2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
9 * ====================================================
13 * from: @(#)fdlibm.h 5.1 93/09/24
16 #ifndef _MATH_PRIVATE_H_
17 #define _MATH_PRIVATE_H_
21 #include <sys/types.h>
24 #include <get-rounding-mode.h>
26 /* Gather machine dependent _Floatn support. */
27 #include <bits/floatn.h>
29 /* The original fdlibm code used statements like:
30 n0 = ((*(int*)&one)>>29)^1; * index of high word *
31 ix0 = *(n0+(int*)&x); * high word of x *
32 ix1 = *((1-n0)+(int*)&x); * low word of x *
33 to dig two 32 bit words out of the 64 bit IEEE floating point
34 value. That is non-ANSI, and, moreover, the gcc instruction
35 scheduler gets it wrong. We instead use the following macros.
36 Unlike the original code, we determine the endianness at compile
37 time, not at run time; I don't see much benefit to selecting
38 endianness at run time. */
40 /* A union which permits us to convert between a double and two 32 bit
43 #if __FLOAT_WORD_ORDER == __BIG_ENDIAN
54 } ieee_double_shape_type
;
58 #if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN
69 } ieee_double_shape_type
;
73 /* Get two 32 bit ints from a double. */
75 #define EXTRACT_WORDS(ix0,ix1,d) \
77 ieee_double_shape_type ew_u; \
79 (ix0) = ew_u.parts.msw; \
80 (ix1) = ew_u.parts.lsw; \
83 /* Get the more significant 32 bit int from a double. */
86 # define GET_HIGH_WORD(i,d) \
88 ieee_double_shape_type gh_u; \
90 (i) = gh_u.parts.msw; \
94 /* Get the less significant 32 bit int from a double. */
97 # define GET_LOW_WORD(i,d) \
99 ieee_double_shape_type gl_u; \
101 (i) = gl_u.parts.lsw; \
105 /* Get all in one, efficient on 64-bit machines. */
106 #ifndef EXTRACT_WORDS64
107 # define EXTRACT_WORDS64(i,d) \
109 ieee_double_shape_type gh_u; \
115 /* Set a double from two 32 bit ints. */
117 # define INSERT_WORDS(d,ix0,ix1) \
119 ieee_double_shape_type iw_u; \
120 iw_u.parts.msw = (ix0); \
121 iw_u.parts.lsw = (ix1); \
126 /* Get all in one, efficient on 64-bit machines. */
127 #ifndef INSERT_WORDS64
128 # define INSERT_WORDS64(d,i) \
130 ieee_double_shape_type iw_u; \
136 /* Set the more significant 32 bits of a double from an int. */
137 #ifndef SET_HIGH_WORD
138 #define SET_HIGH_WORD(d,v) \
140 ieee_double_shape_type sh_u; \
142 sh_u.parts.msw = (v); \
147 /* Set the less significant 32 bits of a double from an int. */
149 # define SET_LOW_WORD(d,v) \
151 ieee_double_shape_type sl_u; \
153 sl_u.parts.lsw = (v); \
158 /* A union which permits us to convert between a float and a 32 bit
165 } ieee_float_shape_type
;
167 /* Get a 32 bit int from a float. */
168 #ifndef GET_FLOAT_WORD
169 # define GET_FLOAT_WORD(i,d) \
171 ieee_float_shape_type gf_u; \
177 /* Set a float from a 32 bit int. */
178 #ifndef SET_FLOAT_WORD
179 # define SET_FLOAT_WORD(d,i) \
181 ieee_float_shape_type sf_u; \
187 /* We need to guarantee an expansion of name when building
188 ldbl-128 files as another type (e.g _Float128). */
189 #define mathx_hidden_def(name) hidden_def(name)
191 /* Get long double macros from a separate header. */
192 #include <math_ldbl.h>
194 /* Include function declarations for each floating-point. */
195 #define _Mdouble_ double
197 #include <math_private_calls.h>
201 #define _Mdouble_ float
203 #define __MATH_DECLARING_FLOAT
