1 /* $OpenBSD: fpu_implode.c,v 1.6 2019/03/15 05:42:38 kevlo Exp $ */ 2 3 /* 4 * Copyright (c) 1992, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * This software was developed by the Computer Systems Engineering group 8 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 9 * contributed to Berkeley. 10 * 11 * All advertising materials mentioning features or use of this software 12 * must display the following acknowledgement: 13 * This product includes software developed by the University of 14 * California, Lawrence Berkeley Laboratory. 15 * 16 * Redistribution and use in source and binary forms, with or without 17 * modification, are permitted provided that the following conditions 18 * are met: 19 * 1. Redistributions of source code must retain the above copyright 20 * notice, this list of conditions and the following disclaimer. 21 * 2. Redistributions in binary form must reproduce the above copyright 22 * notice, this list of conditions and the following disclaimer in the 23 * documentation and/or other materials provided with the distribution. 24 * 3. All advertising materials mentioning features or use of this software 25 * must display the following acknowledgement: 26 * This product includes software developed by the University of 27 * California, Berkeley and its contributors. 28 * 4. Neither the name of the University nor the names of its contributors 29 * may be used to endorse or promote products derived from this software 30 * without specific prior written permission. 31 * 32 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 33 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 34 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 35 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 36 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 37 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 38 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 39 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 40 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 41 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 42 * SUCH DAMAGE. 43 * 44 * @(#)fpu_implode.c 8.1 (Berkeley) 6/11/93 45 * $NetBSD: fpu_implode.c,v 1.8 2001/08/26 05:44:46 eeh Exp $ 46 */ 47 48 /* 49 * FPU subroutines: `implode' internal format numbers into the machine's 50 * `packed binary' format. 51 */ 52 53 #include <sys/param.h> 54 55 #include <machine/frame.h> 56 #include <machine/fsr.h> 57 #include <machine/ieee.h> 58 #include <machine/instr.h> 59 60 #include "fpu_arith.h" 61 #include "fpu_emu.h" 62 #include "fpu_extern.h" 63 64 static int fpround(struct fpemu *, struct fpn *); 65 static int toinf(struct fpemu *, int); 66 67 #define FSR_GET_RD(fsr) (((fsr) >> FSR_RD_SHIFT) & FSR_RD_MASK) 68 69 /* 70 * Round a number (algorithm from Motorola MC68882 manual, modified for 71 * our internal format). Set inexact exception if rounding is required. 72 * Return true iff we rounded up. 73 * 74 * After rounding, we discard the guard and round bits by shifting right 75 * 2 bits (a la fpu_shr(), but we do not bother with fp->fp_sticky). 76 * This saves effort later. 77 * 78 * Note that we may leave the value 2.0 in fp->fp_mant; it is the caller's 79 * responsibility to fix this if necessary. 