diff options
Diffstat (limited to 'libc/src/math/generic')
| -rw-r--r-- | libc/src/math/generic/CMakeLists.txt | 22 | ||||
| -rw-r--r-- | libc/src/math/generic/atanhf16.cpp | 86 | ||||
| -rw-r--r-- | libc/src/math/generic/cbrt.cpp | 328 | ||||
| -rw-r--r-- | libc/src/math/generic/common_constants.cpp | 78 | ||||
| -rw-r--r-- | libc/src/math/generic/common_constants.h | 8 | ||||
| -rw-r--r-- | libc/src/math/generic/explogxf.h | 43 |
6 files changed, 6 insertions, 559 deletions
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index bac043f..a866195 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -3932,17 +3932,7 @@ add_entrypoint_object( HDRS ../atanhf16.h DEPENDS - .explogxf - libc.hdr.errno_macros - libc.hdr.fenv_macros - libc.src.__support.FPUtil.cast - libc.src.__support.FPUtil.except_value_utils - libc.src.__support.FPUtil.fenv_impl - libc.src.__support.FPUtil.fp_bits - libc.src.__support.FPUtil.multiply_add - libc.src.__support.FPUtil.polyeval - libc.src.__support.macros.optimization - libc.src.__support.macros.properties.types + libc.src.__support.math.atanhf16 ) add_entrypoint_object( @@ -4763,15 +4753,7 @@ add_entrypoint_object( HDRS ../cbrt.h DEPENDS - libc.hdr.fenv_macros - libc.src.__support.FPUtil.double_double - libc.src.__support.FPUtil.dyadic_float - libc.src.__support.FPUtil.fenv_impl - libc.src.__support.FPUtil.fp_bits - libc.src.__support.FPUtil.multiply_add - libc.src.__support.FPUtil.polyeval - libc.src.__support.macros.optimization - libc.src.__support.integer_literals + libc.src.__support.math.cbrt ) add_entrypoint_object( diff --git a/libc/src/math/generic/atanhf16.cpp b/libc/src/math/generic/atanhf16.cpp index 57885ac..0539bac 100644 --- a/libc/src/math/generic/atanhf16.cpp +++ b/libc/src/math/generic/atanhf16.cpp @@ -7,92 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/atanhf16.h" -#include "explogxf.h" -#include "hdr/errno_macros.h" -#include "hdr/fenv_macros.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/cast.h" -#include "src/__support/FPUtil/except_value_utils.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/common.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" +#include "src/__support/math/atanhf16.h" namespace LIBC_NAMESPACE_DECL { -static constexpr size_t N_EXCEPTS = 1; -static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANHF16_EXCEPTS{{ - // (input, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.a5cp-4, atanhf16(x) = 0x1.a74p-4 (RZ) - {0x2E97, 0x2E9D, 1, 0, 0}, -}}; - -LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) { - using FPBits = fputil::FPBits<float16>; - - FPBits xbits(x); - Sign sign = xbits.sign(); - uint16_t x_abs = xbits.abs().uintval(); - - // |x| >= 1 - if (LIBC_UNLIKELY(x_abs >= 0x3c00U)) { - if (xbits.is_nan()) { - if (xbits.is_signaling_nan()) { - fputil::raise_except_if_required(FE_INVALID); - return FPBits::quiet_nan().get_val(); - } - return x; - } - - // |x| == 1.0 - if (x_abs == 0x3c00U) { - fputil::set_errno_if_required(ERANGE); - fputil::raise_except_if_required(FE_DIVBYZERO); - return