Richard Henderson | 7c45bad | 2020-10-23 16:47:04 -0700 | [diff] [blame] | 1 | /* |
| 2 | * QEMU float support |
| 3 | * |
| 4 | * The code in this source file is derived from release 2a of the SoftFloat |
| 5 | * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and |
| 6 | * some later contributions) are provided under that license, as detailed below. |
| 7 | * It has subsequently been modified by contributors to the QEMU Project, |
| 8 | * so some portions are provided under: |
| 9 | * the SoftFloat-2a license |
| 10 | * the BSD license |
| 11 | * GPL-v2-or-later |
| 12 | * |
| 13 | * Any future contributions to this file after December 1st 2014 will be |
| 14 | * taken to be licensed under the Softfloat-2a license unless specifically |
| 15 | * indicated otherwise. |
| 16 | */ |
| 17 | |
| 18 | static void partsN(return_nan)(FloatPartsN *a, float_status *s) |
| 19 | { |
| 20 | switch (a->cls) { |
| 21 | case float_class_snan: |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 22 | float_raise(float_flag_invalid | float_flag_invalid_snan, s); |
Richard Henderson | 7c45bad | 2020-10-23 16:47:04 -0700 | [diff] [blame] | 23 | if (s->default_nan_mode) { |
| 24 | parts_default_nan(a, s); |
| 25 | } else { |
| 26 | parts_silence_nan(a, s); |
| 27 | } |
| 28 | break; |
| 29 | case float_class_qnan: |
| 30 | if (s->default_nan_mode) { |
| 31 | parts_default_nan(a, s); |
| 32 | } |
| 33 | break; |
| 34 | default: |
| 35 | g_assert_not_reached(); |
| 36 | } |
| 37 | } |
Richard Henderson | 22c355f | 2020-10-23 17:03:11 -0700 | [diff] [blame] | 38 | |
| 39 | static FloatPartsN *partsN(pick_nan)(FloatPartsN *a, FloatPartsN *b, |
| 40 | float_status *s) |
| 41 | { |
| 42 | if (is_snan(a->cls) || is_snan(b->cls)) { |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 43 | float_raise(float_flag_invalid | float_flag_invalid_snan, s); |
Richard Henderson | 22c355f | 2020-10-23 17:03:11 -0700 | [diff] [blame] | 44 | } |
| 45 | |
| 46 | if (s->default_nan_mode) { |
| 47 | parts_default_nan(a, s); |
| 48 | } else { |
| 49 | int cmp = frac_cmp(a, b); |
| 50 | if (cmp == 0) { |
| 51 | cmp = a->sign < b->sign; |
| 52 | } |
| 53 | |
| 54 | if (pickNaN(a->cls, b->cls, cmp > 0, s)) { |
| 55 | a = b; |
| 56 | } |
| 57 | if (is_snan(a->cls)) { |
| 58 | parts_silence_nan(a, s); |
| 59 | } |
| 60 | } |
| 61 | return a; |
| 62 | } |
Richard Henderson | 979582d | 2020-10-23 17:12:12 -0700 | [diff] [blame] | 63 | |
| 64 | static FloatPartsN *partsN(pick_nan_muladd)(FloatPartsN *a, FloatPartsN *b, |
| 65 | FloatPartsN *c, float_status *s, |
| 66 | int ab_mask, int abc_mask) |
| 67 | { |
| 68 | int which; |
| 69 | |
| 70 | if (unlikely(abc_mask & float_cmask_snan)) { |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 71 | float_raise(float_flag_invalid | float_flag_invalid_snan, s); |
Richard Henderson | 979582d | 2020-10-23 17:12:12 -0700 | [diff] [blame] | 72 | } |
| 73 | |
| 74 | which = pickNaNMulAdd(a->cls, b->cls, c->cls, |
| 75 | ab_mask == float_cmask_infzero, s); |
| 76 | |
| 77 | if (s->default_nan_mode || which == 3) { |
| 78 | /* |
| 79 | * Note that this check is after pickNaNMulAdd so that function |
| 80 | * has an opportunity to set the Invalid flag for infzero. |
| 81 | */ |
| 82 | parts_default_nan(a, s); |
| 83 | return a; |
| 84 | } |
| 85 | |
| 86 | switch (which) { |
| 87 | case 0: |
| 88 | break; |
| 89 | case 1: |
| 90 | a = b; |
| 91 | break; |
| 92 | case 2: |
| 93 | a = c; |
| 94 | break; |
| 95 | default: |
| 96 | g_assert_not_reached(); |
| 97 | } |
| 98 | if (is_snan(a->cls)) { |
| 99 | parts_silence_nan(a, s); |
| 100 | } |
| 101 | return a; |
| 102 | } |
Richard Henderson | d46975b | 2020-11-08 13:01:55 -0800 | [diff] [blame] | 103 | |
| 104 | /* |
| 105 | * Canonicalize the FloatParts structure. Determine the class, |
| 106 | * unbias the exponent, and normalize the fraction. |
| 107 | */ |
| 108 | static void partsN(canonicalize)(FloatPartsN *p, float_status *status, |
| 109 | const FloatFmt *fmt) |
| 110 | { |
| 111 | if (unlikely(p->exp == 0)) { |
| 112 | if (likely(frac_eqz(p))) { |
| 113 | p->cls = float_class_zero; |
| 114 | } else if (status->flush_inputs_to_zero) { |
| 115 | float_raise(float_flag_input_denormal, status); |
| 116 | p->cls = float_class_zero; |
| 117 | frac_clear(p); |
| 118 | } else { |
| 119 | int shift = frac_normalize(p); |
| 120 | p->cls = float_class_normal; |
| 121 | p->exp = fmt->frac_shift - fmt->exp_bias - shift + 1; |
| 122 | } |
| 123 | } else if (likely(p->exp < fmt->exp_max) || fmt->arm_althp) { |
| 124 | p->cls = float_class_normal; |
| 125 | p->exp -= fmt->exp_bias; |
| 126 | frac_shl(p, fmt->frac_shift); |
| 127 | p->frac_hi |= DECOMPOSED_IMPLICIT_BIT; |
| 128 | } else if (likely(frac_eqz(p))) { |
| 129 | p->cls = float_class_inf; |
| 130 | } else { |
| 131 | frac_shl(p, fmt->frac_shift); |
| 132 | p->cls = (parts_is_snan_frac(p->frac_hi, status) |
| 133 | ? float_class_snan : float_class_qnan); |
| 134 | } |
| 135 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 136 | |
| 137 | /* |
| 138 | * Round and uncanonicalize a floating-point number by parts. There |
| 139 | * are FRAC_SHIFT bits that may require rounding at the bottom of the |
| 140 | * fraction; these bits will be removed. The exponent will be biased |
| 141 | * by EXP_BIAS and must be bounded by [EXP_MAX-1, 0]. |
| 142 | */ |
Richard Henderson | 25fdedf | 2020-11-20 12:11:08 -0800 | [diff] [blame] | 143 | static void partsN(uncanon_normal)(FloatPartsN *p, float_status *s, |
| 144 | const FloatFmt *fmt) |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 145 | { |
| 146 | const int exp_max = fmt->exp_max; |
| 147 | const int frac_shift = fmt->frac_shift; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 148 | const uint64_t round_mask = fmt->round_mask; |
Richard Henderson | d6e1f0c | 2020-11-20 18:28:31 -0800 | [diff] [blame] | 149 | const uint64_t frac_lsb = round_mask + 1; |
| 150 | const uint64_t frac_lsbm1 = round_mask ^ (round_mask >> 1); |
| 151 | const uint64_t roundeven_mask = round_mask | frac_lsb; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 152 | uint64_t inc; |
Richard Henderson | 25fdedf | 2020-11-20 12:11:08 -0800 | [diff] [blame] | 153 | bool overflow_norm = false; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 154 | int exp, flags = 0; |
| 155 | |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 156 | switch (s->float_rounding_mode) { |
| 157 | case float_round_nearest_even: |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 158 | if (N > 64 && frac_lsb == 0) { |
| 159 | inc = ((p->frac_hi & 1) || (p->frac_lo & round_mask) != frac_lsbm1 |
| 160 | ? frac_lsbm1 : 0); |
| 161 | } else { |
| 162 | inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1 |
| 163 | ? frac_lsbm1 : 0); |
| 164 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 165 | break; |
| 166 | case float_round_ties_away: |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 167 | inc = frac_lsbm1; |
| 168 | break; |
| 169 | case float_round_to_zero: |
