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 #ifdef __GNUCLIKE_ASM 575 576 /* Asm versions of some functions. */ 577 578 #ifdef __amd64__ 579 static __inline int 580 irint(double x) 581 { 582 int n; 583 584 asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x)); 585 return (n); 586 } 587 #define HAVE_EFFICIENT_IRINT 588 #endif 589 590 #ifdef __i386__ 591 static __inline int 592 irint(double x) 593 { 594 int n; 595 596 asm("fistl %0" : "=m" (n) : "t" (x)); 597 return (n); 598 } 599 #define HAVE_EFFICIENT_IRINT 600 #endif 601 602 #if defined(__amd64__) || defined(__i386__) 603 static __inline int 604 irintl(long double x) 605 { 606 int n; 607 608 asm("fistl %0" : "=m" (n) : "t" (x)); 609 return (n); 610 } 611 #define HAVE_EFFICIENT_IRINTL 612 #endif 613 614 #endif /* __GNUCLIKE_ASM */ 615 616 #ifdef DEBUG 617 #if defined(__amd64__) || defined(__i386__) 618 #define breakpoint() asm("int $3") 619 #else 620 #include <signal.h> 621 622 #define breakpoint() raise(SIGTRAP) 623 #endif 624 #endif 625 626 /* Write a pari script to test things externally. */ 627 #ifdef DOPRINT 628 #include <stdio.h> 629 630 #ifndef DOPRINT_SWIZZLE 631 #define DOPRINT_SWIZZLE 0 632 #endif 633 634 #ifdef DOPRINT_LD80 635 636 #define DOPRINT_START(xp) do { \ 637 uint64_t __lx; \ 638 uint16_t __hx; \ 639 \ 640 /* Hack to give more-problematic args. */ \ 641 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \ 642 __lx ^= DOPRINT_SWIZZLE; \ 643 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \ 644 printf("x = %.21Lg; ", (long double)*xp); \ 645 } while (0) 646 #define DOPRINT_END1(v) \ 647 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 648 #define DOPRINT_END2(hi, lo) \ 649 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 650 (long double)(hi), (long double)(lo)) 651 652 #elif defined(DOPRINT_D64) 653 654 #define DOPRINT_START(xp) do { \ 655 uint32_t __hx, __lx; \ 656 \ 657 EXTRACT_WORDS(__hx, __lx, *xp); \ 658 __lx ^= DOPRINT_SWIZZLE; \ 659 INSERT_WORDS(*xp, __hx, __lx); \ 660 printf("x = %.21Lg; ", (long double)*xp); \ 661 } while (0) 662 #define DOPRINT_END1(v) \ 663 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 664 #define DOPRINT_END2(hi, lo) \ 665 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 666 (long double)(hi), (long double)(lo)) 667 668 #elif defined(DOPRINT_F32) 669 670 #define DOPRINT_START(xp) do { \ 671 uint32_t __hx; \ 672 \ 673 GET_FLOAT_WORD(__hx, *xp); \ 674 __hx ^= DOPRINT_SWIZZLE; \ 675 SET_FLOAT_WORD(*xp, __hx); \ 676 printf("x = %.21Lg; ", (long double)*xp); \ 677 } while (0) 678 #define DOPRINT_END1(v) \ 679 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v)) 680 #define DOPRINT_END2(hi, lo) \ 681 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \ 682 (long double)(hi), (long double)(lo)) 683 684 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */ 685 686 #ifndef DOPRINT_SWIZZLE_HIGH 687 #define DOPRINT_SWIZZLE_HIGH 0 688 #endif 689 690 #define DOPRINT_START(xp) do { \ 691 uint64_t __lx, __llx; \ 692 uint16_t __hx; \ 693 \ 694 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \ 695 __llx ^= DOPRINT_SWIZZLE; \ 696 __lx ^= DOPRINT_SWIZZLE_HIGH; \ 697 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \ 698 printf("x = %.36Lg; ", (long double)*xp); \ 699 } while (0) 700 #define DOPRINT_END1(v) \ 701 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v)) 702 #define DOPRINT_END2(hi, lo) \ 703 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \ 704 (long double)(hi), (long double)(lo)) 705 706 #endif /* DOPRINT_LD80 */ 707 708 #else /* !DOPRINT */ 709 #define DOPRINT_START(xp) 710 #define DOPRINT_END1(v) 711 #define DOPRINT_END2(hi, lo) 712 #endif /* DOPRINT */ 713 714 #define RETURNP(x) do { \ 715 DOPRINT_END1(x); \ 716 RETURNF(x); \ 717 } while (0) 718 #define RETURNPI(x) do { \ 719 DOPRINT_END1(x); \ 720 RETURNI(x); \ 721 } while (0) 722 #define RETURN2P(x, y) do { \ 723 DOPRINT_END2((x), (y)); \ 724 RETURNF((x) + (y)); \ 725 } while (0) 726 #define RETURN2PI(x, y) do { \ 727 DOPRINT_END2((x), (y)); \ 728 RETURNI((x) + (y)); \ 729 } while (0) 730 #ifdef STRUCT_RETURN 731 #define RETURNSP(rp) do { \ 732 if (!