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/* @(#)e_acos.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef lint
static char rcsid
[] = "$\Id: e_acos.c,v 1.2.6.1 1997/02/23 11:02:58 joerg Exp $";
#endif
/* __ieee754_acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one
= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi
= 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi
= 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo
= 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0
= 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1
= -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2
= 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3
= -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4
= 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5
= 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1
= -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2
= 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3
= -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4
= 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __generic___ieee754_acos
(double x
)
#else
double __generic___ieee754_acos
(x
)
double x
;
#endif
{
double z
,p
,q
,r
,w
,s
,c
,df
;
int32_t hx
,ix
;
GET_HIGH_WORD
(hx
,x
);
ix
= hx
&0x7fffffff;
if(ix
>=0x3ff00000) { /* |x| >= 1 */
u_int32_t lx
;
GET_LOW_WORD
(lx
,x
);
if(((ix
-0x3ff00000)|lx
)==0) { /* |x|==1 */
if(hx
>0) return 0.0; /* acos(1) = 0 */
else return pi
+2.0*pio2_lo
; /* acos(-1)= pi */
}
return (x
-x
)/(x
-x
); /* acos(|x|>1) is NaN */
}
if(ix
<0x3fe00000) { /* |x| < 0.5 */
if(ix
<=0x3c600000) return pio2_hi
+pio2_lo
;/*if|x|<2**-57*/
z
= x
*x
;
p
= z
*(pS0
+z
*(pS1
+z
*(pS2
+z
*(pS3
+z
*(pS4
+z
*pS5
)))));
q
= one
+z
*(qS1
+z
*(qS2
+z
*(qS3
+z
*qS4
)));
r
= p
/q
;
return pio2_hi
- (x
- (pio2_lo
-x
*r
));
} else if (hx
<0) { /* x < -0.5 */
z
= (one
+x
)*0.5;
p
= z
*(pS0
+z
*(pS1
+z
*(pS2
+z
*(pS3
+z
*(pS4
+z
*pS5
)))));
q
= one
+z
*(qS1
+z
*(qS2
+z
*(qS3
+z
*qS4
)));
s
= sqrt(z
);
r
= p
/q
;
w
= r
*s
-pio2_lo
;
return pi
- 2.0*(s
+w
);
} else { /* x > 0.5 */
z
= (one
-x
)*0.5;
s
= sqrt(z
);
df
= s
;
SET_LOW_WORD
(df
,0);
c
= (z
-df
*df
)/(s
+df
);
p
= z
*(pS0
+z
*(pS1
+z
*(pS2
+z
*(pS3
+z
*(pS4
+z
*pS5
)))));
q
= one
+z
*(qS1
+z
*(qS2
+z
*(qS3
+z
*qS4
)));
r
= p
/q
;
w
= r
*s
+c
;
return 2.0*(df
+w
);
}
}