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 */ 15 16 #ifndef _MATH_PRIVATE_H_ 17 #define _MATH_PRIVATE_H_ 18 19 #include <sys/types.h> 20 #include <machine/endian.h> 21 22 /* 23 * The original fdlibm code used statements like: 24 * n0 = ((*(int*)&one)>>29)^1; * index of high word * 25 * ix0 = *(n0+(int*)&x); * high word of x * 26 * ix1 = *((1-n0)+(int*)&x); * low word of x * 27 * to dig two 32 bit words out of the 64 bit IEEE floating point 28 * value. That is non-ANSI, and, moreover, the gcc instruction 29 * scheduler gets it wrong. We instead use the following macros. 30 * Unlike the original code, we determine the endianness at compile 31 * time, not at run time; I don't see much benefit to selecting 32 * endianness at run time. 33 */ 34 35 /* 36 * A union which permits us to convert between a double and two 32 bit 37 * ints. 38 */ 39 40 #ifdef __arm__ 41 #if defined(__VFP_FP__) || defined(__ARM_EABI__) 42 #define IEEE_WORD_ORDER BYTE_ORDER 43 #else 44 #define IEEE_WORD_ORDER BIG_ENDIAN 45 #endif 46 #else /* __arm__ */ 47 #define IEEE_WORD_ORDER BYTE_ORDER 48 #endif 49 50 /* A union which permits us to convert between a long double and 51 four 32 bit ints. */ 52 53 #if IEEE_WORD_ORDER == BIG_ENDIAN 54 55 typedef union 56 { 57 long double value; 58 struct { 59 u_int32_t mswhi; 60 u_int32_t mswlo; 61 u_int32_t lswhi; 62 u_int32_t lswlo; 63 } parts32; 64 struct { 65 u_int64_t msw; 66 u_int64_t lsw; 67 } parts64; 68 } ieee_quad_shape_type; 69 70 #endif 71 72 #if IEEE_WORD_ORDER == LITTLE_ENDIAN 73 74 typedef union 75 { 76 long double value; 77 struct { 78 u_int32_t lswlo; 79 u_int32_t lswhi; 80 u_int32_t mswlo; 81 u_int32_t mswhi; 82 } parts32; 83 struct { 84 u_int64_t lsw; 85 u_int64_t msw; 86 } parts64; 87 } ieee_quad_shape_type; 88 89 #endif 90 91 #if IEEE_WORD_ORDER == BIG_ENDIAN 92 93 typedef union 94 { 95 double value; 96 struct 97 { 98 u_int32_t msw; 99 u_int32_t lsw; 100 } parts; 101 struct 102 { 103 u_int64_t w; 104 } xparts; 105 } ieee_double_shape_type; 106 107 #endif 108 109 #if IEEE_WORD_ORDER == LITTLE_ENDIAN 110 111 typedef union 112 { 113 double value; 114 struct 115 { 116 u_int32_t lsw; 117 u_int32_t msw; 118 } parts; 119 struct 120 { 121 u_int64_t w; 122 } xparts; 123 } ieee_double_shape_type; 124 125 #endif 126 127 /* Get two 32 bit ints from a double. */ 128 129 #define EXTRACT_WORDS(ix0,ix1,d) \ 130 do { \ 131 ieee_double_shape_type ew_u; \ 132 ew_u.value = (d); \ 133 (ix0) = ew_u.parts.msw; \ 134 (ix1) = ew_u.parts.lsw; \ 135 } while (0) 136 137 /* Get a 64-bit int from a double. */ 138 #define EXTRACT_WORD64(ix,d) \ 139 do { \ 140 ieee_double_shape_type ew_u; \ 141 ew_u.value = (d); \ 142 (ix) = ew_u.xparts.w; \ 143 } while (0) 144 145 /* Get the more significant 32 bit int from a double. */ 146 147 #define GET_HIGH_WORD(i,d) \ 148 do { \ 149 ieee_double_shape_type gh_u; \ 150 gh_u.value = (d); \ 151 (i) = gh_u.parts.msw; \ 152 } while (0) 153 154 /* Get the less significant 32 bit int from a double. */ 155 156 #define GET_LOW_WORD(i,d) \ 157 do { \ 158 ieee_double_shape_type gl_u; \ 159 gl_u.value = (d); \ 160 (i) = gl_u.parts.lsw; \ 161 } while (0) 162 163 /* Set a double from two 32 bit ints. */ 164 165 #define INSERT_WORDS(d,ix0,ix1) \ 166 do { \ 167 ieee_double_shape_type iw_u; \ 168 iw_u.parts.msw = (ix0); \ 169 iw_u.parts.lsw = (ix1); \ 170 (d) = iw_u.value; \ 171 } while (0) 172 173 /* Set a double from a 64-bit int. */ 174 #define INSERT_WORD64(d,ix) \ 175 do { \ 176 ieee_double_shape_type iw_u; \ 177 iw_u.xparts.w = (ix); \ 178 (d) = iw_u.value; \ 179 } while (0) 180 181 /* Set the more significant 32 bits of a double from an int. */ 182 183 #define SET_HIGH_WORD(d,v) \ 184 do { \ 185 ieee_double_shape_type sh_u; \ 186 sh_u.value = (d); \ 187 sh_u.parts.msw = (v); \ 188 (d) = sh_u.value; \ 189 } while (0) 190 191 /* Set the less