| 170 | overflow_norm = true; |
| 171 | inc = 0; |
| 172 | break; |
| 173 | case float_round_up: |
| 174 | inc = p->sign ? 0 : round_mask; |
| 175 | overflow_norm = p->sign; |
| 176 | break; |
| 177 | case float_round_down: |
| 178 | inc = p->sign ? round_mask : 0; |
| 179 | overflow_norm = !p->sign; |
| 180 | break; |
| 181 | case float_round_to_odd: |
| 182 | overflow_norm = true; |
Richard Henderson | 60c8f72 | 2021-05-25 15:58:10 -0700 | [diff] [blame] | 183 | /* fall through */ |
| 184 | case float_round_to_odd_inf: |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 185 | if (N > 64 && frac_lsb == 0) { |
| 186 | inc = p->frac_hi & 1 ? 0 : round_mask; |
| 187 | } else { |
| 188 | inc = p->frac_lo & frac_lsb ? 0 : round_mask; |
| 189 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 190 | break; |
| 191 | default: |
| 192 | g_assert_not_reached(); |
| 193 | } |
| 194 | |
| 195 | exp = p->exp + fmt->exp_bias; |
| 196 | if (likely(exp > 0)) { |
| 197 | if (p->frac_lo & round_mask) { |
| 198 | flags |= float_flag_inexact; |
| 199 | if (frac_addi(p, p, inc)) { |
| 200 | frac_shr(p, 1); |
| 201 | p->frac_hi |= DECOMPOSED_IMPLICIT_BIT; |
| 202 | exp++; |
| 203 | } |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 204 | p->frac_lo &= ~round_mask; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 205 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 206 | |
| 207 | if (fmt->arm_althp) { |
| 208 | /* ARM Alt HP eschews Inf and NaN for a wider exponent. */ |
| 209 | if (unlikely(exp > exp_max)) { |
| 210 | /* Overflow. Return the maximum normal. */ |
| 211 | flags = float_flag_invalid; |
| 212 | exp = exp_max; |
| 213 | frac_allones(p); |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 214 | p->frac_lo &= ~round_mask; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 215 | } |
| 216 | } else if (unlikely(exp >= exp_max)) { |
| 217 | flags |= float_flag_overflow | float_flag_inexact; |
| 218 | if (overflow_norm) { |
| 219 | exp = exp_max - 1; |
| 220 | frac_allones(p); |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 221 | p->frac_lo &= ~round_mask; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 222 | } else { |
| 223 | p->cls = float_class_inf; |
| 224 | exp = exp_max; |
| 225 | frac_clear(p); |
| 226 | } |
| 227 | } |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 228 | frac_shr(p, frac_shift); |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 229 | } else if (s->flush_to_zero) { |
| 230 | flags |= float_flag_output_denormal; |
| 231 | p->cls = float_class_zero; |
| 232 | exp = 0; |
| 233 | frac_clear(p); |
| 234 | } else { |
| 235 | bool is_tiny = s->tininess_before_rounding || exp < 0; |
| 236 | |
| 237 | if (!is_tiny) { |
| 238 | FloatPartsN discard; |
| 239 | is_tiny = !frac_addi(&discard, p, inc); |
| 240 | } |
| 241 | |
| 242 | frac_shrjam(p, 1 - exp); |
| 243 | |
| 244 | if (p->frac_lo & round_mask) { |
| 245 | /* Need to recompute round-to-even/round-to-odd. */ |
| 246 | switch (s->float_rounding_mode) { |
| 247 | case float_round_nearest_even: |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 248 | if (N > 64 && frac_lsb == 0) { |
| 249 | inc = ((p->frac_hi & 1) || |
| 250 | (p->frac_lo & round_mask) != frac_lsbm1 |
| 251 | ? frac_lsbm1 : 0); |
| 252 | } else { |
| 253 | inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1 |
| 254 | ? frac_lsbm1 : 0); |
| 255 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 256 | break; |
| 257 | case float_round_to_odd: |
Richard Henderson | 60c8f72 | 2021-05-25 15:58:10 -0700 | [diff] [blame] | 258 | case float_round_to_odd_inf: |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 259 | if (N > 64 && frac_lsb == 0) { |
| 260 | inc = p->frac_hi & 1 ? 0 : round_mask; |
| 261 | } else { |
| 262 | inc = p->frac_lo & frac_lsb ? 0 : round_mask; |
| 263 | } |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 264 | break; |
| 265 | default: |
| 266 | break; |
| 267 | } |
| 268 | flags |= float_flag_inexact; |
| 269 | frac_addi(p, p, inc); |
Richard Henderson | 98b3cff | 2020-11-21 16:35:54 -0800 | [diff] [blame] | 270 | p->frac_lo &= ~round_mask; |
Richard Henderson | ee6959f | 2020-10-23 17:53:55 -0700 | [diff] [blame] | 271 | } |
| 272 | |
| 273 | exp = (p->frac_hi & DECOMPOSED_IMPLICIT_BIT) != 0; |
| 274 | frac_shr(p, frac_shift); |
| 275 | |
| 276 | if (is_tiny && (flags & float_flag_inexact)) { |
| 277 | flags |= float_flag_underflow; |
| 278 | } |
| 279 | if (exp == 0 && frac_eqz(p)) { |
| 280 | p->cls = float_class_zero; |
| 281 | } |
| 282 | } |
| 283 | p->exp = exp; |
| 284 | float_raise(flags, s); |
| 285 | } |
Richard Henderson | da10a90 | 2020-10-22 15:22:55 -0700 | [diff] [blame] | 286 | |
Richard Henderson | 25fdedf | 2020-11-20 12:11:08 -0800 | [diff] [blame] | 287 | static void partsN(uncanon)(FloatPartsN *p, float_status *s, |
| 288 | const FloatFmt *fmt) |
| 289 | { |
| 290 | if (likely(p->cls == float_class_normal)) { |
| 291 | parts_uncanon_normal(p, s, fmt); |
| 292 | } else { |
| 293 | switch (p->cls) { |
| 294 | case float_class_zero: |
| 295 | p->exp = 0; |
| 296 | frac_clear(p); |
| 297 | return; |
| 298 | case float_class_inf: |
| 299 | g_assert(!fmt->arm_althp); |
| 300 | p->exp = fmt->exp_max; |
| 301 | frac_clear(p); |
| 302 | return; |
| 303 | case float_class_qnan: |
| 304 | case float_class_snan: |
| 305 | g_assert(!fmt->arm_althp); |
| 306 | p->exp = fmt->exp_max; |
| 307 | frac_shr(p, fmt->frac_shift); |
| 308 | return; |
| 309 | default: |
| 310 | break; |
| 311 | } |
| 312 | g_assert_not_reached(); |
| 313 | } |
| 314 | } |
| 315 | |
Richard Henderson | da10a90 | 2020-10-22 15:22:55 -0700 | [diff] [blame] | 316 | /* |
| 317 | * Returns the result of adding or subtracting the values of the |
| 318 | * floating-point values `a' and `b'. The operation is performed |
| 319 | * according to the IEC/IEEE Standard for Binary Floating-Point |
| 320 | * Arithmetic. |
| 321 | */ |
| 322 | static FloatPartsN *partsN(addsub)(FloatPartsN *a, FloatPartsN *b, |
| 323 | float_status *s, bool subtract) |
| 324 | { |
| 325 | bool b_sign = b->sign ^ subtract; |
| 326 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 327 | |
| 328 | if (a->sign != b_sign) { |
| 329 | /* Subtraction */ |
| 330 | if (likely(ab_mask == float_cmask_normal)) { |
| 331 | if (parts_sub_normal(a, b)) { |
| 332 | return a; |
| 333 | } |
| 334 | /* Subtract was exact, fall through to set sign. */ |
| 335 | ab_mask = float_cmask_zero; |
| 336 | } |
| 337 | |
| 338 | if (ab_mask == float_cmask_zero) { |
| 339 | a->sign = s->float_rounding_mode == float_round_down; |
| 340 | return a; |
| 341 | } |
| 342 | |
| 343 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 344 | goto p_nan; |
| 345 | } |
| 346 | |
| 347 | if (ab_mask & float_cmask_inf) { |
| 348 | if (a->cls != float_class_inf) { |
| 349 | /* N - Inf */ |
| 350 | goto return_b; |
| 351 | } |
| 352 | if (b->cls != float_class_inf) { |
| 353 | /* Inf - N */ |
| 354 | return a; |
| 355 | } |
| 356 | /* Inf - Inf */ |