80 */ 81 static int 82 fpround(struct fpemu *fe, struct fpn *fp) 83 { 84 u_int m0, m1, m2, m3; 85 int gr, s; 86 87 m0 = fp->fp_mant[0]; 88 m1 = fp->fp_mant[1]; 89 m2 = fp->fp_mant[2]; 90 m3 = fp->fp_mant[3]; 91 gr = m3 & 3; 92 s = fp->fp_sticky; 93 94 /* mant >>= FP_NG */ 95 m3 = (m3 >> FP_NG) | (m2 << (32 - FP_NG)); 96 m2 = (m2 >> FP_NG) | (m1 << (32 - FP_NG)); 97 m1 = (m1 >> FP_NG) | (m0 << (32 - FP_NG)); 98 m0 >>= FP_NG; 99 100 if ((gr | s) == 0) /* result is exact: no rounding needed */ 101 goto rounddown; 102 103 fe->fe_cx |= FSR_NX; /* inexact */ 104 105 /* Go to rounddown to round down; break to round up. */ 106 switch (FSR_GET_RD(fe->fe_fsr)) { 107 case FSR_RD_RN: 108 default: 109 /* 110 * Round only if guard is set (gr & 2). If guard is set, 111 * but round & sticky both clear, then we want to round 112 * but have a tie, so round to even, i.e., add 1 iff odd. 113 */ 114 if ((gr & 2) == 0) 115 goto rounddown; 116 if ((gr & 1) || fp->fp_sticky || (m3 & 1)) 117 break; 118 goto rounddown; 119 120 case FSR_RD_RZ: 121 /* Round towards zero, i.e., down. */ 122 goto rounddown; 123 124 case FSR_RD_RM: 125 /* Round towards -Inf: up if negative, down if positive. */ 126 if (fp->fp_sign) 127 break; 128 goto rounddown; 129 130 case FSR_RD_RP: 131 /* Round towards +Inf: up if positive, down otherwise. */ 132 if (!fp->fp_sign) 133 break; 134 goto rounddown; 135 } 136 137 /* Bump low bit of mantissa, with carry. */ 138 FPU_ADDS(m3, m3, 1); 139 FPU_ADDCS(m2, m2, 0); 140 FPU_ADDCS(m1, m1, 0); 141 FPU_ADDC(m0, m0, 0); 142 fp->fp_mant[0] = m0; 143 fp->fp_mant[1] = m1; 144 fp->fp_mant[2] = m2; 145 fp->fp_mant[3] = m3; 146 return (1); 147 148 rounddown: 149 fp->fp_mant[0] = m0; 150 fp->fp_mant[1] = m1; 151 fp->fp_mant[2] = m2; 152 fp->fp_mant[3] = m3; 153 return (0); 154 } 155 156 /* 157 * For overflow: return true if overflow is to go to +/-Inf, according 158 * to the sign of the overflowing result. If false, overflow is to go 159 * to the largest magnitude value instead. 160 */ 161 static int 162 toinf(struct fpemu *fe, int sign) 163 { 164 int inf; 165 166 /* look at rounding direction */ 167 switch (FSR_GET_RD(fe->fe_fsr)) { 168 default: 169 case FSR_RD_RN: /* the nearest value is always Inf */ 170 inf = 1; 171 break; 172 173 case FSR_RD_RZ: /* toward 0 => never towards Inf */ 174 inf = 0; 175 break; 176 177 case FSR_RD_RP: /* toward +Inf iff positive */ 178 inf = sign == 0; 179 break; 180 181 case FSR_RD_RM: /* toward -Inf iff negative */ 182 inf = sign; 183 break; 184 } 185 return (inf); 186 } 187 188 /* 189 * fpn -> int (int value returned as return value). 190 * 191 * N.B.: this conversion always rounds towards zero (this is a peculiarity 192 * of the SPARC instruction set). 193 */ 194 u_int 195 __fpu_ftoi(fe, fp) 196 struct fpemu *fe; 197 struct fpn *fp; 198 { 199 u_int i; 200 int sign, exp; 201 202 sign = fp->fp_sign; 203 switch (fp->fp_class) { 204 205 case FPC_ZERO: 206 return (0); 207 208 case FPC_NUM: 209 /* 210 * If exp >= 2^32, overflow. Otherwise shift value right 211 * into last mantissa word (this will not exceed 0xffffffff), 212 * shifting any guard and round bits out into the sticky 213 * bit. Then ``round'' towards zero, i.e., just set an 214 * inexact exception if sticky is set (see fpround()). 