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 #include <stdint.h>
24 typedef uint32_t u_int32_t;
25 typedef uint64_t u_int64_t;
26
27 /*
28 * The original fdlibm code used statements like:
29 * n0 = ((*(int*)&one)>>29)^1; * index of high word *
30 * ix0 = *(n0+(int*)&x); * high word of x *
31 * ix1 = *((1-n0)+(int*)&x); * low word of x *
32 * to dig two 32 bit words out of the 64 bit IEEE floating point
33 * value. That is non-ANSI, and, moreover, the gcc instruction
34 * scheduler gets it wrong. We instead use the following macros.
35 * Unlike the original code, we determine the endianness at compile
36 * time, not at run time; I don't see much benefit to selecting
37 * endianness at run time.
38 */
39
40 /*
41 * A union which permits us to convert between a double and two 32 bit
42 * ints.
43 */
44
45 #ifdef __arm__
46 #if defined(__VFP_FP__) || defined(__ARM_EABI__)
47 #define IEEE_WORD_ORDER BYTE_ORDER
48 #else
49 #define IEEE_WORD_ORDER BIG_ENDIAN
50 #endif
51 #else /* __arm__ */
52 #define IEEE_WORD_ORDER BYTE_ORDER
53 #endif
54
55 #if IEEE_WORD_ORDER == BIG_ENDIAN
56
57 typedef union
58 {
59 double value;
60 struct
61 {
62 u_int32_t msw;
63 u_int32_t lsw;
64 } parts;
65 struct
66 {
67 u_int64_t w;
68 } xparts;
69 } ieee_double_shape_type;
70
71 #endif
72
73 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
74
75 typedef union
76 {
77 double value;
78 struct
79 {
80 u_int32_t lsw;
81 u_int32_t msw;
82 } parts;
83 struct
84 {
85 u_int64_t w;
86 } xparts;
87 } ieee_double_shape_type;
88
89 #endif
90
91 /* Get two 32 bit ints from a double. */
92
93 #define EXTRACT_WORDS(ix0,ix1,d) \
94 do { \
95 ieee_double_shape_type ew_u; \
96 ew_u.value = (d); \
97 (ix0) = ew_u.parts.msw; \
98 (ix1) = ew_u.parts.lsw; \
99 } while (0)
100
101 /* Get a 64-bit int from a double. */
102 #define EXTRACT_WORD64(ix,d) \
103 do { \
104 ieee_double_shape_type ew_u; \
105 ew_u.value = (d); \
106 (ix) = ew_u.xparts.w; \
107 } while (0)
108
109 /* Get the more significant 32 bit int from a double. */
110
111 #define GET_HIGH_WORD(i,d) \
112 do { \
113 ieee_double_shape_type gh_u; \
114 gh_u.value = (d); \
115 (i) = gh_u.parts.msw; \
116 } while (0)
117
118 /* Get the less significant 32 bit int from a double. */
119
120 #define GET_LOW_WORD(i,d) \
121 do { \
122 ieee_double_shape_type gl_u; \
123 gl_u.value = (d); \
124 (i) = gl_u.parts.lsw; \
125 } while (0)
126
127 /* Set a double from two 32 bit ints. */
128
129 #define INSERT_WORDS(d,ix0,ix1) \
130 do { \
131 ieee_double_shape_type iw_u; \
132 iw_u.parts.msw = (ix0); \
133 iw_u.parts.lsw = (ix1); \
134 (d) = iw_u.value; \
135 } while (0)
136
137 /* Set a double from a 64-bit int. */
138 #define INSERT_WORD64(d,ix) \
139 do { \
140 ieee_double_shape_type iw_u; \
141 iw_u.xparts.w = (ix); \
142 (d) = iw_u.value; \
143 } while (0)
144
145 /* Set the more significant 32 bits of a double from an int. */
146
147 #define SET_HIGH_WORD(d,v) \
148 do { \
149 ieee_double_shape_type sh_u; \
150 sh_u.value = (d); \
151 sh_u.parts.msw = (v); \
152 (d) = sh_u.value; \
153 } while (0)
154
155 /* Set the less significant 32 bits of a double from an int. */
156
157 #define SET_LOW_WORD(d,v) \
158 do { \
159 ieee_double_shape_type sl_u; \
160 sl_u.value = (d); \
161 sl_u.parts.lsw = (v); \
162 (d) = sl_u.value; \
163 } while (0)
164
165 /*
166 * A union which permits us to convert between a float and a 32 bit
167 * int.
