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 typedef unsigned int u_int32_t;
52 typedef unsigned long u_int64_t;
53 typedef signed int int32_t;
54 typedef signed short int16_t;
55 typedef double __double_t;
56 typedef float __float_t;
57 /* A union which permits us to convert between a long double and
58 four 32 bit ints. */
59
60 #if IEEE_WORD_ORDER == BIG_ENDIAN
61
62 typedef union
63 {
64 long double value;
65 struct {
66 u_int32_t mswhi;
67 u_int32_t mswlo;
68 u_int32_t lswhi;
69 u_int32_t lswlo;
70 } parts32;
71 struct {
72 u_int64_t msw;
73 u_int64_t lsw;
74 } parts64;
75 } ieee_quad_shape_type;
76
77 #endif
78
79 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
80
81 typedef union
82 {
83 long double value;
84 struct {
85 u_int32_t lswlo;
86 u_int32_t lswhi;
87 u_int32_t mswlo;
88 u_int32_t mswhi;
89 } parts32;
90 struct {
91 u_int64_t lsw;
92 u_int64_t msw;
93 } parts64;
94 } ieee_quad_shape_type;
95
96 #endif
97
98 #if IEEE_WORD_ORDER == BIG_ENDIAN
99
100 typedef union
101 {
102 double value;
103 struct
104 {
105 u_int32_t msw;
106 u_int32_t lsw;
107 } parts;
108 struct
109 {
110 u_int64_t w;
111 } xparts;
112 } ieee_double_shape_type;
113
114 #endif
115
116 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
117
118 typedef union
119 {
120 double value;
121 struct
122 {
123 u_int32_t lsw;
124 u_int32_t msw;
125 } parts;
126 struct
127 {
128 u_int64_t w;
129 } xparts;
130 } ieee_double_shape_type;
131
132 #endif
133
134 /* Get two 32 bit ints from a double. */
135
136 #define EXTRACT_WORDS(ix0,ix1,d) \
137 do { \
138 ieee_double_shape_type ew_u; \
139 ew_u.value = (d); \
140 (ix0) = ew_u.parts.msw; \
141 (ix1) = ew_u.parts.lsw; \
142 } while (0)
143
144 /* Get a 64-bit int from a double. */
145 #define EXTRACT_WORD64(ix,d) \
146 do { \
147 ieee_double_shape_type ew_u; \
148 ew_u.value = (d); \
149 (ix) = ew_u.xparts.w; \
150 } while (0)
151
152 /* Get the more significant 32 bit int from a double. */
153
154 #define GET_HIGH_WORD(i,d) \
155 do { \
156 ieee_double_shape_type gh_u; \
157 gh_u.value = (d); \
158 (i) = gh_u.parts.msw; \
159 } while (0)
160
161 /* Get the less significant 32 bit int from a double. */
162
163 #define GET_LOW_WORD(i,d) \
164 do { \
165 ieee_double_shape_type gl_u; \
166 gl_u.value = (d); \
167 (i) = gl_u.parts.lsw; \
168 } while (0)
169
170 /* Set a double from two 32 bit ints. */
171
172 #define INSERT_WORDS(d,ix0,ix1) \
173 do { \
174 ieee_double_shape_type iw_u; \
175 iw_u.parts.msw = (ix0); \
176 iw_u.parts.lsw = (ix1); \
177 (d) = iw_u.value; \
178 } while (0)
179
180 /* Set a double from a 64-bit int. */
181 #define INSERT_WORD64(d,ix) \
182 do { \
183 ieee_double_shape_type iw_u; \
184 iw_u.xparts.w = (ix); \
185 (d) = iw_u.value; \
186 } while (0)
187
188 /* Set the more significant 32 bits of a double from an int. */
189
190 #define SET_HIGH_WORD(d,v) \
191 do { \
192 ieee_double_shape_type sh_u; \
193 sh_u.value = (d); \
194 sh_u.parts.msw = (v); \
195 (d) = sh_u.value; \
196 } while (0)
197
198 /* Set the less significant 32 bits of a double from an int. */
199
200 #define SET_LOW_WORD(d,v) \
201 do { \
202 ieee_double_shape_type sl_u; \
203 sl_u.value = (d); \
204 sl_u.parts.lsw = (v); \
205 (d) = sl_u.value; \
206 } while (0)
207
208 /*
209 * A union which permits us to convert between a float and a 32 bit
210 * int.
