1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 /* 13 * from: @(#)fdlibm.h 5.1 93/09/24 14 * $FreeBSD: head/lib/msun/src/math_private.h 336663 2018-07-24 10:10:16Z bde $ 15 */ 16 17 #ifndef _MATH_PRIVATE_H_ 18 #define _MATH_PRIVATE_H_ 19 20 #include <sys/types.h> 21 #include <machine/endian.h> 22 23 /* 24 * The original fdlibm code used statements like: 25 * n0 = ((*(int*)&one)>>29)^1; * index of high word * 26 * ix0 = *(n0+(int*)&x); * high word of x * 27 * ix1 = *((1-n0)+(int*)&x); * low word of x * 28 * to dig two 32 bit words out of the 64 bit IEEE floating point 29 * value. That is non-ANSI, and, moreover, the gcc instruction 30 * scheduler gets it wrong. We instead use the following macros. 31 * Unlike the original code, we determine the endianness at compile 32 * time, not at run time; I don't see much benefit to selecting 33 * endianness at run time. 34 */ 35 36 /* 37 * A union which permits us to convert between a double and two 32 bit 38 * ints. 39 */ 40 41 #ifdef __arm__ 42 #if defined(__VFP_FP__) || defined(__ARM_EABI__) 43 #define IEEE_WORD_ORDER BYTE_ORDER 44 #else 45 #define IEEE_WORD_ORDER BIG_ENDIAN 46 #endif 47 #else /* __arm__ */ 48 #define IEEE_WORD_ORDER BYTE_ORDER 49 #endif 50 51 /* A union which permits us to convert between a long double and 52 four 32 bit ints. */ 53 54 #if IEEE_WORD_ORDER == BIG_ENDIAN 55 56 typedef union 57 { 58 long double value; 59 struct { 60 u_int32_t mswhi; 61 u_int32_t mswlo; 62 u_int32_t lswhi; 63 u_int32_t lswlo; 64 } parts32; 65 struct { 66 u_int64_t msw; 67 u_int64_t lsw; 68 } parts64; 69 } ieee_quad_shape_type; 70 71 #endif 72 73 #if IEEE_WORD_ORDER == LITTLE_ENDIAN 74 75 typedef union 76 { 77 long double value; 78 struct { 79 u_int32_t lswlo; 80 u_int32_t lswhi; 81 u_int32_t mswlo; 82 u_int32_t mswhi; 83 } parts32; 84 struct { 85 u_int64_t lsw; 86 u_int64_t msw; 87 } parts64; 88 } ieee_quad_shape_type; 89 90 #endif 91 92 #if IEEE_WORD_ORDER == BIG_ENDIAN 93 94 typedef union 95 { 96 double value; 97 struct 98 { 99 u_int32_t msw; 100 u_int32_t lsw; 101 } parts; 102 struct 103 { 104 u_int64_t w; 105 } xparts; 106 } ieee_double_shape_type; 107 108 #endif 109 110 #if IEEE_WORD_ORDER == LITTLE_ENDIAN 111 112 typedef union 113 { 114 double value; 115 struct 116 { 117 u_int32_t lsw; 118 u_int32_t msw; 119 } parts; 120 struct 121 { 122 u_int64_t w; 123 } xparts; 124 } ieee_double_shape_type; 125 126 #endif 127 128 /* Get two 32 bit ints from a double. */ 129 130 #define EXTRACT_WORDS(ix0,ix1,d) \ 131 do { \ 132 ieee_double_shape_type ew_u; \ 133 ew_u.value = (d); \ 134 (ix0) = ew_u.parts.msw; \ 135 (ix1) = ew_u.parts.lsw; \ 136 } while (0) 137 138 /* Get a 64-bit int from a double. */ 139 #define EXTRACT_WORD64(ix,d) \ 140 do { \ 141 ieee_double_shape_type ew_u; \ 142 ew_u.value = (d); \ 143 (ix) = ew_u.xparts.w; \ 144 } while (0) 145 146 /* Get the more significant 32 bit int from a double. */ 147 148 #define GET_HIGH_WORD(i,d) \ 149 do { \ 150 ieee_double_shape_type gh_u; \ 151 gh_u.value = (d); \ 152 (i) = gh_u.parts.msw; \ 153 } while (0) 154 155 /* Get the less significant 32 bit int from a double. */ 156 157 #define GET_LOW_WORD(i,d) \ 158 do { \ 159 ieee_double_shape_type gl_u; \ 160 gl_u.value = (d); \ 161 (i) = gl_u.parts.lsw; \ 162 } while (0) 163 164 /* Set a double from two 32 bit ints. */ 165 166 #define INSERT_WORDS(d,ix0,ix1) \ 