215 * If the result is > 0x80000000, or is positive and equals 216 * 0x80000000, overflow; otherwise the last fraction word 217 * is the result. 218 */ 219 if ((exp = fp->fp_exp) >= 32) 220 break; 221 /* NB: the following includes exp < 0 cases */ 222 if (__fpu_shr(fp, FP_NMANT - 1 - exp) != 0) 223 fe->fe_cx |= FSR_NX; 224 i = fp->fp_mant[3]; 225 if (i >= ((u_int)0x80000000 + sign)) 226 break; 227 return (sign ? -i : i); 228 229 default: /* Inf, qNaN, sNaN */ 230 break; 231 } 232 /* overflow: replace any inexact exception with invalid */ 233 fe->fe_cx = (fe->fe_cx & ~FSR_NX) | FSR_NV; 234 return (0x7fffffff + sign); 235 } 236 237 /* 238 * fpn -> extended int (high bits of int value returned as return value). 239 * 240 * N.B.: this conversion always rounds towards zero (this is a peculiarity 241 * of the SPARC instruction set). 242 */ 243 u_int 244 __fpu_ftox(fe, fp, res) 245 struct fpemu *fe; 246 struct fpn *fp; 247 u_int *res; 248 { 249 u_int64_t i; 250 int sign, exp; 251 252 sign = fp->fp_sign; 253 switch (fp->fp_class) { 254 255 case FPC_ZERO: 256 res[1] = 0; 257 return (0); 258 259 case FPC_NUM: 260 /* 261 * If exp >= 2^64, overflow. Otherwise shift value right 262 * into last mantissa word (this will not exceed 263 * 0xffffffffffffffff), shifting any guard and round bits out 264 * into the sticky bit. Then ``round'' towards zero, i.e., 265 * just set an inexact exception if sticky is set (see 266 * fpround()). If the result is > 0x8000000000000000, or is 267 * positive and equals 0x8000000000000000, overflow; 268 * otherwise the last fraction word is the result. 269 */ 270 if ((exp = fp->fp_exp) >= 64) 271 break; 272 /* NB: the following includes exp < 0 cases */ 273 if (__fpu_shr(fp, FP_NMANT - 1 - exp) != 0) 274 fe->fe_cx |= FSR_NX; 275 i = ((u_int64_t)fp->fp_mant[2]<<32)|fp->fp_mant[3]; 276 if (i >= ((u_int64_t)0x8000000000000000LL + sign)) 277 break; 278 if (sign) 279 i = -i; 280 res[1] = (int)i; 281 return (i >> 32); 282 283 default: /* Inf, qNaN, sNaN */ 284 break; 285 } 286 /* overflow: replace any inexact exception with invalid */ 287 fe->fe_cx = (fe->fe_cx & ~FSR_NX) | FSR_NV; 288 return (0x7fffffffffffffffLL + sign); 289 } 290 291 /* 292 * fpn -> single (32 bit single returned as return value). 293 * We assume <= 29 bits in a single-precision fraction (1.f part). 294 */ 295 u_int 296 __fpu_ftos(fe, fp) 297 struct fpemu *fe; 298 struct fpn *fp; 299 { 300 u_int sign = fp->fp_sign << 31; 301 int exp; 302 303 #define SNG_EXP(e) ((e) << SNG_FRACBITS) /* makes e an exponent */ 304 #define SNG_MASK (SNG_EXP(1) - 1) /* mask for fraction */ 305 306 /* Take care of non-numbers first. */ 307 if (ISNAN(fp)) { 308 /* 309 * Preserve upper bits of NaN, per SPARC V8 appendix N. 310 * Note that fp->fp_mant[0] has the quiet bit set, 311 * even if it is classified as a signalling NaN. 312 */ 313 (void) __fpu_shr(fp, FP_NMANT - 1 - SNG_FRACBITS); 314 exp = SNG_EXP_INFNAN; 315 goto done; 316 } 317 if (ISINF(fp)) 318 return (sign | SNG_EXP(SNG_EXP_INFNAN)); 319 if (ISZERO(fp)) 320 return (sign); 321 322 /* 323 * Normals (including subnormals). Drop