significant 32 bits of a double from an int. */ 192 193 #define SET_LOW_WORD(d,v) \ 194 do { \ 195 ieee_double_shape_type sl_u; \ 196 sl_u.value = (d); \ 197 sl_u.parts.lsw = (v); \ 198 (d) = sl_u.value; \ 199 } while (0) 200 201 /* 202 * A union which permits us to convert between a float and a 32 bit 203 * int. 204 */ 205 206 typedef union 207 { 208 float value; 209 /* FIXME: Assumes 32 bit int. */ 210 unsigned int word; 211 } ieee_float_shape_type; 212 213 /* Get a 32 bit int from a float. */ 214 215 #define GET_FLOAT_WORD(i,d) \ 216 do { \ 217 ieee_float_shape_type gf_u; \ 218 gf_u.value = (d); \ 219 (i) = gf_u.word; \ 220 } while (0) 221 222 /* Set a float from a 32 bit int. */ 223 224 #define SET_FLOAT_WORD(d,i) \ 225 do { \ 226 ieee_float_shape_type sf_u; \ 227 sf_u.word = (i); \ 228 (d) = sf_u.value; \ 229 } while (0) 230 231 /* 232 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long 233 * double. 234 */ 235 236 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \ 237 do { \ 238 union IEEEl2bits ew_u; \ 239 ew_u.e = (d); \ 240 (ix0) = ew_u.xbits.expsign; \ 241 (ix1) = ew_u.xbits.man; \ 242 } while (0) 243 244 /* 245 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit 246 * long double. 247 */ 248 249 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \ 250 do { \ 251 union IEEEl2bits ew_u; \ 252 ew_u.e = (d); \ 253 (ix0) = ew_u.xbits.expsign; \ 254 (ix1) = ew_u.xbits.manh; \ 255 (ix2) = ew_u.xbits.manl; \ 256 } while (0) 257 258 /* Get expsign as a 16 bit int from a long double. */ 259 260 #define GET_LDBL_EXPSIGN(i,d) \ 261 do { \ 262 union IEEEl2bits ge_u; \ 263 ge_u.e = (d); \ 264 (i) = ge_u.xbits.expsign; \ 265 } while (0) 266 267 /* 268 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int 269 * mantissa. 270 */ 271 272 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \ 273 do { \ 274 union IEEEl2bits iw_u; \ 275 iw_u.xbits.expsign = (ix0); \ 276 iw_u.xbits.man = (ix1); \ 277 (d) = iw_u.e; \ 278 } while (0) 279 280 /* 281 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints 282 * comprising the mantissa. 283 */ 284 285 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \ 286 do { \ 287 union IEEEl2bits iw_u; \ 288 iw_u.xbits.expsign = (ix0); \ 289 iw_u.xbits.manh = (ix1); \ 290 iw_u.xbits.manl = (ix2); \ 291 (d) = iw_u.e; \ 292 } while (0) 293 294 /* Set expsign of a long double from a 16 bit int. */ 295 296 #define SET_LDBL_EXPSIGN(d,v) \ 297 do { \ 298 union IEEEl2bits se_u; \ 299 se_u.e = (d); \ 300 se_u.xbits.expsign = (v); \ 301 (d) = se_u.e; \ 302 } while (0) 303 304 #ifdef __i386__ 305 /* Long double constants are broken on i386. */ 306 #define LD80C(m, ex, v) { \ 307 .xbits.man = __CONCAT(m, ULL), \ 308 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \ 309 } 310 #else 311 /* The above works on non-i386 too, but we use this to check v. */ 312 #define LD80C(m, ex, v) { .e = (v), } 313 #endif 314 315 #ifdef FLT_EVAL_METHOD 316 /* 317 * Attempt to get strict C99 semantics for assignment with non-C99 compilers. 318 */ 319 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 320 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) 321 #else 322 #define STRICT_ASSIGN(type, lval, rval) do { \ 323 volatile type __lval; \ 324 \ 325 if (sizeof(type) >= sizeof(long double)) \ 326 (lval) = (rval); \ 327 else { \ 328 __lval = (rval); \ 329 (lval) = __lval; \ 330 } \ 331 } while (0) 332 #endif 333 #endif /* FLT_EVAL_METHOD */ 334 335 /* Support switching the mode to FP_PE if necessary. */ 336 #if defined(__i386__) && !defined(NO_FPSETPREC) 337 #define ENTERI() ENTERIT(long double) 338 #define ENTERIT(returntype) \ 339 returntype __retval; \ 340 fp_prec_t __oprec; \ 341 \ 342 if ((__oprec = fpgetprec()) != FP_PE) \ 343 fpsetprec(FP_PE) 344 #define RETURNI(x) do { \ 345 __retval = (x); \ 346 if (__oprec != FP_PE) \ 347 fpsetprec(__oprec); \ 