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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