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-rw-r--r--src/math/__expo2.c49
-rw-r--r--src/math/__expo2f.c49
2 files changed, 14 insertions, 84 deletions
diff --git a/src/math/__expo2.c b/src/math/__expo2.c
index ef14e5f5..740ac680 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 <das@FreeBSD.ORG>
- * 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|
- */
-static const uint32_t k = 1799;
-static const double kln2 = 1246.97177782734161156;
+/* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
+static const int k = 2043;
+static const double kln2 = 0x1.62066151add8bp+10;
-/* exp(x)/2 when x is huge */
+/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
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, (uint32_t)(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 192838f7..5163e418 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 <das@FreeBSD.ORG>
- * 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|
- */
-static const uint32_t k = 235;
-static const float kln2 = 162.88958740f;
+/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
+static const int k = 235;
+static const float kln2 = 0x1.45c778p+7f;
-/* expf(x)/2 when x is huge */
+/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
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, (uint32_t)(0x7f + k/2) << 23);
+ /* exp(x - k ln2) * 2**(k-1) */
return expf(x - kln2) * scale * scale;
}