764 lines
19 KiB
C
764 lines
19 KiB
C
/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* from: @(#)fdlibm.h 5.1 93/09/24
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* $FreeBSD$
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*/
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#ifndef _MATH_PRIVATE_H_
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#define _MATH_PRIVATE_H_
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#include <sys/types.h>
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#include <machine/endian.h>
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/*
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* The original fdlibm code used statements like:
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* n0 = ((*(int*)&one)>>29)^1; * index of high word *
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* ix0 = *(n0+(int*)&x); * high word of x *
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* ix1 = *((1-n0)+(int*)&x); * low word of x *
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* to dig two 32 bit words out of the 64 bit IEEE floating point
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* value. That is non-ANSI, and, moreover, the gcc instruction
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* scheduler gets it wrong. We instead use the following macros.
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* Unlike the original code, we determine the endianness at compile
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* time, not at run time; I don't see much benefit to selecting
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* endianness at run time.
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*/
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/*
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* A union which permits us to convert between a double and two 32 bit
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* ints.
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*/
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#ifdef __arm__
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#if defined(__VFP_FP__) || defined(__ARM_EABI__)
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#define IEEE_WORD_ORDER BYTE_ORDER
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#else
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#define IEEE_WORD_ORDER BIG_ENDIAN
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#endif
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#else /* __arm__ */
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#define IEEE_WORD_ORDER BYTE_ORDER
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#endif
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#if IEEE_WORD_ORDER == BIG_ENDIAN
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typedef union
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{
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double value;
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struct
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{
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u_int32_t msw;
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u_int32_t lsw;
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} parts;
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struct
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{
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u_int64_t w;
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} xparts;
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} ieee_double_shape_type;
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#endif
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#if IEEE_WORD_ORDER == LITTLE_ENDIAN
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typedef union
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{
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double value;
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struct
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{
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u_int32_t lsw;
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u_int32_t msw;
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} parts;
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struct
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{
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u_int64_t w;
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} xparts;
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} ieee_double_shape_type;
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#endif
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/* Get two 32 bit ints from a double. */
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#define EXTRACT_WORDS(ix0,ix1,d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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/* Get a 64-bit int from a double. */
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#define EXTRACT_WORD64(ix,d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix) = ew_u.xparts.w; \
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} while (0)
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/* Get the more significant 32 bit int from a double. */
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#define GET_HIGH_WORD(i,d) \
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do { \
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ieee_double_shape_type gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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} while (0)
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/* Get the less significant 32 bit int from a double. */
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#define GET_LOW_WORD(i,d) \
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do { \
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ieee_double_shape_type gl_u; \
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gl_u.value = (d); \
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(i) = gl_u.parts.lsw; \
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} while (0)
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/* Set a double from two 32 bit ints. */
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#define INSERT_WORDS(d,ix0,ix1) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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/* Set a double from a 64-bit int. */
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#define INSERT_WORD64(d,ix) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.xparts.w = (ix); \
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(d) = iw_u.value; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_HIGH_WORD(d,v) \
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do { \
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ieee_double_shape_type sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the less significant 32 bits of a double from an int. */
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#define SET_LOW_WORD(d,v) \
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do { \
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ieee_double_shape_type sl_u; \
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sl_u.value = (d); \
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sl_u.parts.lsw = (v); \
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(d) = sl_u.value; \
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} while (0)
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/*
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* A union which permits us to convert between a float and a 32 bit
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* int.
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*/
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typedef union
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{
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float value;
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/* FIXME: Assumes 32 bit int. */
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unsigned int word;
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} ieee_float_shape_type;
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/* Get a 32 bit int from a float. */
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#define GET_FLOAT_WORD(i,d) \
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do { \
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ieee_float_shape_type gf_u; \
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gf_u.value = (d); \
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(i) = gf_u.word; \
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} while (0)
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/* Set a float from a 32 bit int. */
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#define SET_FLOAT_WORD(d,i) \
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do { \
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ieee_float_shape_type sf_u; \
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sf_u.word = (i); \
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(d) = sf_u.value; \
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} while (0)
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/*
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* Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
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* double.
