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 336663 2018-07-24 10:10:16Z bde $
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 /* A union which permits us to convert between a long double and
52 four 32 bit ints. */
53
54 #if IEEE_WORD_ORDER == BIG_ENDIAN
55
56 typedef union
57 {
58 long double value;
59 struct {
60 u_int32_t mswhi;
61 u_int32_t mswlo;
62 u_int32_t lswhi;
63 u_int32_t lswlo;
64 } parts32;
65 struct {
66 u_int64_t msw;
67 u_int64_t lsw;
68 } parts64;
69 } ieee_quad_shape_type;
70
71 #endif
72
73 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
74
75 typedef union
76 {
77 long double value;
78 struct {
79 u_int32_t lswlo;
80 u_int32_t lswhi;
81 u_int32_t mswlo;
82 u_int32_t mswhi;
83 } parts32;
84 struct {
85 u_int64_t lsw;
86 u_int64_t msw;
87 } parts64;
88 } ieee_quad_shape_type;
89
90 #endif
91
92 #if IEEE_WORD_ORDER == BIG_ENDIAN
93
94 typedef union
95 {
96 double value;
97 struct
98 {
99 u_int32_t msw;
100 u_int32_t lsw;
101 } parts;
102 struct
103 {
104 u_int64_t w;
105 } xparts;
106 } ieee_double_shape_type;
107
108 #endif
109
110 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
111
112 typedef union
113 {
114 double value;
115 struct
116 {
117 u_int32_t lsw;
118 u_int32_t msw;
119 } parts;
120 struct
121 {
122 u_int64_t w;
123 } xparts;
124 } ieee_double_shape_type;
125
126 #endif
127
128 /* Get two 32 bit ints from a double. */
129
130 #define EXTRACT_WORDS(ix0,ix1,d) \
131 do { \
132 ieee_double_shape_type ew_u; \
133 ew_u.value = (d); \
134 (ix0) = ew_u.parts.msw; \
135 (ix1) = ew_u.parts.lsw; \
136 } while (0)
137
138 /* Get a 64-bit int from a double. */
139 #define EXTRACT_WORD64(ix,d) \
140 do { \
141 ieee_double_shape_type ew_u; \
142 ew_u.value = (d); \
143 (ix) = ew_u.xparts.w; \
144 } while (0)
145
146 /* Get the more significant 32 bit int from a double. */
147
148 #define GET_HIGH_WORD(i,d) \
149 do { \
150 ieee_double_shape_type gh_u; \
151 gh_u.value = (d); \
152 (i) = gh_u.parts.msw; \
153 } while (0)
154
155 /* Get the less significant 32 bit int from a double. */
156
157 #define GET_LOW_WORD(i,d) \
158 do { \
159 ieee_double_shape_type gl_u; \
160 gl_u.value = (d); \
161 (i) = gl_u.parts.lsw; \
162 } while (0)
163
164 /* Set a double from two 32 bit ints. */
165
166 #define INSERT_WORDS(d,ix0,ix1) \
167 do { \
168 ieee_double_shape_type iw_u; \
169 iw_u.parts.msw = (ix0); \
170 iw_u.parts.lsw = (ix1); \
171 (d) = iw_u.value; \
172 } while (0)
173
174 /* Set a double from a 64-bit int. */
175 #define INSERT_WORD64(d,ix) \
176 do { \
177 ieee_double_shape_type iw_u; \
178 iw_u.xparts.w = (ix); \
179 (d) = iw_u.value; \
180 } while (0)
181
182 /* Set the more significant 32 bits of a double from an int. */
183
184 #define SET_HIGH_WORD(d,v) \
185 do { \
186 ieee_double_shape_type sh_u; \
187 sh_u.value = (d); \
188 sh_u.parts.msw = (v); \
189 (d) = sh_u.value; \
190 } while (0)
191
192 /* Set the less significant 32 bits of a double from an int. */
193
194 #define SET_LOW_WORD(d,v) \
195 do { \
196 ieee_double_shape_type sl_u; \
197 sl_u.value = (d); \
198 sl_u.parts.lsw = (v); \
199 (d) = sl_u.value; \
200 } while (0)
201
202 /*
203 * A union which permits us to convert between a float and a 32 bit
204 * int.
