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 * $FreeBSD$ 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 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 addition. The result is typically the arg whose mantissa 487 * bits (considered as in integer) are largest. 488 * 489 * Technical complications: the result in bits might depend on the precision 490 * and/or on compiler optimizations, especially when different register sets 491 * are used for different precisions. Try to make the result not depend on 492 * at least the precision by always doing the main mixing step in long double 493 * precision. Try to reduce dependencies on optimizations by adding the 494 * the 0's in different precisions (unless everything is in long double 495 * precision). 496 */ 497 #define nan_mix(x, y) (((x) + 0.0L) + ((y) + 0)) 498 499 #ifdef _COMPLEX_H 500 501 /* 502 * C99 specifies that complex numbers have the same representation as 503 * an array of two elements, where the first element is the real part 504 * and the second element is the imaginary part. 505 */ 506 typedef union { 507 float complex f; 508 float a[2]; 509 } float_complex; 510 typedef union { 511 double complex f; 512 double a[2]; 513 } double_complex; 514 typedef union { 515 long double complex f; 516 long double a[2]; 517 } long_double_complex; 518 #define REALPART(z) ((z).a[0]) 519 #define IMAGPART(z) ((z).a[1]) 520 521 /* 522 * Inline functions that can be used to construct complex values. 523 * 524 * The C99 standard intends x+I*y to be used for this, but x+I*y is 525 * currently unusable in general since gcc introduces many overflow, 526 * underflow, sign and efficiency bugs by rewriting I*y as 527 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. 528 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted 529 * to -0.0+I*0.0. 530 * 531 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() 532 * to construct complex values. Compilers that conform to the C99 533 * standard require the following functions to avoid the above issues. 534 */ 535 536 #ifndef CMPLXF 537 static __inline float complex 538 CMPLXF(float x, float y) 539 { 540 float_complex z; 541 542 REALPART(z) = x; 543 IMAGPART(z) = y; 544 return (z.f); 545 } 546 #endif 547 548 #ifndef CMPLX 549 static __inline double complex 550 CMPLX(double x, double y) 551 { 552 double_complex z; 553 554 REALPART(z) = x; 555 IMAGPART(z) = y; 556 return (z.f); 557 } 558 #endif 559 560 #ifndef CMPLXL 561 static __inline long double complex 562 CMPLXL(long double x, long double y) 563 { 564 long_double_complex z; 565 566 REALPART(z) = x; 567 IMAGPART(z) = y; 568 return (z.f); 569 } 570 #endif 571 572 #endif /* _COMPLEX_H */ 573 574 /* 575 * The rnint() family rounds to the nearest integer for a restricted range 576 * range of args (up to about 2**MANT_DIG). We assume that the current 577 * rounding mode is FE_TONEAREST so that this can be done efficiently. 578 * Extra precision causes more problems in practice, and we only centralize 579 * this here to reduce those problems, and have not solved the efficiency 580 * problems. The exp2() family uses a more delicate version of this that 581 * requires extracting bits from the intermediate value, so it is not 582 * centralized here and should copy any solution of the efficiency problems. 583 */ 584 585 static inline double 586 rnint(__double_t x) 587 { 588 /* 589 * This casts to double to kill any extra precision. This depends 590 * on the cast being applied to a double_t to avoid compiler bugs 591 * (this is a cleaner version of STRICT_ASSIGN()). This is 592 * inefficient if there actually is extra precision, but is hard 593 * to improve on. We use double_t in the API to minimise conversions 594 * for just calling here. Note that we cannot easily change the 595 * magic number to the one that works directly with double_t, since 596 * the rounding precision is variable at runtime on x86 so the 597 * magic number would need to be variable. Assuming that the 598 * rounding precision is always the default is too fragile. This 599 * and many other complications will move when the default is 600 * changed to FP_PE. 601 */ 602 return ((double)(x + 0x1.8p52) - 0x1.8p52); 603 } 604 605 static inline float 606 rnintf(__float_t x) 607 { 608 /* 609 * As for rnint(), except we could just call that to handle the 610 * extra precision case, usually without losing efficiency. 