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*/
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#define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
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do { \
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union IEEEl2bits ew_u; \
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ew_u.e = (d); \
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(ix0) = ew_u.xbits.expsign; \
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(ix1) = ew_u.xbits.man; \
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} while (0)
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/*
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* Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
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* long double.
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*/
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#define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
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do { \
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union IEEEl2bits ew_u; \
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ew_u.e = (d); \
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(ix0) = ew_u.xbits.expsign; \
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(ix1) = ew_u.xbits.manh; \
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(ix2) = ew_u.xbits.manl; \
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} while (0)
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/* Get expsign as a 16 bit int from a long double. */
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#define GET_LDBL_EXPSIGN(i,d) \
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do { \
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union IEEEl2bits ge_u; \
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ge_u.e = (d); \
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(i) = ge_u.xbits.expsign; \
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} while (0)
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/*
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* Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
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* mantissa.
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*/
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#define INSERT_LDBL80_WORDS(d,ix0,ix1) \
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do { \
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union IEEEl2bits iw_u; \
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iw_u.xbits.expsign = (ix0); \
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iw_u.xbits.man = (ix1); \
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(d) = iw_u.e; \
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} while (0)
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/*
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* Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
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* comprising the mantissa.
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*/
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#define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
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do { \
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union IEEEl2bits iw_u; \
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iw_u.xbits.expsign = (ix0); \
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iw_u.xbits.manh = (ix1); \
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iw_u.xbits.manl = (ix2); \
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(d) = iw_u.e; \
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} while (0)
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/* Set expsign of a long double from a 16 bit int. */
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#define SET_LDBL_EXPSIGN(d,v) \
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do { \
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union IEEEl2bits se_u; \
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se_u.e = (d); \
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se_u.xbits.expsign = (v); \
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(d) = se_u.e; \
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} while (0)
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#ifdef __i386__
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/* Long double constants are broken on i386. */
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#define LD80C(m, ex, v) { \
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.xbits.man = __CONCAT(m, ULL), \
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.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
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}
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#else
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/* The above works on non-i386 too, but we use this to check v. */
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#define LD80C(m, ex, v) { .e = (v), }
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#endif
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#ifdef FLT_EVAL_METHOD
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/*
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* Attempt to get strict C99 semantics for assignment with non-C99 compilers.
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*/
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#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
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#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
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#else
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#define STRICT_ASSIGN(type, lval, rval) do { \
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volatile type __lval; \
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\
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if (sizeof(type) >= sizeof(long double)) \
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(lval) = (rval); \
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else { \
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__lval = (rval); \
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(lval) = __lval; \
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} \
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} while (0)
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#endif
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#endif /* FLT_EVAL_METHOD */
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/* Support switching the mode to FP_PE if necessary. */
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#if defined(__i386__) && !defined(NO_FPSETPREC)
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#define ENTERI() \
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long double __retval; \
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fp_prec_t __oprec; \
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\
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if ((__oprec = fpgetprec()) != FP_PE) \
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fpsetprec(FP_PE)
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#define RETURNI(x) do { \
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__retval = (x); \
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if (__oprec != FP_PE) \
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fpsetprec(__oprec); \
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RETURNF(__retval); \
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} while (0)
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#else
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#define ENTERI(x)
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#define RETURNI(x) RETURNF(x)
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#endif
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/* Default return statement if hack*_t() is not used. */
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#define RETURNF(v) return (v)
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/*
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* 2sum gives the same result as 2sumF without requiring |a| >= |b| or
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* a == 0, but is slower.
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*/
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#define _2sum(a, b) do { \
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__typeof(a) __s, __w; \
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\
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__w = (a) + (b); \
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__s = __w - (a); \
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(b) = ((a) - (__w - __s)) + ((b) - __s); \
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(a) = __w; \
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} while (0)
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/*
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* 2sumF algorithm.
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*
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* "Normalize" the terms in the infinite-precision expression a + b for
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* the sum of 2 floating point values so that b is as small as possible
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* relative to 'a'. (The resulting 'a' is the value of the expression in
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* the same precision as 'a' and the resulting b is the rounding error.)