205 */
206
207 typedef union
208 {
209 float value;
210 /* FIXME: Assumes 32 bit int. */
211 unsigned int word;
212 } ieee_float_shape_type;
213
214 /* Get a 32 bit int from a float. */
215
216 #define GET_FLOAT_WORD(i,d) \
217 do { \
218 ieee_float_shape_type gf_u; \
219 gf_u.value = (d); \
220 (i) = gf_u.word; \
221 } while (0)
222
223 /* Set a float from a 32 bit int. */
224
225 #define SET_FLOAT_WORD(d,i) \
226 do { \
227 ieee_float_shape_type sf_u; \
228 sf_u.word = (i); \
229 (d) = sf_u.value; \
230 } while (0)
231
232 /*
233 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
234 * double.
235 */
236
237 #define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
238 do { \
239 union IEEEl2bits ew_u; \
240 ew_u.e = (d); \
241 (ix0) = ew_u.xbits.expsign; \
242 (ix1) = ew_u.xbits.man; \
243 } while (0)
244
245 /*
246 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
247 * long double.
248 */
249
250 #define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
251 do { \
252 union IEEEl2bits ew_u; \
253 ew_u.e = (d); \
254 (ix0) = ew_u.xbits.expsign; \
255 (ix1) = ew_u.xbits.manh; \
256 (ix2) = ew_u.xbits.manl; \
257 } while (0)
258
259 /* Get expsign as a 16 bit int from a long double. */
260
261 #define GET_LDBL_EXPSIGN(i,d) \
262 do { \
263 union IEEEl2bits ge_u; \
264 ge_u.e = (d); \
265 (i) = ge_u.xbits.expsign; \
266 } while (0)
267
268 /*
269 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
270 * mantissa.
271 */
272
273 #define INSERT_LDBL80_WORDS(d,ix0,ix1) \
274 do { \
275 union IEEEl2bits iw_u; \
276 iw_u.xbits.expsign = (ix0); \
277 iw_u.xbits.man = (ix1); \
278 (d) = iw_u.e; \
279 } while (0)
280
281 /*
282 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
283 * comprising the mantissa.
284 */
285
286 #define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
287 do { \
288 union IEEEl2bits iw_u; \
289 iw_u.xbits.expsign = (ix0); \
290 iw_u.xbits.manh = (ix1); \
291 iw_u.xbits.manl = (ix2); \
292 (d) = iw_u.e; \
293 } while (0)
294
295 /* Set expsign of a long double from a 16 bit int. */
296
297 #define SET_LDBL_EXPSIGN(d,v) \
298 do { \
299 union IEEEl2bits se_u; \
300 se_u.e = (d); \
301 se_u.xbits.expsign = (v); \
302 (d) = se_u.e; \
303 } while (0)
304
305 #ifdef __i386__
306 /* Long double constants are broken on i386. */
307 #define LD80C(m, ex, v) { \
308 .xbits.man = __CONCAT(m, ULL), \
309 .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
310 }
311 #else
312 /* The above works on non-i386 too, but we use this to check v. */
313 #define LD80C(m, ex, v) { .e = (v), }
314 #endif
315
316 #ifdef FLT_EVAL_METHOD
317 /*
318 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
319 */
320 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
321 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
322 #else
323 #define STRICT_ASSIGN(type, lval, rval) do { \
324 volatile type __lval; \
325 \
326 if (sizeof(type) >= sizeof(long double)) \
327 (lval) = (rval); \
328 else { \
329 __lval = (rval); \
330 (lval) = __lval; \
331 } \
332 } while (0)
333 #endif
334 #endif /* FLT_EVAL_METHOD */
335
336 /* Support switching the mode to FP_PE if necessary. */
337 #if defined(__i386__) && !defined(NO_FPSETPREC)
338 #define ENTERI() ENTERIT(long double)
339 #define ENTERIT(returntype) \
340 returntype __retval; \
341 fp_prec_t __oprec; \
342 \
343 if ((__oprec = fpgetprec()) != FP_PE) \
344 fpsetprec(FP_PE)
345 #define RETURNI(x) do { \
346 __retval = (x); \
347 if (__oprec != FP_PE) \
348 fpsetprec(__oprec); \
349 RETURNF(__retval); \
350 } while (0)
351 #define ENTERV() \
352 fp_prec_t __oprec; \
353 \
354 if ((__oprec = fpgetprec()) != FP_PE) \
355 fpsetprec(FP_PE)
356 #define RETURNV() do { \
357 if (__oprec != FP_PE) \
358 fpsetprec(__oprec); \
359 return; \
360 } while (0)
361 #else
362 #define ENTERI()
363 #define ENTERIT(x)
364 #define RETURNI(x) RETURNF(x)
365 #define ENTERV()
366 #define RETURNV() return
367 #endif
368
369 /* Default return statement if hack*_t() is not used. */
370 #define RETURNF(v) return (v)
371
372 /*
373 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
374 * a == 0, but is slower.
