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EDK2 doxygen online documents - Firmware Encoding Index

StdLib/LibC/Math/e_asin.c

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00001 /* @(#)e_asin.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice
00009  * is preserved.
00010  * ====================================================
00011  */
00012 #include  <LibConfig.h>
00013 #include  <sys/EfiCdefs.h>
00014 #if defined(LIBM_SCCS) && !defined(lint)
00015 __RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
00016 #endif
00017 
00018 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
00019 // C4723: potential divide by zero.
00020 #pragma warning ( disable : 4723 )
00021 #endif
00022 
00023 /* __ieee754_asin(x)
00024  * Method :
00025  *  Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
00026  *  we approximate asin(x) on [0,0.5] by
00027  *    asin(x) = x + x*x^2*R(x^2)
00028  *  where
00029  *    R(x^2) is a rational approximation of (asin(x)-x)/x^3
00030  *  and its remez error is bounded by
00031  *    |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
00032  *
00033  *  For x in [0.5,1]
00034  *    asin(x) = pi/2-2*asin(sqrt((1-x)/2))
00035  *  Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
00036  *  then for x>0.98
00037  *    asin(x) = pi/2 - 2*(s+s*z*R(z))
00038  *      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
00039  *  For x<=0.98, let pio4_hi = pio2_hi/2, then
00040  *    f = hi part of s;
00041  *    c = sqrt(z) - f = (z-f*f)/(s+f)   ...f+c=sqrt(z)
00042  *  and
00043  *    asin(x) = pi/2 - 2*(s+s*z*R(z))
00044  *      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
00045  *      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
00046  *
00047  * Special cases:
00048  *  if x is NaN, return x itself;
00049  *  if |x|>1, return NaN with invalid signal.
00050  *
00051  */
00052 
00053 
00054 #include "math.h"
00055 #include "math_private.h"
00056 
00057 static const double
00058 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
00059 huge =  1.000e+300,
00060 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
00061 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
00062 pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
00063   /* coefficient for R(x^2) */
00064 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
00065 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
00066 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
00067 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
00068 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
00069 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
00070 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
00071 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
00072 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
00073 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
00074 
00075 double
00076 __ieee754_asin(double x)
00077 {
00078   double t,w,p,q,c,r,s;
00079   int32_t hx,ix;
00080 
00081   t = 0;
00082   GET_HIGH_WORD(hx,x);
00083   ix = hx&0x7fffffff;
00084   if(ix>= 0x3ff00000) {   /* |x|>= 1 */
00085       u_int32_t lx;
00086       GET_LOW_WORD(lx,x);
00087       if(((ix-0x3ff00000)|lx)==0)
00088         /* asin(1)=+-pi/2 with inexact */
00089     return x*pio2_hi+x*pio2_lo;
00090       return (x-x)/(x-x);   /* asin(|x|>1) is NaN */
00091   } else if (ix<0x3fe00000) { /* |x|<0.5 */
00092       if(ix<0x3e400000) {   /* if |x| < 2**-27 */
00093     if(huge+x>one) return x;/* return x with inexact if x!=0*/
00094       } else
00095     t = x*x;
00096     p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
00097     q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
00098     w = p/q;
00099     return x+x*w;
00100   }
00101   /* 1> |x|>= 0.5 */
00102   w = one-fabs(x);
00103   t = w*0.5;
00104   p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
00105   q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
00106   s = __ieee754_sqrt(t);
00107   if(ix>=0x3FEF3333) {  /* if |x| > 0.975 */
00108       w = p/q;
00109       t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
00110   } else {
00111       w  = s;
00112       SET_LOW_WORD(w,0);
00113       c  = (t-w*w)/(s+w);
00114       r  = p/q;
00115       p  = 2.0*s*r-(pio2_lo-2.0*c);
00116       q  = pio4_hi-2.0*w;
00117       t  = pio4_hi-(p-q);
00118   }
00119   if(hx>0) return t; else return -t;
00120 }
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