2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
9 * ====================================================
14 * acos(x) = pi/2 - asin(x)
15 * acos(-x) = pi/2 + asin(x)
17 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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).
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)
30 * if x is NaN, return x itself;
31 * if |x|>1, return NaN with invalid signal.
33 * Function needed: __ieee754_sqrt
37 #include "math_private.h"
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 */
55 double attribute_hidden
__ieee754_acos(double x
)
57 double z
,p
,q
,r
,w
,s
,c
,df
;
61 if(ix
>=0x3ff00000) { /* |x| >= 1 */
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 */
68 return (x
-x
)/(x
-x
); /* acos(|x|>1) is NaN */
70 if(ix
<0x3fe00000) { /* |x| < 0.5 */
71 if(ix
<=0x3c600000) return pio2_hi
+pio2_lo
;/*if|x|<2**-57*/
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
)));
76 return pio2_hi
- (x
- (pio2_lo
-x
*r
));
77 } else if (hx
<0) { /* 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
);
84 return pi
- 2.0*(s
+w
);
85 } else { /* x > 0.5 */
87 s
= __ieee754_sqrt(z
);
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
)));
103 double acos(double x
)
105 double z
= __ieee754_acos(x
);
106 if (_LIB_VERSION
== _IEEE_
|| isnan(x
))
109 return __kernel_standard(x
, x
, 1); /* acos(|x|>1) */
113 strong_alias(__ieee754_acos
, acos
)
115 libm_hidden_def(acos
)