1 /*****************************************************************************/
2 /*****************************************************************************/
3 // asinf from musl-0.9.15
4 /*****************************************************************************/
5 /*****************************************************************************/
6
7 /* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.c */
8 /*
9 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
10 */
11 /*
12 * ====================================================
13 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
14 *
15 * Developed at SunPro, a Sun Microsystems, Inc. business.
16 * Permission to use, copy, modify, and distribute this
17 * software is freely granted, provided that this notice
18 * is preserved.
19 * ====================================================
20 */
21
22 #include "libm.h"
23
24 // dpgeorge: pio2 was double in original implementation of asinf
25 static const float
26 pio2_hi = 1.5707962513e+00f, /* 0x3fc90fda */
27 pio2_lo = 7.5497894159e-08f; /* 0x33a22168 */
28
29 static const float
30 /* coefficients for R(x^2) */
31 pS0 = 1.6666586697e-01f,
32 pS1 = -4.2743422091e-02f,
33 pS2 = -8.6563630030e-03f,
34 qS1 = -7.0662963390e-01f;
35
R(float z)36 static float R(float z)
37 {
38 float_t p, q;
39 p = z*(pS0+z*(pS1+z*pS2));
40 q = 1.0f+z*qS1;
41 return p/q;
42 }
43
asinf(float x)44 float asinf(float x)
45 {
46 // dpgeorge: s was double in original implementation
47 float s,z;
48 uint32_t hx,ix;
49
50 GET_FLOAT_WORD(hx, x);
51 ix = hx & 0x7fffffff;
52 if (ix >= 0x3f800000) { /* |x| >= 1 */
53 if (ix == 0x3f800000) /* |x| == 1 */
54 return x*pio2_hi + 0x1p-120f; /* asin(+-1) = +-pi/2 with inexact */
55 return 0/(x-x); /* asin(|x|>1) is NaN */
56 }
57 if (ix < 0x3f000000) { /* |x| < 0.5 */
58 /* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
59 if (ix < 0x39800000 && ix >= 0x00800000)
60 return x;
61 return x + x*R(x*x);
62 }
63 /* 1 > |x| >= 0.5 */
64 z = (1 - fabsf(x))*0.5f;
65 s = sqrtf(z);
66 x = pio2_hi - (2*(s+s*R(z)) - pio2_lo); // dpgeorge: use pio2_hi and pio2_lo
67 if (hx >> 31)
68 return -x;
69 return x;
70 }
71
72 /*****************************************************************************/
73 /*****************************************************************************/
74 // acosf from musl-0.9.15
75 /*****************************************************************************/
76 /*****************************************************************************/
77
78 /* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */
79 /*
80 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
81 */
82 /*
83 * ====================================================
84 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
85 *
86 * Developed at SunPro, a Sun Microsystems, Inc. business.
87 * Permission to use, copy, modify, and distribute this
88 * software is freely granted, provided that this notice
89 * is preserved.
90 * ====================================================
91 */
92
acosf(float x)93 float acosf(float x)
94 {
95 float z,w,s,c,df;
96 uint32_t hx,ix;
97
98 GET_FLOAT_WORD(hx, x);
99 ix = hx & 0x7fffffff;
100 /* |x| >= 1 or nan */
101 if (ix >= 0x3f800000) {
102 if (ix == 0x3f800000) {
103 if (hx >> 31)
104 return 2*pio2_hi + 0x1p-120f;
105 return 0;
106 }
107 return 0/(x-x);
108 }
109 /* |x| < 0.5 */
110 if (ix < 0x3f000000) {
111 if (ix <= 0x32800000) /* |x| < 2**-26 */
112 return pio2_hi + 0x1p-120f;
113 return pio2_hi - (x - (pio2_lo-x*R(x*x)));
114 }
115 /* x < -0.5 */
116 if (hx >> 31) {
117 z = (1+x)*0.5f;
118 s = sqrtf(z);
119 w = R(z)*s-pio2_lo;
120 return 2*(pio2_hi - (s+w));
121 }
122 /* x > 0.5 */
123 z = (1-x)*0.5f;
124 s = sqrtf(z);
125 GET_FLOAT_WORD(hx,s);
126 SET_FLOAT_WORD(df,hx&0xfffff000);
127 c = (z-df*df)/(s+df);
128 w = R(z)*s+c;
129 return 2*(df+w);
130 }
131