Fix a bug about the iSCSI DHCP dependency issue.

[mirror_edk2.git] / StdLib / LibC / Math / e_asin.c

/* @(#)e_asin.c 5.1 93/09/24 */\r
/*\r
 * ====================================================\r
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r
 *\r
 * Developed at SunPro, a Sun Microsystems, Inc. business.\r
 * Permission to use, copy, modify, and distribute this\r
 * software is freely granted, provided that this notice\r
 * is preserved.\r
 * ====================================================\r
 */\r
#include  <LibConfig.h>\r
#include  <sys/EfiCdefs.h>\r
#if defined(LIBM_SCCS) && !defined(lint)\r
__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");\r
#endif\r
\r
#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */\r
// C4723: potential divide by zero.\r
#pragma warning ( disable : 4723 )\r
#endif\r
\r
/* __ieee754_asin(x)\r
 * Method :\r
 *  Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...\r
 *  we approximate asin(x) on [0,0.5] by\r
 *    asin(x) = x + x*x^2*R(x^2)\r
 *  where\r
 *    R(x^2) is a rational approximation of (asin(x)-x)/x^3\r
 *  and its remez error is bounded by\r
 *    |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)\r
 *\r
 *  For x in [0.5,1]\r
 *    asin(x) = pi/2-2*asin(sqrt((1-x)/2))\r
 *  Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;\r
 *  then for x>0.98\r
 *    asin(x) = pi/2 - 2*(s+s*z*R(z))\r
 *      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)\r
 *  For x<=0.98, let pio4_hi = pio2_hi/2, then\r
 *    f = hi part of s;\r
 *    c = sqrt(z) - f = (z-f*f)/(s+f)   ...f+c=sqrt(z)\r
 *  and\r
 *    asin(x) = pi/2 - 2*(s+s*z*R(z))\r
 *      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)\r
 *      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))\r
 *\r
 * Special cases:\r
 *  if x is NaN, return x itself;\r
 *  if |x|>1, return NaN with invalid signal.\r
 *\r
 */\r
\r
\r
#include "math.h"\r
#include "math_private.h"\r
\r
static const double\r
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */\r
huge =  1.000e+300,\r
pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */\r
pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */\r
pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */\r
  /* coefficient for R(x^2) */\r
pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */\r
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */\r
pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */\r
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */\r
pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */\r
pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */\r
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */\r
qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */\r
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */\r
qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */\r
\r
double\r
__ieee754_asin(double x)\r
{\r
  double t,w,p,q,c,r,s;\r
  int32_t hx,ix;\r
\r
  t = 0;\r
  GET_HIGH_WORD(hx,x);\r
  ix = hx&0x7fffffff;\r
  if(ix>= 0x3ff00000) {   /* |x|>= 1 */\r
      u_int32_t lx;\r
      GET_LOW_WORD(lx,x);\r
      if(((ix-0x3ff00000)|lx)==0)\r
        /* asin(1)=+-pi/2 with inexact */\r
    return x*pio2_hi+x*pio2_lo;\r
      return (x-x)/(x-x);   /* asin(|x|>1) is NaN */\r
  } else if (ix<0x3fe00000) { /* |x|<0.5 */\r
      if(ix<0x3e400000) {   /* if |x| < 2**-27 */\r
    if(huge+x>one) return x;/* return x with inexact if x!=0*/\r
      } else\r
    t = x*x;\r
    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));\r
    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));\r
    w = p/q;\r
    return x+x*w;\r
  }\r
  /* 1> |x|>= 0.5 */\r
  w = one-fabs(x);\r
  t = w*0.5;\r
  p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));\r
  q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));\r
  s = __ieee754_sqrt(t);\r
  if(ix>=0x3FEF3333) {  /* if |x| > 0.975 */\r
      w = p/q;\r
      t = pio2_hi-(2.0*(s+s*w)-pio2_lo);\r
  } else {\r
      w  = s;\r
      SET_LOW_WORD(w,0);\r
      c  = (t-w*w)/(s+w);\r
      r  = p/q;\r
      p  = 2.0*s*r-(pio2_lo-2.0*c);\r
      q  = pio4_hi-2.0*w;\r
      t  = pio4_hi-(p-q);\r
  }\r
  if(hx>0) return t; else return -t;\r
}\r