211 */
212
213 typedef union
214 {
215 float value;
216 /* FIXME: Assumes 32 bit int. */
217 unsigned int word;
218 } ieee_float_shape_type;
219
220 /* Get a 32 bit int from a float. */
221
222 #define GET_FLOAT_WORD(i,d) \
223 do { \
224 ieee_float_shape_type gf_u; \
225 gf_u.value = (d); \
226 (i) = gf_u.word; \
227 } while (0)
228
229 /* Set a float from a 32 bit int. */
230
231 #define SET_FLOAT_WORD(d,i) \
232 do { \
233 ieee_float_shape_type sf_u; \
234 sf_u.word = (i); \
235 (d) = sf_u.value; \
236 } while (0)
237
238 /*
239 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
240 * double.
241 */
242
243 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
244 do { \
245 union IEEEl2bits ew_u; \
246 ew_u.e = (d); \
247 (ix0) = ew_u.xbits.expsign; \
248 (ix1) = ew_u.xbits.man; \
249 } while (0)
250
251 /*
252 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
253 * long double.
254 */
255
256 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
257 do { \
258 union IEEEl2bits ew_u; \
259 ew_u.e = (d); \
260 (ix0) = ew_u.xbits.expsign; \
261 (ix1) = ew_u.xbits.manh; \
262 (ix2) = ew_u.xbits.manl; \
263 } while (0)
264
265 /* Get expsign as a 16 bit int from a long double. */
266
267 #define GET_LDBL_EXPSIGN(i,d) \
268 do { \
269 union IEEEl2bits ge_u; \
270 ge_u.e = (d); \
271 (i) = ge_u.xbits.expsign; \
272 } while (0)
273
274 /*
275 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
276 * mantissa.
277 */
278
279 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
280 do { \
281 union IEEEl2bits iw_u; \
282 iw_u.xbits.expsign = (ix0); \
283 iw_u.xbits.man = (ix1); \
284 (d) = iw_u.e; \
285 } while (0)
286
287 /*
288 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
289 * comprising the mantissa.
290 */
291
292 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
293 do { \
294 union IEEEl2bits iw_u; \
295 iw_u.xbits.expsign = (ix0); \
296 iw_u.xbits.manh = (ix1); \
297 iw_u.xbits.manl = (ix2); \
298 (d) = iw_u.e; \
299 } while (0)
300
301 /* Set expsign of a long double from a 16 bit int. */
302
303 #define SET_LDBL_EXPSIGN(d,v) \
304 do { \
305 union IEEEl2bits se_u; \
306 se_u.e = (d); \
307 se_u.xbits.expsign = (v); \
308 (d) = se_u.e; \
309 } while (0)
310
311 #ifdef __i386__
312 /* Long double constants are broken on i386. */
313 #define LD80C(m, ex, v) { \
314 .xbits.man = __CONCAT(m, ULL), \
315 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
316 }
317 #else
318 /* The above works on non-i386 too, but we use this to check v. */
319 #define LD80C(m, ex, v) { .e = (v), }
320 #endif
321
322 #ifdef FLT_EVAL_METHOD
323 /*
324 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
325 */
326 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
327 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
328 #else
329 #define STRICT_ASSIGN(type, lval, rval) do { \
330 volatile type __lval; \
331 \
332 if (sizeof(type) >= sizeof(long double)) \
333 (lval) = (rval); \
334 else { \
335 __lval = (rval); \
336 (lval) = __lval; \
337 } \
338 } while (0)
339 #endif
340 #endif /* FLT_EVAL_METHOD */
341
342 /* Support switching the mode to FP_PE if necessary. */
343 #if defined(__i386__) && !defined(NO_FPSETPREC)
344 #define ENTERI() ENTERIT(long double)
345 #define ENTERIT(returntype) \
346 returntype __retval; \
347 fp_prec_t __oprec; \
348 \
349 if ((__oprec = fpgetprec()) != FP_PE) \
350 fpsetprec(FP_PE)
351 #define RETURNI(x) do { \
352 __retval = (x); \
353 if (__oprec != FP_PE) \
354 fpsetprec(__oprec); \
355 RETURNF(__retval); \
356 } while (0)
357 #define ENTERV() \
358 fp_prec_t __oprec; \
359 \
360 if ((__oprec = fpgetprec()) != FP_PE) \
361 fpsetprec(FP_PE)
362 #define RETURNV() do { \
363 if (__oprec != FP_PE) \
364 fpsetprec(__oprec); \
365 return; \
366 } while (0)
367 #else
368 #define ENTERI()
369 #define ENTERIT(x)
370 #define RETURNI(x) RETURNF(x)
371 #define ENTERV()
372 #define RETURNV() return
373 #endif
374
375 /* Default return statement if hack*_t() is not used. */
376 #define RETURNF(v) return (v)
377
378 /*
379 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
380 * a == 0, but is slower.