167 do { \ 168 ieee_double_shape_type iw_u; \ 169 iw_u.parts.msw = (ix0); \ 170 iw_u.parts.lsw = (ix1); \ 171 (d) = iw_u.value; \ 172 } while (0) 173 174 /* Set a double from a 64-bit int. */ 175 #define INSERT_WORD64(d,ix) \ 176 do { \ 177 ieee_double_shape_type iw_u; \ 178 iw_u.xparts.w = (ix); \ 179 (d) = iw_u.value; \ 180 } while (0) 181 182 /* Set the more significant 32 bits of a double from an int. */ 183 184 #define SET_HIGH_WORD(d,v) \ 185 do { \ 186 ieee_double_shape_type sh_u; \ 187 sh_u.value = (d); \ 188 sh_u.parts.msw = (v); \ 189 (d) = sh_u.value; \ 190 } while (0) 191 192 /* Set the less significant 32 bits of a double from an int. */ 193 194 #define SET_LOW_WORD(d,v) \ 195 do { \ 196 ieee_double_shape_type sl_u; \ 197 sl_u.value = (d); \ 198 sl_u.parts.lsw = (v); \ 199 (d) = sl_u.value; \ 200 } while (0) 201 202 /* 203 * A union which permits us to convert between a float and a 32 bit 204 * int. 205 */ 206 207 typedef union 208 { 209 float value; 210 /* FIXME: Assumes 32 bit int. */ 211 unsigned int word; 212 } ieee_float_shape_type; 213 214 /* Get a 32 bit int from a float. */ 215 216 #define GET_FLOAT_WORD(i,d) \ 217 do { \ 218 ieee_float_shape_type gf_u; \ 219 gf_u.value = (d); \ 220 (i) = gf_u.word; \ 221 } while (0) 222 223 /* Set a float from a 32 bit int. */ 224 225 #define SET_FLOAT_WORD(d,i) \ 226 do { \ 227 ieee_float_shape_type sf_u; \ 228 sf_u.word = (i); \ 229 (d) = sf_u.value; \ 230 } while (0) 231 232 /* 233 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long 234 * double. 235 */ 236 237 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \ 238 do { \ 239 union IEEEl2bits ew_u; \ 240 ew_u.e = (d); \ 241 (ix0) = ew_u.xbits.expsign; \ 242 (ix1) = ew_u.xbits.man; \ 243 } while (0) 244 245 /* 246 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit 247 * long double. 248 */ 249 250 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \ 251 do { \ 252 union IEEEl2bits ew_u; \ 253 ew_u.e = (d); \ 254 (ix0) = ew_u.xbits.expsign; \ 255 (ix1) = ew_u.xbits.manh; \ 256 (ix2) = ew_u.xbits.manl; \ 257 } while (0) 258 259 /* Get expsign as a 16 bit int from a long double. */ 260 261 #define GET_LDBL_EXPSIGN(i,d) \ 262 do { \ 263 union IEEEl2bits ge_u; \ 264 ge_u.e = (d); \ 265 (i) = ge_u.xbits.expsign; \ 266 } while (0) 267 268 /* 269 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int 270 * mantissa. 271 */ 272 273 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \ 274 do { \ 275 union IEEEl2bits iw_u; \ 276 iw_u.xbits.expsign = (ix0); \ 277 iw_u.xbits.man = (ix1); \ 278 (d) = iw_u.e; \ 279 } while (0) 280 281 /* 282 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints 283 * comprising the mantissa. 284 */ 285 286 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \ 287 do { \ 288 union IEEEl2bits iw_u; \ 289 iw_u.xbits.expsign = (ix0); \ 290 iw_u.xbits.manh = (ix1); \ 291 iw_u.xbits.manl = (ix2); \ 292 (d) = iw_u.e; \ 293 } while (0) 294 295 /* Set expsign of a long double from a 16 bit int. */ 296 297 #define SET_LDBL_EXPSIGN(d,v) \ 298 do { \ 299 union IEEEl2bits se_u; \ 300 se_u.e = (d); \ 301 se_u.xbits.expsign = (v); \ 302 (d) = se_u.e; \ 303 } while (0) 304 305 #ifdef __i386__ 306 /* Long double constants are broken on i386. */ 307 #define LD80C(m, ex, v) { \ 308 .xbits.man = __CONCAT(m, ULL), \ 309 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \ 310 } 311 #else 312 /* The above works on non-i386 too, but we use this to check v. */ 313 #define LD80C(m, ex, v) { .e = (v), } 314 #endif 315 316 #ifdef FLT_EVAL_METHOD 317 /* 318 * Attempt to get strict C99 semantics for assignment with non-C99 compilers. 