1 /* @(#)e_acos.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
12 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
13 for performance improvement on pipelined processors.
16 #if defined(LIBM_SCCS) && !defined(lint)
17 static char rcsid
[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
22 * acos(x) = pi/2 - asin(x)
23 * acos(-x) = pi/2 + asin(x)
25 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
27 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
28 * = 2asin(sqrt((1-x)/2))
29 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
30 * = 2f + (2c + 2s*z*R(z))
31 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
32 * for f so that f+c ~ sqrt(z).
34 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
35 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
38 * if x is NaN, return x itself;
39 * if |x|>1, return NaN with invalid signal.
41 * Function needed: __ieee754_sqrt
45 #include "math_private.h"
53 pi
= 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
54 pio2_hi
= 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
55 pio2_lo
= 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
56 pS
[] = {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
57 -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
58 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
59 -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
60 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
61 3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */
62 qS
[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
63 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
64 -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
65 7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */
68 double __ieee754_acos(double x
)
70 double __ieee754_acos(x
)
74 double z
,p
,q
,r
,w
,s
,c
,df
,p1
,p2
,p3
,q1
,q2
,z2
,z4
,z6
;
78 if(ix
>=0x3ff00000) { /* |x| >= 1 */
81 if(((ix
-0x3ff00000)|lx
)==0) { /* |x|==1 */
82 if(hx
>0) return 0.0; /* acos(1) = 0 */
83 else return pi
+2.0*pio2_lo
; /* acos(-1)= pi */
85 return (x
-x
)/(x
-x
); /* acos(|x|>1) is NaN */
87 if(ix
<0x3fe00000) { /* |x| < 0.5 */
88 if(ix
<=0x3c600000) return pio2_hi
+pio2_lo
;/*if|x|<2**-57*/
90 #ifdef DO_NOT_USE_THIS
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
)));
95 p2
= pS
[1]+z
*pS
[2]; z4
=z2
*z2
;
96 p3
= pS
[3]+z
*pS
[4]; z6
=z4
*z2
;
99 p
= p1
+ z2
*p2
+ z4
*p3
+ z6
*pS
[5];
100 q
= q1
+ z2
*q2
+ z4
*qS
[4];
103 return pio2_hi
- (x
- (pio2_lo
-x
*r
));
104 } else if (hx
<0) { /* x < -0.5 */
106 #ifdef DO_NOT_USE_THIS
107 p
= z
*(pS0
+z
*(pS1
+z
*(pS2
+z
*(pS3
+z
*(pS4
+z
*pS5
)))));
108 q
= one
+z
*(qS1
+z
*(qS2
+z
*(qS3
+z
*qS4
)));
110 p1
= z
*pS
[0]; z2
=z
*z
;
111 p2
= pS
[1]+z
*pS
[2]; z4
=z2
*z2
;
112 p3
= pS
[3]+z
*pS
[4]; z6
=z4
*z2
;
115 p
= p1
+ z2
*p2
+ z4
*p3
+ z6
*pS
[5];
116 q
= q1
+ z2
*q2
+ z4
*qS
[4];
118 s
= __ieee754_sqrt(z
);
121 return pi
- 2.0*(s
+w
);
122 } else { /* x > 0.5 */
124 s
= __ieee754_sqrt(z
);
127 c
= (z
-df
*df
)/(s
+df
);
128 #ifdef DO_NOT_USE_THIS
129 p
= z
*(pS0
+z
*(pS1
+z
*(pS2
+z
*(pS3
+z
*(pS4
+z
*pS5
)))));
130 q
= one
+z
*(qS1
+z
*(qS2
+z
*(qS3
+z
*qS4
)));
132 p1
= z
*pS
[0]; z2
=z
*z
;
133 p2
= pS
[1]+z
*pS
[2]; z4
=z2
*z2
;
134 p3
= pS
[3]+z
*pS
[4]; z6
=z4
*z2
;
137 p
= p1
+ z2
*p2
+ z4
*p3
+ z6
*pS
[5];
138 q
= q1
+ z2
*q2
+ z4
*qS
[4];