381 */
382 #define _2sum(a, b) do { \
383 __typeof(a) __s, __w; \
384 \
385 __w = (a) + (b); \
386 __s = __w - (a); \
387 (b) = ((a) - (__w - __s)) + ((b) - __s); \
388 (a) = __w; \
389 } while (0)
390
391 /*
392 * 2sumF algorithm.
393 *
394 * "Normalize" the terms in the infinite-precision expression a + b for
395 * the sum of 2 floating point values so that b is as small as possible
396 * relative to 'a'. (The resulting 'a' is the value of the expression in
397 * the same precision as 'a' and the resulting b is the rounding error.)
398 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
399 * exponent overflow or underflow must not occur. This uses a Theorem of
400 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
401 * is apparently due to Skewchuk (1997).
402 *
403 * For this to always work, assignment of a + b to 'a' must not retain any
404 * extra precision in a + b. This is required by C standards but broken
405 * in many compilers. The brokenness cannot be worked around using
406 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
407 * algorithm would be destroyed by non-null strict assignments. (The
408 * compilers are correct to be broken -- the efficiency of all floating
409 * point code calculations would be destroyed similarly if they forced the
410 * conversions.)
411 *
412 * Fortunately, a case that works well can usually be arranged by building
413 * any extra precision into the type of 'a' -- 'a' should have type float_t,
414 * double_t or long double. b's type should be no larger than 'a's type.
415 * Callers should use these types with scopes as large as possible, to
416 * reduce their own extra-precision and efficiciency problems. In
417 * particular, they shouldn't convert back and forth just to call here.
418 */
419 #ifdef DEBUG
420 #define _2sumF(a, b) do { \
421 __typeof(a) __w; \
422 volatile __typeof(a) __ia, __ib, __r, __vw; \
423 \
424 __ia = (a); \
425 __ib = (b); \
426 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
427 \
428 __w = (a) + (b); \
429 (b) = ((a) - __w) + (b); \
430 (a) = __w; \
431 \
432 /* The next 2 assertions are weak if (a) is already long double. */ \
433 assert((long double)__ia + __ib == (long double)(a) + (b)); \
434 __vw = __ia + __ib; \
435 __r = __ia - __vw; \
436 __r += __ib; \
437 assert(__vw == (a) && __r == (b)); \
438 } while (0)
439 #else /* !DEBUG */
440 #define _2sumF(a, b) do { \
441 __typeof(a) __w; \
442 \
443 __w = (a) + (b); \
444 (b) = ((a) - __w) + (b); \
445 (a) = __w; \
446 } while (0)
447 #endif /* DEBUG */
448
449 /*
450 * Set x += c, where x is represented in extra precision as a + b.
451 * x must be sufficiently normalized and sufficiently larger than c,
452 * and the result is then sufficiently normalized.
453 *
454 * The details of ordering are that |a| must be >= |c| (so that (a, c)
455 * can be normalized without extra work to swap 'a' with c). The details of
456 * the normalization are that b must be small relative to the normalized 'a'.
