2aa62f2bc9
This set of three packages: AppPkg, StdLib, StdLibPrivateInternalFiles; contains the implementation of libraries based upon non-UEFI standards such as ISO/IEC-9899, the library portion of the C Language Standard, POSIX, etc. AppPkg contains applications that make use of the standard libraries defined in the StdLib Package. StdLib contains header (include) files and the implementations of the standard libraries. StdLibPrivateInternalFiles contains files for the exclusive use of the library implementations in StdLib. These files should never be directly referenced from applications or other code. git-svn-id: https://edk2.svn.sourceforge.net/svnroot/edk2/trunk/edk2@11600 6f19259b-4bc3-4df7-8a09-765794883524
121 lines
3.9 KiB
C
121 lines
3.9 KiB
C
/* @(#)e_asin.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <LibConfig.h>
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#include <sys/EfiCdefs.h>
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#if defined(LIBM_SCCS) && !defined(lint)
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__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
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#endif
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#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
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// C4723: potential divide by zero.
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#pragma warning ( disable : 4723 )
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#endif
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/* __ieee754_asin(x)
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* Method :
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* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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* we approximate asin(x) on [0,0.5] by
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* asin(x) = x + x*x^2*R(x^2)
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* where
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* R(x^2) is a rational approximation of (asin(x)-x)/x^3
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* and its remez error is bounded by
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* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
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*
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* For x in [0.5,1]
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* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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* then for x>0.98
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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* For x<=0.98, let pio4_hi = pio2_hi/2, then
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* f = hi part of s;
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* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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* and
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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*/
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#include "math.h"
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#include "math_private.h"
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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huge = 1.000e+300,
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pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
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pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
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pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
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/* coefficient for R(x^2) */
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pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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double
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__ieee754_asin(double x)
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{
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double t,w,p,q,c,r,s;
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int32_t hx,ix;
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t = 0;
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GET_HIGH_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix>= 0x3ff00000) { /* |x|>= 1 */
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u_int32_t lx;
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GET_LOW_WORD(lx,x);
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if(((ix-0x3ff00000)|lx)==0)
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/* asin(1)=+-pi/2 with inexact */
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return x*pio2_hi+x*pio2_lo;
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return (x-x)/(x-x); /* asin(|x|>1) is NaN */
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} else if (ix<0x3fe00000) { /* |x|<0.5 */
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if(ix<0x3e400000) { /* if |x| < 2**-27 */
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if(huge+x>one) return x;/* return x with inexact if x!=0*/
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} else
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t = x*x;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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w = p/q;
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return x+x*w;
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}
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/* 1> |x|>= 0.5 */
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w = one-fabs(x);
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t = w*0.5;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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s = __ieee754_sqrt(t);
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if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
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w = p/q;
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t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
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} else {
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w = s;
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SET_LOW_WORD(w,0);
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c = (t-w*w)/(s+w);
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r = p/q;
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p = 2.0*s*r-(pio2_lo-2.0*c);
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q = pio4_hi-2.0*w;
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t = pio4_hi-(p-q);
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}
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if(hx>0) return t; else return -t;
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}
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