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 */
14
15 #ifndef _MATH_PRIVATE_H_
16 #define _MATH_PRIVATE_H_
17
18 #include <sys/types.h>
19 #include <machine/endian.h>
20
21 /*
22 * The original fdlibm code used statements like:
23 * n0 = ((*(int*)&one)>>29)^1; * index of high word *
24 * ix0 = *(n0+(int*)&x); * high word of x *
25 * ix1 = *((1-n0)+(int*)&x); * low word of x *
26 * to dig two 32 bit words out of the 64 bit IEEE floating point
27 * value. That is non-ANSI, and, moreover, the gcc instruction
28 * scheduler gets it wrong. We instead use the following macros.
29 * Unlike the original code, we determine the endianness at compile
30 * time, not at run time; I don't see much benefit to selecting
31 * endianness at run time.
32 */
33
34 /*
35 * A union which permits us to convert between a double and two 32 bit
36 * ints.
37 */
38
39 #ifdef __arm__
40 #if defined(__VFP_FP__) || defined(__ARM_EABI__)
41 #define IEEE_WORD_ORDER BYTE_ORDER
42 #else
43 #define IEEE_WORD_ORDER BIG_ENDIAN
44 #endif
45 #else /* __arm__ */
46 #define IEEE_WORD_ORDER BYTE_ORDER
47 #endif
48
49 /* A union which permits us to convert between a long double and
50 four 32 bit ints. */
51
52 #if IEEE_WORD_ORDER == BIG_ENDIAN
53
54 typedef union
55 {
56 long double value;
57 struct {
58 u_int32_t mswhi;
59 u_int32_t mswlo;
60 u_int32_t lswhi;
61 u_int32_t lswlo;
62 } parts32;
63 struct {
64 u_int64_t msw;
65 u_int64_t lsw;
66 } parts64;
67 } ieee_quad_shape_type;
68
69 #endif
70
71 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
72
73 typedef union
74 {
75 long double value;
76 struct {
77 u_int32_t lswlo;
78 u_int32_t lswhi;
79 u_int32_t mswlo;
80 u_int32_t mswhi;
81 } parts32;
82 struct {
83 u_int64_t lsw;
84 u_int64_t msw;
85 } parts64;
86 } ieee_quad_shape_type;
87
88 #endif
89
90 #if IEEE_WORD_ORDER == BIG_ENDIAN
91
92 typedef union
93 {
94 double value;
95 struct
96 {
97 u_int32_t msw;
98 u_int32_t lsw;
99 } parts;
100 struct
101 {
102 u_int64_t w;
103 } xparts;
104 } ieee_double_shape_type;
105
106 #endif
107
108 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
109
110 typedef union
111 {
112 double value;
113 struct
114 {
115 u_int32_t lsw;
116 u_int32_t msw;
117 } parts;
118 struct
119 {
120 u_int64_t w;
121 } xparts;
122 } ieee_double_shape_type;
123
124 #endif
125
126 /* Get two 32 bit ints from a double. */
127
128 #define EXTRACT_WORDS(ix0,ix1,d) \
129 do { \
130 ieee_double_shape_type ew_u; \
131 ew_u.value = (d); \
132 (ix0) = ew_u.parts.msw; \
133 (ix1) = ew_u.parts.lsw; \
134 } while (0)
135
136 /* Get a 64-bit int from a double. */
137 #define EXTRACT_WORD64(ix,d) \
138 do { \
139 ieee_double_shape_type ew_u; \
140 ew_u.value = (d); \
141 (ix) = ew_u.xparts.w; \
142 } while (0)
143
144 /* Get the more significant 32 bit int from a double. */
145
146 #define GET_HIGH_WORD(i,d) \
147 do { \
148 ieee_double_shape_type gh_u; \
149 gh_u.value = (d); \
150 (i) = gh_u.parts.msw; \
151 } while (0)
152
153 /* Get the less significant 32 bit int from a double. */
154
155 #define GET_LOW_WORD(i,d) \
156 do { \
157 ieee_double_shape_type gl_u; \
158 gl_u.value = (d); \
159 (i) = gl_u.parts.lsw; \
160 } while (0)
161
162 /* Set a double from two 32 bit ints. */
163
164 #define INSERT_WORDS(d,ix0,ix1) \
165 do { \
166 ieee_double_shape_type iw_u; \
167 iw_u.parts.msw = (ix0); \
168 iw_u.parts.lsw = (ix1); \
169 (d) = iw_u.value; \
170 } while (0)
171
172 /* Set a double from a 64-bit int. */
173 #define INSERT_WORD64(d,ix) \
174 do { \
175 ieee_double_shape_type iw_u; \
176 iw_u.xparts.w = (ix); \
177 (d) = iw_u.value; \
178 } while (0)
179
180 /* Set the more significant 32 bits of a double from an int. */
181
182 #define SET_HIGH_WORD(d,v) \
183 do { \
184 ieee_double_shape_type sh_u; \
185 sh_u.value = (d); \
186 sh_u.parts.msw = (v); \
187 (d) = sh_u.value; \
188 } while (0)
189
190 /* Set the less significant 32 bits of a double from an int. */
191
192 #define SET_LOW_WORD(d,v) \
193 do { \
194 ieee_double_shape_type sl_u; \
195 sl_u.value = (d); \
196 sl_u.parts.lsw = (v); \
197 (d) = sl_u.value; \
198 } while (0)
199
200 /*
201 * A union which permits us to convert between a float and a 32 bit
202 * int.