457 * Normalization of (a, c) makes the normalized c tiny relative to the
458 * normalized a, so b remains small relative to 'a' in the result. However,
459 * b need not ever be tiny relative to 'a'. For example, b might be about
460 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
461 * That is usually enough, and adding c (which by normalization is about
462 * 2**53 times smaller than a) cannot change b significantly. However,
463 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
464 * significantly relative to b. The caller must ensure that significant
465 * cancellation doesn't occur, either by having c of the same sign as 'a',
466 * or by having |c| a few percent smaller than |a|. Pre-normalization of
467 * (a, b) may help.
468 *
469 * This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
470 * exercise 19). We gain considerable efficiency by requiring the terms to
471 * be sufficiently normalized and sufficiently increasing.
472 */
473 #define _3sumF(a, b, c) do { \
474 __typeof(a) __tmp; \
475 \
476 __tmp = (c); \
477 _2sumF(__tmp, (a)); \
478 (b) += (a); \
479 (a) = __tmp; \
480 } while (0)
481
482 /*
483 * Common routine to process the arguments to nan(), nanf(), and nanl().
484 */
485 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
486
487 /*
488 * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns
489 * signaling NaNs into quiet NaNs by setting a quiet bit. We do this
490 * because we want to never return a signaling NaN, and also because we
491 * don't want the quiet bit to affect the result. Then mix the converted
492 * args using the specified operation.
493 *
494 * When one arg is NaN, the result is typically that arg quieted. When both
495 * args are NaNs, the result is typically the quietening of the arg whose
496 * mantissa is largest after quietening. When neither arg is NaN, the
497 * result may be NaN because it is indeterminate, or finite for subsequent
498 * construction of a NaN as the indeterminate 0.0L/0.0L.
499 *
500 * Technical complications: the result in bits after rounding to the final
501 * precision might depend on the runtime precision and/or on compiler
502 * optimizations, especially when different register sets are used for
503 * different precisions. Try to make the result not depend on at least the
504 * runtime precision by always doing the main mixing step in long double
505 * precision. Try to reduce dependencies on optimizations by adding the
506 * the 0's in different precisions (unless everything is in long double
507 * precision).
508 */
509 #define nan_mix(x, y) (nan_mix_op((x), (y), +))
510 #define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0))
511
512 #ifdef _COMPLEX_H
513
514 /*
515 * C99 specifies that complex numbers have the same representation as
516 * an array of two elements, where the first element is the real part
517 * and the second element is the imaginary part.
518 */
519 typedef union {
520 float complex f;
521 float a[2];
522 } float_complex;
523 typedef union {
524 double complex f;
525 double a[2];
526 } double_complex;
527 typedef union {
528 long double complex f;
529 long double a[2];
530 } long_double_complex;
531 #define REALPART(z) ((z).a[0])
532 #define IMAGPART(z) ((z).a[1])
533
534 /*
535 * Inline functions that can be used to construct complex values.
536 *
537 * The C99 standard intends x+I*y to be used for this, but x+I*y is
538 * currently unusable in general since gcc introduces many overflow,
539 * underflow, sign and efficiency bugs by rewriting I*y as
540 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
541 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
542 * to -0.0+I*0.0.
543 *
544 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
545 * to construct complex values. Compilers that conform to the C99
546 * standard require the following functions to avoid the above issues.
547 */
548
549 #ifndef CMPLXF
550 static __inline float complex
CMPLXF(float x,float y)551 CMPLXF(float x, float y)
552 {
553 float_complex z;
554
555 REALPART(z) = x;
556 IMAGPART(z) = y;
557 return (z.f);
558 }
559 #endif
560
561 #ifndef CMPLX
562 static __inline double complex
CMPLX(double x,double y)563 CMPLX(double x, double y)
564 {
565 double_complex z;
566
567 REALPART(z) = x;
568 IMAGPART(z) = y;
569 return (z.f);
570 }
571 #endif
572
573 #ifndef CMPLXL
574 static __inline long double complex
CMPLXL(long double x,long double y)575 CMPLXL(long double x, long double y)
576 {
577 long_double_complex z;
578
579 REALPART(z) = x;
580 IMAGPART(z) = y;
581 return (z.f);
582 }
583 #endif
584
585 #endif /* _COMPLEX_H */
586
587 /*
588 * The rnint() family rounds to the nearest integer for a restricted range
589 * range of args (up to about 2**MANT_DIG). We assume that the current
590 * rounding mode is FE_TONEAREST so that this can be done efficiently.