Richard Henderson | ba11446 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 357 | float_raise(float_flag_invalid | float_flag_invalid_isi, s); |
Richard Henderson | da10a90 | 2020-10-22 15:22:55 -0700 | [diff] [blame] | 358 | parts_default_nan(a, s); |
| 359 | return a; |
| 360 | } |
| 361 | } else { |
| 362 | /* Addition */ |
| 363 | if (likely(ab_mask == float_cmask_normal)) { |
| 364 | parts_add_normal(a, b); |
| 365 | return a; |
| 366 | } |
| 367 | |
| 368 | if (ab_mask == float_cmask_zero) { |
| 369 | return a; |
| 370 | } |
| 371 | |
| 372 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 373 | goto p_nan; |
| 374 | } |
| 375 | |
| 376 | if (ab_mask & float_cmask_inf) { |
| 377 | a->cls = float_class_inf; |
| 378 | return a; |
| 379 | } |
| 380 | } |
| 381 | |
| 382 | if (b->cls == float_class_zero) { |
| 383 | g_assert(a->cls == float_class_normal); |
| 384 | return a; |
| 385 | } |
| 386 | |
| 387 | g_assert(a->cls == float_class_zero); |
| 388 | g_assert(b->cls == float_class_normal); |
| 389 | return_b: |
| 390 | b->sign = b_sign; |
| 391 | return b; |
| 392 | |
| 393 | p_nan: |
| 394 | return parts_pick_nan(a, b, s); |
| 395 | } |
Richard Henderson | aca8452 | 2020-11-11 20:44:57 -0800 | [diff] [blame] | 396 | |
| 397 | /* |
| 398 | * Returns the result of multiplying the floating-point values `a' and |
| 399 | * `b'. The operation is performed according to the IEC/IEEE Standard |
| 400 | * for Binary Floating-Point Arithmetic. |
| 401 | */ |
| 402 | static FloatPartsN *partsN(mul)(FloatPartsN *a, FloatPartsN *b, |
| 403 | float_status *s) |
| 404 | { |
| 405 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 406 | bool sign = a->sign ^ b->sign; |
| 407 | |
| 408 | if (likely(ab_mask == float_cmask_normal)) { |
| 409 | FloatPartsW tmp; |
| 410 | |
| 411 | frac_mulw(&tmp, a, b); |
| 412 | frac_truncjam(a, &tmp); |
| 413 | |
| 414 | a->exp += b->exp + 1; |
| 415 | if (!(a->frac_hi & DECOMPOSED_IMPLICIT_BIT)) { |
| 416 | frac_add(a, a, a); |
| 417 | a->exp -= 1; |
| 418 | } |
| 419 | |
| 420 | a->sign = sign; |
| 421 | return a; |
| 422 | } |
| 423 | |
| 424 | /* Inf * Zero == NaN */ |
| 425 | if (unlikely(ab_mask == float_cmask_infzero)) { |
Richard Henderson | bead3c9 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 426 | float_raise(float_flag_invalid | float_flag_invalid_imz, s); |
Richard Henderson | aca8452 | 2020-11-11 20:44:57 -0800 | [diff] [blame] | 427 | parts_default_nan(a, s); |
| 428 | return a; |
| 429 | } |
| 430 | |
| 431 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 432 | return parts_pick_nan(a, b, s); |
| 433 | } |
| 434 | |
| 435 | /* Multiply by 0 or Inf */ |
| 436 | if (ab_mask & float_cmask_inf) { |
| 437 | a->cls = float_class_inf; |
| 438 | a->sign = sign; |
| 439 | return a; |
| 440 | } |
| 441 | |
| 442 | g_assert(ab_mask & float_cmask_zero); |
| 443 | a->cls = float_class_zero; |
| 444 | a->sign = sign; |
| 445 | return a; |
| 446 | } |
Richard Henderson | dedd123 | 2020-10-24 06:04:19 -0700 | [diff] [blame] | 447 | |
| 448 | /* |
| 449 | * Returns the result of multiplying the floating-point values `a' and |
| 450 | * `b' then adding 'c', with no intermediate rounding step after the |
| 451 | * multiplication. The operation is performed according to the |
| 452 | * IEC/IEEE Standard for Binary Floating-Point Arithmetic 754-2008. |
| 453 | * The flags argument allows the caller to select negation of the |
| 454 | * addend, the intermediate product, or the final result. (The |
| 455 | * difference between this and having the caller do a separate |
| 456 | * negation is that negating externally will flip the sign bit on NaNs.) |
| 457 | * |
| 458 | * Requires A and C extracted into a double-sized structure to provide the |
| 459 | * extra space for the widening multiply. |
| 460 | */ |
| 461 | static FloatPartsN *partsN(muladd)(FloatPartsN *a, FloatPartsN *b, |
| 462 | FloatPartsN *c, int flags, float_status *s) |
| 463 | { |
| 464 | int ab_mask, abc_mask; |
| 465 | FloatPartsW p_widen, c_widen; |
| 466 | |
| 467 | ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 468 | abc_mask = float_cmask(c->cls) | ab_mask; |
| 469 | |
| 470 | /* |
| 471 | * It is implementation-defined whether the cases of (0,inf,qnan) |
| 472 | * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN |
| 473 | * they return if they do), so we have to hand this information |
| 474 | * off to the target-specific pick-a-NaN routine. |
| 475 | */ |
| 476 | if (unlikely(abc_mask & float_cmask_anynan)) { |
| 477 | return parts_pick_nan_muladd(a, b, c, s, ab_mask, abc_mask); |
| 478 | } |
| 479 | |
| 480 | if (flags & float_muladd_negate_c) { |
| 481 | c->sign ^= 1; |
| 482 | } |
| 483 | |
| 484 | /* Compute the sign of the product into A. */ |
| 485 | a->sign ^= b->sign; |
| 486 | if (flags & float_muladd_negate_product) { |
| 487 | a->sign ^= 1; |
| 488 | } |
| 489 | |
| 490 | if (unlikely(ab_mask != float_cmask_normal)) { |
| 491 | if (unlikely(ab_mask == float_cmask_infzero)) { |
Richard Henderson | bead3c9 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 492 | float_raise(float_flag_invalid | float_flag_invalid_imz, s); |
Richard Henderson | dedd123 | 2020-10-24 06:04:19 -0700 | [diff] [blame] | 493 | goto d_nan; |
| 494 | } |
| 495 | |
| 496 | if (ab_mask & float_cmask_inf) { |
| 497 | if (c->cls == float_class_inf && a->sign != c->sign) { |
Richard Henderson | ba11446 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 498 | float_raise(float_flag_invalid | float_flag_invalid_isi, s); |
Richard Henderson | dedd123 | 2020-10-24 06:04:19 -0700 | [diff] [blame] | 499 | goto d_nan; |
| 500 | } |
| 501 | goto return_inf; |
| 502 | } |
| 503 | |
| 504 | g_assert(ab_mask & float_cmask_zero); |
| 505 | if (c->cls == float_class_normal) { |
| 506 | *a = *c; |
| 507 | goto return_normal; |
| 508 | } |
| 509 | if (c->cls == float_class_zero) { |
| 510 | if (a->sign != c->sign) { |
| 511 | goto return_sub_zero; |
| 512 | } |
| 513 | goto return_zero; |
| 514 | } |
| 515 | g_assert(c->cls == float_class_inf); |
| 516 | } |
| 517 | |
| 518 | if (unlikely(c->cls == float_class_inf)) { |
| 519 | a->sign = c->sign; |
| 520 | goto return_inf; |
| 521 | } |
| 522 | |
| 523 | /* Perform the multiplication step. */ |
| 524 | p_widen.sign = a->sign; |
| 525 | p_widen.exp = a->exp + b->exp + 1; |
| 526 | frac_mulw(&p_widen, a, b); |
| 527 | if (!(p_widen.frac_hi & DECOMPOSED_IMPLICIT_BIT)) { |
| 528 | frac_add(&p_widen, &p_widen, &p_widen); |
| 529 | p_widen.exp -= 1; |
| 530 | } |
| 531 | |
| 532 | /* Perform the addition step. */ |
| 533 | if (c->cls != float_class_zero) { |
| 534 | /* Zero-extend C to less significant bits. */ |
| 535 | frac_widen(&c_widen, c); |
| 536 | c_widen.exp = c->exp; |
| 537 | |
| 538 | if (a->sign == c->sign) { |
| 539 | parts_add_normal(&p_widen, &c_widen); |
| 540 | } else if (!parts_sub_normal(&p_widen, &c_widen)) { |
| 541 | goto return_sub_zero; |
| 542 | } |
| 543 | } |
| 544 | |
| 545 | /* Narrow with sticky bit, for proper rounding later. */ |
| 546 | frac_truncjam(a, &p_widen); |
