1 | /* Implementation of gamma function according to ISO C. |
2 | Copyright (C) 1997-2018 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. |
5 | |
6 | The GNU C Library is free software; you can redistribute it and/or |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either |
9 | version 2.1 of the License, or (at your option) any later version. |
10 | |
11 | The GNU C Library is distributed in the hope that it will be useful, |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ |
19 | |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | #include <float.h> |
23 | |
24 | /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's |
25 | approximation to gamma function. */ |
26 | |
27 | static const float gamma_coeff[] = |
28 | { |
29 | 0x1.555556p-4f, |
30 | -0xb.60b61p-12f, |
31 | 0x3.403404p-12f, |
32 | }; |
33 | |
34 | #define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) |
35 | |
36 | /* Return gamma (X), for positive X less than 42, in the form R * |
37 | 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to |
38 | avoid overflow or underflow in intermediate calculations. */ |
39 | |
40 | static float |
41 | gammaf_positive (float x, int *exp2_adj) |
42 | { |
43 | int local_signgam; |
44 | if (x < 0.5f) |
45 | { |
46 | *exp2_adj = 0; |
47 | return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x; |
48 | } |
49 | else if (x <= 1.5f) |
50 | { |
51 | *exp2_adj = 0; |
52 | return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam)); |
53 | } |
54 | else if (x < 2.5f) |
55 | { |
56 | *exp2_adj = 0; |
57 | float x_adj = x - 1; |
58 | return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam)) |
59 | * x_adj); |
60 | } |
61 | else |
62 | { |
63 | float eps = 0; |
64 | float x_eps = 0; |
65 | float x_adj = x; |
66 | float prod = 1; |
67 | if (x < 4.0f) |
68 | { |
69 | /* Adjust into the range for applying Stirling's |
70 | approximation. */ |
71 | float n = __ceilf (4.0f - x); |
72 | x_adj = math_narrow_eval (x + n); |
73 | x_eps = (x - (x_adj - n)); |
74 | prod = __gamma_productf (x_adj - n, x_eps, n, &eps); |
75 | } |
76 | /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). |
77 | Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, |
78 | starting by computing pow (X_ADJ, X_ADJ) with a power of 2 |
79 | factored out. */ |
80 | float exp_adj = -eps; |
81 | float x_adj_int = __roundf (x_adj); |
82 | float x_adj_frac = x_adj - x_adj_int; |
83 | int x_adj_log2; |
84 | float x_adj_mant = __frexpf (x_adj, &x_adj_log2); |
85 | if (x_adj_mant < (float) M_SQRT1_2) |
86 | { |
87 | x_adj_log2--; |
88 | x_adj_mant *= 2.0f; |
89 | } |
90 | *exp2_adj = x_adj_log2 * (int) x_adj_int; |
91 | float ret = (__ieee754_powf (x_adj_mant, x_adj) |
92 | * __ieee754_exp2f (x_adj_log2 * x_adj_frac) |
93 | * __ieee754_expf (-x_adj) |
94 | * __ieee754_sqrtf (2 * (float) M_PI / x_adj) |
95 | / prod); |
96 | exp_adj += x_eps * __ieee754_logf (x_adj); |
97 | float bsum = gamma_coeff[NCOEFF - 1]; |
98 | float x_adj2 = x_adj * x_adj; |
99 | for (size_t i = 1; i <= NCOEFF - 1; i++) |
100 | bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; |
101 | exp_adj += bsum / x_adj; |
102 | return ret + ret * __expm1f (exp_adj); |
103 | } |
104 | } |
105 | |
106 | float |
107 | __ieee754_gammaf_r (float x, int *signgamp) |
108 | { |
109 | int32_t hx; |
110 | float ret; |
111 | |
112 | GET_FLOAT_WORD (hx, x); |
113 | |
114 | if (__glibc_unlikely ((hx & 0x7fffffff) == 0)) |
115 | { |
116 | /* Return value for x == 0 is Inf with divide by zero exception. */ |
117 | *signgamp = 0; |
118 | return 1.0 / x; |
119 | } |
120 | if (__builtin_expect (hx < 0, 0) |
121 | && (uint32_t) hx < 0xff800000 && __rintf (x) == x) |
122 | { |
123 | /* Return value for integer x < 0 is NaN with invalid exception. */ |
124 | *signgamp = 0; |
125 | return (x - x) / (x - x); |
126 | } |
127 | if (__glibc_unlikely (hx == 0xff800000)) |
128 | { |
129 | /* x == -Inf. According to ISO this is NaN. */ |
130 | *signgamp = 0; |
131 | return x - x; |
132 | } |
133 | if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000)) |
134 | { |
135 | /* Positive infinity (return positive infinity) or NaN (return |
136 | NaN). */ |
137 | *signgamp = 0; |
138 | return x + x; |
139 | } |
140 | |
141 | if (x >= 36.0f) |
142 | { |
143 | /* Overflow. */ |
144 | *signgamp = 0; |
145 | ret = math_narrow_eval (FLT_MAX * FLT_MAX); |
146 | return ret; |
147 | } |
148 | else |
149 | { |
150 | SET_RESTORE_ROUNDF (FE_TONEAREST); |
151 | if (x > 0.0f) |
152 | { |
153 | *signgamp = 0; |
154 | int exp2_adj; |
155 | float tret = gammaf_positive (x, &exp2_adj); |
156 | ret = __scalbnf (tret, exp2_adj); |
157 | } |
158 | else if (x >= -FLT_EPSILON / 4.0f) |
159 | { |
160 | *signgamp = 0; |
161 | ret = 1.0f / x; |
162 | } |
163 | else |
164 | { |
165 | float tx = __truncf (x); |
166 | *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1; |
167 | if (x <= -42.0f) |
168 | /* Underflow. */ |
169 | ret = FLT_MIN * FLT_MIN; |
170 | else |
171 | { |
172 | float frac = tx - x; |
173 | if (frac > 0.5f) |
174 | frac = 1.0f - frac; |
175 | float sinpix = (frac <= 0.25f |
176 | ? __sinf ((float) M_PI * frac) |
177 | : __cosf ((float) M_PI * (0.5f - frac))); |
178 | int exp2_adj; |
179 | float tret = (float) M_PI / (-x * sinpix |
180 | * gammaf_positive (-x, &exp2_adj)); |
181 | ret = __scalbnf (tret, -exp2_adj); |
182 | math_check_force_underflow_nonneg (ret); |
183 | } |
184 | } |
185 | ret = math_narrow_eval (ret); |
186 | } |
187 | if (isinf (ret) && x != 0) |
188 | { |
189 | if (*signgamp < 0) |
190 | { |
191 | ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX); |
192 | ret = -ret; |
193 | } |
194 | else |
195 | ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX); |
196 | return ret; |
197 | } |
198 | else if (ret == 0) |
199 | { |
200 | if (*signgamp < 0) |
201 | { |
202 | ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN); |
203 | ret = -ret; |
204 | } |
205 | else |
206 | ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN); |
207 | return ret; |
208 | } |
209 | else |
210 | return ret; |
211 | } |
212 | strong_alias (__ieee754_gammaf_r, __gammaf_r_finite) |
213 | |