Annotation of src/lib/libm/src/e_acos.c, Revision 1.7
1.1 jtc 1: /* @(#)e_acos.c 5.1 93/09/24 */
2: /*
3: * ====================================================
4: * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5: *
6: * Developed at SunPro, 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: */
1.3 jtc 12:
1.7 ! jtc 13: #if defined(LIBM_SCCS) && !defined(lint)
! 14: static char rcsid[] = "$Id: e_acos.c,v 1.6 1994/08/18 23:04:51 jtc Exp $";
1.3 jtc 15: #endif
1.1 jtc 16:
17: /* __ieee754_acos(x)
18: * Method :
19: * acos(x) = pi/2 - asin(x)
20: * acos(-x) = pi/2 + asin(x)
21: * For |x|<=0.5
22: * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
23: * For x>0.5
24: * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
25: * = 2asin(sqrt((1-x)/2))
26: * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
27: * = 2f + (2c + 2s*z*R(z))
28: * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
29: * for f so that f+c ~ sqrt(z).
30: * For x<-0.5
31: * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
32: * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
33: *
34: * Special cases:
35: * if x is NaN, return x itself;
36: * if |x|>1, return NaN with invalid signal.
37: *
38: * Function needed: sqrt
39: */
40:
1.5 jtc 41: #include "math.h"
42: #include "math_private.h"
1.1 jtc 43:
44: #ifdef __STDC__
45: static const double
46: #else
47: static double
48: #endif
49: one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
50: pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
51: pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
52: pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
53: pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
54: pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
55: pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
56: pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
57: pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
58: pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
59: qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
60: qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
61: qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
62: qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
63:
64: #ifdef __STDC__
65: double __ieee754_acos(double x)
66: #else
67: double __ieee754_acos(x)
68: double x;
69: #endif
70: {
71: double z,p,q,r,w,s,c,df;
1.6 jtc 72: int32_t hx,ix;
1.5 jtc 73: GET_HIGH_WORD(hx,x);
1.1 jtc 74: ix = hx&0x7fffffff;
75: if(ix>=0x3ff00000) { /* |x| >= 1 */
1.6 jtc 76: u_int32_t lx;
1.5 jtc 77: GET_LOW_WORD(lx,x);
78: if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
1.1 jtc 79: if(hx>0) return 0.0; /* acos(1) = 0 */
80: else return pi+2.0*pio2_lo; /* acos(-1)= pi */
81: }
82: return (x-x)/(x-x); /* acos(|x|>1) is NaN */
83: }
84: if(ix<0x3fe00000) { /* |x| < 0.5 */
85: if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
86: z = x*x;
87: p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
88: q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
89: r = p/q;
90: return pio2_hi - (x - (pio2_lo-x*r));
91: } else if (hx<0) { /* x < -0.5 */
92: z = (one+x)*0.5;
93: p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
94: q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
95: s = sqrt(z);
96: r = p/q;
97: w = r*s-pio2_lo;
98: return pi - 2.0*(s+w);
99: } else { /* x > 0.5 */
100: z = (one-x)*0.5;
101: s = sqrt(z);
102: df = s;
1.5 jtc 103: SET_LOW_WORD(df,0);
1.1 jtc 104: c = (z-df*df)/(s+df);
105: p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
106: q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
107: r = p/q;
108: w = r*s+c;
109: return 2.0*(df+w);
110: }
111: }
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