319 */ 320 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 321 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) 322 #else 323 #define STRICT_ASSIGN(type, lval, rval) do { \ 324 volatile type __lval; \ 325 \ 326 if (sizeof(type) >= sizeof(long double)) \ 327 (lval) = (rval); \ 328 else { \ 329 __lval = (rval); \ 330 (lval) = __lval; \ 331 } \ 332 } while (0) 333 #endif 334 #endif /* FLT_EVAL_METHOD */ 335 336 /* Support switching the mode to FP_PE if necessary. */ 337 #if defined(__i386__) && !defined(NO_FPSETPREC) 338 #define ENTERI() ENTERIT(long double) 339 #define ENTERIT(returntype) \ 340 returntype __retval; \ 341 fp_prec_t __oprec; \ 342 \ 343 if ((__oprec = fpgetprec()) != FP_PE) \ 344 fpsetprec(FP_PE) 345 #define RETURNI(x) do { \ 346 __retval = (x); \ 347 if (__oprec != FP_PE) \ 348 fpsetprec(__oprec); \ 349 RETURNF(__retval); \ 350 } while (0) 351 #define ENTERV() \ 352 fp_prec_t __oprec; \ 353 \ 354 if ((__oprec = fpgetprec()) != FP_PE) \ 355 fpsetprec(FP_PE) 356 #define RETURNV() do { \ 357 if (__oprec != FP_PE) \ 358 fpsetprec(__oprec); \ 359 return; \ 360 } while (0) 361 #else 362 #define ENTERI() 363 #define ENTERIT(x) 364 #define RETURNI(x) RETURNF(x) 365 #define ENTERV() 366 #define RETURNV() return 367 #endif 368 369 /* Default return statement if hack*_t() is not used. */ 370 #define RETURNF(v) return (v) 371 372 /* 373 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or 374 * a == 0, but is slower. 375 */ 376 #define _2sum(a, b) do { \ 377 __typeof(a) __s, __w; \ 378 \ 379 __w = (a) + (b); \ 380 __s = __w - (a); \ 381 (b) = ((a) - (__w - __s)) + ((b) - __s); \ 382 (a) = __w; \ 383 } while (0) 384 385 /* 386 * 2sumF algorithm. 387 * 388 * "Normalize" the terms in the infinite-precision expression a + b for 389 * the sum of 2 floating point values so that b is as small as possible 390 * relative to 'a'. (The resulting 'a' is the value of the expression in 391 * the same precision as 'a' and the resulting b is the rounding error.) 392 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and 393 * exponent overflow or underflow must not occur. This uses a Theorem of 394 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum" 395 * is apparently due to Skewchuk (1997). 396 * 397 * For this to always work, assignment of a + b to 'a' must not retain any 398 * extra precision in a + b. This is required by C standards but broken 399 * in many compilers. The brokenness cannot be worked around using 400 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this 401 * algorithm would be destroyed by non-null strict assignments. (The 402 * compilers are correct to be broken -- the efficiency of all floating 403 * point code calculations would be destroyed similarly if they forced the 404 * conversions.) 