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
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.
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
28 static char rcsid
[] = "$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $";
32 #include "math_private.h"
35 #define TBLSIZE (1 << TBLBITS)
38 redux
= 0x1.8p23f
/ TBLSIZE
,
44 static const volatile float
45 huge
__attribute__ ((__section__(".rodata"))) = 0x1p
100f
,
46 twom100
__attribute__ ((__section__(".rodata"))) = 0x1p
-100f
;
48 static const double exp2ft
[TBLSIZE
] = {
68 * exp2f(x): compute the base 2 exponential of x
70 * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
72 * Method: (equally-spaced tables)
75 * x = 2**k + y, for integer k and |y| <= 1/2.
76 * Thus we have exp2f(x) = 2**k * exp2(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).
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.
88 * This method is due to Tang, but I do not use his suggested parameters:
90 * Tang, P. Table-driven Implementation of the Exponential Function
91 * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
96 double tv
, twopk
, u
, z
;
101 /* Filter out exceptional cases. */
102 GET_FLOAT_WORD(hx
, x
);
103 ix
= hx
& 0x7fffffff; /* high word of |x| */
104 if(ix
>= 0x43000000) { /* |x| >= 128 */
105 if(ix
>= 0x7f800000) {
106 if ((ix
& 0x7fffff) != 0 || (hx
& 0x80000000) == 0)
107 return (x
+ x
); /* x is NaN or +Inf */
109 return (0.0); /* x is -Inf */
112 return (huge
* huge
); /* overflow */
114 return (twom100
* twom100
); /* underflow */
115 } else if (ix
<= 0x33000000) { /* |x| <= 0x1p-25 */
119 /* Reduce x, computing z, i0, and k. */
120 STRICT_ASSIGN(float, t
, x
+ redux
);
121 GET_FLOAT_WORD(i0
, t
);
123 k
= (i0
>> TBLBITS
) << 20;
127 INSERT_WORDS(twopk
, 0x3ff00000 + k
, 0);
129 /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
132 tv
= tv
+ u
* (P1
+ z
* P2
) + u
* (z
* z
) * (P3
+ z
* P4
);
134 /* Scale by 2**(k>>20). */