StdLib/LibC/Math/e_acos.c

   1 /** @file
   2   Compute acos(x) using ieee FP math.
   3
   4   Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
   5   This program and the accompanying materials are licensed and made available under
   6   the terms and conditions of the BSD License that accompanies this distribution.
   7   The full text of the license may be found at
   8   http://opensource.org/licenses/bsd-license.
   9
  10   THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
  11   WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
  12
  13  * ====================================================
  14  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  15  *
  16  * Developed at SunPro, a Sun Microsystems, Inc. business.
  17  * Permission to use, copy, modify, and distribute this
  18  * software is freely granted, provided that this notice
  19  * is preserved.
  20  * ====================================================
  21
  22   e_acos.c 5.1 93/09/24
  23   NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp
  24  */
  25 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  26   // Keep older compilers quiet about floating-point divide-by-zero
  27   #pragma warning ( disable : 4723 )
  28 #endif
  29
  30 #include  <LibConfig.h>
  31 #include  <sys/EfiCdefs.h>
  32
  33 /* __ieee754_acos(x)
  34  * Method :
  35  *  acos(x)  = pi/2 - asin(x)
  36  *  acos(-x) = pi/2 + asin(x)
  37  * For |x|<=0.5
  38  *  acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
  39  * For x>0.5
  40  *  acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  41  *    = 2asin(sqrt((1-x)/2))
  42  *    = 2s + 2s*z*R(z)  ...z=(1-x)/2, s=sqrt(z)
  43  *    = 2f + (2c + 2s*z*R(z))
  44  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  45  *     for f so that f+c ~ sqrt(z).
  46  * For x<-0.5
  47  *  acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  48  *    = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  49  *
  50  * Special cases:
  51  *  if x is NaN, return x itself;
  52  *  if |x|>1, return NaN with invalid signal.
  53  *
  54  * Function needed: __ieee754_sqrt
  55  */
  56
  57 #include "math.h"
  58 #include "math_private.h"
  59
  60 static const double
  61 one     =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  62 pi      =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  63 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
  64 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
  65 pS0     =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
  66 pS1     = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  67 pS2     =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
  68 pS3     = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  69 pS4     =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  70 pS5     =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
  71 qS1     = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  72 qS2     =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
  73 qS3     = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  74 qS4     =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
  75
  76 double
  77 __ieee754_acos(double x)
  78 {
  79   double z,p,q,r,w,s,c,df;
  80   int32_t hx,ix;
  81   GET_HIGH_WORD(hx,x);
  82   ix = hx&0x7fffffff;
  83   if(ix>=0x3ff00000) {  /* |x| >= 1 */
  84     u_int32_t lx;
  85
  86     GET_LOW_WORD(lx,x);
  87     if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
  88       if(hx>0)  return 0.0;             /* acos(1) = 0  */
  89       else      return pi+2.0*pio2_lo;  /* acos(-1)= pi */
  90     }
  91     return (x-x)/(x-x);   /* acos(|x|>1) is NaN */
  92   }
  93   if(ix<0x3fe00000) { /* |x| < 0.5 */
  94     if(ix<=0x3c600000) return pio2_hi+pio2_lo;  /*if|x|<2**-57*/
  95     z = x*x;
  96     p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  97     q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  98     r = p/q;
  99     return pio2_hi - (x - (pio2_lo-x*r));
 100   }
 101   else  if (hx<0) {   /* x < -0.5 */
 102     z = (one+x)*0.5;
 103     p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
 104     q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
 105     s = __ieee754_sqrt(z);
 106     r = p/q;
 107     w = r*s-pio2_lo;
 108     return pi - 2.0*(s+w);
 109   }
 110   else {      /* x > 0.5 */
 111     z = (one-x)*0.5;
 112     s = __ieee754_sqrt(z);
 113     df = s;
 114     SET_LOW_WORD(df,0);
 115     c  = (z-df*df)/(s+df);
 116     p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
 117     q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
 118     r = p/q;
 119     w = r*s+c;
 120     return 2.0*(df+w);
 121   }
 122 }