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

fusl/src/complex/ctanh.c

+/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.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 unmodified, 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 ``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 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.
+ */
+/*
+ * Hyperbolic tangent of a complex argument z = x + i y.
+ *
+ * The algorithm is from:
+ *
+ *   W. Kahan.  Branch Cuts for Complex Elementary Functions or Much
+ *   Ado About Nothing's Sign Bit.  In The State of the Art in
+ *   Numerical Analysis, pp. 165 ff.  Iserles and Powell, eds., 1987.
+ *
+ * Method:
+ *
+ *   Let t    = tan(x)
+ *       beta = 1/cos^2(y)
+ *       s    = sinh(x)
+ *       rho  = cosh(x)
+ *
+ *   We have:
+ *
+ *   tanh(z) = sinh(z) / cosh(z)
+ *
+ *             sinh(x) cos(y) + i cosh(x) sin(y)
+ *           = ---------------------------------
+ *             cosh(x) cos(y) + i sinh(x) sin(y)
+ *
+ *             cosh(x) sinh(x) / cos^2(y) + i tan(y)
+ *           = -------------------------------------
+ *                    1 + sinh^2(x) / cos^2(y)
+ *
+ *             beta rho s + i t
+ *           = ----------------
+ *               1 + beta s^2
+ *
+ * Modifications:
+ *
+ *   I omitted the original algorithm's handling of overflow in tan(x) after
+ *   verifying with nearpi.c that this can't happen in IEEE single or double
+ *   precision.  I also handle large x differently.
+ */
+
+#include "libm.h"
+
+double complex ctanh(double complex z)
+{
+        double x, y;
+        double t, beta, s, rho, denom;
+        uint32_t hx, ix, lx;
+
+        x = creal(z);
+        y = cimag(z);
+
+        EXTRACT_WORDS(hx, lx, x);
+        ix = hx & 0x7fffffff;
+
+        /*
+         * ctanh(NaN + i 0) = NaN + i 0
+         *
+         * ctanh(NaN + i y) = NaN + i NaN               for y != 0
+         *
+         * The imaginary part has the sign of x*sin(2*y), but there's no
+         * special effort to get this right.
+         *
+         * ctanh(+-Inf +- i Inf) = +-1 +- 0
+         *
+         * ctanh(+-Inf + i y) = +-1 + 0 sin(2y)         for y finite
+         *
+         * The imaginary part of the sign is unspecified.  This special
+         * case is only needed to avoid a spurious invalid exception when
+         * y is infinite.
+         */
+        if (ix >= 0x7ff00000) {
+                if ((ix & 0xfffff) | lx)        /* x is NaN */
+                        return CMPLX(x, (y == 0 ? y : x * y));
+                SET_HIGH_WORD(x, hx - 0x40000000);      /* x = copysign(1, x) */
+                return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
+        }
+
+        /*
+         * ctanh(+-0 + i NAN) = +-0 + i NaN
+         * ctanh(+-0 +- i Inf) = +-0 + i NaN
+         * ctanh(x + i NAN) = NaN + i NaN
+         * ctanh(x +- i Inf) = NaN + i NaN
+         */
+        if (!isfinite(y))
+                return CMPLX(x ? y - y : x, y - y);
+
+        /*
+         * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
+         * approximation sinh^2(huge) ~= exp(2*huge) / 4.
+         * We use a modified formula to avoid spurious overflow.
+         */
+        if (ix >= 0x40360000) { /* x >= 22 */
+                double exp_mx = exp(-fabs(x));
+                return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
+        }
+
+        /* Kahan's algorithm */
+        t = tan(y);
+        beta = 1.0 + t * t;     /* = 1 / cos^2(y) */
+        s = sinh(x);
+        rho = sqrt(1 + s * s);  /* = cosh(x) */
+        denom = 1 + beta * s * s;
+        return CMPLX((beta * rho * s) / denom, t / denom);
+}