168 */
169
170 typedef union
171 {
172 float value;
173 /* FIXME: Assumes 32 bit int. */
174 unsigned int word;
175 } ieee_float_shape_type;
176
177 /* Get a 32 bit int from a float. */
178
179 #define GET_FLOAT_WORD(i,d) \
180 do { \
181 ieee_float_shape_type gf_u; \
182 gf_u.value = (d); \
183 (i) = gf_u.word; \
184 } while (0)
185
186 /* Set a float from a 32 bit int. */
187
188 #define SET_FLOAT_WORD(d,i) \
189 do { \
190 ieee_float_shape_type sf_u; \
191 sf_u.word = (i); \
192 (d) = sf_u.value; \
193 } while (0)
194
195 /*
196 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
197 * double.
198 */
199
200 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
201 do { \
202 union IEEEl2bits ew_u; \
203 ew_u.e = (d); \
204 (ix0) = ew_u.xbits.expsign; \
205 (ix1) = ew_u.xbits.man; \
206 } while (0)
207
208 /*
209 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
210 * long double.
211 */
212
213 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
214 do { \
215 union IEEEl2bits ew_u; \
216 ew_u.e = (d); \
217 (ix0) = ew_u.xbits.expsign; \
218 (ix1) = ew_u.xbits.manh; \
219 (ix2) = ew_u.xbits.manl; \
220 } while (0)
221
222 /* Get expsign as a 16 bit int from a long double. */
223
224 #define GET_LDBL_EXPSIGN(i,d) \
225 do { \
226 union IEEEl2bits ge_u; \
227 ge_u.e = (d); \
228 (i) = ge_u.xbits.expsign; \
229 } while (0)
230
231 /*
232 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
233 * mantissa.
234 */
235
236 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
237 do { \
238 union IEEEl2bits iw_u; \
239 iw_u.xbits.expsign = (ix0); \
240 iw_u.xbits.man = (ix1); \
241 (d) = iw_u.e; \
242 } while (0)
243
244 /*
245 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
246 * comprising the mantissa.
247 */
248
249 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
250 do { \
251 union IEEEl2bits iw_u; \
252 iw_u.xbits.expsign = (ix0); \
253 iw_u.xbits.manh = (ix1); \
254 iw_u.xbits.manl = (ix2); \
255 (d) = iw_u.e; \
256 } while (0)
257
258 /* Set expsign of a long double from a 16 bit int. */
259
260 #define SET_LDBL_EXPSIGN(d,v) \
261 do { \
262 union IEEEl2bits se_u; \
263 se_u.e = (d); \
264 se_u.xbits.expsign = (v); \
265 (d) = se_u.e; \
266 } while (0)
267
268 #ifdef __i386__
269 /* Long double constants are broken on i386. */
270 #define LD80C(m, ex, v) { \
271 .xbits.man = __CONCAT(m, ULL), \
272 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
273 }
274 #else
275 /* The above works on non-i386 too, but we use this to check v. */
276 #define LD80C(m, ex, v) { .e = (v), }
277 #endif
278
279 #ifdef FLT_EVAL_METHOD
280 /*
281 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
282 */
283 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
284 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
285 #else
286 #define STRICT_ASSIGN(type, lval, rval) do { \
287 volatile type __lval; \
288 \
289 if (sizeof(type) >= sizeof(long double)) \
290 (lval) = (rval); \
291 else { \
292 __lval = (rval); \
293 (lval) = __lval; \
294 } \
295 } while (0)
296 #endif
297 #endif /* FLT_EVAL_METHOD */
298
299 /* Support switching the mode to FP_PE if necessary. */
300 #if defined(__i386__) && !defined(NO_FPSETPREC)
301 #define ENTERI() \
302 long double __retval; \
303 fp_prec_t __oprec; \
304 \
305 if ((__oprec = fpgetprec()) != FP_PE) \
306 fpsetprec(FP_PE)
307 #define RETURNI(x) do { \
308 __retval = (x); \
309 if (__oprec != FP_PE) \
310 fpsetprec(__oprec); \
311 RETURNF(__retval); \
312 } while (0)
313 #else
314 #define ENTERI(x)
315 #define RETURNI(x) RETURNF(x)
316 #endif
317
318 /* Default return statement if hack*_t() is not used. */
319 #define RETURNF(v) return (v)
320
321 /*
322 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
323 * a == 0, but is slower.
