libgcc/config/libbid/bid_from_int.c

   1 /* Copyright (C) 2007-2017 Free Software Foundation, Inc.
   2
   3 This file is part of GCC.
   4
   5 GCC is free software; you can redistribute it and/or modify it under
   6 the terms of the GNU General Public License as published by the Free
   7 Software Foundation; either version 3, or (at your option) any later
   8 version.
   9
  10 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  11 WARRANTY; without even the implied warranty of MERCHANTABILITY or
  12 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  13 for more details.
  14
  15 Under Section 7 of GPL version 3, you are granted additional
  16 permissions described in the GCC Runtime Library Exception, version
  17 3.1, as published by the Free Software Foundation.
  18
  19 You should have received a copy of the GNU General Public License and
  20 a copy of the GCC Runtime Library Exception along with this program;
  21 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  22 <http://www.gnu.org/licenses/>.  */
  23
  24 #include "bid_internal.h"
  25
  26 /*****************************************************************************
  27  *  BID64_round_integral_exact
  28  ****************************************************************************/
  29
  30 #if DECIMAL_CALL_BY_REFERENCE
  31 void
  32 bid64_from_int32 (UINT64 * pres,
  33                   int *px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  34   int x = *px;
  35 #else
  36 UINT64
  37 bid64_from_int32 (int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  38 #endif
  39   UINT64 res;
  40
  41   // if integer is negative, put the absolute value
  42   // in the lowest 32bits of the result
  43   if ((x & SIGNMASK32) == SIGNMASK32) {
  44     // negative int32
  45     x = ~x + 1; // 2's complement of x
  46     res = (unsigned int) x | 0xb1c0000000000000ull;
  47     // (exp << 53)) = biased exp. is 0
  48   } else {      // positive int32
  49     res = x | 0x31c0000000000000ull;    // (exp << 53)) = biased exp. is 0
  50   }
  51   BID_RETURN (res);
  52 }
  53
  54 #if DECIMAL_CALL_BY_REFERENCE
  55 void
  56 bid64_from_uint32 (UINT64 * pres, unsigned int *px
  57                    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  58   unsigned int x = *px;
  59 #else
  60 UINT64
  61 bid64_from_uint32 (unsigned int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  62 #endif
  63   UINT64 res;
  64
  65   res = x | 0x31c0000000000000ull;      // (exp << 53)) = biased exp. is 0
  66   BID_RETURN (res);
  67 }
  68
  69 #if DECIMAL_CALL_BY_REFERENCE
  70 void
  71 bid64_from_int64 (UINT64 * pres, SINT64 * px
  72                   _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
  73                   _EXC_INFO_PARAM) {
  74   SINT64 x = *px;
  75 #if !DECIMAL_GLOBAL_ROUNDING
  76   unsigned int rnd_mode = *prnd_mode;
  77 #endif
  78 #else
  79 UINT64
  80 bid64_from_int64 (SINT64 x
  81                   _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
  82                   _EXC_INFO_PARAM) {
  83 #endif
  84
  85   UINT64 res;
  86   UINT64 x_sign, C;
  87   unsigned int q, ind;
  88   int incr_exp = 0;
  89   int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0;
  90   int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  91
  92   x_sign = x & 0x8000000000000000ull;
  93   // if the integer is negative, use the absolute value
  94   if (x_sign)
  95     C = ~((UINT64) x) + 1;
  96   else
  97     C = x;
  98   if (C <= BID64_SIG_MAX) {     // |C| <= 10^16-1 and the result is exact
  99     if (C < 0x0020000000000000ull) {    // C < 2^53
 100       res = x_sign | 0x31c0000000000000ull | C;
 101     } else {    // C >= 2^53
 102       res =
 103         x_sign | 0x6c70000000000000ull | (C & 0x0007ffffffffffffull);
 104     }
 105   } else {      // |C| >= 10^16 and the result may be inexact
 106     // the smallest |C| is 10^16 which has 17 decimal digits
 107     // the largest |C| is 0x8000000000000000 = 9223372036854775808 w/ 19 digits
 108     if (C < 0x16345785d8a0000ull) {     // x < 10^17
 109       q = 17;
 110       ind = 1;  // number of digits to remove for q = 17
 111     } else if (C < 0xde0b6b3a7640000ull) {      // C < 10^18
 112       q = 18;
 113       ind = 2;  // number of digits to remove for q = 18
 114     } else {    // C < 10^19
 115       q = 19;
 116       ind = 3;  // number of digits to remove for q = 19
 117     }
 118     // overflow and underflow are not possible