204 #include <math_private_calls.h>
205 #undef __MATH_DECLARING_FLOAT
209 #define _Mdouble_ long double
211 #define __MATH_DECLARING_LONG_DOUBLE
212 #include <math_private_calls.h>
213 #undef __MATH_DECLARING_LONG_DOUBLE
217 #if __HAVE_DISTINCT_FLOAT128
218 # define _Mdouble_ _Float128
220 # define __MATH_DECLARING_FLOATN
221 # include <math_private_calls.h>
222 # undef __MATH_DECLARING_FLOATN
227 #if __HAVE_DISTINCT_FLOAT128
229 /* __builtin_isinf_sign is broken in GCC < 7 for float128. */
230 # if ! __GNUC_PREREQ (7, 0)
231 # include <ieee754_float128.h>
233 __isinff128 (_Float128 x
)
236 GET_FLOAT128_WORDS64 (hx
, lx
, x
);
237 lx
|= (hx
& 0x7fffffffffffffffLL
) ^ 0x7fff000000000000LL
;
239 return ~(lx
>> 63) & (hx
>> 62);
243 extern inline _Float128
244 fabsf128 (_Float128 x
)
246 return __builtin_fabsf128 (x
);
252 /* fdlibm kernel function */
253 extern double __kernel_standard (double,double,int);
254 extern float __kernel_standard_f (float,float,int);
255 extern long double __kernel_standard_l (long double,long double,int);
257 /* Prototypes for functions of the IBM Accurate Mathematical Library. */
258 extern double __exp1 (double __x
, double __xx
, double __error
);
259 extern double __sin (double __x
);
260 extern double __cos (double __x
);
261 extern int __branred (double __x
, double *__a
, double *__aa
);
262 extern void __doasin (double __x
, double __dx
, double __v
[]);
263 extern void __dubsin (double __x
, double __dx
, double __v
[]);
264 extern void __dubcos (double __x
, double __dx
, double __v
[]);
265 extern double __halfulp (double __x
, double __y
);
266 extern double __sin32 (double __x
, double __res
, double __res1
);
267 extern double __cos32 (double __x
, double __res
, double __res1
);
268 extern double __mpsin (double __x
, double __dx
, bool __range_reduce
);
269 extern double __mpcos (double __x
, double __dx
, bool __range_reduce
);
270 extern double __slowexp (double __x
);
271 extern double __slowpow (double __x
, double __y
, double __z
);
272 extern void __docos (double __x
, double __dx
, double __v
[]);
274 #ifndef math_opt_barrier
275 # define math_opt_barrier(x) \
276 ({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; })
277 # define math_force_eval(x) \
278 ({ __typeof (x) __x = (x); __asm __volatile__ ("" : : "m" (__x)); })
281 /* math_narrow_eval reduces its floating-point argument to the range
282 and precision of its semantic type. (The original evaluation may
283 still occur with excess range and precision, so the result may be
284 affected by double rounding.) */
285 #if FLT_EVAL_METHOD == 0
286 # define math_narrow_eval(x) (x)
288 # if FLT_EVAL_METHOD == 1
289 # define excess_precision(type) __builtin_types_compatible_p (type, float)
291 # define excess_precision(type) (__builtin_types_compatible_p (type, float) \
292 || __builtin_types_compatible_p (type, \
295 # define math_narrow_eval(x) \
297 __typeof (x) math_narrow_eval_tmp = (x); \
298 if (excess_precision (__typeof (math_narrow_eval_tmp))) \
299 __asm__ ("" : "+m" (math_narrow_eval_tmp)); \
300 math_narrow_eval_tmp; \
304 #if __HAVE_DISTINCT_FLOAT128
305 # define __EXPR_FLT128(x, yes, no) \
306 __builtin_choose_expr (__builtin_types_compatible_p \
307 (x, long double), no, yes)
309 # define __EXPR_FLT128(x, yes, no) no
