsint=0; // 1 if rhs is an integer
1797 Flag useint=0; // 1 if can use integer calculation
1798 Flag isoddint=0; // 1 if rhs is an integer and odd
1799 Int i; // work
1800 #if DECSUBSET
1801 Int dropped; // ..
1802 #endif
1803 uInt needbytes; // buffer size needed
1804 Flag seenbit; // seen a bit while powering
1805 Int residue=0; // rounding residue
1806 uInt status=0; // accumulators
1807 uByte bits=0; // result sign if errors
1808 decContext aset; // working context
1809 decNumber dnOne; // work value 1...
1810 // local accumulator buffer [a decNumber, with digits+elength+1 digits]
1811 decNumber dacbuff[D2N(DECBUFFER+9)];
1812 decNumber *dac=dacbuff; // -> result accumulator
1813 // same again for possible 1/lhs calculation
1814 decNumber invbuff[D2N(DECBUFFER+9)];
1815
1816 do { // protect allocated storage
1817 #if DECSUBSET
1818 if (!set->extended) { // reduce operands and set status, as needed
1819 if (lhs->digits>reqdigits) {
1820 alloclhs=decRoundOperand(lhs, set, &status);
1821 if (alloclhs==NULL) break;
1822 lhs=alloclhs;
1823 }
1824 if (rhs->digits>reqdigits) {
1825 allocrhs=decRoundOperand(rhs, set, &status);
1826 if (allocrhs==NULL) break;
1827 rhs=allocrhs;
1828 }
1829 }
1830 #endif
1831 // [following code does not require input rounding]
1832
1833 // handle NaNs and rhs Infinity (lhs infinity is harder)
1834 if (SPECIALARGS) {
1835 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs
1836 decNaNs(res, lhs, rhs, set, &status);
1837 break;}
1838 if (decNumberIsInfinite(rhs)) { // rhs Infinity
1839 Flag rhsneg=rhs->bits&DECNEG; // save rhs sign
1840 if (decNumberIsNegative(lhs) // lhs<0
1841 && !decNumberIsZero(lhs)) // ..
1842 status|=DEC_Invalid_operation;
1843 else { // lhs >=0
1844 decNumberZero(&dnOne); // set up 1
1845 dnOne.lsu[0]=1;
1846 decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1
1847 decNumberZero(res); // prepare for 0/1/Infinity
1848 if (decNumberIsNegative(dac)) { // lhs<1
1849 if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
1850 }
1851 else if (dac->lsu[0]==0) { // lhs=1
1852 // 1**Infinity is inexact, so return fully-padded 1.0000
1853 Int shift=set->digits-1;
1854 *res->lsu=1; // was 0, make int 1
1855 res->digits=decShiftToMost(res->lsu, 1, shift);
1856 res->exponent=-shift; // make 1.0000...
1857 status|=DEC_Inexact|DEC_Rounded; // deemed inexact
1858 }
1859 else { // lhs>1
1860 if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
1861 }
1862 } // lhs>=0
1863 break;}
1864 // [lhs infinity drops through]
1865 } // specials
1866
1867 // Original rhs may be an integer that fits and is in range
1868 n=decGetInt(rhs);
1869 if (n!=BADINT) { // it is an integer
1870 rhsint=1; // record the fact for 1**n
1871 isoddint=(Flag)n&1; // [works even if big]
1872 if (n!=BIGEVEN && n!=BIGODD) // can use integer path?
1873 useint=1; // looks good
1874 }
1875
1876 if (decNumberIsNegative(lhs) // -x ..
1877 && isoddint) bits=DECNEG; // .. to an odd power
1878
1879 // handle LHS infinity
1880 if (decNumberIsInfinite(lhs)) { // [NaNs already handled]
1881 uByte rbits=rhs->bits; // save
1882 decNumberZero(res); // prepare
1883 if (n==0) *res->lsu=1; // [-]Inf**0 => 1
1884 else {
1885 // -Inf**nonint -> error
1886 if (!rhsint && decNumberIsNegative(lhs)) {
1887 status|=DEC_Invalid_operation; // -Inf**nonint is error
1888 break;}
1889 if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n
1890 // [otherwise will be 0 or -0]
1891 res->bits=bits;
1892 }
1893 break;}
1894
1895 // similarly handle LHS zero
1896 if (decNumberIsZero(lhs)) {
1897 if (n==0) { // 0**0 => Error
1898 #if DECSUBSET
1899 if (!set->extended) { // [unless subset]
1900 decNumberZero(res);
1901 *res->lsu=1; // return 1
1902 break;}
1903 #endif
1904 status|=DEC_Invalid_operation;
1905 }
1906 else { // 0**x
1907 uByte rbits=rhs->bits; // save
1908 if (rbits & DECNEG) { // was a 0**(-n)
1909 #if DECSUBSET
1910 if (!set->extended) { // [bad if subset]
1911 status|=DEC_Invalid_operation;
1912 break;}
1913 #endif
1914 bits|=DECINF;
1915 }
1916 decNumberZero(res); // prepare
1917 // [otherwise will be 0 or -0]
1918 res->bits=bits;
1919 }
1920 break;}
1921
1922 // here both lhs and rhs are finite; rhs==0 is handled in the
1923 // integer path. Next handle the non-integer cases
1924 if (!useint) { // non-integral rhs
1925 // any -ve lhs is bad, as is either operand or context out of
1926 // bounds
1927 if (decNumberIsNegative(lhs)) {
1928 status|=DEC_Invalid_operation;
1929 break;}
1930 if (decCheckMath(lhs, set, &status)
1931 || decCheckMath(rhs, set, &status)) break; // variable status
1932
1933 decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
1934 aset.emax=DEC_MAX_MATH; // usual bounds
1935 aset.emin=-DEC_MAX_MATH; // ..
1936 aset.clamp=0; // and no concrete format
1937
1938 // calculate the result using exp(ln(lhs)*rhs), which can
1939 // all be done into the accumulator, dac. The precision needed
1940 // is enough to contain the full information in the lhs (which
1941 // is the total digits, including exponent), or the requested
1942 // precision, if larger, + 4; 6 is used for the exponent
1943 // maximum length, and this is also used when it is shorter
1944 // than the requested digits as it greatly reduces the >0.5 ulp
1945 // cases at little cost (because Ln doubles digits each
1946 // iteration so a few extra digits rarely causes an extra
1947 // iteration)
1948 aset.digits=MAXI(lhs->digits, set->digits)+6+4;
1949 } // non-integer rhs
1950
1951 else { // rhs is in-range integer
1952 if (n==0) { // x**0 = 1
1953 // (0**0 was handled above)
1954 decNumberZero(res); // result=1
1955 *res->lsu=1; // ..
1956 break;}
1957 // rhs is a non-zero integer
1958 if (n<0) n=-n; // use abs(n)
1959
1960 aset=*set; // clone the context
1961 aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced
1962 // calculate the working DIGITS
1963 aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
1964 aset.emax=DEC_MAX_EMAX; // usual bounds
1965 aset.emin=DEC_MIN_EMIN; // ..
1966 aset.clamp=0; // and no concrete format
1967 #if DECSUBSET
1968 if (!set->extended) aset.digits--; // use classic precision
1969 #endif
1970 // it's an error if this is more than can be handled
1971 if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
1972 } // integer path
1973
1974 // aset.digits is the count of digits for the accumulator needed
1975 // if accumulator is too long for local storage, then allocate
1976 needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
1977 // [needbytes also used below if 1/lhs needed]
1978 if (needbytes>sizeof(dacbuff)) {
1979 allocdac=(decNumber *)malloc(needbytes);
1980 if (allocdac==NULL) { // hopeless -- abandon
1981 status|=DEC_Insufficient_storage;
1982 break;}
1983 dac=allocdac; // use the allocated space
1984 }
1985 // here, aset is set up and accumulator is ready for use
1986
1987 if (!useint) { // non-integral rhs
1988 // x ** y; special-case x=1 here as it will otherwise always
1989 // reduce to integer 1; decLnOp has a fastpath which detects
1990 // the case of x=1
1991 decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs)
1992 // [no error possible, as lhs 0 already handled]
1993 if (ISZERO(dac)) { // x==1, 1.0, etc.
1994 // need to return fully-padded 1.0000 etc., but rhsint->1
1995 *dac->lsu=1; // was 0, make int 1
1996 if (!rhsint) { // add padding
1997 Int shift=set->digits-1;
1998 dac->digits=decShiftToMost(dac->lsu, 1, shift);
1999 dac->exponent=-shift; // make 1.0000...
2000 status|=DEC_Inexact|DEC_Rounded; // deemed inexact
2001 }
2002 }
2003 else {
2004 decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs
2005 decExpOp(dac, dac, &aset, &status); // dac=exp(dac)
2006 }
2007 // and drop through for final rounding
2008 } // non-integer rhs
2009
2010 else { // carry on with integer
2011 decNumberZero(dac); // acc=1
2012 *dac->lsu=1; // ..
2013
2014 // if a negative power the constant 1 is needed, and if not subset
2015 // invert the lhs now rather than inverting the result later
2016 if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
2017 decNumber *inv=invbuff; // assume use fixed buffer
2018 decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later]
2019 #if DECSUBSET
2020 if (set->extended) { // need to calculate 1/lhs
2021 #endif
2022 // divide lhs into 1, putting result in dac [dac=1/dac]
2023 decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
2024 // now locate or allocate space for the inverted lhs
2025 if (needbytes>sizeof(invbuff)) {
2026 allocinv=(decNumber *)malloc(needbytes);
2027 if (allocinv==NULL) { // hopeless -- abandon
2028 status|=DEC_Insufficient_storage;
2029 break;}
2030 inv=allocinv; // use the allocated space
2031 }
2032 // [inv now points to big-enough buffer or allocated storage]
2033 decNumberCopy(inv, dac); // copy the 1/lhs
2034 #if defined(__GNUC__) && !defined(__PCC__) && \
2035 ( !defined(__clang__) || !defined(__llvm__) )
2036 if (dnOne.digits > 1) __builtin_unreachable ();
2037 #endif /* if defined(__GNUC__) && !defined(__PCC__) &&
2038 ( !defined(__clang__) || !defined(__llvm__) ) */
2039 decNumberCopy(dac, &dnOne); // restore acc=1
2040 lhs=inv; // .. and go forward with new lhs
2041 #if DECSUBSET
2042 }
2043 #endif
2044 }
2045
2046 // Raise-to-the-power loop...
2047 seenbit=0; // set once a 1-bit is encountered
2048 for (i=1;;i++){ // for each bit [top bit ignored]
2049 // abandon if had overflow or terminal underflow
2050 if (status & (DEC_Overflow|DEC_Underflow)) { // interesting?
2051 if (status&DEC_Overflow || ISZERO(dac)) break;
2052 }
2053 // [the following two lines revealed an optimizer bug in a C++
2054 // compiler, with symptom: 5**3 -> 25, when n=n+n was used]
2055 n=n<<1; // move next bit to testable position
2056 if (n<0) { // top bit is set
2057 seenbit=1; // OK, significant bit seen
2058 decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x
2059 }
2060 if (i==31) break; // that was the last bit
2061 if (!seenbit) continue; // no need to square 1
2062 decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square]
2063 } /*i*/ // 32 bits
2064
2065 // complete internal overflow or underflow processing
2066 if (status & (DEC_Overflow|DEC_Underflow)) {
2067 #if DECSUBSET
2068 // If subset, and power was negative, reverse the kind of -erflow
2069 // [1/x not yet done]
2070 if (!set->extended && decNumberIsNegative(rhs)) {
2071 if (status & DEC_Overflow)
2072 status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
2073 else { // trickier -- Underflow may or may not be set
2074 status&=~(DEC_Underflow | DEC_Subnormal); // [one or both]
2075 status|=DEC_Overflow;
2076 }
2077 }
2078 #endif
2079 dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign
2080 // round subnormals [to set.digits rather than aset.digits]
2081 // or set overflow result similarly as required
2082 decFinalize(dac, set, &residue, &status);
2083 decNumberCopy(res, dac); // copy to result (is now OK length)
2084 break;
2085 }
2086
2087 #if DECSUBSET
2088 if (!set->extended && // subset math
2089 decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
2090 // so divide result into 1 [dac=1/dac]
2091 decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
2092 }
2093 #endif
2094 } // rhs integer path
2095
2096 // reduce result to the requested length and copy to result
2097 decCopyFit(res, dac, set, &residue, &status);
2098 decFinish(res, set, &residue, &status); // final cleanup
2099 #if DECSUBSET
2100 if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros
2101 #endif
2102 } while(0); // end protected
2103
2104 if (allocdac!=NULL) FREE(allocdac); // drop any storage used
2105 if (allocinv!=NULL) FREE(allocinv); // ..
2106 #if DECSUBSET
2107 if (alloclhs!=NULL) FREE(alloclhs); // ..
2108 if (allocrhs!=NULL) FREE(allocrhs); // ..
2109 #endif
2110 if (status!=0) decStatus(res, status, set);
2111 return res;
2112 } // decNumberPower
2113
2114 /* ------------------------------------------------------------------ */
2115 /* decNumberQuantize -- force exponent to requested value */
2116 /* */
2117 /* This computes C = op(A, B), where op adjusts the coefficient */
2118 /* of C (by rounding or shifting) such that the exponent (-scale) */
2119 /* of C has exponent of B. The numerical value of C will equal A, */
2120 /* except for the effects of any rounding that occurred. */
2121 /* */
2122 /* res is C, the result. C may be A or B */
2123 /* lhs is A, the number to adjust */
2124 /* rhs is B, the number with exponent to match */
2125 /* set is the context */
2126 /* */
2127 /* C must have space for set->digits digits. */
2128 /* */
2129 /* Unless there is an error or the result is infinite, the exponent */
2130 /* after the operation is guaranteed to be equal to that of B. */
2131 /* ------------------------------------------------------------------ */
2132 decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
/* */
2133 const decNumber *rhs, decContext *set) {
2134 uInt status=0; // accumulator
2135 decQuantizeOp(res, lhs, rhs, set, 1, &status);
2136 if (status!=0) decStatus(res, status, set);
2137 return res;
2138 } // decNumberQuantize
2139
2140 /* ------------------------------------------------------------------ */
2141 /* decNumberReduce -- remove trailing zeros */
2142 /* */
2143 /* This computes C = 0 + A, and normalizes the result */
2144 /* */
2145 /* res is C, the result. C may be A */
2146 /* rhs is A */
2147 /* set is the context */
2148 /* */
2149 /* C must have space for set->digits digits. */
2150 /* ------------------------------------------------------------------ */
2151 // Previously known as Normalize
2152 decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
/* */
2153 decContext *set) {
2154 return decNumberReduce(res, rhs, set);
2155 } // decNumberNormalize
2156
2157 decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
/* */
2158 decContext *set) {
2159 #if DECSUBSET
2160 decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
2161 #endif
2162 uInt status=0; // as usual
2163 Int residue=0; // as usual
2164 Int dropped; // work
2165
2166 do { // protect allocated storage
2167 #if DECSUBSET
2168 if (!set->extended) {
2169 // reduce operand and set lostDigits status, as needed
2170 if (rhs->digits>set->digits) {
2171 allocrhs=decRoundOperand(rhs, set, &status);
2172 if (allocrhs==NULL) break;
2173 rhs=allocrhs;
2174 }
2175 }
2176 #endif
2177 // [following code does not require input rounding]
2178
2179 // Infinities copy through; NaNs need usual treatment
2180 if (decNumberIsNaN(rhs)) {
2181 decNaNs(res, rhs, NULL, set, &status);
2182 break;
2183 }
2184
2185 // reduce result to the requested length and copy to result
2186 decCopyFit(res, rhs, set, &residue, &status); // copy & round
2187 decFinish(res, set, &residue, &status); // cleanup/set flags
2188 decTrim(res, set, 1, 0, &dropped); // normalize in place
2189 // [may clamp]
2190 } while(0); // end protected
2191
2192 #if DECSUBSET
2193 if (allocrhs !=NULL) FREE(allocrhs); // ..
2194 #endif
2195 if (status!=0) decStatus(res, status, set);// then report status
2196 return res;
2197 } // decNumberReduce
2198
2199 /* ------------------------------------------------------------------ */
2200 /* decNumberRescale -- force exponent to requested value */
2201 /* */
2202 /* This computes C = op(A, B), where op adjusts the coefficient */
2203 /* of C (by rounding or shifting) such that the exponent (-scale) */
2204 /* of C has the value B. The numerical value of C will equal A, */
2205 /* except for the effects of any rounding that occurred. */
2206 /* */
2207 /* res is C, the result. C may be A or B */
2208 /* lhs is A, the number to adjust */
2209 /* rhs is B, the requested exponent */
2210 /* set is the context */
2211 /* */
2212 /* C must have space for set->digits digits. */
2213 /* */
2214 /* Unless there is an error or the result is infinite, the exponent */
2215 /* after the operation is guaranteed to be equal to B. */
2216 /* ------------------------------------------------------------------ */
2217 decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
/* */
2218 const decNumber *rhs, decContext *set) {
2219 uInt status=0; // accumulator
2220 decQuantizeOp(res, lhs, rhs, set, 0, &status);
2221 if (status!=0) decStatus(res, status, set);
2222 return res;
2223 } // decNumberRescale
2224
2225 /* ------------------------------------------------------------------ */
2226 /* decNumberRemainder -- divide and return remainder */
2227 /* */
2228 /* This computes C = A % B */
2229 /* */
2230 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */
2231 /* lhs is A */
2232 /* rhs is B */
2233 /* set is the context */
2234 /* */
2235 /* C must have space for set->digits digits. */
2236 /* ------------------------------------------------------------------ */
2237 decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
/* */
2238 const decNumber *rhs, decContext *set) {
2239 uInt status=0; // accumulator
2240 decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
2241 if (status!=0) decStatus(res, status, set);
2242 return res;
2243 } // decNumberRemainder
2244
2245 /* ------------------------------------------------------------------ */
2246 /* decNumberRemainderNear -- divide and return remainder from nearest */
2247 /* */
2248 /* This computes C = A % B, where % is the IEEE remainder operator */
2249 /* */
2250 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */
2251 /* lhs is A */
2252 /* rhs is B */
2253 /* set is the context */
2254 /* */
2255 /* C must have space for set->digits digits. */
2256 /* ------------------------------------------------------------------ */
2257 decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
/* */
2258 const decNumber *rhs, decContext *set) {
2259 uInt status=0; // accumulator
2260 decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
2261 if (status!=0) decStatus(res, status, set);
2262 return res;
2263 } // decNumberRemainderNear
2264
2265 /* ------------------------------------------------------------------ */
2266 /* decNumberRotate -- rotate the coefficient of a Number left/right */
2267 /* */
2268 /* This computes C = A rot B (in base ten and rotating set->digits */
2269 /* digits). */
2270 /* */
2271 /* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
2272 /* lhs is A */
2273 /* rhs is B, the number of digits to rotate (-ve to right) */
2274 /* set is the context */
2275 /* */
2276 /* The digits of the coefficient of A are rotated to the left (if B */
2277 /* is positive) or to the right (if B is negative) without adjusting */
2278 /* the exponent or the sign of A. If lhs->digits is less than */
2279 /* set->digits the coefficient is padded with zeros on the left */
2280 /* before the rotate. Any leading zeros in the result are removed */
2281 /* as usual. */
2282 /* */
2283 /* B must be an integer (q=0) and in the range -set->digits through */
2284 /* +set->digits. */
2285 /* C must have space for set->digits digits. */
2286 /* NaNs are propagated as usual. Infinities are unaffected (but */
2287 /* B must be valid). No status is set unless B is invalid or an */
2288 /* operand is an sNaN. */
2289 /* ------------------------------------------------------------------ */
2290 decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
/* */
2291 const decNumber *rhs, decContext *set) {
2292 uInt status=0; // accumulator
2293 Int rotate; // rhs as an Int
2294
2295 // NaNs propagate as normal
2296 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2297 decNaNs(res, lhs, rhs, set, &status);
2298 // rhs must be an integer
2299 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2300 status=DEC_Invalid_operation;
2301 else { // both numeric, rhs is an integer
2302 rotate=decGetInt(rhs); // [cannot fail]
2303 if (rotate==BADINT // something bad ..
2304 || rotate==BIGODD || rotate==BIGEVEN // .. very big ..
2305 || abs(rotate)>set->digits) // .. or out of range
2306 status=DEC_Invalid_operation;
2307 else { // rhs is OK
2308 decNumberCopy(res, lhs);
2309 if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
2310 // convert -ve rotate to equivalent positive rotation
2311 if (rotate<0) rotate=set->digits+rotate;
2312 if (rotate!=0 && rotate!=set->digits // zero or full rotation
2313 && !decNumberIsInfinite(res)) { // lhs was infinite
2314 // left-rotate to do; 0 < rotate < set->digits
2315 uInt units, shift; // work
2316 uInt msudigits; // digits in result msu
2317 Unit *msu=res->lsu+D2U(res->digits)-1; // current msu
2318 Unit *msumax=res->lsu+D2U(set->digits)-1; //-V778 // rotation msu
2319 for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0
2320 res->digits=set->digits; // now full-length
2321 msudigits=MSUDIGITS(res->digits); // actual digits in msu
2322
2323 // rotation here is done in-place, in three steps
2324 // 1. shift all to least up to one unit to unit-align final
2325 // lsd [any digits shifted out are rotated to the left,
2326 // abutted to the original msd (which may require split)]
2327 //
2328 // [if there are no whole units left to rotate, the
2329 // rotation is now complete]
2330 //
2331 // 2. shift to least, from below the split point only, so that
2332 // the final msd is in the right place in its Unit [any
2333 // digits shifted out will fit exactly in the current msu,
2334 // left aligned, no split required]
2335 //
2336 // 3. rotate all the units by reversing left part, right
2337 // part, and then whole
2338 //
2339 // example: rotate right 8 digits (2 units + 2), DECDPUN=3.
2340 //
2341 // start: 00a bcd efg hij klm npq
2342 //
2343 // 1a 000 0ab cde fgh|ijk lmn [pq saved]
2344 // 1b 00p qab cde fgh|ijk lmn
2345 //
2346 // 2a 00p qab cde fgh|00i jkl [mn saved]
2347 // 2b mnp qab cde fgh|00i jkl
2348 //
2349 // 3a fgh cde qab mnp|00i jkl
2350 // 3b fgh cde qab mnp|jkl 00i
2351 // 3c 00i jkl mnp qab cde fgh
2352
2353 // Step 1: amount to shift is the partial right-rotate count
2354 rotate=set->digits-rotate; // make it right-rotate
2355 units=rotate/DECDPUN; // whole units to rotate
2356 shift=rotate%DECDPUN; // left-over digits count
2357 if (shift>0) { // not an exact number of units
2358 uInt save=res->lsu[0]%powers[shift]; //-V557 // save low digit(s)
2359 decShiftToLeast(res->lsu, D2U(res->digits), shift);
2360 if (shift>msudigits) { // msumax-1 needs >0 digits
2361 uInt rem=save%powers[shift-msudigits];// split save
2362 *msumax=(Unit)(save/powers[shift-msudigits]); // and insert
2363 *(msumax-1)=*(msumax-1)
2364 +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // ..
2365 }
2366 else { // all fits in msumax
2367 *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1]
2368 }
2369 } // digits shift needed
2370
2371 // If whole units to rotate...
2372 if (units>0) { // some to do
2373 // Step 2: the units to touch are the whole ones in rotate,
2374 // if any, and the shift is DECDPUN-msudigits (which may be
2375 // 0, again)
2376 shift=DECDPUN-msudigits;
2377 if (shift>0) { // not an exact number of units
2378 uInt save=res->lsu[0]%powers[shift]; // save low digit(s)
2379 decShiftToLeast(res->lsu, units, shift);
2380 *msumax=*msumax+(Unit)(save*powers[msudigits]);
2381 } // partial shift needed
2382
2383 // Step 3: rotate the units array using triple reverse
2384 // (reversing is easy and fast)
2385 decReverse(res->lsu+units, msumax); // left part
2386 decReverse(res->lsu, res->lsu+units-1); // right part
2387 decReverse(res->lsu, msumax); // whole
2388 } // whole units to rotate
2389 // the rotation may have left an undetermined number of zeros
2390 // on the left, so true length needs to be calculated
2391 res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
2392 } // rotate needed
2393 } // rhs OK
2394 } // numerics
2395 if (status!=0) decStatus(res, status, set);
2396 return res;
2397 } // decNumberRotate
2398
2399 /* ------------------------------------------------------------------ */
2400 /* decNumberSameQuantum -- test for equal exponents */
2401 /* */
2402 /* res is the result number, which will contain either 0 or 1 */
2403 /* lhs is a number to test */
2404 /* rhs is the second (usually a pattern) */
2405 /* */
2406 /* No errors are possible and no context is needed. */
2407 /* ------------------------------------------------------------------ */
2408 decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
/* */
2409 const decNumber *rhs) {
2410 Unit ret=0; // return value
2411
2412 if (SPECIALARGS) {
2413 if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
2414 else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
2415 // [anything else with a special gives 0]
2416 }
2417 else if (lhs->exponent==rhs->exponent) ret=1;
2418
2419 decNumberZero(res); // OK to overwrite an operand now
2420 *res->lsu=ret;
2421 return res;
2422 } // decNumberSameQuantum
2423
2424 /* ------------------------------------------------------------------ */
2425 /* decNumberScaleB -- multiply by a power of 10 */
2426 /* */
2427 /* This computes C = A x 10**B where B is an integer (q=0) with */
2428 /* maximum magnitude 2*(emax+digits) */
2429 /* */
2430 /* res is C, the result. C may be A or B */
2431 /* lhs is A, the number to adjust */
2432 /* rhs is B, the requested power of ten to use */
2433 /* set is the context */
2434 /* */
2435 /* C must have space for set->digits digits. */
2436 /* */
2437 /* The result may underflow or overflow. */
2438 /* ------------------------------------------------------------------ */
2439 decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
/* */
2440 const decNumber *rhs, decContext *set) {
2441 Int reqexp; // requested exponent change [B]
2442 uInt status=0; // accumulator
2443 Int residue; // work
2444
2445 // Handle special values except lhs infinite
2446 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2447 decNaNs(res, lhs, rhs, set, &status);
2448 // rhs must be an integer
2449 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2450 status=DEC_Invalid_operation;
2451 else {
2452 // lhs is a number; rhs is a finite with q==0
2453 reqexp=decGetInt(rhs); // [cannot fail]
2454 // maximum range is larger than getInt can handle, so this is
2455 // more restrictive than the specification
2456 if (reqexp==BADINT // something bad ..
2457 || reqexp==BIGODD || reqexp==BIGEVEN // it was huge
2458 || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range
2459 status=DEC_Invalid_operation;
2460 else { // rhs is OK
2461 decNumberCopy(res, lhs); // all done if infinite lhs
2462 if (!decNumberIsInfinite(res)) { // prepare to scale
2463 Int exp=res->exponent; // save for overflow test
2464 res->exponent+=reqexp; // adjust the exponent
2465 if (((exp^reqexp)>=0) // same sign ...
2466 && ((exp^res->exponent)<0)) { // .. but result had different
2467 // the calculation overflowed, so force right treatment
2468 if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS;
2469 else res->exponent=DEC_MAX_EMAX+1;
2470 }
2471 residue=0;
2472 decCopyFit(res, res, set, &residue, &status);
2473 decFinalize(res, set, &residue, &status); // final check
2474 } // finite LHS
2475 } // rhs OK
2476 } // rhs finite
2477 if (status!=0) decStatus(res, status, set);
2478 return res;
2479 } // decNumberScaleB
2480
2481 /* ------------------------------------------------------------------ */
2482 /* decNumberShift -- shift the coefficient of a Number left or right */
2483 /* */
2484 /* This computes C = A << B or C = A >> -B (in base ten). */
2485 /* */
2486 /* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
2487 /* lhs is A */
2488 /* rhs is B, the number of digits to shift (-ve to right) */
2489 /* set is the context */
2490 /* */
2491 /* The digits of the coefficient of A are shifted to the left (if B */
2492 /* is positive) or to the right (if B is negative) without adjusting */
2493 /* the exponent or the sign of A. */
2494 /* */
2495 /* B must be an integer (q=0) and in the range -set->digits through */
2496 /* +set->digits. */
2497 /* C must have space for set->digits digits. */
2498 /* NaNs are propagated as usual. Infinities are unaffected (but */
2499 /* B must be valid). No status is set unless B is invalid or an */
2500 /* operand is an sNaN. */
2501 /* ------------------------------------------------------------------ */
2502 decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
/* */
2503 const decNumber *rhs, decContext *set) {
2504 uInt status=0; // accumulator
2505 Int shift; // rhs as an Int
2506
2507 // NaNs propagate as normal
2508 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
2509 decNaNs(res, lhs, rhs, set, &status);
2510 // rhs must be an integer
2511 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
2512 status=DEC_Invalid_operation;
2513 else { // both numeric, rhs is an integer
2514 shift=decGetInt(rhs); // [cannot fail]
2515 if (shift==BADINT // something bad ..
