1333577Skib/*- 2333577Skib * Copyright (c) 2013 Bruce D. Evans 3333577Skib * All rights reserved. 4333577Skib * 5333577Skib * Redistribution and use in source and binary forms, with or without 6333577Skib * modification, are permitted provided that the following conditions 7333577Skib * are met: 8333577Skib * 1. Redistributions of source code must retain the above copyright 9333577Skib * notice unmodified, this list of conditions, and the following 10333577Skib * disclaimer. 11333577Skib * 2. Redistributions in binary form must reproduce the above copyright 12333577Skib * notice, this list of conditions and the following disclaimer in the 13333577Skib * documentation and/or other materials provided with the distribution. 14333577Skib * 15333577Skib * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16333577Skib * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17333577Skib * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18333577Skib * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19333577Skib * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20333577Skib * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21333577Skib * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22333577Skib * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23333577Skib * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24333577Skib * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25333577Skib */ 26333577Skib 27333577Skib#include <sys/cdefs.h> 28333577Skib__FBSDID("$FreeBSD: stable/11/lib/msun/src/s_clog.c 334654 2018-06-05 13:46:18Z kib $"); 29333577Skib 30333577Skib#include <complex.h> 31333577Skib#include <float.h> 32333577Skib 33333577Skib#include "fpmath.h" 34333577Skib#include "math.h" 35333577Skib#include "math_private.h" 36333577Skib 37333577Skib#define MANT_DIG DBL_MANT_DIG 38333577Skib#define MAX_EXP DBL_MAX_EXP 39333577Skib#define MIN_EXP DBL_MIN_EXP 40333577Skib 41333577Skibstatic const double 42333577Skibln2_hi = 6.9314718055829871e-1, /* 0x162e42fefa0000.0p-53 */ 43333577Skibln2_lo = 1.6465949582897082e-12; /* 0x1cf79abc9e3b3a.0p-92 */ 44333577Skib 45333577Skibdouble complex 46333577Skibclog(double complex z) 47333577Skib{ 48333577Skib double_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t; 49333577Skib double x, y, v; 50333577Skib uint32_t hax, hay; 51333577Skib int kx, ky; 52333577Skib 53333577Skib x = creal(z); 54333577Skib y = cimag(z); 55333577Skib v = atan2(y, x); 56333577Skib 57333577Skib ax = fabs(x); 58333577Skib ay = fabs(y); 59333577Skib if (ax < ay) { 60333577Skib t = ax; 61333577Skib ax = ay; 62333577Skib ay = t; 63333577Skib } 64333577Skib 65333577Skib GET_HIGH_WORD(hax, ax); 66333577Skib kx = (hax >> 20) - 1023; 67333577Skib GET_HIGH_WORD(hay, ay); 68333577Skib ky = (hay >> 20) - 1023; 69333577Skib 70333577Skib /* Handle NaNs and Infs using the general formula. */ 71333577Skib if (kx == MAX_EXP || ky == MAX_EXP) 72333577Skib return (CMPLX(log(hypot(x, y)), v)); 73333577Skib 74333577Skib /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */ 75333577Skib if (ax == 1) { 76333577Skib if (ky < (MIN_EXP - 1) / 2) 77333577Skib return (CMPLX((ay / 2) * ay, v)); 78333577Skib return (CMPLX(log1p(ay * ay) / 2, v)); 79333577Skib } 80333577Skib 81333577Skib /* Avoid underflow when ax is not small. Also handle zero args. */ 82333577Skib if (kx - ky > MANT_DIG || ay == 0) 83333577Skib return (CMPLX(log(ax), v)); 84333577Skib 85333577Skib /* Avoid overflow. */ 86333577Skib if (kx >= MAX_EXP - 1) 87333577Skib return (CMPLX(log(hypot(x * 0x1p-1022, y * 0x1p-1022)) + 88333577Skib (MAX_EXP - 2) * ln2_lo + (MAX_EXP - 2) * ln2_hi, v)); 89333577Skib if (kx >= (MAX_EXP - 1) / 2) 90333577Skib return (CMPLX(log(hypot(x, y)), v)); 91333577Skib 92333577Skib /* Reduce inaccuracies and avoid underflow when ax is denormal. */ 93333577Skib if (kx <= MIN_EXP - 2) 94333577Skib return (CMPLX(log(hypot(x * 0x1p1023, y * 0x1p1023)) + 95333577Skib (MIN_EXP - 2) * ln2_lo + (MIN_EXP - 2) * ln2_hi, v)); 96333577Skib 97333577Skib /* Avoid remaining underflows (when ax is small but not denormal). */ 98333577Skib if (ky < (MIN_EXP - 1) / 2 + MANT_DIG) 99333577Skib return (CMPLX(log(hypot(x, y)), v)); 100333577Skib 101333577Skib /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */ 102333577Skib t = (double)(ax * (0x1p27 + 1)); 103333577Skib axh = (double)(ax - t) + t; 104333577Skib axl = ax - axh; 105333577Skib ax2h = ax * ax; 106333577Skib ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl; 107333577Skib t = (double)(ay * (0x1p27 + 1)); 108333577Skib ayh = (double)(ay - t) + t; 109333577Skib ayl = ay - ayh; 110333577Skib ay2h = ay * ay; 111333577Skib ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl; 112333577Skib 113333577Skib /* 114333577Skib * When log(|z|) is far from 1, accuracy in calculating the sum 115333577Skib * of the squares is not very important since log() reduces 116333577Skib * inaccuracies. We depended on this to use the general 117333577Skib * formula when log(|z|) is very far from 1. When log(|z|) is 118333577Skib * moderately far from 1, we go through the extra-precision 119333577Skib * calculations to reduce branches and gain a little accuracy. 120333577Skib * 121333577Skib * When |z| is near 1, we subtract 1 and use log1p() and don't 122333577Skib * leave it to log() to subtract 1, since we gain at least 1 bit 123333577Skib * of accuracy in this way. 124333577Skib * 125333577Skib * When |z| is very near 1, subtracting 1 can cancel almost 126333577Skib * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in 127333577Skib * doubled precision, and then do the rest of the calculation 128333577Skib * in sloppy doubled precision. Although large cancellations 129333577Skib * often lose lots of accuracy, here the final result is exact 130333577Skib * in doubled precision if the large calculation occurs (because 131333577Skib * then it is exact in tripled precision and the cancellation 132333577Skib * removes enough bits to fit in doubled precision). Thus the 133333577Skib * result is accurate in sloppy doubled precision, and the only 134333577Skib * significant loss of accuracy is when it is summed and passed 135333577Skib * to log1p(). 136333577Skib */ 137333577Skib sh = ax2h; 138333577Skib sl = ay2h; 139333577Skib _2sumF(sh, sl); 140333577Skib if (sh < 0.5 || sh >= 3) 141333577Skib return (CMPLX(log(ay2l + ax2l + sl + sh) / 2, v)); 142333577Skib sh -= 1; 143333577Skib _2sum(sh, sl); 144333577Skib _2sum(ax2l, ay2l); 145333577Skib /* Briggs-Kahan algorithm (except we discard the final low term): */ 146333577Skib _2sum(sh, ax2l); 147333577Skib _2sum(sl, ay2l); 148333577Skib t = ax2l + sl; 149333577Skib _2sumF(sh, t); 150333577Skib return (CMPLX(log1p(ay2l + t + sh) / 2, v)); 151333577Skib} 152333577Skib 153333577Skib#if (LDBL_MANT_DIG == 53) 154333577Skib__weak_reference(clog, clogl); 155333577Skib#endif 156