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/* Translated from Cython into C++ by SciPy developers in 2023. * * Original author: Josh Wilson, 2016. / / Implement sin(piz) and cos(piz) for complex z. Since the periods * of these functions are integral (and thus better representable in * floating point), it's possible to compute them with greater accuracy * than sin(z), cos(z). / #pragma once #include "cephes/trig.h" #include "config.h" #include "evalpoly.h" namespace special { SPECFUN_HOST_DEVICE inline std::complex<double> sinpi(std::complex<double> z) { double x = z.real(); double piy = M_PI z.imag(); double abspiy = std::abs(piy); double sinpix = cephes::sinpi(x); double cospix = cephes::cospi(x); if (abspiy < 700) { return {sinpix * std::cosh(piy), cospix * std::sinh(piy)}; } /* Have to be careful--sinh/cosh could overflow while cos/sin are small. * At this large of values * * cosh(y) ~ exp(y)/2 * sinh(y) ~ sgn(y)exp(y)/2 * so we can compute exp(y/2), scale by the right factor of sin/cos * and then multiply by exp(y/2) to avoid overflow. / double exphpiy = std::exp(abspiy / 2); double coshfac; double sinhfac; if (exphpiy == std::numeric_limits<double>::infinity()) { if (sinpix == 0.0) { // Preserve the sign of zero. coshfac = std::copysign(0.0, sinpix); } else { coshfac = std::copysign(std::numeric_limits<double>::infinity(), sinpix); } if (cospix == 0.0) { // Preserve the sign of zero. sinhfac = std::copysign(0.0, cospix); } else { sinhfac = std::copysign(std::numeric_limits<double>::infinity(), cospix); } return {coshfac, sinhfac}; } coshfac = 0.5 sinpix * exphpiy; sinhfac = 0.5 * cospix * exphpiy; return {coshfac * exphpiy, sinhfac * exphpiy}; } SPECFUN_HOST_DEVICE inline std::complex<double> cospi(std::complex<double> z) { double x = z.real(); double piy = M_PI * z.imag(); double abspiy = std::abs(piy); double sinpix = cephes::sinpi(x); double cospix = cephes::cospi(x); if (abspiy < 700) { return {cospix * std::cosh(piy), -sinpix * std::sinh(piy)}; } // See csinpi(z) for an idea of what's going on here. double exphpiy = std::exp(abspiy / 2); double coshfac; double sinhfac; if (exphpiy == std::numeric_limits<double>::infinity()) { if (sinpix == 0.0) { // Preserve the sign of zero. coshfac = std::copysign(0.0, cospix); } else { coshfac = std::copysign(std::numeric_limits<double>::infinity(), cospix); } if (cospix == 0.0) { // Preserve the sign of zero. sinhfac = std::copysign(0.0, sinpix); } else { sinhfac = std::copysign(std::numeric_limits<double>::infinity(), sinpix); } return {coshfac, sinhfac}; } coshfac = 0.5 * cospix * exphpiy; sinhfac = 0.5 * sinpix * exphpiy; return {coshfac * exphpiy, sinhfac * exphpiy}; } } // namespace special

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