203 */
204
205 typedef union
206 {
207 float value;
208 /* FIXME: Assumes 32 bit int. */
209 unsigned int word;
210 } ieee_float_shape_type;
211
212 /* Get a 32 bit int from a float. */
213
214 #define GET_FLOAT_WORD(i,d) \
215 do { \
216 ieee_float_shape_type gf_u; \
217 gf_u.value = (d); \
218 (i) = gf_u.word; \
219 } while (0)
220
221 /* Set a float from a 32 bit int. */
222
223 #define SET_FLOAT_WORD(d,i) \
224 do { \
225 ieee_float_shape_type sf_u; \
226 sf_u.word = (i); \
227 (d) = sf_u.value; \
228 } while (0)
229
230 /*
231 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
232 * double.
233 */
234
235 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
236 do { \
237 union IEEEl2bits ew_u; \
238 ew_u.e = (d); \
239 (ix0) = ew_u.xbits.expsign; \
240 (ix1) = ew_u.xbits.man; \
241 } while (0)
242
243 /*
244 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
245 * long double.
246 */
247
248 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
249 do { \
250 union IEEEl2bits ew_u; \
251 ew_u.e = (d); \
252 (ix0) = ew_u.xbits.expsign; \
253 (ix1) = ew_u.xbits.manh; \
254 (ix2) = ew_u.xbits.manl; \
255 } while (0)
256
257 /* Get expsign as a 16 bit int from a long double. */
258
259 #define GET_LDBL_EXPSIGN(i,d) \
260 do { \
261 union IEEEl2bits ge_u; \
262 ge_u.e = (d); \
263 (i) = ge_u.xbits.expsign; \
264 } while (0)
265
266 /*
267 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
268 * mantissa.
269 */
270
271 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
272 do { \
273 union IEEEl2bits iw_u; \
274 iw_u.xbits.expsign = (ix0); \
275 iw_u.xbits.man = (ix1); \
276 (d) = iw_u.e; \
277 } while (0)
278
279 /*
280 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
281 * comprising the mantissa.