591 * Extra precision causes more problems in practice, and we only centralize
592 * this here to reduce those problems, and have not solved the efficiency
593 * problems. The exp2() family uses a more delicate version of this that
594 * requires extracting bits from the intermediate value, so it is not
595 * centralized here and should copy any solution of the efficiency problems.
596 */
597
598 static inline double
rnint(__double_t x)599 rnint(__double_t x)
600 {
601 /*
602 * This casts to double to kill any extra precision. This depends
603 * on the cast being applied to a double_t to avoid compiler bugs
604 * (this is a cleaner version of STRICT_ASSIGN()). This is
605 * inefficient if there actually is extra precision, but is hard
606 * to improve on. We use double_t in the API to minimise conversions
607 * for just calling here. Note that we cannot easily change the
608 * magic number to the one that works directly with double_t, since
609 * the rounding precision is variable at runtime on x86 so the
610 * magic number would need to be variable. Assuming that the
611 * rounding precision is always the default is too fragile. This
612 * and many other complications will move when the default is
613 * changed to FP_PE.
614 */
615 return ((double)(x + 0x1.8p52) - 0x1.8p52);
616 }
617
618 static inline float
rnintf(__float_t x)619 rnintf(__float_t x)
620 {
621 /*
622 * As for rnint(), except we could just call that to handle the
623 * extra precision case, usually without losing efficiency.
624 */
625 return ((float)(x + 0x1.8p23F) - 0x1.8p23F);
626 }
627
628 #ifdef LDBL_MANT_DIG
629 /*
630 * The complications for extra precision are smaller for rnintl() since it
631 * can safely assume that the rounding precision has been increased from
632 * its default to FP_PE on x86. We don't exploit that here to get small
633 * optimizations from limiting the rangle to double. We just need it for
634 * the magic number to work with long doubles. ld128 callers should use
635 * rnint() instead of this if possible. ld80 callers should prefer
636 * rnintl() since for amd64 this avoids swapping the register set, while
637 * for i386 it makes no difference (assuming FP_PE), and for other arches
638 * it makes little difference.
639 */
640 static inline long double
rnintl(long double x)641 rnintl(long double x)
642 {
643 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 -
644 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2);
645 }
646 #endif /* LDBL_MANT_DIG */
647
648 /*
649 * irint() and i64rint() give the same result as casting to their integer
650 * return type provided their arg is a floating point integer. They can
651 * sometimes be more efficient because no rounding is required.
652 */
653 #if defined(amd64) || defined(__i386__)
654 #define irint(x) \
655 (sizeof(x) == sizeof(float) && \
656 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \
657 sizeof(x) == sizeof(double) && \
658 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \
659 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x))
660 #else
661 #define irint(x) ((int)(x))
662 #endif
663
664 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */
665
666 #if defined(__i386__)
667 static __inline int
irintf(float x)668 irintf(float x)
669 {
670 int n;
671
672 __asm("fistl %0" : "=m" (n) : "t" (x));
673 return (n);
674 }
675
676 static __inline int
irintd(double x)677 irintd(double x)
678 {
679 int n;
680
681 __asm("fistl %0" : "=m" (n) : "t" (x));
682 return (n);
683 }
684 #endif
685
686 #if defined(__amd64__) || defined(__i386__)
687 static __inline int
irintl(long double x)688 irintl(long double x)
689 {
690 int n;
691
692 __asm("fistl %0" : "=m" (n) : "t" (x));
693 return (n);
694 }
695 #endif
696
697 #ifdef DEBUG
698 #if defined(__amd64__) || defined(__i386__)