| 547 | a->sign = p_widen.sign; |
| 548 | a->exp = p_widen.exp; |
| 549 | |
| 550 | return_normal: |
| 551 | if (flags & float_muladd_halve_result) { |
| 552 | a->exp -= 1; |
| 553 | } |
| 554 | finish_sign: |
| 555 | if (flags & float_muladd_negate_result) { |
| 556 | a->sign ^= 1; |
| 557 | } |
| 558 | return a; |
| 559 | |
| 560 | return_sub_zero: |
| 561 | a->sign = s->float_rounding_mode == float_round_down; |
| 562 | return_zero: |
| 563 | a->cls = float_class_zero; |
| 564 | goto finish_sign; |
| 565 | |
| 566 | return_inf: |
| 567 | a->cls = float_class_inf; |
| 568 | goto finish_sign; |
| 569 | |
| 570 | d_nan: |
Richard Henderson | dedd123 | 2020-10-24 06:04:19 -0700 | [diff] [blame] | 571 | parts_default_nan(a, s); |
| 572 | return a; |
| 573 | } |
Richard Henderson | ec961b8 | 2020-11-11 12:50:44 -0800 | [diff] [blame] | 574 | |
| 575 | /* |
| 576 | * Returns the result of dividing the floating-point value `a' by the |
| 577 | * corresponding value `b'. The operation is performed according to |
| 578 | * the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 579 | */ |
| 580 | static FloatPartsN *partsN(div)(FloatPartsN *a, FloatPartsN *b, |
| 581 | float_status *s) |
| 582 | { |
| 583 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 584 | bool sign = a->sign ^ b->sign; |
| 585 | |
| 586 | if (likely(ab_mask == float_cmask_normal)) { |
| 587 | a->sign = sign; |
| 588 | a->exp -= b->exp + frac_div(a, b); |
| 589 | return a; |
| 590 | } |
| 591 | |
| 592 | /* 0/0 or Inf/Inf => NaN */ |
Richard Henderson | 10cc964 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 593 | if (unlikely(ab_mask == float_cmask_zero)) { |
| 594 | float_raise(float_flag_invalid | float_flag_invalid_zdz, s); |
| 595 | goto d_nan; |
| 596 | } |
| 597 | if (unlikely(ab_mask == float_cmask_inf)) { |
| 598 | float_raise(float_flag_invalid | float_flag_invalid_idi, s); |
| 599 | goto d_nan; |
Richard Henderson | ec961b8 | 2020-11-11 12:50:44 -0800 | [diff] [blame] | 600 | } |
| 601 | |
| 602 | /* All the NaN cases */ |
| 603 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 604 | return parts_pick_nan(a, b, s); |
| 605 | } |
| 606 | |
| 607 | a->sign = sign; |
| 608 | |
| 609 | /* Inf / X */ |
| 610 | if (a->cls == float_class_inf) { |
| 611 | return a; |
| 612 | } |
| 613 | |
| 614 | /* 0 / X */ |
| 615 | if (a->cls == float_class_zero) { |
| 616 | return a; |
| 617 | } |
| 618 | |
| 619 | /* X / Inf */ |
| 620 | if (b->cls == float_class_inf) { |
| 621 | a->cls = float_class_zero; |
| 622 | return a; |
| 623 | } |
| 624 | |
| 625 | /* X / 0 => Inf */ |
| 626 | g_assert(b->cls == float_class_zero); |
| 627 | float_raise(float_flag_divbyzero, s); |
| 628 | a->cls = float_class_inf; |
| 629 | return a; |
Richard Henderson | 10cc964 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 630 | |
| 631 | d_nan: |
| 632 | parts_default_nan(a, s); |
| 633 | return a; |
Richard Henderson | ec961b8 | 2020-11-11 12:50:44 -0800 | [diff] [blame] | 634 | } |
Richard Henderson | afc3493 | 2020-11-14 12:53:12 -0800 | [diff] [blame] | 635 | |
| 636 | /* |
Richard Henderson | feaf2e9 | 2021-05-07 18:40:28 -0700 | [diff] [blame] | 637 | * Floating point remainder, per IEC/IEEE, or modulus. |
| 638 | */ |
| 639 | static FloatPartsN *partsN(modrem)(FloatPartsN *a, FloatPartsN *b, |
| 640 | uint64_t *mod_quot, float_status *s) |
| 641 | { |
| 642 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 643 | |
| 644 | if (likely(ab_mask == float_cmask_normal)) { |
| 645 | frac_modrem(a, b, mod_quot); |
| 646 | return a; |
| 647 | } |
| 648 | |
| 649 | if (mod_quot) { |
| 650 | *mod_quot = 0; |
| 651 | } |
| 652 | |
| 653 | /* All the NaN cases */ |
| 654 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 655 | return parts_pick_nan(a, b, s); |
| 656 | } |
| 657 | |
| 658 | /* Inf % N; N % 0 */ |
| 659 | if (a->cls == float_class_inf || b->cls == float_class_zero) { |
| 660 | float_raise(float_flag_invalid, s); |
| 661 | parts_default_nan(a, s); |
| 662 | return a; |
| 663 | } |
| 664 | |
| 665 | /* N % Inf; 0 % N */ |
| 666 | g_assert(b->cls == float_class_inf || a->cls == float_class_zero); |
| 667 | return a; |
| 668 | } |
| 669 | |
| 670 | /* |
Richard Henderson | 9261b24 | 2020-11-18 12:14:37 -0800 | [diff] [blame] | 671 | * Square Root |
| 672 | * |
| 673 | * The base algorithm is lifted from |
| 674 | * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtf.c |
| 675 | * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrt.c |
| 676 | * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtl.c |
| 677 | * and is thus MIT licenced. |
| 678 | */ |
| 679 | static void partsN(sqrt)(FloatPartsN *a, float_status *status, |
| 680 | const FloatFmt *fmt) |
| 681 | { |
| 682 | const uint32_t three32 = 3u << 30; |
| 683 | const uint64_t three64 = 3ull << 62; |
| 684 | uint32_t d32, m32, r32, s32, u32; /* 32-bit computation */ |
| 685 | uint64_t d64, m64, r64, s64, u64; /* 64-bit computation */ |
| 686 | uint64_t dh, dl, rh, rl, sh, sl, uh, ul; /* 128-bit computation */ |
| 687 | uint64_t d0h, d0l, d1h, d1l, d2h, d2l; |
| 688 | uint64_t discard; |
| 689 | bool exp_odd; |
| 690 | size_t index; |
| 691 | |
| 692 | if (unlikely(a->cls != float_class_normal)) { |
| 693 | switch (a->cls) { |
| 694 | case float_class_snan: |
| 695 | case float_class_qnan: |
| 696 | parts_return_nan(a, status); |
| 697 | return; |
| 698 | case float_class_zero: |
| 699 | return; |
| 700 | case float_class_inf: |
| 701 | if (unlikely(a->sign)) { |
| 702 | goto d_nan; |
| 703 | } |
| 704 | return; |
| 705 | default: |
| 706 | g_assert_not_reached(); |
| 707 | } |
| 708 | } |
| 709 | |
| 710 | if (unlikely(a->sign)) { |
| 711 | goto d_nan; |
| 712 | } |
| 713 | |
| 714 | /* |
| 715 | * Argument reduction. |
| 716 | * x = 4^e frac; with integer e, and frac in [1, 4) |
| 717 | * m = frac fixed point at bit 62, since we're in base 4. |
| 718 | * If base-2 exponent is odd, exchange that for multiply by 2, |
| 719 | * which results in no shift. |
| 720 | */ |
| 721 | exp_odd = a->exp & 1; |
| 722 | index = extract64(a->frac_hi, 57, 6) | (!exp_odd << 6); |
| 723 | if (!exp_odd) { |
| 724 | frac_shr(a, 1); |
| 725 | } |
| 726 | |
| 727 | /* |
| 728 | * Approximate r ~= 1/sqrt(m) and s ~= sqrt(m) when m in [1, 4). |
| 729 | * |
| 730 | * Initial estimate: |
| 731 | * 7-bit lookup table (1-bit exponent and 6-bit significand). |
| 732 | * |
| 733 | * The relative error (e = r0*sqrt(m)-1) of a linear estimate |
| 734 | * (r0 = a*m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best; |
| 735 | * a table lookup is faster and needs one less iteration. |
| 736 | * The 7-bit table gives |e| < 0x1.fdp-9. |
| 737 | * |
| 738 | * A Newton-Raphson iteration for r is |
| 739 | * s = m*r |
| 740 | * d = s*r |
| 741 | * u = 3 - d |
| 742 | * r = r*u/2 |
| 743 | * |
| 744 | * Fixed point representations: |
| 745 | * m, s, d, u, three are all 2.30; r is 0.32 |
| 746 | */ |
| 747 | m64 = a->frac_hi; |
| 748 | m32 = m64 >> 32; |
| 749 | |
| 750 | r32 = rsqrt_tab[index] << 16; |
