From 5b0b42043c70ae677322aba55af6558eb2db6bb8 Mon Sep 17 00:00:00 2001 From: nsz Date: Tue, 13 Mar 2012 02:58:22 +0100 Subject: [PATCH] __expo2 cleanup --- src/math/__expo2.c | 45 +++++---------------------------------------- src/math/__expo2f.c | 45 +++++---------------------------------------- 2 files changed, 10 insertions(+), 80 deletions(-) diff --git a/src/math/__expo2.c b/src/math/__expo2.c index ef14e5f..61ae7fd 100644 --- a/src/math/__expo2.c +++ b/src/math/__expo2.c @@ -1,51 +1,16 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */ -/*- - * Copyright (c) 2011 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - #include "libm.h" -/* - * We use exp(x) = exp(x - kln2) * 2**k, - * k is carefully chosen to minimize |exp(kln2) - 2**k| - */ +/* k minimizes |exp(k ln2) - 2**k|, see cmath/__cexp.c */ static const uint32_t k = 1799; static const double kln2 = 1246.97177782734161156; -/* exp(x)/2 when x is huge */ +/* exp(x)/2 for large x */ double __expo2(double x) { double scale; - int n; - /* - * efficient scalbn(y, k-1): - * 2**(k-1) cannot be represented - * so we use that k-1 is even and scale in two steps - */ - n = (k - 1)/2; - INSERT_WORDS(scale, (0x3ff + n) << 20, 0); + /* note that k is odd and scale*scale overflows */ + INSERT_WORDS(scale, (0x3ff + k/2) << 20, 0); + /* exp(x - k ln2) * 2**(k-1) */ return exp(x - kln2) * scale * scale; } diff --git a/src/math/__expo2f.c b/src/math/__expo2f.c index 192838f..d35f440 100644 --- a/src/math/__expo2f.c +++ b/src/math/__expo2f.c @@ -1,51 +1,16 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_expf.c */ -/*- - * Copyright (c) 2011 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - #include "libm.h" -/* - * We use exp(x) = exp(x - kln2) * 2**k, - * k is carefully chosen to minimize |exp(kln2) - 2**k| - */ +/* k minimizes |exp(k ln2) - 2**k|, see cmath/__cexpf.c */ static const uint32_t k = 235; static const float kln2 = 162.88958740f; -/* expf(x)/2 when x is huge */ +/* expf(x)/2 for large x */ float __expo2f(float x) { float scale; - int n; - /* - * efficient scalbnf(y, k-1): - * 2**(k-1) cannot be represented - * so we use that k-1 is even and scale in two steps - */ - n = (k - 1)/2; - SET_FLOAT_WORD(scale, (0x7f + n) << 23); + /* note that k is odd and scale*scale overflows */ + SET_FLOAT_WORD(scale, (0x7f + k/2) << 23); + /* exp(x - k ln2) * 2**(k-1) */ return expf(x - kln2) * scale * scale; } -- 2.20.1