/* @(#)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. | |
* ==================================================== | |
*/ | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
#if defined(LIBM_SCCS) && !defined(lint) | |
__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $"); | |
#endif | |
#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ | |
// C4723: potential divide by zero. | |
#pragma warning ( disable : 4723 ) | |
#endif | |
/* __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 "math.h" | |
#include "math_private.h" | |
static const double | |
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 */ | |
double | |
__ieee754_asin(double x) | |
{ | |
double t,w,p,q,c,r,s; | |
int32_t hx,ix; | |
t = 0; | |
GET_HIGH_WORD(hx,x); | |
ix = hx&0x7fffffff; | |
if(ix>= 0x3ff00000) { /* |x|>= 1 */ | |
u_int32_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; | |
} |