| 751 | /* |r*sqrt(m) - 1| < 0x1.FDp-9 */ |
| 752 | |
| 753 | s32 = ((uint64_t)m32 * r32) >> 32; |
| 754 | d32 = ((uint64_t)s32 * r32) >> 32; |
| 755 | u32 = three32 - d32; |
| 756 | |
| 757 | if (N == 64) { |
| 758 | /* float64 or smaller */ |
| 759 | |
| 760 | r32 = ((uint64_t)r32 * u32) >> 31; |
| 761 | /* |r*sqrt(m) - 1| < 0x1.7Bp-16 */ |
| 762 | |
| 763 | s32 = ((uint64_t)m32 * r32) >> 32; |
| 764 | d32 = ((uint64_t)s32 * r32) >> 32; |
| 765 | u32 = three32 - d32; |
| 766 | |
| 767 | if (fmt->frac_size <= 23) { |
| 768 | /* float32 or smaller */ |
| 769 | |
| 770 | s32 = ((uint64_t)s32 * u32) >> 32; /* 3.29 */ |
| 771 | s32 = (s32 - 1) >> 6; /* 9.23 */ |
| 772 | /* s < sqrt(m) < s + 0x1.08p-23 */ |
| 773 | |
| 774 | /* compute nearest rounded result to 2.23 bits */ |
| 775 | uint32_t d0 = (m32 << 16) - s32 * s32; |
| 776 | uint32_t d1 = s32 - d0; |
| 777 | uint32_t d2 = d1 + s32 + 1; |
| 778 | s32 += d1 >> 31; |
| 779 | a->frac_hi = (uint64_t)s32 << (64 - 25); |
| 780 | |
| 781 | /* increment or decrement for inexact */ |
| 782 | if (d2 != 0) { |
| 783 | a->frac_hi += ((int32_t)(d1 ^ d2) < 0 ? -1 : 1); |
| 784 | } |
| 785 | goto done; |
| 786 | } |
| 787 | |
| 788 | /* float64 */ |
| 789 | |
| 790 | r64 = (uint64_t)r32 * u32 * 2; |
| 791 | /* |r*sqrt(m) - 1| < 0x1.37-p29; convert to 64-bit arithmetic */ |
| 792 | mul64To128(m64, r64, &s64, &discard); |
| 793 | mul64To128(s64, r64, &d64, &discard); |
| 794 | u64 = three64 - d64; |
| 795 | |
| 796 | mul64To128(s64, u64, &s64, &discard); /* 3.61 */ |
| 797 | s64 = (s64 - 2) >> 9; /* 12.52 */ |
| 798 | |
| 799 | /* Compute nearest rounded result */ |
| 800 | uint64_t d0 = (m64 << 42) - s64 * s64; |
| 801 | uint64_t d1 = s64 - d0; |
| 802 | uint64_t d2 = d1 + s64 + 1; |
| 803 | s64 += d1 >> 63; |
| 804 | a->frac_hi = s64 << (64 - 54); |
| 805 | |
| 806 | /* increment or decrement for inexact */ |
| 807 | if (d2 != 0) { |
| 808 | a->frac_hi += ((int64_t)(d1 ^ d2) < 0 ? -1 : 1); |
| 809 | } |
| 810 | goto done; |
| 811 | } |
| 812 | |
| 813 | r64 = (uint64_t)r32 * u32 * 2; |
| 814 | /* |r*sqrt(m) - 1| < 0x1.7Bp-16; convert to 64-bit arithmetic */ |
| 815 | |
| 816 | mul64To128(m64, r64, &s64, &discard); |
| 817 | mul64To128(s64, r64, &d64, &discard); |
| 818 | u64 = three64 - d64; |
| 819 | mul64To128(u64, r64, &r64, &discard); |
| 820 | r64 <<= 1; |
| 821 | /* |r*sqrt(m) - 1| < 0x1.a5p-31 */ |
| 822 | |
| 823 | mul64To128(m64, r64, &s64, &discard); |
| 824 | mul64To128(s64, r64, &d64, &discard); |
| 825 | u64 = three64 - d64; |
| 826 | mul64To128(u64, r64, &rh, &rl); |
| 827 | add128(rh, rl, rh, rl, &rh, &rl); |
| 828 | /* |r*sqrt(m) - 1| < 0x1.c001p-59; change to 128-bit arithmetic */ |
| 829 | |
| 830 | mul128To256(a->frac_hi, a->frac_lo, rh, rl, &sh, &sl, &discard, &discard); |
| 831 | mul128To256(sh, sl, rh, rl, &dh, &dl, &discard, &discard); |
| 832 | sub128(three64, 0, dh, dl, &uh, &ul); |
| 833 | mul128To256(uh, ul, sh, sl, &sh, &sl, &discard, &discard); /* 3.125 */ |
| 834 | /* -0x1p-116 < s - sqrt(m) < 0x3.8001p-125 */ |
| 835 | |
| 836 | sub128(sh, sl, 0, 4, &sh, &sl); |
| 837 | shift128Right(sh, sl, 13, &sh, &sl); /* 16.112 */ |
| 838 | /* s < sqrt(m) < s + 1ulp */ |
| 839 | |
| 840 | /* Compute nearest rounded result */ |
| 841 | mul64To128(sl, sl, &d0h, &d0l); |
| 842 | d0h += 2 * sh * sl; |
| 843 | sub128(a->frac_lo << 34, 0, d0h, d0l, &d0h, &d0l); |
| 844 | sub128(sh, sl, d0h, d0l, &d1h, &d1l); |
| 845 | add128(sh, sl, 0, 1, &d2h, &d2l); |
| 846 | add128(d2h, d2l, d1h, d1l, &d2h, &d2l); |
| 847 | add128(sh, sl, 0, d1h >> 63, &sh, &sl); |
| 848 | shift128Left(sh, sl, 128 - 114, &sh, &sl); |
| 849 | |
| 850 | /* increment or decrement for inexact */ |
| 851 | if (d2h | d2l) { |
| 852 | if ((int64_t)(d1h ^ d2h) < 0) { |
| 853 | sub128(sh, sl, 0, 1, &sh, &sl); |
| 854 | } else { |
| 855 | add128(sh, sl, 0, 1, &sh, &sl); |
| 856 | } |
| 857 | } |
| 858 | a->frac_lo = sl; |
| 859 | a->frac_hi = sh; |
| 860 | |
| 861 | done: |
| 862 | /* Convert back from base 4 to base 2. */ |
| 863 | a->exp >>= 1; |
| 864 | if (!(a->frac_hi & DECOMPOSED_IMPLICIT_BIT)) { |
| 865 | frac_add(a, a, a); |
| 866 | } else { |
| 867 | a->exp += 1; |
| 868 | } |
| 869 | return; |
| 870 | |
| 871 | d_nan: |
Richard Henderson | f8718aa | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 872 | float_raise(float_flag_invalid | float_flag_invalid_sqrt, status); |
Richard Henderson | 9261b24 | 2020-11-18 12:14:37 -0800 | [diff] [blame] | 873 | parts_default_nan(a, status); |
| 874 | } |
| 875 | |
| 876 | /* |
Richard Henderson | afc3493 | 2020-11-14 12:53:12 -0800 | [diff] [blame] | 877 | * Rounds the floating-point value `a' to an integer, and returns the |
| 878 | * result as a floating-point value. The operation is performed |
| 879 | * according to the IEC/IEEE Standard for Binary Floating-Point |
| 880 | * Arithmetic. |
| 881 | * |
| 882 | * parts_round_to_int_normal is an internal helper function for |
| 883 | * normal numbers only, returning true for inexact but not directly |
| 884 | * raising float_flag_inexact. |
| 885 | */ |
| 886 | static bool partsN(round_to_int_normal)(FloatPartsN *a, FloatRoundMode rmode, |
| 887 | int scale, int frac_size) |
| 888 | { |
| 889 | uint64_t frac_lsb, frac_lsbm1, rnd_even_mask, rnd_mask, inc; |
| 890 | int shift_adj; |
| 891 | |
| 892 | scale = MIN(MAX(scale, -0x10000), 0x10000); |
| 893 | a->exp += scale; |
| 894 | |
| 895 | if (a->exp < 0) { |
| 896 | bool one; |
| 897 | |
| 898 | /* All fractional */ |
| 899 | switch (rmode) { |
| 900 | case float_round_nearest_even: |
| 901 | one = false; |
| 902 | if (a->exp == -1) { |
| 903 | FloatPartsN tmp; |
| 904 | /* Shift left one, discarding DECOMPOSED_IMPLICIT_BIT */ |
| 905 | frac_add(&tmp, a, a); |
| 906 | /* Anything remaining means frac > 0.5. */ |
| 907 | one = !frac_eqz(&tmp); |
| 908 | } |
| 909 | break; |
| 910 | case float_round_ties_away: |
| 911 | one = a->exp == -1; |
| 912 | break; |
| 913 | case float_round_to_zero: |
| 914 | one = false; |
| 915 | break; |
| 916 | case float_round_up: |
| 917 | one = !a->sign; |
| 918 | break; |
| 919 | case float_round_down: |
| 920 | one = a->sign; |
| 921 | break; |
| 922 | case float_round_to_odd: |
| 923 | one = true; |
| 924 | break; |
| 925 | default: |
| 926 | g_assert_not_reached(); |
| 927 | } |
| 928 | |
| 929 | frac_clear(a); |
| 930 | a->exp = 0; |
| 931 | if (one) { |
| 932 | a->frac_hi = DECOMPOSED_IMPLICIT_BIT; |
| 933 | } else { |
| 934 | a->cls = float_class_zero; |
| 935 | } |
| 936 | return true; |
| 937 | } |
| 938 | |
| 939 | if (a->exp >= frac_size) { |
| 940 | /* All integral */ |
| 941 | return false; |
| 942 | } |
| 943 | |
| 944 | if (N > 64 && a->exp < N - 64) { |
| 945 | /* |
| 946 | * Rounding is not in the low word -- shift lsb to bit 2, |
| 947 | * which leaves room for sticky and rounding bit. |
| 948 | */ |
| 949 | shift_adj = (N - 1) - (a->exp + 2); |
| 950 | frac_shrjam(a, shift_adj); |
| 951 | frac_lsb = 1 << 2; |
| 952 | } else { |
| 953 | shift_adj = 0; |
| 954 | frac_lsb = DECOMPOSED_IMPLICIT_BIT >> (a->exp & 63); |
