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
__ieee754_acos(double x)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