282 */
283
284 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
285 do { \
286 union IEEEl2bits iw_u; \
287 iw_u.xbits.expsign = (ix0); \
288 iw_u.xbits.manh = (ix1); \
289 iw_u.xbits.manl = (ix2); \
290 (d) = iw_u.e; \
291 } while (0)
292
293 /* Set expsign of a long double from a 16 bit int. */
294
295 #define SET_LDBL_EXPSIGN(d,v) \
296 do { \
297 union IEEEl2bits se_u; \
298 se_u.e = (d); \
299 se_u.xbits.expsign = (v); \
300 (d) = se_u.e; \
301 } while (0)
302
303 #ifdef __i386__
304 /* Long double constants are broken on i386. */
305 #define LD80C(m, ex, v) { \
306 .xbits.man = __CONCAT(m, ULL), \
307 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
308 }
309 #else
310 /* The above works on non-i386 too, but we use this to check v. */
311 #define LD80C(m, ex, v) { .e = (v), }
312 #endif
313
314 #ifdef FLT_EVAL_METHOD
315 /*
316 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
317 */
318 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
319 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
320 #else
321 #define STRICT_ASSIGN(type, lval, rval) do { \
322 volatile type __lval; \
323 \
324 if (sizeof(type) >= sizeof(long double)) \
325 (lval) = (rval); \
326 else { \
327 __lval = (rval); \
328 (lval) = __lval; \
329 } \
330 } while (0)
331 #endif
332 #endif /* FLT_EVAL_METHOD */
333
334 /* Support switching the mode to FP_PE if necessary. */
335 #if defined(__i386__) && !defined(NO_FPSETPREC)
336 #define ENTERI() ENTERIT(long double)
337 #define ENTERIT(returntype) \
338 returntype __retval; \
339 fp_prec_t __oprec; \
340 \
341 if ((__oprec = fpgetprec()) != FP_PE) \
342 fpsetprec(FP_PE)
343 #define RETURNI(x) do { \
344 __retval = (x); \
345 if (__oprec != FP_PE) \
346 fpsetprec(__oprec); \
347 RETURNF(__retval); \
348 } while (0)
349 #define ENTERV() \
350 fp_prec_t __oprec; \
351 \
352 if ((__oprec = fpgetprec()) != FP_PE) \
353 fpsetprec(FP_PE)
354 #define RETURNV() do { \
355 if (__oprec != FP_PE) \
356 fpsetprec(__oprec); \
357 return; \
358 } while (0)
359 #else
360 #define ENTERI()
361 #define ENTERIT(x)
362 #define RETURNI(x) RETURNF(x)
363 #define ENTERV()
364 #define RETURNV() return
365 #endif
366
367 /* Default return statement if hack*_t() is not used. */
368 #define RETURNF(v) return (v)
369
370 /*
371 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
372 * a == 0, but is slower.
373 */
374 #define _2sum(a, b) do { \
375 __typeof(a) __s, __w; \
376 \
377 __w = (a) + (b); \
378 __s = __w - (a); \
379 (b) = ((a) - (__w - __s)) + ((b) - __s); \
380 (a) = __w; \
381 } while (0)
382
383 /*
384 * 2sumF algorithm.
385 *
386 * "Normalize" the terms in the infinite-precision expression a + b for
387 * the sum of 2 floating point values so that b is as small as possible
388 * relative to 'a'. (The resulting 'a' is the value of the expression in
389 * the same precision as 'a' and the resulting b is the rounding error.)
390 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
391 * exponent overflow or underflow must not occur. This uses a Theorem of
392 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
393 * is apparently due to Skewchuk (1997).
394 *
395 * For this to always work, assignment of a + b to 'a' must not retain any
396 * extra precision in a + b. This is required by C standards but broken
397 * in many compilers. The brokenness cannot be worked around using
398 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
399 * algorithm would be destroyed by non-null strict assignments. (The
400 * compilers are correct to be broken -- the efficiency of all floating
401 * point code calculations would be destroyed similarly if they forced the
402 * conversions.)
403 *
404 * Fortunately, a case that works well can usually be arranged by building
405 * any extra precision into the type of 'a' -- 'a' should have type float_t,
406 * double_t or long double. b's type should be no larger than 'a's type.
407 * Callers should use these types with scopes as large as possible, to
408 * reduce their own extra-precision and efficiciency problems. In
409 * particular, they shouldn't convert back and forth just to call here.
410 */
411 #ifdef DEBUG
412 #define _2sumF(a, b) do { \
413 __typeof(a) __w; \
414 volatile __typeof(a) __ia, __ib, __r, __vw; \
415 \
416 __ia = (a); \
417 __ib = (b); \
418 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
419 \
420 __w = (a) + (b); \
421 (b) = ((a) - __w) + (b); \
422 (a) = __w; \
423 \
424 /* The next 2 assertions are weak if (a) is already long double. */ \
425 assert((long double)__ia + __ib == (long double)(a) + (b)); \
426 __vw = __ia + __ib; \
427 __r = __ia - __vw; \
428 __r += __ib; \
429 assert(__vw == (a) && __r == (b)); \
430 } while (0)
431 #else /* !DEBUG */
432 #define _2sumF(a, b) do { \
433 __typeof(a) __w; \
434 \
435 __w = (a) + (b); \
436 (b) = ((a) - __w) + (b); \
437 (a) = __w; \
438 } while (0)
439 #endif /* DEBUG */
440
441 /*
442 * Set x += c, where x is represented in extra precision as a + b.
