109 lines
3.6 KiB
C
109 lines
3.6 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 "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/k_exp.c,v 1.1 2011/10/21 06:27:56 das Exp $");
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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static const u_int32_t k = 1799; /* constant for reduction */
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static const double kln2 = 1246.97177782734161156; /* k * ln2 */
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/*
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* Compute exp(x), scaled to avoid spurious overflow. An exponent is
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* returned separately in 'expt'.
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*
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* Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
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* Output: 2**1023 <= y < 2**1024
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*/
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static double
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__frexp_exp(double x, int *expt)
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{
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double exp_x;
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u_int32_t hx;
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/*
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* We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
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* minimize |exp(kln2) - 2**k|. We also scale the exponent of
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* exp_x to MAX_EXP so that the result can be multiplied by
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* a tiny number without losing accuracy due to denormalization.
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*/
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exp_x = exp(x - kln2);
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GET_HIGH_WORD(hx, exp_x);
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*expt = (hx >> 20) - (0x3ff + 1023) + k;
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SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
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return (exp_x);
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}
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/*
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* __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
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* They are intended for large arguments (real part >= ln(DBL_MAX))
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* where care is needed to avoid overflow.
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*
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* The present implementation is narrowly tailored for our hyperbolic and
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* exponential functions. We assume expt is small (0 or -1), and the caller
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* has filtered out very large x, for which overflow would be inevitable.
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*/
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OLM_DLLEXPORT double
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__ldexp_exp(double x, int expt)
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{
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double exp_x, scale;
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int ex_expt;
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exp_x = __frexp_exp(x, &ex_expt);
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expt += ex_expt;
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INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
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return (exp_x * scale);
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}
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OLM_DLLEXPORT double complex
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__ldexp_cexp(double complex z, int expt)
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{
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double x, y, exp_x, scale1, scale2;
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int ex_expt, half_expt;
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x = creal(z);
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y = cimag(z);
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exp_x = __frexp_exp(x, &ex_expt);
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expt += ex_expt;
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/*
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* Arrange so that scale1 * scale2 == 2**expt. We use this to
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* compensate for scalbn being horrendously slow.
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*/
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half_expt = expt / 2;
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INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
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half_expt = expt - half_expt;
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INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
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return (CMPLX(cos(y) * exp_x * scale1 * scale2,
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sin(y) * exp_x * scale1 * scale2));
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}
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