1 files changed, 83 insertions, 0 deletions
diff --git a/modules/fdlibm/src/k_exp.cpp b/modules/fdlibm/src/k_exp.cpp
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+++ b/modules/fdlibm/src/k_exp.cpp
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+/*-
+ * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
+ *
+ * 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 <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+ #include "math_private.h"
+
+static const uint32_t k = 1799;		/* constant for reduction */
+static const double kln2 =  1246.97177782734161156;	/* k * ln2 */
+
+/*
+ * Compute exp(x), scaled to avoid spurious overflow.  An exponent is
+ * returned separately in 'expt'.
+ *
+ * Input:  ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
+ * Output: 2**1023 <= y < 2**1024
+ */
+static double
+__frexp_exp(double x, int *expt)
+{
+	double exp_x;
+	uint32_t hx;
+
+	/*
+	 * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
+	 * minimize |exp(kln2) - 2**k|.  We also scale the exponent of
+	 * exp_x to MAX_EXP so that the result can be multiplied by
+	 * a tiny number without losing accuracy due to denormalization.
+	 */
+	exp_x = exp(x - kln2);
+	GET_HIGH_WORD(hx, exp_x);
+	*expt = (hx >> 20) - (0x3ff + 1023) + k;
+	SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
+	return (exp_x);
+}
+
+/*
+ * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
+ * They are intended for large arguments (real part >= ln(DBL_MAX))
+ * where care is needed to avoid overflow.
+ *
+ * The present implementation is narrowly tailored for our hyperbolic and
+ * exponential functions.  We assume expt is small (0 or -1), and the caller
+ * has filtered out very large x, for which overflow would be inevitable.
+ */
+
+double
+__ldexp_exp(double x, int expt)
+{
+	double exp_x, scale;
+	int ex_expt;
+
+	exp_x = __frexp_exp(x, &ex_expt);
+	expt += ex_expt;
+	INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
+	return (exp_x * scale);
+}