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
60static const double
61one     =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
62pi      =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
63pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
64pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
65pS0     =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
66pS1     = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
67pS2     =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
68pS3     = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
69pS4     =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
70pS5     =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
71qS1     = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
72qS2     =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
73qS3     = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
74qS4     =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
75
76double
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}
123