1
2 /* @(#)e_acos.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /* acos(x)
15 * Method :
16 * acos(x) = pi/2 - asin(x)
17 * acos(-x) = pi/2 + asin(x)
18 * For |x|<=0.5
19 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
20 * For x>0.5
21 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
22 * = 2asin(sqrt((1-x)/2))
23 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
24 * = 2f + (2c + 2s*z*R(z))
25 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
26 * for f so that f+c ~ sqrt(z).
27 * For x<-0.5
28 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
29 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
30 *
31 * Special cases:
32 * if x is NaN, return x itself;
33 * if |x|>1, return NaN with invalid signal.
34 *
35 * Function needed: sqrt
36 */
37
38 #include "fdlibm.h"
39
40 #ifdef _NEED_FLOAT64
41
42 static const __float64
43 one = _F_64(1.00000000000000000000e+00), /* 0x3FF00000, 0x00000000 */
44 pi = _F_64(3.14159265358979311600e+00), /* 0x400921FB, 0x54442D18 */
45 pio2_hi = _F_64(1.57079632679489655800e+00), /* 0x3FF921FB, 0x54442D18 */
46 pio2_lo = _F_64(6.12323399573676603587e-17), /* 0x3C91A626, 0x33145C07 */
47 pS0 = _F_64(1.66666666666666657415e-01), /* 0x3FC55555, 0x55555555 */
48 pS1 = _F_64(-3.25565818622400915405e-01), /* 0xBFD4D612, 0x03EB6F7D */
49 pS2 = _F_64(2.01212532134862925881e-01), /* 0x3FC9C155, 0x0E884455 */
50 pS3 = _F_64(-4.00555345006794114027e-02), /* 0xBFA48228, 0xB5688F3B */
51 pS4 = _F_64(7.91534994289814532176e-04), /* 0x3F49EFE0, 0x7501B288 */
52 pS5 = _F_64(3.47933107596021167570e-05), /* 0x3F023DE1, 0x0DFDF709 */
53 qS1 = _F_64(-2.40339491173441421878e+00), /* 0xC0033A27, 0x1C8A2D4B */
54 qS2 = _F_64(2.02094576023350569471e+00), /* 0x40002AE5, 0x9C598AC8 */
55 qS3 = _F_64(-6.88283971605453293030e-01), /* 0xBFE6066C, 0x1B8D0159 */
56 qS4 = _F_64(7.70381505559019352791e-02); /* 0x3FB3B8C5, 0xB12E9282 */
57
58 __float64
acos64(__float64 x)59 acos64(__float64 x)
60 {
61 __float64 z, p, q, r, w, s, c, df;
62 __int32_t hx, ix;
63 GET_HIGH_WORD(hx, x);
64 ix = hx & 0x7fffffff;
65 if (ix >= 0x3ff00000) { /* |x| >= 1 */
66 __uint32_t lx;
67 GET_LOW_WORD(lx, x);
68 if (((ix - 0x3ff00000) | lx) == 0) { /* |x|==1 */
69 if (hx > 0)
70 return _F_64(0.0); /* acos(1) = 0 */
71 else
72 return pi + _F_64(2.0) * pio2_lo; /* acos(-1)= pi */
73 }
74 return __math_invalid(x); /* acos(|x|>1) is NaN */
75 }
76 if (ix < 0x3fe00000) { /* |x| < 0.5 */
77 if (ix <= 0x3c600000)
78 return pio2_hi + pio2_lo; /*if|x|<2**-57*/
79 z = x * x;
80 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
81 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
82 r = p / q;
83 return pio2_hi - (x - (pio2_lo - x * r));
84 } else if (hx < 0) { /* x < -0.5 */
85 z = (one + x) * _F_64(0.5);
86 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
87 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
88 s = sqrt64(z);
89 r = p / q;
90 w = r * s - pio2_lo;
91 return pi - _F_64(2.0) * (s + w);
92 } else { /* x > 0.5 */
93 z = (one - x) * _F_64(0.5);
94 s = sqrt64(z);
95 df = s;
96 SET_LOW_WORD(df, 0);
97 c = (z - df * df) / (s + df);
98 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
99 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
100 r = p / q;
101 w = r * s + c;
102 return _F_64(2.0) * (df + w);
103 }
104 }
105
106 _MATH_ALIAS_d_d(acos)
107
108 #endif /* _NEED_FLOAT64 */
109