348 RETURNF(__retval); \ 349 } while (0) 350 #define ENTERV() \ 351 fp_prec_t __oprec; \ 352 \ 353 if ((__oprec = fpgetprec()) != FP_PE) \ 354 fpsetprec(FP_PE) 355 #define RETURNV() do { \ 356 if (__oprec != FP_PE) \ 357 fpsetprec(__oprec); \ 358 return; \ 359 } while (0) 360 #else 361 #define ENTERI() 362 #define ENTERIT(x) 363 #define RETURNI(x) RETURNF(x) 364 #define ENTERV() 365 #define RETURNV() return 366 #endif 367 368 /* Default return statement if hack*_t() is not used. */ 369 #define RETURNF(v) return (v) 370 371 /* 372 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or 373 * a == 0, but is slower. 374 */ 375 #define _2sum(a, b) do { \ 376 __typeof(a) __s, __w; \ 377 \ 378 __w = (a) + (b); \ 379 __s = __w - (a); \ 380 (b) = ((a) - (__w - __s)) + ((b) - __s); \ 381 (a) = __w; \ 382 } while (0) 383 384 /* 385 * 2sumF algorithm. 386 * 387 * "Normalize" the terms in the infinite-precision expression a + b for 388 * the sum of 2 floating point values so that b is as small as possible 389 * relative to 'a'. (The resulting 'a' is the value of the expression in 390 * the same precision as 'a' and the resulting b is the rounding error.) 391 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and 392 * exponent overflow or underflow must not occur. This uses a Theorem of 393 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum" 394 * is apparently due to Skewchuk (1997). 395 * 396 * For this to always work, assignment of a + b to 'a' must not retain any 397 * extra precision in a + b. This is required by C standards but broken 398 * in many compilers. The brokenness cannot be worked around using 399 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this 400 * algorithm would be destroyed by non-null strict assignments. (The 401 * compilers are correct to be broken -- the efficiency of all floating 402 * point code calculations would be destroyed similarly if they forced the 403 * conversions.) 404 * 405 * Fortunately, a case that works well can usually be arranged by building 406 * any extra precision into the type of 'a' -- 'a' should have type float_t, 407 * double_t or long double. b's type should be no larger than 'a's type. 408 * Callers should use these types with scopes as large as possible, to 409 * reduce their own extra-precision and efficiciency problems. In 410 * particular, they shouldn't convert back and forth just to call here. 411 */ 412 #ifdef DEBUG 413 #define _2sumF(a, b) do { \ 414 __typeof(a) __w; \ 415 volatile __typeof(a) __ia, __ib, __r, __vw; \ 416 \ 417 __ia = (a); \ 418 __ib = (b); \ 419 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \ 420 \ 421 __w = (a) + (b); \ 422 (b) = ((a) - __w) + (b); \ 423 (a) = __w; \ 424 \ 425 /* The next 2 assertions are weak if (a) is already long double. */ \ 426 assert((long double)__ia + __ib == (long double)(a) + (b)); \ 427 __vw = __ia + __ib; \ 428 __r = __ia - __vw; \ 429 __r += __ib; \ 430 assert(__vw == (a) && __r == (b)); \ 431 } while (0) 432 #else /* !DEBUG */ 433 #define _2sumF(a, b) do { \ 434 __typeof(a) __w; \ 435 \ 436 __w = (a) + (b); \ 437 (b) = ((a) - __w) + (b); \ 438 (a) = __w; \ 439 } while (0) 440 #endif /* DEBUG */ 441 442 /* 443 * Set x += c, where x is represented in extra precision as a + b. 444 * x must be sufficiently normalized and sufficiently larger than c, 445 * and the result is then sufficiently normalized. 446 * 447 * The details of ordering are that |a| must be >= |c| (so that (a, c) 448 * can be normalized without extra work to swap 'a' with c). The details of 449 * the normalization are that b must be small relative to the normalized 'a'. 450 * Normalization of (a, c) makes the normalized c tiny relative to the 451 * normalized a, so b remains small relative to 'a' in the result. However, 452 * b need not ever be tiny relative to 'a'. For example, b might be about 453 * 2**20 times smaller than 'a' to give about 20 extra bits of precision. 