1*12188b77SDavid Schultz /*- 2*12188b77SDavid Schultz * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 3*12188b77SDavid Schultz * All rights reserved. 4*12188b77SDavid Schultz * 5*12188b77SDavid Schultz * Redistribution and use in source and binary forms, with or without 6*12188b77SDavid Schultz * modification, are permitted provided that the following conditions 7*12188b77SDavid Schultz * are met: 8*12188b77SDavid Schultz * 1. Redistributions of source code must retain the above copyright 9*12188b77SDavid Schultz * notice, this list of conditions and the following disclaimer. 10*12188b77SDavid Schultz * 2. Redistributions in binary form must reproduce the above copyright 11*12188b77SDavid Schultz * notice, this list of conditions and the following disclaimer in the 12*12188b77SDavid Schultz * documentation and/or other materials provided with the distribution. 13*12188b77SDavid Schultz * 14*12188b77SDavid Schultz * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15*12188b77SDavid Schultz * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16*12188b77SDavid Schultz * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17*12188b77SDavid Schultz * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18*12188b77SDavid Schultz * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19*12188b77SDavid Schultz * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20*12188b77SDavid Schultz * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21*12188b77SDavid Schultz * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22*12188b77SDavid Schultz * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23*12188b77SDavid Schultz * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24*12188b77SDavid Schultz * SUCH DAMAGE. 25*12188b77SDavid Schultz */ 26*12188b77SDavid Schultz 27*12188b77SDavid Schultz #include <sys/cdefs.h> 28*12188b77SDavid Schultz __FBSDID("$FreeBSD$"); 29*12188b77SDavid Schultz 30*12188b77SDavid Schultz #include <complex.h> 31*12188b77SDavid Schultz 32*12188b77SDavid Schultz #include "math.h" 33*12188b77SDavid Schultz #include "math_private.h" 34*12188b77SDavid Schultz 35*12188b77SDavid Schultz static const uint32_t k = 235; /* constant for reduction */ 36*12188b77SDavid Schultz static const float kln2 = 162.88958740F; /* k * ln2 */ 37*12188b77SDavid Schultz 38*12188b77SDavid Schultz /* 39*12188b77SDavid Schultz * See k_exp.c for details. 40*12188b77SDavid Schultz * 41*12188b77SDavid Schultz * Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7 42*12188b77SDavid Schultz * Output: 2**127 <= y < 2**128 43*12188b77SDavid Schultz */ 44*12188b77SDavid Schultz static float 45*12188b77SDavid Schultz __frexp_expf(float x, int *expt) 46*12188b77SDavid Schultz { 47*12188b77SDavid Schultz double exp_x; 48*12188b77SDavid Schultz uint32_t hx; 49*12188b77SDavid Schultz 50*12188b77SDavid Schultz exp_x = expf(x - kln2); 51*12188b77SDavid Schultz GET_FLOAT_WORD(hx, exp_x); 52*12188b77SDavid Schultz *expt = (hx >> 23) - (0x7f + 127) + k; 53*12188b77SDavid Schultz SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23)); 54*12188b77SDavid Schultz return (exp_x); 55*12188b77SDavid Schultz } 56*12188b77SDavid Schultz 57*12188b77SDavid Schultz float 58*12188b77SDavid Schultz __ldexp_expf(float x, int expt) 59*12188b77SDavid Schultz { 60*12188b77SDavid Schultz float exp_x, scale; 61*12188b77SDavid Schultz int ex_expt; 62*12188b77SDavid Schultz 63*12188b77SDavid Schultz exp_x = __frexp_expf(x, &ex_expt); 64*12188b77SDavid Schultz expt += ex_expt; 65*12188b77SDavid Schultz SET_FLOAT_WORD(scale, (0x7f + expt) << 23); 66*12188b77SDavid Schultz return (exp_x * scale); 67*12188b77SDavid Schultz } 68*12188b77SDavid Schultz 69*12188b77SDavid Schultz float complex 70*12188b77SDavid Schultz __ldexp_cexpf(float complex z, int expt) 71*12188b77SDavid Schultz { 72*12188b77SDavid Schultz float x, y, exp_x, scale1, scale2; 73*12188b77SDavid Schultz int ex_expt, half_expt; 74*12188b77SDavid Schultz 75*12188b77SDavid Schultz x = crealf(z); 76*12188b77SDavid Schultz y = cimagf(z); 77*12188b77SDavid Schultz exp_x = __frexp_expf(x, &ex_expt); 78*12188b77SDavid Schultz expt += ex_expt; 79*12188b77SDavid Schultz 80*12188b77SDavid Schultz half_expt = expt / 2; 81*12188b77SDavid Schultz SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23); 82*12188b77SDavid Schultz half_expt = expt - half_expt; 83*12188b77SDavid Schultz SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23); 84*12188b77SDavid Schultz 85*12188b77SDavid Schultz return (cpackf(cosf(y) * exp_x * scale1 * scale2, 86*12188b77SDavid Schultz sinf(y) * exp_x * scale1 * scale2)); 87*12188b77SDavid Schultz } 88