[352] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */
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| 2 | /*-
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| 3 | * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
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| 4 | * All rights reserved.
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| 5 | *
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| 6 | * Redistribution and use in source and binary forms, with or without
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| 7 | * modification, are permitted provided that the following conditions
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| 8 | * are met:
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| 9 | * 1. Redistributions of source code must retain the above copyright
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| 10 | * notice, this list of conditions and the following disclaimer.
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| 11 | * 2. Redistributions in binary form must reproduce the above copyright
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| 12 | * notice, this list of conditions and the following disclaimer in the
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| 13 | * documentation and/or other materials provided with the distribution.
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| 14 | *
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| 15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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| 16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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| 17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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| 18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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| 19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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| 20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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| 21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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| 22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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| 23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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| 24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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| 25 | * SUCH DAMAGE.
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| 26 | */
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| 27 |
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| 28 | #include "libm.h"
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| 29 |
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| 30 | static const uint32_t k = 1799; /* constant for reduction */
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| 31 | static const double kln2 = 1246.97177782734161156; /* k * ln2 */
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| 32 |
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| 33 | /*
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| 34 | * Compute exp(x), scaled to avoid spurious overflow. An exponent is
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| 35 | * returned separately in 'expt'.
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| 36 | *
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| 37 | * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
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| 38 | * Output: 2**1023 <= y < 2**1024
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| 39 | */
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| 40 | static double __frexp_exp(double x, int *expt)
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| 41 | {
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| 42 | double exp_x;
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| 43 | uint32_t hx;
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| 44 |
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| 45 | /*
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| 46 | * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
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| 47 | * minimize |exp(kln2) - 2**k|. We also scale the exponent of
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| 48 | * exp_x to MAX_EXP so that the result can be multiplied by
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| 49 | * a tiny number without losing accuracy due to denormalization.
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| 50 | */
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| 51 | exp_x = exp(x - kln2);
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| 52 | GET_HIGH_WORD(hx, exp_x);
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| 53 | *expt = (hx >> 20) - (0x3ff + 1023) + k;
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| 54 | SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
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| 55 | return exp_x;
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| 56 | }
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| 57 |
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| 58 | /*
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| 59 | * __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
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| 60 | * It is intended for large arguments (real part >= ln(DBL_MAX))
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| 61 | * where care is needed to avoid overflow.
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| 62 | *
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| 63 | * The present implementation is narrowly tailored for our hyperbolic and
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| 64 | * exponential functions. We assume expt is small (0 or -1), and the caller
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| 65 | * has filtered out very large x, for which overflow would be inevitable.
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| 66 | */
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| 67 | double complex __ldexp_cexp(double complex z, int expt)
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| 68 | {
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| 69 | double x, y, exp_x, scale1, scale2;
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| 70 | int ex_expt, half_expt;
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| 71 |
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| 72 | x = creal(z);
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| 73 | y = cimag(z);
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| 74 | exp_x = __frexp_exp(x, &ex_expt);
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| 75 | expt += ex_expt;
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| 76 |
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| 77 | /*
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| 78 | * Arrange so that scale1 * scale2 == 2**expt. We use this to
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| 79 | * compensate for scalbn being horrendously slow.
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| 80 | */
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| 81 | half_expt = expt / 2;
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| 82 | INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
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| 83 | half_expt = expt - half_expt;
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| 84 | INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
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| 85 |
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| 86 | return CMPLX(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
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| 87 | }
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