1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /*
13 * from: @(#)fdlibm.h 5.1 93/09/24
14 * $FreeBSD: head/lib/msun/src/math_private.h 276176 2014-12-24 10:13:53Z ed $
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 #if IEEE_WORD_ORDER == BIG_ENDIAN
52
53 typedef union
54 {
55 double value;
56 struct
57 {
58 u_int32_t msw;
59 u_int32_t lsw;
60 } parts;
61 struct
62 {
63 u_int64_t w;
64 } xparts;
65 } ieee_double_shape_type;
66
67 #endif
68
69 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
70
71 typedef union
72 {
73 double value;
74 struct
75 {
76 u_int32_t lsw;
77 u_int32_t msw;
78 } parts;
79 struct
80 {
81 u_int64_t w;
82 } xparts;
83 } ieee_double_shape_type;
84
85 #endif
86
87 /* Get two 32 bit ints from a double. */
88
89 #define EXTRACT_WORDS(ix0,ix1,d) \
90 do { \
91 ieee_double_shape_type ew_u; \
92 ew_u.value = (d); \
93 (ix0) = ew_u.parts.msw; \
94 (ix1) = ew_u.parts.lsw; \
95 } while (0)
96
97 /* Get a 64-bit int from a double. */
98 #define EXTRACT_WORD64(ix,d) \
99 do { \
100 ieee_double_shape_type ew_u; \
101 ew_u.value = (d); \
102 (ix) = ew_u.xparts.w; \
103 } while (0)
104
105 /* Get the more significant 32 bit int from a double. */
106
107 #define GET_HIGH_WORD(i,d) \
108 do { \
109 ieee_double_shape_type gh_u; \
110 gh_u.value = (d); \
111 (i) = gh_u.parts.msw; \
112 } while (0)
113
114 /* Get the less significant 32 bit int from a double. */
115
116 #define GET_LOW_WORD(i,d) \
117 do { \
118 ieee_double_shape_type gl_u; \
119 gl_u.value = (d); \
120 (i) = gl_u.parts.lsw; \
121 } while (0)
122
123 /* Set a double from two 32 bit ints. */
124
125 #define INSERT_WORDS(d,ix0,ix1) \
126 do { \
127 ieee_double_shape_type iw_u; \
128 iw_u.parts.msw = (ix0); \
129 iw_u.parts.lsw = (ix1); \
130 (d) = iw_u.value; \
131 } while (0)
132
133 /* Set a double from a 64-bit int. */
134 #define INSERT_WORD64(d,ix) \
135 do { \
136 ieee_double_shape_type iw_u; \
137 iw_u.xparts.w = (ix); \
138 (d) = iw_u.value; \
139 } while (0)
140
141 /* Set the more significant 32 bits of a double from an int. */
142
143 #define SET_HIGH_WORD(d,v) \
144 do { \
145 ieee_double_shape_type sh_u; \
146 sh_u.value = (d); \
147 sh_u.parts.msw = (v); \
148 (d) = sh_u.value; \
149 } while (0)
150
151 /* Set the less significant 32 bits of a double from an int. */
152
153 #define SET_LOW_WORD(d,v) \
154 do { \
155 ieee_double_shape_type sl_u; \
156 sl_u.value = (d); \
157 sl_u.parts.lsw = (v); \
158 (d) = sl_u.value; \
159 } while (0)
160
161 /*
162 * A union which permits us to convert between a float and a 32 bit
163 * int.
164 */
165
166 typedef union
167 {
168 float value;
169 /* FIXME: Assumes 32 bit int. */
170 unsigned int word;
171 } ieee_float_shape_type;
172
173 /* Get a 32 bit int from a float. */
174
175 #define GET_FLOAT_WORD(i,d) \
176 do { \
177 ieee_float_shape_type gf_u; \
178 gf_u.value = (d); \
179 (i) = gf_u.word; \
180 } while (0)
181
182 /* Set a float from a 32 bit int. */
183
184 #define SET_FLOAT_WORD(d,i) \
185 do { \
186 ieee_float_shape_type sf_u; \
187 sf_u.word = (i); \
188 (d) = sf_u.value; \
189 } while (0)
190
191 /*
192 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
193 * double.