699 #define breakpoint() asm("int $3")
700 #else
701 #include <signal.h>
702
703 #define breakpoint() raise(SIGTRAP)
704 #endif
705 #endif
706
707 /* Write a pari script to test things externally. */
708 #ifdef DOPRINT
709 #include <stdio.h>
710
711 #ifndef DOPRINT_SWIZZLE
712 #define DOPRINT_SWIZZLE 0
713 #endif
714
715 #ifdef DOPRINT_LD80
716
717 #define DOPRINT_START(xp) do { \
718 uint64_t __lx; \
719 uint16_t __hx; \
720 \
721 /* Hack to give more-problematic args. */ \
722 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
723 __lx ^= DOPRINT_SWIZZLE; \
724 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
725 printf("x = %.21Lg; ", (long double)*xp); \
726 } while (0)
727 #define DOPRINT_END1(v) \
728 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
729 #define DOPRINT_END2(hi, lo) \
730 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
731 (long double)(hi), (long double)(lo))
732
733 #elif defined(DOPRINT_D64)
734
735 #define DOPRINT_START(xp) do { \
736 uint32_t __hx, __lx; \
737 \
738 EXTRACT_WORDS(__hx, __lx, *xp); \
739 __lx ^= DOPRINT_SWIZZLE; \
740 INSERT_WORDS(*xp, __hx, __lx); \
741 printf("x = %.21Lg; ", (long double)*xp); \
742 } while (0)
743 #define DOPRINT_END1(v) \
744 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
745 #define DOPRINT_END2(hi, lo) \
746 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
747 (long double)(hi), (long double)(lo))
748
749 #elif defined(DOPRINT_F32)
750
751 #define DOPRINT_START(xp) do { \
752 uint32_t __hx; \
753 \
754 GET_FLOAT_WORD(__hx, *xp); \
755 __hx ^= DOPRINT_SWIZZLE; \
756 SET_FLOAT_WORD(*xp, __hx); \
757 printf("x = %.21Lg; ", (long double)*xp); \
758 } while (0)
759 #define DOPRINT_END1(v) \
760 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
761 #define DOPRINT_END2(hi, lo) \
762 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
763 (long double)(hi), (long double)(lo))
764
765 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
766
767 #ifndef DOPRINT_SWIZZLE_HIGH
768 #define DOPRINT_SWIZZLE_HIGH 0
769 #endif
770
771 #define DOPRINT_START(xp) do { \
772 uint64_t __lx, __llx; \
773 uint16_t __hx; \
774 \
775 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
776 __llx ^= DOPRINT_SWIZZLE; \
777 __lx ^= DOPRINT_SWIZZLE_HIGH; \
778 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
779 printf("x = %.36Lg; ", (long double)*xp); \
780 } while (0)
781 #define DOPRINT_END1(v) \
782 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
783 #define DOPRINT_END2(hi, lo) \
784 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
785 (long double)(hi), (long double)(lo))
786
787 #endif /* DOPRINT_LD80 */
788
789 #else /* !DOPRINT */
790 #define DOPRINT_START(xp)
791 #define DOPRINT_END1(v)
792 #define DOPRINT_END2(hi, lo)
793 #endif /* DOPRINT */
794
795 #define RETURNP(x) do { \
796 DOPRINT_END1(x); \
797 RETURNF(x); \
798 } while (0)
799 #define RETURNPI(x) do { \
800 DOPRINT_END1(x); \
801 RETURNI(x); \
802 } while (0)
803 #define RETURN2P(x, y) do { \
804 DOPRINT_END2((x), (y)); \
805 RETURNF((x) + (y)); \
806 } while (0)
807 #define RETURN2PI(x, y) do { \
808 DOPRINT_END2((x), (y)); \
809 RETURNI((x) + (y)); \
810 } while (0)
811 #ifdef STRUCT_RETURN
812 #define RETURNSP(rp) do { \
813 if (!(rp)->lo_set) \
814 RETURNP((rp)->hi); \
815 RETURN2P((rp)->hi, (rp)->lo); \
816 } while (0)
817 #define RETURNSPI(rp) do { \
818 if (!(rp)->lo_set) \
819 RETURNPI((rp)->hi); \
820 RETURN2PI((rp)->hi, (rp)->lo); \
821 } while (0)
822 #endif
823 #define SUM2P(x, y) ({ \
824 const __typeof (x) __x = (x); \
825 const __typeof (y) __y = (y); \
826 \
827 DOPRINT_END2(__x, __y); \
828 __x + __y; \
829 })
830
831 /*
832 * ieee style elementary functions
833 *
834 * We rename functions here to improve other sources' diffability
835 * against fdlibm.