FPBits::inf(sign).get_val(); - } - // |x| > 1.0 - fputil::set_errno_if_required(EDOM); - fputil::raise_except_if_required(FE_INVALID); - return FPBits::quiet_nan().get_val(); - } - - if (auto r = ATANHF16_EXCEPTS.lookup(xbits.uintval()); - LIBC_UNLIKELY(r.has_value())) - return r.value(); - - // For |x| less than approximately 0.24 - if (LIBC_UNLIKELY(x_abs <= 0x33f3U)) { - // atanh(+/-0) = +/-0 - if (LIBC_UNLIKELY(x_abs == 0U)) - return x; - // The Taylor expansion of atanh(x) is: - // atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + x^11/11 - // = x * [1 + x^2/3 + x^4/5 + x^6/7 + x^8/9 + x^10/11] - // When |x| < 2^-5 (0x0800U), this can be approximated by: - // atanh(x) ≈ x + (1/3)*x^3 - if (LIBC_UNLIKELY(x_abs < 0x0800U)) { - float xf = x; - return fputil::cast<float16>(xf + 0x1.555556p-2f * xf * xf * xf); - } - - // For 2^-5 <= |x| <= 0x1.fccp-3 (~0.24): - // Let t = x^2. - // Define P(t) ≈ (1/3)*t + (1/5)*t^2 + (1/7)*t^3 + (1/9)*t^4 + (1/11)*t^5. - // Coefficients (from Sollya, RN, hexadecimal): - // 1/3 = 0x1.555556p-2, 1/5 = 0x1.99999ap-3, 1/7 = 0x1.24924ap-3, - // 1/9 = 0x1.c71c72p-4, 1/11 = 0x1.745d18p-4 - // Thus, atanh(x) ≈ x * (1 + P(x^2)). - float xf = x; - float x2 = xf * xf; - float pe = fputil::polyeval(x2, 0.0f, 0x1.555556p-2f, 0x1.99999ap-3f, - 0x1.24924ap-3f, 0x1.c71c72p-4f, 0x1.745d18p-4f); - return fputil::cast<float16>(fputil::multiply_add(xf, pe, xf)); - } - - float xf = x; - return fputil::cast<float16>(0.5 * log_eval_f((xf + 1.0f) / (xf - 1.0f))); -} +LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) { return math::atanhf16(x); } } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/src/math/generic/cbrt.cpp b/libc/src/math/generic/cbrt.cpp index ce227e6..e9b69bb 100644 --- a/libc/src/math/generic/cbrt.cpp +++ b/libc/src/math/generic/cbrt.cpp @@ -7,334 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/cbrt.h" -#include "hdr/fenv_macros.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/double_double.h" -#include "src/__support/FPUtil/dyadic_float.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/common.h" -#include "src/__support/integer_literals.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY - -#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0) -#define LIBC_MATH_CBRT_SKIP_ACCURATE_PASS -#endif +#include "src/__support/math/cbrt.h" namespace LIBC_NAMESPACE_DECL { -using DoubleDouble = fputil::DoubleDouble; -using Float128 = fputil::DyadicFloat<128>; - -namespace { - -// Initial approximation of x^(-2/3) for 1 <= x < 2. -// Polynomial generated by Sollya with: -// > P = fpminimax(x^(-2/3), 7, [|D...