A cube root. #1802
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A cube root. #1802
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pleroy
reviewed
Apr 30, 2018
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| constexpr std::uint64_t C = 0x2A9F7893782DA1CE; | ||
| static const __m128d sign_bit = | ||
| _mm_castsi128_pd(_mm_cvtsi64_si128(0x8000'0000'0000'0000)); |
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In other places we condition the use of intrinsics on some preprocessor symbol and use a slow path otherwise. Should we do the same in this function?
| namespace principia { | ||
| namespace numerics { | ||
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| constexpr std::uint64_t C = 0x2A9F7893782DA1CE; |
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No idea what this constant does and how it was computed. Could we have references to some literature in this code?
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numerics/cbrt.cpp
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| double const denominator = | ||
| (7 * x³ + 42 * abs_y) * x⁶ + (30 * x³ + 2 * abs_y) * y²; | ||
| return _mm_cvtsd_f64( | ||
| _mm_or_pd(_mm_set_sd(x - numerator / denominator), sign)); |
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Is this faster than multiplying by sign?
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Yes, but we could gain a cycle by moving this or away from the critical path.
numerics/cbrt_test.cpp
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| class CubeRootTest : public ::testing::Test { | ||
| protected: | ||
| static std::uint64_t bits(double const x) { |
numerics/cbrt.hpp
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| // Computes ∛y with a maximal error in [0.50005, 0.50022] ULPs; the result is | ||
| // incorrectly rounded for approximately 5 inputs per million. | ||
| double cbrt(double y); |
numerics/cbrt_test.cpp
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| Eq(-std::numeric_limits<double>::infinity())); | ||
| EXPECT_THAT(cbrt(std::numeric_limits<double>::quiet_NaN()), | ||
| Truly(&std::isnan<double>)); | ||
| EXPECT_THAT(cbrt(-std::numeric_limits<double>::quiet_NaN()), |
numerics/cbrt_test.cpp
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| } | ||
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| TEST_F(CubeRootTest, ParticularlyBadRounding) { | ||
| EXPECT_THAT(cbrt(0x1.14E35E87EA5DFp0), Eq(0x1.06C80FCCA8E18p0)); |
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How do we know that it's bad? Could we log some indication of error?
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retest this please |
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This is part of the effort on #1760.