2 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
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12 * documentation and/or other materials provided with the distribution.
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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
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26 * $NetBSD: s_exp2f.c,v 1.1 2010/01/11 16:28:39 christos Exp $
32 #include "math_private.h"
35 #define TBLSIZE (1 << TBLBITS)
39 redux = 0x1.8p23f / TBLSIZE,
45 static volatile float twom100 = 0x1p-100f;
47 static const double exp2ft[TBLSIZE] = {
67 * exp2f(x): compute the base 2 exponential of x
69 * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
71 * Method: (equally-spaced tables)
74 * x = 2**k + y, for integer k and |y| <= 1/2.
75 * Thus we have exp2f(x) = 2**k * exp2(y).
78 * y = i/TBLSIZE + z for integer i near y * TBLSIZE.
79 * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
80 * with |z| <= 2**-(TBLSIZE+1).
82 * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
83 * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
84 * Using double precision for everything except the reduction makes
85 * roundoff error insignificant and simplifies the scaling step.
87 * This method is due to Tang, but I do not use his suggested parameters:
89 * Tang, P. Table-driven Implementation of the Exponential Function
90 * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
95 double tv, twopk, u, z;
100 /* Filter out exceptional cases. */
101 GET_FLOAT_WORD(hx, x);
102 ix = hx & 0x7fffffff; /* high word of |x| */
103 if(ix >= 0x43000000) { /* |x| >= 128 */
104 if(ix >= 0x7f800000) {
105 if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
106 return (x + x); /* x is NaN or +Inf */
108 return (0.0); /* x is -Inf */
111 return (huge * huge); /* overflow */
113 return (twom100 * twom100); /* underflow */
114 } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
118 /* Reduce x, computing z, i0, and k. */
119 STRICT_ASSIGN(float, t, x + redux);
120 GET_FLOAT_WORD(i0, t);
122 k = (i0 >> TBLBITS) << 20;
126 INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
128 /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
131 tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
133 /* Scale by 2**(k>>20). */