|], [1, 2]); -// > dirtyinfnorm(P/x^(-2/3) - 1, [1, 2]); -// 0x1.28...p-21 -double intial_approximation(double x) { - constexpr double COEFFS[8] = { - 0x1.bc52aedead5c6p1, -0x1.b52bfebf110b3p2, 0x1.1d8d71d53d126p3, - -0x1.de2db9e81cf87p2, 0x1.0154ca06153bdp2, -0x1.5973c66ee6da7p0, - 0x1.07bf6ac832552p-2, -0x1.5e53d9ce41cb8p-6, - }; - - double x_sq = x * x; - - double c0 = fputil::multiply_add(x, COEFFS[1], COEFFS[0]); - double c1 = fputil::multiply_add(x, COEFFS[3], COEFFS[2]); - double c2 = fputil::multiply_add(x, COEFFS[5], COEFFS[4]); - double c3 = fputil::multiply_add(x, COEFFS[7], COEFFS[6]); - - double x_4 = x_sq * x_sq; - double d0 = fputil::multiply_add(x_sq, c1, c0); - double d1 = fputil::multiply_add(x_sq, c3, c2); - - return fputil::multiply_add(x_4, d1, d0); -} - -// Get the error term for Newton iteration: -// h(x) = x^3 * a^2 - 1, -#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE -double get_error(const DoubleDouble &x_3, const DoubleDouble &a_sq) { - return fputil::multiply_add(x_3.hi, a_sq.hi, -1.0) + - fputil::multiply_add(x_3.lo, a_sq.hi, x_3.hi * a_sq.lo); -} -#else -double get_error(const DoubleDouble &x_3, const DoubleDouble &a_sq) { - DoubleDouble x_3_a_sq = fputil::quick_mult(a_sq, x_3); - return (x_3_a_sq.hi - 1.0) + x_3_a_sq.lo; -} -#endif - -} // anonymous namespace - -// Correctly rounded cbrt algorithm: -// -// === Step 1 - Range reduction === -// For x = (-1)^s * 2^e * (1.m), we get 2 reduced arguments x_r and a as: -// x_r = 1.m -// a = (-1)^s * 2^(e % 3) * (1.m) -// Then cbrt(x) = x^(1/3) can be computed as: -// x^(1/3) = 2^(e / 3) * a^(1/3). -// -// In order to avoid division, we compute a^(-2/3) using Newton method and then -// multiply the results by a: -// a^(1/3) = a * a^(-2/3). -// -// === Step 2 - First approximation to a^(-2/3) === -// First, we use a degree-7 minimax polynomial generated by Sollya to -// approximate x_r^(-2/3) for 1 <= x_r < 2. -// p = P(x_r) ~ x_r^(-2/3), -// with relative errors bounded by: -// | p / x_r^(-2/3) - 1 | < 1.16 * 2^-21. -// -// Then we multiply with 2^(e % 3) from a small lookup table to get: -// x_0 = 2^(-2*(e % 3)/3) * p -// ~ 2^(-2*(e % 3)/3) * x_r^(-2/3) -// = a^(-2/3) -// With relative errors: -// | x_0 / a^(-2/3) - 1 | < 1.16 * 2^-21. -// This step is done in double precision. -// -// === Step 3 - First Newton iteration === -// We follow the method described in: -// Sibidanov, A. and Zimmermann, P., "Correctly rounded cubic root evaluation -// in double precision", https://core-math.gitlabpages.inria.fr/cbrt64.pdf -// to derive multiplicative Newton iterations as below: -// Let x_n be the nth approximation to a^(-2/3). Define the n^th error as: -// h_n = x_n^3 * a^2 - 1 -// Then: -// a^(-2/3) = x_n / (1 + h_n)^(1/3) -// = x_n * (1 - (1/3) * h_n + (2/9) * h_n^2 - (14/81) * h_n^3 + ...) -// using the Taylor series expansion of (1 + h_n)^(-1/3). -// -// Apply to x_0 above: -// h_0 = x_0^3 * a^2 - 1 -// = a^2 * (x_0 - a^(-2/3)) * (x_0^2 + x_0 * a^(-2/3) + a^(-4/3)), -// it's bounded by: -// |h_0| < 4 * 3 * 1.16 * 2^-21 * 4 < 2^-17. -// So in the first iteration step, we use: -// x_1 = x_0 * (1 - (1/3) * h_n + (2/9) * h_n^2 - (14/81) * h_n^3) -// Its relative error is bounded by: -// | x_1 / a^(-2/3) - 1 | < 35/242 * |h_0|^4 < 2^-70. -// Then we perform Ziv's rounding test and check if the answer is exact. -// This step is done in double-double precision. -// -// === Step 4 - Second Newton iteration === -// If