1df930be7Sderaadt /* @(#)e_acos.c 5.1 93/09/24 */
2df930be7Sderaadt /*
3df930be7Sderaadt * ====================================================
4df930be7Sderaadt * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5df930be7Sderaadt *
6df930be7Sderaadt * Developed at SunPro, a Sun Microsystems, Inc. business.
7df930be7Sderaadt * Permission to use, copy, modify, and distribute this
8df930be7Sderaadt * software is freely granted, provided that this notice
9df930be7Sderaadt * is preserved.
10df930be7Sderaadt * ====================================================
11df930be7Sderaadt */
12df930be7Sderaadt
137b36286aSmartynas /* acos(x)
14df930be7Sderaadt * Method :
15df930be7Sderaadt * acos(x) = pi/2 - asin(x)
16df930be7Sderaadt * acos(-x) = pi/2 + asin(x)
17df930be7Sderaadt * For |x|<=0.5
18df930be7Sderaadt * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
19df930be7Sderaadt * For x>0.5
20df930be7Sderaadt * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
21df930be7Sderaadt * = 2asin(sqrt((1-x)/2))
22df930be7Sderaadt * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
23df930be7Sderaadt * = 2f + (2c + 2s*z*R(z))
24df930be7Sderaadt * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
25df930be7Sderaadt * for f so that f+c ~ sqrt(z).
26df930be7Sderaadt * For x<-0.5
27df930be7Sderaadt * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
28df930be7Sderaadt * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
29df930be7Sderaadt *
30df930be7Sderaadt * Special cases:
31df930be7Sderaadt * if x is NaN, return x itself;
32df930be7Sderaadt * if |x|>1, return NaN with invalid signal.
33df930be7Sderaadt *
347b36286aSmartynas * Function needed: sqrt
35df930be7Sderaadt */
36df930be7Sderaadt
37390c8400Smartynas #include <float.h>
38390c8400Smartynas #include <math.h>
39390c8400Smartynas
40df930be7Sderaadt #include "math_private.h"
41df930be7Sderaadt
42df930be7Sderaadt static const double
43df930be7Sderaadt one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
44df930be7Sderaadt pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
45df930be7Sderaadt pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
46df930be7Sderaadt pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
47df930be7Sderaadt pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
48df930be7Sderaadt pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
49df930be7Sderaadt pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
50df930be7Sderaadt pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
51df930be7Sderaadt pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
52df930be7Sderaadt pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
53df930be7Sderaadt qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
54df930be7Sderaadt qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
55df930be7Sderaadt qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
56df930be7Sderaadt qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
57df930be7Sderaadt
58e7beb4a7Smillert double
acos(double x)597b36286aSmartynas acos(double x)
60df930be7Sderaadt {
61df930be7Sderaadt double z,p,q,r,w,s,c,df;
62df930be7Sderaadt int32_t hx,ix;
63df930be7Sderaadt GET_HIGH_WORD(hx,x);
64df930be7Sderaadt ix = hx&0x7fffffff;
65df930be7Sderaadt if(ix>=0x3ff00000) { /* |x| >= 1 */
66df930be7Sderaadt u_int32_t lx;
67df930be7Sderaadt GET_LOW_WORD(lx,x);
68df930be7Sderaadt if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
69df930be7Sderaadt if(hx>0) return 0.0; /* acos(1) = 0 */
70df930be7Sderaadt else return pi+2.0*pio2_lo; /* acos(-1)= pi */
71df930be7Sderaadt }
72df930be7Sderaadt return (x-x)/(x-x); /* acos(|x|>1) is NaN */
73df930be7Sderaadt }
74df930be7Sderaadt if(ix<0x3fe00000) { /* |x| < 0.5 */
75df930be7Sderaadt if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
76df930be7Sderaadt z = x*x;
77df930be7Sderaadt p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
78df930be7Sderaadt q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
79df930be7Sderaadt r = p/q;
80df930be7Sderaadt return pio2_hi - (x - (pio2_lo-x*r));
81df930be7Sderaadt } else if (hx<0) { /* x < -0.5 */
82df930be7Sderaadt z = (one+x)*0.5;
83df930be7Sderaadt p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
84df930be7Sderaadt q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
857b36286aSmartynas s = sqrt(z);
86df930be7Sderaadt r = p/q;
87df930be7Sderaadt w = r*s-pio2_lo;
88df930be7Sderaadt return pi - 2.0*(s+w);
89df930be7Sderaadt } else { /* x > 0.5 */
90df930be7Sderaadt z = (one-x)*0.5;
917b36286aSmartynas s = sqrt(z);
92df930be7Sderaadt df = s;
93df930be7Sderaadt SET_LOW_WORD(df,0);
94df930be7Sderaadt c = (z-df*df)/(s+df);
95df930be7Sderaadt p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
96df930be7Sderaadt q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
97df930be7Sderaadt r = p/q;
98df930be7Sderaadt w = r*s+c;
99df930be7Sderaadt return 2.0*(df+w);
100df930be7Sderaadt }
101df930be7Sderaadt }
102*2f2c0062Sguenther DEF_STD(acos);
103*2f2c0062Sguenther LDBL_MAYBE_UNUSED_CLONE(acos);
104