0,0 → 1,121 |
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/* @(#)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. |
* ==================================================== |
*/ |
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/* __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. |
* |
*/ |
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#include "fdlibm.h" |
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#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 */ |
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#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; |
} |
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#endif /* defined(_DOUBLE_IS_32BITS) */ |