src/dps8/dps8_math128.c

/* */
This source file includes following definitions.
iszero_128
isnonzero_128
iseq_128
isgt_128
islt_128
isge_128
islt_s128
isgt_s128
and_128
and_s128
or_128
xor_128
complement_128
add_128
subtract_128
negate_128
negate_s128
lshift_128
lshift_s128
rshift_128
rshift_s128
mulmn
mulmns
nlz
divmnu
multiply_128
multiply_s128
divide_128
divide_128_16
divide_128_32
tisz
tand
tor
tcomp
tadd
tsub
tneg
tgt
tls
trs
tmul
tsmul
tdiv16
tdiv32
test_math128
__udivti3
__udivmodti3
__divti3
__modti3
__umodti3
__multi3
   1 /*
   2  * vim: filetype=c:tabstop=4:ai:expandtab
   3  * SPDX-License-Identifier: ICU
   4  * SPDX-License-Identifier: Multics
   5  * scspell-id: 928c0e86-f62e-11ec-ab5c-80ee73e9b8e7
   6  *
   7  * ---------------------------------------------------------------------------
   8  *
   9  * Copyright (c) 2016 Jean-Michel Merliot
  10  * Copyright (c) 2021-2022 The DPS8M Development Team
  11  *
  12  * All rights reserved.
  13  *
  14  * This software is made available under the terms of the ICU
  15  * License, version 1.8.1 or later.  For more details, see the
  16  * LICENSE.md file at the top-level directory of this distribution.
  17  *
  18  * ---------------------------------------------------------------------------
  19  *
  20  * This source file may contain code comments that adapt, include, and/or
  21  * incorporate Multics program code and/or documentation distributed under
  22  * the Multics License.  In the event of any discrepancy between code
  23  * comments herein and the original Multics materials, the original Multics
  24  * materials should be considered authoritative unless otherwise noted.
  25  * For more details and historical background, see the LICENSE.md file at
  26  * the top-level directory of this distribution.
  27  *
  28  * ---------------------------------------------------------------------------
  29  */
  30 
  31 #ifndef DPS8_MATH128
  32 # define DPS8_MATH128
  33 # include "dps8.h"
  34 # include "dps8_math128.h"
  35 
  36 # ifdef NEED_128
  37 
  38 bool iszero_128 (uint128 w)
     /*  */
  39   {
  40     if (w.h || w.l)
  41       return false;
  42     return true;
  43   }
  44 
  45 bool isnonzero_128 (uint128 w)
     /*  */
  46   {
  47     if (w.h || w.l)
  48       return true;
  49     return false;
  50   }
  51 
  52 bool iseq_128 (uint128 a, uint128 b)
     /*  */
  53   {
  54     return a.h == b.h && a.l == b.l;
  55   }
  56 
  57 bool isgt_128 (uint128 a, uint128 b)
     /*  */
  58   {
  59     if (a.h > b.h) return true;
  60     if (a.h < b.h) return false;
  61     if (a.l > b.l) return true;
  62     return false;
  63   }
  64 
  65 bool islt_128 (uint128 a, uint128 b)
     /*  */
  66   {
  67     if (a.h < b.h) return true;
  68     if (a.h > b.h) return false;
  69     if (a.l < b.l) return true;
  70     return false;
  71   }
  72 
  73 bool isge_128 (uint128 a, uint128 b)
     /*  */
  74   {
  75     if (a.h >  b.h) return true;
  76     if (a.h <  b.h) return false;
  77     if (a.l >= b.l) return true;
  78     return false;
  79   }
  80 
  81 bool islt_s128 (int128 a, int128 b)
     /*  */
  82   {
  83     if (a.h < b.h) return true;
  84     if (a.h > b.h) return false;
  85     if (a.l < b.l) return true;
  86     return false;
  87   }
  88 
  89 bool isgt_s128 (int128 a, int128 b)
     /*  */
  90   {
  91     if (a.h > b.h) return true;
  92     if (a.h < b.h) return false;
  93     if (a.l > b.l) return true;
  94     return false;
  95   }
  96 
  97 uint128 and_128 (uint128 a, uint128 b)
     /*  */
  98   {
  99     return (uint128) {a.h & b.h, a.l & b.l};
 100   }
 101 
 102 int128 and_s128 (int128 a, uint128 b)
     /*  */
 103   {
 104     return (int128) {a.h & (int64_t)b.h, a.l & b.l};
 105   }
 106 
 107 uint128 or_128 (uint128 a, uint128 b)
     /*  */
 108   {
 109     return (uint128) {a.h | b.h, a.l | b.l};
 110   }
 111 
 112 uint128 xor_128 (uint128 a, uint128 b)
     /*  */
 113   {
 114     return (uint128) {a.h ^ b.h, a.l ^ b.l};
 115   }
 116 
 117 uint128 complement_128 (uint128 a)
     /*  */
 118   {
 119     return (uint128) {~ a.h, ~ a.l};
 120   }
 121 
 122 uint128 add_128 (uint128 a, uint128 b)
     /*  */
 123   {
 124 // To do carry detection from low to high, bust the low into 1 bit/63
 125 // bit fields; add the 63 bit fields checking for carry in the "sign"
 126 // bit; add the 1 bit fields plus that carry
 127 
 128     uint64_t al63 = a.l & MASK63;  // low 63 bits of a
 129     uint64_t bl63 = b.l & MASK63;  // low 63 bits of b
 130     uint64_t l63 = al63 + bl63;    // low 63 bits of a + b, with carry into bit 64