454 * That is usually enough, and adding c (which by normalization is about 455 * 2**53 times smaller than a) cannot change b significantly. However, 456 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a' 457 * significantly relative to b. The caller must ensure that significant 458 * cancellation doesn't occur, either by having c of the same sign as 'a', 459 * or by having |c| a few percent smaller than |a|. Pre-normalization of 460 * (a, b) may help. 461 * 462 * This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2 463 * exercise 19). We gain considerable efficiency by requiring the terms to 464 * be sufficiently normalized and sufficiently increasing. 465 */ 466 #define _3sumF(a, b, c) do { \ 467 __typeof(a) __tmp; \ 468 \ 469 __tmp = (c); \ 470 _2sumF(__tmp, (a)); \ 471 (b) += (a); \ 472 (a) = __tmp; \ 473 } while (0) 474 475 /* 476 * Common routine to process the arguments to nan(), nanf(), and nanl(). 477 */ 478 void _scan_nan(uint32_t *__words, int __num_words, const char *__s); 479 480 /* 481 * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns 482 * signaling NaNs into quiet NaNs by setting a quiet bit. We do this 483 * because we want to never return a signaling NaN, and also because we 484 * don't want the quiet bit to affect the result. Then mix the converted 485 * args using the specified operation. 486 * 487 * When one arg is NaN, the result is typically that arg quieted. When both 488 * args are NaNs, the result is typically the quietening of the arg whose 489 * mantissa is largest after quietening. When neither arg is NaN, the 490 * result may be NaN because it is indeterminate, or finite for subsequent 491 * construction of a NaN as the indeterminate 0.0L/0.0L. 492 * 493 * Technical complications: the result in bits after rounding to the final 494 * precision might depend on the runtime precision and/or on compiler 495 * optimizations, especially when different register sets are used for 496 * different precisions. Try to make the result not depend on at least the 497 * runtime precision by always doing the main mixing step in long double 498 * precision. Try to reduce dependencies on optimizations by adding the 499 * the 0's in different precisions (unless everything is in long double 500 * precision). 501 */ 502 #define nan_mix(x, y) (nan_mix_op((x), (y), +)) 503 #define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0)) 504 505 #ifdef _COMPLEX_H 506 507 /* 508 * C99 specifies that complex numbers have the same representation as 509 * an array of two elements, where the first element is the real part 510 * and the second element is the imaginary part. 511 */ 512 typedef union { 513 float complex f; 514 float a[2]; 515 } float_complex; 516 typedef union { 517 double complex f; 518 double a[2]; 519 } double_complex; 520 typedef union { 521 long double complex f; 522 long double a[2]; 523 } long_double_complex; 524 #define REALPART(z) ((z).a[0]) 525 #define IMAGPART(z) ((z).a[1]) 526 527 /* 528 * Inline functions that can be used to construct complex values. 529 * 530 * The C99 standard intends x+I*y to be used for this, but x+I*y is 531 * currently unusable in general since gcc introduces many overflow, 532 * underflow, sign and efficiency bugs by rewriting I*y as 533 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. 534 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted 535 * to -0.0+I*0.0. 536 * 537 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() 538 * to construct complex values. Compilers that conform to the C99 539 * standard require the following functions to avoid the above issues. 