2516 || shift==BIGODD || shift==BIGEVEN // .. very big ..
2517 || abs(shift)>set->digits) // .. or out of range
2518 status=DEC_Invalid_operation;
2519 else { // rhs is OK
2520 decNumberCopy(res, lhs);
2521 if (shift!=0 && !decNumberIsInfinite(res)) { // something to do
2522 if (shift>0) { // to left
2523 if (shift==set->digits) { // removing all
2524 *res->lsu=0; // so place 0
2525 res->digits=1; // ..
2526 }
2527 else { //
2528 // first remove leading digits if necessary
2529 if (res->digits+shift>set->digits) {
2530 decDecap(res, res->digits+shift-set->digits);
2531 // that updated res->digits; may have gone to 1 (for a
2532 // single digit or for zero
2533 }
2534 if (res->digits>1 || *res->lsu) // if non-zero..
2535 res->digits=decShiftToMost(res->lsu, res->digits, shift);
2536 } // partial left
2537 } // left
2538 else { // to right
2539 if (-shift>=res->digits) { // discarding all
2540 *res->lsu=0; // so place 0
2541 res->digits=1; // ..
2542 }
2543 else {
2544 decShiftToLeast(res->lsu, D2U(res->digits), -shift);
2545 res->digits-=(-shift);
2546 }
2547 } // to right
2548 } // non-0 non-Inf shift
2549 } // rhs OK
2550 } // numerics
2551 if (status!=0) decStatus(res, status, set);
2552 return res;
2553 } // decNumberShift
2554
2555 /* ------------------------------------------------------------------ */
2556 /* decNumberSquareRoot -- square root operator */
2557 /* */
2558 /* This computes C = squareroot(A) */
2559 /* */
2560 /* res is C, the result. C may be A */
2561 /* rhs is A */
2562 /* set is the context; note that rounding mode has no effect */
2563 /* */
2564 /* C must have space for set->digits digits. */
2565 /* ------------------------------------------------------------------ */
2566 /* This uses the following varying-precision algorithm in: */
2567 /* */
2568 /* Properly Rounded Variable Precision Square Root, T. E. Hull and */
2569 /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
2570 /* pp229-237, ACM, September 1985. */
2571 /* */
2572 /* The square-root is calculated using Newton's method, after which */
2573 /* a check is made to ensure the result is correctly rounded. */
2574 /* */
2575 /* % [Reformatted original Numerical Turing source code follows.] */
2576 /* function sqrt(x : real) : real */
2577 /* % sqrt(x) returns the properly rounded approximation to the square */
2578 /* % root of x, in the precision of the calling environment, or it */
2579 /* % fails if x < 0. */
2580 /* % t e hull and a abrham, august, 1984 */
2581 /* if x <= 0 then */
2582 /* if x < 0 then */
2583 /* assert false */
2584 /* else */
2585 /* result 0 */
2586 /* end if */
2587 /* end if */
2588 /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
2589 /* var e := getexp(x) % exponent part of x */
2590 /* var approx : real */
2591 /* if e mod 2 = 0 then */
2592 /* approx := .259 + .819 * f % approx to root of f */
2593 /* else */
2594 /* f := f/l0 % adjustments */
2595 /* e := e + 1 % for odd */
2596 /* approx := .0819 + 2.59 * f % exponent */
2597 /* end if */
2598 /* */
2599 /* var p:= 3 */
2600 /* const maxp := currentprecision + 2 */
2601 /* loop */
2602 /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
2603 /* precision p */
2604 /* approx := .5 * (approx + f/approx) */
2605 /* exit when p = maxp */
2606 /* end loop */
2607 /* */
2608 /* % approx is now within 1 ulp of the properly rounded square root */
2609 /* % of f; to ensure proper rounding, compare squares of (approx - */
2610 /* % l/2 ulp) and (approx + l/2 ulp) with f. */
2611 /* p := currentprecision */
2612 /* begin */
2613 /* precision p + 2 */
2614 /* const approxsubhalf := approx - setexp(.5, -p) */
2615 /* if mulru(approxsubhalf, approxsubhalf) > f then */
2616 /* approx := approx - setexp(.l, -p + 1) */
2617 /* else */
2618 /* const approxaddhalf := approx + setexp(.5, -p) */
2619 /* if mulrd(approxaddhalf, approxaddhalf) < f then */
2620 /* approx := approx + setexp(.l, -p + 1) */
2621 /* end if */
2622 /* end if */
2623 /* end */
2624 /* result setexp(approx, e div 2) % fix exponent */
2625 /* end sqrt */
2626 /* ------------------------------------------------------------------ */
2627 decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
/* */
2628 decContext *set) {
2629 decContext workset, approxset; // work contexts
2630 decNumber dzero; // used for constant zero
2631 Int maxp; // largest working precision
2632 Int workp; // working precision
2633 Int residue=0; // rounding residue
2634 uInt status=0, ignore=0; // status accumulators
2635 uInt rstatus; // ..
2636 Int exp; // working exponent
2637 Int ideal; // ideal (preferred) exponent
2638 Int needbytes; // work
2639 Int dropped; // ..
2640
2641 #if DECSUBSET
2642 decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
2643 #endif
2644 // buffer for f [needs +1 in case DECBUFFER 0]
2645 decNumber buff[D2N(DECBUFFER+1)];
2646 // buffer for a [needs +2 to match likely maxp]
2647 decNumber bufa[D2N(DECBUFFER+2)];
2648 // buffer for temporary, b [must be same size as a]
2649 decNumber bufb[D2N(DECBUFFER+2)];
2650 decNumber *allocbuff=NULL; // -> allocated buff, iff allocated
2651 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
2652 decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
2653 decNumber *f=buff; // reduced fraction
2654 decNumber *a=bufa; // approximation to result
2655 decNumber *b=bufb; // intermediate result
2656 // buffer for temporary variable, up to 3 digits
2657 decNumber buft[D2N(3)];
2658 decNumber *t=buft; // up-to-3-digit constant or work
2659
2660 do { // protect allocated storage
2661 #if DECSUBSET
2662 if (!set->extended) {
2663 // reduce operand and set lostDigits status, as needed
2664 if (rhs->digits>set->digits) {
2665 allocrhs=decRoundOperand(rhs, set, &status);
2666 if (allocrhs==NULL) break;
2667 // [Note: 'f' allocation below could reuse this buffer if
2668 // used, but as this is rare they are kept separate for clarity.]
2669 rhs=allocrhs;
2670 }
2671 }
2672 #endif
2673 // [following code does not require input rounding]
2674
2675 // handle infinities and NaNs
2676 if (SPECIALARG) {
2677 if (decNumberIsInfinite(rhs)) { // an infinity
2678 if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
2679 else decNumberCopy(res, rhs); // +Infinity
2680 }
2681 else decNaNs(res, rhs, NULL, set, &status); // a NaN
2682 break;
2683 }
2684
2685 // calculate the ideal (preferred) exponent [floor(exp/2)]
2686 // [It would be nicer to write: ideal=rhs->exponent>>1, but this
2687 // generates a compiler warning. Generated code is the same.]
2688 ideal=(rhs->exponent&~1)/2; // target
2689
2690 // handle zeros
2691 if (ISZERO(rhs)) {
2692 decNumberCopy(res, rhs); // could be 0 or -0
2693 res->exponent=ideal; // use the ideal [safe]
2694 // use decFinish to clamp any out-of-range exponent, etc.
2695 decFinish(res, set, &residue, &status);
2696 break;
2697 }
2698
2699 // any other -x is an oops
2700 if (decNumberIsNegative(rhs)) {
2701 status|=DEC_Invalid_operation;
2702 break;
2703 }
2704
2705 // space is needed for three working variables
2706 // f -- the same precision as the RHS, reduced to 0.01->0.99...
2707 // a -- Hull's approximation -- precision, when assigned, is
2708 // currentprecision+1 or the input argument precision,
2709 // whichever is larger (+2 for use as temporary)
2710 // b -- intermediate temporary result (same size as a)
2711 // if any is too long for local storage, then allocate
2712 workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision
2713 workp=MAXI(workp, 7); // at least 7 for low cases
2714 maxp=workp+2; // largest working precision
2715
2716 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
2717 if (needbytes>(Int)sizeof(buff)) {
2718 allocbuff=(decNumber *)malloc(needbytes);
2719 if (allocbuff==NULL) { // hopeless -- abandon
2720 status|=DEC_Insufficient_storage;
2721 break;}
2722 f=allocbuff; // use the allocated space
2723 }
2724 // a and b both need to be able to hold a maxp-length number
2725 needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
2726 if (needbytes>(Int)sizeof(bufa)) { // [same applies to b]
2727 allocbufa=(decNumber *)malloc(needbytes);
2728 allocbufb=(decNumber *)malloc(needbytes);
2729 if (allocbufa==NULL || allocbufb==NULL) { // hopeless
2730 status|=DEC_Insufficient_storage;
2731 break;}
2732 a=allocbufa; // use the allocated spaces
2733 b=allocbufb; // ..
2734 }
2735
2736 // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1
2737 decNumberCopy(f, rhs);
2738 exp=f->exponent+f->digits; // adjusted to Hull rules
2739 f->exponent=-(f->digits); // to range
2740
2741 // set up working context
2742 decContextDefault(&workset, DEC_INIT_DECIMAL64);
2743 workset.emax=DEC_MAX_EMAX;
2744 workset.emin=DEC_MIN_EMIN;
2745
2746 // [Until further notice, no error is possible and status bits
2747 // (Rounded, etc.) should be ignored, not accumulated.]
2748
2749 // Calculate initial approximation, and allow for odd exponent
2750 workset.digits=workp; // p for initial calculation
2751 t->bits=0; t->digits=3;
2752 a->bits=0; a->digits=3;
2753 if ((exp & 1)==0) { // even exponent
2754 // Set t=0.259, a=0.819
2755 t->exponent=-3;
2756 a->exponent=-3;
2757 #if DECDPUN>=3
2758 t->lsu[0]=259;
2759 a->lsu[0]=819;
2760 #elif DECDPUN==2
2761 t->lsu[0]=59; t->lsu[1]=2;
2762 a->lsu[0]=19; a->lsu[1]=8;
2763 #else
2764 t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
2765 a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
2766 #endif
2767 }
2768 else { // odd exponent
2769 // Set t=0.0819, a=2.59
2770 f->exponent--; // f=f/10
2771 exp++; // e=e+1
2772 t->exponent=-4;
2773 a->exponent=-2;
2774 #if DECDPUN>=3
2775 t->lsu[0]=819;
2776 a->lsu[0]=259;
2777 #elif DECDPUN==2
2778 t->lsu[0]=19; t->lsu[1]=8;
2779 a->lsu[0]=59; a->lsu[1]=2;
2780 #else
2781 t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
2782 a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
2783 #endif
2784 }
2785
2786 decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f
2787 decAddOp(a, a, t, &workset, 0, &ignore); // ..+t
2788 // [a is now the initial approximation for sqrt(f), calculated with
2789 // currentprecision, which is also a's precision.]
2790
2791 // the main calculation loop
2792 decNumberZero(&dzero); // make 0
2793 decNumberZero(t); // set t = 0.5
2794 t->lsu[0]=5; // ..
2795 t->exponent=-1; // ..
2796 workset.digits=3; // initial p
2797 for (; workset.digits<maxp;) {
2798 // set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp]
2799 workset.digits=MINI(workset.digits*2-2, maxp);
2800 // a = 0.5 * (a + f/a)
2801 // [calculated at p then rounded to currentprecision]
2802 decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a
2803 decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a
2804 decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5
2805 } // loop
2806
2807 // Here, 0.1 <= a < 1 [Hull], and a has maxp digits
2808 // now reduce to length, etc.; this needs to be done with a
2809 // having the correct exponent so as to handle subnormals
2810 // correctly
2811 approxset=*set; // get emin, emax, etc.
2812 approxset.round=DEC_ROUND_HALF_EVEN;
2813 a->exponent+=exp/2; // set correct exponent
2814 rstatus=0; // clear status
2815 residue=0; // .. and accumulator
2816 decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed)
2817 decFinish(a, &approxset, &residue, &rstatus); // clean and finalize
2818
2819 // Overflow was possible if the input exponent was out-of-range,
2820 // in which case quit
2821 if (rstatus&DEC_Overflow) {
2822 status=rstatus; // use the status as-is
2823 decNumberCopy(res, a); // copy to result
2824 break;
2825 }
2826
2827 // Preserve status except Inexact/Rounded
2828 status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
2829
2830 // Carry out the Hull correction
2831 a->exponent-=exp/2; // back to 0.1->1
2832
2833 // a is now at final precision and within 1 ulp of the properly
2834 // rounded square root of f; to ensure proper rounding, compare
2835 // squares of (a - l/2 ulp) and (a + l/2 ulp) with f.
2836 // Here workset.digits=maxp and t=0.5, and a->digits determines
2837 // the ulp
2838 workset.digits--; // maxp-1 is OK now
2839 t->exponent=-a->digits-1; // make 0.5 ulp
2840 decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp
2841 workset.round=DEC_ROUND_UP;
2842 decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b)
2843 decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed
2844 if (decNumberIsNegative(b)) { // f < b [i.e., b > f]
2845 // this is the more common adjustment, though both are rare
2846 t->exponent++; // make 1.0 ulp
2847 t->lsu[0]=1; // ..
2848 decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp
2849 // assign to approx [round to length]
2850 approxset.emin-=exp/2; // adjust to match a
2851 approxset.emax-=exp/2;
2852 decAddOp(a, &dzero, a, &approxset, 0, &ignore);
2853 }
2854 else {
2855 decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp
2856 workset.round=DEC_ROUND_DOWN;
2857 decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b)
2858 decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f
2859 if (decNumberIsNegative(b)) { // b < f
2860 t->exponent++; // make 1.0 ulp
2861 t->lsu[0]=1; // ..
2862 decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp
2863 // assign to approx [round to length]
2864 approxset.emin-=exp/2; // adjust to match a
2865 approxset.emax-=exp/2;
2866 decAddOp(a, &dzero, a, &approxset, 0, &ignore);
2867 }
2868 }
2869 // [no errors are possible in the above, and rounding/inexact during
2870 // estimation are irrelevant, so status was not accumulated]
2871
2872 // Here, 0.1 <= a < 1 (still), so adjust back
2873 a->exponent+=exp/2; // set correct exponent
2874
2875 // count droppable zeros [after any subnormal rounding] by
2876 // trimming a copy
2877 decNumberCopy(b, a);
2878 decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros]
2879
2880 // Set Inexact and Rounded. The answer can only be exact if
2881 // it is short enough so that squaring it could fit in workp
2882 // digits, so this is the only (relatively rare) condition that
2883 // a careful check is needed
2884 if (b->digits*2-1 > workp) { // cannot fit
2885 status|=DEC_Inexact|DEC_Rounded;
2886 }
2887 else { // could be exact/unrounded
2888 uInt mstatus=0; // local status
2889 decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply
2890 if (mstatus&DEC_Overflow) { // result just won't fit
2891 status|=DEC_Inexact|DEC_Rounded;
2892 }
2893 else { // plausible
2894 decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs
2895 if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal
2896 else { // is Exact
2897 // here, dropped is the count of trailing zeros in 'a'
2898 // use closest exponent to ideal...
2899 Int todrop=ideal-a->exponent; // most that can be dropped
2900 if (todrop<0) status|=DEC_Rounded; // ideally would add 0s
2901 else { // unrounded
2902 // there are some to drop, but emax may not allow all
2903 Int maxexp=set->emax-set->digits+1;
2904 Int maxdrop=maxexp-a->exponent;
2905 if (todrop>maxdrop && set->clamp) { // apply clamping
2906 todrop=maxdrop;
2907 status|=DEC_Clamped;
2908 }
2909 if (dropped<todrop) { // clamp to those available
2910 todrop=dropped;
2911 status|=DEC_Clamped;
2912 }
2913 if (todrop>0) { // have some to drop
2914 decShiftToLeast(a->lsu, D2U(a->digits), todrop);
2915 a->exponent+=todrop; // maintain numerical value
2916 a->digits-=todrop; // new length
2917 }
2918 }
2919 }
2920 }
2921 }
2922
2923 // double-check Underflow, as perhaps the result could not have
2924 // been subnormal (initial argument too big), or it is now Exact
2925 if (status&DEC_Underflow) {
2926 Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
2927 // check if truly subnormal
2928 #if DECEXTFLAG // DEC_Subnormal too
2929 if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
2930 #else
2931 if (ae>=set->emin*2) status&=~DEC_Underflow;
2932 #endif
2933 // check if truly inexact
2934 if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
2935 }
2936
2937 decNumberCopy(res, a); // a is now the result
2938 } while(0); // end protected
2939
2940 if (allocbuff!=NULL) FREE(allocbuff); // drop any storage used
2941 if (allocbufa!=NULL) FREE(allocbufa); // ..
2942 if (allocbufb!=NULL) FREE(allocbufb); // ..
2943 #if DECSUBSET
2944 if (allocrhs !=NULL) FREE(allocrhs); // ..
2945 #endif
2946 if (status!=0) decStatus(res, status, set);// then report status
2947 return res;
2948 } // decNumberSquareRoot
2949
2950 /* ------------------------------------------------------------------ */
2951 /* decNumberSubtract -- subtract two Numbers */
2952 /* */
2953 /* This computes C = A - B */
2954 /* */
2955 /* res is C, the result. C may be A and/or B (e.g., X=X-X) */
2956 /* lhs is A */
2957 /* rhs is B */
2958 /* set is the context */
2959 /* */
2960 /* C must have space for set->digits digits. */
2961 /* ------------------------------------------------------------------ */
2962 decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
/* */
2963 const decNumber *rhs, decContext *set) {
2964 uInt status=0; // accumulator
2965
2966 decAddOp(res, lhs, rhs, set, DECNEG, &status);
2967 if (status!=0) decStatus(res, status, set);
2968 return res;
2969 } // decNumberSubtract
2970
2971 /* ------------------------------------------------------------------ */
2972 /* decNumberToIntegralExact -- round-to-integral-value with InExact */
2973 /* decNumberToIntegralValue -- round-to-integral-value */
2974 /* */
2975 /* res is the result */
2976 /* rhs is input number */
2977 /* set is the context */
2978 /* */
2979 /* res must have space for any value of rhs. */
2980 /* */
2981 /* This implements the IEEE special operators and therefore treats */
2982 /* special values as valid. For finite numbers it returns */
2983 /* rescale(rhs, 0) if rhs->exponent is <0. */
2984 /* Otherwise the result is rhs (so no error is possible, except for */
2985 /* sNaN). */
2986 /* */
2987 /* The context is used for rounding mode and status after sNaN, but */
2988 /* the digits setting is ignored. The Exact version will signal */
2989 /* Inexact if the result differs numerically from rhs; the other */
2990 /* never signals Inexact. */
2991 /* ------------------------------------------------------------------ */
2992 decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
/* */
2993 decContext *set) {
2994 decNumber dn;
2995 decContext workset; // working context
2996 uInt status=0; // accumulator
2997
2998 // handle infinities and NaNs
2999 if (SPECIALARG) {
3000 if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity
3001 else decNaNs(res, rhs, NULL, set, &status); // a NaN
3002 }
3003 else { // finite
3004 // have a finite number; no error possible (res must be big enough)
3005 if (rhs->exponent>=0) return decNumberCopy(res, rhs);
3006 // that was easy, but if negative exponent there is work to do...
3007 workset=*set; // clone rounding, etc.
3008 workset.digits=rhs->digits; // no length rounding
3009 workset.traps=0; // no traps
3010 decNumberZero(&dn); // make a number with exponent 0
3011 decNumberQuantize(res, rhs, &dn, &workset);
3012 status|=workset.status;
3013 }
3014 if (status!=0) decStatus(res, status, set);
3015 return res;
3016 } // decNumberToIntegralExact
3017
3018 decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
/* */
3019 decContext *set) {
3020 decContext workset=*set; // working context
3021 workset.traps=0; // no traps
3022 decNumberToIntegralExact(res, rhs, &workset);
3023 // this never affects set, except for sNaNs; NaN will have been set
3024 // or propagated already, so no need to call decStatus
3025 set->status|=workset.status&DEC_Invalid_operation;
3026 return res;
3027 } // decNumberToIntegralValue
3028
3029 /* ------------------------------------------------------------------ */
3030 /* decNumberXor -- XOR two Numbers, digitwise */
3031 /* */
3032 /* This computes C = A ^ B */
3033 /* */
3034 /* res is C, the result. C may be A and/or B (e.g., X=X^X) */
3035 /* lhs is A */
3036 /* rhs is B */
3037 /* set is the context (used for result length and error report) */
3038 /* */
3039 /* C must have space for set->digits digits. */
3040 /* */
3041 /* Logical function restrictions apply (see above); a NaN is */
3042 /* returned with Invalid_operation if a restriction is violated. */
3043 /* ------------------------------------------------------------------ */
3044 decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
/* */
3045 const decNumber *rhs, decContext *set) {
3046 const Unit *ua, *ub; // -> operands
3047 const Unit *msua, *msub; // -> operand msus
3048 Unit *uc, *msuc; // -> result and its msu
3049 Int msudigs; // digits in res msu
3050
3051 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
3052 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
3053 decStatus(res, DEC_Invalid_operation, set);
3054 return res;
3055 }
3056 // operands are valid
3057 ua=lhs->lsu; // bottom-up
3058 ub=rhs->lsu; // ..
3059 uc=res->lsu; // ..
3060 msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
3061 msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
3062 msuc=uc+D2U(set->digits)-1; // -> msu of result
3063 msudigs=MSUDIGITS(set->digits); // [faster than remainder]
3064 for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
3065 Unit a, b; // extract units
3066 if (ua>msua) a=0;
3067 else a=*ua;
3068 if (ub>msub) b=0;
3069 else b=*ub;
3070 *uc=0; // can now write back
3071 if (a|b) { // maybe 1 bits to examine
3072 Int i, j;
3073 // This loop could be unrolled and/or use BIN2BCD tables
3074 for (i=0; i<DECDPUN; i++) {
3075 if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR
3076 j=a%10;
3077 a=a/10;
3078 j|=b%10;
3079 b=b/10;
3080 if (j>1) {
3081 decStatus(res, DEC_Invalid_operation, set);
3082 return res;
3083 }
3084 if (uc==msuc && i==msudigs-1) break; // just did final digit
3085 } // each digit
3086 } // non-zero
3087 } // each unit
3088 // [here uc-1 is the msu of the result]
3089 res->digits=decGetDigits(res->lsu, uc-res->lsu);
3090 res->exponent=0; // integer
3091 res->bits=0; // sign=0
3092 return res; // [no status to set]
3093 } // decNumberXor
3094
3095 /* ================================================================== */
3096 /* Utility routines */
3097 /* ================================================================== */
3098
3099 /* ------------------------------------------------------------------ */
3100 /* decNumberClass -- return the decClass of a decNumber */
3101 /* dn -- the decNumber to test */
3102 /* set -- the context to use for Emin */
3103 /* returns the decClass enum */
3104 /* ------------------------------------------------------------------ */
3105 enum decClass decNumberClass(const decNumber *dn, decContext *set) {
/* */
3106 if (decNumberIsSpecial(dn)) {
3107 if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
3108 if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
3109 // must be an infinity
3110 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
3111 return DEC_CLASS_POS_INF;
3112 }
3113 // is finite
3114 if (decNumberIsNormal(dn, set)) { // most common
3115 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
3116 return DEC_CLASS_POS_NORMAL;
3117 }
3118 // is subnormal or zero
3119 if (decNumberIsZero(dn)) { // most common
3120 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
3121 return DEC_CLASS_POS_ZERO;
3122 }
3123 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
3124 return DEC_CLASS_POS_SUBNORMAL;
3125 } // decNumberClass
3126
3127 /* ------------------------------------------------------------------ */
3128 /* decNumberClassToString -- convert decClass to a string */
3129 /* */
3130 /* eclass is a valid decClass */
3131 /* returns a constant string describing the class (max 13+1 chars) */
3132 /* ------------------------------------------------------------------ */
3133 const char *decNumberClassToString(enum decClass eclass) {
/* */
3134 if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
3135 if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
3136 if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
3137 if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
3138 if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
3139 if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
3140 if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
3141 if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
3142 if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
3143 if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
3144 return DEC_ClassString_UN; // Unknown
3145 } // decNumberClassToString
3146
3147 /* ------------------------------------------------------------------ */
3148 /* decNumberCopy -- copy a number */
3149 /* */
3150 /* dest is the target decNumber */
3151 /* src is the source decNumber */
3152 /* returns dest */
3153 /* */
3154 /* (dest==src is allowed and is a no-op) */
3155 /* All fields are updated as required. This is a utility operation, */
3156 /* so special values are unchanged and no error is possible. */
3157 /* ------------------------------------------------------------------ */
3158 decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
/* */
3159 /* cppcheck-suppress uninitvar */
3160 if (dest==src) return dest; // no copy required
3161
3162 // Use explicit assignments here as structure assignment could copy
3163 // more than just the lsu (for small DECDPUN). This would not affect
3164 // the value of the results, but could disturb test harness spill
3165 // checking.
3166 dest->bits=src->bits;
3167 dest->exponent=src->exponent;
3168 dest->digits=src->digits;
3169 dest->lsu[0]=src->lsu[0];
3170 if (src->digits>DECDPUN) { // more Units to come
3171 const Unit *smsup, *s; // work
3172 Unit *d; // ..
3173 // memcpy for the remaining Units would be safe as they cannot
3174 // overlap. However, this explicit loop is faster in short cases.
