xref: /freebsd/lib/msun/src/e_acosf.c (revision 87b759f0fa1f7554d50ce640c40138512bbded44)
1 /* e_acosf.c -- float version of e_acos.c.
2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3  */
4 
5 /*
6  * ====================================================
7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8  *
9  * Developed at SunPro, a Sun Microsystems, Inc. business.
10  * Permission to use, copy, modify, and distribute this
11  * software is freely granted, provided that this notice
12  * is preserved.
13  * ====================================================
14  */
15 
16 #include "math.h"
17 #include "math_private.h"
18 
19 static const float
20 one =  1.0000000000e+00, /* 0x3F800000 */
21 pi =  3.1415925026e+00, /* 0x40490fda */
22 pio2_hi =  1.5707962513e+00; /* 0x3fc90fda */
23 static volatile float
24 pio2_lo =  7.5497894159e-08; /* 0x33a22168 */
25 
26 /*
27  * The coefficients for the rational approximation were generated over
28  *  0x1p-12f <= x <= 0.5f.  The maximum error satisfies log2(e) < -30.084.
29  */
30 static const float
31 pS0 =  1.66666672e-01f, /* 0x3e2aaaab */
32 pS1 = -1.19510300e-01f, /* 0xbdf4c1d1 */
33 pS2 =  5.47002675e-03f, /* 0x3bb33de9 */
34 qS1 = -1.16706085e+00f, /* 0xbf956240 */
35 qS2 =  2.90115148e-01f; /* 0x3e9489f9 */
36 
37 float
38 acosf(float x)
39 {
40 	float z,p,q,r,w,s,c,df;
41 	int32_t hx,ix;
42 	GET_FLOAT_WORD(hx,x);
43 	ix = hx&0x7fffffff;
44 	if(ix>=0x3f800000) {		/* |x| >= 1 */
45 	    if(ix==0x3f800000) {	/* |x| == 1 */
46 		if(hx>0) return 0.0;	/* acos(1) = 0 */
47 		else return pi+(float)2.0*pio2_lo;	/* acos(-1)= pi */
48 	    }
49 	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
50 	}
51 	if(ix<0x3f000000) {	/* |x| < 0.5 */
52 	    if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/
53 	    z = x*x;
54 	    p = z*(pS0+z*(pS1+z*pS2));
55 	    q = one+z*(qS1+z*qS2);
56 	    r = p/q;
57 	    return pio2_hi - (x - (pio2_lo-x*r));
58 	} else  if (hx<0) {		/* x < -0.5 */
59 	    z = (one+x)*(float)0.5;
60 	    p = z*(pS0+z*(pS1+z*pS2));
61 	    q = one+z*(qS1+z*qS2);
62 	    s = sqrtf(z);
63 	    r = p/q;
64 	    w = r*s-pio2_lo;
65 	    return pi - (float)2.0*(s+w);
66 	} else {			/* x > 0.5 */
67 	    int32_t idf;
68 	    z = (one-x)*(float)0.5;
69 	    s = sqrtf(z);
70 	    df = s;
71 	    GET_FLOAT_WORD(idf,df);
72 	    SET_FLOAT_WORD(df,idf&0xfffff000);
73 	    c  = (z-df*df)/(s+df);
74 	    p = z*(pS0+z*(pS1+z*pS2));
75 	    q = one+z*(qS1+z*qS2);
76 	    r = p/q;
77 	    w = r*s+c;
78 	    return (float)2.0*(df+w);
79 	}
80 }
81