313 #define fabs_tg(x) __MATH_TG ((x), (__typeof (x)) __builtin_fabs, (x))
315 #define min_of_type(type) __builtin_choose_expr \
316 (__builtin_types_compatible_p (type, float), \
318 __builtin_choose_expr \
319 (__builtin_types_compatible_p (type, double), \
321 __EXPR_FLT128 (type, FLT128_MIN, LDBL_MIN)))
323 /* If X (which is not a NaN) is subnormal, force an underflow
325 #define math_check_force_underflow(x) \
328 __typeof (x) force_underflow_tmp = (x); \
329 if (fabs_tg (force_underflow_tmp) \
330 < min_of_type (__typeof (force_underflow_tmp))) \
332 __typeof (force_underflow_tmp) force_underflow_tmp2 \
333 = force_underflow_tmp * force_underflow_tmp; \
334 math_force_eval (force_underflow_tmp2); \
338 /* Likewise, but X is also known to be nonnegative. */
339 #define math_check_force_underflow_nonneg(x) \
342 __typeof (x) force_underflow_tmp = (x); \
343 if (force_underflow_tmp \
344 < min_of_type (__typeof (force_underflow_tmp))) \
346 __typeof (force_underflow_tmp) force_underflow_tmp2 \
347 = force_underflow_tmp * force_underflow_tmp; \
348 math_force_eval (force_underflow_tmp2); \
352 /* Likewise, for both real and imaginary parts of a complex
354 #define math_check_force_underflow_complex(x) \
357 __typeof (x) force_underflow_complex_tmp = (x); \
358 math_check_force_underflow (__real__ force_underflow_complex_tmp); \
359 math_check_force_underflow (__imag__ force_underflow_complex_tmp); \
363 /* The standards only specify one variant of the fenv.h interfaces.
364 But at least for some architectures we can be more efficient if we
365 know what operations are going to be performed. Therefore we
366 define additional interfaces. By default they refer to the normal
369 static __always_inline
void
370 default_libc_feholdexcept (fenv_t
*e
)
372 (void) __feholdexcept (e
);
375 #ifndef libc_feholdexcept
376 # define libc_feholdexcept default_libc_feholdexcept
378 #ifndef libc_feholdexceptf
379 # define libc_feholdexceptf default_libc_feholdexcept
381 #ifndef libc_feholdexceptl
382 # define libc_feholdexceptl default_libc_feholdexcept
385 static __always_inline
void
386 default_libc_fesetround (int r
)
388 (void) __fesetround (r
);
391 #ifndef libc_fesetround
392 # define libc_fesetround default_libc_fesetround
394 #ifndef libc_fesetroundf
395 # define libc_fesetroundf default_libc_fesetround
397 #ifndef libc_fesetroundl
398 # define libc_fesetroundl default_libc_fesetround
401 static __always_inline
void
402 default_libc_feholdexcept_setround (fenv_t
*e
, int r
)
408 #ifndef libc_feholdexcept_setround
409 # define libc_feholdexcept_setround default_libc_feholdexcept_setround
411 #ifndef libc_feholdexcept_setroundf
412 # define libc_feholdexcept_setroundf default_libc_feholdexcept_setround
414 #ifndef libc_feholdexcept_setroundl
415 # define libc_feholdexcept_setroundl default_libc_feholdexcept_setround
418 #ifndef libc_feholdsetround_53bit
419 # define libc_feholdsetround_53bit libc_feholdsetround
422 #ifndef libc_fetestexcept
423 # define libc_fetestexcept fetestexcept
425 #ifndef libc_fetestexceptf
426 # define libc_fetestexceptf fetestexcept
428 #ifndef libc_fetestexceptl
429 # define libc_fetestexceptl fetestexcept
432 static __always_inline
void
433 default_libc_fesetenv (fenv_t
*e
)
435 (void) __fesetenv (e