324 */
325 #define _2sum(a, b) do { \
326 __typeof(a) __s, __w; \
327 \
328 __w = (a) + (b); \
329 __s = __w - (a); \
330 (b) = ((a) - (__w - __s)) + ((b) - __s); \
331 (a) = __w; \
332 } while (0)
333
334 /*
335 * 2sumF algorithm.
336 *
337 * "Normalize" the terms in the infinite-precision expression a + b for
338 * the sum of 2 floating point values so that b is as small as possible
339 * relative to 'a'. (The resulting 'a' is the value of the expression in
340 * the same precision as 'a' and the resulting b is the rounding error.)
341 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
342 * exponent overflow or underflow must not occur. This uses a Theorem of
343 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
344 * is apparently due to Skewchuk (1997).
345 *
346 * For this to always work, assignment of a + b to 'a' must not retain any
347 * extra precision in a + b. This is required by C standards but broken
348 * in many compilers. The brokenness cannot be worked around using
349 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
350 * algorithm would be destroyed by non-null strict assignments. (The
351 * compilers are correct to be broken -- the efficiency of all floating
352 * point code calculations would be destroyed similarly if they forced the
353 * conversions.)
354 *
355 * Fortunately, a case that works well can usually be arranged by building
356 * any extra precision into the type of 'a' -- 'a' should have type float_t,
357 * double_t or long double. b's type should be no larger than 'a's type.
358 * Callers should use these types with scopes as large as possible, to
359 * reduce their own extra-precision and efficiciency problems. In
360 * particular, they shouldn't convert back and forth just to call here.
361 */
362 #ifdef DEBUG
363 #define _2sumF(a, b) do { \
364 __typeof(a) __w; \
365 volatile __typeof(a) __ia, __ib, __r, __vw; \
366 \
367 __ia = (a); \
368 __ib = (b); \
369 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
370 \
371 __w = (a) + (b); \
372 (b) = ((a) - __w) + (b); \
373 (a) = __w; \
374 \
375 /* The next 2 assertions are weak if (a) is already long double. */ \
376 assert((long double)__ia + __ib == (long double)(a) + (b)); \
377 __vw = __ia + __ib; \
378 __r = __ia - __vw; \
379 __r += __ib; \
380 assert(__vw == (a) && __r == (b)); \
381 } while (0)
382 #else /* !DEBUG */
383 #define _2sumF(a, b) do { \
384 __typeof(a) __w; \
385 \
386 __w = (a) + (b); \
387 (b) = ((a) - __w) + (b); \
388 (a) = __w; \
389 } while (0)
390 #endif /* DEBUG */
391
392 /*
393 * Set x += c, where x is represented in extra precision as a + b.
394 * x must be sufficiently normalized and sufficiently larger than c,
395 * and the result is then sufficiently normalized.
396 *
397 * The details of ordering are that |a| must be >= |c| (so that (a, c)
398 * can be normalized without extra work to swap 'a' with c). The details of
399 * the normalization are that b must be small relative to the normalized 'a'.
400 * Normalization of (a, c) makes the normalized c tiny relative to the
401 * normalized a, so b remains small relative to 'a' in the result. However,
402 * b need not ever be tiny relative to 'a'. For example, b might be about
403 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
404 * That is usually enough, and adding c (which by normalization is about
405 * 2**53 times smaller than a) cannot change b significantly. However,
406 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
407 * significantly relative to b. The caller must ensure that significant
408 * cancellation doesn't occur, either by having c of the same sign as 'a',
409 * or by having |c| a few percent smaller than |a|. Pre-normalization of
410 * (a, b) may help.