836 */
837 #define __ieee754_sqrt sqrt
838 #define __ieee754_acos acos
839 #define __ieee754_acosh acosh
840 #define __ieee754_log log
841 #define __ieee754_log2 log2
842 #define __ieee754_atanh atanh
843 #define __ieee754_asin asin
844 #define __ieee754_atan2 atan2
845 #define __ieee754_exp exp
846 #define __ieee754_cosh cosh
847 #define __ieee754_fmod fmod
848 #define __ieee754_pow pow
849 #define __ieee754_lgamma lgamma
850 #define __ieee754_gamma gamma
851 #define __ieee754_lgamma_r lgamma_r
852 #define __ieee754_gamma_r gamma_r
853 #define __ieee754_log10 log10
854 #define __ieee754_sinh sinh
855 #define __ieee754_hypot hypot
856 #define __ieee754_j0 j0
857 #define __ieee754_j1 j1
858 #define __ieee754_y0 y0
859 #define __ieee754_y1 y1
860 #define __ieee754_jn jn
861 #define __ieee754_yn yn
862 #define __ieee754_remainder remainder
863 #define __ieee754_scalb scalb
864 #define __ieee754_sqrtf sqrtf
865 #define __ieee754_acosf acosf
866 #define __ieee754_acoshf acoshf
867 #define __ieee754_logf logf
868 #define __ieee754_atanhf atanhf
869 #define __ieee754_asinf asinf
870 #define __ieee754_atan2f atan2f
871 #define __ieee754_expf expf
872 #define __ieee754_coshf coshf
873 #define __ieee754_fmodf fmodf
874 #define __ieee754_powf powf
875 #define __ieee754_lgammaf lgammaf
876 #define __ieee754_gammaf gammaf
877 #define __ieee754_lgammaf_r lgammaf_r
878 #define __ieee754_gammaf_r gammaf_r
879 #define __ieee754_log10f log10f
880 #define __ieee754_log2f log2f
881 #define __ieee754_sinhf sinhf
882 #define __ieee754_hypotf hypotf
883 #define __ieee754_j0f j0f
884 #define __ieee754_j1f j1f
885 #define __ieee754_y0f y0f
886 #define __ieee754_y1f y1f
887 #define __ieee754_jnf jnf
888 #define __ieee754_ynf ynf
889 #define __ieee754_remainderf remainderf
890 #define __ieee754_scalbf scalbf
891
892 /* fdlibm kernel function */
893 int __kernel_rem_pio2(double*,double*,int,int,int);
894
895 /* double precision kernel functions */
896 #ifndef INLINE_REM_PIO2
897 int __ieee754_rem_pio2(double,double*);
898 #endif
899 double __kernel_sin(double,double,int);
900 double __kernel_cos(double,double);
901 double __kernel_tan(double,double,int);
902 double __ldexp_exp(double,int);
903 #ifdef _COMPLEX_H
904 double complex __ldexp_cexp(double complex,int);
905 #endif
906
907 /* float precision kernel functions */
908 #ifndef INLINE_REM_PIO2F
909 int __ieee754_rem_pio2f(float,double*);
910 #endif
911 #ifndef INLINE_KERNEL_SINDF
912 float __kernel_sindf(double);
913 #endif
914 #ifndef INLINE_KERNEL_COSDF
915 float __kernel_cosdf(double);
916 #endif
917 #ifndef INLINE_KERNEL_TANDF
918 float __kernel_tandf(double,int);
919 #endif
920 float __ldexp_expf(float,int);
921 #ifdef _COMPLEX_H
922 float complex __ldexp_cexpf(float complex,int);
923 #endif
924
925 /* long double precision kernel functions */
926 long double __kernel_sinl(long double, long double, int);
927 long double __kernel_cosl(long double, long double);
928 long double __kernel_tanl(long double, long double, int);
929
930 #endif /* !_MATH_PRIVATE_H_ */
931