405 * 406 * Fortunately, a case that works well can usually be arranged by building 407 * any extra precision into the type of 'a' -- 'a' should have type float_t, 408 * double_t or long double. b's type should be no larger than 'a's type. 409 * Callers should use these types with scopes as large as possible, to 410 * reduce their own extra-precision and efficiciency problems. In 411 * particular, they shouldn't convert back and forth just to call here. 412 */ 413 #ifdef DEBUG 414 #define _2sumF(a, b) do { \ 415 __typeof(a) __w; \ 416 volatile __typeof(a) __ia, __ib, __r, __vw; \ 417 \ 418 __ia = (a); \ 419 __ib = (b); \ 420 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \ 421 \ 422 __w = (a) + (b); \ 423 (b) = ((a) - __w) + (b); \ 424 (a) = __w; \ 425 \ 426 /* The next 2 assertions are weak if (a) is already long double. */ \ 427 assert((long double)__ia + __ib == (long double)(a) + (b)); \ 428 __vw = __ia + __ib; \ 429 __r = __ia - __vw; \ 430 __r += __ib; \ 431 assert(__vw == (a) && __r == (b)); \ 432 } while (0) 433 #else /* !DEBUG */ 434 #define _2sumF(a, b) do { \ 435 __typeof(a) __w; \ 436 \ 437 __w = (a) + (b); \ 438 (b) = ((a) - __w) + (b); \ 439 (a) = __w; \ 440 } while (0) 441 #endif /* DEBUG */ 442 443 /* 444 * Set x += c, where x is represented in extra precision as a + b. 445 * x must be sufficiently normalized and sufficiently larger than c, 446 * and the result is then sufficiently normalized. 447 * 448 * The details of ordering are that |a| must be >= |c| (so that (a, c) 449 * can be normalized without extra work to swap 'a' with c). The details of 450 * the normalization are that b must be small relative to the normalized 'a'. 451 * Normalization of (a, c) makes the normalized c tiny relative to the 452 * normalized a, so b remains small relative to 'a' in the result. However, 453 * b need not ever be tiny relative to 'a'. For example, b might be about 454 * 2**20 times smaller than 'a' to give about 20 extra bits of precision. 455 * That is usually enough, and adding c (which by normalization is about 456 * 2**53 times smaller than a) cannot change b significantly. However, 457 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a' 458 * significantly relative to b. The caller must ensure that significant 459 * cancellation doesn't occur, either by having c of the same sign as 'a', 460 * or by having |c| a few percent smaller than |a|. Pre-normalization of 461 * (a, b) may help. 462 * 463 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2 464 * exercise 19). We gain considerable efficiency by requiring the terms to 465 * be sufficiently normalized and sufficiently increasing. 466 */ 467 #define _3sumF(a, b, c) do { \ 468 __typeof(a) __tmp; \ 469 \ 470 __tmp = (c); \ 471 _2sumF(__tmp, (a)); \ 472 (b) += (a); \ 473 (a) = __tmp; \ 474 } while (0) 475 476 /* 477 * Common routine to process the arguments to nan(), nanf(), and nanl(). 478 */ 479 void _scan_nan(uint32_t *__words, int __num_words, const char *__s); 480 481 /* 482 * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns 483 * signaling NaNs into quiet NaNs by setting a quiet bit. We do this 484 * because we want to never return a signaling NaN, and also because we 485 * don't want the quiet bit to affect the result. Then mix the converted 486 * args using the specified operation. 