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* |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
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* exponent overflow or underflow must not occur. This uses a Theorem of
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* Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
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* is apparently due to Skewchuk (1997).
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*
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* For this to always work, assignment of a + b to 'a' must not retain any
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* extra precision in a + b. This is required by C standards but broken
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* in many compilers. The brokenness cannot be worked around using
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* STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
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* algorithm would be destroyed by non-null strict assignments. (The
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* compilers are correct to be broken -- the efficiency of all floating
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* point code calculations would be destroyed similarly if they forced the
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* conversions.)
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*
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* Fortunately, a case that works well can usually be arranged by building
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* any extra precision into the type of 'a' -- 'a' should have type float_t,
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* double_t or long double. b's type should be no larger than 'a's type.
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* Callers should use these types with scopes as large as possible, to
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* reduce their own extra-precision and efficiciency problems. In
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* particular, they shouldn't convert back and forth just to call here.
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*/
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#ifdef DEBUG
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#define _2sumF(a, b) do { \
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__typeof(a) __w; \
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volatile __typeof(a) __ia, __ib, __r, __vw; \
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\
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__ia = (a); \
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__ib = (b); \
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assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
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\
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__w = (a) + (b); \
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(b) = ((a) - __w) + (b); \
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(a) = __w; \
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\
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/* The next 2 assertions are weak if (a) is already long double. */ \
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assert((long double)__ia + __ib == (long double)(a) + (b)); \
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__vw = __ia + __ib; \
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__r = __ia - __vw; \
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__r += __ib; \
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assert(__vw == (a) && __r == (b)); \
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} while (0)
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#else /* !DEBUG */
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#define _2sumF(a, b) do { \
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__typeof(a) __w; \
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\
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__w = (a) + (b); \
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(b) = ((a) - __w) + (b); \
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(a) = __w; \
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} while (0)
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#endif /* DEBUG */
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/*
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* Set x += c, where x is represented in extra precision as a + b.
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* x must be sufficiently normalized and sufficiently larger than c,
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* and the result is then sufficiently normalized.
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*
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* The details of ordering are that |a| must be >= |c| (so that (a, c)
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* can be normalized without extra work to swap 'a' with c). The details of
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* the normalization are that b must be small relative to the normalized 'a'.
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* Normalization of (a, c) makes the normalized c tiny relative to the
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* normalized a, so b remains small relative to 'a' in the result. However,
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* b need not ever be tiny relative to 'a'. For example, b might be about
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* 2**20 times smaller than 'a' to give about 20 extra bits of precision.
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* That is usually enough, and adding c (which by normalization is about
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* 2**53 times smaller than a) cannot change b significantly. However,
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* cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
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* significantly relative to b. The caller must ensure that significant
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* cancellation doesn't occur, either by having c of the same sign as 'a',
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* or by having |c| a few percent smaller than |a|. Pre-normalization of
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* (a, b) may help.
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*
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* This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
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* exercise 19). We gain considerable efficiency by requiring the terms to
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* be sufficiently normalized and sufficiently increasing.
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*/
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#define _3sumF(a, b, c) do { \
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__typeof(a) __tmp; \
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\
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__tmp = (c); \
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_2sumF(__tmp, (a)); \
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(b) += (a); \
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(a) = __tmp; \
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} while (0)
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/*
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* Common routine to process the arguments to nan(), nanf(), and nanl().
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*/
|
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void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
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#ifdef _COMPLEX_H
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/*
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* C99 specifies that complex numbers have the same representation as
|
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* an array of two elements, where the first element is the real part
|
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* and the second element is the imaginary part.