411 *
412 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
413 * exercise 19). We gain considerable efficiency by requiring the terms to
414 * be sufficiently normalized and sufficiently increasing.
415 */
416 #define _3sumF(a, b, c) do { \
417 __typeof(a) __tmp; \
418 \
419 __tmp = (c); \
420 _2sumF(__tmp, (a)); \
421 (b) += (a); \
422 (a) = __tmp; \
423 } while (0)
424
425 /*
426 * Common routine to process the arguments to nan(), nanf(), and nanl().
427 */
428 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
429
430 #ifdef _COMPLEX_H
431
432 /*
433 * C99 specifies that complex numbers have the same representation as
434 * an array of two elements, where the first element is the real part
435 * and the second element is the imaginary part.
436 */
437 typedef union {
438 float complex f;
439 float a[2];
440 } float_complex;
441 typedef union {
442 double complex f;
443 double a[2];
444 } double_complex;
445 typedef union {
446 long double complex f;
447 long double a[2];
448 } long_double_complex;
449 #define REALPART(z) ((z).a[0])
450 #define IMAGPART(z) ((z).a[1])
451
452 /*
453 * Inline functions that can be used to construct complex values.
454 *
455 * The C99 standard intends x+I*y to be used for this, but x+I*y is
456 * currently unusable in general since gcc introduces many overflow,
457 * underflow, sign and efficiency bugs by rewriting I*y as
458 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
459 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
460 * to -0.0+I*0.0.
461 */
462 static __inline float complex
cpackf(float x,float y)463 cpackf(float x, float y)
464 {
465 float_complex z;
466
467 REALPART(z) = x;
468 IMAGPART(z) = y;
469 return (z.f);
470 }
471
472 static __inline double complex
cpack(double x,double y)473 cpack(double x, double y)
474 {
475 double_complex z;
476
477 REALPART(z) = x;
478 IMAGPART(z) = y;
479 return (z.f);
480 }
481
482 static __inline long double complex
cpackl(long double x,long double y)483 cpackl(long double x, long double y)
484 {
485 long_double_complex z;
486
487 REALPART(z) = x;
488 IMAGPART(z) = y;
489 return (z.f);
490 }
491 #endif /* _COMPLEX_H */
492
493 #ifdef __GNUCLIKE_ASM
494
495 /* Asm versions of some functions. */
496
497 #ifdef __amd64__
498 static __inline int
irint(double x)499 irint(double x)
500 {
501 int n;
502
503 asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
504 return (n);
505 }
506 #define HAVE_EFFICIENT_IRINT
507 #endif
508
509 #ifdef __i386__
510 static __inline int
irint(double x)511 irint(double x)
512 {
513 int n;
514
515 asm("fistl %0" : "=m" (n) : "t" (x));
516 return (n);
517 }
518 #define HAVE_EFFICIENT_IRINT
519 #endif
520
521 #if defined(__amd64__) || defined(__i386__)
522 static __inline int
irintl(long double x)523 irintl(long double x)
524 {
525 int n;
526
527 asm("fistl %0" : "=m" (n) : "t" (x));
528 return (n);
529 }
530 #define HAVE_EFFICIENT_IRINTL
531 #endif
532
533 #endif /* __GNUCLIKE_ASM */
534
535 #ifdef DEBUG
536 #if defined(__amd64__) || defined(__i386__)
537 #define breakpoint() asm("int $3")
538 #else
539 #include <signal.h>
540
541 #define breakpoint() raise(SIGTRAP)
542 #endif
543 #endif
544
545 /* Write a pari script to test things externally. */
546 #ifdef DOPRINT
547 #include <stdio.h>
548
549 #ifndef DOPRINT_SWIZZLE
550 #define DOPRINT_SWIZZLE 0
551 #endif
552
553 #ifdef DOPRINT_LD80
554
555 #define DOPRINT_START(xp) do { \