the Ziv's rounding test from the previous step fails, we define the error -// term: -// h_1 = x_1^3 * a^2 - 1, -// And perform another iteration: -// x_2 = x_1 * (1 - h_1 / 3) -// with the relative errors exceed the precision of double-double. -// We then check the Ziv's accuracy test with relative errors < 2^-102 to -// compensate for rounding errors. -// -// === Step 5 - Final iteration === -// If the Ziv's accuracy test from the previous step fails, we perform another -// iteration in 128-bit precision and check for exact outputs. -// -// TODO: It is possible to replace this costly computation step with special -// exceptional handling, similar to what was done in the CORE-MATH project: -// https://gitlab.inria.fr/core-math/core-math/-/blob/master/src/binary64/cbrt/cbrt.c - -LLVM_LIBC_FUNCTION(double, cbrt, (double x)) { - using FPBits = fputil::FPBits<double>; - - uint64_t x_abs = FPBits(x).abs().uintval(); - - unsigned exp_bias_correction = 682; // 1023 * 2/3 - - if (LIBC_UNLIKELY(x_abs < FPBits::min_normal().uintval() || - x_abs >= FPBits::inf().uintval())) { - if (x == 0.0 || x_abs >= FPBits::inf().uintval()) - // x is 0, Inf, or NaN. - // Make sure it works for FTZ/DAZ modes. - return static_cast<double>(x + x); - - // x is non-zero denormal number. - // Normalize x. - x *= 0x1.0p60; - exp_bias_correction -= 20; - } - - FPBits x_bits(x); - - // When using biased exponent of x in double precision, - // x_e = real_exponent_of_x + 1023 - // Then: - // x_e / 3 = real_exponent_of_x / 3 + 1023/3 - // = real_exponent_of_x / 3 + 341 - // So to make it the correct biased exponent of x^(1/3), we add - // 1023 - 341 = 682 - // to the quotient x_e / 3. - unsigned x_e = static_cast<unsigned>(x_bits.get_biased_exponent()); - unsigned out_e = (x_e / 3 + exp_bias_correction); - unsigned shift_e = x_e % 3; - - // Set x_r = 1.mantissa - double x_r = - FPBits(x_bits.get_mantissa() | - (static_cast<uint64_t>(FPBits::EXP_BIAS) << FPBits::FRACTION_LEN)) - .get_val(); - - // Set a = (-1)^x_sign * 2^(x_e % 3) * (1.mantissa) - uint64_t a_bits = x_bits.uintval() & 0x800F'FFFF'FFFF'FFFF; - a_bits |= - (static_cast<uint64_t>(shift_e + static_cast<unsigned>(FPBits::EXP_BIAS)) - << FPBits::FRACTION_LEN); - double a = FPBits(a_bits).get_val(); - - // Initial approximation of x_r^(-2/3). - double p = intial_approximation(x_r); - - // Look up for 2^(-2*n/3) used for first approximation step. - constexpr double EXP2_M2_OVER_3[3] = {1.0, 0x1.428a2f98d728bp-1, - 0x1.965fea53d6e3dp-2}; - - // x0 is an initial approximation of a^(-2/3) for 1 <= |a| < 8. - // Relative error: < 1.16 * 2^(-21). - double x0 = static_cast<double>(EXP2_M2_OVER_3[shift_e] * p); - - // First iteration in double precision. - DoubleDouble a_sq = fputil::exact_mult(a, a); - - // h0 = x0^3 * a^2 - 1 - DoubleDouble x0_sq = fputil::exact_mult(x0, x0); - DoubleDouble x0_3 = fputil::quick_mult(x0, x0_sq); - - double h0 = get_error(x0_3, a_sq); - -#ifdef LIBC_MATH_CBRT_SKIP_ACCURATE_PASS - constexpr double REL_ERROR = 0; -#else - constexpr double