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 <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 #if IEEE_WORD_ORDER == BIG_ENDIAN
52
53 typedef union {
54 double value;
55 struct {
56 u_int32_t msw;
57 u_int32_t lsw;
58 } parts;
59 struct {
60 u_int64_t w;
61 } xparts;
62 } ieee_double_shape_type;
63
64 #endif
65
66 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
67
68 typedef union {
69 double value;
70 struct {
71 u_int32_t lsw;
72 u_int32_t msw;
73 } parts;
74 struct {
75 u_int64_t w;
76 } xparts;
77 } ieee_double_shape_type;
78
79 #endif
80
81 /* Get two 32 bit ints from a double. */
82
83 #define EXTRACT_WORDS(ix0,ix1,d) \
84 do { \
85 ieee_double_shape_type ew_u; \
86 ew_u.value = (d); \
87 (ix0) = ew_u.parts.msw; \
88 (ix1) = ew_u.parts.lsw; \
89 } while (0)
90
91 /* Get a 64-bit int from a double. */
92 #define EXTRACT_WORD64(ix,d) \
93 do { \
94 ieee_double_shape_type ew_u; \
95 ew_u.value = (d); \
96 (ix) = ew_u.xparts.w; \
97 } while (0)
98
99 /* Get the more significant 32 bit int from a double. */
100
101 #define GET_HIGH_WORD(i,d) \
102 do { \
103 ieee_double_shape_type gh_u; \
104 gh_u.value = (d); \
105 (i) = gh_u.parts.msw; \
106 } while (0)
107
108 /* Get the less significant 32 bit int from a double. */
109
110 #define GET_LOW_WORD(i,d) \
111 do { \
112 ieee_double_shape_type gl_u; \
113 gl_u.value = (d); \
114 (i) = gl_u.parts.lsw; \
115 } while (0)
116
117 /* Set a double from two 32 bit ints. */
118
119 #define INSERT_WORDS(d,ix0,ix1) \
120 do { \
121 ieee_double_shape_type iw_u; \
122 iw_u.parts.msw = (ix0); \
123 iw_u.parts.lsw = (ix1); \
124 (d) = iw_u.value; \
125 } while (0)
126
127 /* Set a double from a 64-bit int. */
128 #define INSERT_WORD64(d,ix) \
129 do { \
130 ieee_double_shape_type iw_u; \
131 iw_u.xparts.w = (ix); \
132 (d) = iw_u.value; \
133 } while (0)
134
135 /* Set the more significant 32 bits of a double from an int. */
136
137 #define SET_HIGH_WORD(d,v) \
138 do { \
139 ieee_double_shape_type sh_u; \
140 sh_u.value = (d); \
141 sh_u.parts.msw = (v); \
142 (d) = sh_u.value; \
143 } while (0)
144
145 /* Set the less significant 32 bits of a double from an int. */
146
147 #define SET_LOW_WORD(d,v) \
148 do { \
149 ieee_double_shape_type sl_u; \
150 sl_u.value = (d); \
151 sl_u.parts.lsw = (v); \
152 (d) = sl_u.value; \
153 } while (0)
154
155 /*
156 * A union which permits us to convert between a float and a 32 bit
157 * int.
158 */
159
160 typedef union {
161 float value;
162 /* FIXME: Assumes 32 bit int. */
163 unsigned int word;
164 } ieee_float_shape_type;
165
166 /* Get a 32 bit int from a float. */
167
168 #define GET_FLOAT_WORD(i,d) \
169 do { \
170 ieee_float_shape_type gf_u; \
171 gf_u.value = (d); \
172 (i) = gf_u.word; \
173 } while (0)
174
175 /* Set a float from a 32 bit int. */
176
177 #define SET_FLOAT_WORD(d,i) \
178 do { \
179 ieee_float_shape_type sf_u; \
180 sf_u.word = (i); \
181 (d) = sf_u.value; \
182 } while (0)
183
184 /*
185 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
186 * double.
187 */
188
189 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
190 do { \
191 union IEEEl2bits ew_u; \
192 ew_u.e = (d); \
193 (ix0) = ew_u.xbits.expsign; \
194 (ix1) = ew_u.xbits.man; \
195 } while (0)
196
197 /*
198 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
199 * long double.
200 */
201
202 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
203 do { \
204 union IEEEl2bits ew_u; \
205 ew_u.e = (d); \
206 (ix0) = ew_u.xbits.expsign; \
207 (ix1) = ew_u.xbits.manh; \
208 (ix2) = ew_u.xbits.manl; \
209 } while (0)
210
211 /* Get expsign as a 16 bit int from a long double. */
212
213 #define GET_LDBL_EXPSIGN(i,d) \
214 do { \
215 union IEEEl2bits ge_u; \
216 ge_u.e = (d); \
217 (i) = ge_u.xbits.expsign; \
218 } while (0)
219
220 /*
221 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
222 * mantissa.