487 * 488 * When one arg is NaN, the result is typically that arg quieted. When both 489 * args are NaNs, the result is typically the quietening of the arg whose 490 * mantissa is largest after quietening. When neither arg is NaN, the 491 * result may be NaN because it is indeterminate, or finite for subsequent 492 * construction of a NaN as the indeterminate 0.0L/0.0L. 493 * 494 * Technical complications: the result in bits after rounding to the final 495 * precision might depend on the runtime precision and/or on compiler 496 * optimizations, especially when different register sets are used for 497 * different precisions. Try to make the result not depend on at least the 498 * runtime precision by always doing the main mixing step in long double 499 * precision. Try to reduce dependencies on optimizations by adding the 500 * the 0's in different precisions (unless everything is in long double 501 * precision). 502 */ 503 #define nan_mix(x, y) (nan_mix_op((x), (y), +)) 504 #define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0)) 505 506 #ifdef _COMPLEX_H 507 508 /* 509 * C99 specifies that complex numbers have the same representation as 510 * an array of two elements, where the first element is the real part 511 * and the second element is the imaginary part. 512 */ 513 typedef union { 514 float complex f; 515 float a[2]; 516 } float_complex; 517 typedef union { 518 double complex f; 519 double a[2]; 520 } double_complex; 521 typedef union { 522 long double complex f; 523 long double a[2]; 524 } long_double_complex; 525 #define REALPART(z) ((z).a[0]) 526 #define IMAGPART(z) ((z).a[1]) 527 528 /* 529 * Inline functions that can be used to construct complex values. 530 * 531 * The C99 standard intends x+I*y to be used for this, but x+I*y is 532 * currently unusable in general since gcc introduces many overflow, 533 * underflow, sign and efficiency bugs by rewriting I*y as 534 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. 535 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted 536 * to -0.0+I*0.0. 537 * 538 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() 539 * to construct complex values. Compilers that conform to the C99 540 * standard require the following functions to avoid the above issues. 541 */ 542 543 #ifndef CMPLXF 544 static __inline float complex 545 CMPLXF(float x, float y) 546 { 547 float_complex z; 548 549 REALPART(z) = x; 550 IMAGPART(z) = y; 551 return (z.f); 552 } 553 #endif 554 555 #ifndef CMPLX 556 static __inline double complex 557 CMPLX(double x, double y) 558 { 559 double_complex z; 560 561 REALPART(z) = x; 562 IMAGPART(z) = y; 563 return (z.f); 564 } 565 #endif 566 567 #ifndef CMPLXL 568 static __inline long double complex 569 CMPLXL(long double x, long double y) 570 { 571 long_double_complex z; 572 573 REALPART(z) = x; 574 IMAGPART(z) = y; 575 return (z.f); 576 } 577 #endif 578 579 #endif /* _COMPLEX_H */ 580 581 /* 582 * The rnint() family rounds to the nearest integer for a restricted range 583 * range of args (up to about 2**MANT_DIG). We assume that the current 584 * rounding mode is FE_TONEAREST so that this can be done efficiently. 585 * Extra precision causes more problems in practice, and we only centralize 586 * this here to reduce those problems, and have not solved the efficiency 587 * problems. The exp2() family uses a more delicate version of this that 588 * requires extracting bits from the intermediate value, so it is not 589 * centralized here and should copy any solution of the efficiency problems. 