ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / e_acos.c
1
2 /* @(#)e_acos.c 1.3 95/01/18 */
3 /* $FreeBSD: head/lib/msun/src/e_acos.c 181074 2008-07-31 22:41:26Z das $ */
4 /*
5  * ====================================================
6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7  *
8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
9  * Permission to use, copy, modify, and distribute this
10  * software is freely granted, provided that this notice 
11  * is preserved.
12  * ====================================================
13  */
14
15 /* __ieee754_acos(x)
16  * Method :                  
17  *      acos(x)  = pi/2 - asin(x)
18  *      acos(-x) = pi/2 + asin(x)
19  * For |x|<=0.5
20  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
21  * For x>0.5
22  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
23  *              = 2asin(sqrt((1-x)/2))  
24  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
25  *              = 2f + (2c + 2s*z*R(z))
26  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
27  *     for f so that f+c ~ sqrt(z).
28  * For x<-0.5
29  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
30  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
31  *
32  * Special cases:
33  *      if x is NaN, return x itself;
34  *      if |x|>1, return NaN with invalid signal.
35  *
36  * Function needed: sqrt
37  */
38
39 #include <float.h>
40
41 #include "math.h"
42 #include "math_private.h"
43
44 static const double
45 one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
46 pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
47 pio2_hi =  1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
48 static volatile double
49 pio2_lo =  6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
50 static const double
51 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
52 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
53 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
54 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
55 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
56 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
57 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
58 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
59 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
60 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
61
62 double
63 __ieee754_acos(double x)
64 {
65         double z,p,q,r,w,s,c,df;
66         int32_t hx,ix;
67         GET_HIGH_WORD(hx,x);
68         ix = hx&0x7fffffff;
69         if(ix>=0x3ff00000) {    /* |x| >= 1 */
70             u_int32_t lx;
71             GET_LOW_WORD(lx,x);
72             if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
73                 if(hx>0) return 0.0;            /* acos(1) = 0  */
74                 else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
75             }
76             return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
77         }
78         if(ix<0x3fe00000) {     /* |x| < 0.5 */
79             if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
80             z = x*x;
81             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
82             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
83             r = p/q;
84             return pio2_hi - (x - (pio2_lo-x*r));
85         } else  if (hx<0) {             /* x < -0.5 */
86             z = (one+x)*0.5;
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             s = sqrt(z);
90             r = p/q;
91             w = r*s-pio2_lo;
92             return pi - 2.0*(s+w);
93         } else {                        /* x > 0.5 */
94             z = (one-x)*0.5;
95             s = sqrt(z);
96             df = s;
97             SET_LOW_WORD(df,0);
98             c  = (z-df*df)/(s+df);
99             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
100             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
101             r = p/q;
102             w = r*s+c;
103             return 2.0*(df+w);
104         }
105 }
106
107 #if LDBL_MANT_DIG == 53
108 __weak_reference(acos, acosl);
109 #endif