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*/
|
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typedef union {
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float complex f;
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float a[2];
|
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} float_complex;
|
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typedef union {
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double complex f;
|
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double a[2];
|
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} double_complex;
|
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typedef union {
|
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long double complex f;
|
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long double a[2];
|
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} long_double_complex;
|
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#define REALPART(z) ((z).a[0])
|
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#define IMAGPART(z) ((z).a[1])
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|
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/*
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* Inline functions that can be used to construct complex values.
|
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*
|
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* The C99 standard intends x+I*y to be used for this, but x+I*y is
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* currently unusable in general since gcc introduces many overflow,
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* underflow, sign and efficiency bugs by rewriting I*y as
|
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* (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
|
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* In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
|
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* to -0.0+I*0.0.
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*/
|
|
static __inline float complex
|
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cpackf(float x, float y)
|
|
{
|
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float_complex z;
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REALPART(z) = x;
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IMAGPART(z) = y;
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return (z.f);
|
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}
|
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|
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static __inline double complex
|
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cpack(double x, double y)
|
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{
|
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double_complex z;
|
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REALPART(z) = x;
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IMAGPART(z) = y;
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return (z.f);
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}
|
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|
|
static __inline long double complex
|
|
cpackl(long double x, long double y)
|
|
{
|
|
long_double_complex z;
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REALPART(z) = x;
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IMAGPART(z) = y;
|
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return (z.f);
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}
|
|
#endif /* _COMPLEX_H */
|
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|
|
#ifdef __GNUCLIKE_ASM
|
|
|
|
/* Asm versions of some functions. */
|
|
|
|
#ifdef __amd64__
|
|
static __inline int
|
|
irint(double x)
|
|
{
|
|
int n;
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|
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asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
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return (n);
|
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}
|
|
#define HAVE_EFFICIENT_IRINT
|
|
#endif
|
|
|
|
#ifdef __i386__
|
|
static __inline int
|
|
irint(double x)
|
|
{
|
|
int n;
|
|
|
|
