diff options
Diffstat (limited to 'Eigen/src/Core/MathFunctions.h')
-rw-r--r-- | Eigen/src/Core/MathFunctions.h | 19 |
1 files changed, 18 insertions, 1 deletions
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h index 4e6053b2e..dadf2cba2 100644 --- a/Eigen/src/Core/MathFunctions.h +++ b/Eigen/src/Core/MathFunctions.h @@ -529,7 +529,24 @@ struct expm1_impl<std::complex<RealScalar> > { EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run( const std::complex<RealScalar>& x) { EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar) - return std_fallback::expm1(x); + RealScalar xr = x.real(); + RealScalar xi = x.imag(); + // expm1(z) = exp(z) - 1 + // = exp(x + i * y) - 1 + // = exp(x) * (cos(y) + i * sin(y)) - 1 + // = exp(x) * cos(y) - 1 + i * exp(x) * sin(y) + // Imag(expm1(z)) = exp(x) * sin(y) + // Real(expm1(z)) = exp(x) * cos(y) - 1 + // = exp(x) * cos(y) - 1. + // = expm1(x) + exp(x) * (cos(y) - 1) + // = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2) + RealScalar erm1 = std_fallback::expm1(xr); + RealScalar er = erm1 + RealScalar(1.); + RealScalar sin2 = sin(xi / RealScalar(2.)); + sin2 = sin2 * sin2; + RealScalar s = sin(xi); + RealScalar real_part = erm1 - RealScalar(2.) * er * sin2; + return std::complex<RealScalar>(real_part, er * s); } }; |