-
-/* @(#)e_asin.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __ieee754_asin(x)
- * Method :
- * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
- * we approximate asin(x) on [0,0.5] by
- * asin(x) = x + x*x^2*R(x^2)
- * where
- * R(x^2) is a rational approximation of (asin(x)-x)/x^3
- * and its remez error is bounded by
- * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
- *
- * For x in [0.5,1]
- * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
- * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
- * then for x>0.98
- * asin(x) = pi/2 - 2*(s+s*z*R(z))
- * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
- * For x<=0.98, let pio4_hi = pio2_hi/2, then
- * f = hi part of s;
- * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
- * and
- * asin(x) = pi/2 - 2*(s+s*z*R(z))
- * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
- * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
- *
- * Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN with invalid signal.
- *
- */
-
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
-huge = 1.000e+300,
-pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
-pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
-pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
- /* coefficient for R(x^2) */
-pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
-pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
-pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
-pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
-pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
-pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
-qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
-qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
-qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
-qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
-
-#ifdef __STDC__
- double __ieee754_asin(double x)
-#else
- double __ieee754_asin(x)
- double x;
-#endif
-{
- double t,w,p,q,c,r,s;
- __int32_t hx,ix;
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>= 0x3ff00000) { /* |x|>= 1 */
- __uint32_t lx;
- GET_LOW_WORD(lx,x);
- if(((ix-0x3ff00000)|lx)==0)
- /* asin(1)=+-pi/2 with inexact */
- return x*pio2_hi+x*pio2_lo;
- return (x-x)/(x-x); /* asin(|x|>1) is NaN */
- } else if (ix<0x3fe00000) { /* |x|<0.5 */
- if(ix<0x3e400000) { /* if |x| < 2**-27 */
- if(huge+x>one) return x;/* return x with inexact if x!=0*/
- } else
- t = x*x;
- p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
- q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
- w = p/q;
- return x+x*w;
- }
- /* 1> |x|>= 0.5 */
- w = one-fabs(x);
- t = w*0.5;
- p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
- q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
- s = __ieee754_sqrt(t);
- if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
- w = p/q;
- t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
- } else {
- w = s;
- SET_LOW_WORD(w,0);
- c = (t-w*w)/(s+w);
- r = p/q;
- p = 2.0*s*r-(pio2_lo-2.0*c);
- q = pio4_hi-2.0*w;
- t = pio4_hi-(p-q);
- }
- if(hx>0) return t; else return -t;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ int32_t hx,ix;
+ uint32_t lx;
-
-/* @(#)fdlibm.h 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-#include <config.h>
-#include <stdlib.h>
-
-/* CYGNUS LOCAL: Include files. */
-#include "ieeefp.h"
-
-/* CYGNUS LOCAL: Default to XOPEN_MODE. */
-#define _XOPEN_MODE
-
-#ifdef __STDC__
-#define __P(p) p
-#else
-#define __P(p) ()
-#endif
-
-#define HUGE ((float)3.40282346638528860e+38)
-
-/*
- * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
- * (one may replace the following line by "#include <values.h>")
- */
-
-#define X_TLOSS 1.41484755040568800000e+16
-
-/* These typedefs are true for the targets running Java. */
-
-#ifndef HAVE_INT32_DEFINED
-typedef int __int32_t;
-typedef unsigned int __uint32_t;
-#endif
-
-#define _IEEE_LIBM
-
-/*
- * ANSI/POSIX
- */
-extern double acos __P((double));
-extern double asin __P((double));
-extern double atan __P((double));
-extern double atan2 __P((double, double));
-extern double cos __P((double));
-extern double sin __P((double));
-extern double tan __P((double));
-
-extern double cosh __P((double));
-extern double sinh __P((double));
-extern double tanh __P((double));
-
-extern double exp __P((double));
-extern double frexp __P((double, int *));
-extern double ldexp __P((double, int));
-extern double log __P((double));
-extern double log10 __P((double));
-extern double modf __P((double, double *));
-
-extern double pow __P((double, double));
-extern double sqrt __P((double));
-
-extern double ceil __P((double));
-extern double fabs __P((double));
-extern double floor __P((double));
-extern double fmod __P((double, double));
-
-extern double erf __P((double));
-extern double erfc __P((double));
-extern double gamma __P((double));
-extern double hypot __P((double, double));
-extern int isnan __P((double));
