1 /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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 * ====================================================
11 */
12 /* acos(x)
13 * Method :
14 * acos(x) = pi/2 - asin(x)
15 * acos(-x) = pi/2 + asin(x)
16 * For |x|<=0.5
17 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
18 * For x>0.5
19 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
20 * = 2asin(sqrt((1-x)/2))
21 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
22 * = 2f + (2c + 2s*z*R(z))
23 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
24 * for f so that f+c ~ sqrt(z).
25 * For x<-0.5
26 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
27 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
28 *
29 * Special cases:
30 * if x is NaN, return x itself;
31 * if |x|>1, return NaN with invalid signal.
32 *
33 * Function needed: sqrt
34 */
35
36 #include "libm.h"
37
38 static const double
39 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
40 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
41 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
42 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
43 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
44 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
45 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
46 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
47 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
48 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
49 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
50 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
51
R(double z)52 static double R(double z)
53 {
54 double_t p, q;
55 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
56 q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
57 return p/q;
58 }
59
acos(double x)60 double acos(double x)
61 {
62 double z,w,s,c,df;
63 uint32_t hx,ix;
64
65 GET_HIGH_WORD(hx, x);
66 ix = hx & 0x7fffffff;
67 /* |x| >= 1 or nan */
68 if (ix >= 0x3ff00000) {
69 uint32_t lx;
70
71 GET_LOW_WORD(lx,x);
72 if ((ix-0x3ff00000 | lx) == 0) {
73 /* acos(1)=0, acos(-1)=pi */
74 if (hx >> 31)
75 return 2*pio2_hi + 0x1p-120f;
76 return 0;
77 }
78 return 0/(x-x);
79 }
80 /* |x| < 0.5 */
81 if (ix < 0x3fe00000) {
82 if (ix <= 0x3c600000) /* |x| < 2**-57 */
83 return pio2_hi + 0x1p-120f;
84 return pio2_hi - (x - (pio2_lo-x*R(x*x)));
85 }
86 /* x < -0.5 */
87 if (hx >> 31) {
88 z = (1.0+x)*0.5;
89 s = sqrt(z);
90 w = R(z)*s-pio2_lo;
91 return 2*(pio2_hi - (s+w));
92 }
93 /* x > 0.5 */
94 z = (1.0-x)*0.5;
95 s = sqrt(z);
96 df = s;
97 SET_LOW_WORD(df,0);
98 c = (z-df*df)/(s+df);
99 w = R(z)*s+c;
100 return 2*(df+w);
101 }
102