540 */ 541 542 #ifndef CMPLXF 543 static __inline float complex 544 CMPLXF(float x, float y) 545 { 546 float_complex z; 547 548 REALPART(z) = x; 549 IMAGPART(z) = y; 550 return (z.f); 551 } 552 #endif 553 554 #ifndef CMPLX 555 static __inline double complex 556 CMPLX(double x, double y) 557 { 558 double_complex z; 559 560 REALPART(z) = x; 561 IMAGPART(z) = y; 562 return (z.f); 563 } 564 #endif 565 566 #ifndef CMPLXL 567 static __inline long double complex 568 CMPLXL(long double x, long double y) 569 { 570 long_double_complex z; 571 572 REALPART(z) = x; 573 IMAGPART(z) = y; 574 return (z.f); 575 } 576 #endif 577 578 #endif /* _COMPLEX_H */ 579 580 /* 581 * The rnint() family rounds to the nearest integer for a restricted range 582 * range of args (up to about 2**MANT_DIG). We assume that the current 583 * rounding mode is FE_TONEAREST so that this can be done efficiently. 584 * Extra precision causes more problems in practice, and we only centralize 585 * this here to reduce those problems, and have not solved the efficiency 586 * problems. The exp2() family uses a more delicate version of this that 587 * requires extracting bits from the intermediate value, so it is not 588 * centralized here and should copy any solution of the efficiency problems. 589 */ 590 591 static inline double 592 rnint(__double_t x) 593 { 594 /* 595 * This casts to double to kill any extra precision. This depends 596 * on the cast being applied to a double_t to avoid compiler bugs 597 * (this is a cleaner version of STRICT_ASSIGN()). This is 598 * inefficient if there actually is extra precision, but is hard 599 * to improve on. We use double_t in the API to minimise conversions 600 * for just calling here. Note that we cannot easily change the 601 * magic number to the one that works directly with double_t, since 602 * the rounding precision is variable at runtime on x86 so the 603 * magic number would need to be variable. Assuming that the 604 * rounding precision is always the default is too fragile. This 605 * and many other complications will move when the default is 606 * changed to FP_PE. 607 */ 608 return ((double)(x + 0x1.8p52) - 0x1.8p52); 609 } 610 611 static inline float 612 rnintf(__float_t x) 613 { 614 /* 615 * As for rnint(), except we could just call that to handle the 616 * extra precision case, usually without losing efficiency. 617 */ 618 return ((float)(x + 0x1.8p23F) - 0x1.8p23F); 619 } 620 621 #ifdef LDBL_MANT_DIG 622 /* 623 * The complications for extra precision are smaller for rnintl() since it 624 * can safely assume that the rounding precision has been increased from 625 * its default to FP_PE on x86. We don't exploit that here to get small 626 * optimizations from limiting the range to double. We just need it for 627 * the magic number to work with long doubles. ld128 callers should use 628 * rnint() instead of this if possible. ld80 callers should prefer 629 * rnintl() since for amd64 this avoids swapping the register set, while 630 * for i386 it makes no difference (assuming FP_PE), and for other arches 631 * it makes little difference. 632 */ 633 static inline long double 634 rnintl(long double x) 635 { 636 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 - 637 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2); 638 } 639 #endif /* LDBL_MANT_DIG */ 640 641 /* 642 * irint() and i64rint() give the same result as casting to their integer 643 * return type provided their arg is a floating point integer. They can 644 * sometimes be more efficient because no rounding is required. 