-extern int finite __P((double));
-extern double j0 __P((double));
-extern double j1 __P((double));
-extern double jn __P((int, double));
-extern double lgamma __P((double));
-extern double y0 __P((double));
-extern double y1 __P((double));
-extern double yn __P((int, double));
-
-extern double acosh __P((double));
-extern double asinh __P((double));
-extern double atanh __P((double));
-extern double cbrt __P((double));
-extern double logb __P((double));
-extern double nextafter __P((double, double));
-extern double remainder __P((double, double));
-
-/* Functions that are not documented, and are not in <math.h>. */
-
-extern double logb __P((double));
-#ifdef _SCALB_INT
-extern double scalb __P((double, int));
-#else
-extern double scalb __P((double, double));
-#endif
-extern double significand __P((double));
-
-/* ieee style elementary functions */
-extern double __ieee754_sqrt __P((double));
-extern double __ieee754_acos __P((double));
-extern double __ieee754_acosh __P((double));
-extern double __ieee754_log __P((double));
-extern double __ieee754_atanh __P((double));
-extern double __ieee754_asin __P((double));
-extern double __ieee754_atan2 __P((double,double));
-extern double __ieee754_exp __P((double));
-extern double __ieee754_cosh __P((double));
-extern double __ieee754_fmod __P((double,double));
-extern double __ieee754_pow __P((double,double));
-extern double __ieee754_lgamma_r __P((double,int *));
-extern double __ieee754_gamma_r __P((double,int *));
-extern double __ieee754_log10 __P((double));
-extern double __ieee754_sinh __P((double));
-extern double __ieee754_hypot __P((double,double));
-extern double __ieee754_j0 __P((double));
-extern double __ieee754_j1 __P((double));
-extern double __ieee754_y0 __P((double));
-extern double __ieee754_y1 __P((double));
-extern double __ieee754_jn __P((int,double));
-extern double __ieee754_yn __P((int,double));
-extern double __ieee754_remainder __P((double,double));
-extern __int32_t __ieee754_rem_pio2 __P((double,double*));
-#ifdef _SCALB_INT
-extern double __ieee754_scalb __P((double,int));
-#else
-extern double __ieee754_scalb __P((double,double));
-#endif
-
-/* fdlibm kernel function */
-extern double __kernel_standard __P((double,double,int));
-extern double __kernel_sin __P((double,double,int));
-extern double __kernel_cos __P((double,double));
-extern double __kernel_tan __P((double,double,int));
-extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*));
-
-/* Undocumented float functions. */
-extern float logbf __P((float));
-#ifdef _SCALB_INT
-extern float scalbf __P((float, int));
-#else
-extern float scalbf __P((float, float));
-#endif
-extern float significandf __P((float));
-
-/*
- * Functions callable from C, intended to support IEEE arithmetic.
- */
-extern double copysign __P((double, double));
-extern int ilogb __P((double));
-extern double rint __P((double));
-extern float rintf __P((float));
-extern double scalbn __P((double, int));
-
-/* ieee style elementary float functions */
-extern float __ieee754_sqrtf __P((float));
-extern float __ieee754_acosf __P((float));
-extern float __ieee754_acoshf __P((float));
-extern float __ieee754_logf __P((float));
-extern float __ieee754_atanhf __P((float));
-extern float __ieee754_asinf __P((float));
-extern float __ieee754_atan2f __P((float,float));
-extern float __ieee754_expf __P((float));
-extern float __ieee754_coshf __P((float));
-extern float __ieee754_fmodf __P((float,float));
-extern float __ieee754_powf __P((float,float));
-extern float __ieee754_lgammaf_r __P((float,int *));
-extern float __ieee754_gammaf_r __P((float,int *));
-extern float __ieee754_log10f __P((float));
-extern float __ieee754_sinhf __P((float));
-extern float __ieee754_hypotf __P((float,float));
-extern float __ieee754_j0f __P((float));
-extern float __ieee754_j1f __P((float));
-extern float __ieee754_y0f __P((float));
-extern float __ieee754_y1f __P((float));
-extern float __ieee754_jnf __P((int,float));
-extern float __ieee754_ynf __P((int,float));
-extern float __ieee754_remainderf __P((float,float));
-extern __int32_t __ieee754_rem_pio2f __P((float,float*));
-#ifdef _SCALB_INT
-extern float __ieee754_scalbf __P((float,int));
-#else
-extern float __ieee754_scalbf __P((float,float));
-#endif
-
-/* float versions of fdlibm kernel functions */
-extern float __kernel_sinf __P((float,float,int));
-extern float __kernel_cosf __P((float,float));
-extern float __kernel_tanf __P((float,float,int));
-extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*));
-
-/* The original code used statements like
- n0 = ((*(int*)&one)>>29)^1; * index of high word *
- ix0 = *(n0+(int*)&x); * high word of x *
- ix1 = *((1-n0)+(int*)&x); * low word of x *
- to dig two 32 bit words out of the 64 bit IEEE floating point
- value. That is non-ANSI, and, moreover, the gcc instruction
- scheduler gets it wrong. We instead use the following macros.
