1
2 /*******************************************************************************
3 MIT License
4 -----------
5
6 Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
7
8 Permission is hereby granted, free of charge, to any person obtaining a copy
9 of this Software and associated documentaon files (the "Software"), to deal
10 in the Software without restriction, including without limitation the rights
11 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
12 copies of the Software, and to permit persons to whom the Software is
13 furnished to do so, subject to the following conditions:
14
15 The above copyright notice and this permission notice shall be included in
16 all copies or substantial portions of the Software.
17
18 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
19 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
20 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
21 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
22 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
23 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
24 THE SOFTWARE.
25 *******************************************************************************/
26
27 #include "libm.h"
28 #include "libm_util.h"
29
30 #define USE_VALF_WITH_FLAGS
31 #define USE_NANF_WITH_FLAGS
32 #define USE_HANDLE_ERRORF
33 #include "libm_inlines.h"
34 #undef USE_NANF_WITH_FLAGS
35 #undef USE_VALF_WITH_FLAGS
36 #undef USE_HANDLE_ERRORF
37
38 #include "libm_errno.h"
39
40 #ifdef _MSC_VER
41 // Disable "C4163: not available as intrinsic function" warning that older
42 // compilers may issue here.
43 #pragma warning(disable:4163)
44 #pragma function(asinf)
45 #endif
46
FN_PROTOTYPE(asinf)47 float FN_PROTOTYPE(asinf)(float x)
48 {
49 /* Computes arcsin(x).
50 The argument is first reduced by noting that arcsin(x)
51 is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
52 For denormal and small arguments arcsin(x) = x to machine
53 accuracy. Remaining argument ranges are handled as follows.
54 For abs(x) <= 0.5 use
55 arcsin(x) = x + x^3*R(x^2)
56 where R(x^2) is a rational minimax approximation to
57 (arcsin(x) - x)/x^3.
58 For abs(x) > 0.5 exploit the identity:
59 arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
60 together with the above rational approximation, and
61 reconstruct the terms carefully.
62 */
63
64 /* Some constants and split constants. */
65
66 static const float
67 piby2_tail = 7.5497894159e-08F, /* 0x33a22168 */
68 hpiby2_head = 7.8539812565e-01F, /* 0x3f490fda */
69 piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */
70 float u, v, y, s = 0.0F, r;
71 int xexp, xnan, transform = 0;
72
73 unsigned int ux, aux, xneg;
74 GET_BITS_SP32(x, ux);
75 aux = ux & ~SIGNBIT_SP32;
76 xneg = (ux & SIGNBIT_SP32);
77 xnan = (aux > PINFBITPATT_SP32);
78 xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
79
80 /* Special cases */
81
82 if (xnan)
83 {
84 return _handle_errorf("asinf", OP_ASIN, ux|0x00400000, _DOMAIN, 0,
85 EDOM, x, 0.0F, 1);
86 }
87 else if (xexp < -14)
88 /* y small enough that arcsin(x) = x */
89 return valf_with_flags(x, AMD_F_INEXACT);
90 else if (xexp >= 0)
91 {
92 /* abs(x) >= 1.0 */
93 if (x == 1.0F)
94 return valf_with_flags(piby2, AMD_F_INEXACT);
95 else if (x == -1.0F)
96 return valf_with_flags(-piby2, AMD_F_INEXACT);
97 else
98 return _handle_errorf("asinf", OP_ASIN, INDEFBITPATT_SP32, _DOMAIN,
99 AMD_F_INVALID, EDOM, x, 0.0F, 1);
100 }
101
102 if (xneg) y = -x;
103 else y = x;
104
105 transform = (xexp >= -1); /* abs(x) >= 0.5 */
106
107 if (transform)
108 { /* Transform y into the range [0,0.5) */
109 r = 0.5F*(1.0F - y);
110 /* VC++ intrinsic call */
111 _mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r)));
112 y = s;
113 }
114 else
115 r = y*y;
116
117 /* Use a rational approximation for [0.0, 0.5] */
118
119 u=r*(0.184161606965100694821398249421F +
120 (-0.0565298683201845211985026327361F +
121 (-0.0133819288943925804214011424456F -
122 0.00396137437848476485201154797087F*r)*r)*r)/
123 (1.10496961524520294485512696706F -
124 0.836411276854206731913362287293F*r);
125
126 if (transform)
127 {
128 /* Reconstruct asin carefully in transformed region */
129 float c, s1, p, q;
130 unsigned int us;
131 GET_BITS_SP32(s, us);
132 PUT_BITS_SP32(0xffff0000 & us, s1);
133 c = (r-s1*s1)/(s+s1);
134 p = 2.0F*s*u - (piby2_tail-2.0F*c);
135 q = hpiby2_head - 2.0F*s1;
136 v = hpiby2_head - (p-q);
137 }
138 else
139 {
140 /* Use a temporary variable to prevent VC++ rearranging
141 y + y*u
142 into
143 y * (1 + u)
144 and getting an incorrectly rounded result */
145 float tmp;
146 tmp = y * u;
147 v = y + tmp;
148 }
149
150 if (xneg) return -v;
151 else return v;
152 }
153