375 */
376 #define _2sum(a, b) do { \
377 __typeof(a) __s, __w; \
378 \
379 __w = (a) + (b); \
380 __s = __w - (a); \
381 (b) = ((a) - (__w - __s)) + ((b) - __s); \
382 (a) = __w; \
383 } while (0)
384
385 /*
386 * 2sumF algorithm.
387 *
388 * "Normalize" the terms in the infinite-precision expression a + b for
389 * the sum of 2 floating point values so that b is as small as possible
390 * relative to 'a'. (The resulting 'a' is the value of the expression in
391 * the same precision as 'a' and the resulting b is the rounding error.)
392 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
393 * exponent overflow or underflow must not occur. This uses a Theorem of
394 * Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
395 * is apparently due to Skewchuk (1997).
396 *
397 * For this to always work, assignment of a + b to 'a' must not retain any
398 * extra precision in a + b. This is required by C standards but broken
399 * in many compilers. The brokenness cannot be worked around using
400 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
401 * algorithm would be destroyed by non-null strict assignments. (The
402 * compilers are correct to be broken -- the efficiency of all floating
403 * point code calculations would be destroyed similarly if they forced the
404 * conversions.)
405 *
406 * Fortunately, a case that works well can usually be arranged by building
407 * any extra precision into the type of 'a' -- 'a' should have type float_t,
408 * double_t or long double. b's type should be no larger than 'a's type.
409 * Callers should use these types with scopes as large as possible, to
410 * reduce their own extra-precision and efficiciency problems. In
411 * particular, they shouldn't convert back and forth just to call here.
412 */
413 #ifdef DEBUG
414 #define _2sumF(a, b) do { \
415 __typeof(a) __w; \
416 volatile __typeof(a) __ia, __ib, __r, __vw; \
417 \
418 __ia = (a); \
419 __ib = (b); \
420 assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
421 \
422 __w = (a) + (b); \
423 (b) = ((a) - __w) + (b); \
424 (a) = __w; \
425 \
426 /* The next 2 assertions are weak if (a) is already long double. */ \
427 assert((long double)__ia + __ib == (long double)(a) + (b)); \
428 __vw = __ia + __ib; \
429 __r = __ia - __vw; \
430 __r += __ib; \
431 assert(__vw == (a) && __r == (b)); \
432 } while (0)
433 #else /* !DEBUG */
434 #define _2sumF(a, b) do { \
435 __typeof(a) __w; \
436 \
437 __w = (a) + (b); \
438 (b) = ((a) - __w) + (b); \
439 (a) = __w; \
440 } while (0)
441 #endif /* DEBUG */
442
443 /*
444 * Set x += c, where x is represented in extra precision as a + b.
445 * x must be sufficiently normalized and sufficiently larger than c,
446 * and the result is then sufficiently normalized.
447 *
448 * The details of ordering are that |a| must be >= |c| (so that (a, c)
449 * can be normalized without extra work to swap 'a' with c). The details of
450 * the normalization are that b must be small relative to the normalized 'a'.