590 */ 591 592 static inline double 593 rnint(__double_t x) 594 { 595 /* 596 * This casts to double to kill any extra precision. This depends 597 * on the cast being applied to a double_t to avoid compiler bugs 598 * (this is a cleaner version of STRICT_ASSIGN()). This is 599 * inefficient if there actually is extra precision, but is hard 600 * to improve on. We use double_t in the API to minimise conversions 601 * for just calling here. Note that we cannot easily change the 602 * magic number to the one that works directly with double_t, since 603 * the rounding precision is variable at runtime on x86 so the 604 * magic number would need to be variable. Assuming that the 605 * rounding precision is always the default is too fragile. This 606 * and many other complications will move when the default is 607 * changed to FP_PE. 608 */ 609 return ((double)(x + 0x1.8p52) - 0x1.8p52); 610 } 611 612 static inline float 613 rnintf(__float_t x) 614 { 615 /* 616 * As for rnint(), except we could just call that to handle the 617 * extra precision case, usually without losing efficiency. 618 */ 619 return ((float)(x + 0x1.8p23F) - 0x1.8p23F); 620 } 621 622 #ifdef LDBL_MANT_DIG 623 /* 624 * The complications for extra precision are smaller for rnintl() since it 625 * can safely assume that the rounding precision has been increased from 626 * its default to FP_PE on x86. We don't exploit that here to get small 627 * optimizations from limiting the rangle to double. We just need it for 628 * the magic number to work with long doubles. ld128 callers should use 629 * rnint() instead of this if possible. ld80 callers should prefer 630 * rnintl() since for amd64 this avoids swapping the register set, while 631 * for i386 it makes no difference (assuming FP_PE), and for other arches 632 * it makes little difference. 633 */ 634 static inline long double 635 rnintl(long double x) 636 { 637 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 - 638 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2); 639 } 640 #endif /* LDBL_MANT_DIG */ 641 642 /* 643 * irint() and i64rint() give the same result as casting to their integer 644 * return type provided their arg is a floating point integer. They can 645 * sometimes be more efficient because no rounding is required. 646 */ 647 #if (defined(amd64) || defined(__i386__)) && defined(__GNUCLIKE_ASM) 648 #define irint(x) \ 649 (sizeof(x) == sizeof(float) && \ 650 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \ 651 sizeof(x) == sizeof(double) && \ 652 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \ 653 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x)) 654 #else 655 #define irint(x) ((int)(x)) 656 #endif 657 658 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */ 659 660 #if defined(__i386__) && defined(__GNUCLIKE_ASM) 661 static __inline int 662 irintf(float x) 663 { 664 int n; 665 666 __asm("fistl %0" : "=m" (n) : "t" (x)); 667 return (n); 668 } 669 670 static __inline int 671 irintd(double x) 672 { 673 int n; 674 675 __asm("fistl %0" : "=m" (n) : "t" (x)); 676 return (n); 677 } 678 #endif 679 680 #if (defined(__amd64__) || defined(__i386__)) && defined(__GNUCLIKE_ASM) 681 static __inline int 682 irintl(long double x) 683 { 684 int n; 685 686 __asm("fistl %0" : "=m" (n) : "t" (x)); 687 return (n); 688 } 689 #endif 690 691 #ifdef DEBUG 692 #if defined(__amd64__) || defined(__i386__) 693 #define breakpoint() asm("int $3") 694 #else 695 #include <signal.h> 696 697 #define breakpoint() raise(SIGTRAP) 698 #endif 699 #endif 700 