611 */ 612 return ((float)(x + 0x1.8p23F) - 0x1.8p23F); 613 } 614 615 #ifdef LDBL_MANT_DIG 616 /* 617 * The complications for extra precision are smaller for rnintl() since it 618 * can safely assume that the rounding precision has been increased from 619 * its default to FP_PE on x86. We don't exploit that here to get small 620 * optimizations from limiting the rangle to double. We just need it for 621 * the magic number to work with long doubles. ld128 callers should use 622 * rnint() instead of this if possible. ld80 callers should prefer 623 * rnintl() since for amd64 this avoids swapping the register set, while 624 * for i386 it makes no difference (assuming FP_PE), and for other arches 625 * it makes little difference. 626 */ 627 static inline long double 628 rnintl(long double x) 629 { 630 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 - 631 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2); 632 } 633 #endif /* LDBL_MANT_DIG */ 634 635 /* 636 * irint() and i64rint() give the same result as casting to their integer 637 * return type provided their arg is a floating point integer. They can 638 * sometimes be more efficient because no rounding is required. 639 */ 640 #if (defined(amd64) || defined(__i386__)) && defined(__GNUCLIKE_ASM) 641 #define irint(x) \ 642 (sizeof(x) == sizeof(float) && \ 643 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \ 644 sizeof(x) == sizeof(double) && \ 645 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \ 646 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x)) 647 #else 648 #define irint(x) ((int)(x)) 649 #endif 650 651 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */ 652 653 #if defined(__i386__) && defined(__GNUCLIKE_ASM) 654 static __inline int 655 irintf(float x) 656 { 657 int n; 658 659 __asm("fistl %0" : "=m" (n) : "t" (x)); 660 return (n); 661 } 662 663 static __inline int 664 irintd(double x) 665 { 666 int n; 667 668 __asm("fistl %0" : "=m" (n) : "t" (x)); 669 return (n); 670 } 671 #endif 672 673 #if (defined(__amd64__) || defined(__i386__)) && defined(__GNUCLIKE_ASM) 674 static __inline int 675 irintl(long double x) 676 { 677 int n; 678 679 __asm("fistl %0" : "=m" (n) : "t" (x)); 680 return (n); 681 } 682 #endif 683 684 #ifdef DEBUG 685 #if defined(__amd64__) || defined(__i386__) 686 #define breakpoint() asm("int $3") 687 #else 688 #include <signal.h> 689 690 #define breakpoint() raise(SIGTRAP) 691 #endif 692 #endif 693 694 /* Write a pari script to test things externally. */ 695 #ifdef DOPRINT 696 #include <stdio.h> 697 698 #ifndef DOPRINT_SWIZZLE 699 #define DOPRINT_SWIZZLE 0 700 #endif 701 702 #ifdef DOPRINT_LD80 703 704 #define DOPRINT_START(xp) do { \ 705 uint64_t __lx; \ 706 uint16_t __hx; \ 707 \ 708 /* Hack to give more-problematic args. */ \ 709 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \ 710 __lx ^= DOPRINT_SWIZZLE; \ 711 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \ 712 printf("x = %.21Lg; ", (long double)*xp); \ 713 } while (0) 714 #define DOPRINT_END1(v) \ 715 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 716 #define DOPRINT_END2(hi, lo) \ 717 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 718 (long double)(hi), (long double)(lo)) 719 720 #elif defined(DOPRINT_D64) 721 722 #define DOPRINT_START(xp) do { \ 723 uint32_t __hx, __lx; \ 724 \ 725 EXTRACT_WORDS(__hx, __lx, *xp); \ 726 __lx ^= DOPRINT_SWIZZLE; \ 727 INSERT_WORDS(*xp, __hx, __lx); \ 728 printf("x = %.21Lg; ", (long double)*xp); \ 729 } while (0) 730 #define DOPRINT_END1(v) \ 731 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 732 #define DOPRINT_END2(hi, lo) \ 733 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 734 (long double)(hi), (long double)(lo)) 735 736 #elif defined(DOPRINT_F32) 737 738 #define DOPRINT_START(xp) do { \ 739 uint32_t __hx; \ 740 \ 741 GET_FLOAT_WORD(__hx, *xp); \ 742 __hx ^= DOPRINT_SWIZZLE; \ 743 SET_FLOAT_WORD(*xp, __hx); \ 744 printf("x = %.21Lg; ", (long double)*xp); \ 745 } while (0) 746 #define DOPRINT_END1(v) \ 747 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 748 #define DOPRINT_END2(hi, lo) \ 749 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 750 (long double)(hi), (long double)(lo)) 751 752 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */ 753 754 #ifndef DOPRINT_SWIZZLE_HIGH 755 #define DOPRINT_SWIZZLE_HIGH 0 756 #endif 757 758 #define DOPRINT_START(xp) do { \ 759 uint64_t __lx, __llx; \ 760 uint16_t __hx; \ 761 \ 762 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \ 763 __llx ^= DOPRINT_SWIZZLE; \ 764 __lx ^= DOPRINT_SWIZZLE_HIGH; \ 765 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \ 766 