194 */
195
196 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
197 do { \
198 union IEEEl2bits ew_u; \
199 ew_u.e = (d); \
200 (ix0) = ew_u.xbits.expsign; \
201 (ix1) = ew_u.xbits.man; \
202 } while (0)
203
204 /*
205 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
206 * long double.
207 */
208
209 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
210 do { \
211 union IEEEl2bits ew_u; \
212 ew_u.e = (d); \
213 (ix0) = ew_u.xbits.expsign; \
214 (ix1) = ew_u.xbits.manh; \
215 (ix2) = ew_u.xbits.manl; \
216 } while (0)
217
218 /* Get expsign as a 16 bit int from a long double. */
219
220 #define GET_LDBL_EXPSIGN(i,d) \
221 do { \
222 union IEEEl2bits ge_u; \
223 ge_u.e = (d); \
224 (i) = ge_u.xbits.expsign; \
225 } while (0)
226
227 /*
228 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
229 * mantissa.
230 */
231
232 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
233 do { \
234 union IEEEl2bits iw_u; \
235 iw_u.xbits.expsign = (ix0); \
236 iw_u.xbits.man = (ix1); \
237 (d) = iw_u.e; \
238 } while (0)
239
240 /*
241 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
242 * comprising the mantissa.
243 */
244
245 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
246 do { \
247 union IEEEl2bits iw_u; \
248 iw_u.xbits.expsign = (ix0); \
249 iw_u.xbits.manh = (ix1); \
250 iw_u.xbits.manl = (ix2); \
251 (d) = iw_u.e; \
252 } while (0)
253
254 /* Set expsign of a long double from a 16 bit int. */
255
256 #define SET_LDBL_EXPSIGN(d,v) \
257 do { \
258 union IEEEl2bits se_u; \
259 se_u.e = (d); \
260 se_u.xbits.expsign = (v); \
261 (d) = se_u.e; \
262 } while (0)
263
264 #ifdef __i386__
265 /* Long double constants are broken on i386. */
266 #define LD80C(m, ex, v) { \
267 .xbits.man = __CONCAT(m, ULL), \
268 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
269 }
270 #else
271 /* The above works on non-i386 too, but we use this to check v. */
272 #define LD80C(m, ex, v) { .e = (v), }
273 #endif
274
275 #ifdef FLT_EVAL_METHOD
276 /*
277 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
278 */
279 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
280 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
281 #else
282 #define STRICT_ASSIGN(type, lval, rval) do { \
283 volatile type __lval; \
284 \
285 if (sizeof(type) >= sizeof(long double)) \
286 (lval) = (rval); \
287 else { \
288 __lval = (rval); \
289 (lval) = __lval; \
290 } \
291 } while (0)
292 #endif
293 #endif /* FLT_EVAL_METHOD */
294
295 /* Support switching the mode to FP_PE if necessary. */
296 #if defined(__i386__) && !defined(NO_FPSETPREC)
297 #define ENTERI() \
298 long double __retval; \
299 fp_prec_t __oprec; \
300 \
301 if ((__oprec = fpgetprec()) != FP_PE) \
302 fpsetprec(FP_PE)
303 #define RETURNI(x) do { \
304 __retval = (x); \
305 if (__oprec != FP_PE) \
306 fpsetprec(__oprec); \
307 RETURNF(__retval); \
308 } while (0)
309 #else
310 #define ENTERI(x)
311 #define RETURNI(x) RETURNF(x)
312 #endif
313
314 /* Default return statement if hack*_t() is not used. */
315 #define RETURNF(v) return (v)
316
317 /*
318 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
319 * a == 0, but is slower.