| 955 | } |
| 956 | |
| 957 | frac_lsbm1 = frac_lsb >> 1; |
| 958 | rnd_mask = frac_lsb - 1; |
| 959 | rnd_even_mask = rnd_mask | frac_lsb; |
| 960 | |
| 961 | if (!(a->frac_lo & rnd_mask)) { |
| 962 | /* Fractional bits already clear, undo the shift above. */ |
| 963 | frac_shl(a, shift_adj); |
| 964 | return false; |
| 965 | } |
| 966 | |
| 967 | switch (rmode) { |
| 968 | case float_round_nearest_even: |
| 969 | inc = ((a->frac_lo & rnd_even_mask) != frac_lsbm1 ? frac_lsbm1 : 0); |
| 970 | break; |
| 971 | case float_round_ties_away: |
| 972 | inc = frac_lsbm1; |
| 973 | break; |
| 974 | case float_round_to_zero: |
| 975 | inc = 0; |
| 976 | break; |
| 977 | case float_round_up: |
| 978 | inc = a->sign ? 0 : rnd_mask; |
| 979 | break; |
| 980 | case float_round_down: |
| 981 | inc = a->sign ? rnd_mask : 0; |
| 982 | break; |
| 983 | case float_round_to_odd: |
| 984 | inc = a->frac_lo & frac_lsb ? 0 : rnd_mask; |
| 985 | break; |
| 986 | default: |
| 987 | g_assert_not_reached(); |
| 988 | } |
| 989 | |
| 990 | if (shift_adj == 0) { |
| 991 | if (frac_addi(a, a, inc)) { |
| 992 | frac_shr(a, 1); |
| 993 | a->frac_hi |= DECOMPOSED_IMPLICIT_BIT; |
| 994 | a->exp++; |
| 995 | } |
| 996 | a->frac_lo &= ~rnd_mask; |
| 997 | } else { |
| 998 | frac_addi(a, a, inc); |
| 999 | a->frac_lo &= ~rnd_mask; |
| 1000 | /* Be careful shifting back, not to overflow */ |
| 1001 | frac_shl(a, shift_adj - 1); |
| 1002 | if (a->frac_hi & DECOMPOSED_IMPLICIT_BIT) { |
| 1003 | a->exp++; |
| 1004 | } else { |
| 1005 | frac_add(a, a, a); |
| 1006 | } |
| 1007 | } |
| 1008 | return true; |
| 1009 | } |
| 1010 | |
| 1011 | static void partsN(round_to_int)(FloatPartsN *a, FloatRoundMode rmode, |
| 1012 | int scale, float_status *s, |
| 1013 | const FloatFmt *fmt) |
| 1014 | { |
| 1015 | switch (a->cls) { |
| 1016 | case float_class_qnan: |
| 1017 | case float_class_snan: |
| 1018 | parts_return_nan(a, s); |
| 1019 | break; |
| 1020 | case float_class_zero: |
| 1021 | case float_class_inf: |
| 1022 | break; |
| 1023 | case float_class_normal: |
| 1024 | if (parts_round_to_int_normal(a, rmode, scale, fmt->frac_size)) { |
| 1025 | float_raise(float_flag_inexact, s); |
| 1026 | } |
| 1027 | break; |
| 1028 | default: |
| 1029 | g_assert_not_reached(); |
| 1030 | } |
| 1031 | } |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1032 | |
| 1033 | /* |
| 1034 | * Returns the result of converting the floating-point value `a' to |
| 1035 | * the two's complement integer format. The conversion is performed |
| 1036 | * according to the IEC/IEEE Standard for Binary Floating-Point |
| 1037 | * Arithmetic---which means in particular that the conversion is |
| 1038 | * rounded according to the current rounding mode. If `a' is a NaN, |
| 1039 | * the largest positive integer is returned. Otherwise, if the |
| 1040 | * conversion overflows, the largest integer with the same sign as `a' |
| 1041 | * is returned. |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1042 | */ |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1043 | static int64_t partsN(float_to_sint)(FloatPartsN *p, FloatRoundMode rmode, |
| 1044 | int scale, int64_t min, int64_t max, |
| 1045 | float_status *s) |
| 1046 | { |
| 1047 | int flags = 0; |
| 1048 | uint64_t r; |
| 1049 | |
| 1050 | switch (p->cls) { |
| 1051 | case float_class_snan: |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1052 | flags |= float_flag_invalid_snan; |
| 1053 | /* fall through */ |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1054 | case float_class_qnan: |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1055 | flags |= float_flag_invalid; |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1056 | r = max; |
| 1057 | break; |
| 1058 | |
| 1059 | case float_class_inf: |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1060 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1061 | r = p->sign ? min : max; |
| 1062 | break; |
| 1063 | |
| 1064 | case float_class_zero: |
| 1065 | return 0; |
| 1066 | |
| 1067 | case float_class_normal: |
| 1068 | /* TODO: N - 2 is frac_size for rounding; could use input fmt. */ |
| 1069 | if (parts_round_to_int_normal(p, rmode, scale, N - 2)) { |
| 1070 | flags = float_flag_inexact; |
| 1071 | } |
| 1072 | |
| 1073 | if (p->exp <= DECOMPOSED_BINARY_POINT) { |
| 1074 | r = p->frac_hi >> (DECOMPOSED_BINARY_POINT - p->exp); |
| 1075 | } else { |
| 1076 | r = UINT64_MAX; |
| 1077 | } |
| 1078 | if (p->sign) { |
| 1079 | if (r <= -(uint64_t)min) { |
| 1080 | r = -r; |
| 1081 | } else { |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1082 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1083 | r = min; |
| 1084 | } |
| 1085 | } else if (r > max) { |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1086 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 463b3f0 | 2020-11-14 13:21:43 -0800 | [diff] [blame] | 1087 | r = max; |
| 1088 | } |
| 1089 | break; |
| 1090 | |
| 1091 | default: |
| 1092 | g_assert_not_reached(); |
| 1093 | } |
| 1094 | |
| 1095 | float_raise(flags, s); |
| 1096 | return r; |
| 1097 | } |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1098 | |
| 1099 | /* |
| 1100 | * Returns the result of converting the floating-point value `a' to |
| 1101 | * the unsigned integer format. The conversion is performed according |
| 1102 | * to the IEC/IEEE Standard for Binary Floating-Point |
| 1103 | * Arithmetic---which means in particular that the conversion is |
| 1104 | * rounded according to the current rounding mode. If `a' is a NaN, |
| 1105 | * the largest unsigned integer is returned. Otherwise, if the |
| 1106 | * conversion overflows, the largest unsigned integer is returned. If |
| 1107 | * the 'a' is negative, the result is rounded and zero is returned; |
| 1108 | * values that do not round to zero will raise the inexact exception |
| 1109 | * flag. |
| 1110 | */ |
| 1111 | static uint64_t partsN(float_to_uint)(FloatPartsN *p, FloatRoundMode rmode, |
| 1112 | int scale, uint64_t max, float_status *s) |
| 1113 | { |
| 1114 | int flags = 0; |
| 1115 | uint64_t r; |
| 1116 | |
| 1117 | switch (p->cls) { |
| 1118 | case float_class_snan: |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1119 | flags |= float_flag_invalid_snan; |
| 1120 | /* fall through */ |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1121 | case float_class_qnan: |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1122 | flags |= float_flag_invalid; |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1123 | r = max; |
| 1124 | break; |
| 1125 | |
| 1126 | case float_class_inf: |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1127 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1128 | r = p->sign ? 0 : max; |
| 1129 | break; |
| 1130 | |
| 1131 | case float_class_zero: |
| 1132 | return 0; |
| 1133 | |
| 1134 | case float_class_normal: |
| 1135 | /* TODO: N - 2 is frac_size for rounding; could use input fmt. */ |
| 1136 | if (parts_round_to_int_normal(p, rmode, scale, N - 2)) { |