451 * Normalization of (a, c) makes the normalized c tiny relative to the
452 * normalized a, so b remains small relative to 'a' in the result. However,
453 * b need not ever be tiny relative to 'a'. For example, b might be about
454 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
455 * That is usually enough, and adding c (which by normalization is about
456 * 2**53 times smaller than a) cannot change b significantly. However,
457 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
458 * significantly relative to b. The caller must ensure that significant
459 * cancellation doesn't occur, either by having c of the same sign as 'a',
460 * or by having |c| a few percent smaller than |a|. Pre-normalization of
461 * (a, b) may help.
462 *
463 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
464 * exercise 19). We gain considerable efficiency by requiring the terms to
465 * be sufficiently normalized and sufficiently increasing.
466 */
467 #define _3sumF(a, b, c) do { \
468 __typeof(a) __tmp; \
469 \
470 __tmp = (c); \
471 _2sumF(__tmp, (a)); \
472 (b) += (a); \
473 (a) = __tmp; \
474 } while (0)
475
476 /*
477 * Common routine to process the arguments to nan(), nanf(), and nanl().
478 */
479 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
480
481 /*
482 * Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns
483 * signaling NaNs into quiet NaNs by setting a quiet bit. We do this
484 * because we want to never return a signaling NaN, and also because we
485 * don't want the quiet bit to affect the result. Then mix the converted
486 * args using the specified operation.
487 *
488 * When one arg is NaN, the result is typically that arg quieted. When both
489 * args are NaNs, the result is typically the quietening of the arg whose
490 * mantissa is largest after quietening. When neither arg is NaN, the
491 * result may be NaN because it is indeterminate, or finite for subsequent
492 * construction of a NaN as the indeterminate 0.0L/0.0L.
493 *
494 * Technical complications: the result in bits after rounding to the final
495 * precision might depend on the runtime precision and/or on compiler
496 * optimizations, especially when different register sets are used for
497 * different precisions. Try to make the result not depend on at least the
498 * runtime precision by always doing the main mixing step in long double
499 * precision. Try to reduce dependencies on optimizations by adding the
500 * the 0's in different precisions (unless everything is in long double
501 * precision).
502 */
503 #define nan_mix(x, y) (nan_mix_op((x), (y), +))
504 #define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0))
505
506 #ifdef _COMPLEX_H
507
508 /*
509 * C99 specifies that complex numbers have the same representation as
510 * an array of two elements, where the first element is the real part
511 * and the second element is the imaginary part.
512 */
513 typedef union {
514 float complex f;
515 float a[2];
516 } float_complex;
517 typedef union {
518 double complex f;
519 double a[2];
520 } double_complex;
521 typedef union {
522 long double complex f;
523 long double a[2];
524 } long_double_complex;
525 #define REALPART(z) ((z).a[0])
526 #define IMAGPART(z) ((z).a[1])
527
528 /*
529 * Inline functions that can be used to construct complex values.
530 *
531 * The C99 standard intends x+I*y to be used for this, but x+I*y is
532 * currently unusable in general since gcc introduces many overflow,
533 * underflow, sign and efficiency bugs by rewriting I*y as
534 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
535 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
536 * to -0.0+I*0.0.
537 *
538 * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
539 * to construct complex values. Compilers that conform to the C99
540 * standard require the following functions to avoid the above issues.
541 */
542
543 #ifndef CMPLXF
544 static __inline float complex
CMPLXF(float x,float y)545 CMPLXF(float x, float y)
546 {
547 float_complex z;
548
549 REALPART(z) = x;
550 IMAGPART(z) = y;
551 return (z.f);
552 }
553 #endif
554
555 #ifndef CMPLX
556 static __inline double complex
CMPLX(double x,double y)557 CMPLX(double x, double y)
558 {
559 double_complex z;
560
561 REALPART(z) = x;
562 IMAGPART(z) = y;
563 return (z.f);
564 }
565 #endif
566
567 #ifndef CMPLXL
568 static __inline long double complex
CMPLXL(long double x,long double y)569 CMPLXL(long double x, long double y)
570 {
571 long_double_complex z;
572
573 REALPART(z) = x;
574 IMAGPART(z) = y;
575 return (z.f);
576 }
577 #endif
578
579 #endif /* _COMPLEX_H */
580
581 /*
582 * The rnint() family rounds to the nearest integer for a restricted range
583 * range of args (up to about 2**MANT_DIG). We assume that the current
584 * rounding mode is FE_TONEAREST so that this can be done efficiently.