443 * x must be sufficiently normalized and sufficiently larger than c,
444 * and the result is then sufficiently normalized.
445 *
446 * The details of ordering are that |a| must be >= |c| (so that (a, c)
447 * can be normalized without extra work to swap 'a' with c). The details of
448 * the normalization are that b must be small relative to the normalized 'a'.
449 * Normalization of (a, c) makes the normalized c tiny relative to the
450 * normalized a, so b remains small relative to 'a' in the result. However,
451 * b need not ever be tiny relative to 'a'. For example, b might be about
452 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
453 * That is usually enough, and adding c (which by normalization is about
454 * 2**53 times smaller than a) cannot change b significantly. However,
455 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
456 * significantly relative to b. The caller must ensure that significant
457 * cancellation doesn't occur, either by having c of the same sign as 'a',
458 * or by having |c| a few percent smaller than |a|. Pre-normalization of
459 * (a, b) may help.
460 *
461 * This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
462 * exercise 19). We gain considerable efficiency by requiring the terms to
463 * be sufficiently normalized and sufficiently increasing.
464 */
465 #define _3sumF(a, b, c) do { \
466 __typeof(a) __tmp; \
467 \
468 __tmp = (c); \
469 _2sumF(__tmp, (a)); \
470 (b) += (a); \
471 (a) = __tmp; \
472 } while (0)
473
474 /*
475 * Common routine to process the arguments to nan(), nanf(), and nanl().
476 */
477 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
478
479 /*
480 * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns
481 * signaling NaNs into quiet NaNs by setting a quiet bit. We do this
482 * because we want to never return a signaling NaN, and also because we
483 * don't want the quiet bit to affect the result. Then mix the converted
484 * args using the specified operation.
485 *
486 * When one arg is NaN, the result is typically that arg quieted. When both
487 * args are NaNs, the result is typically the quietening of the arg whose
488 * mantissa is largest after quietening. When neither arg is NaN, the
489 * result may be NaN because it is indeterminate, or finite for subsequent
490 * construction of a NaN as the indeterminate 0.0L/0.0L.
491 *
492 * Technical complications: the result in bits after rounding to the final
493 * precision might depend on the runtime precision and/or on compiler
494 * optimizations, especially when different register sets are used for
495 * different precisions. Try to make the result not depend on at least the
496 * runtime precision by always doing the main mixing step in long double
497 * precision. Try to reduce dependencies on optimizations by adding the
498 * the 0's in different precisions (unless everything is in long double
499 * precision).
500 */
501 #define nan_mix(x, y) (nan_mix_op((x), (y), +))
502 #define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0))
503
504 #ifdef _COMPLEX_H
505
506 /*
507 * C99 specifies that complex numbers have the same representation as
508 * an array of two elements, where the first element is the real part
509 * and the second element is the imaginary part.
510 */
511 typedef union {
512 float complex f;
513 float a[2];
514 } float_complex;
515 typedef union {
516 double complex f;
517 double a[2];
518 } double_complex;
519 typedef union {
520 long double complex f;
521 long double a[2];
522 } long_double_complex;
523 #define REALPART(z) ((z).a[0])
524 #define IMAGPART(z) ((z).a[1])
525
526 /*
527 * Inline functions that can be used to construct complex values.
528 *
529 * The C99 standard intends x+I*y to be used for this, but x+I*y is
530 * currently unusable in general since gcc introduces many overflow,
531 * underflow, sign and efficiency bugs by rewriting I*y as
532 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
533 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
534 * to -0.0+I*0.0.
535 *
536 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
537 * to construct complex values. Compilers that conform to the C99
538 * standard require the following functions to avoid the above issues.
539 */
540
541 #ifndef CMPLXF
542 static __inline float complex
CMPLXF(float x,float y)543 CMPLXF(float x, float y)
544 {
545 float_complex z;
546
547 REALPART(z) = x;
548 IMAGPART(z) = y;
549 return (z.f);
550 }
551 #endif
552
553 #ifndef CMPLX
554 static __inline double complex
CMPLX(double x,double y)555 CMPLX(double x, double y)
556 {
557 double_complex z;
558
559 REALPART(z) = x;
560 IMAGPART(z) = y;
561 return (z.f);
562 }
563 #endif
564
565 #ifndef CMPLXL
566 static __inline long double complex
CMPLXL(long double x,long double y)567 CMPLXL(long double x, long double y)
568 {
569 long_double_complex z;
570
571 REALPART(z) = x;
572 IMAGPART(z) = y;
573 return (z.f);
574 }
575 #endif
576
577 #endif /* _COMPLEX_H */
578
579 /*
580 * The rnint() family rounds to the nearest integer for a restricted range
581 * range of args (up to about 2**MANT_DIG). We assume that the current
582 * rounding mode is FE_TONEAREST so that this can be done efficiently.