320 */
321 #define _2sum(a, b) do { \
322 __typeof(a) __s, __w; \
323 \
324 __w = (a) + (b); \
325 __s = __w - (a); \
326 (b) = ((a) - (__w - __s)) + ((b) - __s); \
327 (a) = __w; \
328 } while (0)
329
330 /*
331 * 2sumF algorithm.
332 *
333 * "Normalize" the terms in the infinite-precision expression a + b for
334 * the sum of 2 floating point values so that b is as small as possible
335 * relative to 'a'. (The resulting 'a' is the value of the expression in
336 * the same precision as 'a' and the resulting b is the rounding error.)
337 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
338 * exponent overflow or underflow must not occur. This uses a Theorem of
339 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
340 * is apparently due to Skewchuk (1997).
341 *
342 * For this to always work, assignment of a + b to 'a' must not retain any
343 * extra precision in a + b. This is required by C standards but broken
344 * in many compilers. The brokenness cannot be worked around using
345 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
346 * algorithm would be destroyed by non-null strict assignments. (The
347 * compilers are correct to be broken -- the efficiency of all floating
348 * point code calculations would be destroyed similarly if they forced the
349 * conversions.)
350 *
351 * Fortunately, a case that works well can usually be arranged by building
352 * any extra precision into the type of 'a' -- 'a' should have type float_t,
353 * double_t or long double. b's type should be no larger than 'a's type.
354 * Callers should use these types with scopes as large as possible, to
355 * reduce their own extra-precision and efficiciency problems. In
356 * particular, they shouldn't convert back and forth just to call here.
357 */
358 #ifdef DEBUG
359 #define _2sumF(a, b) do { \
360 __typeof(a) __w; \
361 volatile __typeof(a) __ia, __ib, __r, __vw; \
362 \
363 __ia = (a); \
364 __ib = (b); \
365 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
366 \
367 __w = (a) + (b); \
368 (b) = ((a) - __w) + (b); \
369 (a) = __w; \
370 \
371 /* The next 2 assertions are weak if (a) is already long double. */ \
372 assert((long double)__ia + __ib == (long double)(a) + (b)); \
373 __vw = __ia + __ib; \
374 __r = __ia - __vw; \
375 __r += __ib; \
376 assert(__vw == (a) && __r == (b)); \
377 } while (0)
378 #else /* !DEBUG */
379 #define _2sumF(a, b) do { \
380 __typeof(a) __w; \
381 \
382 __w = (a) + (b); \
383 (b) = ((a) - __w) + (b); \
384 (a) = __w; \
385 } while (0)
386 #endif /* DEBUG */
387
388 /*
389 * Set x += c, where x is represented in extra precision as a + b.
390 * x must be sufficiently normalized and sufficiently larger than c,
391 * and the result is then sufficiently normalized.
392 *
393 * The details of ordering are that |a| must be >= |c| (so that (a, c)
394 * can be normalized without extra work to swap 'a' with c). The details of
395 * the normalization are that b must be small relative to the normalized 'a'.
396 * Normalization of (a, c) makes the normalized c tiny relative to the
397 * normalized a, so b remains small relative to 'a' in the result. However,
398 * b need not ever be tiny relative to 'a'. For example, b might be about
399 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
400 * That is usually enough, and adding c (which by normalization is about
401 * 2**53 times smaller than a) cannot change b significantly. However,
402 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
403 * significantly relative to b. The caller must ensure that significant
404 * cancellation doesn't occur, either by having c of the same sign as 'a',
405 * or by having |c| a few percent smaller than |a|. Pre-normalization of
406 * (a, b) may help.
407 *
408 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
409 * exercise 19). We gain considerable efficiency by requiring the terms to
410 * be sufficiently normalized and sufficiently increasing.
411 */
412 #define _3sumF(a, b, c) do { \
413 __typeof(a) __tmp; \
414 \
415 __tmp = (c); \
416 _2sumF(__tmp, (a)); \
417 (b) += (a); \
418 (a) = __tmp; \
419 } while (0)
420
421 /*
422 * Common routine to process the arguments to nan(), nanf(), and nanl().
