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
acosf(float x)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