3175 d=dest->lsu+1; // -> first destination
3176 smsup=src->lsu+D2U(src->digits); // -> source msu+1
3177 for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
3178 }
3179 return dest;
3180 } // decNumberCopy
3181
3182 /* ------------------------------------------------------------------ */
3183 /* decNumberCopyAbs -- quiet absolute value operator */
3184 /* */
3185 /* This sets C = abs(A) */
3186 /* */
3187 /* res is C, the result. C may be A */
3188 /* rhs is A */
3189 /* */
3190 /* C must have space for set->digits digits. */
3191 /* No exception or error can occur; this is a quiet bitwise operation.*/
3192 /* See also decNumberAbs for a checking version of this. */
3193 /* ------------------------------------------------------------------ */
3194 decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
/* */
3195 decNumberCopy(res, rhs);
3196 res->bits&=~DECNEG; // turn off sign
3197 return res;
3198 } // decNumberCopyAbs
3199
3200 /* ------------------------------------------------------------------ */
3201 /* decNumberCopyNegate -- quiet negate value operator */
3202 /* */
3203 /* This sets C = negate(A) */
3204 /* */
3205 /* res is C, the result. C may be A */
3206 /* rhs is A */
3207 /* */
3208 /* C must have space for set->digits digits. */
3209 /* No exception or error can occur; this is a quiet bitwise operation.*/
3210 /* See also decNumberMinus for a checking version of this. */
3211 /* ------------------------------------------------------------------ */
3212 decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
/* */
3213 decNumberCopy(res, rhs);
3214 res->bits^=DECNEG; // invert the sign
3215 return res;
3216 } // decNumberCopyNegate
3217
3218 /* ------------------------------------------------------------------ */
3219 /* decNumberCopySign -- quiet copy and set sign operator */
3220 /* */
3221 /* This sets C = A with the sign of B */
3222 /* */
3223 /* res is C, the result. C may be A */
3224 /* lhs is A */
3225 /* rhs is B */
3226 /* */
3227 /* C must have space for set->digits digits. */
3228 /* No exception or error can occur; this is a quiet bitwise operation.*/
3229 /* ------------------------------------------------------------------ */
3230 decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
/* */
3231 const decNumber *rhs) {
3232 uByte sign; // rhs sign
3233 sign=rhs->bits & DECNEG; // save sign bit
3234 decNumberCopy(res, lhs);
3235 res->bits&=~DECNEG; // clear the sign
3236 res->bits|=sign; // set from rhs
3237 return res;
3238 } // decNumberCopySign
3239
3240 /* ------------------------------------------------------------------ */
3241 /* decNumberGetBCD -- get the coefficient in BCD8 */
3242 /* dn is the source decNumber */
3243 /* bcd is the uInt array that will receive dn->digits BCD bytes, */
3244 /* most-significant at offset 0 */
3245 /* returns bcd */
3246 /* */
3247 /* bcd must have at least dn->digits bytes. No error is possible; if */
3248 /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
3249 /* ------------------------------------------------------------------ */
3250 uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
/* */
3251 uByte *ub=bcd+dn->digits-1; // -> lsd
3252 const Unit *up=dn->lsu; // Unit pointer, -> lsu
3253
3254 #if DECDPUN==1 // trivial simple copy
3255 for (; ub>=bcd; ub--, up++) *ub=*up;
3256 #else // chopping needed
3257 uInt u=*up; // work
3258 uInt cut=DECDPUN; // downcounter through unit
3259 for (; ub>=bcd; ub--) {
3260 *ub=(uByte)(u%10); // [*6554 trick inhibits, here]
3261 u=u/10;
3262 cut--;
3263 if (cut>0) continue; // more in this unit
3264 up++;
3265 u=*up;
3266 cut=DECDPUN;
3267 }
3268 #endif
3269 return bcd;
3270 } // decNumberGetBCD
3271
3272 /* ------------------------------------------------------------------ */
3273 /* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
3274 /* dn is the target decNumber */
3275 /* bcd is the uInt array that will source n BCD bytes, most- */
3276 /* significant at offset 0 */
3277 /* n is the number of digits in the source BCD array (bcd) */
3278 /* returns dn */
3279 /* */
3280 /* dn must have space for at least n digits. No error is possible; */
3281 /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
3282 /* and bcd[0] zero. */
3283 /* ------------------------------------------------------------------ */
3284 decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
/* */
3285 Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer]
3286 const uByte *ub=bcd; // -> source msd
3287
3288 #if DECDPUN==1 // trivial simple copy
3289 for (; ub<bcd+n; ub++, up--) *up=*ub;
3290 #else // some assembly needed
3291 // calculate how many digits in msu, and hence first cut
3292 Int cut=MSUDIGITS(n); // [faster than remainder]
3293 for (;up>=dn->lsu; up--) { // each Unit from msu
3294 *up=0; // will take <=DECDPUN digits
3295 for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
3296 cut=DECDPUN; // next Unit has all digits
3297 }
3298 #endif
3299 dn->digits=n; // set digit count
3300 return dn;
3301 } // decNumberSetBCD
3302
3303 /* ------------------------------------------------------------------ */
3304 /* decNumberIsNormal -- test normality of a decNumber */
3305 /* dn is the decNumber to test */
3306 /* set is the context to use for Emin */
3307 /* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
3308 /* ------------------------------------------------------------------ */
3309 Int decNumberIsNormal(const decNumber *dn, decContext *set) {
/* */
3310 Int ae; // adjusted exponent
3311
3312 if (decNumberIsSpecial(dn)) return 0; // not finite
3313 if (decNumberIsZero(dn)) return 0; // not non-zero
3314
3315 ae=dn->exponent+dn->digits-1; // adjusted exponent
3316 if (ae<set->emin) return 0; // is subnormal
3317 return 1;
3318 } // decNumberIsNormal
3319
3320 /* ------------------------------------------------------------------ */
3321 /* decNumberIsSubnormal -- test subnormality of a decNumber */
3322 /* dn is the decNumber to test */
3323 /* set is the context to use for Emin */
3324 /* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
3325 /* ------------------------------------------------------------------ */
3326 Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
/* */
3327 Int ae; // adjusted exponent
3328
3329 if (decNumberIsSpecial(dn)) return 0; // not finite
3330 if (decNumberIsZero(dn)) return 0; // not non-zero
3331
3332 ae=dn->exponent+dn->digits-1; // adjusted exponent
3333 if (ae<set->emin) return 1; // is subnormal
3334 return 0;
3335 } // decNumberIsSubnormal
3336
3337 /* ------------------------------------------------------------------ */
3338 /* decNumberTrim -- remove insignificant zeros */
3339 /* */
3340 /* dn is the number to trim */
3341 /* returns dn */
3342 /* */
3343 /* All fields are updated as required. This is a utility operation, */
3344 /* so special values are unchanged and no error is possible. The */
3345 /* zeros are removed unconditionally. */
3346 /* ------------------------------------------------------------------ */
3347 decNumber * decNumberTrim(decNumber *dn) {
/* */
3348 Int dropped; // work
3349 decContext set; // ..
3350 decContextDefault(&set, DEC_INIT_BASE); // clamp=0
3351 return decTrim(dn, &set, 0, 1, &dropped);
3352 } // decNumberTrim
3353
3354 /* ------------------------------------------------------------------ */
3355 /* decNumberVersion -- return the name and version of this module */
3356 /* */
3357 /* No error is possible. */
3358 /* ------------------------------------------------------------------ */
3359 const char * decNumberVersion(void) {
/* */
3360 return DECVERSION;
3361 } // decNumberVersion
3362
3363 /* ------------------------------------------------------------------ */
3364 /* decNumberZero -- set a number to 0 */
3365 /* */
3366 /* dn is the number to set, with space for one digit */
3367 /* returns dn */
3368 /* */
3369 /* No error is possible. */
3370 /* ------------------------------------------------------------------ */
3371 // Memset is not used as it is much slower in some environments.
3372 decNumber * decNumberZero(decNumber *dn) {
/* */
3373 dn->bits=0;
3374 dn->exponent=0;
3375 dn->digits=1;
3376 dn->lsu[0]=0;
3377 return dn;
3378 } // decNumberZero
3379
3380 /* ================================================================== */
3381 /* Local routines */
3382 /* ================================================================== */
3383
3384 /* ------------------------------------------------------------------ */
3385 /* decToString -- lay out a number into a string */
3386 /* */
3387 /* dn is the number to lay out */
3388 /* string is where to lay out the number */
3389 /* eng is 1 if Engineering, 0 if Scientific */
3390 /* */
3391 /* string must be at least dn->digits+14 characters long */
3392 /* No error is possible. */
3393 /* */
3394 /* Note that this routine can generate a -0 or 0.000. These are */
3395 /* never generated in subset to-number or arithmetic, but can occur */
3396 /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
3397 /* ------------------------------------------------------------------ */
3398 static void decToString(const decNumber *dn, char *string, Flag eng) {
/* */
3399 Int exp=dn->exponent; // local copy
3400 Int e; // E-part value
3401 Int pre; // digits before the '.'
3402 Int cut; // for counting digits in a Unit
3403 char *c=string; // work [output pointer]
3404 const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer]
3405 uInt u, pow; // work
3406
3407 if (decNumberIsNegative(dn)) { // Negatives get a minus
3408 *c='-';
3409 c++;
3410 }
3411 if (dn->bits&DECSPECIAL) { // Is a special value
3412 if (decNumberIsInfinite(dn)) {
3413 strcpy(c, "Inf");
3414 strcpy(c+3, "inity");
3415 return;}
3416 // a NaN
3417 if (dn->bits&DECSNAN) { // signalling NaN
3418 *c='s';
3419 c++;
3420 }
3421 strcpy(c, "NaN");
3422 c+=3; // step past
3423 // if not a clean non-zero coefficient, that's all there is in a
3424 // NaN string
3425 if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
3426 // [drop through to add integer]
3427 }
3428
3429 // calculate how many digits in msu, and hence first cut
3430 cut=MSUDIGITS(dn->digits); // [faster than remainder]
3431 cut--; // power of ten for digit
3432
3433 if (exp==0) { // simple integer [common fastpath]
3434 for (;up>=dn->lsu; up--) { // each Unit from msu
3435 u=*up; // contains DECDPUN digits to lay out
3436 for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
3437 cut=DECDPUN-1; // next Unit has all digits
3438 }
3439 *c='\0'; // terminate the string
3440 return;}
3441
3442 /* non-0 exponent -- assume plain form */
3443 pre=dn->digits+exp; // digits before '.'
3444 e=0; // no E
3445 if ((exp>0) || (pre<-5)) { // need exponential form
3446 e=exp+dn->digits-1; // calculate E value
3447 pre=1; // assume one digit before '.'
3448 if (eng && (e!=0)) { // engineering: may need to adjust
3449 Int adj; // adjustment
3450 // The C remainder operator is undefined for negative numbers, so
3451 // a positive remainder calculation must be used here
3452 if (e<0) {
3453 adj=(-e)%3;
3454 if (adj!=0) adj=3-adj;
3455 }
3456 else { // e>0
3457 adj=e%3;
3458 }
3459 e=e-adj;
3460 // if dealing with zero still produce an exponent which is a
3461 // multiple of three, as expected, but there will only be the
3462 // one zero before the E, still. Otherwise note the padding.
3463 if (!ISZERO(dn)) pre+=adj;
3464 else { // is zero
3465 if (adj!=0) { // 0.00Esnn needed
3466 e=e+3;
3467 pre=-(2-adj);
3468 }
3469 } // zero
3470 } // eng
3471 } // need exponent
3472
3473 /* lay out the digits of the coefficient, adding 0s and . as needed */
3474 u=*up;
3475 if (pre>0) { // xxx.xxx or xx00 (engineering) form
3476 Int n=pre;
3477 for (; pre>0; pre--, c++, cut--) {
3478 if (cut<0) { // need new Unit
3479 if (up==dn->lsu) break; // out of input digits (pre>digits)
3480 up--;
3481 cut=DECDPUN-1;
3482 u=*up;
3483 }
3484 TODIGIT(u, cut, c, pow);
3485 }
3486 if (n<dn->digits) { // more to come, after '.'
3487 *c='.'; c++;
3488 for (;; c++, cut--) {
3489 if (cut<0) { // need new Unit
3490 if (up==dn->lsu) break; // out of input digits
3491 up--;
3492 cut=DECDPUN-1;
3493 u=*up;
3494 }
3495 TODIGIT(u, cut, c, pow);
3496 }
3497 }
3498 else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed
3499 }
3500 else { // 0.xxx or 0.000xxx form
3501 *c='0'; c++;
3502 *c='.'; c++;
3503 for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.'
3504 for (; ; c++, cut--) {
3505 if (cut<0) { // need new Unit
3506 if (up==dn->lsu) break; // out of input digits
3507 up--;
3508 cut=DECDPUN-1;
3509 u=*up;
3510 }
3511 TODIGIT(u, cut, c, pow);
3512 }
3513 }
3514
3515 /* Finally add the E-part, if needed. It will never be 0, has a
3516 base maximum and minimum of +999999999 through -999999999, but
3517 could range down to -1999999998 for abnormal numbers */
3518 if (e!=0) {
3519 Flag had=0; // 1=had non-zero
3520 *c='E'; c++;
3521 *c='+'; c++; // assume positive
3522 u=e; // ..
3523 if (e<0) {
3524 *(c-1)='-'; // oops, need -
3525 u=-e; // uInt, please
3526 }
3527 // lay out the exponent [_itoa or equivalent is not ANSI C]
3528 for (cut=9; cut>=0; cut--) {
3529 TODIGIT(u, cut, c, pow);
3530 if (*c=='0' && !had) continue; // skip leading zeros
3531 had=1; // had non-0
3532 c++; // step for next
3533 } // cut
3534 }
3535 *c='\0'; // terminate the string (all paths)
3536 return;
3537 } // decToString
3538
3539 /* ------------------------------------------------------------------ */
3540 /* decAddOp -- add/subtract operation */
3541 /* */
3542 /* This computes C = A + B */
3543 /* */
3544 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
3545 /* lhs is A */
3546 /* rhs is B */
3547 /* set is the context */
3548 /* negate is DECNEG if rhs should be negated, or 0 otherwise */
3549 /* status accumulates status for the caller */
3550 /* */
3551 /* C must have space for set->digits digits. */
3552 /* Inexact in status must be 0 for correct Exact zero sign in result */
3553 /* ------------------------------------------------------------------ */
3554 /* If possible, the coefficient is calculated directly into C. */
3555 /* However, if: */
3556 /* -- a digits+1 calculation is needed because the numbers are */
3557 /* unaligned and span more than set->digits digits */
3558 /* -- a carry to digits+1 digits looks possible */
3559 /* -- C is the same as A or B, and the result would destructively */
3560 /* overlap the A or B coefficient */
3561 /* then the result must be calculated into a temporary buffer. In */
3562 /* this case a local (stack) buffer is used if possible, and only if */
3563 /* too long for that does malloc become the final resort. */
3564 /* */
3565 /* Misalignment is handled as follows: */
3566 /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
3567 /* BPad: Apply the padding by a combination of shifting (whole */
3568 /* units) and multiplication (part units). */
3569 /* */
3570 /* Addition, especially x=x+1, is speed-critical. */
3571 /* The static buffer is larger than might be expected to allow for */
3572 /* calls from higher-level functions (notable exp). */
3573 /* ------------------------------------------------------------------ */
3574 static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
/* */
3575 const decNumber *rhs, decContext *set,
3576 uByte negate, uInt *status) {
3577 #if DECSUBSET
3578 decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
3579 decNumber *allocrhs=NULL; // .., rhs
3580 #endif
3581 decNumber dtiny; // lhs, adjusted to avoid a huge shift
3582 Int rhsshift; // working shift (in Units)
3583 Int maxdigits; // longest logical length
3584 Int mult; // multiplier
3585 Int residue; // rounding accumulator
3586 uByte bits; // result bits
3587 Flag diffsign; // non-0 if arguments have different sign
3588 Unit *acc; // accumulator for result
3589 Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many
3590 // allocations when called from
3591 // other operations, notable exp]
3592 Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
3593 Int reqdigits=set->digits; // local copy; requested DIGITS
3594 Int padding; // work
3595
3596 do { // protect allocated storage
3597 #if DECSUBSET
3598 if (!set->extended) {
3599 // reduce operands and set lostDigits status, as needed
3600 if (lhs->digits>reqdigits) {
3601 alloclhs=decRoundOperand(lhs, set, status);
3602 if (alloclhs==NULL) break;
3603 lhs=alloclhs;
3604 }
3605 if (rhs->digits>reqdigits) {
3606 allocrhs=decRoundOperand(rhs, set, status);
3607 if (allocrhs==NULL) break;
3608 rhs=allocrhs;
3609 }
3610 }
3611 #endif
3612 // [following code does not require input rounding]
3613
3614 // note whether signs differ [used all paths]
3615 diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
3616
3617 // handle infinities and NaNs
3618 if (SPECIALARGS) { // a special bit set
3619 if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN
3620 decNaNs(res, lhs, rhs, set, status);
3621 else { // one or two infinities
3622 if (decNumberIsInfinite(lhs)) { // LHS is infinity
3623 // two infinities with different signs is invalid
3624 if (decNumberIsInfinite(rhs) && diffsign) {
3625 *status|=DEC_Invalid_operation;
3626 break;
3627 }
3628 bits=lhs->bits & DECNEG; // get sign from LHS
3629 }
3630 else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity
3631 bits|=DECINF;
3632 decNumberZero(res);
3633 res->bits=bits; // set +/- infinity
3634 } // an infinity
3635 break;
3636 }
3637
3638 // Quick exit for add 0s; return the non-0, modified as need be
3639 if (ISZERO(lhs)) {
3640 Int adjust; // work
3641 Int lexp=lhs->exponent; // save in case LHS==RES
3642 bits=lhs->bits; // ..
3643 (void)bits;
3644 residue=0; // clear accumulator
3645 decCopyFit(res, rhs, set, &residue, status); // copy (as needed)
3646 res->bits^=negate; // flip if rhs was negated
3647 #if DECSUBSET
3648 if (set->extended) { // exponents on zeros count
3649 #endif
3650 // exponent will be the lower of the two
3651 adjust=lexp-res->exponent; // adjustment needed [if -ve]
3652 if (ISZERO(res)) { // both 0: special IEEE 754 rules
3653 if (adjust<0) res->exponent=lexp; // set exponent
3654 // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0
3655 if (diffsign) {
3656 if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
3657 else res->bits=DECNEG; // preserve 0 sign
3658 }
3659 }
3660 else { // non-0 res
3661 if (adjust<0) { // 0-padding needed
3662 if ((res->digits-adjust)>set->digits) {
3663 adjust=res->digits-set->digits; // to fit exactly
3664 *status|=DEC_Rounded; // [but exact]
3665 }
3666 res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
3667 res->exponent+=adjust; // set the exponent.
3668 }
3669 } // non-0 res
3670 #if DECSUBSET
3671 } // extended
3672 #endif
3673 decFinish(res, set, &residue, status); // clean and finalize
3674 break;}
3675
3676 if (ISZERO(rhs)) { // [lhs is non-zero]
3677 Int adjust; // work
3678 Int rexp=rhs->exponent; // save in case RHS==RES
3679 bits=rhs->bits; // be clean
3680 (void)bits;
3681 residue=0; // clear accumulator
3682 decCopyFit(res, lhs, set, &residue, status); // copy (as needed)
3683 #if DECSUBSET
3684 if (set->extended) { // exponents on zeros count
3685 #endif
3686 // exponent will be the lower of the two
3687 // [0-0 case handled above]
3688 adjust=rexp-res->exponent; // adjustment needed [if -ve]
3689 if (adjust<0) { // 0-padding needed
3690 if ((res->digits-adjust)>set->digits) {
3691 adjust=res->digits-set->digits; // to fit exactly
3692 *status|=DEC_Rounded; // [but exact]
3693 }
3694 res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
3695 res->exponent+=adjust; // set the exponent.
3696 }
3697 #if DECSUBSET
3698 } // extended
3699 #endif
3700 decFinish(res, set, &residue, status); // clean and finalize
3701 break;}
3702
3703 // [NB: both fastpath and mainpath code below assume these cases
3704 // (notably 0-0) have already been handled]
3705
3706 // calculate the padding needed to align the operands
3707 padding=rhs->exponent-lhs->exponent;
3708
3709 // Fastpath cases where the numbers are aligned and normal, the RHS
3710 // is all in one unit, no operand rounding is needed, and no carry,
3711 // lengthening, or borrow is needed
3712 if (padding==0
3713 && rhs->digits<=DECDPUN
3714 && rhs->exponent>=set->emin // [some normals drop through]
3715 && rhs->exponent<=set->emax-set->digits+1 // [could clamp]
3716 && rhs->digits<=reqdigits
3717 && lhs->digits<=reqdigits) {
3718 Int partial=*lhs->lsu;
3719 if (!diffsign) { // adding
3720 partial+=*rhs->lsu;
3721 if ((partial<=DECDPUNMAX) // result fits in unit
3722 && (lhs->digits>=DECDPUN || // .. and no digits-count change
3723 partial<(Int)powers[lhs->digits])) { // ..
3724 if (res!=lhs) decNumberCopy(res, lhs); // not in place
3725 *res->lsu=(Unit)partial; // [copy could have overwritten RHS]
3726 break;
3727 }
3728 // else drop out for careful add
3729 }
3730 else { // signs differ
3731 partial-=*rhs->lsu;
3732 if (partial>0) { // no borrow needed, and non-0 result
3733 if (res!=lhs) decNumberCopy(res, lhs); // not in place
3734 *res->lsu=(Unit)partial;
3735 // this could have reduced digits [but result>0]
3736 res->digits=decGetDigits(res->lsu, D2U(res->digits));
3737 break;
3738 }
3739 // else drop out for careful subtract
3740 }
3741 }
3742
3743 // Now align (pad) the lhs or rhs so they can be added or
3744 // subtracted, as necessary.
3745 rhsshift=0; // rhs shift to left (padding) in Units
3746 bits=lhs->bits; // assume sign is that of LHS
3747 mult=1; // likely multiplier
3748
3749 // [if padding==0 the operands are aligned; no padding is needed]
3750 if (padding!=0) {
3751 // some padding needed; always pad the RHS, as any required
3752 // padding can then be effected by a simple combination of
3753 // shifts and a multiply
3754 Int exponent; // new exponent of LHS (if adjusted)
3755 if (padding<0) { // LHS needs the padding
3756 const decNumber *t;
3757 padding=-padding; // will be +ve
3758 bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS
3759 t=lhs; lhs=rhs; rhs=t;
3760 }
3761
3762 exponent = rhs->exponent-1;
3763 exponent += (rhs->digits>reqdigits) ? 0 : rhs->digits-reqdigits-1;
3764 if (lhs->digits+lhs->exponent-1 < exponent) {
3765 // Adjust lhs and padding to avoid huge shifts.
3766 dtiny.bits=lhs->bits;
3767 dtiny.exponent=exponent;
3768 dtiny.digits=1;
3769 dtiny.lsu[0]=1;
3770 lhs=&dtiny;
3771 padding=rhs->exponent-exponent;
3772 // Fall through to add/subtract the modified lhs.
3773 }
3774
3775 // LHS digits may affect result
3776 rhsshift=D2U(padding+1)-1; // this much by Unit shift ..
3777 mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication
3778 } // padding needed
3779
3780 if (diffsign) mult=-mult; // signs differ
3781
3782 // determine the longer operand
3783 maxdigits=rhs->digits+padding; // virtual length of RHS
3784 if (lhs->digits>maxdigits) maxdigits=lhs->digits;
3785
3786 // Decide on the result buffer to use; if possible place directly
3787 // into result.
3788 acc=res->lsu; // assume add direct to result
3789 // If destructive overlap, or the number is too long, or a carry or
3790 // borrow to DIGITS+1 might be possible, a buffer must be used.
3791 // [Might be worth more sophisticated tests when maxdigits==reqdigits]
3792 if ((maxdigits>=reqdigits) // is, or could be, too large
3793 || (res==rhs && rhsshift>0)) { // destructive overlap
3794 // buffer needed, choose it; units for maxdigits digits will be
3795 // needed, +1 Unit for carry or borrow
3796 Int need=D2U(maxdigits)+1;
3797 acc=accbuff; // assume use local buffer
3798 if (need*sizeof(Unit)>sizeof(accbuff)) {
3799 allocacc=(Unit *)malloc(need*sizeof(Unit));
3800 if (allocacc==NULL) { // hopeless -- abandon
3801 *status|=DEC_Insufficient_storage;
3802 break;}
3803 acc=allocacc;
3804 }
3805 }
3806
3807 res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite..
3808 res->exponent=lhs->exponent; // .. operands (even if aliased)
3809
3810 // add [A+B*m] or subtract [A+B*(-m)]
3811 res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
3812 rhs->lsu, D2U(rhs->digits),
3813 rhsshift, acc, mult)
3814 *DECDPUN; // [units -> digits]
3815 if (res->digits<0) { // borrowed...
3816 res->digits=-res->digits;
3817 res->bits^=DECNEG; // flip the sign
3818 }
3819
3820 // If a buffer was used the result must be copied back, possibly
3821 // shortening. (If no buffer was used then the result must have
3822 // fit, so can't need rounding and residue must be 0.)
3823 residue=0; // clear accumulator
3824 if (acc!=res->lsu) {
3825 #if DECSUBSET
3826 if (set->extended) { // round from first significant digit
3827 #endif
3828 // remove leading zeros that were added due to rounding up to
3829 // integral Units -- before the test for rounding.
3830 if (res->digits>reqdigits)
3831 res->digits=decGetDigits(acc, D2U(res->digits));
3832 decSetCoeff(res, set, acc, res->digits, &residue, status);
3833 #if DECSUBSET
3834 }
3835 else { // subset arithmetic rounds from original significant digit
3836 // May have an underestimate. This only occurs when both
3837 // numbers fit in DECDPUN digits and are padding with a
3838 // negative multiple (-10, -100...) and the top digit(s) become
3839 // 0. (This only matters when using X3.274 rules where the
3840 // leading zero could be included in the rounding.)
3841 if (res->digits<maxdigits) {
3842 *(acc+D2U(res->digits))=0; // ensure leading 0 is there
3843 res->digits=maxdigits;
3844 }
3845 else {
3846 // remove leading zeros that added due to rounding up to
3847 // integral Units (but only those in excess of the original
3848 // maxdigits length, unless extended) before test for rounding.
3849 if (res->digits>reqdigits) {
3850 res->digits=decGetDigits(acc, D2U(res->digits));
3851 if (res->digits<maxdigits) res->digits=maxdigits;
3852 }
3853 }
3854 decSetCoeff(res, set, acc, res->digits, &residue, status);
3855 // Now apply rounding if needed before removing leading zeros.
3856 // This is safe because subnormals are not a possibility
3857 if (residue!=0) {
3858 decApplyRound(res, set, residue, status);
3859 residue=0; // did what needed to be done
3860 }
3861 } // subset
3862 #endif
3863 } // used buffer
3864
3865 // strip leading zeros [these were left on in case of subset subtract]
3866 res->digits=decGetDigits(res->lsu, D2U(res->digits));
3867
3868 // apply checks and rounding
3869 decFinish(res, set, &residue, status);
3870
3871 // "When the sum of two operands with opposite signs is exactly
3872 // zero, the sign of that sum shall be '+' in all rounding modes
3873 // except round toward -Infinity, in which mode that sign shall be
3874 // '-'." [Subset zeros also never have '-', set by decFinish.]
3875 if (ISZERO(res) && diffsign
3876 #if DECSUBSET
3877 && set->extended
3878 #endif
3879 && (*status&DEC_Inexact)==0) {
3880 if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign -
3881 else res->bits&=~DECNEG; // sign +
3882 }
3883 } while(0); // end protected
3884
3885 if (allocacc!=NULL) FREE(allocacc); // drop any storage used
3886 #if DECSUBSET
3887 if (allocrhs!=NULL) FREE(allocrhs); // ..
3888 if (alloclhs!=NULL) FREE(alloclhs); // ..
3889 #endif
3890 return res;
3891 } // decAddOp
3892
3893 /* ------------------------------------------------------------------ */
3894 /* decDivideOp -- division operation */
3895 /* */
3896 /* This routine performs the calculations for all four division */
3897 /* operators (divide, divideInteger, remainder, remainderNear). */
3898 /* */
3899 /* C=A op B */
3900 /* */
3901 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */
3902 /* lhs is A */
3903 /* rhs is B */
3904 /* set is the context */
3905 /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
3906 /* status is the usual accumulator */
3907 /* */
3908 /* C must have space for set->digits digits. */
3909 /* */
3910 /* ------------------------------------------------------------------ */
3911 /* The underlying algorithm of this routine is the same as in the */
3912 /* 1981 S/370 implementation, that is, non-restoring long division */
3913 /* with bi-unit (rather than bi-digit) estimation for each unit */
3914 /* multiplier. In this pseudocode overview, complications for the */
3915 /* Remainder operators and division residues for exact rounding are */
3916 /* omitted for clarity. */
3917 /* */
3918 /* Prepare operands and handle special values */
3919 /* Test for x/0 and then 0/x */
3920 /* Exp =Exp1 - Exp2 */
3921 /* Exp =Exp +len(var1) -len(var2) */
3922 /* Sign=Sign1 * Sign2 */
3923 /* Pad accumulator (Var1) to double-length with 0's (pad1) */
3924 /* Pad Var2 to same length as Var1 */
3925 /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
3926 /* have=0 */
3927 /* Do until (have=digits+1 OR residue=0) */
3928 /* if exp<0 then if integer divide/residue then leave */
3929 /* this_unit=0 */
3930 /* Do forever */
3931 /* compare numbers */
3932 /* if <0 then leave inner_loop */
3933 /* if =0 then (* quick exit without subtract *) do */
3934 /* this_unit=this_unit+1; output this_unit */
3935 /* leave outer_loop; end */
3936 /* Compare lengths of numbers (mantissa): */
3937 /* If same then tops2=msu2pair -- {units 1&2 of var2} */
3938 /* else tops2=msu2plus -- {0, unit 1 of var2} */
3939 /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
3940 /* mult=tops1/tops2 -- Good and safe guess at divisor */
3941 /* if mult=0 then mult=1 */
3942 /* this_unit=this_unit+mult */
3943 /* subtract */
3944 /* end inner_loop */
3945 /* if have\=0 | this_unit\=0 then do */
3946 /* output this_unit */
3947 /* have=have+1; end */
3948 /* var2=var2/10 */
3949 /* exp=exp-1 */
3950 /* end outer_loop */
3951 /* exp=exp+1 -- set the proper exponent */
3952 /* if have=0 then generate answer=0 */
3953 /* Return (Result is defined by Var1) */
3954 /* */
3955 /* ------------------------------------------------------------------ */
3956 /* Two working buffers are needed during the division; one (digits+ */
3957 /* 1) to accumulate the result, and the other (up to 2*digits+1) for */
3958 /* long subtractions. These are acc and var1 respectively. */
3959 /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
3960 /* The static buffers may be larger than might be expected to allow */
3961 /* for calls from higher-level functions (notable exp). */
3962 /* ------------------------------------------------------------------ */
3963 static decNumber * decDivideOp(decNumber *res,
/* */
3964 const decNumber *lhs, const decNumber *rhs,
3965 decContext *set, Flag op, uInt *status) {
3966 #if DECSUBSET
3967 decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
3968 decNumber *allocrhs=NULL; // .., rhs
3969 #endif
3970 Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer
3971 Unit *acc=accbuff; // -> accumulator array for result
3972 Unit *allocacc=NULL; // -> allocated buffer, iff allocated
3973 Unit *accnext; // -> where next digit will go
3974 Int acclength; // length of acc needed [Units]
3975 Int accunits; // count of units accumulated
3976 Int accdigits; // count of digits accumulated
3977
3978 Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1
3979 Unit *var1=varbuff; // -> var1 array for long subtraction
3980 Unit *varalloc=NULL; // -> allocated buffer, iff used
3981 Unit *msu1; // -> msu of var1
3982
3983 const Unit *var2; // -> var2 array
3984 const Unit *msu2; // -> msu of var2
3985 Int msu2plus; // msu2 plus one [does not vary]
3986 eInt msu2pair; // msu2 pair plus one [does not vary]
3987
3988 Int var1units, var2units; // actual lengths
3989 Int var2ulen; // logical length (units)
3990 Int var1initpad=0; // var1 initial padding (digits)
3991 Int maxdigits; // longest LHS or required acc length
3992 Int mult; // multiplier for subtraction
3993 Unit thisunit; // current unit being accumulated
3994 Int residue; // for rounding
3995 Int reqdigits=set->digits; // requested DIGITS
3996 Int exponent; // working exponent
3997 Int maxexponent=0; // DIVIDE maximum exponent if unrounded
3998 uByte bits; // working sign
3999 Unit *target; // work
4000 const Unit *source; // ..