223 */
224
225 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
226 do { \
227 union IEEEl2bits iw_u; \
228 iw_u.xbits.expsign = (ix0); \
229 iw_u.xbits.man = (ix1); \
230 (d) = iw_u.e; \
231 } while (0)
232
233 /*
234 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
235 * comprising the mantissa.
236 */
237
238 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
239 do { \
240 union IEEEl2bits iw_u; \
241 iw_u.xbits.expsign = (ix0); \
242 iw_u.xbits.manh = (ix1); \
243 iw_u.xbits.manl = (ix2); \
244 (d) = iw_u.e; \
245 } while (0)
246
247 /* Set expsign of a long double from a 16 bit int. */
248
249 #define SET_LDBL_EXPSIGN(d,v) \
250 do { \
251 union IEEEl2bits se_u; \
252 se_u.e = (d); \
253 se_u.xbits.expsign = (v); \
254 (d) = se_u.e; \
255 } while (0)
256
257 #ifdef __i386__
258 /* Long double constants are broken on i386. */
259 #define LD80C(m, ex, v) { \
260 .xbits.man = __CONCAT(m, ULL), \
261 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
262 }
263 #else
264 /* The above works on non-i386 too, but we use this to check v. */
265 #define LD80C(m, ex, v) { .e = (v), }
266 #endif
267
268 #ifdef FLT_EVAL_METHOD
269 /*
270 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
271 */
272 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
273 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
274 #else
275 #define STRICT_ASSIGN(type, lval, rval) do { \
276 volatile type __lval; \
277 \
278 if (sizeof(type) >= sizeof(long double)) \
279 (lval) = (rval); \
280 else { \
281 __lval = (rval); \
282 (lval) = __lval; \
283 } \
284 } while (0)
285 #endif
286 #endif /* FLT_EVAL_METHOD */
287
288 /* Support switching the mode to FP_PE if necessary. */
289 #if defined(__i386__) && !defined(NO_FPSETPREC)
290 #define ENTERI() \
291 long double __retval; \
292 fp_prec_t __oprec; \
293 \
294 if ((__oprec = fpgetprec()) != FP_PE) \
295 fpsetprec(FP_PE)
296 #define RETURNI(x) do { \
297 __retval = (x); \
298 if (__oprec != FP_PE) \
299 fpsetprec(__oprec); \
300 RETURNF(__retval); \
301 } while (0)
302 #else
303 #define ENTERI(x)
304 #define RETURNI(x) RETURNF(x)
305 #endif
306
307 /* Default return statement if hack*_t() is not used. */
308 #define RETURNF(v) return (v)
309
310 /*
311 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
312 * a == 0, but is slower.
313 */
314 #define _2sum(a, b) do { \
315 __typeof(a) __s, __w; \
316 \
317 __w = (a) + (b); \
318 __s = __w - (a); \
319 (b) = ((a) - (__w - __s)) + ((b) - __s); \
320 (a) = __w; \
321 } while (0)
322
323 /*
324 * 2sumF algorithm.
325 *
326 * "Normalize" the terms in the infinite-precision expression a + b for
327 * the sum of 2 floating point values so that b is as small as possible
328 * relative to 'a'. (The resulting 'a' is the value of the expression in
329 * the same precision as 'a' and the resulting b is the rounding error.)
330 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
331 * exponent overflow or underflow must not occur. This uses a Theorem of
332 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
333 * is apparently due to Skewchuk (1997).
334 *
335 * For this to always work, assignment of a + b to 'a' must not retain any
336 * extra precision in a + b. This is required by C standards but broken
337 * in many compilers. The brokenness cannot be worked around using
338 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
339 * algorithm would be destroyed by non-null strict assignments. (The
340 * compilers are correct to be broken -- the efficiency of all floating
341 * point code calculations would be destroyed similarly if they forced the
342 * conversions.)
343 *
344 * Fortunately, a case that works well can usually be arranged by building
345 * any extra precision into the type of 'a' -- 'a' should have type float_t,
346 * double_t or long double. b's type should be no larger than 'a's type.
347 * Callers should use these types with scopes as large as possible, to
348 * reduce their own extra-precision and efficiciency problems. In
349 * particular, they shouldn't convert back and forth just to call here.