583 * Extra precision causes more problems in practice, and we only centralize
584 * this here to reduce those problems, and have not solved the efficiency
585 * problems. The exp2() family uses a more delicate version of this that
586 * requires extracting bits from the intermediate value, so it is not
587 * centralized here and should copy any solution of the efficiency problems.
588 */
589
590 static inline double
rnint(__double_t x)591 rnint(__double_t x)
592 {
593 /*
594 * This casts to double to kill any extra precision. This depends
595 * on the cast being applied to a double_t to avoid compiler bugs
596 * (this is a cleaner version of STRICT_ASSIGN()). This is
597 * inefficient if there actually is extra precision, but is hard
598 * to improve on. We use double_t in the API to minimise conversions
599 * for just calling here. Note that we cannot easily change the
600 * magic number to the one that works directly with double_t, since
601 * the rounding precision is variable at runtime on x86 so the
602 * magic number would need to be variable. Assuming that the
603 * rounding precision is always the default is too fragile. This
604 * and many other complications will move when the default is
605 * changed to FP_PE.
606 */
607 return ((double)(x + 0x1.8p52) - 0x1.8p52);
608 }
609
610 static inline float
rnintf(__float_t x)611 rnintf(__float_t x)
612 {
613 /*
614 * As for rnint(), except we could just call that to handle the
615 * extra precision case, usually without losing efficiency.
616 */
617 return ((float)(x + 0x1.8p23F) - 0x1.8p23F);
618 }
619
620 #ifdef LDBL_MANT_DIG
621 /*
622 * The complications for extra precision are smaller for rnintl() since it
623 * can safely assume that the rounding precision has been increased from
624 * its default to FP_PE on x86. We don't exploit that here to get small
625 * optimizations from limiting the range to double. We just need it for
626 * the magic number to work with long doubles. ld128 callers should use
627 * rnint() instead of this if possible. ld80 callers should prefer
628 * rnintl() since for amd64 this avoids swapping the register set, while
629 * for i386 it makes no difference (assuming FP_PE), and for other arches
630 * it makes little difference.
631 */
632 static inline long double
rnintl(long double x)633 rnintl(long double x)
634 {
635 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 -
636 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2);
637 }
638 #endif /* LDBL_MANT_DIG */
639
640 /*
641 * irint() and i64rint() give the same result as casting to their integer
642 * return type provided their arg is a floating point integer. They can
643 * sometimes be more efficient because no rounding is required.
644 */
645 #if defined(amd64) || defined(__i386__)
646 #define irint(x) \
647 (sizeof(x) == sizeof(float) && \
648 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \
649 sizeof(x) == sizeof(double) && \
650 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \
651 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x))
652 #else
653 #define irint(x) ((int)(x))
654 #endif
655
656 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */
657
658 #if defined(__i386__)
659 static __inline int
irintf(float x)660 irintf(float x)
661 {
662 int n;
663
664 __asm("fistl %0" : "=m" (n) : "t" (x));
665 return (n);
666 }
667
668 static __inline int
irintd(double x)669 irintd(double x)
670 {
671 int n;
672
673 __asm("fistl %0" : "=m" (n) : "t" (x));
674 return (n);
675 }
676 #endif
677
678 #if defined(__amd64__) || defined(__i386__)
679 static __inline int
irintl(long double x)680 irintl(long double x)
681 {
682 int n;
683
684 __asm("fistl %0" : "=m" (n) : "t" (x));
685 return (n);
686 }
687 #endif
688
689 /*
690 * The following are fast floor macros for 0 <= |x| < 0x1p(N-1), where
691 * N is the precision of the type of x. These macros are used in the
692 * half-cycle trignometric functions (e.g., sinpi(x)).