 131     uint64_t c63 = l63 & SIGN64;   // the carry out of low 63 a + b
 132     l63 &= MASK63;                 // lose the carry bit
 133 
 134     unsigned int al64 = (a.l >> 63) & 1; // bit 64 of a
 135     unsigned int bl64 = (b.l >> 63) & 1; // bit 64 of b
 136     unsigned int cl64 = (c63 >> 63) & 1; // the carry out of bit 63
 137     uint64_t l64 = al64 + bl64 + cl64;   // bit 64 a + b + carry in
 138     unsigned int c64 = l64 > 1 ? 1 : 0;  // carry out of bit 64
 139     l64 = (l64 & 1) << 63;               // put bit 64 in the right place
 140     l64 |= l63;                          // put low 63 bits in
 141     uint64_t h64 = a.h + b.h + c64;      // compute the high
 142     return construct_128 (h64, l64);
 143   }
 144 
 145 uint128 subtract_128 (uint128 a, uint128 b)
     /*  */
 146   {
 147 //printf ("sub a %016llx %016llx\n", a.h, a.l);
 148 //printf ("sub b %016llx %016llx\n", b.h, b.l);
 149     bool borrow = !! (b.l > a.l);
 150     uint128 res = construct_128 (a.h - b.h, a.l - b.l);
 151     if (borrow)
 152       res.h --;
 153 //printf ("sub res %016llx %016llx\n", res.h, res.l);
 154     return res;
 155   }
 156 
 157 uint128 negate_128 (uint128 a)
     /*  */
 158   {
 159     return add_128 (complement_128 (a), construct_128 (0, 1));
 160   }
 161 
 162 int128 negate_s128 (int128 a)
     /*  */
 163   {
 164     uint128 t = add_128 (complement_128 (cast_128 (a)), construct_128 (0, 1));
 165     return cast_s128 (t);
 166   }
 167 
 168 uint128 lshift_128 (uint128 a, unsigned int n)
     /*  */
 169 #  if ( defined(__clang__) || defined(__clang_version__) ) && defined(__llvm__)
 170 #   ifdef NEED_128
 171 __attribute__ ((optnone))
 172 #   endif /* NEED_128 */
 173 #  endif /* if ( defined(__clang__) || defined(__clang_version__) ) && defined(__llvm__) */
 174   {
 175     if (n < 64)
 176       {
 177         uint64_t nmask = (uint64_t) ((~(MASK64 << n)));
 178 //printf ("nmask %016llx\r\n", nmask);
 179         // capture the high bits of the low half
 180         uint64_t keep = (a.l >> (64 - n)) & nmask;
 181 //printf ("keep %016llx\r\n", keep);
 182         // shift the low half
 183         uint64_t l = a.l << n;
 184 //printf ("l %016llx\r\n", l);
 185         // shift the high half
 186         uint64_t h = a.h << n;
 187 //printf ("h %016llx\r\n", h);
 188         // put the bits from the low into the high
 189         h |= keep;
 190 //printf ("h|keep %016llx\r\n", h);
 191         return construct_128 (h, l);
 192       }
 193     uint64_t h = a.l << (n - 64);
 194     return construct_128 (h, 0);
 195   }
 196 
 197 int128 lshift_s128 (int128 a, unsigned int n)
     /*  */
 198   {
 199     uint128 t = lshift_128 (cast_128 (a), n);
 200     return cast_s128 (t);
 201   }
 202 
 203 uint128 rshift_128 (uint128 a, unsigned int n)
     /*  */
 204   {
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 252 
 253     uint64_t h = a.h;
 254     uint64_t l = a.l;
 255     uint64_t sign = a.h & SIGN64;
 256     while (n)
 257       {
 258         uint64_t b = (h & 1) ? SIGN64 : 0;
 259         h >>= 1;
 260         h |= sign;
 261         l >>= 1;
 262         l &= MASK63;
 263         l |= b;
 264         n --;
 265       }
 266     return construct_128 (h, l);
 267   }
 268 
 269 int128 rshift_s128 (int128 a, unsigned int n)
     /*  */
 270   {
 271     uint128 t = rshift_128 (cast_128 (a), n);
 272     return cast_s128 (t);
 273   }
 274 
 275 // See: https://web.archive.org/web/20190219173849/http://www.hackersdelight.org/
 276 
 277 static void mulmn (uint32_t w[], uint32_t u[],
     /*  */
 278                    uint32_t v[], int m, int n)
 279   {
 280 //for (int i = m - 1; i >= 0; i --) fprintf (stderr, "%08x", u [i]);
 281 //fprintf (stderr, "  ");
 282 //for (int i = n - 1; i >= 0; i --) fprintf (stderr, "%08x", v [i]);
 283 //fprintf (stderr, "\n");
 284     uint64_t k, t;
 285     int i, j;
 286 
 287     for (i = 0; i < m; i++)
 288        w[i] = 0;
 289 
 290     for (j = 0; j < n; j++)
 291       {
 292         k = 0;
 293         for (i = 0; i < m; i++)
 294           {
 295             t = (uint64_t) u[i] * (uint64_t) v[j] + (uint64_t) w[i + j] + k;
 296 //printf ("%d %d %016llx\n",i, j, t);
 297             w[i + j] = (uint32_t) t;        // (i.e., t & 0xFFFF).
 298             k = t >> 32;
 299           }
 300         w[j + m] = (uint32_t) k;
 301       }
 302   }
 303 
 304 static void mulmns (uint32_t w[], uint32_t u[],
     /*  */
 305                     uint32_t v[], int m, int n)
 306   {
 307     mulmn (w, u, v, m, n);
 308 
 309     // Now w[] has the unsigned product. Correct by
 310     // subtracting v*2**16m if u < 0, and
 311     // subtracting u*2**16n if v < 0.