4001 uInt const *pow; // ..
4002 Int shift, cut; // ..
4003 #if DECSUBSET
4004 Int dropped; // work
4005 #endif
4006
4007 do { // protect allocated storage
4008 #if DECSUBSET
4009 if (!set->extended) {
4010 // reduce operands and set lostDigits status, as needed
4011 if (lhs->digits>reqdigits) {
4012 alloclhs=decRoundOperand(lhs, set, status);
4013 if (alloclhs==NULL) break;
4014 lhs=alloclhs;
4015 }
4016 if (rhs->digits>reqdigits) {
4017 allocrhs=decRoundOperand(rhs, set, status);
4018 if (allocrhs==NULL) break;
4019 rhs=allocrhs;
4020 }
4021 }
4022 #endif
4023 // [following code does not require input rounding]
4024
4025 bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions
4026 (void)bits;
4027 // handle infinities and NaNs
4028 if (SPECIALARGS) { // a special bit set
4029 if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
4030 decNaNs(res, lhs, rhs, set, status);
4031 break;
4032 }
4033 // one or two infinities
4034 if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite
4035 if (decNumberIsInfinite(rhs) || // two infinities are invalid ..
4036 op & (REMAINDER | REMNEAR)) { // as is remainder of infinity
4037 *status|=DEC_Invalid_operation;
4038 break;
4039 }
4040 // [Note that infinity/0 raises no exceptions]
4041 decNumberZero(res);
4042 res->bits=bits|DECINF; // set +/- infinity
4043 break;
4044 }
4045 else { // RHS (divisor) is infinite
4046 residue=0;
4047 if (op&(REMAINDER|REMNEAR)) {
4048 // result is [finished clone of] lhs
4049 decCopyFit(res, lhs, set, &residue, status);
4050 }
4051 else { // a division
4052 decNumberZero(res);
4053 res->bits=bits; // set +/- zero
4054 // for DIVIDEINT the exponent is always 0. For DIVIDE, result
4055 // is a 0 with infinitely negative exponent, clamped to minimum
4056 if (op&DIVIDE) {
4057 res->exponent=set->emin-set->digits+1;
4058 *status|=DEC_Clamped;
4059 }
4060 }
4061 decFinish(res, set, &residue, status);
4062 break;
4063 }
4064 }
4065
4066 // handle 0 rhs (x/0)
4067 if (ISZERO(rhs)) { // x/0 is always exceptional
4068 if (ISZERO(lhs)) {
4069 decNumberZero(res); // [after lhs test]
4070 *status|=DEC_Division_undefined;// 0/0 will become NaN
4071 }
4072 else {
4073 decNumberZero(res);
4074 if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
4075 else {
4076 *status|=DEC_Division_by_zero; // x/0
4077 res->bits=bits|DECINF; // .. is +/- Infinity
4078 }
4079 }
4080 break;}
4081
4082 // handle 0 lhs (0/x)
4083 if (ISZERO(lhs)) { // 0/x [x!=0]
4084 #if DECSUBSET
4085 if (!set->extended) decNumberZero(res);
4086 else {
4087 #endif
4088 if (op&DIVIDE) {
4089 exponent=lhs->exponent-rhs->exponent; // ideal exponent
4090 decNumberCopy(res, lhs); // [zeros always fit]
4091 res->bits=bits; // sign as computed
4092 res->exponent=exponent; // exponent, too
4093 }
4094 else if (op&DIVIDEINT) {
4095 decNumberZero(res); // integer 0
4096 res->bits=bits; // sign as computed
4097 }
4098 else { // a remainder
4099 exponent=rhs->exponent; // [save in case overwrite]
4100 decNumberCopy(res, lhs); // [zeros always fit]
4101 if (exponent<res->exponent) res->exponent=exponent; // use lower
4102 }
4103 residue=0;
4104 decFinalize(res, set, &residue, status); // check exponent
4105 #if DECSUBSET
4106 }
4107 #endif
4108 break;}
4109
4110 // Precalculate exponent. This starts off adjusted (and hence fits
4111 // in 31 bits) and becomes the usual unadjusted exponent as the
4112 // division proceeds. The order of evaluation is important, here,
4113 // to avoid wrap.
4114 exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
4115
4116 // If the working exponent is -ve, then some quick exits are
4117 // possible because the quotient is known to be <1
4118 // [for REMNEAR, it needs to be < -1, as -0.5 could need work]
4119 if (exponent<0 && !(op==DIVIDE)) {
4120 if (op&DIVIDEINT) {
4121 decNumberZero(res); // integer part is 0
4122 #if DECSUBSET
4123 if (set->extended)
4124 #endif
4125 res->bits=bits; // set +/- zero
4126 break;}
4127 // fastpath remainders so long as the lhs has the smaller
4128 // (or equal) exponent
4129 if (lhs->exponent<=rhs->exponent) {
4130 if (op&REMAINDER || exponent<-1) {
4131 // It is REMAINDER or safe REMNEAR; result is [finished
4132 // clone of] lhs (r = x - 0*y)
4133 residue=0;
4134 decCopyFit(res, lhs, set, &residue, status);
4135 decFinish(res, set, &residue, status);
4136 break;
4137 }
4138 // [unsafe REMNEAR drops through]
4139 }
4140 } // fastpaths
4141
4142 /* Long (slow) division is needed; roll up the sleeves... */
4143
4144 // The accumulator will hold the quotient of the division.
4145 // If it needs to be too long for stack storage, then allocate.
4146 acclength=D2U(reqdigits+DECDPUN); // in Units
4147 if (acclength*sizeof(Unit)>sizeof(accbuff)) {
4148 allocacc=(Unit *)malloc(acclength*sizeof(Unit));
4149 if (allocacc==NULL) { // hopeless -- abandon
4150 *status|=DEC_Insufficient_storage;
4151 break;}
4152 acc=allocacc; // use the allocated space
4153 }
4154
4155 // var1 is the padded LHS ready for subtractions.
4156 // If it needs to be too long for stack storage, then allocate.
4157 // The maximum units needed for var1 (long subtraction) is:
4158 // Enough for
4159 // (rhs->digits+reqdigits-1) -- to allow full slide to right
4160 // or (lhs->digits) -- to allow for long lhs
4161 // whichever is larger
4162 // +1 -- for rounding of slide to right
4163 // +1 -- for leading 0s
4164 // +1 -- for pre-adjust if a remainder or DIVIDEINT
4165 // [Note: unused units do not participate in decUnitAddSub data]
4166 maxdigits=rhs->digits+reqdigits-1;
4167 if (lhs->digits>maxdigits) maxdigits=lhs->digits;
4168 var1units=D2U(maxdigits)+2;
4169 // allocate a guard unit above msu1 for REMAINDERNEAR
4170 if (!(op&DIVIDE)) var1units++;
4171 if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
4172 varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
4173 if (varalloc==NULL) { // hopeless -- abandon
4174 *status|=DEC_Insufficient_storage;
4175 break;}
4176 var1=varalloc; // use the allocated space
4177 }
4178
4179 // Extend the lhs and rhs to full long subtraction length. The lhs
4180 // is truly extended into the var1 buffer, with 0 padding, so a
4181 // subtract in place is always possible. The rhs (var2) has
4182 // virtual padding (implemented by decUnitAddSub).
4183 // One guard unit was allocated above msu1 for rem=rem+rem in
4184 // REMAINDERNEAR.
4185 msu1=var1+var1units-1; // msu of var1
4186 source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array
4187 for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
4188 for (; target>=var1; target--) *target=0;
4189
4190 // rhs (var2) is left-aligned with var1 at the start
4191 var2ulen=var1units; // rhs logical length (units)
4192 var2units=D2U(rhs->digits); // rhs actual length (units)
4193 var2=rhs->lsu; // -> rhs array
4194 msu2=var2+var2units-1; // -> msu of var2 [never changes]
4195 // now set up the variables which will be used for estimating the
4196 // multiplication factor. If these variables are not exact, add
4197 // 1 to make sure that the multiplier is never overestimated.
4198 msu2plus=*msu2; // it's value ..
4199 if (var2units>1) msu2plus++; // .. +1 if any more
4200 msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair ..
4201 if (var2units>1) { // .. [else treat 2nd as 0]
4202 msu2pair+=*(msu2-1); // ..
4203 if (var2units>2) msu2pair++; // .. +1 if any more
4204 }
4205
4206 // The calculation is working in units, which may have leading zeros,
4207 // but the exponent was calculated on the assumption that they are
4208 // both left-aligned. Adjust the exponent to compensate: add the
4209 // number of leading zeros in var1 msu and subtract those in var2 msu.
4210 // [This is actually done by counting the digits and negating, as
4211 // lead1=DECDPUN-digits1, and similarly for lead2.]
4212 for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
4213 for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
4214
4215 // Now, if doing an integer divide or remainder, ensure that
4216 // the result will be Unit-aligned. To do this, shift the var1
4217 // accumulator towards least if need be. (It's much easier to
4218 // do this now than to reassemble the residue afterwards, if
4219 // doing a remainder.) Also ensure the exponent is not negative.
4220 if (!(op&DIVIDE)) {
4221 Unit *u; // work
4222 // save the initial 'false' padding of var1, in digits
4223 var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
4224 // Determine the shift to do.
4225 if (exponent<0) cut=-exponent;
4226 else cut=DECDPUN-exponent%DECDPUN;
4227 decShiftToLeast(var1, var1units, cut);
4228 exponent+=cut; // maintain numerical value
4229 var1initpad-=cut; // .. and reduce padding
4230 // clean any most-significant units which were just emptied
4231 for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
4232 } // align
4233 else { // is DIVIDE
4234 maxexponent=lhs->exponent-rhs->exponent; // save
4235 // optimization: if the first iteration will just produce 0,
4236 // preadjust to skip it [valid for DIVIDE only]
4237 if (*msu1<*msu2) {
4238 var2ulen--; // shift down
4239 exponent-=DECDPUN; // update the exponent
4240 }
4241 }
4242
4243 // ---- start the long-division loops ------------------------------
4244 accunits=0; // no units accumulated yet
4245 accdigits=0; // .. or digits
4246 accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1]
4247 for (;;) { // outer forever loop
4248 thisunit=0; // current unit assumed 0
4249 // find the next unit
4250 for (;;) { // inner forever loop
4251 // strip leading zero units [from either pre-adjust or from
4252 // subtract last time around]. Leave at least one unit.
4253 for (; *msu1==0 && msu1>var1; msu1--) var1units--;
4254
4255 if (var1units<var2ulen) break; // var1 too low for subtract
4256 if (var1units==var2ulen) { // unit-by-unit compare needed
4257 // compare the two numbers, from msu
4258 const Unit *pv1, *pv2;
4259 Unit v2; // units to compare
4260 pv2=msu2; // -> msu
4261 for (pv1=msu1; ; pv1--, pv2--) {
4262 // v1=*pv1 -- always OK
4263 v2=0; // assume in padding
4264 if (pv2>=var2) v2=*pv2; // in range
4265 if (*pv1!=v2) break; // no longer the same
4266 if (pv1==var1) break; // done; leave pv1 as is
4267 }
4268 // here when all inspected or a difference seen
4269 if (*pv1<v2) break; // var1 too low to subtract
4270 if (*pv1==v2) { // var1 == var2
4271 // reach here if var1 and var2 are identical; subtraction
4272 // would increase digit by one, and the residue will be 0 so
4273 // the calculation is done; leave the loop with residue=0.
4274 thisunit++; // as though subtracted
4275 *var1=0; // set var1 to 0
4276 var1units=1; // ..
4277 break; // from inner
4278 } // var1 == var2
4279 // *pv1>v2. Prepare for real subtraction; the lengths are equal
4280 // Estimate the multiplier (there's always a msu1-1)...
4281 // Bring in two units of var2 to provide a good estimate.
4282 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
4283 } // lengths the same
4284 else { // var1units > var2ulen, so subtraction is safe
4285 // The var2 msu is one unit towards the lsu of the var1 msu,
4286 // so only one unit for var2 can be used.
4287 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
4288 }
4289 if (mult==0) mult=1; // must always be at least 1
4290 // subtraction needed; var1 is > var2
4291 thisunit=(Unit)(thisunit+mult); // accumulate
4292 // subtract var1-var2, into var1; only the overlap needs
4293 // processing, as this is an in-place calculation
4294 shift=var2ulen-var2units;
4295 decUnitAddSub(&var1[shift], var1units-shift,
4296 var2, var2units, 0,
4297 &var1[shift], -mult);
4298 // var1 now probably has leading zeros; these are removed at the
4299 // top of the inner loop.
4300 } // inner loop
4301
4302 // The next unit has been calculated in full; unless it's a
4303 // leading zero, add to acc
4304 if (accunits!=0 || thisunit!=0) { // is first or non-zero
4305 *accnext=thisunit; // store in accumulator
4306 // account exactly for the new digits
4307 if (accunits==0) {
4308 accdigits++; // at least one
4309 for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
4310 }
4311 else accdigits+=DECDPUN;
4312 accunits++; // update count
4313 accnext--; // ready for next
4314 if (accdigits>reqdigits) break; // have enough digits
4315 }
4316
4317 // if the residue is zero, the operation is done (unless divide
4318 // or divideInteger and still not enough digits yet)
4319 #if defined(__clang_analyzer__)
4320 *var1=0;
4321 #endif /* if defined(__clang_analyzer__) */
4322 if (*var1==0 && var1units==1) { // residue is 0
4323 if (op&(REMAINDER|REMNEAR)) break;
4324 if ((op&DIVIDE) && (exponent<=maxexponent)) break;
4325 // [drop through if divideInteger]
4326 }
4327 // also done enough if calculating remainder or integer
4328 // divide and just did the last ('units') unit
4329 if (exponent==0 && !(op&DIVIDE)) break;
4330
4331 // to get here, var1 is less than var2, so divide var2 by the per-
4332 // Unit power of ten and go for the next digit
4333 var2ulen--; // shift down
4334 exponent-=DECDPUN; // update the exponent
4335 } // outer loop
4336
4337 // ---- division is complete ---------------------------------------
4338 // here: acc has at least reqdigits+1 of good results (or fewer
4339 // if early stop), starting at accnext+1 (its lsu)
4340 // var1 has any residue at the stopping point
4341 // accunits is the number of digits collected in acc
4342 if (accunits==0) { // acc is 0
4343 accunits=1; // show have a unit ..
4344 accdigits=1; // ..
4345 *accnext=0; // .. whose value is 0
4346 }
4347 else accnext++; // back to last placed
4348 // accnext now -> lowest unit of result
4349
4350 residue=0; // assume no residue
4351 if (op&DIVIDE) {
4352 // record the presence of any residue, for rounding
4353 if (*var1!=0 || var1units>1) residue=1;
4354 else { // no residue
4355 // Had an exact division; clean up spurious trailing 0s.
4356 // There will be at most DECDPUN-1, from the final multiply,
4357 // and then only if the result is non-0 (and even) and the
4358 // exponent is 'loose'.
4359 #if DECDPUN>1
4360 Unit lsu=*accnext;
4361 if (!(lsu&0x01) && (lsu!=0)) {
4362 // count the trailing zeros
4363 Int drop=0;
4364 for (;; drop++) { // [will terminate because lsu!=0]
4365 if (exponent>=maxexponent) break; // don't chop real 0s
4366 # if DECDPUN<=4
4367 if ((lsu-QUOT10(lsu, drop+1)
4368 *powers[drop+1])!=0) break; // found non-0 digit
4369 # else
4370 if (lsu%powers[drop+1]!=0) break; // found non-0 digit
4371 # endif
4372 exponent++;
4373 }
4374 if (drop>0) {
4375 accunits=decShiftToLeast(accnext, accunits, drop);
4376 accdigits=decGetDigits(accnext, accunits);
4377 accunits=D2U(accdigits);
4378 (void)accunits;
4379 // [exponent was adjusted in the loop]
4380 }
4381 } // neither odd nor 0
4382 #endif
4383 } // exact divide
4384 } // divide
4385 else /* op!=DIVIDE */ {
4386 // check for coefficient overflow
4387 if (accdigits+exponent>reqdigits) {
4388 *status|=DEC_Division_impossible;
4389 break;
4390 }
4391 if (op & (REMAINDER|REMNEAR)) {
4392 // [Here, the exponent will be 0, because var1 was adjusted
4393 // appropriately.]
4394 Int postshift; // work
4395 Flag wasodd=0; // integer was odd
4396 Unit *quotlsu; // for save
4397 Int quotdigits; // ..
4398
4399 bits=lhs->bits; // remainder sign is always as lhs
4400
4401 // Fastpath when residue is truly 0 is worthwhile [and
4402 // simplifies the code below]
4403 if (*var1==0 && var1units==1) { // residue is 0
4404 Int exp=lhs->exponent; // save min(exponents)
4405 if (rhs->exponent<exp) exp=rhs->exponent;
4406 decNumberZero(res); // 0 coefficient
4407 #if DECSUBSET
4408 if (set->extended)
4409 #endif
4410 res->exponent=exp; // .. with proper exponent
4411 res->bits=(uByte)(bits&DECNEG); // [cleaned]
4412 decFinish(res, set, &residue, status); // might clamp
4413 break;
4414 }
4415 // note if the quotient was odd
4416 if (*accnext & 0x01) wasodd=1; // acc is odd
4417 quotlsu=accnext; // save in case need to reinspect
4418 quotdigits=accdigits; // ..
4419
4420 // treat the residue, in var1, as the value to return, via acc
4421 // calculate the unused zero digits. This is the smaller of:
4422 // var1 initial padding (saved above)
4423 // var2 residual padding, which happens to be given by:
4424 postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
4425 // [the 'exponent' term accounts for the shifts during divide]
4426 if (var1initpad<postshift) postshift=var1initpad;
4427
4428 // shift var1 the requested amount, and adjust its digits
4429 var1units=decShiftToLeast(var1, var1units, postshift);
4430 accnext=var1;
4431 accdigits=decGetDigits(var1, var1units);
4432 accunits=D2U(accdigits);
4433
4434 exponent=lhs->exponent; // exponent is smaller of lhs & rhs
4435 if (rhs->exponent<exponent) exponent=rhs->exponent;
4436
4437 // Now correct the result if doing remainderNear; if it
4438 // (looking just at coefficients) is > rhs/2, or == rhs/2 and
4439 // the integer was odd then the result should be rem-rhs.
4440 if (op&REMNEAR) {
4441 Int compare, tarunits; // work
4442 Unit *up; // ..
4443 // calculate remainder*2 into the var1 buffer (which has
4444 // 'headroom' of an extra unit and hence enough space)
4445 // [a dedicated 'double' loop would be faster, here]
4446 tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
4447 0, accnext, 1);
4448 // decDumpAr('r', accnext, tarunits);
4449
4450 // Here, accnext (var1) holds tarunits Units with twice the
4451 // remainder's coefficient, which must now be compared to the
4452 // RHS. The remainder's exponent may be smaller than the RHS's.
4453 compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
4454 rhs->exponent-exponent);
4455 if (compare==BADINT) { // deep trouble
4456 *status|=DEC_Insufficient_storage;
4457 break;}
4458
4459 // now restore the remainder by dividing by two; the lsu
4460 // is known to be even.
4461 for (up=accnext; up<accnext+tarunits; up++) {
4462 Int half; // half to add to lower unit
4463 half=*up & 0x01;
4464 *up/=2; // [shift]
4465 if (!half) continue;
4466 *(up-1)+=(DECDPUNMAX+1)/2;
4467 }
4468 // [accunits still describes the original remainder length]
4469
4470 if (compare>0 || (compare==0 && wasodd)) { // adjustment needed
4471 Int exp, expunits, exprem; // work
4472 // This is effectively causing round-up of the quotient,
4473 // so if it was the rare case where it was full and all
4474 // nines, it would overflow and hence division-impossible
4475 // should be raised
4476 Flag allnines=0; // 1 if quotient all nines
4477 if (quotdigits==reqdigits) { // could be borderline
4478 for (up=quotlsu; ; up++) {
4479 if (quotdigits>DECDPUN) {
4480 if (*up!=DECDPUNMAX) break;// non-nines
4481 }
4482 else { // this is the last Unit
4483 if (*up==powers[quotdigits]-1) allnines=1;
4484 break;
4485 }
4486 quotdigits-=DECDPUN; // checked those digits
4487 } // up
4488 } // borderline check
4489 if (allnines) {
4490 *status|=DEC_Division_impossible;
4491 break;}
4492
4493 // rem-rhs is needed; the sign will invert. Again, var1
4494 // can safely be used for the working Units array.
4495 exp=rhs->exponent-exponent; // RHS padding needed
4496 // Calculate units and remainder from exponent.
4497 expunits=exp/DECDPUN;
4498 exprem=exp%DECDPUN;
4499 // subtract [A+B*(-m)]; the result will always be negative
4500 accunits=-decUnitAddSub(accnext, accunits,
4501 rhs->lsu, D2U(rhs->digits),
4502 expunits, accnext, -(Int)powers[exprem]);
4503 accdigits=decGetDigits(accnext, accunits); // count digits exactly
4504 accunits=D2U(accdigits); // and recalculate the units for copy
4505 (void)accunits;
4506 // [exponent is as for original remainder]
4507 bits^=DECNEG; // flip the sign
4508 }
4509 } // REMNEAR
4510 } // REMAINDER or REMNEAR
4511 } // not DIVIDE
4512
4513 // Set exponent and bits
4514 res->exponent=exponent;
4515 res->bits=(uByte)(bits&DECNEG); // [cleaned]
4516
4517 // Now the coefficient.
4518 decSetCoeff(res, set, accnext, accdigits, &residue, status);
4519
4520 decFinish(res, set, &residue, status); // final cleanup
4521
4522 #if DECSUBSET
4523 // If a divide then strip trailing zeros if subset [after round]
4524 if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
4525 #endif
4526 } while(0); // end protected
4527
4528 if (varalloc!=NULL) FREE(varalloc); // drop any storage used
4529 if (allocacc!=NULL) FREE(allocacc); // ..
4530 #if DECSUBSET
4531 if (allocrhs!=NULL) FREE(allocrhs); // ..
4532 if (alloclhs!=NULL) FREE(alloclhs); // ..
4533 #endif
4534 return res;
4535 } // decDivideOp
4536
4537 /* ------------------------------------------------------------------ */
4538 /* decMultiplyOp -- multiplication operation */
4539 /* */
4540 /* This routine performs the multiplication C=A x B. */
4541 /* */
4542 /* res is C, the result. C may be A and/or B (e.g., X=X*X) */
4543 /* lhs is A */
4544 /* rhs is B */
4545 /* set is the context */
4546 /* status is the usual accumulator */
4547 /* */
4548 /* C must have space for set->digits digits. */
4549 /* */
4550 /* ------------------------------------------------------------------ */
4551 /* 'Classic' multiplication is used rather than Karatsuba, as the */
4552 /* latter would give only a minor improvement for the short numbers */
4553 /* expected to be handled most (and uses much more memory). */
4554 /* */
4555 /* There are two major paths here: the general-purpose ('old code') */
4556 /* path which handles all DECDPUN values, and a fastpath version */
4557 /* which is used if 64-bit ints are available, DECDPUN<=4, and more */
4558 /* than two calls to decUnitAddSub would be made. */
4559 /* */
4560 /* The fastpath version lumps units together into 8-digit or 9-digit */
4561 /* chunks, and also uses a lazy carry strategy to minimize expensive */
4562 /* 64-bit divisions. The chunks are then broken apart again into */
4563 /* units for continuing processing. Despite this overhead, the */
4564 /* fastpath can speed up some 16-digit operations by 10x (and much */
4565 /* more for higher-precision calculations). */
4566 /* */
4567 /* A buffer always has to be used for the accumulator; in the */
4568 /* fastpath, buffers are also always needed for the chunked copies of */
4569 /* of the operand coefficients. */
4570 /* Static buffers are larger than needed just for multiply, to allow */
4571 /* for calls from other operations (notably exp). */
4572 /* ------------------------------------------------------------------ */
4573 #define FASTMUL (DECUSE64 && DECDPUN<5)
4574 static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
/* */
4575 const decNumber *rhs, decContext *set,
4576 uInt *status) {
4577 Int accunits; // Units of accumulator in use
4578 Int exponent; // work
4579 Int residue=0; // rounding residue
4580 uByte bits; // result sign
4581 Unit *acc; // -> accumulator Unit array
4582 Int needbytes; // size calculator
4583 void *allocacc=NULL; // -> allocated accumulator, iff allocated
4584 Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0,
4585 // *4 for calls from other operations)
4586 const Unit *mer, *mermsup; // work
4587 Int madlength; // Units in multiplicand
4588 Int shift; // Units to shift multiplicand by
4589
4590 #if FASTMUL
4591 // if DECDPUN is 1 or 3 work in base 10**9, otherwise
4592 // (DECDPUN is 2 or 4) then work in base 10**8
4593 # if DECDPUN & 1 // odd
4594 # define FASTBASE 1000000000 // base
4595 # define FASTDIGS 9 // digits in base
4596 # define FASTLAZY 18 // carry resolution point [1->18]
4597 # else
4598 # define FASTBASE 100000000
4599 # define FASTDIGS 8
4600 # define FASTLAZY 1844 // carry resolution point [1->1844]
4601 # endif
4602 // three buffers are used, two for chunked copies of the operands
4603 // (base 10**8 or base 10**9) and one base 2**64 accumulator with
4604 // lazy carry evaluation
4605 uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
4606 uInt *zlhi=zlhibuff; // -> lhs array
4607 uInt *alloclhi=NULL; // -> allocated buffer, iff allocated
4608 uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
4609 uInt *zrhi=zrhibuff; // -> rhs array
4610 uInt *allocrhi=NULL; // -> allocated buffer, iff allocated
4611 uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0)
4612 // [allocacc is shared for both paths, as only one will run]
4613 uLong *zacc=zaccbuff; // -> accumulator array for exact result
4614 # if DECDPUN==1
4615 Int zoff; // accumulator offset
4616 # endif
4617 uInt *lip, *rip; // item pointers
4618 uInt *lmsi, *rmsi; // most significant items
4619 Int ilhs, irhs, iacc; // item counts in the arrays
4620 Int lazy; // lazy carry counter
4621 uLong lcarry; // uLong carry
4622 uInt carry; // carry (NB not uLong)
4623 Int count; // work
4624 const Unit *cup; // ..
4625 Unit *up; // ..
4626 uLong *lp; // ..
