1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __ieee754_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: __ieee754_sqrt
34 */
35
36 #include "math.h"
37 #include "math_private.h"
38
39 static const double
40 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
41 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
42 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
43 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
44 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
45 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
46 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
47 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
48 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
49 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
50 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
51 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
52 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
53 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
54
__ieee754_acos(double x)55 double __ieee754_acos(double x)
56 {
57 double z,p,q,r,w,s,c,df;
58 int32_t hx,ix;
59 GET_HIGH_WORD(hx,x);
60 ix = hx&0x7fffffff;
61 if(ix>=0x3ff00000) { /* |x| >= 1 */
62 u_int32_t lx;
63 GET_LOW_WORD(lx,x);
64 if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
65 if(hx>0) return 0.0; /* acos(1) = 0 */
66 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
67 }
68 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
69 }
70 if(ix<0x3fe00000) { /* |x| < 0.5 */
71 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
72 z = x*x;
73 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
74 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
75 r = p/q;
76 return pio2_hi - (x - (pio2_lo-x*r));
77 } else if (hx<0) { /* x < -0.5 */
78 z = (one+x)*0.5;
79 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
80 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
81 s = __ieee754_sqrt(z);
82 r = p/q;
83 w = r*s-pio2_lo;
84 return pi - 2.0*(s+w);
85 } else { /* x > 0.5 */
86 z = (one-x)*0.5;
87 s = __ieee754_sqrt(z);
88 df = s;
89 SET_LOW_WORD(df,0);
90 c = (z-df*df)/(s+df);
91 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
92 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
93 r = p/q;
94 w = r*s+c;
95 return 2.0*(df+w);
96 }
97 }
98
99 /*
100 * wrap_acos(x)
101 */
102 #ifndef _IEEE_LIBM
acos(double x)103 double acos(double x)
104 {
105 double z = __ieee754_acos(x);
106 if (_LIB_VERSION == _IEEE_ || isnan(x))
107 return z;
108 if (fabs(x) > 1.0)
109 return __kernel_standard(x, x, 1); /* acos(|x|>1) */
110 return z;
111 }
112 #else
113 strong_alias(__ieee754_acos, acos)
114 #endif
115 libm_hidden_def(acos)
116