12188b77a2
exp(x) scaled down by some factor, and the challenge is doing this accurately when exp(x) would overflow. This change replaces all of the tricks we've been using with common __ldexp_exp() and __ldexp_cexp() routines that handle all the scaling. bde plans to improve on this further by moving the guts of exp() into k_exp.c and handling the scaling in a more direct manner. But the current approach is simple and adequate for now.
90 lines
2.8 KiB
C
90 lines
2.8 KiB
C
/*-
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* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <math.h>
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#include "math_private.h"
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static const uint32_t
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exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */
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cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
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float complex
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cexpf(float complex z)
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{
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float x, y, exp_x;
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uint32_t hx, hy;
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x = crealf(z);
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y = cimagf(z);
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GET_FLOAT_WORD(hy, y);
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hy &= 0x7fffffff;
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/* cexp(x + I 0) = exp(x) + I 0 */
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if (hy == 0)
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return (cpackf(expf(x), y));
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GET_FLOAT_WORD(hx, x);
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/* cexp(0 + I y) = cos(y) + I sin(y) */
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if ((hx & 0x7fffffff) == 0)
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return (cpackf(cosf(y), sinf(y)));
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if (hy >= 0x7f800000) {
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if ((hx & 0x7fffffff) != 0x7f800000) {
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/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
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return (cpackf(y - y, y - y));
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} else if (hx & 0x80000000) {
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/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
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return (cpackf(0.0, 0.0));
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} else {
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/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
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return (cpackf(x, y - y));
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}
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}
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if (hx >= exp_ovfl && hx <= cexp_ovfl) {
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/*
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* x is between 88.7 and 192, so we must scale to avoid
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* overflow in expf(x).
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*/
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return (__ldexp_cexpf(z, 0));
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} else {
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/*
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* Cases covered here:
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* - x < exp_ovfl and exp(x) won't overflow (common case)
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* - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
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* - x = +-Inf (generated by exp())
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* - x = NaN (spurious inexact exception from y)
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*/
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exp_x = expf(x);
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return (cpackf(exp_x * cosf(y), exp_x * sinf(y)));
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}
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}
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