- Unlike the original code, we determine the endianness at compile
- time, not at run time; I don't see much benefit to selecting
- endianness at run time. */
-
-#ifndef __IEEE_BIG_ENDIAN
-#ifndef __IEEE_LITTLE_ENDIAN
- #error Must define endianness
-#endif
-#endif
-
-/* A union which permits us to convert between a double and two 32 bit
- ints. */
-
-#ifdef __IEEE_BIG_ENDIAN
-
-typedef union
-{
- double value;
- struct
- {
- __uint32_t msw;
- __uint32_t lsw;
- } parts;
-} ieee_double_shape_type;
-
-#endif
-
-#ifdef __IEEE_LITTLE_ENDIAN
-
-typedef union
-{
- double value;
- struct
- {
- __uint32_t lsw;
- __uint32_t msw;
- } parts;
-} ieee_double_shape_type;
-
-#endif
-
-/* Get two 32 bit ints from a double. */
-
-#define EXTRACT_WORDS(ix0,ix1,d) \
-do { \
- ieee_double_shape_type ew_u; \
- ew_u.value = (d); \
- (ix0) = ew_u.parts.msw; \
- (ix1) = ew_u.parts.lsw; \
-} while (0)
-
-/* Get the more significant 32 bit int from a double. */
-
-#define GET_HIGH_WORD(i,d) \
-do { \
- ieee_double_shape_type gh_u; \
- gh_u.value = (d); \
- (i) = gh_u.parts.msw; \
-} while (0)
-
-/* Get the less significant 32 bit int from a double. */
-
-#define GET_LOW_WORD(i,d) \
-do { \
- ieee_double_shape_type gl_u; \
- gl_u.value = (d); \
- (i) = gl_u.parts.lsw; \
-} while (0)
-
-/* Set a double from two 32 bit ints. */
-
-#define INSERT_WORDS(d,ix0,ix1) \
-do { \
- ieee_double_shape_type iw_u; \
- iw_u.parts.msw = (ix0); \
- iw_u.parts.lsw = (ix1); \
- (d) = iw_u.value; \
-} while (0)
-
-/* Set the more significant 32 bits of a double from an int. */
-
-#define SET_HIGH_WORD(d,v) \
-do { \
- ieee_double_shape_type sh_u; \
- sh_u.value = (d); \
- sh_u.parts.msw = (v); \
- (d) = sh_u.value; \
-} while (0)
-
-/* Set the less significant 32 bits of a double from an int. */
-
-#define SET_LOW_WORD(d,v) \
-do { \
- ieee_double_shape_type sl_u; \
- sl_u.value = (d); \
- sl_u.parts.lsw = (v); \
- (d) = sl_u.value; \
-} while (0)
-
-/* A union which permits us to convert between a float and a 32 bit
- int. */
-
-typedef union
-{
- float value;
- __uint32_t word;
-} ieee_float_shape_type;
-
-/* Get a 32 bit int from a float. */
-
-#define GET_FLOAT_WORD(i,d) \
-do { \
- ieee_float_shape_type gf_u; \
- gf_u.value = (d); \
- (i) = gf_u.word; \
-} while (0)
-
-/* Set a float from a 32 bit int. */
-
-#define SET_FLOAT_WORD(d,i) \
-do { \
- ieee_float_shape_type sf_u; \
- sf_u.word = (i); \
- (d) = sf_u.value; \
-} while (0)
-
-#ifdef __cplusplus
-}
-#endif
-
+#include "mprec.h"
+
+#ifndef HUGE
+#endif
+extern int32_t __ieee754_rem_pio2 __P((double,double*));
+extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int32_t*));
+extern int32_t __ieee754_rem_pio2f __P((float,float*));
+extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int32_t*));
+ uint32_t msw;
+ uint32_t lsw;
+ uint32_t lsw;
+ uint32_t msw;
+ uint32_t word;
projects / thirdparty / gcc.git / commitdiff