(rp)->lo_set) \ 733 RETURNP((rp)->hi); \ 734 RETURN2P((rp)->hi, (rp)->lo); \ 735 } while (0) 736 #define RETURNSPI(rp) do { \ 737 if (!(rp)->lo_set) \ 738 RETURNPI((rp)->hi); \ 739 RETURN2PI((rp)->hi, (rp)->lo); \ 740 } while (0) 741 #endif 742 #define SUM2P(x, y) ({ \ 743 const __typeof (x) __x = (x); \ 744 const __typeof (y) __y = (y); \ 745 \ 746 DOPRINT_END2(__x, __y); \ 747 __x + __y; \ 748 }) 749 750 /* 751 * ieee style elementary functions 752 * 753 * We rename functions here to improve other sources' diffability 754 * against fdlibm. 755 */ 756 #define __ieee754_sqrt sqrt 757 #define __ieee754_acos acos 758 #define __ieee754_acosh acosh 759 #define __ieee754_log log 760 #define __ieee754_log2 log2 761 #define __ieee754_atanh atanh 762 #define __ieee754_asin asin 763 #define __ieee754_atan2 atan2 764 #define __ieee754_exp exp 765 #define __ieee754_cosh cosh 766 #define __ieee754_fmod fmod 767 #define __ieee754_pow pow 768 #define __ieee754_lgamma lgamma 769 #define __ieee754_gamma gamma 770 #define __ieee754_lgamma_r lgamma_r 771 #define __ieee754_gamma_r gamma_r 772 #define __ieee754_log10 log10 773 #define __ieee754_sinh sinh 774 #define __ieee754_hypot hypot 775 #define __ieee754_j0 j0 776 #define __ieee754_j1 j1 777 #define __ieee754_y0 y0 778 #define __ieee754_y1 y1 779 #define __ieee754_jn jn 780 #define __ieee754_yn yn 781 #define __ieee754_remainder remainder 782 #define __ieee754_scalb scalb 783 #define __ieee754_sqrtf sqrtf 784 #define __ieee754_acosf acosf 785 #define __ieee754_acoshf acoshf 786 #define __ieee754_logf logf 787 #define __ieee754_atanhf atanhf 788 #define __ieee754_asinf asinf 789 #define __ieee754_atan2f atan2f 790 #define __ieee754_expf expf 791 #define __ieee754_coshf coshf 792 #define __ieee754_fmodf fmodf 793 #define __ieee754_powf powf 794 #define __ieee754_lgammaf lgammaf 795 #define __ieee754_gammaf gammaf 796 #define __ieee754_lgammaf_r lgammaf_r 797 #define __ieee754_gammaf_r gammaf_r 798 #define __ieee754_log10f log10f 799 #define __ieee754_log2f log2f 800 #define __ieee754_sinhf sinhf 801 #define __ieee754_hypotf hypotf 802 #define __ieee754_j0f j0f 803 #define __ieee754_j1f j1f 804 #define __ieee754_y0f y0f 805 #define __ieee754_y1f y1f 806 #define __ieee754_jnf jnf 807 #define __ieee754_ynf ynf 808 #define __ieee754_remainderf remainderf 809 #define __ieee754_scalbf scalbf 810 811 /* fdlibm kernel function */ 812 int __kernel_rem_pio2(double*,double*,int,int,int); 813 814 /* double precision kernel functions */ 815 #ifndef INLINE_REM_PIO2 816 int __ieee754_rem_pio2(double,double*); 817 #endif 818 double __kernel_sin(double,double,int); 819 double __kernel_cos(double,double); 820 double __kernel_tan(double,double,int); 821 double __ldexp_exp(double,int); 822 #ifdef _COMPLEX_H 823 double complex __ldexp_cexp(double complex,int); 824 #endif 825 826 /* float precision kernel functions */ 827 #ifndef INLINE_REM_PIO2F 828 int __ieee754_rem_pio2f(float,double*); 829 #endif 830 #ifndef INLINE_KERNEL_SINDF 831 float __kernel_sindf(double); 832 #endif 833 #ifndef INLINE_KERNEL_COSDF 834 float __kernel_cosdf(double); 835 #endif 836 #ifndef INLINE_KERNEL_TANDF 837 float __kernel_tandf(double,int); 838 #endif 839 float __ldexp_expf(float,int); 840 #ifdef _COMPLEX_H 841 float complex __ldexp_cexpf(float complex,int); 842 #endif 843 844 /* long double precision kernel functions */ 845 long double __kernel_sinl(long double, long double, int); 846 long double __kernel_cosl(long double, long double); 847 long double __kernel_tanl(long double, long double, int); 848 849 long double __p1evll(long double, void *, int); 850 long double __polevll(long double, void *, int); 851 852 #endif /* !_MATH_PRIVATE_H_ */ 853