k_exp.cpp (3002B)
1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 //#include <sys/cdefs.h> 30 //__FBSDID("$FreeBSD$"); 31 32 #include "math_private.h" 33 34 static const uint32_t k = 1799; /* constant for reduction */ 35 static const double kln2 = 1246.97177782734161156; /* k * ln2 */ 36 37 /* 38 * Compute exp(x), scaled to avoid spurious overflow. An exponent is 39 * returned separately in 'expt'. 40 * 41 * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91 42 * Output: 2**1023 <= y < 2**1024 43 */ 44 static double 45 __frexp_exp(double x, int *expt) 46 { 47 double exp_x; 48 uint32_t hx; 49 50 /* 51 * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to 52 * minimize |exp(kln2) - 2**k|. We also scale the exponent of 53 * exp_x to MAX_EXP so that the result can be multiplied by 54 * a tiny number without losing accuracy due to denormalization. 55 */ 56 exp_x = exp(x - kln2); 57 GET_HIGH_WORD(hx, exp_x); 58 *expt = (hx >> 20) - (0x3ff + 1023) + k; 59 SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20)); 60 return (exp_x); 61 } 62 63 /* 64 * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt. 65 * They are intended for large arguments (real part >= ln(DBL_MAX)) 66 * where care is needed to avoid overflow. 67 * 68 * The present implementation is narrowly tailored for our hyperbolic and 69 * exponential functions. We assume expt is small (0 or -1), and the caller 70 * has filtered out very large x, for which overflow would be inevitable. 71 */ 72 73 double 74 __ldexp_exp(double x, int expt) 75 { 76 double exp_x, scale; 77 int ex_expt; 78 79 exp_x = __frexp_exp(x, &ex_expt); 80 expt += ex_expt; 81 INSERT_WORDS(scale, (0x3ff + expt) << 20, 0); 82 return (exp_x * scale); 83 }