 312 
 313     if ((int32_t)u[m - 1] < 0)
 314       {
 315         int b = 0;  // Initialize borrow.
 316         for (int j = 0; j < n; j++)
 317           {
 318             int t = (int) w[j + m] - (int) v[j] - b;
 319             w[j + m] = (uint32_t) t;
 320             b = (t & 0x40000000) ? 1 : 0;
 321           }
 322       }
 323     if ((int32_t)v[n - 1] < 0)
 324       {
 325         int b = 0;
 326         for (int i = 0; i < m; i++)
 327           {
 328             int t = (int) w[i + n] - (int) u[i] - b;
 329             w[i + n] = (uint32_t) t;
 330             b = (t & 0x40000000) ? 1 : 0;
 331           }
 332       }
 333     return;
 334   }
 335 
 336 static int
 337 nlz (unsigned x)
     /*  */
 338 {
 339   int n;
 340 
 341   if (x == 0)
 342     return (32);
 343 
 344   n = 0;
 345 
 346   if (x <= 0x0000FFFF)
 347     {
 348       n = n  + 16;
 349       x = x << 16;
 350     }
 351 
 352   if (x <= 0x00FFFFFF)
 353     {
 354       n = n  + 8;
 355       x = x << 8;
 356     }
 357 
 358   if (x <= 0x0FFFFFFF)
 359     {
 360       n = n  + 4;
 361       x = x << 4;
 362     }
 363 
 364   if (x <= 0x3FFFFFFF)
 365     {
 366       n = n  + 2;
 367       x = x << 2;
 368     }
 369 
 370   if (x <= 0x7FFFFFFF)
 371     {
 372       n = n + 1;
 373     }
 374 
 375   return n;
 376 }
 377 
 378 unsigned int kd_div_errors = 0;
 379 
 380 int divmnu (uint16_t q[], uint16_t r[],
     /*  */
 381             const uint16_t u[], const uint16_t v[],
 382             int m, int n)
 383   {
 384 
 385     const uint32_t b = 65536;   // Number base (16 bits).
 386     //uint16_t *un, *vn;        // Normalized form of u, v.
 387     unsigned qhat;              // Estimated quotient digit.
 388     unsigned rhat;              // A remainder.
 389     unsigned p;                 // Product of two digits.
 390     int s, i, j, t, k;
 391 
 392     if (m < n || n <= 0 || v[n-1] == 0)
 393       return 1;                 // Return if invalid param.
 394 
 395     // Take care of the case of a single-digit span
 396     if (n == 1)
 397       {
 398         k = 0;
 399         for (j = m - 1; j >= 0; j--)
 400           {
 401             q[j] = (uint16_t) (((unsigned int) k*b + u[j])/v[0]);    // divisor here.
 402             k = (int) (((unsigned int) k*b + u[j]) - q[j]*v[0]);
 403           }
 404         if (r != NULL) r[0] = (uint16_t) k;
 405         return 0;
 406       }
 407 
 408     // Normalize by shifting v left just enough so that
 409     // its high-order bit is on, and shift u left the
 410     // same amount. We may have to append a high-order
 411     // digit on the dividend; we do that unconditionally.
 412 
 413     s = nlz (v[n-1]) - 16;      // 0 <= s <= 16.
 414     //vn = (uint16_t *) alloca (2*n);
 415     uint16_t vn [n];
 416     for (i = n - 1; i > 0; i--)
 417       vn[i] = (uint16_t) (v[i] << s) | (uint16_t) (v[i-1] >> (16-s));
 418     vn[0] = (uint16_t) (v[0] << s);
 419 
 420     //un = (uint16_t *)alloca(2*(m + 1));
 421     uint16_t un [m+1];
 422     un[m] = u[m-1] >> (16-s);
 423     for (i = m - 1; i > 0; i--)
 424       un[i] = (uint16_t) (u[i] << s) | (uint16_t) (u[i-1] >> (16-s));
 425     un[0] = (uint16_t) (u[0] << s);
 426     for (j = m - n; j >= 0; j--)
 427       {       // Main loop.
 428         // Compute estimate qhat of q[j].
 429         qhat = (un[j+n]*b + un[j+n-1])/vn[n-1];
 430         rhat = (un[j+n]*b + un[j+n-1])%vn[n-1];
 431 cmp_again:
 432         if (qhat >= b || (unsigned)qhat*(unsigned long long)vn[n-2] > b*rhat + un[j+n-2])
 433           {
 434             qhat = qhat - 1;
 435             rhat = rhat + vn[n-1];
 436             if (rhat < b) goto cmp_again;
 437           }
 438 
 439         // Multiply and subtract.
 440         k = 0;
 441         for (i = 0; i < n; i++)
 442           {
 443             p = (unsigned)qhat*(unsigned long long)vn[i];
 444             t = (int32_t) un[i+j] - k - (int32_t) (p & 0xFFFF);
 445             un[i+j] = (uint16_t) t;
 446             k = (int) (p >> 16) - (t >> 16);
 447           }
 448         t = un[j+n] - k;
 449         un[j+n] = (uint16_t) t;
 450 
 451         q[j] = (uint16_t) qhat;  // Store quotient digit.
 452         if (t < 0)
 453           {                      // If we subtracted too
 454             q[j] = q[j] - 1;     // much, add back.