585 * Extra precision causes more problems in practice, and we only centralize
586 * this here to reduce those problems, and have not solved the efficiency
587 * problems. The exp2() family uses a more delicate version of this that
588 * requires extracting bits from the intermediate value, so it is not
589 * centralized here and should copy any solution of the efficiency problems.
590 */
591
592 static inline double
rnint(__double_t x)593 rnint(__double_t x)
594 {
595 /*
596 * This casts to double to kill any extra precision. This depends
597 * on the cast being applied to a double_t to avoid compiler bugs
598 * (this is a cleaner version of STRICT_ASSIGN()). This is
599 * inefficient if there actually is extra precision, but is hard
600 * to improve on. We use double_t in the API to minimise conversions
601 * for just calling here. Note that we cannot easily change the
602 * magic number to the one that works directly with double_t, since
603 * the rounding precision is variable at runtime on x86 so the
604 * magic number would need to be variable. Assuming that the
605 * rounding precision is always the default is too fragile. This
606 * and many other complications will move when the default is
607 * changed to FP_PE.
608 */
609 return ((double)(x + 0x1.8p52) - 0x1.8p52);
610 }
611
612 static inline float
rnintf(__float_t x)613 rnintf(__float_t x)
614 {
615 /*
616 * As for rnint(), except we could just call that to handle the
617 * extra precision case, usually without losing efficiency.
618 */
619 return ((float)(x + 0x1.8p23F) - 0x1.8p23F);
620 }
621
622 #ifdef LDBL_MANT_DIG
623 /*
624 * The complications for extra precision are smaller for rnintl() since it
625 * can safely assume that the rounding precision has been increased from
626 * its default to FP_PE on x86. We don't exploit that here to get small
627 * optimizations from limiting the rangle to double. We just need it for
628 * the magic number to work with long doubles. ld128 callers should use
629 * rnint() instead of this if possible. ld80 callers should prefer
630 * rnintl() since for amd64 this avoids swapping the register set, while
631 * for i386 it makes no difference (assuming FP_PE), and for other arches
632 * it makes little difference.
633 */
634 static inline long double
rnintl(long double x)635 rnintl(long double x)
636 {
637 return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 -
638 __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2);
639 }
640 #endif /* LDBL_MANT_DIG */
641
642 /*
643 * irint() and i64rint() give the same result as casting to their integer
644 * return type provided their arg is a floating point integer. They can
645 * sometimes be more efficient because no rounding is required.
646 */
647 #if (defined(amd64) || defined(__i386__)) && defined(__GNUCLIKE_ASM)
648 #define irint(x) \
649 (sizeof(x) == sizeof(float) && \
650 sizeof(__float_t) == sizeof(long double) ? irintf(x) : \
651 sizeof(x) == sizeof(double) && \
652 sizeof(__double_t) == sizeof(long double) ? irintd(x) : \
653 sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x))
654 #else
655 #define irint(x) ((int)(x))
656 #endif
657
658 #define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */
659
660 #if defined(__i386__) && defined(__GNUCLIKE_ASM)
661 static __inline int
irintf(float x)662 irintf(float x)
663 {
664 int n;
665
666 __asm("fistl %0" : "=m" (n) : "t" (x));
667 return (n);
668 }
669
670 static __inline int
irintd(double x)671 irintd(double x)
672 {
673 int n;
674
675 __asm("fistl %0" : "=m" (n) : "t" (x));
676 return (n);
677 }
678 #endif
679
680 #if (defined(__amd64__) || defined(__i386__)) && defined(__GNUCLIKE_ASM)
681 static __inline int
irintl(long double x)682 irintl(long double x)
683 {
684 int n;
685
686 __asm("fistl %0" : "=m" (n) : "t" (x));
687 return (n);
688 }
689 #endif
690
691 #ifdef DEBUG