4627 Int p; // ..
4628 #endif
4629
4630 #if DECSUBSET
4631 decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated
4632 decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated
4633 #endif
4634
4635 // precalculate result sign
4636 bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
4637 (void)bits;
4638 // handle infinities and NaNs
4639 if (SPECIALARGS) { // a special bit set
4640 if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
4641 decNaNs(res, lhs, rhs, set, status);
4642 return res;}
4643 // one or two infinities; Infinity * 0 is invalid
4644 if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
4645 ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
4646 *status|=DEC_Invalid_operation;
4647 return res;}
4648 decNumberZero(res);
4649 res->bits=bits|DECINF; // infinity
4650 return res;}
4651
4652 // For best speed, as in DMSRCN [the original Rexx numerics
4653 // module], use the shorter number as the multiplier (rhs) and
4654 // the longer as the multiplicand (lhs) to minimize the number of
4655 // adds (partial products)
4656 if (lhs->digits<rhs->digits) { // swap...
4657 const decNumber *hold=lhs;
4658 lhs=rhs;
4659 rhs=hold;
4660 }
4661
4662 do { // protect allocated storage
4663 #if DECSUBSET
4664 if (!set->extended) {
4665 // reduce operands and set lostDigits status, as needed
4666 if (lhs->digits>set->digits) {
4667 alloclhs=decRoundOperand(lhs, set, status);
4668 if (alloclhs==NULL) break;
4669 lhs=alloclhs;
4670 }
4671 if (rhs->digits>set->digits) {
4672 allocrhs=decRoundOperand(rhs, set, status);
4673 if (allocrhs==NULL) break;
4674 rhs=allocrhs;
4675 }
4676 }
4677 #endif
4678 // [following code does not require input rounding]
4679
4680 #if FASTMUL // fastpath can be used
4681 // use the fast path if there are enough digits in the shorter
4682 // operand to make the setup and takedown worthwhile
4683 # define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls
4684 if (rhs->digits>NEEDTWO) { // use fastpath...
4685 // calculate the number of elements in each array
4686 ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling]
4687 irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // ..
4688 iacc=ilhs+irhs;
4689
4690 // allocate buffers if required, as usual
4691 needbytes=ilhs*sizeof(uInt);
4692 if (needbytes>(Int)sizeof(zlhibuff)) {
4693 alloclhi=(uInt *)malloc(needbytes);
4694 zlhi=alloclhi;}
4695 needbytes=irhs*sizeof(uInt);
4696 if (needbytes>(Int)sizeof(zrhibuff)) {
4697 allocrhi=(uInt *)malloc(needbytes);
4698 zrhi=allocrhi;}
4699
4700 // Allocating the accumulator space needs a special case when
4701 // DECDPUN=1 because when converting the accumulator to Units
4702 // after the multiplication each 8-byte item becomes 9 1-byte
4703 // units. Therefore iacc extra bytes are needed at the front
4704 // (rounded up to a multiple of 8 bytes), and the uLong
4705 // accumulator starts offset the appropriate number of units
4706 // to the right to avoid overwrite during the unchunking.
4707 needbytes=iacc*sizeof(uLong);
4708 # if DECDPUN==1
4709 zoff=(iacc+7)/8; // items to offset by
4710 needbytes+=zoff*8;
4711 # endif
4712 if (needbytes>(Int)sizeof(zaccbuff)) {
4713 allocacc=(uLong *)malloc(needbytes);
4714 zacc=(uLong *)allocacc;}
4715 if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
4716 *status|=DEC_Insufficient_storage;
4717 break;}
4718
4719 acc=(Unit *)zacc; // -> target Unit array
4720 # if DECDPUN==1
4721 zacc+=zoff; // start uLong accumulator to right
4722 # endif
4723
4724 // assemble the chunked copies of the left and right sides
4725 for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
4726 for (p=0, *lip=0; p<FASTDIGS && count>0;
4727 p+=DECDPUN, cup++, count-=DECDPUN)
4728 *lip+=*cup*powers[p];
4729 lmsi=lip-1; // save -> msi
4730 for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
4731 for (p=0, *rip=0; p<FASTDIGS && count>0;
4732 p+=DECDPUN, cup++, count-=DECDPUN)
4733 *rip+=*cup*powers[p];
4734 rmsi=rip-1; // save -> msi
4735
4736 // zero the accumulator
4737 for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
4738
4739 /* Start the multiplication */
4740 // Resolving carries can dominate the cost of accumulating the
4741 // partial products, so this is only done when necessary.
4742 // Each uLong item in the accumulator can hold values up to
4743 // 2**64-1, and each partial product can be as large as
4744 // (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to
4745 // itself 18.4 times in a uLong without overflowing, so during
4746 // the main calculation resolution is carried out every 18th
4747 // add -- every 162 digits. Similarly, when FASTDIGS=8, the
4748 // partial products can be added to themselves 1844.6 times in
4749 // a uLong without overflowing, so intermediate carry
4750 // resolution occurs only every 14752 digits. Hence for common
4751 // short numbers usually only the one final carry resolution
4752 // occurs.
4753 // (The count is set via FASTLAZY to simplify experiments to
4754 // measure the value of this approach: a 35% improvement on a
4755 // [34x34] multiply.)
4756 lazy=FASTLAZY; // carry delay count
4757 for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs
4758 lp=zacc+(rip-zrhi); // where to add the lhs
4759 for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs
4760 *lp+=(uLong)(*lip)*(*rip); // [this should in-line]
4761 } // lip loop
4762 lazy--;
4763 if (lazy>0 && rip!=rmsi) continue;
4764 lazy=FASTLAZY; // reset delay count
4765 // spin up the accumulator resolving overflows
4766 for (lp=zacc; lp<zacc+iacc; lp++) {
4767 if (*lp<FASTBASE) continue; // it fits
4768 lcarry=*lp/FASTBASE; // top part [slow divide]
4769 // lcarry can exceed 2**32-1, so check again; this check
4770 // and occasional extra divide (slow) is well worth it, as
4771 // it allows FASTLAZY to be increased to 18 rather than 4
4772 // in the FASTDIGS=9 case
4773 if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual]
4774 else { // two-place carry [fairly rare]
4775 uInt carry2=(uInt)(lcarry/FASTBASE); // top top part
4776 *(lp+2)+=carry2; // add to item+2
4777 *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow]
4778 carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline]
4779 }
4780 *(lp+1)+=carry; // add to item above [inline]
4781 *lp-=((uLong)FASTBASE*carry); // [inline]
4782 } // carry resolution
4783 } // rip loop
4784
4785 // The multiplication is complete; time to convert back into
4786 // units. This can be done in-place in the accumulator and in
4787 // 32-bit operations, because carries were resolved after the
4788 // final add. This needs N-1 divides and multiplies for
4789 // each item in the accumulator (which will become up to N
4790 // units, where 2<=N<=9).
4791 for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
4792 uInt item=(uInt)*lp; // decapitate to uInt
4793 for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
4794 uInt part=item/(DECDPUNMAX+1);
4795 *up=(Unit)(item-(part*(DECDPUNMAX+1)));
4796 item=part;
4797 } // p
4798 *up=(Unit)item; up++; // [final needs no division]
4799 } // lp
4800 accunits=up-acc; // count of units
4801 }
4802 else { // here to use units directly, without chunking ['old code']
4803 #endif
4804
4805 // if accumulator will be too long for local storage, then allocate
4806 acc=accbuff; // -> assume buffer for accumulator
4807 needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
4808 if (needbytes>(Int)sizeof(accbuff)) {
4809 allocacc=(Unit *)malloc(needbytes);
4810 if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
4811 acc=(Unit *)allocacc; // use the allocated space
4812 }
4813
4814 /* Now the main long multiplication loop */
4815 // Unlike the equivalent in the IBM Java implementation, there
4816 // is no advantage in calculating from msu to lsu. So, do it
4817 // by the book, as it were.
4818 // Each iteration calculates ACC=ACC+MULTAND*MULT
4819 accunits=1; // accumulator starts at '0'
4820 *acc=0; // .. (lsu=0)
4821 shift=0; // no multiplicand shift at first
4822 madlength=D2U(lhs->digits); // this won't change
4823 mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier
4824
4825 for (mer=rhs->lsu; mer<mermsup; mer++) {
4826 // Here, *mer is the next Unit in the multiplier to use
4827 // If non-zero [optimization] add it...
4828 if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
4829 lhs->lsu, madlength, 0,
4830 &acc[shift], *mer)
4831 + shift;
4832 else { // extend acc with a 0; it will be used shortly
4833 *(acc+accunits)=0; // [this avoids length of <=0 later]
4834 accunits++;
4835 }
4836 // multiply multiplicand by 10**DECDPUN for next Unit to left
4837 shift++; // add this for 'logical length'
4838 } // n
4839 #if FASTMUL
4840 } // unchunked units
4841 #endif
4842 // common end-path
4843
4844 // acc now contains the exact result of the multiplication,
4845 // possibly with a leading zero unit; build the decNumber from
4846 // it, noting if any residue
4847 res->bits=bits; // set sign
4848 res->digits=decGetDigits(acc, accunits); // count digits exactly
4849
4850 // There can be a 31-bit wrap in calculating the exponent.
4851 // This can only happen if both input exponents are negative and
4852 // both their magnitudes are large. If there was a wrap, set a
4853 // safe very negative exponent, from which decFinalize() will
4854 // raise a hard underflow shortly.
4855 exponent=lhs->exponent+rhs->exponent; // calculate exponent
4856 if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
4857 exponent=-2*DECNUMMAXE; // force underflow
4858 res->exponent=exponent; // OK to overwrite now
4859
4860 // Set the coefficient. If any rounding, residue records
4861 decSetCoeff(res, set, acc, res->digits, &residue, status);
4862 decFinish(res, set, &residue, status); // final cleanup
4863 } while(0); // end protected
4864
4865 if (allocacc!=NULL) FREE(allocacc); // drop any storage used
4866 #if DECSUBSET
4867 if (allocrhs!=NULL) FREE(allocrhs); // ..
4868 if (alloclhs!=NULL) FREE(alloclhs); // ..
4869 #endif
4870 #if FASTMUL
4871 if (allocrhi!=NULL) FREE(allocrhi); // ..
4872 if (alloclhi!=NULL) FREE(alloclhi); // ..
4873 #endif
4874 return res;
4875 } // decMultiplyOp
4876
4877 /* ------------------------------------------------------------------ */
4878 /* decExpOp -- effect exponentiation */
4879 /* */
4880 /* This computes C = exp(A) */
4881 /* */
4882 /* res is C, the result. C may be A */
4883 /* rhs is A */
4884 /* set is the context; note that rounding mode has no effect */
4885 /* */
4886 /* C must have space for set->digits digits. status is updated but */
4887 /* not set. */
4888 /* */
4889 /* Restrictions: */
4890 /* */
4891 /* digits, emax, and -emin in the context must be less than */
4892 /* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
4893 /* bounds or a zero. This is an internal routine, so these */
4894 /* restrictions are contractual and not enforced. */
4895 /* */
4896 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
4897 /* almost always be correctly rounded, but may be up to 1 ulp in */
4898 /* error in rare cases. */
4899 /* */
4900 /* Finite results will always be full precision and Inexact, except */
4901 /* when A is a zero or -Infinity (giving 1 or 0 respectively). */
4902 /* ------------------------------------------------------------------ */
4903 /* This approach used here is similar to the algorithm described in */
4904 /* */
4905 /* Variable Precision Exponential Function, T. E. Hull and */
4906 /* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
4907 /* pp79-91, ACM, June 1986. */
4908 /* */
4909 /* with the main difference being that the iterations in the series */
4910 /* evaluation are terminated dynamically (which does not require the */
4911 /* extra variable-precision variables which are expensive in this */
4912 /* context). */
4913 /* */
4914 /* The error analysis in Hull & Abrham's paper applies except for the */
4915 /* round-off error accumulation during the series evaluation. This */
4916 /* code does not precalculate the number of iterations and so cannot */
4917 /* use Horner's scheme. Instead, the accumulation is done at double- */
4918 /* precision, which ensures that the additions of the terms are exact */
4919 /* and do not accumulate round-off (and any round-off errors in the */
4920 /* terms themselves move 'to the right' faster than they can */
4921 /* accumulate). This code also extends the calculation by allowing, */
4922 /* in the spirit of other decNumber operators, the input to be more */
4923 /* precise than the result (the precision used is based on the more */
4924 /* precise of the input or requested result). */
4925 /* */
4926 /* Implementation notes: */
4927 /* */
4928 /* 1. This is separated out as decExpOp so it can be called from */
4929 /* other Mathematical functions (notably Ln) with a wider range */
4930 /* than normal. In particular, it can handle the slightly wider */
4931 /* (double) range needed by Ln (which has to be able to calculate */
4932 /* exp(-x) where x can be the tiniest number (Ntiny). */
4933 /* */
4934 /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
4935 /* iterations by approximately a third with additional (although */
4936 /* diminishing) returns as the range is reduced to even smaller */
4937 /* fractions. However, h (the power of 10 used to correct the */
4938 /* result at the end, see below) must be kept <=8 as otherwise */
4939 /* the final result cannot be computed. Hence the leverage is a */
4940 /* sliding value (8-h), where potentially the range is reduced */
4941 /* more for smaller values. */
4942 /* */
4943 /* The leverage that can be applied in this way is severely */
4944 /* limited by the cost of the raise-to-the power at the end, */
4945 /* which dominates when the number of iterations is small (less */
4946 /* than ten) or when rhs is short. As an example, the adjustment */
4947 /* x**10,000,000 needs 31 multiplications, all but one full-width. */
4948 /* */
4949 /* 3. The restrictions (especially precision) could be raised with */
4950 /* care, but the full decNumber range seems very hard within the */
4951 /* 32-bit limits. */
4952 /* */
4953 /* 4. The working precisions for the static buffers are twice the */
4954 /* obvious size to allow for calls from decNumberPower. */
4955 /* ------------------------------------------------------------------ */
4956 decNumber * decExpOp(decNumber *res, const decNumber *rhs,
/* */
4957 decContext *set, uInt *status) {
4958 uInt ignore=0; // working status
4959 Int h; // adjusted exponent for 0.xxxx
4960 Int p; // working precision
4961 Int residue; // rounding residue
4962 uInt needbytes; // for space calculations
4963 const decNumber *x=rhs; // (may point to safe copy later)
4964 decContext aset, tset, dset; // working contexts
4965 Int comp; // work
4966
4967 // the argument is often copied to normalize it, so (unusually) it
4968 // is treated like other buffers, using DECBUFFER, +1 in case
4969 // DECBUFFER is 0
4970 decNumber bufr[D2N(DECBUFFER*2+1)];
4971 decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated
4972
4973 // the working precision will be no more than set->digits+8+1
4974 // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER
4975 // is 0 (and twice that for the accumulator)
4976
4977 // buffer for t, term (working precision plus)
4978 decNumber buft[D2N(DECBUFFER*2+9+1)];
4979 decNumber *allocbuft=NULL; // -> allocated buft, iff allocated
4980 decNumber *t=buft; // term
4981 // buffer for a, accumulator (working precision * 2), at least 9
4982 decNumber bufa[D2N(DECBUFFER*4+18+1)];
4983 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
4984 decNumber *a=bufa; // accumulator
4985 // decNumber for the divisor term; this needs at most 9 digits
4986 // and so can be fixed size [16 so can use standard context]
4987 decNumber bufd[D2N(16)];
4988 decNumber *d=bufd; // divisor
4989 decNumber numone; // constant 1
4990
4991 do { // protect allocated storage
4992 if (SPECIALARG) { // handle infinities and NaNs
4993 if (decNumberIsInfinite(rhs)) { // an infinity
4994 if (decNumberIsNegative(rhs)) // -Infinity -> +0
4995 decNumberZero(res);
4996 else decNumberCopy(res, rhs); // +Infinity -> self
4997 }
4998 else decNaNs(res, rhs, NULL, set, status); // a NaN
4999 break;}
5000
5001 if (ISZERO(rhs)) { // zeros -> exact 1
5002 decNumberZero(res); // make clean 1
5003 *res->lsu=1; // ..
5004 break;} // [no status to set]
5005
5006 // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path
5007 // positive and negative tiny cases which will result in inexact
5008 // 1. This also allows the later add-accumulate to always be
5009 // exact (because its length will never be more than twice the
5010 // working precision).
5011 // The comparator (tiny) needs just one digit, so use the
5012 // decNumber d for it (reused as the divisor, etc., below); its
5013 // exponent is such that if x is positive it will have
5014 // set->digits-1 zeros between the decimal point and the digit,
5015 // which is 4, and if x is negative one more zero there as the
5016 // more precise result will be of the form 0.9999999 rather than
5017 // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0
5018 // or 0.00000004 if digits=7 and x<0. If RHS not larger than
5019 // this then the result will be 1.000000
5020 decNumberZero(d); // clean
5021 *d->lsu=4; // set 4 ..
5022 d->exponent=-set->digits; // * 10**(-d)
5023 if (decNumberIsNegative(rhs)) d->exponent--; // negative case
5024 comp=decCompare(d, rhs, 1); // signless compare
5025 if (comp==BADINT) {
5026 *status|=DEC_Insufficient_storage;
5027 break;}
5028 if (comp>=0) { // rhs < d
5029 Int shift=set->digits-1;
5030 decNumberZero(res); // set 1
5031 *res->lsu=1; // ..
5032 res->digits=decShiftToMost(res->lsu, 1, shift);
5033 res->exponent=-shift; // make 1.0000...
5034 *status|=DEC_Inexact | DEC_Rounded; // .. inexactly
5035 break;} // tiny
5036
5037 // set up the context to be used for calculating a, as this is
5038 // used on both paths below
5039 decContextDefault(&aset, DEC_INIT_DECIMAL64);
5040 // accumulator bounds are as requested (could underflow)
5041 aset.emax=set->emax; // usual bounds
5042 aset.emin=set->emin; // ..
5043 aset.clamp=0; // and no concrete format
5044
5045 // calculate the adjusted (Hull & Abrham) exponent (where the
5046 // decimal point is just to the left of the coefficient msd)
5047 h=rhs->exponent+rhs->digits;
5048 // if h>8 then 10**h cannot be calculated safely; however, when
5049 // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at
5050 // least 6.59E+4342944, so (due to the restriction on Emax/Emin)
5051 // overflow (or underflow to 0) is guaranteed -- so this case can
5052 // be handled by simply forcing the appropriate excess
5053 if (h>8) { // overflow/underflow
5054 // set up here so Power call below will over or underflow to
5055 // zero; set accumulator to either 2 or 0.02
5056 // [stack buffer for a is always big enough for this]
5057 decNumberZero(a);
5058 *a->lsu=2; // not 1 but < exp(1)
5059 if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02
5060 h=8; // clamp so 10**h computable
5061 p=9; // set a working precision
5062 }
5063 else { // h<=8
5064 Int maxlever=(rhs->digits>8?1:0);
5065 // [could/should increase this for precisions >40 or so, too]
5066
5067 // if h is 8, cannot normalize to a lower upper limit because
5068 // the final result will not be computable (see notes above),
5069 // but leverage can be applied whenever h is less than 8.
5070 // Apply as much as possible, up to a MAXLEVER digits, which
5071 // sets the tradeoff against the cost of the later a**(10**h).
5072 // As h is increased, the working precision below also
5073 // increases to compensate for the "constant digits at the
5074 // front" effect.
5075 Int lever=MINI(8-h, maxlever); // leverage attainable
5076 Int use=-rhs->digits-lever; // exponent to use for RHS
5077 h+=lever; // apply leverage selected
5078 if (h<0) { // clamp
5079 use+=h; // [may end up subnormal]
5080 h=0;
5081 }
5082 // Take a copy of RHS if it needs normalization (true whenever x>=1)
5083 if (rhs->exponent!=use) {
5084 decNumber *newrhs=bufr; // assume will fit on stack
5085 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
5086 if (needbytes>sizeof(bufr)) { // need malloc space
5087 allocrhs=(decNumber *)malloc(needbytes);
5088 if (allocrhs==NULL) { // hopeless -- abandon
5089 *status|=DEC_Insufficient_storage;
5090 break;}
5091 newrhs=allocrhs; // use the allocated space
5092 }
5093 decNumberCopy(newrhs, rhs); // copy to safe space
5094 newrhs->exponent=use; // normalize; now <1
5095 x=newrhs; // ready for use
5096 // decNumberShow(x);
5097 }
5098
5099 // Now use the usual power series to evaluate exp(x). The
5100 // series starts as 1 + x + x^2/2 ... so prime ready for the
5101 // third term by setting the term variable t=x, the accumulator
5102 // a=1, and the divisor d=2.
5103
5104 // First determine the working precision. From Hull & Abrham
5105 // this is set->digits+h+2. However, if x is 'over-precise' we
5106 // need to allow for all its digits to potentially participate
5107 // (consider an x where all the excess digits are 9s) so in
5108 // this case use x->digits+h+2
5109 p=MAXI(x->digits, set->digits)+h+2; // [h<=8]
5110
5111 // a and t are variable precision, and depend on p, so space
5112 // must be allocated for them if necessary
5113
5114 // the accumulator needs to be able to hold 2p digits so that
5115 // the additions on the second and subsequent iterations are
5116 // sufficiently exact.
5117 needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
5118 if (needbytes>sizeof(bufa)) { // need malloc space
5119 allocbufa=(decNumber *)malloc(needbytes);
5120 if (allocbufa==NULL) { // hopeless -- abandon
5121 *status|=DEC_Insufficient_storage;
5122 break;}
5123 a=allocbufa; // use the allocated space
5124 }
5125 // the term needs to be able to hold p digits (which is
5126 // guaranteed to be larger than x->digits, so the initial copy
5127 // is safe); it may also be used for the raise-to-power
5128 // calculation below, which needs an extra two digits
5129 needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
5130 if (needbytes>sizeof(buft)) { // need malloc space
5131 allocbuft=(decNumber *)malloc(needbytes);
5132 if (allocbuft==NULL) { // hopeless -- abandon
5133 *status|=DEC_Insufficient_storage;
5134 break;}
5135 t=allocbuft; // use the allocated space
5136 }
5137
5138 decNumberCopy(t, x); // term=x
5139 decNumberZero(a); *a->lsu=1; // accumulator=1
5140 decNumberZero(d); *d->lsu=2; // divisor=2
5141 decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment
5142
5143 // set up the contexts for calculating a, t, and d
5144 decContextDefault(&tset, DEC_INIT_DECIMAL64);
5145 dset=tset;
5146 // accumulator bounds are set above, set precision now
5147 aset.digits=p*2; // double
5148 // term bounds avoid any underflow or overflow
5149 tset.digits=p;
5150 tset.emin=DEC_MIN_EMIN; // [emax is plenty]
5151 // [dset.digits=16, etc., are sufficient]
5152
5153 // finally ready to roll
5154 for (;;) {
5155 // only the status from the accumulation is interesting
5156 // [but it should remain unchanged after first add]
5157 decAddOp(a, a, t, &aset, 0, status); // a=a+t
5158 decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x
5159 decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d
5160 // the iteration ends when the term cannot affect the result,
5161 // if rounded to p digits, which is when its value is smaller
5162 // than the accumulator by p+1 digits. There must also be
5163 // full precision in a.
5164 if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
5165 && (a->digits>=p)) break;
5166 decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1
5167 } // iterate
5168 } // h<=8
5169
5170 // apply postconditioning: a=a**(10**h) -- this is calculated
5171 // at a slightly higher precision than Hull & Abrham suggest
5172 if (h>0) {
5173 Int seenbit=0; // set once a 1-bit is seen
5174 Int i; // counter
5175 Int n=powers[h]; // always positive
5176 aset.digits=p+2; // sufficient precision
5177 // avoid the overhead and many extra digits of decNumberPower
5178 // as all that is needed is the short 'multipliers' loop; here
5179 // accumulate the answer into t
5180 decNumberZero(t); *t->lsu=1; // acc=1
5181 for (i=1;;i++){ // for each bit [top bit ignored]
5182 // abandon if have had overflow or terminal underflow
5183 if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting?
5184 if (*status&DEC_Overflow || ISZERO(t)) break;}
5185 n=n<<1; // move next bit to testable position
5186 if (n<0) { // top bit is set
5187 seenbit=1; // OK, have a significant bit
5188 decMultiplyOp(t, t, a, &aset, status); // acc=acc*x
5189 }
5190 if (i==31) break; // that was the last bit
5191 if (!seenbit) continue; // no need to square 1
5192 decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square]
5193 } /*i*/ // 32 bits
5194 // decNumberShow(t);
5195 a=t; // and carry on using t instead of a
5196 }
5197
5198 // Copy and round the result to res
5199 residue=1; // indicate dirt to right ..
5200 if (ISZERO(a)) residue=0; // .. unless underflowed to 0
5201 aset.digits=set->digits; // [use default rounding]
5202 decCopyFit(res, a, &aset, &residue, status); // copy & shorten
5203 decFinish(res, set, &residue, status); // cleanup/set flags
5204 } while(0); // end protected
5205
5206 if (allocrhs !=NULL) FREE(allocrhs); // drop any storage used
5207 if (allocbufa!=NULL) FREE(allocbufa); // ..
5208 if (allocbuft!=NULL) FREE(allocbuft); // ..
5209 // [status is handled by caller]
5210 return res;
5211 } // decExpOp
5212
5213 /* ------------------------------------------------------------------ */
5214 /* Initial-estimate natural logarithm table */
5215 /* */
5216 /* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
5217 /* The result is a 4-digit encode of the coefficient (c=the */
5218 /* top 14 bits encoding 0-9999) and a 2-digit encode of the */
5219 /* exponent (e=the bottom 2 bits encoding 0-3) */
5220 /* */
5221 /* The resulting value is given by: */
5222 /* */
5223 /* v = -c * 10**(-e-3) */
5224 /* */
5225 /* where e and c are extracted from entry k = LNnn[x-10] */
5226 /* where x is truncated (NB) into the range 10 through 99, */
5227 /* and then c = k>>2 and e = k&3. */
5228 /* ------------------------------------------------------------------ */
5229 const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
5230 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
5231 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
5232 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
5233 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
5234 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
5235 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
5236 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
5237 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
5238 10130, 6046, 20055};
5239
5240 /* ------------------------------------------------------------------ */
5241 /* decLnOp -- effect natural logarithm */
5242 /* */
5243 /* This computes C = ln(A) */
5244 /* */
5245 /* res is C, the result. C may be A */
5246 /* rhs is A */
5247 /* set is the context; note that rounding mode has no effect */
5248 /* */
5249 /* C must have space for set->digits digits. */
5250 /* */
5251 /* Notable cases: */
5252 /* A<0 -> Invalid */
5253 /* A=0 -> -Infinity (Exact) */
5254 /* A=+Infinity -> +Infinity (Exact) */
5255 /* A=1 exactly -> 0 (Exact) */
5256 /* */
5257 /* Restrictions (as for Exp): */
5258 /* */
5259 /* digits, emax, and -emin in the context must be less than */
5260 /* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
5261 /* bounds or a zero. This is an internal routine, so these */
5262 /* restrictions are contractual and not enforced. */
5263 /* */
5264 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
5265 /* almost always be correctly rounded, but may be up to 1 ulp in */
5266 /* error in rare cases. */
5267 /* ------------------------------------------------------------------ */
5268 /* The result is calculated using Newton's method, with each */
5269 /* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
5270 /* Epperson 1989. */
5271 /* */
5272 /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
5273 /* This has to be calculated at the sum of the precision of x and the */
5274 /* working precision. */
5275 /* */
5276 /* Implementation notes: */
5277 /* */
5278 /* 1. This is separated out as decLnOp so it can be called from */
5279 /* other Mathematical functions (e.g., Log 10) with a wider range */
5280 /* than normal. In particular, it can handle the slightly wider */
5281 /* (+9+2) range needed by a power function. */
5282 /* */
5283 /* 2. The speed of this function is about 10x slower than exp, as */
5284 /* it typically needs 4-6 iterations for short numbers, and the */
5285 /* extra precision needed adds a squaring effect, twice. */
5286 /* */
5287 /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
5288 /* as these are common requests. ln(10) is used by log10(x). */
5289 /* */
5290 /* 4. An iteration might be saved by widening the LNnn table, and */
5291 /* would certainly save at least one if it were made ten times */
5292 /* bigger, too (for truncated fractions 0.100 through 0.999). */
5293 /* However, for most practical evaluations, at least four or five */
5294 /* iterations will be needed -- so this would only speed up by */
5295 /* 20-25% and that probably does not justify increasing the table */
5296 /* size. */
5297 /* */
5298 /* 5. The static buffers are larger than might be expected to allow */
5299 /* for calls from decNumberPower. */
5300 /* ------------------------------------------------------------------ */
5301 decNumber * decLnOp(decNumber *res, const decNumber *rhs,
/* */
5302 decContext *set, uInt *status) {
5303 uInt ignore=0; // working status accumulator
5304 uInt needbytes; // for space calculations
5305 Int residue; // rounding residue
5306 Int r; // rhs=f*10**r [see below]
5307 Int p; // working precision
5308 Int pp; // precision for iteration
5309 Int t; // work
5310
5311 // buffers for a (accumulator, typically precision+2) and b
5312 // (adjustment calculator, same size)
5313 decNumber bufa[D2N(DECBUFFER+12)];
5314 decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
5315 decNumber *a=bufa; // accumulator/work
5316 decNumber bufb[D2N(DECBUFFER*2+2)];
5317 decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated
5318 decNumber *b=bufb; // adjustment/work
5319
5320 decNumber numone; // constant 1
5321 decNumber cmp; // work
5322 decContext aset, bset; // working contexts
5323
5324 do { // protect allocated storage
5325 if (SPECIALARG) { // handle infinities and NaNs
5326 if (decNumberIsInfinite(rhs)) { // an infinity
5327 if (decNumberIsNegative(rhs)) // -Infinity -> error
5328 *status|=DEC_Invalid_operation;
5329 else decNumberCopy(res, rhs); // +Infinity -> self
5330 }
5331 else decNaNs(res, rhs, NULL, set, status); // a NaN
5332 break;}
5333
5334 if (ISZERO(rhs)) { // +/- zeros -> -Infinity
5335 decNumberZero(res); // make clean
5336 res->bits=DECINF|DECNEG; // set - infinity
5337 break;} // [no status to set]
5338
5339 // Non-zero negatives are bad...