 455             k = 0;
 456             for (i = 0; i < n; i++)
 457               {
 458                 t = un[i+j] + vn[i] + k;
 459                 un[i+j] = (uint16_t) t;
 460                 k = t >> 16;
 461                }
 462              un[j+n] = (uint16_t) (un[j+n] + k);
 463           }
 464       } // End j.
 465     // If the caller wants the remainder, denormalize
 466     // it and pass it back.
 467     if (r != NULL)
 468       {
 469         for (i = 0; i < n; i++)
 470           r[i] = (uint16_t) (un[i] >> s) | (uint16_t) (un[i+1] << (16-s));
 471       }
 472     return 0;
 473   }
 474 
 475 uint128 multiply_128 (uint128 a, uint128 b)
     /*  */
 476   {
 477 //printf ("%016llx%016llx %016llx%016llx\n", a.h,a.l,b.h,b.l);
 478     const int l = 4;
 479     uint32_t w[l+l], u[l], v[l];
 480 
 481     u[3] = (uint32_t) (a.h >> 32);
 482     u[2] = (uint32_t)  a.h;
 483     u[1] = (uint32_t) (a.l >> 32);
 484     u[0] = (uint32_t)  a.l;
 485     v[3] = (uint32_t) (b.h >> 32);
 486     v[2] = (uint32_t)  b.h;
 487     v[1] = (uint32_t) (b.l >> 32);
 488     v[0] = (uint32_t)  b.l;
 489     mulmn (w, u, v, l, l);
 490     return construct_128 (
 491        (((uint64_t) w[3]) << 32) | w[2],
 492        (((uint64_t) w[1]) << 32) | w[0]);
 493   }
 494 
 495 int128 multiply_s128 (int128 a, int128 b)
     /*  */
 496   {
 497 //printf ("%016llx%016llx %016llx%016llx\n", a.h,a.l,b.h,b.l);
 498     const int l = 4;
 499     uint32_t w[l+l], u[l], v[l];
 500 
 501     u[3] = (uint32_t) (a.h >> 32);
 502     u[2] = (uint32_t)  a.h;
 503     u[1] = (uint32_t) (a.l >> 32);
 504     u[0] = (uint32_t)  a.l;
 505     v[3] = (uint32_t) (b.h >> 32);
 506     v[2] = (uint32_t)  b.h;
 507     v[1] = (uint32_t) (b.l >> 32);
 508     v[0] = (uint32_t)  b.l;
 509     mulmns (w, u, v, l, l);
 510     return construct_s128 (
 511        (((int64_t)  w[3]) << 32) | w[2],
 512        (((uint64_t) w[1]) << 32) | w[0]);
 513   }
 514 
 515 // Note: divisor is < 2^16
 516 uint128 divide_128 (uint128 a, uint128 b, uint128 * remp)
     /*  */
 517   {
 518     const int m = 8;
 519     const int n = 8;
 520     uint16_t q[m], u[m], v[n];
 521     u[0] = (uint16_t)  a.l;
 522     u[1] = (uint16_t) (a.l >> 16);
 523     u[2] = (uint16_t) (a.l >> 32);
 524     u[3] = (uint16_t) (a.l >> 48);
 525     u[4] = (uint16_t)  a.h;
 526     u[5] = (uint16_t) (a.h >> 16);
 527     u[6] = (uint16_t) (a.h >> 32);
 528     u[7] = (uint16_t) (a.h >> 48);
 529 
 530     v[0] = (uint16_t)  b.l;
 531     v[1] = (uint16_t) (b.l >> 16);
 532     v[2] = (uint16_t) (b.l >> 32);
 533     v[3] = (uint16_t) (b.l >> 48);
 534     v[4] = (uint16_t)  b.h;
 535     v[5] = (uint16_t) (b.h >> 16);
 536     v[6] = (uint16_t) (b.h >> 32);
 537     v[7] = (uint16_t) (b.h >> 48);
 538 
 539     q[0] = q[1] = q[2] = q[3] = q[4] = q[5] = q[6] = q[7] = 0;
 540 
 541     int normlen;
 542     for (normlen = 8; normlen > 0; normlen --)
 543       if (v [normlen - 1])
 544         break;
 545     uint16_t r [8] = { 8 * 0 };
 546     divmnu (q, remp ? r : NULL, u, v, m, normlen);
 547     if (remp)
 548       {
 549         * remp =  construct_128 (
 550        (((uint64_t) r [7]) << 48) |
 551        (((uint64_t) r [6]) << 32) |
 552        (((uint64_t) r [5]) << 16) |
 553        (((uint64_t) r [4]) <<  0),
 554        (((uint64_t) r [3]) << 48) |
 555        (((uint64_t) r [2]) << 32) |
 556        (((uint64_t) r [1]) << 16) |
 557        (((uint64_t) r [0]) <<  0));
 558       }
 559     return construct_128 (
 560        (((uint64_t) q [7]) << 48) |
 561        (((uint64_t) q [6]) << 32) |
 562        (((uint64_t) q [5]) << 16) |
 563        (((uint64_t) q [4]) <<  0),
 564        (((uint64_t) q [3]) << 48) |
 565        (((uint64_t) q [2]) << 32) |
 566        (((uint64_t) q [1]) << 16) |
 567        (((uint64_t) q [0]) <<  0));
 568   }
 569 
 570 // Note: divisor is < 2^16
 571 uint128 divide_128_16 (uint128 a, uint16_t b, uint16_t * remp)
     /*  */
 572   {
 573     const int m = 8;
 574     const int n = 1;
 575     uint16_t q[m], u[m], v[n];
 576     u[0] = (uint16_t)  a.l;
 577     u[1] = (uint16_t) (a.l >> 16);
 578     u[2] = (uint16_t) (a.l >> 32);
 579     u[3] = (uint16_t) (a.l >> 48);
 580     u[4] = (uint16_t)  a.h;
 581     u[5] = (uint16_t) (a.h >> 16);
 582     u[6] = (uint16_t) (a.h >> 32);
 583     u[7] = (uint16_t) (a.h >> 48);
 584 
 585     v[0] = (uint16_t) b;
 586 
 587     q[0] = q[1] = q[2] = q[3] = q[4] = q[5] = q[6] = q[7] = 0;
 588 
 589     divmnu (q, remp, u, v, m, n);
 590     return construct_128 (
 591        (((uint64_t) q [7]) << 48) |
 592        (((uint64_t) q [6]) << 32) |
 593        (((uint64_t) q [5]) << 16) |
 594        (((uint64_t) q [4]) <<  0),
