]>
Commit | Line | Data |
---|---|---|
e70c1768 | 1 | /* Double-precision e^x function. |
04277e02 | 2 | Copyright (C) 2018-2019 Free Software Foundation, Inc. |
e70c1768 SN |
3 | This file is part of the GNU C Library. |
4 | ||
5 | The GNU C Library is free software; you can redistribute it and/or | |
6 | modify it under the terms of the GNU Lesser General Public | |
7 | License as published by the Free Software Foundation; either | |
8 | version 2.1 of the License, or (at your option) any later version. | |
9 | ||
10 | The GNU C Library is distributed in the hope that it will be useful, | |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 | Lesser General Public License for more details. | |
14 | ||
15 | You should have received a copy of the GNU Lesser General Public | |
16 | License along with the GNU C Library; if not, see | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
e4d82761 | 18 | |
f3426898 | 19 | #include <math.h> |
e70c1768 | 20 | #include <stdint.h> |
b4d5b8b0 | 21 | #include <math-barriers.h> |
e70c1768 | 22 | #include <math-narrow-eval.h> |
c20a1056 SN |
23 | #include <math-svid-compat.h> |
24 | #include <shlib-compat.h> | |
25 | #include <libm-alias-double.h> | |
e70c1768 SN |
26 | #include "math_config.h" |
27 | ||
28 | #define N (1 << EXP_TABLE_BITS) | |
29 | #define InvLn2N __exp_data.invln2N | |
30 | #define NegLn2hiN __exp_data.negln2hiN | |
31 | #define NegLn2loN __exp_data.negln2loN | |
32 | #define Shift __exp_data.shift | |
33 | #define T __exp_data.tab | |
34 | #define C2 __exp_data.poly[5 - EXP_POLY_ORDER] | |
35 | #define C3 __exp_data.poly[6 - EXP_POLY_ORDER] | |
36 | #define C4 __exp_data.poly[7 - EXP_POLY_ORDER] | |
37 | #define C5 __exp_data.poly[8 - EXP_POLY_ORDER] | |
38 | ||
39 | /* Handle cases that may overflow or underflow when computing the result that | |
40 | is scale*(1+TMP) without intermediate rounding. The bit representation of | |
41 | scale is in SBITS, however it has a computed exponent that may have | |
42 | overflown into the sign bit so that needs to be adjusted before using it as | |
43 | a double. (int32_t)KI is the k used in the argument reduction and exponent | |
44 | adjustment of scale, positive k here means the result may overflow and | |
45 | negative k means the result may underflow. */ | |
46 | static inline double | |
47 | specialcase (double_t tmp, uint64_t sbits, uint64_t ki) | |
48 | { | |
49 | double_t scale, y; | |
50 | ||
51 | if ((ki & 0x80000000) == 0) | |
52 | { | |
53 | /* k > 0, the exponent of scale might have overflowed by <= 460. */ | |
54 | sbits -= 1009ull << 52; | |
55 | scale = asdouble (sbits); | |
56 | y = 0x1p1009 * (scale + scale * tmp); | |
57 | return check_oflow (y); | |
58 | } | |
59 | /* k < 0, need special care in the subnormal range. */ | |
60 | sbits += 1022ull << 52; | |
61 | scale = asdouble (sbits); | |
62 | y = scale + scale * tmp; | |
63 | if (y < 1.0) | |
64 | { | |
65 | /* Round y to the right precision before scaling it into the subnormal | |
66 | range to avoid double rounding that can cause 0.5+E/2 ulp error where | |
67 | E is the worst-case ulp error outside the subnormal range. So this | |
68 | is only useful if the goal is better than 1 ulp worst-case error. */ | |
69 | double_t hi, lo; | |
70 | lo = scale - y + scale * tmp; | |
71 | hi = 1.0 + y; | |
72 | lo = 1.0 - hi + y + lo; | |
73 | y = math_narrow_eval (hi + lo) - 1.0; | |
74 | /* Avoid -0.0 with downward rounding. */ | |
75 | if (WANT_ROUNDING && y == 0.0) | |