5340 if (decNumberIsNegative(rhs)) { // -x -> error
5341 *status|=DEC_Invalid_operation;
5342 break;}
5343
5344 // Here, rhs is positive, finite, and in range
5345
5346 // lookaside fastpath code for ln(2) and ln(10) at common lengths
5347 if (rhs->exponent==0 && set->digits<=40) {
5348 #if DECDPUN==1
5349 if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10)
5350 #else
5351 if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10)
5352 #endif
5353 aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
5354 #define LN10 "2.302585092994045684017991454684364207601"
5355 decNumberFromString(res, LN10, &aset);
5356 *status|=(DEC_Inexact | DEC_Rounded); // is inexact
5357 break;}
5358 if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2)
5359 aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
5360 #define LN2 "0.6931471805599453094172321214581765680755"
5361 decNumberFromString(res, LN2, &aset);
5362 *status|=(DEC_Inexact | DEC_Rounded);
5363 break;}
5364 } // integer and short
5365
5366 // Determine the working precision. This is normally the
5367 // requested precision + 2, with a minimum of 9. However, if
5368 // the rhs is 'over-precise' then allow for all its digits to
5369 // potentially participate (consider an rhs where all the excess
5370 // digits are 9s) so in this case use rhs->digits+2.
5371 p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
5372
5373 // Allocate space for the accumulator and the high-precision
5374 // adjustment calculator, if necessary. The accumulator must
5375 // be able to hold p digits, and the adjustment up to
5376 // rhs->digits+p digits. They are also made big enough for 16
5377 // digits so that they can be used for calculating the initial
5378 // estimate.
5379 needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
5380 if (needbytes>sizeof(bufa)) { // need malloc space
5381 allocbufa=(decNumber *)malloc(needbytes);
5382 if (allocbufa==NULL) { // hopeless -- abandon
5383 *status|=DEC_Insufficient_storage;
5384 break;}
5385 a=allocbufa; // use the allocated space
5386 }
5387 pp=p+rhs->digits;
5388 needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
5389 if (needbytes>sizeof(bufb)) { // need malloc space
5390 allocbufb=(decNumber *)malloc(needbytes);
5391 if (allocbufb==NULL) { // hopeless -- abandon
5392 *status|=DEC_Insufficient_storage;
5393 break;}
5394 b=allocbufb; // use the allocated space
5395 }
5396
5397 // Prepare an initial estimate in acc. Calculate this by
5398 // considering the coefficient of x to be a normalized fraction,
5399 // f, with the decimal point at far left and multiplied by
5400 // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and
5401 // ln(x) = ln(f) + ln(10)*r
5402 // Get the initial estimate for ln(f) from a small lookup
5403 // table (see above) indexed by the first two digits of f,
5404 // truncated.
5405
5406 decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended
5407 r=rhs->exponent+rhs->digits; // 'normalised' exponent
5408 decNumberFromInt32(a, r); // a=r
5409 decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585)
5410 b->exponent=-6; // ..
5411 decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b
5412 // now get top two digits of rhs into b by simple truncate and
5413 // force to integer
5414 residue=0; // (no residue)
5415 aset.digits=2; aset.round=DEC_ROUND_DOWN;
5416 decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten
5417 b->exponent=0; // make integer
5418 t=decGetInt(b); // [cannot fail]
5419 #if defined(__clang_analyzer__)
5420 if (t<0) t=10;
5421 #endif /* if defined(__clang_analyzer__) */
5422 if (t<10) t=X10(t); // adjust single-digit b
5423 #if !defined(__clang_analyzer__)
5424 t=LNnn[t-10]; // look up ln(b)
5425 #endif /* if !defined(__clang_analyzer__) */
5426 decNumberFromInt32(b, t>>2); // b=ln(b) coefficient
5427 b->exponent=-(t&3)-3; // set exponent
5428 b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve
5429 aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore
5430 decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b
5431 // the initial estimate is now in a, with up to 4 digits correct.
5432 // When rhs is at or near Nmax the estimate will be low, so we
5433 // will approach it from below, avoiding overflow when calling exp.
5434
5435 decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment
5436
5437 // accumulator bounds are as requested (could underflow, but
5438 // cannot overflow)
5439 aset.emax=set->emax;
5440 aset.emin=set->emin;
5441 aset.clamp=0; // no concrete format
5442 if (rhs->digits > set->digits) {
5443 aset.emax=DEC_MAX_MATH*2;
5444 aset.emin=-DEC_MAX_MATH*2;
5445 }
5446 // set up a context to be used for the multiply and subtract
5447 bset=aset;
5448 bset.emax=DEC_MAX_MATH*2; // use double bounds for the
5449 bset.emin=-DEC_MAX_MATH*2; // adjustment calculation
5450 // [see decExpOp call below]
5451 // for each iteration double the number of digits to calculate,
5452 // up to a maximum of p
5453 pp=9; // initial precision
5454 // [initially 9 as then the sequence starts 7+2, 16+2, and
5455 // 34+2, which is ideal for standard-sized numbers]
5456 aset.digits=pp; // working context
5457 bset.digits=pp+rhs->digits; // wider context
5458 for (;;) { // iterate
5459 // calculate the adjustment (exp(-a)*x-1) into b. This is a
5460 // catastrophic subtraction but it really is the difference
5461 // from 1 that is of interest.
5462 // Use the internal entry point to Exp as it allows the double
5463 // range for calculating exp(-a) when a is the tiniest subnormal.
5464 a->bits^=DECNEG; // make -a
5465 decExpOp(b, a, &bset, &ignore); // b=exp(-a)
5466 a->bits^=DECNEG; // restore sign of a
5467 // now multiply by rhs and subtract 1, at the wider precision
5468 decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs
5469 decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1
5470
5471 // the iteration ends when the adjustment cannot affect the
5472 // result by >=0.5 ulp (at the requested digits), which
5473 // is when its value is smaller than the accumulator by
5474 // set->digits+1 digits (or it is zero) -- this is a looser
5475 // requirement than for Exp because all that happens to the
5476 // accumulator after this is the final rounding (but note that
5477 // there must also be full precision in a, or a=0).
5478
5479 if (decNumberIsZero(b) ||
5480 (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
5481 if (a->digits==p) break;
5482 if (decNumberIsZero(a)) {
5483 decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ?
5484 if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0
5485 else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact
5486 break;
5487 }
5488 // force padding if adjustment has gone to 0 before full length
5489 if (decNumberIsZero(b)) b->exponent=a->exponent-p;
5490 }
5491
5492 // not done yet ...
5493 decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate
5494 if (pp==p) continue; // precision is at maximum
5495 // lengthen the next calculation
5496 pp=pp*2; // double precision
5497 if (pp>p) pp=p; // clamp to maximum
5498 aset.digits=pp; // working context
5499 bset.digits=pp+rhs->digits; // wider context
5500 } // Newton's iteration
5501
5502 // Copy and round the result to res
5503 residue=1; // indicate dirt to right
5504 if (ISZERO(a)) residue=0; // .. unless underflowed to 0
5505 aset.digits=set->digits; // [use default rounding]
5506 decCopyFit(res, a, &aset, &residue, status); // copy & shorten
5507 decFinish(res, set, &residue, status); // cleanup/set flags
5508 } while(0); // end protected
5509
5510 if (allocbufa!=NULL) FREE(allocbufa); // drop any storage used
5511 if (allocbufb!=NULL) FREE(allocbufb); // ..
5512 // [status is handled by caller]
5513 return res;
5514 } // decLnOp
5515
5516 /* ------------------------------------------------------------------ */
5517 /* decQuantizeOp -- force exponent to requested value */
5518 /* */
5519 /* This computes C = op(A, B), where op adjusts the coefficient */
5520 /* of C (by rounding or shifting) such that the exponent (-scale) */
5521 /* of C has the value B or matches the exponent of B. */
5522 /* The numerical value of C will equal A, except for the effects of */
5523 /* any rounding that occurred. */
5524 /* */
5525 /* res is C, the result. C may be A or B */
5526 /* lhs is A, the number to adjust */
5527 /* rhs is B, the requested exponent */
5528 /* set is the context */
5529 /* quant is 1 for quantize or 0 for rescale */
5530 /* status is the status accumulator (this can be called without */
5531 /* risk of control loss) */
5532 /* */
5533 /* C must have space for set->digits digits. */
5534 /* */
5535 /* Unless there is an error or the result is infinite, the exponent */
5536 /* after the operation is guaranteed to be that requested. */
5537 /* ------------------------------------------------------------------ */
5538 static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
/* */
5539 const decNumber *rhs, decContext *set,
5540 Flag quant, uInt *status) {
5541 #if DECSUBSET
5542 decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
5543 decNumber *allocrhs=NULL; // .., rhs
5544 #endif
5545 const decNumber *inrhs=rhs; // save original rhs
5546 Int reqdigits=set->digits; // requested DIGITS
5547 Int reqexp; // requested exponent [-scale]
5548 Int residue=0; // rounding residue
5549 Int etiny=set->emin-(reqdigits-1);
5550
5551 do { // protect allocated storage
5552 #if DECSUBSET
5553 if (!set->extended) {
5554 // reduce operands and set lostDigits status, as needed
5555 if (lhs->digits>reqdigits) {
5556 alloclhs=decRoundOperand(lhs, set, status);
5557 if (alloclhs==NULL) break;
5558 lhs=alloclhs;
5559 }
5560 if (rhs->digits>reqdigits) { // [this only checks lostDigits]
5561 allocrhs=decRoundOperand(rhs, set, status);
5562 if (allocrhs==NULL) break;
5563 rhs=allocrhs;
5564 }
5565 }
5566 #endif
5567 // [following code does not require input rounding]
5568
5569 // Handle special values
5570 if (SPECIALARGS) {
5571 // NaNs get usual processing
5572 if (SPECIALARGS & (DECSNAN | DECNAN))
5573 decNaNs(res, lhs, rhs, set, status);
5574 // one infinity but not both is bad
5575 else if ((lhs->bits ^ rhs->bits) & DECINF)
5576 *status|=DEC_Invalid_operation;
5577 // both infinity: return lhs
5578 else decNumberCopy(res, lhs); // [nop if in place]
5579 break;
5580 }
5581
5582 // set requested exponent
5583 if (quant) reqexp=inrhs->exponent; // quantize -- match exponents
5584 else { // rescale -- use value of rhs
5585 // Original rhs must be an integer that fits and is in range,
5586 // which could be from -1999999997 to +999999999, thanks to
5587 // subnormals
5588 reqexp=decGetInt(inrhs); // [cannot fail]
5589 }
5590
5591 #if DECSUBSET
5592 if (!set->extended) etiny=set->emin; // no subnormals
5593 #endif
5594
5595 if (reqexp==BADINT // bad (rescale only) or ..
5596 || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or ..
5597 || (reqexp<etiny) // < lowest
5598 || (reqexp>set->emax)) { // > emax
5599 *status|=DEC_Invalid_operation;
5600 break;}
5601
5602 // the RHS has been processed, so it can be overwritten now if necessary
5603 if (ISZERO(lhs)) { // zero coefficient unchanged
5604 decNumberCopy(res, lhs); // [nop if in place]
5605 res->exponent=reqexp; // .. just set exponent
5606 #if DECSUBSET
5607 if (!set->extended) res->bits=0; // subset specification; no -0
5608 #endif
5609 }
5610 else { // non-zero lhs
5611 Int adjust=reqexp-lhs->exponent; // digit adjustment needed
5612 // if adjusted coefficient will definitely not fit, give up now
5613 if ((lhs->digits-adjust)>reqdigits) {
5614 *status|=DEC_Invalid_operation;
5615 break;
5616 }
5617
5618 if (adjust>0) { // increasing exponent
5619 // this will decrease the length of the coefficient by adjust
5620 // digits, and must round as it does so
5621 decContext workset; // work
5622 workset=*set; // clone rounding, etc.
5623 workset.digits=lhs->digits-adjust; // set requested length
5624 // [note that the latter can be <1, here]
5625 decCopyFit(res, lhs, &workset, &residue, status); // fit to result
5626 decApplyRound(res, &workset, residue, status); // .. and round
5627 residue=0; // [used]
5628 // If just rounded a 999s case, exponent will be off by one;
5629 // adjust back (after checking space), if so.
5630 if (res->exponent>reqexp) {
5631 // re-check needed, e.g., for quantize(0.9999, 0.001) under
5632 // set->digits==3
5633 if (res->digits==reqdigits) { // cannot shift by 1
5634 *status&=~(DEC_Inexact | DEC_Rounded); // [clean these]
5635 *status|=DEC_Invalid_operation;
5636 break;
5637 }
5638 res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift
5639 res->exponent--; // (re)adjust the exponent.
5640 }
5641 #if DECSUBSET
5642 if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0
5643 #endif
5644 } // increase
5645 else /* adjust<=0 */ { // decreasing or = exponent
5646 // this will increase the length of the coefficient by -adjust
5647 // digits, by adding zero or more trailing zeros; this is
5648 // already checked for fit, above
5649 decNumberCopy(res, lhs); // [it will fit]
5650 // if padding needed (adjust<0), add it now...
5651 if (adjust<0) {
5652 res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
5653 res->exponent+=adjust; // adjust the exponent
5654 }
5655 } // decrease
5656 } // non-zero
5657
5658 // Check for overflow [do not use Finalize in this case, as an
5659 // overflow here is a "don't fit" situation]
5660 if (res->exponent>set->emax-res->digits+1) { // too big
5661 *status|=DEC_Invalid_operation;
5662 break;
5663 }
5664 else {
5665 decFinalize(res, set, &residue, status); // set subnormal flags
5666 *status&=~DEC_Underflow; // suppress Underflow [as per 754]
5667 }
5668 } while(0); // end protected
5669
5670 #if DECSUBSET
5671 if (allocrhs!=NULL) FREE(allocrhs); // drop any storage used
5672 if (alloclhs!=NULL) FREE(alloclhs); // ..
5673 #endif
5674 return res;
5675 } // decQuantizeOp
5676
5677 /* ------------------------------------------------------------------ */
5678 /* decCompareOp -- compare, min, or max two Numbers */
5679 /* */
5680 /* This computes C = A ? B and carries out one of four operations: */
5681 /* COMPARE -- returns the signum (as a number) giving the */
5682 /* result of a comparison unless one or both */
5683 /* operands is a NaN (in which case a NaN results) */
5684 /* COMPSIG -- as COMPARE except that a quiet NaN raises */
5685 /* Invalid operation. */
5686 /* COMPMAX -- returns the larger of the operands, using the */
5687 /* 754 maxnum operation */
5688 /* COMPMAXMAG -- ditto, comparing absolute values */
5689 /* COMPMIN -- the 754 minnum operation */
5690 /* COMPMINMAG -- ditto, comparing absolute values */
5691 /* COMTOTAL -- returns the signum (as a number) giving the */
5692 /* result of a comparison using 754 total ordering */
5693 /* */
5694 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
5695 /* lhs is A */
5696 /* rhs is B */
5697 /* set is the context */
5698 /* op is the operation flag */
5699 /* status is the usual accumulator */
5700 /* */
5701 /* C must have space for one digit for COMPARE or set->digits for */
5702 /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
5703 /* ------------------------------------------------------------------ */
5704 /* The emphasis here is on speed for common cases, and avoiding */
5705 /* coefficient comparison if possible. */
5706 /* ------------------------------------------------------------------ */
5707 decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
/* */
5708 const decNumber *rhs, decContext *set,
5709 Flag op, uInt *status) {
5710 #if DECSUBSET
5711 decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
5712 decNumber *allocrhs=NULL; // .., rhs
5713 #endif
5714 Int result=0; // default result value
5715 uByte merged; // work
5716
5717 do { // protect allocated storage
5718 #if DECSUBSET
5719 if (!set->extended) {
5720 // reduce operands and set lostDigits status, as needed
5721 if (lhs->digits>set->digits) {
5722 alloclhs=decRoundOperand(lhs, set, status);
5723 if (alloclhs==NULL) {result=BADINT; break;}
5724 lhs=alloclhs;
5725 }
5726 if (rhs->digits>set->digits) {
5727 allocrhs=decRoundOperand(rhs, set, status);
5728 if (allocrhs==NULL) {result=BADINT; break;}
5729 rhs=allocrhs;
5730 }
5731 }
5732 #endif
5733 // [following code does not require input rounding]
5734
5735 // If total ordering then handle differing signs 'up front'
5736 if (op==COMPTOTAL) { // total ordering
5737 /* cppcheck-suppress bitwiseOnBoolean */
5738 /* cppcheck-suppress clarifyCondition */
5739 if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) {
5740 result=-1;
5741 break;
5742 }
5743 /* cppcheck-suppress bitwiseOnBoolean */
5744 /* cppcheck-suppress clarifyCondition */
5745 if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) {
5746 result=+1;
5747 break;
5748 }
5749 }
5750
5751 // handle NaNs specially; let infinities drop through
5752 // This assumes sNaN (even just one) leads to NaN.
5753 merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
5754 if (merged) { // a NaN bit set
5755 if (op==COMPARE); // result will be NaN
5756 else if (op==COMPSIG) // treat qNaN as sNaN
5757 *status|=DEC_Invalid_operation | DEC_sNaN;
5758 else if (op==COMPTOTAL) { // total ordering, always finite
5759 // signs are known to be the same; compute the ordering here
5760 // as if the signs are both positive, then invert for negatives
5761 if (!decNumberIsNaN(lhs)) result=-1;
5762 else if (!decNumberIsNaN(rhs)) result=+1;
5763 // here if both NaNs
5764 else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
5765 else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
5766 else { // both NaN or both sNaN
5767 // now it just depends on the payload
5768 result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
5769 rhs->lsu, D2U(rhs->digits), 0);
5770 // [Error not possible, as these are 'aligned']
5771 } // both same NaNs
5772 if (decNumberIsNegative(lhs)) result=-result;
5773 break;
5774 } // total order
5775
5776 else if (merged & DECSNAN); // sNaN -> qNaN
5777 else { // here if MIN or MAX and one or two quiet NaNs
5778 // min or max -- 754 rules ignore single NaN
5779 if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
5780 // just one NaN; force choice to be the non-NaN operand
5781 op=COMPMAX;
5782 if (lhs->bits & DECNAN) result=-1; // pick rhs
5783 else result=+1; // pick lhs
5784 break;
5785 }
5786 } // max or min
5787 op=COMPNAN; // use special path
5788 decNaNs(res, lhs, rhs, set, status); // propagate NaN
5789 break;
5790 }
5791 // have numbers
5792 if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
5793 else result=decCompare(lhs, rhs, 0); // sign matters
5794 } while(0); // end protected
5795
5796 if (result==BADINT) *status|=DEC_Insufficient_storage; // rare
5797 else {
5798 if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum
5799 if (op==COMPTOTAL && result==0) {
5800 // operands are numerically equal or same NaN (and same sign,
5801 // tested first); if identical, leave result 0
5802 if (lhs->exponent!=rhs->exponent) {
5803 if (lhs->exponent<rhs->exponent) result=-1;
5804 else result=+1;
5805 if (decNumberIsNegative(lhs)) result=-result;
5806 } // lexp!=rexp
5807 } // total-order by exponent
5808 decNumberZero(res); // [always a valid result]
5809 if (result!=0) { // must be -1 or +1
5810 *res->lsu=1;
5811 if (result<0) res->bits=DECNEG;
5812 }
5813 }
5814 else if (op==COMPNAN); // special, drop through
5815 else { // MAX or MIN, non-NaN result
5816 Int residue=0; // rounding accumulator
5817 // choose the operand for the result
5818 const decNumber *choice;
5819 if (result==0) { // operands are numerically equal
5820 // choose according to sign then exponent (see 754)
5821 uByte slhs=(lhs->bits & DECNEG);
5822 uByte srhs=(rhs->bits & DECNEG);
5823 #if DECSUBSET
5824 if (!set->extended) { // subset: force left-hand
5825 op=COMPMAX;
5826 result=+1;
5827 }
5828 else
5829 #endif
5830 if (slhs!=srhs) { // signs differ
5831 if (slhs) result=-1; // rhs is max
5832 else result=+1; // lhs is max
5833 }
5834 /* cppcheck-suppress knownConditionTrueFalse */
5835 else if (slhs && srhs) { // both negative
5836 if (lhs->exponent<rhs->exponent) result=+1;
5837 else result=-1;
5838 // [if equal, use lhs, technically identical]
5839 }
5840 else { // both positive
5841 if (lhs->exponent>rhs->exponent) result=+1;
5842 else result=-1;
5843 // [ditto]
5844 }
5845 } // numerically equal
5846 // here result will be non-0; reverse if looking for MIN
5847 if (op==COMPMIN || op==COMPMINMAG) result=-result;
5848 choice=(result>0 ? lhs : rhs); // choose
5849 // copy chosen to result, rounding if need be
5850 decCopyFit(res, choice, set, &residue, status);
5851 decFinish(res, set, &residue, status);
5852 }
5853 }
5854 #if DECSUBSET
5855 if (allocrhs!=NULL) FREE(allocrhs); // free any storage used
5856 if (alloclhs!=NULL) FREE(alloclhs); // ..
5857 #endif
5858 return res;
5859 } // decCompareOp
5860
5861 /* ------------------------------------------------------------------ */
5862 /* decCompare -- compare two decNumbers by numerical value */
5863 /* */
5864 /* This routine compares A ? B without altering them. */
5865 /* */
5866 /* Arg1 is A, a decNumber which is not a NaN */
5867 /* Arg2 is B, a decNumber which is not a NaN */
5868 /* Arg3 is 1 for a sign-independent compare, 0 otherwise */
5869 /* */
5870 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
5871 /* (the only possible failure is an allocation error) */
5872 /* ------------------------------------------------------------------ */
5873 static Int decCompare(const decNumber *lhs, const decNumber *rhs,
/* */
5874 Flag abs) {
5875 Int result; // result value
5876 Int sigr; // rhs signum
5877 Int compare; // work
5878
5879 result=1; // assume signum(lhs)
5880 if (ISZERO(lhs)) result=0;
5881 if (abs) {
5882 if (ISZERO(rhs)) return result; // LHS wins or both 0
5883 // RHS is non-zero
5884 if (result==0) return -1; // LHS is 0; RHS wins
5885 // [here, both non-zero, result=1]
5886 }
5887 else { // signs matter
5888 if (result && decNumberIsNegative(lhs)) result=-1;
5889 sigr=1; // compute signum(rhs)
5890 if (ISZERO(rhs)) sigr=0;
5891 else if (decNumberIsNegative(rhs)) sigr=-1;
5892 if (result > sigr) return +1; // L > R, return 1
5893 if (result < sigr) return -1; // L < R, return -1
5894 if (result==0) return 0; // both 0
5895 }
5896
5897 // signums are the same; both are non-zero
5898 if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities
5899 if (decNumberIsInfinite(rhs)) {
5900 if (decNumberIsInfinite(lhs)) result=0;// both infinite
5901 else result=-result; // only rhs infinite
5902 }
5903 return result;
5904 }
5905 // must compare the coefficients, allowing for exponents
5906 if (lhs->exponent>rhs->exponent) { // LHS exponent larger
5907 // swap sides, and sign
5908 const decNumber *temp=lhs;
5909 lhs=rhs;
5910 rhs=temp;
5911 result=-result;
5912 }
5913 compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
5914 rhs->lsu, D2U(rhs->digits),
5915 rhs->exponent-lhs->exponent);
5916 if (compare!=BADINT) compare*=result; // comparison succeeded
5917 return compare;
5918 } // decCompare
5919
5920 /* ------------------------------------------------------------------ */
5921 /* decUnitCompare -- compare two >=0 integers in Unit arrays */
5922 /* */
5923 /* This routine compares A ? B*10**E where A and B are unit arrays */
5924 /* A is a plain integer */
5925 /* B has an exponent of E (which must be non-negative) */
5926 /* */
5927 /* Arg1 is A first Unit (lsu) */
5928 /* Arg2 is A length in Units */
5929 /* Arg3 is B first Unit (lsu) */
5930 /* Arg4 is B length in Units */
5931 /* Arg5 is E (0 if the units are aligned) */
5932 /* */
5933 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
5934 /* (the only possible failure is an allocation error, which can */
5935 /* only occur if E!=0) */
5936 /* ------------------------------------------------------------------ */
5937 static Int decUnitCompare(const Unit *a, Int alength,
/* */
5938 const Unit *b, Int blength, Int exp) {
5939 Unit *acc; // accumulator for result
5940 Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer
5941 Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
5942 Int accunits, need; // units in use or needed for acc
5943 const Unit *l, *r, *u; // work
5944 Int expunits, exprem, result; // ..
5945
5946 if (exp==0) { // aligned; fastpath
5947 if (alength>blength) return 1;
5948 if (alength<blength) return -1;
5949 // same number of units in both -- need unit-by-unit compare
5950 l=a+alength-1;
5951 r=b+alength-1;
5952 for (;l>=a; l--, r--) {
5953 if (*l>*r) return 1;
5954 if (*l<*r) return -1;
5955 }
5956 return 0; // all units match
5957 } // aligned
5958
5959 // Unaligned. If one is >1 unit longer than the other, padded
5960 // approximately, then can return easily
5961 if (alength>blength+(Int)D2U(exp)) return 1;
5962 if (alength+1<blength+(Int)D2U(exp)) return -1;
5963
5964 // Need to do a real subtract. For this, a result buffer is needed
5965 // even though only the sign is of interest. Its length needs
5966 // to be the larger of alength and padded blength, +2
5967 need=blength+D2U(exp); // maximum real length of B
5968 if (need<alength) need=alength;
5969 need+=2;
5970 acc=accbuff; // assume use local buffer
5971 if (need*sizeof(Unit)>sizeof(accbuff)) {
5972 allocacc=(Unit *)malloc(need*sizeof(Unit));
5973 if (allocacc==NULL) return BADINT; // hopeless -- abandon
5974 acc=allocacc;
5975 }
5976 // Calculate units and remainder from exponent.