printf("x = %.36Lg; ", (long double)*xp); \ 767 } while (0) 768 #define DOPRINT_END1(v) \ 769 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v)) 770 #define DOPRINT_END2(hi, lo) \ 771 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \ 772 (long double)(hi), (long double)(lo)) 773 774 #endif /* DOPRINT_LD80 */ 775 776 #else /* !DOPRINT */ 777 #define DOPRINT_START(xp) 778 #define DOPRINT_END1(v) 779 #define DOPRINT_END2(hi, lo) 780 #endif /* DOPRINT */ 781 782 #define RETURNP(x) do { \ 783 DOPRINT_END1(x); \ 784 RETURNF(x); \ 785 } while (0) 786 #define RETURNPI(x) do { \ 787 DOPRINT_END1(x); \ 788 RETURNI(x); \ 789 } while (0) 790 #define RETURN2P(x, y) do { \ 791 DOPRINT_END2((x), (y)); \ 792 RETURNF((x) + (y)); \ 793 } while (0) 794 #define RETURN2PI(x, y) do { \ 795 DOPRINT_END2((x), (y)); \ 796 RETURNI((x) + (y)); \ 797 } while (0) 798 #ifdef STRUCT_RETURN 799 #define RETURNSP(rp) do { \ 800 if (!(rp)->lo_set) \ 801 RETURNP((rp)->hi); \ 802 RETURN2P((rp)->hi, (rp)->lo); \ 803 } while (0) 804 #define RETURNSPI(rp) do { \ 805 if (!(rp)->lo_set) \ 806 RETURNPI((rp)->hi); \ 807 RETURN2PI((rp)->hi, (rp)->lo); \ 808 } while (0) 809 #endif 810 #define SUM2P(x, y) ({ \ 811 const __typeof (x) __x = (x); \ 812 const __typeof (y) __y = (y); \ 813 \ 814 DOPRINT_END2(__x, __y); \ 815 __x + __y; \ 816 }) 817 818 /* 819 * ieee style elementary functions 820 * 821 * We rename functions here to improve other sources' diffability 822 * against fdlibm. 823 */ 824 #define __ieee754_sqrt sqrt 825 #define __ieee754_acos acos 826 #define __ieee754_acosh acosh 827 #define __ieee754_log log 828 #define __ieee754_log2 log2 829 #define __ieee754_atanh atanh 830 #define __ieee754_asin asin 831 #define __ieee754_atan2 atan2 832 #define __ieee754_exp exp 833 #define __ieee754_cosh cosh 834 #define __ieee754_fmod fmod 835 #define __ieee754_pow pow 836 #define __ieee754_lgamma lgamma 837 #define __ieee754_gamma gamma 838 #define __ieee754_lgamma_r lgamma_r 839 #define __ieee754_gamma_r gamma_r 840 #define __ieee754_log10 log10 841 #define __ieee754_sinh sinh 842 #define __ieee754_hypot hypot 843 #define __ieee754_j0 j0 844 #define __ieee754_j1 j1 845 #define __ieee754_y0 y0 846 #define __ieee754_y1 y1 847 #define __ieee754_jn jn 848 #define __ieee754_yn yn 849 #define __ieee754_remainder remainder 850 #define __ieee754_scalb scalb 851 #define __ieee754_sqrtf sqrtf 852 #define __ieee754_acosf acosf 853 #define __ieee754_acoshf acoshf 854 #define __ieee754_logf logf 855 #define __ieee754_atanhf atanhf 856 #define __ieee754_asinf asinf 857 #define __ieee754_atan2f atan2f 858 #define __ieee754_expf expf 859 #define __ieee754_coshf coshf 860 #define __ieee754_fmodf fmodf 861 #define __ieee754_powf powf 862 #define __ieee754_lgammaf lgammaf 863 #define __ieee754_gammaf gammaf 864 #define __ieee754_lgammaf_r lgammaf_r 865 #define __ieee754_gammaf_r gammaf_r 866 #define __ieee754_log10f log10f 867 #define __ieee754_log2f log2f 868 #define __ieee754_sinhf sinhf 869 #define __ieee754_hypotf hypotf 870 #define __ieee754_j0f j0f 871 #define __ieee754_j1f j1f 872 #define __ieee754_y0f y0f 873 #define __ieee754_y1f y1f 874 #define __ieee754_jnf jnf 875 #define __ieee754_ynf ynf 876 #define __ieee754_remainderf remainderf 877 #define __ieee754_scalbf scalbf 878 879 /* fdlibm kernel function */ 880 int __kernel_rem_pio2(double*,double*,int,int,int); 881 882 /* double precision kernel functions */ 883 #ifndef INLINE_REM_PIO2 884 int __ieee754_rem_pio2(double,double*); 885 #endif 886 double __kernel_sin(double,double,int); 887 double __kernel_cos(double,double); 888 double __kernel_tan(double,double,int); 889 double __ldexp_exp(double,int); 890 #ifdef _COMPLEX_H 891 double complex __ldexp_cexp(double complex,int); 892 #endif 893 894 /* float precision kernel functions */ 895 #ifndef INLINE_REM_PIO2F 896 int __ieee754_rem_pio2f(float,double*); 897 #endif 898 #ifndef INLINE_KERNEL_SINDF 899 float __kernel_sindf(double); 900 #endif 901 #ifndef INLINE_KERNEL_COSDF 902 float __kernel_cosdf(double); 903 #endif 904 #ifndef INLINE_KERNEL_TANDF 905 float __kernel_tandf(double,int); 906 #endif 907 float __ldexp_expf(float,int); 908 #ifdef _COMPLEX_H 909 float complex __ldexp_cexpf(float complex,int); 910 #endif 911 912 /* long double precision kernel functions */ 913 long double __kernel_sinl(long double, long double, int); 914 long double __kernel_cosl(long double, long double); 915 long double __kernel_tanl(long double, long double, int); 916 917 #endif /* !_MATH_PRIVATE_H_ */ 918