556 uint64_t __lx; \
557 uint16_t __hx; \
558 \
559 /* Hack to give more-problematic args. */ \
560 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
561 __lx ^= DOPRINT_SWIZZLE; \
562 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
563 printf("x = %.21Lg; ", (long double)*xp); \
564 } while (0)
565 #define DOPRINT_END1(v) \
566 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
567 #define DOPRINT_END2(hi, lo) \
568 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
569 (long double)(hi), (long double)(lo))
570
571 #elif defined(DOPRINT_D64)
572
573 #define DOPRINT_START(xp) do { \
574 uint32_t __hx, __lx; \
575 \
576 EXTRACT_WORDS(__hx, __lx, *xp); \
577 __lx ^= DOPRINT_SWIZZLE; \
578 INSERT_WORDS(*xp, __hx, __lx); \
579 printf("x = %.21Lg; ", (long double)*xp); \
580 } while (0)
581 #define DOPRINT_END1(v) \
582 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
583 #define DOPRINT_END2(hi, lo) \
584 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
585 (long double)(hi), (long double)(lo))
586
587 #elif defined(DOPRINT_F32)
588
589 #define DOPRINT_START(xp) do { \
590 uint32_t __hx; \
591 \
592 GET_FLOAT_WORD(__hx, *xp); \
593 __hx ^= DOPRINT_SWIZZLE; \
594 SET_FLOAT_WORD(*xp, __hx); \
595 printf("x = %.21Lg; ", (long double)*xp); \
596 } while (0)
597 #define DOPRINT_END1(v) \
598 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
599 #define DOPRINT_END2(hi, lo) \
600 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
601 (long double)(hi), (long double)(lo))
602
603 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
604
605 #ifndef DOPRINT_SWIZZLE_HIGH
606 #define DOPRINT_SWIZZLE_HIGH 0
607 #endif
608
609 #define DOPRINT_START(xp) do { \
610 uint64_t __lx, __llx; \
611 uint16_t __hx; \
612 \
613 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
614 __llx ^= DOPRINT_SWIZZLE; \
615 __lx ^= DOPRINT_SWIZZLE_HIGH; \
616 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
617 printf("x = %.36Lg; ", (long double)*xp); \
618 } while (0)
619 #define DOPRINT_END1(v) \
620 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
621 #define DOPRINT_END2(hi, lo) \
622 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
623 (long double)(hi), (long double)(lo))
624
625 #endif /* DOPRINT_LD80 */
626
627 #else /* !DOPRINT */
628 #define DOPRINT_START(xp)
629 #define DOPRINT_END1(v)
630 #define DOPRINT_END2(hi, lo)
631 #endif /* DOPRINT */
632
633 #define RETURNP(x) do { \
634 DOPRINT_END1(x); \
635 RETURNF(x); \
636 } while (0)
637 #define RETURNPI(x) do { \
638 DOPRINT_END1(x); \
639 RETURNI(x); \
640 } while (0)
641 #define RETURN2P(x, y) do { \
642 DOPRINT_END2((x), (y)); \
643 RETURNF((x) + (y)); \
644 } while (0)
645 #define RETURN2PI(x, y) do { \
646 DOPRINT_END2((x), (y)); \
647 RETURNI((x) + (y)); \
648 } while (0)
649 #ifdef STRUCT_RETURN
650 #define RETURNSP(rp) do { \
651 if (!(rp)->lo_set) \
652 RETURNP((rp)->hi); \
653 RETURN2P((rp)->hi, (rp)->lo); \
654 } while (0)
655 #define RETURNSPI(rp) do { \
656 if (!(rp)->lo_set) \
657 RETURNPI((rp)->hi); \
658 RETURN2PI((rp)->hi, (rp)->lo); \
659 } while (0)
660 #endif
661 #define SUM2P(x, y) ({ \
662 const __typeof (x) __x = (x); \
663 const __typeof (y) __y = (y); \
664 \
665 DOPRINT_END2(__x, __y); \
666 __x + __y; \
667 })
668
669 /*
670 * ieee style elementary functions
671 *
672 * We rename functions here to improve other sources' diffability
673 * against fdlibm.