350 */
351 #ifdef DEBUG
352 #define _2sumF(a, b) do { \
353 __typeof(a) __w; \
354 volatile __typeof(a) __ia, __ib, __r, __vw; \
355 \
356 __ia = (a); \
357 __ib = (b); \
358 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
359 \
360 __w = (a) + (b); \
361 (b) = ((a) - __w) + (b); \
362 (a) = __w; \
363 \
364 /* The next 2 assertions are weak if (a) is already long double. */ \
365 assert((long double)__ia + __ib == (long double)(a) + (b)); \
366 __vw = __ia + __ib; \
367 __r = __ia - __vw; \
368 __r += __ib; \
369 assert(__vw == (a) && __r == (b)); \
370 } while (0)
371 #else /* !DEBUG */
372 #define _2sumF(a, b) do { \
373 __typeof(a) __w; \
374 \
375 __w = (a) + (b); \
376 (b) = ((a) - __w) + (b); \
377 (a) = __w; \
378 } while (0)
379 #endif /* DEBUG */
380
381 /*
382 * Set x += c, where x is represented in extra precision as a + b.
383 * x must be sufficiently normalized and sufficiently larger than c,
384 * and the result is then sufficiently normalized.
385 *
386 * The details of ordering are that |a| must be >= |c| (so that (a, c)
387 * can be normalized without extra work to swap 'a' with c). The details of
388 * the normalization are that b must be small relative to the normalized 'a'.
389 * Normalization of (a, c) makes the normalized c tiny relative to the
390 * normalized a, so b remains small relative to 'a' in the result. However,
391 * b need not ever be tiny relative to 'a'. For example, b might be about
392 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
393 * That is usually enough, and adding c (which by normalization is about
394 * 2**53 times smaller than a) cannot change b significantly. However,
395 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
396 * significantly relative to b. The caller must ensure that significant
397 * cancellation doesn't occur, either by having c of the same sign as 'a',
398 * or by having |c| a few percent smaller than |a|. Pre-normalization of
399 * (a, b) may help.
400 *
401 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
402 * exercise 19). We gain considerable efficiency by requiring the terms to
403 * be sufficiently normalized and sufficiently increasing.
404 */
405 #define _3sumF(a, b, c) do { \
406 __typeof(a) __tmp; \
407 \
408 __tmp = (c); \
409 _2sumF(__tmp, (a)); \
410 (b) += (a); \
411 (a) = __tmp; \
412 } while (0)
413
414 /*
415 * Common routine to process the arguments to nan(), nanf(), and nanl().
416 */
417 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
418
419 #ifdef _COMPLEX_H
420
421 /*
422 * C99 specifies that complex numbers have the same representation as
423 * an array of two elements, where the first element is the real part
424 * and the second element is the imaginary part.
425 */
426 typedef union {
427 float complex f;
428 float a[2];
429 } float_complex;
430 typedef union {
431 double complex f;
432 double a[2];
433 } double_complex;
434 typedef union {
435 long double complex f;
436 long double a[2];
437 } long_double_complex;
438 #define REALPART(z) ((z).a[0])
439 #define IMAGPART(z) ((z).a[1])
440
441 /*
442 * Inline functions that can be used to construct complex values.
443 *
444 * The C99 standard intends x+I*y to be used for this, but x+I*y is
445 * currently unusable in general since gcc introduces many overflow,
446 * underflow, sign and efficiency bugs by rewriting I*y as
447 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
448 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
449 * to -0.0+I*0.0.
