fdisk - Use heads = 255 on file images
[dragonfly.git] / lib / libm / src / e_acos.c
blob685a94e5c4decc1a6c37d8558d72eb0e5cf9258b
1 /* @(#)e_acos.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
12 * $NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp $
13 * $DragonFly: src/lib/libm/src/e_acos.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
16 /* acos(x)
17 * Method :
18 * acos(x) = pi/2 - asin(x)
19 * acos(-x) = pi/2 + asin(x)
20 * For |x|<=0.5
21 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
22 * For x>0.5
23 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
24 * = 2asin(sqrt((1-x)/2))
25 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
26 * = 2f + (2c + 2s*z*R(z))
27 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
28 * for f so that f+c ~ sqrt(z).
29 * For x<-0.5
30 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
31 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
33 * Special cases:
34 * if x is NaN, return x itself;
35 * if |x|>1, return NaN with invalid signal.
37 * Function needed: sqrt
40 #include <math.h>
41 #include "math_private.h"
43 static const double
44 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
45 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
46 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
47 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
48 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
49 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
50 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
51 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
52 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
53 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
54 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
55 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
56 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
57 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
59 double
60 acos(double x)
62 double z,p,q,r,w,s,c,df;
63 int32_t hx,ix;
64 GET_HIGH_WORD(hx,x);
65 ix = hx&0x7fffffff;
66 if(ix>=0x3ff00000) { /* |x| >= 1 */
67 u_int32_t lx;
68 GET_LOW_WORD(lx,x);
69 if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
70 if(hx>0) return 0.0; /* acos(1) = 0 */
71 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
73 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
75 if(ix<0x3fe00000) { /* |x| < 0.5 */
76 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
77 z = x*x;
78 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
79 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
80 r = p/q;
81 return pio2_hi - (x - (pio2_lo-x*r));
82 } else if (hx<0) { /* x < -0.5 */
83 z = (one+x)*0.5;
84 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
85 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
86 s = sqrt(z);
87 r = p/q;
88 w = r*s-pio2_lo;
89 return pi - 2.0*(s+w);
90 } else { /* x > 0.5 */
91 z = (one-x)*0.5;
92 s = sqrt(z);
93 df = s;
94 SET_LOW_WORD(df,0);
95 c = (z-df*df)/(s+df);
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 w = r*s+c;
100 return 2.0*(df+w);