692 #if defined(__amd64__) || defined(__i386__)
693 #define breakpoint() asm("int $3")
694 #else
695 #include <signal.h>
696
697 #define breakpoint() raise(SIGTRAP)
698 #endif
699 #endif
700
701 /* Write a pari script to test things externally. */
702 #ifdef DOPRINT
703 #include <stdio.h>
704
705 #ifndef DOPRINT_SWIZZLE
706 #define DOPRINT_SWIZZLE 0
707 #endif
708
709 #ifdef DOPRINT_LD80
710
711 #define DOPRINT_START(xp) do { \
712 uint64_t __lx; \
713 uint16_t __hx; \
714 \
715 /* Hack to give more-problematic args. */ \
716 EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
717 __lx ^= DOPRINT_SWIZZLE; \
718 INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
719 printf("x = %.21Lg; ", (long double)*xp); \
720 } while (0)
721 #define DOPRINT_END1(v) \
722 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
723 #define DOPRINT_END2(hi, lo) \
724 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
725 (long double)(hi), (long double)(lo))
726
727 #elif defined(DOPRINT_D64)
728
729 #define DOPRINT_START(xp) do { \
730 uint32_t __hx, __lx; \
731 \
732 EXTRACT_WORDS(__hx, __lx, *xp); \
733 __lx ^= DOPRINT_SWIZZLE; \
734 INSERT_WORDS(*xp, __hx, __lx); \
735 printf("x = %.21Lg; ", (long double)*xp); \
736 } while (0)
737 #define DOPRINT_END1(v) \
738 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
739 #define DOPRINT_END2(hi, lo) \
740 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
741 (long double)(hi), (long double)(lo))
742
743 #elif defined(DOPRINT_F32)
744
745 #define DOPRINT_START(xp) do { \
746 uint32_t __hx; \
747 \
748 GET_FLOAT_WORD(__hx, *xp); \
749 __hx ^= DOPRINT_SWIZZLE; \
750 SET_FLOAT_WORD(*xp, __hx); \
751 printf("x = %.21Lg; ", (long double)*xp); \
752 } while (0)
753 #define DOPRINT_END1(v) \
754 printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
755 #define DOPRINT_END2(hi, lo) \
756 printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
757 (long double)(hi), (long double)(lo))
758
759 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
760
761 #ifndef DOPRINT_SWIZZLE_HIGH
762 #define DOPRINT_SWIZZLE_HIGH 0
763 #endif
764
765 #define DOPRINT_START(xp) do { \
766 uint64_t __lx, __llx; \
767 uint16_t __hx; \
768 \
769 EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
770 __llx ^= DOPRINT_SWIZZLE; \
771 __lx ^= DOPRINT_SWIZZLE_HIGH; \
772 INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
773 printf("x = %.36Lg; ", (long double)*xp); \
774 } while (0)
775 #define DOPRINT_END1(v) \
776 printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
777 #define DOPRINT_END2(hi, lo) \
778 printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
779 (long double)(hi), (long double)(lo))
780
781 #endif /* DOPRINT_LD80 */
782
783 #else /* !DOPRINT */
784 #define DOPRINT_START(xp)
785 #define DOPRINT_END1(v)
786 #define DOPRINT_END2(hi, lo)
787 #endif /* DOPRINT */
788
789 #define RETURNP(x) do { \
790 DOPRINT_END1(x); \
791 RETURNF(x); \
792 } while (0)
793 #define RETURNPI(x) do { \
794 DOPRINT_END1(x); \
795 RETURNI(x); \
796 } while (0)
797 #define RETURN2P(x, y) do { \
798 DOPRINT_END2((x), (y)); \
799 RETURNF((x) + (y)); \
800 } while (0)
801 #define RETURN2PI(x, y) do { \
802 DOPRINT_END2((x), (y)); \
803 RETURNI((x) + (y)); \
804 } while (0)
805 #ifdef STRUCT_RETURN
806 #define RETURNSP(rp) do { \
807 if (!(rp)->lo_set) \
808 RETURNP((rp)->hi); \
809 RETURN2P((rp)->hi, (rp)->lo); \
810 } while (0)
811 #define RETURNSPI(rp) do { \
812 if (!(rp)->lo_set) \
813 RETURNPI((rp)->hi); \
814 RETURN2PI((rp)->hi, (rp)->lo); \
815 } while (0)
816 #endif
817 #define SUM2P(x, y) ({ \
818 const __typeof (x) __x = (x); \
819 const __typeof (y) __y = (y); \
820 \
821 DOPRINT_END2(__x, __y); \
822 __x + __y; \
823 })
824
825 /*
826 * ieee style elementary functions
827 *
828 * We rename functions here to improve other sources' diffability
829 * against fdlibm.