450 */
451 static __inline float complex
cpackf(float x,float y)452 cpackf(float x, float y)
453 {
454 float_complex z;
455
456 REALPART(z) = x;
457 IMAGPART(z) = y;
458 return (z.f);
459 }
460
461 static __inline double complex
cpack(double x,double y)462 cpack(double x, double y)
463 {
464 double_complex z;
465
466 REALPART(z) = x;
467 IMAGPART(z) = y;
468 return (z.f);
469 }
470
471 static __inline long double complex
cpackl(long double x,long double y)472 cpackl(long double x, long double y)
473 {
474 long_double_complex z;
475
476 REALPART(z) = x;
477 IMAGPART(z) = y;
478 return (z.f);
479 }
480 #endif /* _COMPLEX_H */
481
482 #ifdef __GNUCLIKE_ASM
483
484 /* Asm versions of some functions. */
485
486 #ifdef __amd64__
487 static __inline int
irint(double x)488 irint(double x)
489 {
490 int n;
491
492 asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
493 return (n);
494 }
495 #define HAVE_EFFICIENT_IRINT
496 #endif
497
498 #ifdef __i386__
499 static __inline int
irint(double x)500 irint(double x)
501 {
502 int n;
503
504 asm("fistl %0" : "=m" (n) : "t" (x));
505 return (n);
506 }
507 #define HAVE_EFFICIENT_IRINT
508 #endif
509
510 #if defined(__amd64__) || defined(__i386__)
511 static __inline int
irintl(long double x)512 irintl(long double x)
513 {
514 int n;
515
516 asm("fistl %0" : "=m" (n) : "t" (x));
517 return (n);
518 }
519 #define HAVE_EFFICIENT_IRINTL
520 #endif
521
522 #endif /* __GNUCLIKE_ASM */
523
524 #ifdef DEBUG
525 #if defined(__amd64__) || defined(__i386__)
526 #define breakpoint() asm("int $3")
527 #else
528 #include <signal.h>
529
530 #define breakpoint() raise(SIGTRAP)
531 #endif
532 #endif
533
534 /* Write a pari script to test things externally. */
535 #ifdef DOPRINT
536 #include <stdio.h>
537
538 #ifndef DOPRINT_SWIZZLE
539 #define DOPRINT_SWIZZLE 0
540 #endif
541
542 #ifdef DOPRINT_LD80
543
544 #define DOPRINT_START(xp) do { \
545 uint64_t __lx; \
546 uint16_t __hx; \
547 \
548 /* Hack to give more-problematic args. */ \
549 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
550 __lx ^= DOPRINT_SWIZZLE; \
551 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
552 printf("x = %.21Lg; ", (long double)*xp); \
553 } while (0)
554 #define DOPRINT_END1(v) \
555 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
556 #define DOPRINT_END2(hi, lo) \
557 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
558 (long double)(hi), (long double)(lo))
559
560 #elif defined(DOPRINT_D64)
561
562 #define DOPRINT_START(xp) do { \
563 uint32_t __hx, __lx; \
564 \
565 EXTRACT_WORDS(__hx, __lx, *xp); \
566 __lx ^= DOPRINT_SWIZZLE; \
567 INSERT_WORDS(*xp, __hx, __lx); \
568 printf("x = %.21Lg; ", (long double)*xp); \
569 } while (0)
570 #define DOPRINT_END1(v) \
571 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
572 #define DOPRINT_END2(hi, lo) \
573 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
574 (long double)(hi), (long double)(lo))
575
576 #elif defined(DOPRINT_F32)
577
578 #define DOPRINT_START(xp) do { \
579 uint32_t __hx; \
580 \
581 GET_FLOAT_WORD(__hx, *xp); \
582 __hx ^= DOPRINT_SWIZZLE; \
583 SET_FLOAT_WORD(*xp, __hx); \
584 printf("x = %.21Lg; ", (long double)*xp); \
585 } while (0)
586 #define DOPRINT_END1(v) \
587 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
588 #define DOPRINT_END2(hi, lo) \
589 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
590 (long double)(hi), (long double)(lo))
591
592 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
593
594 #ifndef DOPRINT_SWIZZLE_HIGH
595 #define DOPRINT_SWIZZLE_HIGH 0
596 #endif
597
598 #define DOPRINT_START(xp) do { \
599 uint64_t __lx, __llx; \
600 uint16_t __hx; \
601 \
602 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
603 __llx ^= DOPRINT_SWIZZLE; \
604 __lx ^= DOPRINT_SWIZZLE_HIGH; \
605 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
606 printf("x = %.36Lg; ", (long double)*xp); \
607 } while (0)
608 #define DOPRINT_END1(v) \
609 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
610 #define DOPRINT_END2(hi, lo) \
611 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
612 (long double)(hi), (long double)(lo))
613
614 #endif /* DOPRINT_LD80 */
615
616 #else /* !DOPRINT */
617 #define DOPRINT_START(xp)
618 #define DOPRINT_END1(v)
619 #define DOPRINT_END2(hi, lo)
620 #endif /* DOPRINT */
621
622 #define RETURNP(x) do { \
623 DOPRINT_END1(x); \
624 RETURNF(x); \
625 } while (0)
626 #define RETURNPI(x) do { \
627 DOPRINT_END1(x); \
628 RETURNI(x); \
629 } while (0)
630 #define RETURN2P(x, y) do { \
631 DOPRINT_END2((x), (y)); \
632 RETURNF((x) + (y)); \
633 } while (0)
634 #define RETURN2PI(x, y) do { \
635 DOPRINT_END2((x), (y)); \
636 RETURNI((x) + (y)); \
637 } while (0)
638 #ifdef STRUCT_RETURN
639 #define RETURNSP(rp) do { \
640 if (!(rp)->lo_set) \
641 RETURNP((rp)->hi); \
642 RETURN2P((rp)->hi, (rp)->lo); \
643 } while (0)
644 #define RETURNSPI(rp) do { \
645 if (!(rp)->lo_set) \
646 RETURNPI((rp)->hi); \
647 RETURN2PI((rp)->hi, (rp)->lo); \
648 } while (0)
649 #endif
650 #define SUM2P(x, y) ({ \
651 const __typeof (x) __x = (x); \
652 const __typeof (y) __y = (y); \
653 \
654 DOPRINT_END2(__x, __y); \
655 __x + __y; \
656 })
657
658 /*
659 * ieee style elementary functions
660 *
661 * We rename functions here to improve other sources' diffability
662 * against fdlibm.