5977 expunits=exp/DECDPUN;
5978 exprem=exp%DECDPUN;
5979 // subtract [A+B*(-m)]
5980 accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
5981 -(Int)powers[exprem]);
5982 // [UnitAddSub result may have leading zeros, even on zero]
5983 if (accunits<0) result=-1; // negative result
5984 else { // non-negative result
5985 // check units of the result before freeing any storage
5986 for (u=acc; u<acc+accunits-1 && *u==0;) u++;
5987 result=(*u==0 ? 0 : +1);
5988 }
5989 // clean up and return the result
5990 if (allocacc!=NULL) FREE(allocacc); // drop any storage used
5991 return result;
5992 } // decUnitCompare
5993
5994 /* ------------------------------------------------------------------ */
5995 /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
5996 /* */
5997 /* This routine performs the calculation: */
5998 /* */
5999 /* C=A+(B*M) */
6000 /* */
6001 /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
6002 /* */
6003 /* A may be shorter or longer than B. */
6004 /* */
6005 /* Leading zeros are not removed after a calculation. The result is */
6006 /* either the same length as the longer of A and B (adding any */
6007 /* shift), or one Unit longer than that (if a Unit carry occurred). */
6008 /* */
6009 /* A and B content are not altered unless C is also A or B. */
6010 /* C may be the same array as A or B, but only if no zero padding is */
6011 /* requested (that is, C may be B only if bshift==0). */
6012 /* C is filled from the lsu; only those units necessary to complete */
6013 /* the calculation are referenced. */
6014 /* */
6015 /* Arg1 is A first Unit (lsu) */
6016 /* Arg2 is A length in Units */
6017 /* Arg3 is B first Unit (lsu) */
6018 /* Arg4 is B length in Units */
6019 /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
6020 /* Arg6 is C first Unit (lsu) */
6021 /* Arg7 is M, the multiplier */
6022 /* */
6023 /* returns the count of Units written to C, which will be non-zero */
6024 /* and negated if the result is negative. That is, the sign of the */
6025 /* returned Int is the sign of the result (positive for zero) and */
6026 /* the absolute value of the Int is the count of Units. */
6027 /* */
6028 /* It is the caller's responsibility to make sure that C size is */
6029 /* safe, allowing space if necessary for a one-Unit carry. */
6030 /* */
6031 /* This routine is severely performance-critical; *any* change here */
6032 /* must be measured (timed) to assure no performance degradation. */
6033 /* In particular, trickery here tends to be counter-productive, as */
6034 /* increased complexity of code hurts register optimizations on */
6035 /* register-poor architectures. Avoiding divisions is nearly */
6036 /* always a Good Idea, however. */
6037 /* */
6038 /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
6039 /* (IBM Warwick, UK) for some of the ideas used in this routine. */
6040 /* ------------------------------------------------------------------ */
6041 static Int decUnitAddSub(const Unit *a, Int alength,
/* */
6042 const Unit *b, Int blength, Int bshift,
6043 Unit *c, Int m) {
6044 const Unit *alsu=a; // A lsu [need to remember it]
6045 Unit *clsu=c; // C ditto
6046 Unit *minC; // low water mark for C
6047 Unit *maxC; // high water mark for C
6048 eInt carry=0; // carry integer (could be Long)
6049 Int add; // work
6050 #if DECDPUN<=4 // myriadal, millenary, etc.
6051 Int est; // estimated quotient
6052 #endif
6053
6054 maxC=c+alength; // A is usually the longer
6055 minC=c+blength; // .. and B the shorter
6056 if (bshift!=0) { // B is shifted; low As copy across
6057 minC+=bshift;
6058 // if in place [common], skip copy unless there's a gap [rare]
6059 if (a==c && bshift<=alength) {
6060 c+=bshift;
6061 a+=bshift;
6062 }
6063 else for (; c<clsu+bshift; a++, c++) { // copy needed
6064 if (a<alsu+alength) *c=*a;
6065 else *c=0;
6066 }
6067 }
6068 if (minC>maxC) { // swap
6069 Unit *hold=minC;
6070 minC=maxC;
6071 maxC=hold;
6072 }
6073
6074 // For speed, do the addition as two loops; the first where both A
6075 // and B contribute, and the second (if necessary) where only one or
6076 // other of the numbers contribute.
6077 // Carry handling is the same (i.e., duplicated) in each case.
6078 for (; c<minC; c++) {
6079 carry+=*a;
6080 a++;
6081 carry+=((eInt)*b)*m; // [special-casing m=1/-1
6082 b++; // here is not a win]
6083 // here carry is new Unit of digits; it could be +ve or -ve
6084 if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
6085 *c=(Unit)carry;
6086 carry=0;
6087 continue;
6088 }
6089 #if DECDPUN==4 // use divide-by-multiply
6090 if (carry>=0) {
6091 est=(((ueInt)carry>>11)*53687)>>18;
6092 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6093 carry=est; // likely quotient [89%]
6094 if (*c<DECDPUNMAX+1) continue; // estimate was correct
6095 carry++;
6096 *c-=DECDPUNMAX+1;
6097 continue;
6098 }
6099 // negative case
6100 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6101 est=(((ueInt)carry>>11)*53687)>>18;
6102 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6103 carry=est-(DECDPUNMAX+1); // correctly negative
6104 if (*c<DECDPUNMAX+1) continue; // was OK
6105 carry++;
6106 *c-=DECDPUNMAX+1;
6107 #elif DECDPUN==3
6108 if (carry>=0) {
6109 est=(((ueInt)carry>>3)*16777)>>21;
6110 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6111 carry=est; // likely quotient [99%]
6112 if (*c<DECDPUNMAX+1) continue; // estimate was correct
6113 carry++;
6114 *c-=DECDPUNMAX+1;
6115 continue;
6116 }
6117 // negative case
6118 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6119 est=(((ueInt)carry>>3)*16777)>>21;
6120 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6121 carry=est-(DECDPUNMAX+1); // correctly negative
6122 if (*c<DECDPUNMAX+1) continue; // was OK
6123 carry++;
6124 *c-=DECDPUNMAX+1;
6125 #elif DECDPUN<=2
6126 // Can use QUOT10 as carry <= 4 digits
6127 if (carry>=0) {
6128 est=QUOT10(carry, DECDPUN);
6129 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6130 carry=est; // quotient
6131 continue;
6132 }
6133 // negative case
6134 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6135 est=QUOT10(carry, DECDPUN);
6136 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6137 carry=est-(DECDPUNMAX+1); // correctly negative
6138 #else
6139 // remainder operator is undefined if negative, so must test
6140 if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1
6141 *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions]
6142 carry=1;
6143 continue;
6144 }
6145 if (carry>=0) {
6146 *c=(Unit)(carry%(DECDPUNMAX+1));
6147 carry=carry/(DECDPUNMAX+1);
6148 continue;
6149 }
6150 // negative case
6151 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6152 *c=(Unit)(carry%(DECDPUNMAX+1));
6153 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
6154 #endif
6155 } // c
6156
6157 // now may have one or other to complete
6158 // [pretest to avoid loop setup/shutdown]
6159 if (c<maxC) for (; c<maxC; c++) {
6160 if (a<alsu+alength) { // still in A
6161 carry+=*a;
6162 a++;
6163 }
6164 else { // inside B
6165 carry+=((eInt)*b)*m;
6166 b++;
6167 }
6168 // here carry is new Unit of digits; it could be +ve or -ve and
6169 // magnitude up to DECDPUNMAX squared
6170 if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
6171 *c=(Unit)carry;
6172 carry=0;
6173 continue;
6174 }
6175 // result for this unit is negative or >DECDPUNMAX
6176 #if DECDPUN==4 // use divide-by-multiply
6177 if (carry>=0) {
6178 est=(((ueInt)carry>>11)*53687)>>18;
6179 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6180 carry=est; // likely quotient [79.7%]
6181 if (*c<DECDPUNMAX+1) continue; // estimate was correct
6182 carry++;
6183 *c-=DECDPUNMAX+1;
6184 continue;
6185 }
6186 // negative case
6187 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6188 est=(((ueInt)carry>>11)*53687)>>18;
6189 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6190 carry=est-(DECDPUNMAX+1); // correctly negative
6191 if (*c<DECDPUNMAX+1) continue; // was OK
6192 carry++;
6193 *c-=DECDPUNMAX+1;
6194 #elif DECDPUN==3
6195 if (carry>=0) {
6196 est=(((ueInt)carry>>3)*16777)>>21;
6197 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6198 carry=est; // likely quotient [99%]
6199 if (*c<DECDPUNMAX+1) continue; // estimate was correct
6200 carry++;
6201 *c-=DECDPUNMAX+1;
6202 continue;
6203 }
6204 // negative case
6205 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6206 est=(((ueInt)carry>>3)*16777)>>21;
6207 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6208 carry=est-(DECDPUNMAX+1); // correctly negative
6209 if (*c<DECDPUNMAX+1) continue; // was OK
6210 carry++;
6211 *c-=DECDPUNMAX+1;
6212 #elif DECDPUN<=2
6213 if (carry>=0) {
6214 est=QUOT10(carry, DECDPUN);
6215 *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
6216 carry=est; // quotient
6217 continue;
6218 }
6219 // negative case
6220 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6221 est=QUOT10(carry, DECDPUN);
6222 *c=(Unit)(carry-est*(DECDPUNMAX+1));
6223 carry=est-(DECDPUNMAX+1); // correctly negative
6224 #else
6225 if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1
6226 *c=(Unit)(carry-(DECDPUNMAX+1));
6227 carry=1;
6228 continue;
6229 }
6230 // remainder operator is undefined if negative, so must test
6231 if (carry>=0) {
6232 *c=(Unit)(carry%(DECDPUNMAX+1));
6233 carry=carry/(DECDPUNMAX+1);
6234 continue;
6235 }
6236 // negative case
6237 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
6238 *c=(Unit)(carry%(DECDPUNMAX+1));
6239 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
6240 #endif
6241 } // c
6242
6243 // OK, all A and B processed; might still have carry or borrow
6244 // return number of Units in the result, negated if a borrow
6245 if (carry==0) return c-clsu; // no carry, so no more to do
6246 if (carry>0) { // positive carry
6247 *c=(Unit)carry; // place as new unit
6248 c++; // ..
6249 return c-clsu;
6250 }
6251 // -ve carry: it's a borrow; complement needed
6252 add=1; // temporary carry...
6253 for (c=clsu; c<maxC; c++) {
6254 add=DECDPUNMAX+add-*c;
6255 if (add<=DECDPUNMAX) {
6256 *c=(Unit)add;
6257 add=0;
6258 }
6259 else {
6260 *c=0;
6261 add=1;
6262 }
6263 }
6264 // add an extra unit iff it would be non-zero
6265 if ((add-carry-1)!=0) {
6266 *c=(Unit)(add-carry-1);
6267 c++; // interesting, include it
6268 }
6269 return clsu-c; // -ve result indicates borrowed
6270 } // decUnitAddSub
6271
6272 /* ------------------------------------------------------------------ */
6273 /* decTrim -- trim trailing zeros or normalize */
6274 /* */
6275 /* dn is the number to trim or normalize */
6276 /* set is the context to use to check for clamp */
6277 /* all is 1 to remove all trailing zeros, 0 for just fraction ones */
6278 /* noclamp is 1 to unconditional (unclamped) trim */
6279 /* dropped returns the number of discarded trailing zeros */
6280 /* returns dn */
6281 /* */
6282 /* If clamp is set in the context then the number of zeros trimmed */
6283 /* may be limited if the exponent is high. */
6284 /* All fields are updated as required. This is a utility operation, */
6285 /* so special values are unchanged and no error is possible. */
6286 /* ------------------------------------------------------------------ */
6287 static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
/* */
6288 Flag noclamp, Int *dropped) {
6289 Int d, exp; // work
6290 uInt cut; // ..
6291 Unit *up; // -> current Unit
6292
6293 *dropped=0; // assume no zeros dropped
6294 if ((dn->bits & DECSPECIAL) // fast exit if special ..
6295 || (*dn->lsu & 0x01)) return dn; // .. or odd
6296 if (ISZERO(dn)) { // .. or 0
6297 dn->exponent=0; // (sign is preserved)
6298 return dn;
6299 }
6300
6301 // have a finite number which is even
6302 exp=dn->exponent;
6303 cut=1; // digit (1-DECDPUN) in Unit
6304 up=dn->lsu; // -> current Unit
6305 for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit]
6306 // slice by powers
6307 #if DECDPUN<=4
6308 uInt quot=QUOT10(*up, cut);
6309 if ((*up-quot*powers[cut])!=0) break; // found non-0 digit
6310 #else
6311 if (*up%powers[cut]!=0) break; // found non-0 digit
6312 #endif
6313 // have a trailing 0
6314 if (!all) { // trimming
6315 // [if exp>0 then all trailing 0s are significant for trim]
6316 if (exp<=0) { // if digit might be significant
6317 if (exp==0) break; // then quit
6318 exp++; // next digit might be significant
6319 }
6320 }
6321 cut++; // next power
6322 if (cut>DECDPUN) { // need new Unit
6323 up++;
6324 cut=1;
6325 }
6326 } // d
6327 if (d==0) return dn; // none to drop
6328
6329 // may need to limit drop if clamping
6330 if (set->clamp && !noclamp) {
6331 Int maxd=set->emax-set->digits+1-dn->exponent;
6332 if (maxd<=0) return dn; // nothing possible
6333 if (d>maxd) d=maxd;
6334 }
6335
6336 // effect the drop
6337 decShiftToLeast(dn->lsu, D2U(dn->digits), d);
6338 dn->exponent+=d; // maintain numerical value
6339 dn->digits-=d; // new length
6340 *dropped=d; // report the count
6341 return dn;
6342 } // decTrim
6343
6344 /* ------------------------------------------------------------------ */
6345 /* decReverse -- reverse a Unit array in place */
6346 /* */
6347 /* ulo is the start of the array */
6348 /* uhi is the end of the array (highest Unit to include) */
6349 /* */
6350 /* The units ulo through uhi are reversed in place (if the number */
6351 /* of units is odd, the middle one is untouched). Note that the */
6352 /* digit(s) in each unit are unaffected. */
6353 /* ------------------------------------------------------------------ */
6354 static void decReverse(Unit *ulo, Unit *uhi) {
/* */
6355 Unit temp;
6356 for (; ulo<uhi; ulo++, uhi--) {
6357 temp=*ulo;
6358 *ulo=*uhi;
6359 *uhi=temp;
6360 }
6361 return;
6362 } // decReverse
6363
6364 /* ------------------------------------------------------------------ */
6365 /* decShiftToMost -- shift digits in array towards most significant */
6366 /* */
6367 /* uar is the array */
6368 /* digits is the count of digits in use in the array */
6369 /* shift is the number of zeros to pad with (least significant); */
6370 /* it must be zero or positive */
6371 /* */
6372 /* returns the new length of the integer in the array, in digits */
6373 /* */
6374 /* No overflow is permitted (that is, the uar array must be known to */
6375 /* be large enough to hold the result, after shifting). */
6376 /* ------------------------------------------------------------------ */
6377 static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
/* */
6378 Unit *target, *source, *first; // work
6379 Int cut; // odd 0's to add
6380 uInt next; // work
6381
6382 if (shift==0) return digits; // [fastpath] nothing to do
6383 if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case
6384 *uar=(Unit)(*uar*powers[shift]);
6385 return digits+shift;
6386 }
6387
6388 next=0; // all paths
6389 source=uar+D2U(digits)-1; // where msu comes from
6390 target=source+D2U(shift); // where upper part of first cut goes
6391 cut=DECDPUN-MSUDIGITS(shift); // where to slice
6392 if (cut==0) { // unit-boundary case
6393 for (; source>=uar; source--, target--) *target=*source;
6394 }
6395 else {
6396 first=uar+D2U(digits+shift)-1; // where msu of source will end up
6397 for (; source>=uar; source--, target--) {
6398 // split the source Unit and accumulate remainder for next
6399 #if DECDPUN<=4
6400 uInt quot=QUOT10(*source, cut);
6401 uInt rem=*source-quot*powers[cut];
6402 next+=quot;
6403 #else
6404 uInt rem=*source%powers[cut];
6405 next+=*source/powers[cut];
6406 #endif
6407 if (target<=first) *target=(Unit)next; // write to target iff valid
6408 next=rem*powers[DECDPUN-cut]; // save remainder for next Unit
6409 }
6410 } // shift-move
6411
6412 // propagate any partial unit to one below and clear the rest
6413 for (; target>=uar; target--) {
6414 *target=(Unit)next;
6415 next=0;
6416 }
6417 return digits+shift;
6418 } // decShiftToMost
6419
6420 /* ------------------------------------------------------------------ */
6421 /* decShiftToLeast -- shift digits in array towards least significant */
6422 /* */
6423 /* uar is the array */
6424 /* units is length of the array, in units */
6425 /* shift is the number of digits to remove from the lsu end; it */
6426 /* must be zero or positive and <= than units*DECDPUN. */
6427 /* */
6428 /* returns the new length of the integer in the array, in units */
6429 /* */
6430 /* Removed digits are discarded (lost). Units not required to hold */
6431 /* the final result are unchanged. */
6432 /* ------------------------------------------------------------------ */
6433 static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
/* */
6434 Unit *target, *up; // work
6435 Int cut, count; // work
6436 Int quot, rem; // for division
6437
6438 if (shift==0) return units; // [fastpath] nothing to do
6439 if (shift==units*DECDPUN) { // [fastpath] little to do
6440 *uar=0; // all digits cleared gives zero
6441 return 1; // leaves just the one
6442 }
6443
6444 target=uar; // both paths
6445 cut=MSUDIGITS(shift);
6446 if (cut==DECDPUN) { // unit-boundary case; easy
6447 up=uar+D2U(shift);
6448 for (; up<uar+units; target++, up++) *target=*up;
6449 return target-uar;
6450 }
6451
6452 // messier
6453 up=uar+D2U(shift-cut); // source; correct to whole Units
6454 count=units*DECDPUN-shift; // the maximum new length
6455 #if DECDPUN<=4
6456 quot=QUOT10(*up, cut);
6457 #else
6458 quot=*up/powers[cut];
6459 #endif
6460 for (; ; target++) {
6461 *target=(Unit)quot;
6462 count-=(DECDPUN-cut);
6463 if (count<=0) break;
6464 up++;
6465 quot=*up;
6466 #if DECDPUN<=4
6467 quot=QUOT10(quot, cut);
6468 rem=*up-quot*powers[cut];
6469 #else
6470 rem=quot%powers[cut];
6471 quot=quot/powers[cut];
6472 #endif
6473 *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
6474 count-=cut;
6475 if (count<=0) break;
6476 }
6477 return target-uar+1;
6478 } // decShiftToLeast
6479
6480 #if DECSUBSET
6481 /* ------------------------------------------------------------------ */
6482 /* decRoundOperand -- round an operand [used for subset only] */
6483 /* */
6484 /* dn is the number to round (dn->digits is > set->digits) */
6485 /* set is the relevant context */
6486 /* status is the status accumulator */
6487 /* */
6488 /* returns an allocated decNumber with the rounded result. */
6489 /* */
6490 /* lostDigits and other status may be set by this. */
6491 /* */
6492 /* Since the input is an operand, it must not be modified. */
6493 /* Instead, return an allocated decNumber, rounded as required. */
6494 /* It is the caller's responsibility to free the allocated storage. */
6495 /* */
6496 /* If no storage is available then the result cannot be used, so NULL */
6497 /* is returned. */
6498 /* ------------------------------------------------------------------ */
6499 static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
/* */
6500 uInt *status) {
6501 decNumber *res; // result structure
6502 uInt newstatus=0; // status from round
6503 Int residue=0; // rounding accumulator
6504
6505 // Allocate storage for the returned decNumber, big enough for the
6506 // length specified by the context
6507 res=(decNumber *)malloc(sizeof(decNumber)
6508 +(D2U(set->digits)-1)*sizeof(Unit));
6509 if (res==NULL) {
6510 *status|=DEC_Insufficient_storage;
6511 return NULL;
6512 }
6513 decCopyFit(res, dn, set, &residue, &newstatus);
6514 decApplyRound(res, set, residue, &newstatus);
6515
6516 // If that set Inexact then "lost digits" is raised...
6517 if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
6518 *status|=newstatus;
6519 return res;
6520 } // decRoundOperand
6521 #endif
6522
6523 /* ------------------------------------------------------------------ */
6524 /* decCopyFit -- copy a number, truncating the coefficient if needed */
6525 /* */
6526 /* dest is the target decNumber */
6527 /* src is the source decNumber */
6528 /* set is the context [used for length (digits) and rounding mode] */
6529 /* residue is the residue accumulator */
6530 /* status contains the current status to be updated */
6531 /* */
6532 /* (dest==src is allowed and will be a no-op if fits) */
6533 /* All fields are updated as required. */
6534 /* ------------------------------------------------------------------ */
6535 static void decCopyFit(decNumber *dest, const decNumber *src,
/* */
6536 decContext *set, Int *residue, uInt *status) {
6537 dest->bits=src->bits;
6538 dest->exponent=src->exponent;
6539 decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
6540 } // decCopyFit
6541
6542 /* ------------------------------------------------------------------ */
6543 /* decSetCoeff -- set the coefficient of a number */
6544 /* */
6545 /* dn is the number whose coefficient array is to be set. */
6546 /* It must have space for set->digits digits */
6547 /* set is the context [for size] */
6548 /* lsu -> lsu of the source coefficient [may be dn->lsu] */
6549 /* len is digits in the source coefficient [may be dn->digits] */
6550 /* residue is the residue accumulator. This has values as in */
6551 /* decApplyRound, and will be unchanged unless the */
6552 /* target size is less than len. In this case, the */
6553 /* coefficient is truncated and the residue is updated to */
6554 /* reflect the previous residue and the dropped digits. */
6555 /* status is the status accumulator, as usual */
6556 /* */
6557 /* The coefficient may already be in the number, or it can be an */
6558 /* external intermediate array. If it is in the number, lsu must == */
6559 /* dn->lsu and len must == dn->digits. */
6560 /* */
6561 /* Note that the coefficient length (len) may be < set->digits, and */
6562 /* in this case this merely copies the coefficient (or is a no-op */
6563 /* if dn->lsu==lsu). */
6564 /* */
6565 /* Note also that (only internally, from decQuantizeOp and */
6566 /* decSetSubnormal) the value of set->digits may be less than one, */
6567 /* indicating a round to left. This routine handles that case */
6568 /* correctly; caller ensures space. */
6569 /* */
6570 /* dn->digits, dn->lsu (and as required), and dn->exponent are */
6571 /* updated as necessary. dn->bits (sign) is unchanged. */
6572 /* */
6573 /* DEC_Rounded status is set if any digits are discarded. */
6574 /* DEC_Inexact status is set if any non-zero digits are discarded, or */
6575 /* incoming residue was non-0 (implies rounded) */
6576 /* ------------------------------------------------------------------ */
6577 // mapping array: maps 0-9 to canonical residues, so that a residue
6578 // can be adjusted in the range [-1, +1] and achieve correct rounding
6579 // 0 1 2 3 4 5 6 7 8 9
6580 static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
6581 static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
/* */
6582 Int len, Int *residue, uInt *status) {
6583 Int discard; // number of digits to discard
6584 uInt cut; // cut point in Unit
6585 const Unit *up; // work
6586 Unit *target; // ..
6587 Int count; // ..
6588 #if DECDPUN<=4
6589 uInt temp; // ..
6590 #endif
6591
6592 discard=len-set->digits; // digits to discard
6593 if (discard<=0) { // no digits are being discarded
6594 if (dn->lsu!=lsu) { // copy needed
6595 // copy the coefficient array to the result number; no shift needed
6596 count=len; // avoids D2U
6597 up=lsu;
6598 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
6599 *target=*up;
6600 dn->digits=len; // set the new length
6601 }
6602 // dn->exponent and residue are unchanged, record any inexactitude
6603 if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
6604 return;
6605 }
6606
6607 // some digits must be discarded ...
6608 dn->exponent+=discard; // maintain numerical value
6609 *status|=DEC_Rounded; // accumulate Rounded status
6610 if (*residue>1) *residue=1; // previous residue now to right, so reduce
6611
6612 if (discard>len) { // everything, +1, is being discarded
6613 // guard digit is 0
6614 // residue is all the number [NB could be all 0s]
6615 if (*residue<=0) { // not already positive
6616 count=len; // avoids D2U
6617 for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0
6618 *residue=1;
6619 break; // no need to check any others
6620 }
6621 }
6622 if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
6623 *dn->lsu=0; // coefficient will now be 0
6624 dn->digits=1; // ..
6625 return;
6626 } // total discard
6627
6628 // partial discard [most common case]
6629 // here, at least the first (most significant) discarded digit exists
6630
6631 // spin up the number, noting residue during the spin, until get to
6632 // the Unit with the first discarded digit. When reach it, extract
6633 // it and remember its position
6634 count=0;
6635 for (up=lsu;; up++) {
6636 count+=DECDPUN;
6637 if (count>=discard) break; // full ones all checked
6638 if (*up!=0) *residue=1;
6639 } // up
6640
6641 // here up -> Unit with first discarded digit
6642 cut=discard-(count-DECDPUN)-1;
6643 if (cut==DECDPUN-1) { // unit-boundary case (fast)
6644 Unit half=(Unit)powers[DECDPUN]>>1;
6645 // set residue directly
6646 if (*up>=half) {
6647 if (*up>half) *residue=7;
6648 else *residue+=5; // add sticky bit
6649 }
6650 else { // <half
6651 if (*up!=0) *residue=3; // [else is 0, leave as sticky bit]
6652 }
6653 if (set->digits<=0) { // special for Quantize/Subnormal :-(
6654 *dn->lsu=0; // .. result is 0
6655 dn->digits=1; // ..
6656 }
6657 else { // shift to least
6658 count=set->digits; // now digits to end up with
6659 dn->digits=count; // set the new length
6660 up++; // move to next
6661 // on unit boundary, so shift-down copy loop is simple
6662 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
6663 *target=*up;
6664 }
6665 } // unit-boundary case
6666
6667 else { // discard digit is in low digit(s), and not top digit
6668 uInt discard1; // first discarded digit
6669 uInt quot, rem; // for divisions
6670 if (cut==0) quot=*up; // is at bottom of unit
6671 else /* cut>0 */ { // it's not at bottom of unit
6672 #if DECDPUN<=4
6673 quot=QUOT10(*up, cut);
6674 rem=*up-quot*powers[cut];
6675 #else
6676 rem=*up%powers[cut];
6677 quot=*up/powers[cut];
6678 #endif
6679 if (rem!=0) *residue=1;
6680 }
6681 // discard digit is now at bottom of quot
6682 #if DECDPUN<=4
6683 temp=(quot*6554)>>16; // fast /10
6684 // Vowels algorithm here not a win (9 instructions)
6685 discard1=quot-X10(temp);
6686 quot=temp;
6687 #else
6688 discard1=quot%10;
6689 quot=quot/10;
6690 #endif
6691 // here, discard1 is the guard digit, and residue is everything
6692 // else [use mapping array to accumulate residue safely]
6693 *residue+=resmap[discard1];
6694 cut++; // update cut
6695 // here: up -> Unit of the array with bottom digit
6696 // cut is the division point for each Unit
6697 // quot holds the uncut high-order digits for the current unit
6698 if (set->digits<=0) { // special for Quantize/Subnormal :-(
6699 *dn->lsu=0; // .. result is 0
6700 dn->digits=1; // ..