asm("fistl %0" : "=m" (n) : "t" (x));
|
|
return (n);
|
|
}
|
|
#define HAVE_EFFICIENT_IRINT
|
|
#endif
|
|
|
|
#if defined(__amd64__) || defined(__i386__)
|
|
static __inline int
|
|
irintl(long double x)
|
|
{
|
|
int n;
|
|
|
|
asm("fistl %0" : "=m" (n) : "t" (x));
|
|
return (n);
|
|
}
|
|
#define HAVE_EFFICIENT_IRINTL
|
|
#endif
|
|
|
|
#endif /* __GNUCLIKE_ASM */
|
|
|
|
#ifdef DEBUG
|
|
#if defined(__amd64__) || defined(__i386__)
|
|
#define breakpoint() asm("int $3")
|
|
#else
|
|
#include <signal.h>
|
|
|
|
#define breakpoint() raise(SIGTRAP)
|
|
#endif
|
|
#endif
|
|
|
|
/* Write a pari script to test things externally. */
|
|
#ifdef DOPRINT
|
|
#include <stdio.h>
|
|
|
|
#ifndef DOPRINT_SWIZZLE
|
|
#define DOPRINT_SWIZZLE 0
|
|
#endif
|
|
|
|
#ifdef DOPRINT_LD80
|
|
|
|
#define DOPRINT_START(xp) do { \
|
|
uint64_t __lx; \
|
|
uint16_t __hx; \
|
|
\
|
|
/* Hack to give more-problematic args. */ \
|
|
EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
|
|
__lx ^= DOPRINT_SWIZZLE; \
|
|
INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
|
|
printf("x = %.21Lg; ", (long double)*xp); \
|
|
} while (0)
|
|
#define DOPRINT_END1(v) \
|
|
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
|
|
#define DOPRINT_END2(hi, lo) \
|
|
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
|
|
(long double)(hi), (long double)(lo))
|
|
|
|
#elif defined(DOPRINT_D64)
|
|
|
|
#define DOPRINT_START(xp) do { \
|
|
uint32_t __hx, __lx; \
|
|
\
|
|
EXTRACT_WORDS(__hx, __lx, *xp); \
|
|
__lx ^= DOPRINT_SWIZZLE; \
|
|
INSERT_WORDS(*xp, __hx, __lx); \
|
|
printf("x = %.21Lg; ", (long double)*xp); \
|
|
} while (0)
|
|
#define DOPRINT_END1(v) \
|
|
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
|
|
#define DOPRINT_END2(hi, lo) \
|
|
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
|
|
(long double)(hi), (long double)(lo))
|
|
|
|
#elif defined(DOPRINT_F32)
|
|
|
|
#define DOPRINT_START(xp) do { \
|
|
uint32_t __hx; \
|
|
\
|
|
GET_FLOAT_WORD(__hx, *xp); \
|
|
__hx ^= DOPRINT_SWIZZLE; \
|
|
SET_FLOAT_WORD(*xp, __hx); \
|
|
printf("x = %.21Lg; ", (long double)*xp); \
|
|
} while (0)
|
|
#define DOPRINT_END1(v) \
|
|
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
|
|
#define DOPRINT_END2(hi, lo) \
|
|
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
|
|
(long double)(hi), (long double)(lo))
|
|
|
|
#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
|
|
|
|
#ifndef DOPRINT_SWIZZLE_HIGH
|
|
#define DOPRINT_SWIZZLE_HIGH 0
|
|
#endif
|
|
|
|
#define DOPRINT_START(xp) do { \
|
|
uint64_t __lx, __llx; \
|
|
uint16_t __hx; \
|
|
\
|
|
EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
|
|
__llx ^= DOPRINT_SWIZZLE; \
|
|
__lx ^= DOPRINT_SWIZZLE_HIGH; \
|
|
INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
|
|
printf("x = %.36Lg; ", (long double)*xp); \
|
|
} while (0)
|
|
#define DOPRINT_END1(v) \
|
|
printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
|
|
#define DOPRINT_END2(hi, lo) \
|
|
printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
|
|
(long double)(hi), (long double)(lo))
|
|
|
|
#endif /* DOPRINT_LD80 */
|
|
|
|
#else /* !DOPRINT */
|
|
#define DOPRINT_START(xp)
|
|
#define DOPRINT_END1(v)
|
|
#define DOPRINT_END2(hi, lo)
|
|
#endif /* DOPRINT */
|
|
|
|
#define RETURNP(x) do { \
|
|
DOPRINT_END1(x); \
|
|
RETURNF(x); \
|
|
} while (0)
|
|
#define RETURNPI(x) do { \
|
|
DOPRINT_END1(x); \
|
|
RETURNI(x); \
|
|
} while (0)
|
|
#define RETURN2P(x, y) do { \
|
|
DOPRINT_END2((x), (y)); \
|
|
RETURNF((x) + (y)); \
|
|
} while (0)
|
|
#define RETURN2PI(x, y) do { \
|
|
DOPRINT_END2((x), (y)); \
|
|
RETURNI((x) + (y)); \
|
|
} while (0)
|
|
#ifdef STRUCT_RETURN
|
|
#define RETURNSP(rp) do { \
|
|
if (!(rp)->lo_set) \
|
|
RETURNP((rp)->hi); \
|
|
RETURN2P((rp)->hi, (rp)->lo); \
|
|
} while (0)
|
|
#define RETURNSPI(rp) do { \
|
|
if (!(rp)->lo_set) \
|
|
RETURNPI((rp)->hi); \
|
|
RETURN2PI((rp)->hi, (rp)->lo); \
|
|
} while (0)
|
|
#endif
|
|
#define SUM2P(x, y) ({ \
|
|
const __typeof (x) __x = (x); \
|
|
const __typeof (y) __y = (y); \
|
|
\
|
|
DOPRINT_END2(__x, __y); \
|
|
__x + __y; \
|
|
})
|
|
|
|
/*
|
|
* ieee style elementary functions
|
|
*
|
|
* We rename functions here to improve other sources' diffability
|
|
* against fdlibm.
