1*05a0b428SJohn Marino /* @(#)e_acos.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* acos(x)
14*05a0b428SJohn Marino * Method :
15*05a0b428SJohn Marino * acos(x) = pi/2 - asin(x)
16*05a0b428SJohn Marino * acos(-x) = pi/2 + asin(x)
17*05a0b428SJohn Marino * For |x|<=0.5
18*05a0b428SJohn Marino * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
19*05a0b428SJohn Marino * For x>0.5
20*05a0b428SJohn Marino * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
21*05a0b428SJohn Marino * = 2asin(sqrt((1-x)/2))
22*05a0b428SJohn Marino * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
23*05a0b428SJohn Marino * = 2f + (2c + 2s*z*R(z))
24*05a0b428SJohn Marino * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
25*05a0b428SJohn Marino * for f so that f+c ~ sqrt(z).
26*05a0b428SJohn Marino * For x<-0.5
27*05a0b428SJohn Marino * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
28*05a0b428SJohn Marino * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
29*05a0b428SJohn Marino *
30*05a0b428SJohn Marino * Special cases:
31*05a0b428SJohn Marino * if x is NaN, return x itself;
32*05a0b428SJohn Marino * if |x|>1, return NaN with invalid signal.
33*05a0b428SJohn Marino *
34*05a0b428SJohn Marino * Function needed: sqrt
35*05a0b428SJohn Marino */
36*05a0b428SJohn Marino
37*05a0b428SJohn Marino #include <float.h>
38*05a0b428SJohn Marino #include <math.h>
39*05a0b428SJohn Marino
40*05a0b428SJohn Marino #include "math_private.h"
41*05a0b428SJohn Marino
42*05a0b428SJohn Marino static const double
43*05a0b428SJohn Marino one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
44*05a0b428SJohn Marino pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
45*05a0b428SJohn Marino pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
46*05a0b428SJohn Marino pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
47*05a0b428SJohn Marino pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
48*05a0b428SJohn Marino pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
49*05a0b428SJohn Marino pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
50*05a0b428SJohn Marino pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
51*05a0b428SJohn Marino pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
52*05a0b428SJohn Marino pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
53*05a0b428SJohn Marino qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
54*05a0b428SJohn Marino qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
55*05a0b428SJohn Marino qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
56*05a0b428SJohn Marino qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
57*05a0b428SJohn Marino
58*05a0b428SJohn Marino double
acos(double x)59*05a0b428SJohn Marino acos(double x)
60*05a0b428SJohn Marino {
61*05a0b428SJohn Marino double z,p,q,r,w,s,c,df;
62*05a0b428SJohn Marino int32_t hx,ix;
63*05a0b428SJohn Marino GET_HIGH_WORD(hx,x);
64*05a0b428SJohn Marino ix = hx&0x7fffffff;
65*05a0b428SJohn Marino if(ix>=0x3ff00000) { /* |x| >= 1 */
66*05a0b428SJohn Marino u_int32_t lx;
67*05a0b428SJohn Marino GET_LOW_WORD(lx,x);
68*05a0b428SJohn Marino if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
69*05a0b428SJohn Marino if(hx>0) return 0.0; /* acos(1) = 0 */
70*05a0b428SJohn Marino else return pi+2.0*pio2_lo; /* acos(-1)= pi */
71*05a0b428SJohn Marino }
72*05a0b428SJohn Marino return (x-x)/(x-x); /* acos(|x|>1) is NaN */
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino if(ix<0x3fe00000) { /* |x| < 0.5 */
75*05a0b428SJohn Marino if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
76*05a0b428SJohn Marino z = x*x;
77*05a0b428SJohn Marino p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
78*05a0b428SJohn Marino q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
79*05a0b428SJohn Marino r = p/q;
80*05a0b428SJohn Marino return pio2_hi - (x - (pio2_lo-x*r));
81*05a0b428SJohn Marino } else if (hx<0) { /* x < -0.5 */
82*05a0b428SJohn Marino z = (one+x)*0.5;
83*05a0b428SJohn Marino p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
84*05a0b428SJohn Marino q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
85*05a0b428SJohn Marino s = sqrt(z);
86*05a0b428SJohn Marino r = p/q;
87*05a0b428SJohn Marino w = r*s-pio2_lo;
88*05a0b428SJohn Marino return pi - 2.0*(s+w);
89*05a0b428SJohn Marino } else { /* x > 0.5 */
90*05a0b428SJohn Marino z = (one-x)*0.5;
91*05a0b428SJohn Marino s = sqrt(z);
92*05a0b428SJohn Marino df = s;
93*05a0b428SJohn Marino SET_LOW_WORD(df,0);
94*05a0b428SJohn Marino c = (z-df*df)/(s+df);
95*05a0b428SJohn Marino p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
96*05a0b428SJohn Marino q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
97*05a0b428SJohn Marino r = p/q;
98*05a0b428SJohn Marino w = r*s+c;
99*05a0b428SJohn Marino return 2.0*(df+w);
100*05a0b428SJohn Marino }
101*05a0b428SJohn Marino }
102*05a0b428SJohn Marino
103*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
104*05a0b428SJohn Marino __strong_alias(acosl, acos);
105*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
106