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