Add a "fork" of musl as //fusl.

fusl/src/complex/__cexp.c

+/* 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"
+
+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_cexp(x, expt) compute exp(x) * 2**expt.
+ * It is 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 complex __ldexp_cexp(double complex z, int expt)
+{
+        double x, y, exp_x, scale1, scale2;
+        int ex_expt, half_expt;
+
+        x = creal(z);
+        y = cimag(z);
+        exp_x = __frexp_exp(x, &ex_expt);
+        expt += ex_expt;
+
+        /*
+         * Arrange so that scale1 * scale2 == 2**expt.  We use this to
+         * compensate for scalbn being horrendously slow.
+         */
+        half_expt = expt / 2;
+        INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
+        half_expt = expt - half_expt;
+        INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
+
+        return CMPLX(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
+}