|
|
*/
|
|
#define __ieee754_sqrt sqrt
|
|
#define __ieee754_acos acos
|
|
#define __ieee754_acosh acosh
|
|
#define __ieee754_log log
|
|
#define __ieee754_log2 log2
|
|
#define __ieee754_atanh atanh
|
|
#define __ieee754_asin asin
|
|
#define __ieee754_atan2 atan2
|
|
#define __ieee754_exp exp
|
|
#define __ieee754_cosh cosh
|
|
#define __ieee754_fmod fmod
|
|
#define __ieee754_pow pow
|
|
#define __ieee754_lgamma lgamma
|
|
#define __ieee754_gamma gamma
|
|
#define __ieee754_lgamma_r lgamma_r
|
|
#define __ieee754_gamma_r gamma_r
|
|
#define __ieee754_log10 log10
|
|
#define __ieee754_sinh sinh
|
|
#define __ieee754_hypot hypot
|
|
#define __ieee754_j0 j0
|
|
#define __ieee754_j1 j1
|
|
#define __ieee754_y0 y0
|
|
#define __ieee754_y1 y1
|
|
#define __ieee754_jn jn
|
|
#define __ieee754_yn yn
|
|
#define __ieee754_remainder remainder
|
|
#define __ieee754_scalb scalb
|
|
#define __ieee754_sqrtf sqrtf
|
|
#define __ieee754_acosf acosf
|
|
#define __ieee754_acoshf acoshf
|
|
#define __ieee754_logf logf
|
|
#define __ieee754_atanhf atanhf
|
|
#define __ieee754_asinf asinf
|
|
#define __ieee754_atan2f atan2f
|
|
#define __ieee754_expf expf
|
|
#define __ieee754_coshf coshf
|
|
#define __ieee754_fmodf fmodf
|
|
#define __ieee754_powf powf
|
|
#define __ieee754_lgammaf lgammaf
|
|
#define __ieee754_gammaf gammaf
|
|
#define __ieee754_lgammaf_r lgammaf_r
|
|
#define __ieee754_gammaf_r gammaf_r
|
|
#define __ieee754_log10f log10f
|
|
#define __ieee754_log2f log2f
|
|
#define __ieee754_sinhf sinhf
|
|
#define __ieee754_hypotf hypotf
|
|
#define __ieee754_j0f j0f
|
|
#define __ieee754_j1f j1f
|
|
#define __ieee754_y0f y0f
|
|
#define __ieee754_y1f y1f
|
|
#define __ieee754_jnf jnf
|
|
#define __ieee754_ynf ynf
|
|
#define __ieee754_remainderf remainderf
|
|
#define __ieee754_scalbf scalbf
|
|
|
|
/* fdlibm kernel function */
|
|
int __kernel_rem_pio2(double*,double*,int,int,int);
|
|
|
|
/* double precision kernel functions */
|
|
#ifndef INLINE_REM_PIO2
|
|
int __ieee754_rem_pio2(double,double*);
|
|
#endif
|
|
double __kernel_sin(double,double,int);
|
|
double __kernel_cos(double,double);
|
|
double __kernel_tan(double,double,int);
|
|
double __ldexp_exp(double,int);
|
|
#ifdef _COMPLEX_H
|
|
double complex __ldexp_cexp(double complex,int);
|
|
#endif
|
|
|
|
/* float precision kernel functions */
|
|
#ifndef INLINE_REM_PIO2F
|
|
int __ieee754_rem_pio2f(float,double*);
|
|
#endif
|
|
#ifndef INLINE_KERNEL_SINDF
|
|
float __kernel_sindf(double);
|
|
#endif
|
|
#ifndef INLINE_KERNEL_COSDF
|
|
float __kernel_cosdf(double);
|
|
#endif
|
|
#ifndef INLINE_KERNEL_TANDF
|
|
float __kernel_tandf(double,int);
|
|
#endif
|
|
float __ldexp_expf(float,int);
|
|
#ifdef _COMPLEX_H
|
|
float complex __ldexp_cexpf(float complex,int);
|
|
#endif
|
|
|
|
/* long double precision kernel functions */
|
|
long double __kernel_sinl(long double, long double, int);
|
|
long double __kernel_cosl(long double, long double);
|
|
long double __kernel_tanl(long double, long double, int);
|
|
|
|
#endif /* !_MATH_PRIVATE_H_ */ |