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Disable use of recurrence for computing twiddle factors. Fixes FFT precision issues for large FFTs. https://github.com/tensorflow/tensorflow/issues/10749#issuecomment-354557689

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This commit is contained in:
RJ Ryan
2017-12-31 10:44:56 -05:00
parent f9bdcea022
commit 59985cfd26
2 changed files with 54 additions and 14 deletions
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40
unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
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@@ -231,20 +231,32 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
// t_n = exp(sqrt(-1) * pi * n^2 / line_len)
// for n = 0, 1,..., line_len-1.
// For n > 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2
pos_j_base_powered[0] = ComplexScalar(1, 0);
if (line_len > 1) {
const RealScalar pi_over_len(EIGEN_PI / line_len);
const ComplexScalar pos_j_base = ComplexScalar(
std::cos(pi_over_len), std::sin(pi_over_len));
pos_j_base_powered[1] = pos_j_base;
if (line_len > 2) {
const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;
for (int j = 2; j < line_len + 1; ++j) {
pos_j_base_powered[j] = pos_j_base_powered[j - 1] *
pos_j_base_powered[j - 1] /
pos_j_base_powered[j - 2] * pos_j_base_sq;
}
}
// The recurrence is correct in exact arithmetic, but causes
// numerical issues for large transforms, especially in
// single-precision floating point.
//
// pos_j_base_powered[0] = ComplexScalar(1, 0);
// if (line_len > 1) {
// const ComplexScalar pos_j_base = ComplexScalar(
// numext::cos(M_PI / line_len), numext::sin(M_PI / line_len));
// pos_j_base_powered[1] = pos_j_base;
// if (line_len > 2) {
// const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;
// for (int i = 2; i < line_len + 1; ++i) {
// pos_j_base_powered[i] = pos_j_base_powered[i - 1] *
// pos_j_base_powered[i - 1] /
// pos_j_base_powered[i - 2] *
// pos_j_base_sq;
// }
// }
// }
// TODO(rmlarsen): Find a way to use Eigen's vectorized sin
// and cosine functions here.
for (int j = 0; j < line_len + 1; ++j) {
double arg = ((EIGEN_PI * j) * j) / line_len;
std::complex<double> tmp(numext::cos(arg), numext::sin(arg));
pos_j_base_powered[j] = static_cast<ComplexScalar>(tmp);
}
}