663 */
664 #define __ieee754_sqrt sqrt
665 #define __ieee754_acos acos
666 #define __ieee754_acosh acosh
667 #define __ieee754_log log
668 #define __ieee754_log2 log2
669 #define __ieee754_atanh atanh
670 #define __ieee754_asin asin
671 #define __ieee754_atan2 atan2
672 #define __ieee754_exp exp
673 #define __ieee754_cosh cosh
674 #define __ieee754_fmod fmod
675 #define __ieee754_pow pow
676 #define __ieee754_lgamma lgamma
677 #define __ieee754_gamma gamma
678 #define __ieee754_lgamma_r lgamma_r
679 #define __ieee754_gamma_r gamma_r
680 #define __ieee754_log10 log10
681 #define __ieee754_sinh sinh
682 #define __ieee754_hypot hypot
683 #define __ieee754_j0 j0
684 #define __ieee754_j1 j1
685 #define __ieee754_y0 y0
686 #define __ieee754_y1 y1
687 #define __ieee754_jn jn
688 #define __ieee754_yn yn
689 #define __ieee754_remainder remainder
690 #define __ieee754_scalb scalb
691 #define __ieee754_sqrtf sqrtf
692 #define __ieee754_acosf acosf
693 #define __ieee754_acoshf acoshf
694 #define __ieee754_logf logf
695 #define __ieee754_atanhf atanhf
696 #define __ieee754_asinf asinf
697 #define __ieee754_atan2f atan2f
698 #define __ieee754_expf expf
699 #define __ieee754_coshf coshf
700 #define __ieee754_fmodf fmodf
701 #define __ieee754_powf powf
702 #define __ieee754_lgammaf lgammaf
703 #define __ieee754_gammaf gammaf
704 #define __ieee754_lgammaf_r lgammaf_r
705 #define __ieee754_gammaf_r gammaf_r
706 #define __ieee754_log10f log10f
707 #define __ieee754_log2f log2f
708 #define __ieee754_sinhf sinhf
709 #define __ieee754_hypotf hypotf
710 #define __ieee754_j0f j0f
711 #define __ieee754_j1f j1f
712 #define __ieee754_y0f y0f
713 #define __ieee754_y1f y1f
714 #define __ieee754_jnf jnf
715 #define __ieee754_ynf ynf
716 #define __ieee754_remainderf remainderf
717 #define __ieee754_scalbf scalbf
718
719 /* fdlibm kernel function */
720 int __kernel_rem_pio2(double*,double*,int,int,int);
721
722 /* double precision kernel functions */
723 #ifndef INLINE_REM_PIO2
724 int __ieee754_rem_pio2(double,double*);
725 #endif
726 double __kernel_sin(double,double,int);
727 double __kernel_cos(double,double);
728 double __kernel_tan(double,double,int);
729 double __ldexp_exp(double,int);
730 #ifdef _COMPLEX_H
731 double complex __ldexp_cexp(double complex,int);
732 #endif
733
734 /* float precision kernel functions */
735 #ifndef INLINE_REM_PIO2F
736 int __ieee754_rem_pio2f(float,double*);
737 #endif
738 #ifndef INLINE_KERNEL_SINDF
739 float __kernel_sindf(double);
740 #endif
741 #ifndef INLINE_KERNEL_COSDF
742 float __kernel_cosdf(double);
743 #endif
744 #ifndef INLINE_KERNEL_TANDF
745 float __kernel_tandf(double,int);
746 #endif
747 float __ldexp_expf(float,int);
748 #ifdef _COMPLEX_H
749 float complex __ldexp_cexpf(float complex,int);
750 #endif
751
752 /* long double precision kernel functions */
753 long double __kernel_sinl(long double, long double, int);
754 long double __kernel_cosl(long double, long double);
755 long double __kernel_tanl(long double, long double, int);
756
757 #endif /* !_MATH_PRIVATE_H_ */
758