all the fraction bits 324 * (including the explicit ``implied'' 1 bit) down into the 325 * single-precision range. If the number is subnormal, move 326 * the ``implied'' 1 into the explicit range as well, and shift 327 * right to introduce leading zeroes. Rounding then acts 328 * differently for normals and subnormals: the largest subnormal 329 * may round to the smallest normal (1.0 x 2^minexp), or may 330 * remain subnormal. In the latter case, signal an underflow 331 * if the result was inexact or if underflow traps are enabled. 332 * 333 * Rounding a normal, on the other hand, always produces another 334 * normal (although either way the result might be too big for 335 * single precision, and cause an overflow). If rounding a 336 * normal produces 2.0 in the fraction, we need not adjust that 337 * fraction at all, since both 1.0 and 2.0 are zero under the 338 * fraction mask. 339 * 340 * Note that the guard and round bits vanish from the number after 341 * rounding. 342 */ 343 if ((exp = fp->fp_exp + SNG_EXP_BIAS) <= 0) { /* subnormal */ 344 /* -NG for g,r; -SNG_FRACBITS-exp for fraction */ 345 (void) __fpu_shr(fp, FP_NMANT - FP_NG - SNG_FRACBITS - exp); 346 if (fpround(fe, fp) && fp->fp_mant[3] == SNG_EXP(1)) 347 return (sign | SNG_EXP(1) | 0); 348 if ((fe->fe_cx & FSR_NX) || 349 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT))) 350 fe->fe_cx |= FSR_UF; 351 return (sign | SNG_EXP(0) | fp->fp_mant[3]); 352 } 353 /* -FP_NG for g,r; -1 for implied 1; -SNG_FRACBITS for fraction */ 354 (void) __fpu_shr(fp, FP_NMANT - FP_NG - 1 - SNG_FRACBITS); 355 #ifdef DIAGNOSTIC 356 if ((fp->fp_mant[3] & SNG_EXP(1 << FP_NG)) == 0) 357 __utrap_panic("fpu_ftos"); 358 #endif 359 if (fpround(fe, fp) && fp->fp_mant[3] == SNG_EXP(2)) 360 exp++; 361 if (exp >= SNG_EXP_INFNAN) { 362 /* overflow to inf or to max single */ 363 fe->fe_cx |= FSR_OF | FSR_NX; 364 if (toinf(fe, sign)) 365 return (sign | SNG_EXP(SNG_EXP_INFNAN)); 366 return (sign | SNG_EXP(SNG_EXP_INFNAN - 1) | SNG_MASK); 367 } 368 done: 369 /* phew, made it */ 370 return (sign | SNG_EXP(exp) | (fp->fp_mant[3] & SNG_MASK)); 371 } 372 373 /* 374 * fpn -> double (32 bit high-order result returned; 32-bit low order result 375 * left in res[1]). Assumes <= 61 bits in double precision fraction. 376 * 377 * This code mimics fpu_ftos; see it for comments. 378 */ 379 u_int 380 __fpu_ftod(fe, fp, res) 381 struct fpemu *fe; 382 struct fpn *fp; 383 u_int *res; 384 { 385 u_int sign = fp->fp_sign << 31; 386 int exp; 387 388 #define DBL_EXP(e) ((e) << (DBL_FRACBITS & 31)) 389 #define DBL_MASK (DBL_EXP(1) - 1) 390 391 if (ISNAN(fp)) { 392 (void) __fpu_shr(fp, FP_NMANT - 1 - DBL_FRACBITS); 393 exp = DBL_EXP_INFNAN; 394 goto done; 395 } 396 if (ISINF(fp)) { 397 sign |= DBL_EXP(DBL_EXP_INFNAN); 398 goto zero; 399 } 400 if (ISZERO(fp)) { 401 zero: res[1] = 0; 402 return (sign); 403 } 404 405 if ((exp = fp->fp_exp + DBL_EXP_BIAS) <= 0) { 406 (void) __fpu_shr(fp, FP_NMANT - FP_NG - DBL_FRACBITS - exp); 407 if (fpround(fe, fp) && fp->fp_mant[2] == DBL_EXP(1)) { 408 res[1] = 0; 409 return (sign | DBL_EXP(1) | 0); 410 } 411 if ((fe->fe_cx & FSR_NX) || 412 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT))) 413 