 595        (((uint64_t) q [3]) << 48) |
 596        (((uint64_t) q [2]) << 32) |
 597        (((uint64_t) q [1]) << 16) |
 598        (((uint64_t) q [0]) <<  0));
 599   }
 600 
 601 //divide_128_32 (
 602 //00000000000000010000000000000000, 00010000) returned
 603 //00000000000000000001000000000000, 00000000
 604 //divide_128_32 (ffffffffffffffffffffffffffffffff, 00010000) returned f771ffffffffffffffffffffffffffff, 0000ffff
 605 
 606 // Note: divisor is < 2^32 and >= 2^16; i.e. high 16 bits *must* be non-zero
 607 uint128 divide_128_32 (uint128 a, uint32_t b, uint32_t * remp)
     /*  */
 608   {
 609     const int m = 8;
 610     const int n = 2;
 611     uint16_t q[m], u[m], v[n], r[2];
 612     u[0] = (uint16_t)  a.l;
 613     u[1] = (uint16_t) (a.l >> 16);
 614     u[2] = (uint16_t) (a.l >> 32);
 615     u[3] = (uint16_t) (a.l >> 48);
 616     u[4] = (uint16_t)  a.h;
 617     u[5] = (uint16_t) (a.h >> 16);
 618     u[6] = (uint16_t) (a.h >> 32);
 619     u[7] = (uint16_t) (a.h >> 48);
 620 
 621     v[0] = (uint16_t) b;
 622     v[1] = (uint16_t) (b >> 16);
 623 
 624     q[0] = q[1] = q[2] = q[3] = q[4] = q[5] = q[6] = q[7] = 0;
 625 
 626     divmnu (q, remp ? r : NULL, u, v, m, n);
 627     if (remp)
 628       * remp = r [0] | (uint32_t) r[1] << 16;
 629 
 630     return construct_128 (
 631        (((uint64_t) q [7]) << 48) |
 632        (((uint64_t) q [6]) << 32) |
 633        (((uint64_t) q [5]) << 16) |
 634        (((uint64_t) q [4]) <<  0),
 635        (((uint64_t) q [3]) << 48) |
 636        (((uint64_t) q [2]) << 32) |
 637        (((uint64_t) q [1]) << 16) |
 638        (((uint64_t) q [0]) <<  0));
 639   }
 640 
 641 unsigned ti_test_iter = 0;
 642 
 643 static void tisz (uint64_t h, uint64_t l, bool expect)
     /*  */
 644   {
 645     bool r = iszero_128 (construct_128 (h, l));
 646     ti_test_iter++;
 647     if (r != expect) {
 648       fprintf (stderr, "FATAL (%u): iszero_128 (%llu, %llu) returned %lu\n",
 649                ti_test_iter,
 650                (unsigned long long)h, (unsigned long long)l, (unsigned long)r);
 651       kd_div_errors++;
 652     }
 653   }
 654 
 655 static void tand (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 656                   uint64_t rh, uint64_t rl)
 657   {
 658     uint128 a = construct_128 (ah, al);
 659     uint128 b = construct_128 (bh, bl);
 660     uint128 r = and_128 (a, b);
 661     ti_test_iter++;
 662     if (r.h != rh || r.l != rl) {
 663       fprintf (stderr, "FATAL (%u): and_128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 664                ti_test_iter,
 665                (unsigned long long)ah, (unsigned long long)al,  (unsigned long long)bh,
 666                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 667       kd_div_errors++;
 668     }
 669   }
 670 
 671 static void tor (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 672                  uint64_t rh, uint64_t rl)
 673   {
 674     uint128 a = construct_128 (ah, al);
 675     uint128 b = construct_128 (bh, bl);
 676     uint128 r = or_128 (a, b);
 677     ti_test_iter++;
 678     if (r.h != rh || r.l != rl) {
 679       fprintf (stderr, "FATAL (%u): or_128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 680                ti_test_iter,
 681                (unsigned long long)ah, (unsigned long long)al, (unsigned long long)bh,
 682                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 683       kd_div_errors++;
 684     }
 685   }
 686 
 687 static void tcomp (uint64_t ah, uint64_t al,
     /*  */
 688                    uint64_t rh, uint64_t rl)
 689   {
 690     uint128 a = construct_128 (ah, al);
 691     uint128 r = complement_128 (a);
 692     ti_test_iter++;
 693     if (r.h != rh || r.l != rl) {
 694       fprintf (stderr, "FATAL (%u): complement_128 (%016llx%016llx) returned %016llx%016llx\n",
 695                ti_test_iter,
 696                (unsigned long long)ah, (unsigned long long)al, (unsigned long long)r.h,
 697                (unsigned long long)r.l);
 698       kd_div_errors++;
 699     }
 700   }
 701 
 702 static void tadd (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 703                   uint64_t rh, uint64_t rl)
 704   {
 705     uint128 a = construct_128 (ah, al);
 706     uint128 b = construct_128 (bh, bl);
 707     uint128 r = add_128 (a, b);
 708     ti_test_iter++;
 709     if (r.h != rh || r.l != rl) {
 710       fprintf (stderr, "FATAL %u): add_128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 711                ti_test_iter,
 712                (unsigned long long)ah, (unsigned long long)al,  (unsigned long long)bh,
 713                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 714       kd_div_errors++;