423 */
424 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
425
426 #ifdef _COMPLEX_H
427
428 /*
429 * C99 specifies that complex numbers have the same representation as
430 * an array of two elements, where the first element is the real part
431 * and the second element is the imaginary part.
432 */
433 typedef union {
434 float complex f;
435 float a[2];
436 } float_complex;
437 typedef union {
438 double complex f;
439 double a[2];
440 } double_complex;
441 typedef union {
442 long double complex f;
443 long double a[2];
444 } long_double_complex;
445 #define REALPART(z) ((z).a[0])
446 #define IMAGPART(z) ((z).a[1])
447
448 /*
449 * Inline functions that can be used to construct complex values.
450 *
451 * The C99 standard intends x+I*y to be used for this, but x+I*y is
452 * currently unusable in general since gcc introduces many overflow,
453 * underflow, sign and efficiency bugs by rewriting I*y as
454 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
455 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
456 * to -0.0+I*0.0.
457 *
458 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
459 * to construct complex values. Compilers that conform to the C99
460 * standard require the following functions to avoid the above issues.
461 */
462
463 #ifndef CMPLXF
464 static __inline float complex
CMPLXF(float x,float y)465 CMPLXF(float x, float y)
466 {
467 float_complex z;
468
469 REALPART(z) = x;
470 IMAGPART(z) = y;
471 return (z.f);
472 }
473 #endif
474
475 #ifndef CMPLX
476 static __inline double complex
CMPLX(double x,double y)477 CMPLX(double x, double y)
478 {
479 double_complex z;
480
481 REALPART(z) = x;
482 IMAGPART(z) = y;
483 return (z.f);
484 }
485 #endif
486
487 #ifndef CMPLXL
488 static __inline long double complex
CMPLXL(long double x,long double y)489 CMPLXL(long double x, long double y)
490 {
491 long_double_complex z;
492
493 REALPART(z) = x;
494 IMAGPART(z) = y;
495 return (z.f);
496 }
497 #endif
498
499 #endif /* _COMPLEX_H */
500
501 #ifdef __GNUCLIKE_ASM
502
503 /* Asm versions of some functions. */
504
505 #ifdef __amd64__
506 static __inline int
irint(double x)507 irint(double x)
508 {
509 int n;
510
511 asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
512 return (n);
513 }
514 #define HAVE_EFFICIENT_IRINT
515 #endif
516
517 #ifdef __i386__
518 static __inline int
irint(double x)519 irint(double x)
520 {
521 int n;
522
523 asm("fistl %0" : "=m" (n) : "t" (x));
524 return (n);
525 }
526 #define HAVE_EFFICIENT_IRINT
527 #endif
528
529 #if defined(__amd64__) || defined(__i386__)
530 static __inline int
irintl(long double x)531 irintl(long double x)
532 {
533 int n;
534
535 asm("fistl %0" : "=m" (n) : "t" (x));
536 return (n);
537 }
538 #define HAVE_EFFICIENT_IRINTL
539 #endif
540
541 #endif /* __GNUCLIKE_ASM */
542
543 #ifdef DEBUG
544 #if defined(__amd64__) || defined(__i386__)
545 #define breakpoint() asm("int $3")
546 #else
547 #include <signal.h>
548
549 #define breakpoint() raise(SIGTRAP)
550 #endif
551 #endif
552
553 /* Write a pari script to test things externally. */
554 #ifdef DOPRINT
555 #include <stdio.h>
556
557 #ifndef DOPRINT_SWIZZLE
558 #define DOPRINT_SWIZZLE 0
559 #endif
560
561 #ifdef DOPRINT_LD80
562
563 #define DOPRINT_START(xp) do { \
564 uint64_t __lx; \
565 uint16_t __hx; \
566 \
567 /* Hack to give more-problematic args. */ \