701 /* Write a pari script to test things externally. */ 702 #ifdef DOPRINT 703 #include <stdio.h> 704 705 #ifndef DOPRINT_SWIZZLE 706 #define DOPRINT_SWIZZLE 0 707 #endif 708 709 #ifdef DOPRINT_LD80 710 711 #define DOPRINT_START(xp) do { \ 712 uint64_t __lx; \ 713 uint16_t __hx; \ 714 \ 715 /* Hack to give more-problematic args. */ \ 716 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \ 717 __lx ^= DOPRINT_SWIZZLE; \ 718 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \ 719 printf("x = %.21Lg; ", (long double)*xp); \ 720 } while (0) 721 #define DOPRINT_END1(v) \ 722 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 723 #define DOPRINT_END2(hi, lo) \ 724 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 725 (long double)(hi), (long double)(lo)) 726 727 #elif defined(DOPRINT_D64) 728 729 #define DOPRINT_START(xp) do { \ 730 uint32_t __hx, __lx; \ 731 \ 732 EXTRACT_WORDS(__hx, __lx, *xp); \ 733 __lx ^= DOPRINT_SWIZZLE; \ 734 INSERT_WORDS(*xp, __hx, __lx); \ 735 printf("x = %.21Lg; ", (long double)*xp); \ 736 } while (0) 737 #define DOPRINT_END1(v) \ 738 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 739 #define DOPRINT_END2(hi, lo) \ 740 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 741 (long double)(hi), (long double)(lo)) 742 743 #elif defined(DOPRINT_F32) 744 745 #define DOPRINT_START(xp) do { \ 746 uint32_t __hx; \ 747 \ 748 GET_FLOAT_WORD(__hx, *xp); \ 749 __hx ^= DOPRINT_SWIZZLE; \ 750 SET_FLOAT_WORD(*xp, __hx); \ 751 printf("x = %.21Lg; ", (long double)*xp); \ 752 } while (0) 753 #define DOPRINT_END1(v) \ 754 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 755 #define DOPRINT_END2(hi, lo) \ 756 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 757 (long double)(hi), (long double)(lo)) 758 759 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */ 760 761 #ifndef DOPRINT_SWIZZLE_HIGH 762 #define DOPRINT_SWIZZLE_HIGH 0 763 #endif 764 765 #define DOPRINT_START(xp) do { \ 766 uint64_t __lx, __llx; \ 767 uint16_t __hx; \ 768 \ 769 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \ 770 __llx ^= DOPRINT_SWIZZLE; \ 771 __lx ^= DOPRINT_SWIZZLE_HIGH; \ 772 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \ 773 printf("x = %.36Lg; ", (long double)*xp); \ 774 } while (0) 775 #define DOPRINT_END1(v) \ 776 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v)) 777 #define DOPRINT_END2(hi, lo) \ 778 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \ 779 (long double)(hi), (long double)(lo)) 780 781 #endif /* DOPRINT_LD80 */ 782 783 #else /* !DOPRINT */ 784 #define DOPRINT_START(xp) 785 #define DOPRINT_END1(v) 786 #define DOPRINT_END2(hi, lo) 787 #endif /* DOPRINT */ 788 789 #define RETURNP(x) do { \ 790 DOPRINT_END1(x); \ 791 RETURNF(x); \ 792 } while (0) 793 #define RETURNPI(x) do { \ 794 DOPRINT_END1(x); \ 795 RETURNI(x); \ 796 } while (0) 797 #define RETURN2P(x, y) do { \ 798 DOPRINT_END2((x), (y)); \ 799 RETURNF((x) + (y)); \ 800 } while (0) 801 #define RETURN2PI(x, y) do { \ 802 DOPRINT_END2((x), (y)); \ 803 RETURNI((x) + (y)); \ 804 } while (0) 805 #ifdef STRUCT_RETURN 806 #define RETURNSP(rp) do { \ 807 if (!(rp)->lo_set) \ 808 RETURNP((rp)->hi); \ 809 RETURN2P((rp)->hi, (rp)->lo); \ 810 } while (0) 811 #define RETURNSPI(rp) do { \ 812 if (!