693 */
694 #define FFLOORF(x, j0, ix) do { \
695 (j0) = (((ix) >> 23) & 0xff) - 0x7f; \
696 (ix) &= ~(0x007fffff >> (j0)); \
697 SET_FLOAT_WORD((x), (ix)); \
698 } while (0)
699
700 #define FFLOOR(x, j0, ix, lx) do { \
701 (j0) = (((ix) >> 20) & 0x7ff) - 0x3ff; \
702 if ((j0) < 20) { \
703 (ix) &= ~(0x000fffff >> (j0)); \
704 (lx) = 0; \
705 } else { \
706 (lx) &= ~((uint32_t)0xffffffff >> ((j0) - 20)); \
707 } \
708 INSERT_WORDS((x), (ix), (lx)); \
709 } while (0)
710
711 #define FFLOORL80(x, j0, ix, lx) do { \
712 j0 = ix - 0x3fff + 1; \
713 if ((j0) < 32) { \
714 (lx) = ((lx) >> 32) << 32; \
715 (lx) &= ~((((lx) << 32)-1) >> (j0)); \
716 } else { \
717 uint64_t _m; \
718 _m = (uint64_t)-1 >> (j0); \
719 if ((lx) & _m) (lx) &= ~_m; \
720 } \
721 INSERT_LDBL80_WORDS((x), (ix), (lx)); \
722 } while (0)
723
724 #define FFLOORL128(x, ai, ar) do { \
725 union IEEEl2bits u; \
726 uint64_t m; \
727 int e; \
728 u.e = (x); \
729 e = u.bits.exp - 16383; \
730 if (e < 48) { \
731 m = ((1llu << 49) - 1) >> (e + 1); \
732 u.bits.manh &= ~m; \
733 u.bits.manl = 0; \
734 } else { \
735 m = (uint64_t)-1 >> (e - 48); \
736 u.bits.manl &= ~m; \
737 } \
738 (ai) = u.e; \
739 (ar) = (x) - (ai); \
740 } while (0)
741
742 #ifdef DEBUG
743 #if defined(__amd64__) || defined(__i386__)
744 #define breakpoint() asm("int $3")
745 #else
746 #include <signal.h>
747
748 #define breakpoint() raise(SIGTRAP)
749 #endif
750 #endif
751
752 #ifdef STRUCT_RETURN
753 #define RETURNSP(rp) do { \
754 if (!(rp)->lo_set) \
755 RETURNF((rp)->hi); \
756 RETURNF((rp)->hi + (rp)->lo); \
757 } while (0)
758 #define RETURNSPI(rp) do { \
759 if (!(rp)->lo_set) \
760 RETURNI((rp)->hi); \
761 RETURNI((rp)->hi + (rp)->lo); \
762 } while (0)
763 #endif
764
765 #define SUM2P(x, y) ({ \
766 const __typeof (x) __x = (x); \
767 const __typeof (y) __y = (y); \
768 __x + __y; \
769 })
770
771 /* fdlibm kernel function */
772 int __kernel_rem_pio2(double*,double*,int,int,int);
773
774 /* double precision kernel functions */
775 #ifndef INLINE_REM_PIO2
776 int __ieee754_rem_pio2(double,double*);
777 #endif
778 double __kernel_sin(double,double,int);
779 double __kernel_cos(double,double);
780 double __kernel_tan(double,double,int);
781 double __ldexp_exp(double,int);
782 #ifdef _COMPLEX_H
783 double complex __ldexp_cexp(double complex,int);
784 #endif
785
786 /* float precision kernel functions */
787 #ifndef INLINE_REM_PIO2F
788 int __ieee754_rem_pio2f(float,double*);
789 #endif
790 #ifndef INLINE_KERNEL_SINDF
791 float __kernel_sindf(double);
792 #endif
793 #ifndef INLINE_KERNEL_COSDF
794 float __kernel_cosdf(double);
795 #endif
796 #ifndef INLINE_KERNEL_TANDF
797 float __kernel_tandf(double,int);
798 #endif
799 float __ldexp_expf(float,int);
800 #ifdef _COMPLEX_H
801 float complex __ldexp_cexpf(float complex,int);
802 #endif
803
804 /* long double precision kernel functions */
805 long double __kernel_sinl(long double, long double, int);
806 long double __kernel_cosl(long double, long double);
807 long double __kernel_tanl(long double, long double, int);
808
809 #endif /* !_MATH_PRIVATE_H_ */
810