645 */ 646 #if defined(amd64) || defined(__i386__) 647 #define irint(x) \ 648 (sizeof(x) == sizeof(float) && \ 649 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \ 650 sizeof(x) == sizeof(double) && \ 651 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \ 652 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x)) 653 #else 654 #define irint(x) ((int)(x)) 655 #endif 656 657 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */ 658 659 #if defined(__i386__) 660 static __inline int 661 irintf(float x) 662 { 663 int n; 664 665 __asm("fistl %0" : "=m" (n) : "t" (x)); 666 return (n); 667 } 668 669 static __inline int 670 irintd(double x) 671 { 672 int n; 673 674 __asm("fistl %0" : "=m" (n) : "t" (x)); 675 return (n); 676 } 677 #endif 678 679 #if defined(__amd64__) || defined(__i386__) 680 static __inline int 681 irintl(long double x) 682 { 683 int n; 684 685 __asm("fistl %0" : "=m" (n) : "t" (x)); 686 return (n); 687 } 688 #endif 689 690 /* 691 * The following are fast floor macros for 0 <= |x| < 0x1p(N-1), where 692 * N is the precision of the type of x. These macros are used in the 693 * half-cycle trignometric functions (e.g., sinpi(x)). 694 */ 695 #define FFLOORF(x, j0, ix) do { \ 696 (j0) = (((ix) >> 23) & 0xff) - 0x7f; \ 697 (ix) &= ~(0x007fffff >> (j0)); \ 698 SET_FLOAT_WORD((x), (ix)); \ 699 } while (0) 700 701 #define FFLOOR(x, j0, ix, lx) do { \ 702 (j0) = (((ix) >> 20) & 0x7ff) - 0x3ff; \ 703 if ((j0) < 20) { \ 704 (ix) &= ~(0x000fffff >> (j0)); \ 705 (lx) = 0; \ 706 } else { \ 707 (lx) &= ~((uint32_t)0xffffffff >> ((j0) - 20)); \ 708 } \ 709 INSERT_WORDS((x), (ix), (lx)); \ 710 } while (0) 711 712 #define FFLOORL80(x, j0, ix, lx) do { \ 713 j0 = ix - 0x3fff + 1; \ 714 if ((j0) < 32) { \ 715 (lx) = ((lx) >> 32) << 32; \ 716 (lx) &= ~((((lx) << 32)-1) >> (j0)); \ 717 } else { \ 718 uint64_t _m; \ 719 _m = (uint64_t)-1 >> (j0); \ 720 if ((lx) & _m) (lx) &= ~_m; \ 721 } \ 722 INSERT_LDBL80_WORDS((x), (ix), (lx)); \ 723 } while (0) 724 725 #define FFLOORL128(x, ai, ar) do { \ 726 union IEEEl2bits u; \ 727 uint64_t m; \ 728 int e; \ 729 u.e = (x); \ 730 e = u.bits.exp - 16383; \ 731 if (e < 48) { \ 732 m = ((1llu << 49) - 1) >> (e + 1); \ 733 u.bits.manh &= ~m; \ 734 u.bits.manl = 0; \ 735 } else { \ 736 m = (uint64_t)-1 >> (e - 48); \ 737 u.bits.manl &= ~m; \ 738 } \ 739 (ai) = u.e; \ 740 (ar) = (x) - (ai); \ 741 } while (0) 742 743 #ifdef DEBUG 744 #if defined(__amd64__) || defined(__i386__) 745 #define breakpoint() asm("int $3") 746 #else 747 #include <signal.h> 748 749 #define breakpoint() raise(SIGTRAP) 750 #endif 751 #endif 752 753 #ifdef STRUCT_RETURN 754 #define RETURNSP(rp) do { \ 755 if (!(rp)->lo_set) \ 756 RETURNF((rp)->hi); \ 757 RETURNF((rp)->hi + (rp)->lo); \ 758 } while (0) 759 #define RETURNSPI(rp) do { \ 760 if (!(rp)->lo_set) \ 761 RETURNI((rp)->hi); \ 762 RETURNI((rp)->hi + (rp)->lo); \ 763 } while (0) 764 #endif 765 766 #define SUM2P(x, y) ({ \ 767 const __typeof (x) __x = (x); \ 768 const __typeof (y) __y = (y); \ 769 __x + __y; \ 770 }) 771 772 /* fdlibm kernel function */ 773 int __kernel_rem_pio2(double*,double*,int,int,int); 774 775 /* double precision kernel functions */ 776 #ifndef INLINE_REM_PIO2 777 int __ieee754_rem_pio2(double,double*); 778 #endif 779 double __kernel_sin(double,double,int); 780 double __kernel_cos(double,double); 781 double __kernel_tan(double,double,int); 782 double __ldexp_exp(double,int); 783 #ifdef _COMPLEX_H 784 double complex __ldexp_cexp(double complex,int); 785 #endif 786 787 /* float precision kernel functions */ 788 #ifndef INLINE_REM_PIO2F 789 int __ieee754_rem_pio2f(float,double*); 790 #endif 791 #ifndef INLINE_KERNEL_SINDF 792 float __kernel_sindf(double); 793 #endif 794 #ifndef INLINE_KERNEL_COSDF 795 float __kernel_cosdf(double); 796 #endif 797 #ifndef INLINE_KERNEL_TANDF 798 float __kernel_tandf(double,int); 799 #endif 800 float __ldexp_expf(float,int); 801 #ifdef _COMPLEX_H 802 float complex __ldexp_cexpf(float complex,int); 803 #endif 804 805 /* long double precision kernel functions */ 806 long double __kernel_sinl(long double, long double, int); 807 long double __kernel_cosl(long double, long double); 808 long double __kernel_tanl(long double, long double, int); 809 810 #endif /* !_MATH_PRIVATE_H_ */ 811