(rp)->lo_set) \ 813 RETURNPI((rp)->hi); \ 814 RETURN2PI((rp)->hi, (rp)->lo); \ 815 } while (0) 816 #endif 817 #define SUM2P(x, y) ({ \ 818 const __typeof (x) __x = (x); \ 819 const __typeof (y) __y = (y); \ 820 \ 821 DOPRINT_END2(__x, __y); \ 822 __x + __y; \ 823 }) 824 825 /* 826 * ieee style elementary functions 827 * 828 * We rename functions here to improve other sources' diffability 829 * against fdlibm. 830 */ 831 #define __ieee754_sqrt sqrt 832 #define __ieee754_acos acos 833 #define __ieee754_acosh acosh 834 #define __ieee754_log log 835 #define __ieee754_log2 log2 836 #define __ieee754_atanh atanh 837 #define __ieee754_asin asin 838 #define __ieee754_atan2 atan2 839 #define __ieee754_exp exp 840 #define __ieee754_cosh cosh 841 #define __ieee754_fmod fmod 842 #define __ieee754_pow pow 843 #define __ieee754_lgamma lgamma 844 #define __ieee754_gamma gamma 845 #define __ieee754_lgamma_r lgamma_r 846 #define __ieee754_gamma_r gamma_r 847 #define __ieee754_log10 log10 848 #define __ieee754_sinh sinh 849 #define __ieee754_hypot hypot 850 #define __ieee754_j0 j0 851 #define __ieee754_j1 j1 852 #define __ieee754_y0 y0 853 #define __ieee754_y1 y1 854 #define __ieee754_jn jn 855 #define __ieee754_yn yn 856 #define __ieee754_remainder remainder 857 #define __ieee754_scalb scalb 858 #define __ieee754_sqrtf sqrtf 859 #define __ieee754_acosf acosf 860 #define __ieee754_acoshf acoshf 861 #define __ieee754_logf logf 862 #define __ieee754_atanhf atanhf 863 #define __ieee754_asinf asinf 864 #define __ieee754_atan2f atan2f 865 #define __ieee754_expf expf 866 #define __ieee754_coshf coshf 867 #define __ieee754_fmodf fmodf 868 #define __ieee754_powf powf 869 #define __ieee754_lgammaf lgammaf 870 #define __ieee754_gammaf gammaf 871 #define __ieee754_lgammaf_r lgammaf_r 872 #define __ieee754_gammaf_r gammaf_r 873 #define __ieee754_log10f log10f 874 #define __ieee754_log2f log2f 875 #define __ieee754_sinhf sinhf 876 #define __ieee754_hypotf hypotf 877 #define __ieee754_j0f j0f 878 #define __ieee754_j1f j1f 879 #define __ieee754_y0f y0f 880 #define __ieee754_y1f y1f 881 #define __ieee754_jnf jnf 882 #define __ieee754_ynf ynf 883 #define __ieee754_remainderf remainderf 884 #define __ieee754_scalbf scalbf 885 886 /* fdlibm kernel function */ 887 int __kernel_rem_pio2(double*,double*,int,int,int); 888 889 /* double precision kernel functions */ 890 #ifndef INLINE_REM_PIO2 891 int __ieee754_rem_pio2(double,double*); 892 #endif 893 double __kernel_sin(double,double,int); 894 double __kernel_cos(double,double); 895 double __kernel_tan(double,double,int); 896 double __ldexp_exp(double,int); 897 #ifdef _COMPLEX_H 898 double complex __ldexp_cexp(double complex,int); 899 #endif 900 901 /* float precision kernel functions */ 902 #ifndef INLINE_REM_PIO2F 903 int __ieee754_rem_pio2f(float,double*); 904 #endif 905 #ifndef INLINE_KERNEL_SINDF 906 float __kernel_sindf(double); 907 #endif 908 #ifndef INLINE_KERNEL_COSDF 909 float __kernel_cosdf(double); 910 #endif 911 #ifndef INLINE_KERNEL_TANDF 912 float __kernel_tandf(double,int); 913 #endif 914 float __ldexp_expf(float,int); 915 #ifdef _COMPLEX_H 916 float complex __ldexp_cexpf(float complex,int); 917 #endif 918 919 /* long double precision kernel functions */ 920 long double __kernel_sinl(long double, long double, int); 921 long double __kernel_cosl(long double, long double); 922 long double __kernel_tanl(long double, long double, int); 923 924 #endif /* !_MATH_PRIVATE_H_ */ 925