);
438 #ifndef libc_fesetenv
439 # define libc_fesetenv default_libc_fesetenv
441 #ifndef libc_fesetenvf
442 # define libc_fesetenvf default_libc_fesetenv
444 #ifndef libc_fesetenvl
445 # define libc_fesetenvl default_libc_fesetenv
448 static __always_inline
void
449 default_libc_feupdateenv (fenv_t
*e
)
451 (void) __feupdateenv (e
);
454 #ifndef libc_feupdateenv
455 # define libc_feupdateenv default_libc_feupdateenv
457 #ifndef libc_feupdateenvf
458 # define libc_feupdateenvf default_libc_feupdateenv
460 #ifndef libc_feupdateenvl
461 # define libc_feupdateenvl default_libc_feupdateenv
464 #ifndef libc_feresetround_53bit
465 # define libc_feresetround_53bit libc_feresetround
468 static __always_inline
int
469 default_libc_feupdateenv_test (fenv_t
*e
, int ex
)
471 int ret
= fetestexcept (ex
);
476 #ifndef libc_feupdateenv_test
477 # define libc_feupdateenv_test default_libc_feupdateenv_test
479 #ifndef libc_feupdateenv_testf
480 # define libc_feupdateenv_testf default_libc_feupdateenv_test
482 #ifndef libc_feupdateenv_testl
483 # define libc_feupdateenv_testl default_libc_feupdateenv_test
486 /* Save and set the rounding mode. The use of fenv_t to store the old mode
487 allows a target-specific version of this function to avoid converting the
488 rounding mode from the fpu format. By default we have no choice but to
489 manipulate the entire env. */
491 #ifndef libc_feholdsetround
492 # define libc_feholdsetround libc_feholdexcept_setround
494 #ifndef libc_feholdsetroundf
495 # define libc_feholdsetroundf libc_feholdexcept_setroundf
497 #ifndef libc_feholdsetroundl
498 # define libc_feholdsetroundl libc_feholdexcept_setroundl
501 /* ... and the reverse. */
503 #ifndef libc_feresetround
504 # define libc_feresetround libc_feupdateenv
506 #ifndef libc_feresetroundf
507 # define libc_feresetroundf libc_feupdateenvf
509 #ifndef libc_feresetroundl
510 # define libc_feresetroundl libc_feupdateenvl
513 /* ... and a version that may also discard exceptions. */
515 #ifndef libc_feresetround_noex
516 # define libc_feresetround_noex libc_fesetenv
518 #ifndef libc_feresetround_noexf
519 # define libc_feresetround_noexf libc_fesetenvf
521 #ifndef libc_feresetround_noexl
522 # define libc_feresetround_noexl libc_fesetenvl
526 # define HAVE_RM_CTX 0
530 /* Set/Restore Rounding Modes only when necessary. If defined, these functions
531 set/restore floating point state only if the state needed within the lexical
532 block is different from the current state. This saves a lot of time when
533 the floating point unit is much slower than the fixed point units. */
535 # ifndef libc_feholdsetround_noex_ctx
536 # define libc_feholdsetround_noex_ctx libc_feholdsetround_ctx
538 # ifndef libc_feholdsetround_noexf_ctx
539 # define libc_feholdsetround_noexf_ctx libc_feholdsetroundf_ctx
541 # ifndef libc_feholdsetround_noexl_ctx
542 # define libc_feholdsetround_noexl_ctx libc_feholdsetroundl_ctx
545 # ifndef libc_feresetround_noex_ctx
546 # define libc_feresetround_noex_ctx libc_fesetenv_ctx
548 # ifndef libc_feresetround_noexf_ctx
549 # define libc_feresetround_noexf_ctx libc_fesetenvf_ctx
551 # ifndef libc_feresetround_noexl_ctx
552 # define libc_feresetround_noexl_ctx libc_fesetenvl_ctx
557 /* Default implementation using standard fenv functions.