568 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
569 __lx ^= DOPRINT_SWIZZLE; \
570 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
571 printf("x = %.21Lg; ", (long double)*xp); \
572 } while (0)
573 #define DOPRINT_END1(v) \
574 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
575 #define DOPRINT_END2(hi, lo) \
576 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
577 (long double)(hi), (long double)(lo))
578
579 #elif defined(DOPRINT_D64)
580
581 #define DOPRINT_START(xp) do { \
582 uint32_t __hx, __lx; \
583 \
584 EXTRACT_WORDS(__hx, __lx, *xp); \
585 __lx ^= DOPRINT_SWIZZLE; \
586 INSERT_WORDS(*xp, __hx, __lx); \
587 printf("x = %.21Lg; ", (long double)*xp); \
588 } while (0)
589 #define DOPRINT_END1(v) \
590 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
591 #define DOPRINT_END2(hi, lo) \
592 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
593 (long double)(hi), (long double)(lo))
594
595 #elif defined(DOPRINT_F32)
596
597 #define DOPRINT_START(xp) do { \
598 uint32_t __hx; \
599 \
600 GET_FLOAT_WORD(__hx, *xp); \
601 __hx ^= DOPRINT_SWIZZLE; \
602 SET_FLOAT_WORD(*xp, __hx); \
603 printf("x = %.21Lg; ", (long double)*xp); \
604 } while (0)
605 #define DOPRINT_END1(v) \
606 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
607 #define DOPRINT_END2(hi, lo) \
608 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
609 (long double)(hi), (long double)(lo))
610
611 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
612
613 #ifndef DOPRINT_SWIZZLE_HIGH
614 #define DOPRINT_SWIZZLE_HIGH 0
615 #endif
616
617 #define DOPRINT_START(xp) do { \
618 uint64_t __lx, __llx; \
619 uint16_t __hx; \
620 \
621 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
622 __llx ^= DOPRINT_SWIZZLE; \
623 __lx ^= DOPRINT_SWIZZLE_HIGH; \
624 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
625 printf("x = %.36Lg; ", (long double)*xp); \
626 } while (0)
627 #define DOPRINT_END1(v) \
628 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
629 #define DOPRINT_END2(hi, lo) \
630 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
631 (long double)(hi), (long double)(lo))
632
633 #endif /* DOPRINT_LD80 */
634
635 #else /* !DOPRINT */
636 #define DOPRINT_START(xp)
637 #define DOPRINT_END1(v)
638 #define DOPRINT_END2(hi, lo)
639 #endif /* DOPRINT */
640
641 #define RETURNP(x) do { \
642 DOPRINT_END1(x); \
643 RETURNF(x); \
644 } while (0)
645 #define RETURNPI(x) do { \
646 DOPRINT_END1(x); \
647 RETURNI(x); \
648 } while (0)
649 #define RETURN2P(x, y) do { \
650 DOPRINT_END2((x), (y)); \
651 RETURNF((x) + (y)); \
652 } while (0)
653 #define RETURN2PI(x, y) do { \
654 DOPRINT_END2((x), (y)); \
655 RETURNI((x) + (y)); \
656 } while (0)
657 #ifdef STRUCT_RETURN
658 #define RETURNSP(rp) do { \
659 if (!(rp)->lo_set) \
660 RETURNP((rp)->hi); \
661 RETURN2P((rp)->hi, (rp)->lo); \
662 } while (0)
663 #define RETURNSPI(rp) do { \
664 if (!(rp)->lo_set) \
665 RETURNPI((rp)->hi); \
666 RETURN2PI((rp)->hi, (rp)->lo); \
667 } while (0)
668 #endif
669 #define SUM2P(x, y) ({ \
670 const __typeof (x) __x = (x); \
671 const __typeof (y) __y = (y); \
672 \
673 DOPRINT_END2(__x, __y); \
674 __x + __y; \
675 })
676
677 /*
678 * ieee style elementary functions
679 *
680 * We rename functions here to improve other sources' diffability
681 * against fdlibm.