| 1137 | flags = float_flag_inexact; |
| 1138 | if (p->cls == float_class_zero) { |
| 1139 | r = 0; |
| 1140 | break; |
| 1141 | } |
| 1142 | } |
| 1143 | |
| 1144 | if (p->sign) { |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1145 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1146 | r = 0; |
| 1147 | } else if (p->exp > DECOMPOSED_BINARY_POINT) { |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1148 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1149 | r = max; |
| 1150 | } else { |
| 1151 | r = p->frac_hi >> (DECOMPOSED_BINARY_POINT - p->exp); |
| 1152 | if (r > max) { |
Richard Henderson | 81254b0 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1153 | flags = float_flag_invalid | float_flag_invalid_cvti; |
Richard Henderson | 4ab4aef | 2020-11-14 14:21:16 -0800 | [diff] [blame] | 1154 | r = max; |
| 1155 | } |
| 1156 | } |
| 1157 | break; |
| 1158 | |
| 1159 | default: |
| 1160 | g_assert_not_reached(); |
| 1161 | } |
| 1162 | |
| 1163 | float_raise(flags, s); |
| 1164 | return r; |
| 1165 | } |
Richard Henderson | e368951 | 2020-11-14 14:40:27 -0800 | [diff] [blame] | 1166 | |
| 1167 | /* |
| 1168 | * Integer to float conversions |
| 1169 | * |
| 1170 | * Returns the result of converting the two's complement integer `a' |
| 1171 | * to the floating-point format. The conversion is performed according |
| 1172 | * to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1173 | */ |
| 1174 | static void partsN(sint_to_float)(FloatPartsN *p, int64_t a, |
| 1175 | int scale, float_status *s) |
| 1176 | { |
| 1177 | uint64_t f = a; |
| 1178 | int shift; |
| 1179 | |
| 1180 | memset(p, 0, sizeof(*p)); |
| 1181 | |
| 1182 | if (a == 0) { |
| 1183 | p->cls = float_class_zero; |
| 1184 | return; |
| 1185 | } |
| 1186 | |
| 1187 | p->cls = float_class_normal; |
| 1188 | if (a < 0) { |
| 1189 | f = -f; |
| 1190 | p->sign = true; |
| 1191 | } |
| 1192 | shift = clz64(f); |
| 1193 | scale = MIN(MAX(scale, -0x10000), 0x10000); |
| 1194 | |
| 1195 | p->exp = DECOMPOSED_BINARY_POINT - shift + scale; |
| 1196 | p->frac_hi = f << shift; |
| 1197 | } |
Richard Henderson | 37c954a | 2020-11-14 14:48:31 -0800 | [diff] [blame] | 1198 | |
| 1199 | /* |
| 1200 | * Unsigned Integer to float conversions |
| 1201 | * |
| 1202 | * Returns the result of converting the unsigned integer `a' to the |
| 1203 | * floating-point format. The conversion is performed according to the |
| 1204 | * IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1205 | */ |
| 1206 | static void partsN(uint_to_float)(FloatPartsN *p, uint64_t a, |
| 1207 | int scale, float_status *status) |
| 1208 | { |
| 1209 | memset(p, 0, sizeof(*p)); |
| 1210 | |
| 1211 | if (a == 0) { |
| 1212 | p->cls = float_class_zero; |
| 1213 | } else { |
| 1214 | int shift = clz64(a); |
| 1215 | scale = MIN(MAX(scale, -0x10000), 0x10000); |
| 1216 | p->cls = float_class_normal; |
| 1217 | p->exp = DECOMPOSED_BINARY_POINT - shift + scale; |
| 1218 | p->frac_hi = a << shift; |
| 1219 | } |
| 1220 | } |
Richard Henderson | e1c4667 | 2020-11-14 16:52:38 -0800 | [diff] [blame] | 1221 | |
| 1222 | /* |
| 1223 | * Float min/max. |
| 1224 | */ |
| 1225 | static FloatPartsN *partsN(minmax)(FloatPartsN *a, FloatPartsN *b, |
| 1226 | float_status *s, int flags) |
| 1227 | { |
| 1228 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
| 1229 | int a_exp, b_exp, cmp; |
| 1230 | |
| 1231 | if (unlikely(ab_mask & float_cmask_anynan)) { |
| 1232 | /* |
Chih-Min Chao | 0e90303 | 2021-10-22 00:08:45 +0800 | [diff] [blame] | 1233 | * For minNum/maxNum (IEEE 754-2008) |
| 1234 | * or minimumNumber/maximumNumber (IEEE 754-2019), |
| 1235 | * if one operand is a QNaN, and the other |
Richard Henderson | e1c4667 | 2020-11-14 16:52:38 -0800 | [diff] [blame] | 1236 | * operand is numerical, then return numerical argument. |
| 1237 | */ |
Chih-Min Chao | 0e90303 | 2021-10-22 00:08:45 +0800 | [diff] [blame] | 1238 | if ((flags & (minmax_isnum | minmax_isnumber)) |
Richard Henderson | e1c4667 | 2020-11-14 16:52:38 -0800 | [diff] [blame] | 1239 | && !(ab_mask & float_cmask_snan) |
| 1240 | && (ab_mask & ~float_cmask_qnan)) { |
| 1241 | return is_nan(a->cls) ? b : a; |
| 1242 | } |
Chih-Min Chao | 0e90303 | 2021-10-22 00:08:45 +0800 | [diff] [blame] | 1243 | |
| 1244 | /* |
| 1245 | * In IEEE 754-2019, minNum, maxNum, minNumMag and maxNumMag |
| 1246 | * are removed and replaced with minimum, minimumNumber, maximum |
| 1247 | * and maximumNumber. |
| 1248 | * minimumNumber/maximumNumber behavior for SNaN is changed to: |
| 1249 | * If both operands are NaNs, a QNaN is returned. |
| 1250 | * If either operand is a SNaN, |
| 1251 | * an invalid operation exception is signaled, |
| 1252 | * but unless both operands are NaNs, |
| 1253 | * the SNaN is otherwise ignored and not converted to a QNaN. |
| 1254 | */ |
| 1255 | if ((flags & minmax_isnumber) |
| 1256 | && (ab_mask & float_cmask_snan) |
| 1257 | && (ab_mask & ~float_cmask_anynan)) { |
| 1258 | float_raise(float_flag_invalid, s); |
| 1259 | return is_nan(a->cls) ? b : a; |
| 1260 | } |
| 1261 | |
Richard Henderson | e1c4667 | 2020-11-14 16:52:38 -0800 | [diff] [blame] | 1262 | return parts_pick_nan(a, b, s); |
| 1263 | } |
| 1264 | |
| 1265 | a_exp = a->exp; |
| 1266 | b_exp = b->exp; |
| 1267 | |
| 1268 | if (unlikely(ab_mask != float_cmask_normal)) { |
| 1269 | switch (a->cls) { |
| 1270 | case float_class_normal: |
| 1271 | break; |
| 1272 | case float_class_inf: |
| 1273 | a_exp = INT16_MAX; |
| 1274 | break; |
| 1275 | case float_class_zero: |
| 1276 | a_exp = INT16_MIN; |
| 1277 | break; |
| 1278 | default: |
| 1279 | g_assert_not_reached(); |
| 1280 | break; |
| 1281 | } |
| 1282 | switch (b->cls) { |
| 1283 | case float_class_normal: |
| 1284 | break; |
| 1285 | case float_class_inf: |
| 1286 | b_exp = INT16_MAX; |
| 1287 | break; |
| 1288 | case float_class_zero: |
| 1289 | b_exp = INT16_MIN; |
| 1290 | break; |
| 1291 | default: |
| 1292 | g_assert_not_reached(); |
| 1293 | break; |
| 1294 | } |
| 1295 | } |
| 1296 | |
| 1297 | /* Compare magnitudes. */ |
| 1298 | cmp = a_exp - b_exp; |
| 1299 | if (cmp == 0) { |
| 1300 | cmp = frac_cmp(a, b); |
| 1301 | } |
| 1302 | |
| 1303 | /* |
| 1304 | * Take the sign into account. |
| 1305 | * For ismag, only do this if the magnitudes are equal. |
| 1306 | */ |
| 1307 | if (!(flags & minmax_ismag) || cmp == 0) { |
| 1308 | if (a->sign != b->sign) { |
| 1309 | /* For differing signs, the negative operand is less. */ |
| 1310 | cmp = a->sign ? -1 : 1; |
| 1311 | } else if (a->sign) { |
| 1312 | /* For two negative operands, invert the magnitude comparison. */ |
| 1313 | cmp = -cmp; |
| 1314 | } |
| 1315 | } |
| 1316 | |
| 1317 | if (flags & minmax_ismin) { |
| 1318 | cmp = -cmp; |
| 1319 | } |
| 1320 | return cmp < 0 ? b : a; |
| 1321 | } |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1322 | |
| 1323 | /* |
| 1324 | * Floating point compare |
| 1325 | */ |
| 1326 | static FloatRelation partsN(compare)(FloatPartsN *a, FloatPartsN *b, |
| 1327 | float_status *s, bool is_quiet) |