558 Avoid unnecessary rounding mode changes by first checking the
559 current rounding mode. Note the use of __glibc_unlikely is
560 important for performance. */
562 static __always_inline
void
563 libc_feholdsetround_ctx (struct rm_ctx
*ctx
, int round
)
565 ctx
->updated_status
= false;
567 /* Update rounding mode only if different. */
568 if (__glibc_unlikely (round
!= get_rounding_mode ()))
570 ctx
->updated_status
= true;
571 __fegetenv (&ctx
->env
);
572 __fesetround (round
);
576 static __always_inline
void
577 libc_feresetround_ctx (struct rm_ctx
*ctx
)
579 /* Restore the rounding mode if updated. */
580 if (__glibc_unlikely (ctx
->updated_status
))
581 __feupdateenv (&ctx
->env
);
584 static __always_inline
void
585 libc_feholdsetround_noex_ctx (struct rm_ctx
*ctx
, int round
)
587 /* Save exception flags and rounding mode. */
588 __fegetenv (&ctx
->env
);
590 /* Update rounding mode only if different. */
591 if (__glibc_unlikely (round
!= get_rounding_mode ()))
592 __fesetround (round
);
595 static __always_inline
void
596 libc_feresetround_noex_ctx (struct rm_ctx
*ctx
)
598 /* Restore exception flags and rounding mode. */
599 __fesetenv (&ctx
->env
);
602 # define libc_feholdsetroundf_ctx libc_feholdsetround_ctx
603 # define libc_feholdsetroundl_ctx libc_feholdsetround_ctx
604 # define libc_feresetroundf_ctx libc_feresetround_ctx
605 # define libc_feresetroundl_ctx libc_feresetround_ctx
607 # define libc_feholdsetround_noexf_ctx libc_feholdsetround_noex_ctx
608 # define libc_feholdsetround_noexl_ctx libc_feholdsetround_noex_ctx
609 # define libc_feresetround_noexf_ctx libc_feresetround_noex_ctx
610 # define libc_feresetround_noexl_ctx libc_feresetround_noex_ctx
614 #ifndef libc_feholdsetround_53bit_ctx
615 # define libc_feholdsetround_53bit_ctx libc_feholdsetround_ctx
617 #ifndef libc_feresetround_53bit_ctx
618 # define libc_feresetround_53bit_ctx libc_feresetround_ctx
621 #define SET_RESTORE_ROUND_GENERIC(RM,ROUNDFUNC,CLEANUPFUNC) \
622 struct rm_ctx ctx __attribute__((cleanup (CLEANUPFUNC ## _ctx))); \
623 ROUNDFUNC ## _ctx (&ctx, (RM))
625 /* Set the rounding mode within a lexical block. Restore the rounding mode to
626 the value at the start of the block. The exception mode must be preserved.
627 Exceptions raised within the block must be set in the exception flags.
628 Non-stop mode may be enabled inside the block. */
630 #define SET_RESTORE_ROUND(RM) \
631 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetround, libc_feresetround)
632 #define SET_RESTORE_ROUNDF(RM) \
633 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetroundf, libc_feresetroundf)
634 #define SET_RESTORE_ROUNDL(RM) \
635 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetroundl, libc_feresetroundl)
637 /* Set the rounding mode within a lexical block. Restore the rounding mode to
638 the value at the start of the block. The exception mode must be preserved.
639 Exceptions raised within the block must be discarded, and exception flags
640 are restored to the value at the start of the block.
641 Non-stop mode may be enabled inside the block. */
643 #define SET_RESTORE_ROUND_NOEX(RM) \
644 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetround_noex, \
645 libc_feresetround_noex)
646 #define SET_RESTORE_ROUND_NOEXF(RM) \
647 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetround_noexf, \
648 libc_feresetround_noexf)
649 #define SET_RESTORE_ROUND_NOEXL(RM) \
650 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetround_noexl, \
651 libc_feresetround_noexl)
653 /* Like SET_RESTORE_ROUND, but also set rounding precision to 53 bits. */
654 #define SET_RESTORE_ROUND_53BIT(RM) \
655 SET_RESTORE_ROUND_GENERIC (RM, libc_feholdsetround_53bit, \
656 libc_feresetround_53bit)
658 #endif /* _MATH_PRIVATE_H_ */