Branch data Line data Source code
1 : : /*-
2 : : * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
3 : : * All rights reserved.
4 : : *
5 : : * Redistribution and use in source and binary forms, with or without
6 : : * modification, are permitted provided that the following conditions
7 : : * are met:
8 : : * 1. Redistributions of source code must retain the above copyright
9 : : * notice, this list of conditions and the following disclaimer.
10 : : * 2. Redistributions in binary form must reproduce the above copyright
11 : : * notice, this list of conditions and the following disclaimer in the
12 : : * documentation and/or other materials provided with the distribution.
13 : : *
14 : : * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 : : * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 : : * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 : : * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 : : * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 : : * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 : : * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 : : * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 : : * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 : : * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 : : * SUCH DAMAGE.
25 : : */
26 : :
27 : : #include "cdefs-compat.h"
28 : : //__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $");
29 : :
30 : : #include <float.h>
31 : : #include <openlibm_math.h>
32 : :
33 : : #include "math_private.h"
34 : :
35 : : #define TBLBITS 4
36 : : #define TBLSIZE (1 << TBLBITS)
37 : :
38 : : static const float
39 : : huge = 0x1p100f,
40 : : redux = 0x1.8p23f / TBLSIZE,
41 : : P1 = 0x1.62e430p-1f,
42 : : P2 = 0x1.ebfbe0p-3f,
43 : : P3 = 0x1.c6b348p-5f,
44 : : P4 = 0x1.3b2c9cp-7f;
45 : :
46 : : static volatile float twom100 = 0x1p-100f;
47 : :
48 : : static const double exp2ft[TBLSIZE] = {
49 : : 0x1.6a09e667f3bcdp-1,
50 : : 0x1.7a11473eb0187p-1,
51 : : 0x1.8ace5422aa0dbp-1,
52 : : 0x1.9c49182a3f090p-1,
53 : : 0x1.ae89f995ad3adp-1,
54 : : 0x1.c199bdd85529cp-1,
55 : : 0x1.d5818dcfba487p-1,
56 : : 0x1.ea4afa2a490dap-1,
57 : : 0x1.0000000000000p+0,
58 : : 0x1.0b5586cf9890fp+0,
59 : : 0x1.172b83c7d517bp+0,
60 : : 0x1.2387a6e756238p+0,
61 : : 0x1.306fe0a31b715p+0,
62 : : 0x1.3dea64c123422p+0,
63 : : 0x1.4bfdad5362a27p+0,
64 : : 0x1.5ab07dd485429p+0,
65 : : };
66 : :
67 : : /*
68 : : * exp2f(x): compute the base 2 exponential of x
69 : : *
70 : : * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
71 : : *
72 : : * Method: (equally-spaced tables)
73 : : *
74 : : * Reduce x:
75 : : * x = 2**k + y, for integer k and |y| <= 1/2.
76 : : * Thus we have exp2f(x) = 2**k * exp2(y).
77 : : *
78 : : * Reduce y:
79 : : * y = i/TBLSIZE + z for integer i near y * TBLSIZE.
80 : : * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
81 : : * with |z| <= 2**-(TBLSIZE+1).
82 : : *
83 : : * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
84 : : * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
85 : : * Using double precision for everything except the reduction makes
86 : : * roundoff error insignificant and simplifies the scaling step.
87 : : *
88 : : * This method is due to Tang, but I do not use his suggested parameters:
89 : : *
90 : : * Tang, P. Table-driven Implementation of the Exponential Function
91 : : * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
92 : : */
93 : : OLM_DLLEXPORT float
94 : 11 : exp2f(float x)
95 : : {
96 : : double tv, twopk, u, z;
97 : : float t;
98 : : u_int32_t hx, ix, i0;
99 : : int32_t k;
100 : :
101 : : /* Filter out exceptional cases. */
102 : 11 : GET_FLOAT_WORD(hx, x);
103 : 11 : ix = hx & 0x7fffffff; /* high word of |x| */
104 [ + + ]: 11 : if(ix >= 0x43000000) { /* |x| >= 128 */
105 [ + + ]: 5 : if(ix >= 0x7f800000) {
106 [ + + + + ]: 3 : if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
107 : 2 : return (x + x); /* x is NaN or +Inf */
108 : : else
109 : 1 : return (0.0); /* x is -Inf */
110 : : }
111 [ + + ]: 2 : if(x >= 0x1.0p7f)
112 : 1 : return (huge * huge); /* overflow */
113 [ + - ]: 1 : if(x <= -0x1.2cp7f)
114 : 1 : return (twom100 * twom100); /* underflow */
115 [ + + ]: 6 : } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
116 : 3 : return (1.0f + x);
117 : : }
118 : :
119 : : /* Reduce x, computing z, i0, and k. */
120 : 3 : STRICT_ASSIGN(float, t, x + redux);
121 : 3 : GET_FLOAT_WORD(i0, t);
122 : 3 : i0 += TBLSIZE / 2;
123 : 3 : k = (i0 >> TBLBITS) << 20;
124 : 3 : i0 &= TBLSIZE - 1;
125 : 3 : t -= redux;
126 : 3 : z = x - t;
127 : 3 : INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
128 : :
129 : : /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
130 : 3 : tv = exp2ft[i0];
131 : 3 : u = tv * z;
132 : 3 : tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
133 : :
134 : : /* Scale by 2**(k>>20). */
135 : 3 : return (tv * twopk);
136 : : }
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