 715     }
 716   }
 717 
 718 static void tsub (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 719                   uint64_t rh, uint64_t rl)
 720   {
 721     uint128 a = construct_128 (ah, al);
 722     uint128 b = construct_128 (bh, bl);
 723     uint128 r = subtract_128 (a, b);
 724     ti_test_iter++;
 725     if (r.h != rh || r.l != rl) {
 726       fprintf (stderr, "FATAL (%u): subtract_128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 727                ti_test_iter,
 728                (unsigned long long)ah, (unsigned long long)al,  (unsigned long long)bh,
 729                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 730       kd_div_errors++;
 731     }
 732   }
 733 
 734 static void tneg (uint64_t ah, uint64_t al,
     /*  */
 735                   uint64_t rh, uint64_t rl)
 736   {
 737     uint128 a = construct_128 (ah, al);
 738     uint128 r = negate_128 (a);
 739     ti_test_iter++;
 740     if (r.h != rh || r.l != rl) {
 741       fprintf (stderr, "FATAL (%u): negate_128 (%016llx%016llx) returned %016llx%016llx\n",
 742                ti_test_iter,
 743                (unsigned long long)ah, (unsigned long long)al, (unsigned long long)r.h,
 744                (unsigned long long)r.l);
 745       kd_div_errors++;
 746     }
 747   }
 748 
 749 static void tgt (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 750                  bool expect)
 751   {
 752     uint128 a = construct_128 (ah, al);
 753     uint128 b = construct_128 (bh, bl);
 754     ti_test_iter++;
 755     bool r = isgt_128 (a, b);
 756     if (r != expect) {
 757       fprintf (stderr, "FATAL (%u): gt_128 (%016llx%016llx, %016llx%016llx) returned %llu\n",
 758                ti_test_iter,
 759                (unsigned long long)ah, (unsigned long long)al, (unsigned long long)bh,
 760                (unsigned long long)bl, (unsigned long long)r);
 761       kd_div_errors++;
 762     }
 763   }
 764 
 765 static void tls (uint64_t ah, uint64_t al, unsigned int n,
     /*  */
 766                  uint64_t rh, uint64_t rl)
 767   {
 768     uint128 a = construct_128 (ah, al);
 769     uint128 r = lshift_128 (a, n);
 770     ti_test_iter++;
 771     if (r.h != rh || r.l != rl) {
 772       fprintf (stderr, "FATAL (%u): lshift_128 (%016llx%016llx, %llu) returned %016llx%016llx\n",
 773                ti_test_iter,
 774                (unsigned long long)ah,  (unsigned long long)al, (unsigned long long)n,
 775                (unsigned long long)r.h, (unsigned long long)r.l);
 776       kd_div_errors++;
 777     }
 778   }
 779 
 780 static void trs (uint64_t ah, uint64_t al, unsigned int n,
     /*  */
 781                  uint64_t rh, uint64_t rl)
 782   {
 783     uint128 a = construct_128 (ah, al);
 784     uint128 r = rshift_128 (a, n);
 785     ti_test_iter++;
 786     if (r.h != rh || r.l != rl) {
 787       fprintf (stderr, "FATAL (%u): rshift_128 (%016llx%016llx, %llu) returned %016llx%016llx\n",
 788                ti_test_iter,
 789                (unsigned long long)ah,  (unsigned long long)al, (unsigned long long)n,
 790                (unsigned long long)r.h, (unsigned long long)r.l);
 791       kd_div_errors++;
 792     }
 793   }
 794 
 795 static void tmul (uint64_t ah, uint64_t al, uint64_t bh, uint64_t bl,
     /*  */
 796                   uint64_t rh, uint64_t rl)
 797   {
 798     uint128 a = construct_128 (ah, al);
 799     uint128 b = construct_128 (bh, bl);
 800     uint128 r = multiply_128 (a, b);
 801     ti_test_iter++;
 802     if (r.h != rh || r.l != rl) {
 803       fprintf (stderr, "FATAL (%u): multiply_128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 804                ti_test_iter,
 805                (unsigned long long)ah, (unsigned long long)al,  (unsigned long long)bh,
 806                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 807       kd_div_errors++;
 808     }
 809   }
 810 
 811 static void tsmul (int64_t ah, uint64_t al, int64_t bh, uint64_t bl,
     /*  */
 812                    int64_t rh, uint64_t rl)
 813   {
 814     int128 a = construct_s128 (ah, al);
 815     int128 b = construct_s128 (bh, bl);
 816     int128 r = multiply_s128 (a, b);
 817     ti_test_iter++;
 818     if (r.h != rh || r.l != rl) {
 819       fprintf (stderr, "FATAL (%u): multiply_s128 (%016llx%016llx, %016llx%016llx) returned %016llx%016llx\n",
 820                ti_test_iter,
 821                (unsigned long long)ah, (unsigned long long)al,  (unsigned long long)bh,
 822                (unsigned long long)bl, (unsigned long long)r.h, (unsigned long long)r.l);
 823       kd_div_errors++;
 824     }
 825   }
 826 
 827 static void tdiv16 (uint64_t ah, uint64_t al, uint16_t b,
