/** @file | |
Compute acos(x) using ieee FP math. | |
Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR> | |
This program and the accompanying materials are licensed and made available under | |
the terms and conditions of the BSD License that accompanies this distribution. | |
The full text of the license may be found at | |
http://opensource.org/licenses/bsd-license. | |
THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, | |
WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED. | |
* ==================================================== | |
* 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. | |
* ==================================================== | |
e_acos.c 5.1 93/09/24 | |
NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp | |
*/ | |
#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ | |
// Keep older compilers quiet about floating-point divide-by-zero | |
#pragma warning ( disable : 4723 ) | |
#endif | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
/* __ieee754_acos(x) | |
* Method : | |
* acos(x) = pi/2 - asin(x) | |
* acos(-x) = pi/2 + asin(x) | |
* For |x|<=0.5 | |
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) | |
* For x>0.5 | |
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) | |
* = 2asin(sqrt((1-x)/2)) | |
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) | |
* = 2f + (2c + 2s*z*R(z)) | |
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term | |
* for f so that f+c ~ sqrt(z). | |
* For x<-0.5 | |
* acos(x) = pi - 2asin(sqrt((1-|x|)/2)) | |
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) | |
* | |
* Special cases: | |
* if x is NaN, return x itself; | |
* if |x|>1, return NaN with invalid signal. | |
* | |
* Function needed: __ieee754_sqrt | |
*/ | |
#include "math.h" | |
#include "math_private.h" | |
static const double | |
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ | |
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ | |
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ | |
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ | |
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_acos(double x) | |
{ | |
double z,p,q,r,w,s,c,df; | |
int32_t hx,ix; | |
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) { /* |x|==1 */ | |
if(hx>0) return 0.0; /* acos(1) = 0 */ | |
else return pi+2.0*pio2_lo; /* acos(-1)= pi */ | |
} | |
return (x-x)/(x-x); /* acos(|x|>1) is NaN */ | |
} | |
if(ix<0x3fe00000) { /* |x| < 0.5 */ | |
if(ix<=0x3c600000) return pio2_hi+pio2_lo; /*if|x|<2**-57*/ | |
z = x*x; | |
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
r = p/q; | |
return pio2_hi - (x - (pio2_lo-x*r)); | |
} | |
else if (hx<0) { /* x < -0.5 */ | |
z = (one+x)*0.5; | |
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
s = __ieee754_sqrt(z); | |
r = p/q; | |
w = r*s-pio2_lo; | |
return pi - 2.0*(s+w); | |
} | |
else { /* x > 0.5 */ | |
z = (one-x)*0.5; | |
s = __ieee754_sqrt(z); | |
df = s; | |
SET_LOW_WORD(df,0); | |
c = (z-df*df)/(s+df); | |
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
r = p/q; | |
w = r*s+c; | |
return 2.0*(df+w); | |
} | |
} |