6701 }
6702 else { // shift to least needed
6703 count=set->digits; // now digits to end up with
6704 dn->digits=count; // set the new length
6705 // shift-copy the coefficient array to the result number
6706 for (target=dn->lsu; ; target++) {
6707 *target=(Unit)quot;
6708 count-=(DECDPUN-cut);
6709 if (count<=0) break;
6710 up++;
6711 #if !defined(__clang_analyzer__)
6712 quot=*up;
6713 #endif
6714 #if DECDPUN<=4
6715 quot=QUOT10(quot, cut);
6716 rem=*up-quot*powers[cut];
6717 #else
6718 rem=quot%powers[cut];
6719 quot=quot/powers[cut];
6720 #endif
6721 *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
6722 count-=cut;
6723 if (count<=0) break;
6724 } // shift-copy loop
6725 } // shift to least
6726 } // not unit boundary
6727
6728 if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
6729 return;
6730 } // decSetCoeff
6731
6732 /* ------------------------------------------------------------------ */
6733 /* decApplyRound -- apply pending rounding to a number */
6734 /* */
6735 /* dn is the number, with space for set->digits digits */
6736 /* set is the context [for size and rounding mode] */
6737 /* residue indicates pending rounding, being any accumulated */
6738 /* guard and sticky information. It may be: */
6739 /* 6-9: rounding digit is >5 */
6740 /* 5: rounding digit is exactly half-way */
6741 /* 1-4: rounding digit is <5 and >0 */
6742 /* 0: the coefficient is exact */
6743 /* -1: as 1, but the hidden digits are subtractive, that */
6744 /* is, of the opposite sign to dn. In this case the */
6745 /* coefficient must be non-0. This case occurs when */
6746 /* subtracting a small number (which can be reduced to */
6747 /* a sticky bit); see decAddOp. */
6748 /* status is the status accumulator, as usual */
6749 /* */
6750 /* This routine applies rounding while keeping the length of the */
6751 /* coefficient constant. The exponent and status are unchanged */
6752 /* except if: */
6753 /* */
6754 /* -- the coefficient was increased and is all nines (in which */
6755 /* case Overflow could occur, and is handled directly here so */
6756 /* the caller does not need to re-test for overflow) */
6757 /* */
6758 /* -- the coefficient was decreased and becomes all nines (in which */
6759 /* case Underflow could occur, and is also handled directly). */
6760 /* */
6761 /* All fields in dn are updated as required. */
6762 /* */
6763 /* ------------------------------------------------------------------ */
6764 static void decApplyRound(decNumber *dn, decContext *set, Int residue,
/* */
6765 uInt *status) {
6766 Int bump; // 1 if coefficient needs to be incremented
6767 // -1 if coefficient needs to be decremented
6768
6769 if (residue==0) return; // nothing to apply
6770
6771 bump=0; // assume a smooth ride
6772
6773 // now decide whether, and how, to round, depending on mode
6774 switch (set->round) {
6775 case DEC_ROUND_05UP: { // round zero or five up (for reround)
6776 // This is the same as DEC_ROUND_DOWN unless there is a
6777 // positive residue and the lsd of dn is 0 or 5, in which case
6778 // it is bumped; when residue is <0, the number is therefore
6779 // bumped down unless the final digit was 1 or 6 (in which
6780 // case it is bumped down and then up -- a no-op)
6781 Int lsd5=*dn->lsu%5; // get lsd and quintate
6782 if (residue<0 && lsd5!=1) bump=-1;
6783 else if (residue>0 && lsd5==0) bump=1;
6784 // [bump==1 could be applied directly; use common path for clarity]
6785 break;} // r-05
6786
6787 case DEC_ROUND_DOWN: {
6788 // no change, except if negative residue
6789 if (residue<0) bump=-1;
6790 break;} // r-d
6791
6792 case DEC_ROUND_HALF_DOWN: {
6793 if (residue>5) bump=1;
6794 break;} // r-h-d
6795
6796 case DEC_ROUND_HALF_EVEN: {
6797 if (residue>5) bump=1; // >0.5 goes up
6798 else if (residue==5) { // exactly 0.5000...
6799 // 0.5 goes up iff [new] lsd is odd
6800 if (*dn->lsu & 0x01) bump=1;
6801 }
6802 break;} // r-h-e
6803
6804 case DEC_ROUND_HALF_UP: {
6805 if (residue>=5) bump=1;
6806 break;} // r-h-u
6807
6808 case DEC_ROUND_UP: {
6809 if (residue>0) bump=1;
6810 break;} // r-u
6811
6812 case DEC_ROUND_CEILING: {
6813 // same as _UP for positive numbers, and as _DOWN for negatives
6814 // [negative residue cannot occur on 0]
6815 if (decNumberIsNegative(dn)) {
6816 if (residue<0) bump=-1;
6817 }
6818 else {
6819 if (residue>0) bump=1;
6820 }
6821 break;} // r-c
6822
6823 case DEC_ROUND_FLOOR: {
6824 // same as _UP for negative numbers, and as _DOWN for positive
6825 // [negative residue cannot occur on 0]
6826 if (!decNumberIsNegative(dn)) {
6827 if (residue<0) bump=-1;
6828 }
6829 else {
6830 if (residue>0) bump=1;
6831 }
6832 break;} // r-f
6833
6834 default: { // e.g., DEC_ROUND_MAX
6835 *status|=DEC_Invalid_context;
6836 break;}
6837 } // switch
6838
6839 // now bump the number, up or down, if need be
6840 if (bump==0) return; // no action required
6841
6842 // Simply use decUnitAddSub unless bumping up and the number is
6843 // all nines. In this special case set to 100... explicitly
6844 // and adjust the exponent by one (as otherwise could overflow
6845 // the array)
6846 // Similarly handle all-nines result if bumping down.
6847 if (bump>0) {
6848 Unit *up; // work
6849 uInt count=dn->digits; // digits to be checked
6850 for (up=dn->lsu; ; up++) {
6851 if (count<=DECDPUN) {
6852 // this is the last Unit (the msu)
6853 if (*up!=powers[count]-1) break; // not still 9s
6854 // here if it, too, is all nines
6855 *up=(Unit)powers[count-1]; // here 999 -> 100 etc.
6856 for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0
6857 dn->exponent++; // and bump exponent
6858 // [which, very rarely, could cause Overflow...]
6859 if ((dn->exponent+dn->digits)>set->emax+1) {
6860 decSetOverflow(dn, set, status);
6861 }
6862 return; // done
6863 }
6864 // a full unit to check, with more to come
6865 if (*up!=DECDPUNMAX) break; // not still 9s
6866 count-=DECDPUN;
6867 } // up
6868 } // bump>0
6869 else { // -1
6870 // here checking for a pre-bump of 1000... (leading 1, all
6871 // other digits zero)
6872 Unit *up, *sup; // work
6873 uInt count=dn->digits; // digits to be checked
6874 for (up=dn->lsu; ; up++) {
6875 if (count<=DECDPUN) {
6876 // this is the last Unit (the msu)
6877 if (*up!=powers[count-1]) break; // not 100..
6878 // here if have the 1000... case
6879 sup=up; // save msu pointer
6880 *up=(Unit)powers[count]-1; // here 100 in msu -> 999
6881 // others all to all-nines, too
6882 for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
6883 dn->exponent--; // and bump exponent
6884
6885 // if the number was at the subnormal boundary (exponent=etiny)
6886 // then the exponent is now out of range, so it will in fact get
6887 // clamped to etiny and the final 9 dropped.
6888 if (dn->exponent+1==set->emin-set->digits+1) { //-V584
6889 if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9]
6890 else {
6891 *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99..
6892 dn->digits--;
6893 }
6894 dn->exponent++;
6895 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
6896 }
6897 return; // done
6898 }
6899
6900 // a full unit to check, with more to come
6901 if (*up!=0) break; // not still 0s
6902 count-=DECDPUN;
6903 } // up
6904
6905 } // bump<0
6906
6907 // Actual bump needed. Do it.
6908 decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
6909 } // decApplyRound
6910
6911 #if DECSUBSET
6912 /* ------------------------------------------------------------------ */
6913 /* decFinish -- finish processing a number */
6914 /* */
6915 /* dn is the number */
6916 /* set is the context */
6917 /* residue is the rounding accumulator (as in decApplyRound) */
6918 /* status is the accumulator */
6919 /* */
6920 /* This finishes off the current number by: */
6921 /* 1. If not extended: */
6922 /* a. Converting a zero result to clean '0' */
6923 /* b. Reducing positive exponents to 0, if would fit in digits */
6924 /* 2. Checking for overflow and subnormals (always) */
6925 /* Note this is just Finalize when no subset arithmetic. */
6926 /* All fields are updated as required. */
6927 /* ------------------------------------------------------------------ */
6928 static void decFinish(decNumber *dn, decContext *set, Int *residue,
/* */
6929 uInt *status) {
6930 if (!set->extended) {
6931 if ISZERO(dn) { // value is zero
6932 dn->exponent=0; // clean exponent ..
6933 dn->bits=0; // .. and sign
6934 return; // no error possible
6935 }
6936 if (dn->exponent>=0) { // non-negative exponent
6937 // >0; reduce to integer if possible
6938 if (set->digits >= (dn->exponent+dn->digits)) {
6939 dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
6940 dn->exponent=0;
6941 }
6942 }
6943 } // !extended
6944
6945 decFinalize(dn, set, residue, status);
6946 } // decFinish
6947 #endif
6948
6949 /* ------------------------------------------------------------------ */
6950 /* decFinalize -- final check, clamp, and round of a number */
6951 /* */
6952 /* dn is the number */
6953 /* set is the context */
6954 /* residue is the rounding accumulator (as in decApplyRound) */
6955 /* status is the status accumulator */
6956 /* */
6957 /* This finishes off the current number by checking for subnormal */
6958 /* results, applying any pending rounding, checking for overflow, */
6959 /* and applying any clamping. */
6960 /* Underflow and overflow conditions are raised as appropriate. */
6961 /* All fields are updated as required. */
6962 /* ------------------------------------------------------------------ */
6963 static void decFinalize(decNumber *dn, decContext *set, Int *residue,
/* */
6964 uInt *status) {
6965 Int shift; // shift needed if clamping
6966 Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary
6967
6968 // Must be careful, here, when checking the exponent as the
6969 // adjusted exponent could overflow 31 bits [because it may already
6970 // be up to twice the expected].
6971
6972 // First test for subnormal. This must be done before any final
6973 // round as the result could be rounded to Nmin or 0.
6974 if (dn->exponent<=tinyexp) { // prefilter
6975 Int comp;
6976 decNumber nmin;
6977 // A very nasty case here is dn == Nmin and residue<0
6978 if (dn->exponent<tinyexp) {
6979 // Go handle subnormals; this will apply round if needed.
6980 decSetSubnormal(dn, set, residue, status);
6981 return;
6982 }
6983 // Equals case: only subnormal if dn=Nmin and negative residue
6984 decNumberZero(&nmin);
6985 nmin.lsu[0]=1;
6986 nmin.exponent=set->emin;
6987 comp=decCompare(dn, &nmin, 1); // (signless compare)
6988 if (comp==BADINT) { // oops
6989 *status|=DEC_Insufficient_storage; // abandon...
6990 return;
6991 }
6992 if (*residue<0 && comp==0) { // neg residue and dn==Nmin
6993 decApplyRound(dn, set, *residue, status); // might force down
6994 decSetSubnormal(dn, set, residue, status);
6995 return;
6996 }
6997 }
6998
6999 // now apply any pending round (this could raise overflow).
7000 if (*residue!=0) decApplyRound(dn, set, *residue, status);
7001
7002 // Check for overflow [redundant in the 'rare' case] or clamp
7003 if (dn->exponent<=set->emax-set->digits+1) return; // neither needed
7004
7005 // here when might have an overflow or clamp to do
7006 if (dn->exponent>set->emax-dn->digits+1) { // too big
7007 decSetOverflow(dn, set, status);
7008 return;
7009 }
7010 // here when the result is normal but in clamp range
7011 if (!set->clamp) return;
7012
7013 // here when need to apply the IEEE exponent clamp (fold-down)
7014 shift=dn->exponent-(set->emax-set->digits+1);
7015
7016 // shift coefficient (if non-zero)
7017 if (!ISZERO(dn)) {
7018 dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
7019 }
7020 dn->exponent-=shift; // adjust the exponent to match
7021 *status|=DEC_Clamped; // and record the dirty deed
7022 return;
7023 } // decFinalize
7024
7025 /* ------------------------------------------------------------------ */
7026 /* decSetOverflow -- set number to proper overflow value */
7027 /* */
7028 /* dn is the number (used for sign [only] and result) */
7029 /* set is the context [used for the rounding mode, etc.] */
7030 /* status contains the current status to be updated */
7031 /* */
7032 /* This sets the sign of a number and sets its value to either */
7033 /* Infinity or the maximum finite value, depending on the sign of */
7034 /* dn and the rounding mode, following IEEE 754 rules. */
7035 /* ------------------------------------------------------------------ */
7036 static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
/* */
7037 Flag needmax=0; // result is maximum finite value
7038 uByte sign=dn->bits&DECNEG; // clean and save sign bit
7039
7040 if (ISZERO(dn)) { // zero does not overflow magnitude
7041 Int emax=set->emax; // limit value
7042 if (set->clamp) emax-=set->digits-1; // lower if clamping
7043 if (dn->exponent>emax) { // clamp required
7044 dn->exponent=emax;
7045 *status|=DEC_Clamped;
7046 }
7047 return;
7048 }
7049
7050 decNumberZero(dn);
7051 switch (set->round) {
7052 case DEC_ROUND_DOWN: {
7053 needmax=1; //-V1037 // never Infinity
7054 break;} // r-d
7055 case DEC_ROUND_05UP: {
7056 needmax=1; //-V1037 // never Infinity
7057 break;} // r-05
7058 case DEC_ROUND_CEILING: {
7059 if (sign) needmax=1; // Infinity if non-negative
7060 break;} // r-c
7061 case DEC_ROUND_FLOOR: {
7062 if (!sign) needmax=1; // Infinity if negative
7063 break;} // r-f
7064 default: break; // Infinity in all other cases
7065 }
7066 if (needmax) {
7067 decSetMaxValue(dn, set);
7068 dn->bits=sign; // set sign
7069 }
7070 else dn->bits=sign|DECINF; // Value is +/-Infinity
7071 *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
7072 } // decSetOverflow
7073
7074 /* ------------------------------------------------------------------ */
7075 /* decSetMaxValue -- set number to +Nmax (maximum normal value) */
7076 /* */
7077 /* dn is the number to set */
7078 /* set is the context [used for digits and emax] */
7079 /* */
7080 /* This sets the number to the maximum positive value. */
7081 /* ------------------------------------------------------------------ */
7082 static void decSetMaxValue(decNumber *dn, decContext *set) {
/* */
7083 Unit *up; // work
7084 Int count=set->digits; // nines to add
7085 dn->digits=count;
7086 // fill in all nines to set maximum value
7087 for (up=dn->lsu; ; up++) {
7088 if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines
7089 else { // this is the msu
7090 *up=(Unit)(powers[count]-1);
7091 break;
7092 }
7093 count-=DECDPUN; // filled those digits
7094 } // up
7095 dn->bits=0; // + sign
7096 dn->exponent=set->emax-set->digits+1;
7097 } // decSetMaxValue
7098
7099 /* ------------------------------------------------------------------ */
7100 /* decSetSubnormal -- process value whose exponent is <Emin */
7101 /* */
7102 /* dn is the number (used as input as well as output; it may have */
7103 /* an allowed subnormal value, which may need to be rounded) */
7104 /* set is the context [used for the rounding mode] */
7105 /* residue is any pending residue */
7106 /* status contains the current status to be updated */
7107 /* */
7108 /* If subset mode, set result to zero and set Underflow flags. */
7109 /* */
7110 /* Value may be zero with a low exponent; this does not set Subnormal */
7111 /* but the exponent will be clamped to Etiny. */
7112 /* */
7113 /* Otherwise ensure exponent is not out of range, and round as */
7114 /* necessary. Underflow is set if the result is Inexact. */
7115 /* ------------------------------------------------------------------ */
7116 static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
/* */
7117 uInt *status) {
7118 decContext workset; // work
7119 Int etiny, adjust; // ..
7120
7121 #if DECSUBSET
7122 // simple set to zero and 'hard underflow' for subset
7123 if (!set->extended) {
7124 decNumberZero(dn);
7125 // always full overflow
7126 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
7127 return;
7128 }
7129 #endif
7130
7131 // Full arithmetic -- allow subnormals, rounded to minimum exponent
7132 // (Etiny) if needed
7133 etiny=set->emin-(set->digits-1); // smallest allowed exponent
7134
7135 if ISZERO(dn) { // value is zero
7136 // residue can never be non-zero here
7137 if (dn->exponent<etiny) { // clamp required
7138 dn->exponent=etiny;
7139 *status|=DEC_Clamped;
7140 }
7141 return;
7142 }
7143
7144 *status|=DEC_Subnormal; // have a non-zero subnormal
7145 adjust=etiny-dn->exponent; // calculate digits to remove
7146 if (adjust<=0) { // not out of range; unrounded
7147 // residue can never be non-zero here, except in the Nmin-residue
7148 // case (which is a subnormal result), so can take fast-path here
7149 // it may already be inexact (from setting the coefficient)
7150 if (*status&DEC_Inexact) *status|=DEC_Underflow;
7151 return;
7152 }
7153
7154 // adjust>0, so need to rescale the result so exponent becomes Etiny
7155 // [this code is similar to that in rescale]
7156 workset=*set; // clone rounding, etc.
7157 workset.digits=dn->digits-adjust; // set requested length
7158 workset.emin-=adjust; // and adjust emin to match
7159 // [note that the latter can be <1, here, similar to Rescale case]
7160 decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
7161 decApplyRound(dn, &workset, *residue, status);
7162
7163 // Use 754 default rule: Underflow is set iff Inexact
7164 // [independent of whether trapped]
7165 if (*status&DEC_Inexact) *status|=DEC_Underflow;
7166
7167 // if rounded up a 999s case, exponent will be off by one; adjust
7168 // back if so [it will fit, because it was shortened earlier]
7169 if (dn->exponent>etiny) {
7170 dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
7171 dn->exponent--; // (re)adjust the exponent.
7172 }
7173
7174 // if rounded to zero, it is by definition clamped...
7175 if (ISZERO(dn)) *status|=DEC_Clamped;
7176 } // decSetSubnormal
7177
7178 /* ------------------------------------------------------------------ */
7179 /* decCheckMath - check entry conditions for a math function */
7180 /* */
7181 /* This checks the context and the operand */
7182 /* */
7183 /* rhs is the operand to check */
7184 /* set is the context to check */
7185 /* status is unchanged if both are good */
7186 /* */
7187 /* returns non-zero if status is changed, 0 otherwise */
7188 /* */
7189 /* Restrictions enforced: */
7190 /* */
7191 /* digits, emax, and -emin in the context must be less than */
7192 /* DEC_MAX_MATH (999999), and A must be within these bounds if */
7193 /* non-zero. Invalid_operation is set in the status if a */
7194 /* restriction is violated. */
7195 /* ------------------------------------------------------------------ */
7196 static uInt decCheckMath(const decNumber *rhs, decContext *set,
/* */
7197 uInt *status) {
7198 uInt save=*status; // record
7199 if (set->digits>DEC_MAX_MATH
7200 || set->emax>DEC_MAX_MATH
7201 || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
7202 else if ((rhs->digits>DEC_MAX_MATH
7203 || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
7204 || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
7205 && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
7206 return (*status!=save);
7207 } // decCheckMath
7208
7209 /* ------------------------------------------------------------------ */
7210 /* decGetInt -- get integer from a number */
7211 /* */
7212 /* dn is the number [which will not be altered] */
7213 /* */
7214 /* returns one of: */
7215 /* BADINT if there is a non-zero fraction */
7216 /* the converted integer */
7217 /* BIGEVEN if the integer is even and magnitude > 2*10**9 */
7218 /* BIGODD if the integer is odd and magnitude > 2*10**9 */
7219 /* */
7220 /* This checks and gets a whole number from the input decNumber. */
7221 /* The sign can be determined from dn by the caller when BIGEVEN or */
7222 /* BIGODD is returned. */
7223 /* ------------------------------------------------------------------ */
7224 static Int decGetInt(const decNumber *dn) {
/* */
7225 Int theInt; // result accumulator
7226 const Unit *up; // work
7227 Int got; // digits (real or not) processed
7228 Int ilength=dn->digits+dn->exponent; // integral length
7229 Flag neg=decNumberIsNegative(dn); // 1 if -ve
7230
7231 // The number must be an integer that fits in 10 digits
7232 // Assert, here, that 10 is enough for any rescale Etiny
7233 #if DEC_MAX_EMAX > 999999999
7234 # error GetInt may need updating [for Emax]
7235 #endif
7236 #if DEC_MIN_EMIN < -999999999
7237 # error GetInt may need updating [for Emin]
7238 #endif
7239 if (ISZERO(dn)) return 0; // zeros are OK, with any exponent
7240
7241 up=dn->lsu; // ready for lsu
7242 theInt=0; // ready to accumulate
7243 if (dn->exponent>=0) { // relatively easy
7244 // no fractional part [usual]; allow for positive exponent
7245 got=dn->exponent;
7246 }
7247 else { // -ve exponent; some fractional part to check and discard
7248 Int count=-dn->exponent; // digits to discard
7249 // spin up whole units until reach the Unit with the unit digit
7250 for (; count>=DECDPUN; up++) {
7251 if (*up!=0) return BADINT; // non-zero Unit to discard
7252 count-=DECDPUN;
7253 }
7254 if (count==0) got=0; // [a multiple of DECDPUN]
7255 else { // [not multiple of DECDPUN]
7256 Int rem; // work
7257 // slice off fraction digits and check for non-zero
7258 #if DECDPUN<=4
7259 theInt=QUOT10(*up, count);
7260 rem=*up-theInt*powers[count];
7261 #else
7262 rem=*up%powers[count]; // slice off discards
7263 theInt=*up/powers[count];
7264 #endif
7265 if (rem!=0) return BADINT; // non-zero fraction
7266 // it looks good
7267 got=DECDPUN-count; // number of digits so far
7268 up++; // ready for next
7269 }
7270 }
7271 // now it's known there's no fractional part
7272
7273 // tricky code now, to accumulate up to 9.3 digits
7274 if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there
7275
7276 if (ilength<11) {
7277 Int save=theInt;
7278 // collect any remaining unit(s)
7279 for (; got<ilength; up++) {
7280 theInt+=*up*powers[got];
7281 got+=DECDPUN;
7282 }
7283 if (ilength==10) { // need to check for wrap
7284 if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
7285 // [that test also disallows the BADINT result case]
7286 else if (neg && theInt>1999999997) ilength=11;
7287 else if (!neg && theInt>999999999) ilength=11;
7288 if (ilength==11) theInt=save; // restore correct low bit
7289 }
7290 }
7291
7292 if (ilength>10) { // too big
7293 if (theInt&1) return BIGODD; // bottom bit 1
7294 return BIGEVEN; // bottom bit 0
7295 }
7296
7297 if (neg) theInt=-theInt; // apply sign
7298 return theInt;
7299 } // decGetInt
7300
7301 /* ------------------------------------------------------------------ */
7302 /* decDecap -- decapitate the coefficient of a number */
7303 /* */
7304 /* dn is the number to be decapitated */
7305 /* drop is the number of digits to be removed from the left of dn; */
7306 /* this must be <= dn->digits (if equal, the coefficient is */
7307 /* set to 0) */
7308 /* */
7309 /* Returns dn; dn->digits will be <= the initial digits less drop */
7310 /* (after removing drop digits there may be leading zero digits */
7311 /* which will also be removed). Only dn->lsu and dn->digits change. */
7312 /* ------------------------------------------------------------------ */
7313 static decNumber *decDecap(decNumber *dn, Int drop) {
/* */
7314 Unit *msu; // -> target cut point
7315 Int cut; // work
7316 if (drop>=dn->digits) { // losing the whole thing
7317 dn->lsu[0]=0;
7318 dn->digits=1;
7319 return dn;
7320 }
7321 msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu
7322 cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu
7323 if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits
7324 // that may have left leading zero digits, so do a proper count...
7325 dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
7326 return dn;
7327 } // decDecap
7328
7329 /* ------------------------------------------------------------------ */
7330 /* decBiStr -- compare string with pairwise options */
7331 /* */
7332 /* targ is the string to compare */
7333 /* str1 is one of the strings to compare against (length may be 0) */
7334 /* str2 is the other; it must be the same length as str1 */
7335 /* */
7336 /* returns 1 if strings compare equal, (that is, it is the same */
7337 /* length as str1 and str2, and each character of targ is in either */
7338 /* str1 or str2 in the corresponding position), or 0 otherwise */
7339 /* */
7340 /* This is used for generic caseless compare, including the awkward */
7341 /* case of the Turkish dotted and dotless Is. Use as (for example): */
7342 /* if (decBiStr(test, "mike", "MIKE")) ... */
7343 /* ------------------------------------------------------------------ */
7344 static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
/* */
7345 for (;;targ++, str1++, str2++) {
7346 if (*targ!=*str1 && *targ!=*str2) return 0;
7347 // *targ has a match in one (or both, if terminator)
7348 if (*targ=='\0') break;
7349 } // forever
7350 return 1;
7351 } // decBiStr
7352
7353 /* ------------------------------------------------------------------ */
7354 /* decNaNs -- handle NaN operand or operands */
7355 /* */
7356 /* res is the result number */
7357 /* lhs is the first operand */
7358 /* rhs is the second operand, or NULL if none */
7359 /* context is used to limit payload length */
7360 /* status contains the current status */
7361 /* returns res in case convenient */
7362 /* */
7363 /* Called when one or both operands is a NaN, and propagates the */
7364 /* appropriate result to res. When an sNaN is found, it is changed */
7365 /* to a qNaN and Invalid operation is set. */
7366 /* ------------------------------------------------------------------ */
7367 static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
/* */
7368 const decNumber *rhs, decContext *set,
7369 uInt *status) {
7370 // This decision tree ends up with LHS being the source pointer,
7371 // and status updated if need be
7372 if (lhs->bits & DECSNAN)
7373 *status|=DEC_Invalid_operation | DEC_sNaN;
7374 else if (rhs==NULL);
7375 else if (rhs->bits & DECSNAN) {
7376 lhs=rhs;
7377 *status|=DEC_Invalid_operation | DEC_sNaN;
7378 }
7379 else if (lhs->bits & DECNAN);
7380 else lhs=rhs;
7381
7382 // propagate the payload
7383 if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy
7384 else { // too long
7385 const Unit *ul;
7386 Unit *ur, *uresp1;
7387 // copy safe number of units, then decapitate
7388 res->bits=lhs->bits; // need sign etc.
7389 uresp1=res->lsu+D2U(set->digits);
7390 #if !defined(__clang_analyzer__)
7391 for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
7392 #endif /* if !defined(__clang_analyzer__) */
7393 res->digits=D2U(set->digits)*DECDPUN;
7394 // maybe still too long
7395 if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
7396 }
7397
7398 res->bits&=~DECSNAN; // convert any sNaN to NaN, while
7399 res->bits|=DECNAN; // .. preserving sign
7400 res->exponent=0; // clean exponent
7401 // [coefficient was copied/decapitated]
7402 return res;
7403 } // decNaNs
7404
7405 /* ------------------------------------------------------------------ */
7406 /* decStatus -- apply non-zero status */
7407 /* */
7408 /* dn is the number to set if error */
7409 /* status contains the current status (not yet in context) */
7410 /* set is the context */
7411 /* */
7412 /* If the status is an error status, the number is set to a NaN, */
7413 /* unless the error was an overflow, divide-by-zero, or underflow, */
7414 /* in which case the number will have already been set. */
7415 /* */
7416 /* The context status is then updated with the new status. Note that */
7417 /* this may raise a signal, so control may never return from this */
7418 /* routine (hence resources must be recovered before it is called). */
7419 /* ------------------------------------------------------------------ */
7420 static void decStatus(decNumber *dn, uInt status, decContext *set) {
/* */
7421 if (status & DEC_NaNs) { // error status -> NaN
7422 // if cause was an sNaN, clear and propagate [NaN is already set up]
7423 if (status & DEC_sNaN) status&=~DEC_sNaN;
7424 else {
7425 decNumberZero(dn); // other error: clean throughout
7426 dn->bits=DECNAN; // and make a quiet NaN
7427 }
7428 }
7429 (void)decContextSetStatus(set, status); // [may not return]
7430 return;
7431 } // decStatus
7432
7433 /* ------------------------------------------------------------------ */
7434 /* decGetDigits -- count digits in a Units array */
7435 /* */
7436 /* uar is the Unit array holding the number (this is often an */
7437 /* accumulator of some sort) */
7438 /* len is the length of the array in units [>=1] */
7439 /* */
7440 /* returns the number of (significant) digits in the array */
7441 /* */
7442 /* All leading zeros are excluded, except the last if the array has */
7443 /* only zero Units. */
7444 /* ------------------------------------------------------------------ */
7445 // This may be called twice during some operations.
7446 static Int decGetDigits(Unit *uar, Int len) {
/* ![[last]](../icons/n_last.png)
*/
7447 Unit *up=uar+(len-1); // -> msu
7448 Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu
7449 #if DECDPUN>4
7450 uInt const *pow; // work
7451 #endif
7452 // (at least 1 in final msu)
7453 for (; up>=uar; up--) {
7454 if (*up==0) { // unit is all 0s
7455 if (digits==1) break; // a zero has one digit
7456 digits-=DECDPUN; // adjust for 0 unit
7457 continue;}
7458 // found the first (most significant) non-zero Unit
7459 #if DECDPUN>1 // not done yet
7460 if (*up<10) break; // is 1-9
7461 digits++;
7462 # if DECDPUN>2 // not done yet
7463 if (*up<100) break; // is 10-99
7464 digits++;
7465 # if DECDPUN>3 // not done yet
7466 if (*up<1000) break; // is 100-999
7467 digits++;
7468 # if DECDPUN>4 // count the rest ...
7469 for (pow=&powers[4]; *up>=*pow; pow++) digits++;
7470 # endif
7471 # endif
7472 # endif
7473 #endif
7474 break;
7475 } // up
7476 return digits;
7477 } // decGetDigits
![[bottom]](../icons/n_bottom.png){kind=icon}
*/