76 | y = 0.0; | |
77 | /* The underflow exception needs to be signaled explicitly. */ | |
78 | math_force_eval (math_opt_barrier (0x1p-1022) * 0x1p-1022); | |
79 | } | |
80 | y = 0x1p-1022 * y; | |
81 | return check_uflow (y); | |
82 | } | |
83 | ||
84 | /* Top 12 bits of a double (sign and exponent bits). */ | |
85 | static inline uint32_t | |
86 | top12 (double x) | |
87 | { | |
88 | return asuint64 (x) >> 52; | |
89 | } | |
90 | ||
424c4f60 SN |
91 | #ifndef SECTION |
92 | # define SECTION | |
93 | #endif | |
94 | ||
95 | double | |
96 | SECTION | |
c20a1056 | 97 | __exp (double x) |
e70c1768 SN |
98 | { |
99 | uint32_t abstop; | |
100 | uint64_t ki, idx, top, sbits; | |
101 | /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ | |
102 | double_t kd, z, r, r2, scale, tail, tmp; | |
103 | ||
104 | abstop = top12 (x) & 0x7ff; | |
105 | if (__glibc_unlikely (abstop - top12 (0x1p-54) | |
106 | >= top12 (512.0) - top12 (0x1p-54))) | |
107 | { | |
108 | if (abstop - top12 (0x1p-54) >= 0x80000000) | |
109 | /* Avoid spurious underflow for tiny x. */ | |
110 | /* Note: 0 is common input. */ | |
111 | return WANT_ROUNDING ? 1.0 + x : 1.0; | |
112 | if (abstop >= top12 (1024.0)) | |
113 | { | |
114 | if (asuint64 (x) == asuint64 (-INFINITY)) | |
115 | return 0.0; | |
116 | if (abstop >= top12 (INFINITY)) | |
117 | return 1.0 + x; | |
118 | if (asuint64 (x) >> 63) | |
119 | return __math_uflow (0); | |
120 | else | |
121 | return __math_oflow (0); | |
122 | } | |
123 | /* Large x is special cased below. */ | |
124 | abstop = 0; | |
125 | } | |
126 | ||
127 | /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ | |
128 | /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ | |
129 | z = InvLn2N * x; | |
130 | #if TOINT_INTRINSICS | |
131 | kd = roundtoint (z); | |
132 | ki = converttoint (z); | |
133 | #else | |
134 | /* z - kd is in [-1, 1] in non-nearest rounding modes. */ | |
135 | kd = math_narrow_eval (z + Shift); | |
136 | ki = asuint64 (kd); | |
137 | kd -= Shift; | |
138 | #endif | |
139 | r = x + kd * NegLn2hiN + kd * NegLn2loN; | |
e70c1768 SN |
140 | /* 2^(k/N) ~= scale * (1 + tail). */ |
141 | idx = 2 * (ki % N); | |
142 | top = ki << (52 - EXP_TABLE_BITS); | |
143 | tail = asdouble (T[idx]); | |
144 | /* This is only a valid scale when -1023*N < k < 1024*N. */ | |
145 | sbits = T[idx + 1] + top; | |
146 | /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ | |
147 | /* Evaluation is optimized assuming superscalar pipelined execution. */ | |
148 | r2 = r * r; | |
149 | /* Without fma the worst case error is 0.25/N ulp larger. */ | |
150 | /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ | |
151 | tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5); | |
152 | if (__glibc_unlikely (abstop == 0)) | |
153 | return specialcase (tmp, sbits, ki); | |
154 | scale = asdouble (sbits); | |
424c4f60 | 155 | /* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-739, so there |
e70c1768 SN |
156 | is no spurious underflow here even without fma. */ |
157 | return scale + scale * tmp; | |
158 | } | |
c20a1056 SN |
159 | #ifndef __exp |
160 | hidden_def (__exp) | |
161 | strong_alias (__exp, __ieee754_exp) | |
162 | strong_alias (__exp, __exp_finite) | |
163 | # if LIBM_SVID_COMPAT | |
164 | versioned_symbol (libm, __exp, exp, GLIBC_2_29); | |
165 | libm_alias_double_other (__exp, exp) | |
166 | # else | |
167 | libm_alias_double (__exp, exp) | |
168 | # endif | |
af968f62 | 169 | #endif |