682 */
683 #define __ieee754_sqrt sqrt
684 #define __ieee754_acos acos
685 #define __ieee754_acosh acosh
686 #define __ieee754_log log
687 #define __ieee754_log2 log2
688 #define __ieee754_atanh atanh
689 #define __ieee754_asin asin
690 #define __ieee754_atan2 atan2
691 #define __ieee754_exp exp
692 #define __ieee754_cosh cosh
693 #define __ieee754_fmod fmod
694 #define __ieee754_pow pow
695 #define __ieee754_lgamma lgamma
696 #define __ieee754_gamma gamma
697 #define __ieee754_lgamma_r lgamma_r
698 #define __ieee754_gamma_r gamma_r
699 #define __ieee754_log10 log10
700 #define __ieee754_sinh sinh
701 #define __ieee754_hypot hypot
702 #define __ieee754_j0 j0
703 #define __ieee754_j1 j1
704 #define __ieee754_y0 y0
705 #define __ieee754_y1 y1
706 #define __ieee754_jn jn
707 #define __ieee754_yn yn
708 #define __ieee754_remainder remainder
709 #define __ieee754_scalb scalb
710 #define __ieee754_sqrtf sqrtf
711 #define __ieee754_acosf acosf
712 #define __ieee754_acoshf acoshf
713 #define __ieee754_logf logf
714 #define __ieee754_atanhf atanhf
715 #define __ieee754_asinf asinf
716 #define __ieee754_atan2f atan2f
717 #define __ieee754_expf expf
718 #define __ieee754_coshf coshf
719 #define __ieee754_fmodf fmodf
720 #define __ieee754_powf powf
721 #define __ieee754_lgammaf lgammaf
722 #define __ieee754_gammaf gammaf
723 #define __ieee754_lgammaf_r lgammaf_r
724 #define __ieee754_gammaf_r gammaf_r
725 #define __ieee754_log10f log10f
726 #define __ieee754_log2f log2f
727 #define __ieee754_sinhf sinhf
728 #define __ieee754_hypotf hypotf
729 #define __ieee754_j0f j0f
730 #define __ieee754_j1f j1f
731 #define __ieee754_y0f y0f
732 #define __ieee754_y1f y1f
733 #define __ieee754_jnf jnf
734 #define __ieee754_ynf ynf
735 #define __ieee754_remainderf remainderf
736 #define __ieee754_scalbf scalbf
737
738 /* fdlibm kernel function */
739 int __kernel_rem_pio2(double*,double*,int,int,int);
740
741 /* double precision kernel functions */
742 #ifndef INLINE_REM_PIO2
743 int __ieee754_rem_pio2(double,double*);
744 #endif
745 double __kernel_sin(double,double,int);
746 double __kernel_cos(double,double);
747 double __kernel_tan(double,double,int);
748 double __ldexp_exp(double,int);
749 #ifdef _COMPLEX_H
750 double complex __ldexp_cexp(double complex,int);
751 #endif
752
753 /* float precision kernel functions */
754 #ifndef INLINE_REM_PIO2F
755 int __ieee754_rem_pio2f(float,double*);
756 #endif
757 #ifndef INLINE_KERNEL_SINDF
758 float __kernel_sindf(double);
759 #endif
760 #ifndef INLINE_KERNEL_COSDF
761 float __kernel_cosdf(double);
762 #endif
763 #ifndef INLINE_KERNEL_TANDF
764 float __kernel_tandf(double,int);
765 #endif
766 float __ldexp_expf(float,int);
767 #ifdef _COMPLEX_H
768 float complex __ldexp_cexpf(float complex,int);
769 #endif
770
771 /* long double precision kernel functions */
772 long double __kernel_sinl(long double, long double, int);
773 long double __kernel_cosl(long double, long double);
774 long double __kernel_tanl(long double, long double, int);
775
776 #endif /* !_MATH_PRIVATE_H_ */
777