     /*  */
 828                     uint64_t resh, uint64_t resl,
 829                     uint16_t remainder)
 830   {
 831     uint128 a = construct_128 (ah, al);
 832     uint16_t rem;
 833     uint128 res = divide_128_16 (a, b, & rem);
 834     ti_test_iter++;
 835     if (res.h != resh || res.l != resl || rem != remainder) {
 836       fprintf (stderr, "FATAL (%u): divide_128_16 (%016llx%016llx, %04x) returned %016llx%016llx, %04x\n",
 837                ti_test_iter,
 838                (unsigned long long)ah,    (unsigned long long)al, b,
 839                (unsigned long long)res.h, (unsigned long long)res.l, rem);
 840       kd_div_errors++;
 841     }
 842   }
 843 
 844 static void tdiv32 (uint64_t ah, uint64_t al, uint32_t b,
     /*  */
 845                     uint64_t resh, uint64_t resl,
 846                     uint32_t remainder)
 847   {
 848     uint128 a = construct_128 (ah, al);
 849     uint32_t rem;
 850     uint128 res = divide_128_32 (a, b, & rem);
 851     ti_test_iter++;
 852     if (res.h != resh || res.l != resl || rem != remainder) {
 853       fprintf (stderr, "FATAL (%u): divide_128_32 (%016llx%016llx, %08x) returned %016llx%016llx, %08x\n",
 854                ti_test_iter,
 855                (unsigned long long)ah,    (unsigned long long)al, b,
 856                (unsigned long long)res.h, (unsigned long long)res.l, rem);
 857       kd_div_errors++;
 858     }
 859   }
 860 
 861 int test_math128 (void)
     /*  */
 862   {
 863     tisz   (0,      0,      true);
 864     tisz   (1,      0,      false);
 865     tisz   (0,      1,      false);
 866     tisz   (1,      1,      false);
 867     tisz   (SIGN64, 0,      false);
 868     tisz   (0,      SIGN64, false);
 869     tisz   (SIGN64, SIGN64, false);
 870     tneg   (0,      0,      0,      0);
 871     tneg   (MASK64, MASK64, 0,      1);
 872     tcomp  (MASK64, MASK64, 0,      0);
 873     tneg   (0,      1,      MASK64, MASK64);
 874     tcomp  (0,      0,      MASK64, MASK64);
 875     tcomp  (0,      1,      MASK64, MASK64-1);
 876     tgt    (0,      0,      0,      0,          false);
 877     tgt    (0,      0,      0,      1,          false);
 878     tgt    (0,      1,      0,      0,          true);
 879     tgt    (MASK64, MASK64, MASK64, MASK64,     false);
 880     tgt    (0,      0,      MASK64, MASK64,     false);
 881     tgt    (MASK64, MASK64, 0,      0,          true);
 882 #  ifndef __PGI
 883 #   ifndef __PGLLVM__
 884 #    ifndef __NVCOMPILER
 885 #     ifndef __NVCOMPILER_LLVM__
 886     tls    (0,      0,      0,      0,          0);
 887     tls    (MASK64, MASK64, 0,      MASK64,     MASK64);
 888 #     endif /* ifndef __PGI */
 889 #    endif /* ifndef __PGLLVM__ */
 890 #   endif /* ifndef __NVCOMPILER */
 891 #  endif /* ifndef __NVCOMPILER_LLVM__ */
 892     tls    (0,      1,      127,    SIGN64,     0);
 893     tls    (0,      MASK64, 64,     MASK64,     0);
 894     tls    (0,      MASK64, 1,      1,          MASK64-1);
 895     tls    (0,      1,      64,     1,          0);
 896     tls    (0,      1,      63,     0,          SIGN64);
 897     tls    (1,      0,      63,     SIGN64,     0);
 898     trs    (0,      0,      0,      0,          0);
 899     trs    (SIGN64, 0,      127,    MASK64,     MASK64);
 900     trs    (MASK64, 0,      64,     MASK64,     MASK64);
 901     trs    (MASK64, 0,      1,      MASK64,     SIGN64);
 902     trs    (1,      0,      64,     0,          1);
 903     trs    (1,      0,      1,      0,          SIGN64);
 904     trs    (MASK64, MASK64, 0,      MASK64,     MASK64);
 905     trs    (SIGN64, 0,      63,     MASK64,     0);
 906     trs    (SIGN64, 0,      64,     MASK64,     SIGN64);
 907     tand   (0,      0,      0,      0,          0,       0);
 908     tand   (MASK64, MASK64, 0,      0,          0,       0);
 909     tand   (0,      0,      MASK64, MASK64,     0,       0);
 910     tand   (MASK64, MASK64, MASK64, MASK64,     MASK64,  MASK64);
 911     tor    (0,      0,      0,      0,          0,       0);
 912     tor    (MASK64, MASK64, 0,      0,          MASK64,  MASK64);
 913     tor    (0,      0,      MASK64, MASK64,     MASK64,  MASK64);
 914     tor    (MASK64, MASK64, MASK64, MASK64,     MASK64,  MASK64);
 915     tadd   (0,      0,      0,      0,          0,       0);
 916     tadd   (0,      0,      0,      1,          0,       1);
 917     tadd   (0,      1,      0,      0,          0,       1);
 918     tadd   (0,      1,      0,      1,          0,       2);
 919     tadd   (0,      1,      0,      MASK64,     1,       0);
 920     tadd   (0,      1,      MASK64, MASK64,     0,       0);
