source: azure_iot_hub/trunk/musl-1.1.18/src/math/exp2f.c@ 389

Last change on this file since 389 was 389, checked in by coas-nagasima, 5 years ago

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1/* origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c */
2/*-
3 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28#include "libm.h"
29
30#define TBLSIZE 16
31
32static const float
33redux = 0x1.8p23f / TBLSIZE,
34P1 = 0x1.62e430p-1f,
35P2 = 0x1.ebfbe0p-3f,
36P3 = 0x1.c6b348p-5f,
37P4 = 0x1.3b2c9cp-7f;
38
39static const double exp2ft[TBLSIZE] = {
40 0x1.6a09e667f3bcdp-1,
41 0x1.7a11473eb0187p-1,
42 0x1.8ace5422aa0dbp-1,
43 0x1.9c49182a3f090p-1,
44 0x1.ae89f995ad3adp-1,
45 0x1.c199bdd85529cp-1,
46 0x1.d5818dcfba487p-1,
47 0x1.ea4afa2a490dap-1,
48 0x1.0000000000000p+0,
49 0x1.0b5586cf9890fp+0,
50 0x1.172b83c7d517bp+0,
51 0x1.2387a6e756238p+0,
52 0x1.306fe0a31b715p+0,
53 0x1.3dea64c123422p+0,
54 0x1.4bfdad5362a27p+0,
55 0x1.5ab07dd485429p+0,
56};
57
58/*
59 * exp2f(x): compute the base 2 exponential of x
60 *
61 * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
62 *
63 * Method: (equally-spaced tables)
64 *
65 * Reduce x:
66 * x = k + y, for integer k and |y| <= 1/2.
67 * Thus we have exp2f(x) = 2**k * exp2(y).
68 *
69 * Reduce y:
70 * y = i/TBLSIZE + z for integer i near y * TBLSIZE.
71 * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
72 * with |z| <= 2**-(TBLSIZE+1).
73 *
74 * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
75 * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
76 * Using double precision for everything except the reduction makes
77 * roundoff error insignificant and simplifies the scaling step.
78 *
79 * This method is due to Tang, but I do not use his suggested parameters:
80 *
81 * Tang, P. Table-driven Implementation of the Exponential Function
82 * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
83 */
84float exp2f(float x)
85{
86 double_t t, r, z;
87 union {float f; uint32_t i;} u = {x};
88 union {double f; uint64_t i;} uk;
89 uint32_t ix, i0, k;
90
91 /* Filter out exceptional cases. */
92 ix = u.i & 0x7fffffff;
93 if (ix > 0x42fc0000) { /* |x| > 126 */
94 if (ix > 0x7f800000) /* NaN */
95 return x;
96 if (u.i >= 0x43000000 && u.i < 0x80000000) { /* x >= 128 */
97 x *= 0x1p127f;
98 return x;
99 }
100 if (u.i >= 0x80000000) { /* x < -126 */
101 if (u.i >= 0xc3160000 || (u.i & 0x0000ffff))
102 FORCE_EVAL(-0x1p-149f/x);
103 if (u.i >= 0xc3160000) /* x <= -150 */
104 return 0;
105 }
106 } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
107 return 1.0f + x;
108 }
109
110 /* Reduce x, computing z, i0, and k. */
111 u.f = x + redux;
112 i0 = u.i;
113 i0 += TBLSIZE / 2;
114 k = i0 / TBLSIZE;
115 uk.i = (uint64_t)(0x3ff + k)<<52;
116 i0 &= TBLSIZE - 1;
117 u.f -= redux;
118 z = x - u.f;
119 /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
120 r = exp2ft[i0];
121 t = r * z;
122 r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
123
124 /* Scale by 2**k */
125 return r * uk.f;
126}
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