830 */
831 #define __ieee754_sqrt sqrt
832 #define __ieee754_acos acos
833 #define __ieee754_acosh acosh
834 #define __ieee754_log log
835 #define __ieee754_log2 log2
836 #define __ieee754_atanh atanh
837 #define __ieee754_asin asin
838 #define __ieee754_atan2 atan2
839 #define __ieee754_exp exp
840 #define __ieee754_cosh cosh
841 #define __ieee754_fmod fmod
842 #define __ieee754_pow pow
843 #define __ieee754_lgamma lgamma
844 #define __ieee754_gamma gamma
845 #define __ieee754_lgamma_r lgamma_r
846 #define __ieee754_gamma_r gamma_r
847 #define __ieee754_log10 log10
848 #define __ieee754_sinh sinh
849 #define __ieee754_hypot hypot
850 #define __ieee754_j0 j0
851 #define __ieee754_j1 j1
852 #define __ieee754_y0 y0
853 #define __ieee754_y1 y1
854 #define __ieee754_jn jn
855 #define __ieee754_yn yn
856 #define __ieee754_remainder remainder
857 #define __ieee754_scalb scalb
858 #define __ieee754_sqrtf sqrtf
859 #define __ieee754_acosf acosf
860 #define __ieee754_acoshf acoshf
861 #define __ieee754_logf logf
862 #define __ieee754_atanhf atanhf
863 #define __ieee754_asinf asinf
864 #define __ieee754_atan2f atan2f
865 #define __ieee754_expf expf
866 #define __ieee754_coshf coshf
867 #define __ieee754_fmodf fmodf
868 #define __ieee754_powf powf
869 #define __ieee754_lgammaf lgammaf
870 #define __ieee754_gammaf gammaf
871 #define __ieee754_lgammaf_r lgammaf_r
872 #define __ieee754_gammaf_r gammaf_r
873 #define __ieee754_log10f log10f
874 #define __ieee754_log2f log2f
875 #define __ieee754_sinhf sinhf
876 #define __ieee754_hypotf hypotf
877 #define __ieee754_j0f j0f
878 #define __ieee754_j1f j1f
879 #define __ieee754_y0f y0f
880 #define __ieee754_y1f y1f
881 #define __ieee754_jnf jnf
882 #define __ieee754_ynf ynf
883 #define __ieee754_remainderf remainderf
884 #define __ieee754_scalbf scalbf
885
886 /* fdlibm kernel function */
887 int __kernel_rem_pio2(double*,double*,int,int,int);
888
889 /* double precision kernel functions */
890 #ifndef INLINE_REM_PIO2
891 int __ieee754_rem_pio2(double,double*);
892 #endif
893 double __kernel_sin(double,double,int);
894 double __kernel_cos(double,double);
895 double __kernel_tan(double,double,int);
896 double __ldexp_exp(double,int);
897 #ifdef _COMPLEX_H
898 double complex __ldexp_cexp(double complex,int);
899 #endif
900
901 /* float precision kernel functions */
902 #ifndef INLINE_REM_PIO2F
903 int __ieee754_rem_pio2f(float,double*);
904 #endif
905 #ifndef INLINE_KERNEL_SINDF
906 float __kernel_sindf(double);
907 #endif
908 #ifndef INLINE_KERNEL_COSDF
909 float __kernel_cosdf(double);
910 #endif
911 #ifndef INLINE_KERNEL_TANDF
912 float __kernel_tandf(double,int);
913 #endif
914 float __ldexp_expf(float,int);
915 #ifdef _COMPLEX_H
916 float complex __ldexp_cexpf(float complex,int);
917 #endif
918
919 /* long double precision kernel functions */
920 long double __kernel_sinl(long double, long double, int);
921 long double __kernel_cosl(long double, long double);
922 long double __kernel_tanl(long double, long double, int);
923
924 #endif /* !_MATH_PRIVATE_H_ */
925