 119     // Note: performace can be improved by inlining this call
 120     round64_2_18 (      // will work for 19 digits too if C fits in 64 bits
 121                    q, ind, C, &res, &incr_exp,
 122                    &is_midpoint_lt_even, &is_midpoint_gt_even,
 123                    &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
 124     if (incr_exp)
 125       ind++;
 126     // set the inexact flag
 127     if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
 128         is_midpoint_lt_even || is_midpoint_gt_even)
 129       *pfpsf |= INEXACT_EXCEPTION;
 130     // general correction from RN to RA, RM, RP, RZ; result uses ind for exp
 131     if (rnd_mode != ROUNDING_TO_NEAREST) {
 132       if ((!x_sign
 133            && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint)
 134                ||
 135                ((rnd_mode == ROUNDING_TIES_AWAY
 136                  || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even)))
 137           || (x_sign
 138               && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint)
 139                   ||
 140                   ((rnd_mode == ROUNDING_TIES_AWAY
 141                     || rnd_mode == ROUNDING_DOWN)
 142                    && is_midpoint_gt_even)))) {
 143         res = res + 1;
 144         if (res == 0x002386f26fc10000ull) {     // res = 10^16 => rounding overflow
 145           res = 0x00038d7ea4c68000ull;  // 10^15
 146           ind = ind + 1;
 147         }
 148       } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) &&
 149                  ((x_sign && (rnd_mode == ROUNDING_UP ||
 150                               rnd_mode == ROUNDING_TO_ZERO)) ||
 151                   (!x_sign && (rnd_mode == ROUNDING_DOWN ||
 152                                rnd_mode == ROUNDING_TO_ZERO)))) {
 153         res = res - 1;
 154         // check if we crossed into the lower decade
 155         if (res == 0x00038d7ea4c67fffull) {     // 10^15 - 1
 156           res = 0x002386f26fc0ffffull;  // 10^16 - 1
 157           ind = ind - 1;
 158         }
 159       } else {
 160         ;       // exact, the result is already correct
 161       }
 162     }
 163     if (res < 0x0020000000000000ull) {  // res < 2^53
 164       res = x_sign | (((UINT64) ind + 398) << 53) | res;
 165     } else {    // res >= 2^53
 166       res =
 167         x_sign | 0x6000000000000000ull | (((UINT64) ind + 398) << 51) |
 168         (res & 0x0007ffffffffffffull);
 169     }
 170   }
 171   BID_RETURN (res);
 172 }
 173
 174 #if DECIMAL_CALL_BY_REFERENCE
 175 void
 176 bid64_from_uint64 (UINT64 * pres, UINT64 * px
 177                    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
 178                    _EXC_INFO_PARAM) {
 179   UINT64 x = *px;
 180 #if !DECIMAL_GLOBAL_ROUNDING
 181   unsigned int rnd_mode = *prnd_mode;
 182 #endif
 183 #else
 184 UINT64
 185 bid64_from_uint64 (UINT64 x
 186                    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
 187                    _EXC_INFO_PARAM) {
 188 #endif
 189
 190   UINT64 res;
 191   UINT128 x128, res128;
 192   unsigned int q, ind;
 193   int incr_exp = 0;
 194   int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0;
 195   int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
 196
 197   if (x <= BID64_SIG_MAX) {     // x <= 10^16-1 and the result is exact
 198     if (x < 0x0020000000000000ull) {    // x < 2^53
 199       res = 0x31c0000000000000ull | x;
 200     } else {    // x >= 2^53
 201       res = 0x6c70000000000000ull | (x & 0x0007ffffffffffffull);
 202     }
 203   } else {      // x >= 10^16 and the result may be inexact
 204     // the smallest x is 10^16 which has 17 decimal digits
 205     // the largest x is 0xffffffffffffffff = 18446744073709551615 w/ 20 digits
 206     if (x < 0x16345785d8a0000ull) {     // x < 10^17
 207       q = 17;
 208       ind = 1;  // number of digits to remove for q = 17
 209     } else if (x < 0xde0b6b3a7640000ull) {      // x < 10^18
 210       q = 18;
 211       ind = 2;  // number of digits to remove for q = 18
 212     } else if (x < 0x8ac7230489e80000ull) {     // x < 10^19
 213       q = 19;
 214       ind = 3;  // number of digits to remove for q = 19
 215     } else {    // x < 10^20
 216       q = 20;
 217       ind = 4;  // number of digits to remove for q = 20
 218     }
 219     // overflow and underflow are not possible
 220     // Note: performace can be improved by inlining this call
 221     if (q <= 19) {
 222       round64_2_18 (    // will work for 20 digits too if x fits in 64 bits