fe->fe_cx |= FSR_UF; 414 exp = 0; 415 goto done; 416 } 417 (void) __fpu_shr(fp, FP_NMANT - FP_NG - 1 - DBL_FRACBITS); 418 if (fpround(fe, fp) && fp->fp_mant[2] == DBL_EXP(2)) 419 exp++; 420 if (exp >= DBL_EXP_INFNAN) { 421 fe->fe_cx |= FSR_OF | FSR_NX; 422 if (toinf(fe, sign)) { 423 res[1] = 0; 424 return (sign | DBL_EXP(DBL_EXP_INFNAN) | 0); 425 } 426 res[1] = ~0; 427 return (sign | DBL_EXP(DBL_EXP_INFNAN) | DBL_MASK); 428 } 429 done: 430 res[1] = fp->fp_mant[3]; 431 return (sign | DBL_EXP(exp) | (fp->fp_mant[2] & DBL_MASK)); 432 } 433 434 /* 435 * fpn -> extended (32 bit high-order result returned; low-order fraction 436 * words left in res[1]..res[3]). Like ftod, which is like ftos ... but 437 * our internal format *is* extended precision, plus 2 bits for guard/round, 438 * so we can avoid a small bit of work. 439 */ 440 u_int 441 __fpu_ftoq(fe, fp, res) 442 struct fpemu *fe; 443 struct fpn *fp; 444 u_int *res; 445 { 446 u_int sign = fp->fp_sign << 31; 447 int exp; 448 449 #define EXT_EXP(e) ((e) << (EXT_FRACBITS & 31)) 450 #define EXT_MASK (EXT_EXP(1) - 1) 451 452 if (ISNAN(fp)) { 453 (void) __fpu_shr(fp, 2); /* since we are not rounding */ 454 exp = EXT_EXP_INFNAN; 455 goto done; 456 } 457 if (ISINF(fp)) { 458 sign |= EXT_EXP(EXT_EXP_INFNAN); 459 goto zero; 460 } 461 if (ISZERO(fp)) { 462 zero: res[1] = res[2] = res[3] = 0; 463 return (sign); 464 } 465 466 if ((exp = fp->fp_exp + EXT_EXP_BIAS) <= 0) { 467 (void) __fpu_shr(fp, FP_NMANT - FP_NG - EXT_FRACBITS - exp); 468 if (fpround(fe, fp) && fp->fp_mant[0] == EXT_EXP(1)) { 469 res[1] = res[2] = res[3] = 0; 470 return (sign | EXT_EXP(1) | 0); 471 } 472 if ((fe->fe_cx & FSR_NX) || 473 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT))) 474 fe->fe_cx |= FSR_UF; 475 exp = 0; 476 goto done; 477 } 478 /* Since internal == extended, no need to shift here. */ 479 if (fpround(fe, fp) && fp->fp_mant[0] == EXT_EXP(2)) 480 exp++; 481 if (exp >= EXT_EXP_INFNAN) { 482 fe->fe_cx |= FSR_OF | FSR_NX; 483 if (toinf(fe, sign)) { 484 res[1] = res[2] = res[3] = 0; 485 return (sign | EXT_EXP(EXT_EXP_INFNAN) | 0); 486 } 487 res[1] = res[2] = res[3] = ~0; 488 return (sign | EXT_EXP(EXT_EXP_INFNAN) | EXT_MASK); 489 } 490 done: 491 res[1] = fp->fp_mant[1]; 492 res[2] = fp->fp_mant[2]; 493 res[3] = fp->fp_mant[3]; 494 return (sign | EXT_EXP(exp) | (fp->fp_mant[0] & EXT_MASK)); 495 } 496 497 /* 498 * Implode an fpn, writing the result into the given space. 499 */ 500 void 501 __fpu_implode(fe, fp, type, space) 502 struct fpemu *fe; 503 struct fpn *fp; 504 int type; 505 u_int *space; 506 { 507 508 switch (type) { 509 510 case FTYPE_LNG: 511 space[0] = __fpu_ftox(fe, fp, space); 512 break; 513 514 case FTYPE_INT: 515 space[0] = __fpu_ftoi(fe, fp); 516 break; 517 518 case FTYPE_SNG: 519 space[0] = __fpu_ftos(fe, fp); 520 break; 521 522 case FTYPE_DBL: 523 space[0] = __fpu_ftod(fe, fp, space); 524 break; 525 526 case FTYPE_EXT: 527 /* funky rounding precision options ?? */ 528 space[0] = __fpu_ftoq(fe, fp, space); 529 break; 530 531 #ifdef DIAGNOSTIC 532 default: 533 __utrap_panic("fpu_implode"); 534 #endif 535 } 536 DPRINTF(FPE_REG, ("fpu_implode: %x %x %x %x\n", 537 space[0], space[1], space[2], space[3])); 538 } 539