674 */
675 #define __ieee754_sqrt sqrt
676 #define __ieee754_acos acos
677 #define __ieee754_acosh acosh
678 #define __ieee754_log log
679 #define __ieee754_log2 log2
680 #define __ieee754_atanh atanh
681 #define __ieee754_asin asin
682 #define __ieee754_atan2 atan2
683 #define __ieee754_exp exp
684 #define __ieee754_cosh cosh
685 #define __ieee754_fmod fmod
686 #define __ieee754_pow pow
687 #define __ieee754_lgamma lgamma
688 #define __ieee754_gamma gamma
689 #define __ieee754_lgamma_r lgamma_r
690 #define __ieee754_gamma_r gamma_r
691 #define __ieee754_log10 log10
692 #define __ieee754_sinh sinh
693 #define __ieee754_hypot hypot
694 #define __ieee754_j0 j0
695 #define __ieee754_j1 j1
696 #define __ieee754_y0 y0
697 #define __ieee754_y1 y1
698 #define __ieee754_jn jn
699 #define __ieee754_yn yn
700 #define __ieee754_remainder remainder
701 #define __ieee754_scalb scalb
702 #define __ieee754_sqrtf sqrtf
703 #define __ieee754_acosf acosf
704 #define __ieee754_acoshf acoshf
705 #define __ieee754_logf logf
706 #define __ieee754_atanhf atanhf
707 #define __ieee754_asinf asinf
708 #define __ieee754_atan2f atan2f
709 #define __ieee754_expf expf
710 #define __ieee754_coshf coshf
711 #define __ieee754_fmodf fmodf
712 #define __ieee754_powf powf
713 #define __ieee754_lgammaf lgammaf
714 #define __ieee754_gammaf gammaf
715 #define __ieee754_lgammaf_r lgammaf_r
716 #define __ieee754_gammaf_r gammaf_r
717 #define __ieee754_log10f log10f
718 #define __ieee754_log2f log2f
719 #define __ieee754_sinhf sinhf
720 #define __ieee754_hypotf hypotf
721 #define __ieee754_j0f j0f
722 #define __ieee754_j1f j1f
723 #define __ieee754_y0f y0f
724 #define __ieee754_y1f y1f
725 #define __ieee754_jnf jnf
726 #define __ieee754_ynf ynf
727 #define __ieee754_remainderf remainderf
728 #define __ieee754_scalbf scalbf
729
730 /* fdlibm kernel function */
731 int __kernel_rem_pio2(double*,double*,int,int,int);
732
733 /* double precision kernel functions */
734 #ifndef INLINE_REM_PIO2
735 int __ieee754_rem_pio2(double,double*);
736 #endif
737 double __kernel_sin(double,double,int);
738 double __kernel_cos(double,double);
739 double __kernel_tan(double,double,int);
740 double __ldexp_exp(double,int);
741 #ifdef _COMPLEX_H
742 double complex __ldexp_cexp(double complex,int);
743 #endif
744
745 /* float precision kernel functions */
746 #ifndef INLINE_REM_PIO2F
747 int __ieee754_rem_pio2f(float,double*);
748 #endif
749 #ifndef INLINE_KERNEL_SINDF
750 float __kernel_sindf(double);
751 #endif
752 #ifndef INLINE_KERNEL_COSDF
753 float __kernel_cosdf(double);
754 #endif
755 #ifndef INLINE_KERNEL_TANDF
756 float __kernel_tandf(double,int);
757 #endif
758 float __ldexp_expf(float,int);
759 #ifdef _COMPLEX_H
760 float complex __ldexp_cexpf(float complex,int);
761 #endif
762
763 /* long double precision kernel functions */
764 long double __kernel_sinl(long double, long double, int);
765 long double __kernel_cosl(long double, long double);
766 long double __kernel_tanl(long double, long double, int);
767
768 #endif /* !_MATH_PRIVATE_H_ */
769