 223                      q, ind, x, &res, &incr_exp,
 224                      &is_midpoint_lt_even, &is_midpoint_gt_even,
 225                      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
 226     } else {    // q = 20
 227       x128.w[1] = 0x0;
 228       x128.w[0] = x;
 229       round128_19_38 (q, ind, x128, &res128, &incr_exp,
 230                       &is_midpoint_lt_even, &is_midpoint_gt_even,
 231                       &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
 232       res = res128.w[0];        // res.w[1] is 0
 233     }
 234     if (incr_exp)
 235       ind++;
 236     // set the inexact flag
 237     if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
 238         is_midpoint_lt_even || is_midpoint_gt_even)
 239       *pfpsf |= INEXACT_EXCEPTION;
 240     // general correction from RN to RA, RM, RP, RZ; result uses ind for exp
 241     if (rnd_mode != ROUNDING_TO_NEAREST) {
 242       if ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) ||
 243           ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP)
 244            && is_midpoint_gt_even)) {
 245         res = res + 1;
 246         if (res == 0x002386f26fc10000ull) {     // res = 10^16 => rounding overflow
 247           res = 0x00038d7ea4c68000ull;  // 10^15
 248           ind = ind + 1;
 249         }
 250       } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) &&
 251                  (rnd_mode == ROUNDING_DOWN ||
 252                   rnd_mode == ROUNDING_TO_ZERO)) {
 253         res = res - 1;
 254         // check if we crossed into the lower decade
 255         if (res == 0x00038d7ea4c67fffull) {     // 10^15 - 1
 256           res = 0x002386f26fc0ffffull;  // 10^16 - 1
 257           ind = ind - 1;
 258         }
 259       } else {
 260         ;       // exact, the result is already correct
 261       }
 262     }
 263     if (res < 0x0020000000000000ull) {  // res < 2^53
 264       res = (((UINT64) ind + 398) << 53) | res;
 265     } else {    // res >= 2^53
 266       res = 0x6000000000000000ull | (((UINT64) ind + 398) << 51) |
 267         (res & 0x0007ffffffffffffull);
 268     }
 269   }
 270   BID_RETURN (res);
 271 }
 272
 273 #if DECIMAL_CALL_BY_REFERENCE
 274 void
 275 bid128_from_int32 (UINT128 * pres,
 276                    int *px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 277   int x = *px;
 278 #else
 279 UINT128
 280 bid128_from_int32 (int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 281 #endif
 282   UINT128 res;
 283
 284   // if integer is negative, use the absolute value
 285   if ((x & SIGNMASK32) == SIGNMASK32) {
 286     res.w[HIGH_128W] = 0xb040000000000000ull;
 287     res.w[LOW_128W] = ~((unsigned int) x) + 1;  // 2's complement of x
 288   } else {
 289     res.w[HIGH_128W] = 0x3040000000000000ull;
 290     res.w[LOW_128W] = (unsigned int) x;
 291   }
 292   BID_RETURN (res);
 293 }
 294
 295 #if DECIMAL_CALL_BY_REFERENCE
 296 void
 297 bid128_from_uint32 (UINT128 * pres, unsigned int *px
 298                     _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 299   unsigned int x = *px;
 300 #else
 301 UINT128
 302 bid128_from_uint32 (unsigned int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 303 #endif
 304   UINT128 res;
 305
 306   res.w[HIGH_128W] = 0x3040000000000000ull;
 307   res.w[LOW_128W] = x;
 308   BID_RETURN (res);
 309 }
 310
 311 #if DECIMAL_CALL_BY_REFERENCE
 312 void
 313 bid128_from_int64 (UINT128 * pres, SINT64 * px
 314                    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 315   SINT64 x = *px;
 316 #else
 317 UINT128
 318 bid128_from_int64 (SINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 319 #endif
 320
 321   UINT128 res;
 322
 323   // if integer is negative, use the absolute value
 324   if ((x & SIGNMASK64) == SIGNMASK64) {
 325     res.w[HIGH_128W] = 0xb040000000000000ull;
 326     res.w[LOW_128W] = ~x + 1;   // 2's complement of x
 327   } else {
 328     res.w[HIGH_128W] = 0x3040000000000000ull;
 329     res.w[LOW_128W] = x;
 330   }
 331   BID_RETURN (res);
 332 }
 333
 334 #if DECIMAL_CALL_BY_REFERENCE
 335 void
 336 bid128_from_uint64 (UINT128 * pres, UINT64 * px
 337                     _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 338   UINT64 x = *px;
 339 #else
 340 UINT128
 341 bid128_from_uint64 (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
 342 #endif
 343
 344   UINT128 res;
 345
 346   res.w[HIGH_128W] = 0x3040000000000000ull;
 347   res.w[LOW_128W] = x;
 348   BID_RETURN (res);
 349 }