Index: fusl/src/complex/ctanh.c |
diff --git a/fusl/src/complex/ctanh.c b/fusl/src/complex/ctanh.c |
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+/* 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); |
+} |