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Diffstat (limited to 'media/libjxl/src/lib/jxl/fast_math-inl.h')
-rw-r--r-- | media/libjxl/src/lib/jxl/fast_math-inl.h | 175 |
1 files changed, 175 insertions, 0 deletions
diff --git a/media/libjxl/src/lib/jxl/fast_math-inl.h b/media/libjxl/src/lib/jxl/fast_math-inl.h new file mode 100644 index 0000000000..60be66829a --- /dev/null +++ b/media/libjxl/src/lib/jxl/fast_math-inl.h @@ -0,0 +1,175 @@ +// Copyright (c) the JPEG XL Project Authors. All rights reserved. +// +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Fast SIMD math ops (log2, encoder only, cos, erf for splines) + +#if defined(LIB_JXL_FAST_MATH_INL_H_) == defined(HWY_TARGET_TOGGLE) +#ifdef LIB_JXL_FAST_MATH_INL_H_ +#undef LIB_JXL_FAST_MATH_INL_H_ +#else +#define LIB_JXL_FAST_MATH_INL_H_ +#endif + +#include <hwy/highway.h> + +#include "lib/jxl/common.h" +#include "lib/jxl/rational_polynomial-inl.h" +HWY_BEFORE_NAMESPACE(); +namespace jxl { +namespace HWY_NAMESPACE { + +// These templates are not found via ADL. +using hwy::HWY_NAMESPACE::Rebind; +using hwy::HWY_NAMESPACE::ShiftLeft; +using hwy::HWY_NAMESPACE::ShiftRight; + +// Computes base-2 logarithm like std::log2. Undefined if negative / NaN. +// L1 error ~3.9E-6 +template <class DF, class V> +V FastLog2f(const DF df, V x) { + // 2,2 rational polynomial approximation of std::log1p(x) / std::log(2). + HWY_ALIGN const float p[4 * (2 + 1)] = {HWY_REP4(-1.8503833400518310E-06f), + HWY_REP4(1.4287160470083755E+00f), + HWY_REP4(7.4245873327820566E-01f)}; + HWY_ALIGN const float q[4 * (2 + 1)] = {HWY_REP4(9.9032814277590719E-01f), + HWY_REP4(1.0096718572241148E+00f), + HWY_REP4(1.7409343003366853E-01f)}; + + const Rebind<int32_t, DF> di; + const auto x_bits = BitCast(di, x); + + // Range reduction to [-1/3, 1/3] - 3 integer, 2 float ops + const auto exp_bits = x_bits - Set(di, 0x3f2aaaab); // = 2/3 + // Shifted exponent = log2; also used to clear mantissa. + const auto exp_shifted = ShiftRight<23>(exp_bits); + const auto mantissa = BitCast(df, x_bits - ShiftLeft<23>(exp_shifted)); + const auto exp_val = ConvertTo(df, exp_shifted); + return EvalRationalPolynomial(df, mantissa - Set(df, 1.0f), p, q) + exp_val; +} + +// max relative error ~3e-7 +template <class DF, class V> +V FastPow2f(const DF df, V x) { + const Rebind<int32_t, DF> di; + auto floorx = Floor(x); + auto exp = BitCast(df, ShiftLeft<23>(ConvertTo(di, floorx) + Set(di, 127))); + auto frac = x - floorx; + auto num = frac + Set(df, 1.01749063e+01); + num = MulAdd(num, frac, Set(df, 4.88687798e+01)); + num = MulAdd(num, frac, Set(df, 9.85506591e+01)); + num = num * exp; + auto den = MulAdd(frac, Set(df, 2.10242958e-01), Set(df, -2.22328856e-02)); + den = MulAdd(den, frac, Set(df, -1.94414990e+01)); + den = MulAdd(den, frac, Set(df, 9.85506633e+01)); + return num / den; +} + +// max relative error ~3e-5 +template <class DF, class V> +V FastPowf(const DF df, V base, V exponent) { + return FastPow2f(df, FastLog2f(df, base) * exponent); +} + +// Computes cosine like std::cos. +// L1 error 7e-5. +template <class DF, class V> +V FastCosf(const DF df, V x) { + // Step 1: range reduction to [0, 2pi) + const auto pi2 = Set(df, kPi * 2.0f); + const auto pi2_inv = Set(df, 0.5f / kPi); + const auto npi2 = Floor(x * pi2_inv) * pi2; + const auto xmodpi2 = x - npi2; + // Step 2: range reduction to [0, pi] + const auto x_pi = Min(xmodpi2, pi2 - xmodpi2); + // Step 3: range reduction to [0, pi/2] + const auto above_pihalf = x_pi >= Set(df, kPi / 2.0f); + const auto x_pihalf = IfThenElse(above_pihalf, Set(df, kPi) - x_pi, x_pi); + // Step 4: Taylor-like approximation, scaled by 2**0.75 to make angle + // duplication steps faster, on x/4. + const auto xs = x_pihalf * Set(df, 0.25f); + const auto x2 = xs * xs; + const auto x4 = x2 * x2; + const auto cosx_prescaling = + MulAdd(x4, Set(df, 0.06960438), + MulAdd(x2, Set(df, -0.84087373), Set(df, 1.68179268))); + // Step 5: angle duplication. + const auto cosx_scale1 = + MulAdd(cosx_prescaling, cosx_prescaling, Set(df, -1.414213562)); + const auto cosx_scale2 = MulAdd(cosx_scale1, cosx_scale1, Set(df, -1)); + // Step 6: change sign if needed. + const Rebind<uint32_t, DF> du; + auto signbit = ShiftLeft<31>(BitCast(du, VecFromMask(df, above_pihalf))); + return BitCast(df, signbit ^ BitCast(du, cosx_scale2)); +} + +// Computes the error function like std::erf. +// L1 error 7e-4. +template <class DF, class V> +V FastErff(const DF df, V x) { + // Formula from + // https://en.wikipedia.org/wiki/Error_function#Numerical_approximations + // but constants have been recomputed. + const auto xle0 = x <= Zero(df); + const auto absx = Abs(x); + // Compute 1 - 1 / ((((x * a + b) * x + c) * x + d) * x + 1)**4 + const auto denom1 = + MulAdd(absx, Set(df, 7.77394369e-02), Set(df, 2.05260015e-04)); + const auto denom2 = MulAdd(denom1, absx, Set(df, 2.32120216e-01)); + const auto denom3 = MulAdd(denom2, absx, Set(df, 2.77820801e-01)); + const auto denom4 = MulAdd(denom3, absx, Set(df, 1.0f)); + const auto denom5 = denom4 * denom4; + const auto inv_denom5 = Set(df, 1.0f) / denom5; + const auto result = NegMulAdd(inv_denom5, inv_denom5, Set(df, 1.0f)); + // Change sign if needed. + const Rebind<uint32_t, DF> du; + auto signbit = ShiftLeft<31>(BitCast(du, VecFromMask(df, xle0))); + return BitCast(df, signbit ^ BitCast(du, result)); +} + +inline float FastLog2f(float f) { + HWY_CAPPED(float, 1) D; + return GetLane(FastLog2f(D, Set(D, f))); +} + +inline float FastPow2f(float f) { + HWY_CAPPED(float, 1) D; + return GetLane(FastPow2f(D, Set(D, f))); +} + +inline float FastPowf(float b, float e) { + HWY_CAPPED(float, 1) D; + return GetLane(FastPowf(D, Set(D, b), Set(D, e))); +} + +inline float FastCosf(float f) { + HWY_CAPPED(float, 1) D; + return GetLane(FastCosf(D, Set(D, f))); +} + +inline float FastErff(float f) { + HWY_CAPPED(float, 1) D; + return GetLane(FastErff(D, Set(D, f))); +} + +// NOLINTNEXTLINE(google-readability-namespace-comments) +} // namespace HWY_NAMESPACE +} // namespace jxl +HWY_AFTER_NAMESPACE(); + +#endif // LIB_JXL_FAST_MATH_INL_H_ + +#if HWY_ONCE + +namespace jxl { +inline float FastLog2f(float f) { return HWY_STATIC_DISPATCH(FastLog2f)(f); } +inline float FastPow2f(float f) { return HWY_STATIC_DISPATCH(FastPow2f)(f); } +inline float FastPowf(float b, float e) { + return HWY_STATIC_DISPATCH(FastPowf)(b, e); +} +inline float FastCosf(float f) { return HWY_STATIC_DISPATCH(FastCosf)(f); } +inline float FastErff(float f) { return HWY_STATIC_DISPATCH(FastErff)(f); } +} // namespace jxl + +#endif // HWY_ONCE |