 921     tsub   (0,      0,      0,      0,          0,       0);
 922     tsub   (0,      1,      0,      1,          0,       0);
 923     tsub   (MASK64, MASK64, MASK64, MASK64,     0,       0);
 924     tsub   (MASK64, MASK64, 0,      0,          MASK64,  MASK64);
 925     tsub   (0,      0,      0,      1,          MASK64,  MASK64);
 926     tmul   (0,      0,      0,      0,          0,       0);
 927     tmul   (MASK64, MASK64, 0,      0,          0,       0);
 928     tmul   (0,      0,      MASK64, MASK64,     0,       0);
 929     tmul   (0,      1,      0,      1,          0,       1);
 930     tmul   (0,      1,      0,      10,         0,       10);
 931     tmul   (0,      10,     0,      10,         0,       100);
 932     tmul   (0,      100,    0,      10,         0,       1000);
 933     tmul   (0,      MASK64, 0,      2,          1,       MASK64-1);
 934     tmul   (MASK64, MASK64, MASK64, MASK64,     0,       1);
 935     tdiv16 (MASK64,   MASK64, 16,   MASK64>>4,  MASK64,  15);
 936     tsmul  (0,      1,      MASK64, MASK64,     MASK64,  MASK64);
 937     tsmul  (MASK64, MASK64, MASK64, MASK64,     0,       1);
 938     tdiv32 (1,      0,      1<<16,  0,          1ll<<48, 0);
 939     tdiv16 (0,      1,      1,      0,          1,       0);
 940     tdiv16 (0,      10,     2,      0,          5,       0);
 941     tdiv16 (0,      3,      2,      0,          1,       1);
 942     tdiv32 (MASK64, MASK64, 1<<16,  MASK64>>16, MASK64,  0xffff);
 943     if (kd_div_errors)
 944       abort();
 945     return 0;
 946   }
 947 # else
 948 #  ifdef NEED_128
 949 #   include "dps8_math128.h"
 950 
 951 void __udivmodti3(UTItype div, UTItype dvd,UTItype *result,UTItype *remain);
 952 UTItype __udivti3(UTItype div, UTItype dvd);
 953 UTItype __umodti3(UTItype div, UTItype dvd);
 954 
 955 UTItype __udivti3(UTItype div, UTItype dvd)
     /*  */
 956 {
 957         UTItype result,remain;
 958 
 959         __udivmodti3(div,dvd,&result,&remain);
 960 
 961         return result;
 962 }
 963 
 964 void __udivmodti3(UTItype div, UTItype dvd,UTItype *result,UTItype *remain)
     /*  */
 965 {
 966         UTItype z1 = dvd;
 967         UTItype z2 = (UTItype)1;
 968 
 969         *result = (UTItype)0;
 970         *remain = div;
 971 
 972         if ( z1 == (UTItype)0)
 973 #   ifndef CPPCHECK
 974           1/0;
 975 #   else
 976           abort();
 977 #   endif /* ifndef CPPCHECK */
 978 
 979         while ( z1 < *remain )
 980           {
 981             z1 <<= 1 ;
 982             z2 <<= 1;
 983           }
 984 
 985         do
 986           {
 987             if ( *remain >= z1 )
 988               {
 989                 *remain -= z1;
 990                 *result += z2;
 991               }
 992             z1 >>= 1;
 993             z2 >>= 1;
 994           } while ( z2 );
 995 }
 996 
 997 TItype __divti3(TItype div, TItype dvd)
     /*  */
 998 {
 999         int sign=1;
1000 
1001         if (div < (TItype)0)
1002           {
1003             sign = -1;
1004             div = -div;
1005           }
1006 
1007         if (dvd < (TItype)0)
1008           {
1009             sign = -sign;
1010             dvd = -dvd;
1011           }
1012 
1013         if (sign > 0)
1014           return (TItype)__udivti3(div,dvd);
1015         else
1016           return -((TItype)__udivti3(div,dvd));
1017 }
1018 
1019 TItype __modti3(TItype div, TItype dvd)
     /*  */
1020 {
1021         int sign=1;
1022 
1023         if (div < (TItype)0)
1024           {
1025             sign = -1;
1026             div = -div;
1027           }
1028 
1029         if (dvd < (TItype)0)
1030           {
1031             sign = -sign;
1032             dvd = -dvd;
1033           }
1034 
1035         if (sign > 0)
1036           return (TItype)__umodti3(div,dvd);
1037         else
1038           return ((TItype)0-(TItype)__umodti3(div,dvd));
1039 }
1040 
1041 UTItype __umodti3(UTItype div, UTItype dvd)
     /*  */
1042 {
1043         UTItype result,remain;
1044 
1045         __udivmodti3(div,dvd,&result,&remain);
1046 
1047         return remain;
1048 }
1049 
1050 TItype __multi3 (TItype u, TItype v)
     /*  */
1051 {
1052         TItype result = (TItype)0;
1053         int sign = 1;
1054 
1055         if (u<0)
1056           {
1057             sign = -1;
1058             u = -u;
1059           }
1060 
1061         while (u != (TItype)0)
1062           {
1063             if ( u&(TItype)1 )
1064               result += v;
1065             u>>=1;
1066             v<<=1;
1067           }
1068 
1069         if ( sign < 0 )
1070           return -result;
1071         else
1072           return result;
1073 }
1074 #  endif
1075 # endif
1076 #endif
/* */
root/src/dps8/dps8_math128.c

DEFINITIONS