| 1328 | { |
| 1329 | int ab_mask = float_cmask(a->cls) | float_cmask(b->cls); |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1330 | |
| 1331 | if (likely(ab_mask == float_cmask_normal)) { |
Richard Henderson | 9343c88 | 2022-04-01 07:22:39 -0600 | [diff] [blame] | 1332 | FloatRelation cmp; |
| 1333 | |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1334 | if (a->sign != b->sign) { |
| 1335 | goto a_sign; |
| 1336 | } |
Richard Henderson | 9343c88 | 2022-04-01 07:22:39 -0600 | [diff] [blame] | 1337 | if (a->exp == b->exp) { |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1338 | cmp = frac_cmp(a, b); |
Richard Henderson | 9343c88 | 2022-04-01 07:22:39 -0600 | [diff] [blame] | 1339 | } else if (a->exp < b->exp) { |
| 1340 | cmp = float_relation_less; |
| 1341 | } else { |
| 1342 | cmp = float_relation_greater; |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1343 | } |
| 1344 | if (a->sign) { |
| 1345 | cmp = -cmp; |
| 1346 | } |
| 1347 | return cmp; |
| 1348 | } |
| 1349 | |
| 1350 | if (unlikely(ab_mask & float_cmask_anynan)) { |
Richard Henderson | e706d44 | 2021-12-17 17:57:14 +0100 | [diff] [blame] | 1351 | if (ab_mask & float_cmask_snan) { |
| 1352 | float_raise(float_flag_invalid | float_flag_invalid_snan, s); |
| 1353 | } else if (!is_quiet) { |
Richard Henderson | 6eb169b | 2020-11-14 19:20:36 -0800 | [diff] [blame] | 1354 | float_raise(float_flag_invalid, s); |
| 1355 | } |
| 1356 | return float_relation_unordered; |
| 1357 | } |
| 1358 | |
| 1359 | if (ab_mask & float_cmask_zero) { |
| 1360 | if (ab_mask == float_cmask_zero) { |
| 1361 | return float_relation_equal; |
| 1362 | } else if (a->cls == float_class_zero) { |
| 1363 | goto b_sign; |
| 1364 | } else { |
| 1365 | goto a_sign; |
| 1366 | } |
| 1367 | } |
| 1368 | |
| 1369 | if (ab_mask == float_cmask_inf) { |
| 1370 | if (a->sign == b->sign) { |
| 1371 | return float_relation_equal; |
| 1372 | } |
| 1373 | } else if (b->cls == float_class_inf) { |
| 1374 | goto b_sign; |
| 1375 | } else { |
| 1376 | g_assert(a->cls == float_class_inf); |
| 1377 | } |
| 1378 | |
| 1379 | a_sign: |
| 1380 | return a->sign ? float_relation_less : float_relation_greater; |
| 1381 | b_sign: |
| 1382 | return b->sign ? float_relation_greater : float_relation_less; |
| 1383 | } |
Richard Henderson | 39626b0 | 2020-11-14 20:28:02 -0800 | [diff] [blame] | 1384 | |
| 1385 | /* |
| 1386 | * Multiply A by 2 raised to the power N. |
| 1387 | */ |
| 1388 | static void partsN(scalbn)(FloatPartsN *a, int n, float_status *s) |
| 1389 | { |
| 1390 | switch (a->cls) { |
| 1391 | case float_class_snan: |
| 1392 | case float_class_qnan: |
| 1393 | parts_return_nan(a, s); |
| 1394 | break; |
| 1395 | case float_class_zero: |
| 1396 | case float_class_inf: |
| 1397 | break; |
| 1398 | case float_class_normal: |
| 1399 | a->exp += MIN(MAX(n, -0x10000), 0x10000); |
| 1400 | break; |
| 1401 | default: |
| 1402 | g_assert_not_reached(); |
| 1403 | } |
| 1404 | } |
Richard Henderson | 2fa3546 | 2020-11-22 10:42:22 -0800 | [diff] [blame] | 1405 | |
| 1406 | /* |
| 1407 | * Return log2(A) |
| 1408 | */ |
| 1409 | static void partsN(log2)(FloatPartsN *a, float_status *s, const FloatFmt *fmt) |
| 1410 | { |
| 1411 | uint64_t a0, a1, r, t, ign; |
| 1412 | FloatPartsN f; |
| 1413 | int i, n, a_exp, f_exp; |
| 1414 | |
| 1415 | if (unlikely(a->cls != float_class_normal)) { |
| 1416 | switch (a->cls) { |
| 1417 | case float_class_snan: |
| 1418 | case float_class_qnan: |
| 1419 | parts_return_nan(a, s); |
| 1420 | return; |
| 1421 | case float_class_zero: |
| 1422 | /* log2(0) = -inf */ |
| 1423 | a->cls = float_class_inf; |
| 1424 | a->sign = 1; |
| 1425 | return; |
| 1426 | case float_class_inf: |
| 1427 | if (unlikely(a->sign)) { |
| 1428 | goto d_nan; |
| 1429 | } |
| 1430 | return; |
| 1431 | default: |
| 1432 | break; |
| 1433 | } |
| 1434 | g_assert_not_reached(); |
| 1435 | } |
| 1436 | if (unlikely(a->sign)) { |
| 1437 | goto d_nan; |
| 1438 | } |
| 1439 | |
| 1440 | /* TODO: This algorithm looses bits too quickly for float128. */ |
| 1441 | g_assert(N == 64); |
| 1442 | |
| 1443 | a_exp = a->exp; |
| 1444 | f_exp = -1; |
| 1445 | |
| 1446 | r = 0; |
| 1447 | t = DECOMPOSED_IMPLICIT_BIT; |
| 1448 | a0 = a->frac_hi; |
| 1449 | a1 = 0; |
| 1450 | |
| 1451 | n = fmt->frac_size + 2; |
| 1452 | if (unlikely(a_exp == -1)) { |
| 1453 | /* |
| 1454 | * When a_exp == -1, we're computing the log2 of a value [0.5,1.0). |
| 1455 | * When the value is very close to 1.0, there are lots of 1's in |
| 1456 | * the msb parts of the fraction. At the end, when we subtract |
| 1457 | * this value from -1.0, we can see a catastrophic loss of precision, |
| 1458 | * as 0x800..000 - 0x7ff..ffx becomes 0x000..00y, leaving only the |
| 1459 | * bits of y in the final result. To minimize this, compute as many |
| 1460 | * digits as we can. |
| 1461 | * ??? This case needs another algorithm to avoid this. |
| 1462 | */ |
| 1463 | n = fmt->frac_size * 2 + 2; |
| 1464 | /* Don't compute a value overlapping the sticky bit */ |
| 1465 | n = MIN(n, 62); |
| 1466 | } |
| 1467 | |
| 1468 | for (i = 0; i < n; i++) { |
| 1469 | if (a1) { |
| 1470 | mul128To256(a0, a1, a0, a1, &a0, &a1, &ign, &ign); |
| 1471 | } else if (a0 & 0xffffffffull) { |
| 1472 | mul64To128(a0, a0, &a0, &a1); |
| 1473 | } else if (a0 & ~DECOMPOSED_IMPLICIT_BIT) { |
| 1474 | a0 >>= 32; |
| 1475 | a0 *= a0; |
| 1476 | } else { |
| 1477 | goto exact; |
| 1478 | } |
| 1479 | |
| 1480 | if (a0 & DECOMPOSED_IMPLICIT_BIT) { |
| 1481 | if (unlikely(a_exp == 0 && r == 0)) { |
| 1482 | /* |
| 1483 | * When a_exp == 0, we're computing the log2 of a value |
| 1484 | * [1.0,2.0). When the value is very close to 1.0, there |
| 1485 | * are lots of 0's in the msb parts of the fraction. |
| 1486 | * We need to compute more digits to produce a correct |
| 1487 | * result -- restart at the top of the fraction. |
| 1488 | * ??? This is likely to lose precision quickly, as for |
| 1489 | * float128; we may need another method. |
| 1490 | */ |
| 1491 | f_exp -= i; |
| 1492 | t = r = DECOMPOSED_IMPLICIT_BIT; |
| 1493 | i = 0; |
| 1494 | } else { |
| 1495 | r |= t; |
| 1496 | } |
| 1497 | } else { |
| 1498 | add128(a0, a1, a0, a1, &a0, &a1); |
| 1499 | } |
| 1500 | t >>= 1; |
| 1501 | } |
| 1502 | |
| 1503 | /* Set sticky for inexact. */ |
| 1504 | r |= (a1 || a0 & ~DECOMPOSED_IMPLICIT_BIT); |
| 1505 | |
| 1506 | exact: |
| 1507 | parts_sint_to_float(a, a_exp, 0, s); |
| 1508 | if (r == 0) { |
| 1509 | return; |
| 1510 | } |
| 1511 | |
| 1512 | memset(&f, 0, sizeof(f)); |
| 1513 | f.cls = float_class_normal; |
| 1514 | f.frac_hi = r; |
| 1515 | f.exp = f_exp - frac_normalize(&f); |
| 1516 | |
| 1517 | if (a_exp < 0) { |
| 1518 | parts_sub_normal(a, &f); |
| 1519 | } else if (a_exp > 0) { |
| 1520 | parts_add_normal(a, &f); |
| 1521 | } else { |
| 1522 | *a = f; |
| 1523 | } |
| 1524 | return; |
| 1525 | |
| 1526 | d_nan: |
| 1527 | float_raise(float_flag_invalid, s); |
| 1528 | parts_default_nan(a, s); |
| 1529 | } |