| /* | |
| * Copyright 2008-2013 NVIDIA Corporation | |
| * Copyright 2013 Filipe RNC Maia | |
| * | |
| * Licensed under the Apache License, Version 2.0 (the "License"); | |
| * you may not use this file except in compliance with the License. | |
| * You may obtain a copy of the License at | |
| * | |
| * http://www.apache.org/licenses/LICENSE-2.0 | |
| * | |
| * Unless required by applicable law or agreed to in writing, software | |
| * distributed under the License is distributed on an "AS IS" BASIS, | |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| * See the License for the specific language governing permissions and | |
| * limitations under the License. | |
| */ | |
| /*- | |
| * 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. | |
| */ | |
| /* | |
| * Adapted from FreeBSD by Filipe Maia <filipe.c.maia@gmail.com>: | |
| * freebsd/lib/msun/src/s_ctanh.c | |
| */ | |
| /* | |
| * 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. | |
| */ | |
| THRUST_NAMESPACE_BEGIN | |
| namespace detail{ | |
| namespace complex{ | |
| using thrust::complex; | |
| __host__ __device__ inline | |
| complex<double> ctanh(const complex<double>& z){ | |
| double x, y; | |
| double t, beta, s, rho, denom; | |
| uint32_t hx, ix, lx; | |
| x = z.real(); | |
| y = z.imag(); | |
| 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 (complex<double>(x, (y == 0 ? y : x * y))); | |
| set_high_word(x, hx - 0x40000000); /* x = copysign(1, x) */ | |
| return (complex<double>(x, copysign(0.0, isinf(y) ? y : sin(y) * cos(y)))); | |
| } | |
| /* | |
| * ctanh(x + i NAN) = NaN + i NaN | |
| * ctanh(x +- i Inf) = NaN + i NaN | |
| */ | |
| if (!isfinite(y)) | |
| return (complex<double>(y - y, 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 (complex<double>(copysign(1.0, x), | |
| 4.0 * 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(1.0 + s * s); /* = cosh(x) */ | |
| denom = 1.0 + beta * s * s; | |
| return (complex<double>((beta * rho * s) / denom, t / denom)); | |
| } | |
| __host__ __device__ inline | |
| complex<double> ctan(complex<double> z){ | |
| /* ctan(z) = -I * ctanh(I * z) */ | |
| z = ctanh(complex<double>(-z.imag(), z.real())); | |
| return (complex<double>(z.imag(), -z.real())); | |
| } | |
| } // namespace complex | |
| } // namespace detail | |
| template <typename ValueType> | |
| __host__ __device__ | |
| inline complex<ValueType> tan(const complex<ValueType>& z){ | |
| return sin(z)/cos(z); | |
| } | |
| template <typename ValueType> | |
| __host__ __device__ | |
| inline complex<ValueType> tanh(const complex<ValueType>& z){ | |
| // This implementation seems better than the simple sin/cos | |
| return (thrust::exp(ValueType(2)*z)-ValueType(1))/ | |
| (thrust::exp(ValueType(2)*z)+ValueType(1)); | |
| } | |
| template <> | |
| __host__ __device__ | |
| inline complex<double> tan(const complex<double>& z){ | |
| return detail::complex::ctan(z); | |
| } | |
| template <> | |
| __host__ __device__ | |
| inline complex<double> tanh(const complex<double>& z){ | |
| return detail::complex::ctanh(z); | |
| } | |
| THRUST_NAMESPACE_END | |