REL_ERROR = 0x1.0p-51; -#endif // LIBC_MATH_CBRT_SKIP_ACCURATE_PASS - - // Taylor polynomial of (1 + h)^(-1/3): - // (1 + h)^(-1/3) = 1 - h/3 + 2 h^2 / 9 - 14 h^3 / 81 + ... - constexpr double ERR_COEFFS[3] = { - -0x1.5555555555555p-2 - REL_ERROR, // -1/3 - relative_error - 0x1.c71c71c71c71cp-3, // 2/9 - -0x1.61f9add3c0ca4p-3, // -14/81 - }; - // e0 = -14 * h^2 / 81 + 2 * h / 9 - 1/3 - relative_error. - double e0 = fputil::polyeval(h0, ERR_COEFFS[0], ERR_COEFFS[1], ERR_COEFFS[2]); - double x0_h0 = x0 * h0; - - // x1 = x0 (1 - h0/3 + 2 h0^2 / 9 - 14 h0^3 / 81) - // x1 approximate a^(-2/3) with relative errors bounded by: - // | x1 / a^(-2/3) - 1 | < (34/243) h0^4 < h0 * REL_ERROR - DoubleDouble x1_dd{x0_h0 * e0, x0}; - - // r1 = x1 * a ~ a^(-2/3) * a = a^(1/3). - DoubleDouble r1 = fputil::quick_mult(a, x1_dd); - - // Lambda function to update the exponent of the result. - auto update_exponent = [=](double r) -> double { - uint64_t r_m = FPBits(r).uintval() - 0x3FF0'0000'0000'0000; - // Adjust exponent and sign. - uint64_t r_bits = - r_m + (static_cast<uint64_t>(out_e) << FPBits::FRACTION_LEN); - return FPBits(r_bits).get_val(); - }; - -#ifdef LIBC_MATH_CBRT_SKIP_ACCURATE_PASS - // TODO: We probably don't need to use double-double if accurate tests and - // passes are skipped. - return update_exponent(r1.hi + r1.lo); -#else - // Accurate checks and passes. - double r1_lower = r1.hi + r1.lo; - double r1_upper = - r1.hi + fputil::multiply_add(x0_h0, 2.0 * REL_ERROR * a, r1.lo); - - // Ziv's accuracy test. - if (LIBC_LIKELY(r1_upper == r1_lower)) { - // Test for exact outputs. - // Check if lower (52 - 17 = 35) bits are 0's. - if (LIBC_UNLIKELY((FPBits(r1_lower).uintval() & 0x0000'0007'FFFF'FFFF) == - 0)) { - double r1_err = (r1_lower - r1.hi) - r1.lo; - if (FPBits(r1_err).abs().get_val() < 0x1.0p69) - fputil::clear_except_if_required(FE_INEXACT); - } - - return update_exponent(r1_lower); - } - - // Accuracy test failed, perform another Newton iteration. - double x1 = x1_dd.hi + (e0 + REL_ERROR) * x0_h0; - - // Second iteration in double-double precision. - // h1 = x1^3 * a^2 - 1. - DoubleDouble x1_sq = fputil::exact_mult(x1, x1); - DoubleDouble x1_3 = fputil::quick_mult(x1, x1_sq); - double h1 = get_error(x1_3, a_sq); - - // e1 = -x1*h1/3. - double e1 = h1 * (x1 * -0x1.5555555555555p-2); - // x2 = x1*(1 - h1/3) = x1 + e1 ~ a^(-2/3) with relative errors < 2^-101. - DoubleDouble x2 = fputil::exact_add(x1, e1); - // r2 = a * x2 ~ a * a^(-2/3) = a^(1/3) with relative errors < 2^-100. - DoubleDouble r2 = fputil::quick_mult(a, x2); - - double r2_upper = r2.hi + fputil::multiply_add(a, 0x1.0p-102, r2.lo); - double r2_lower = r2.hi + fputil::multiply_add(a, -0x1.0p-102, r2.lo); - - // Ziv's accuracy test. - if (LIBC_LIKELY(r2_upper == r2_lower)) - return update_exponent(r2_upper); - - // TODO: Investigate removing float128 and just list exceptional cases. - // Apply another Newton iteration with ~126-bit accuracy. - Float128 x2_f128 = fputil::quick_add(Float128(x2.hi), Float128(x2.lo)); - // x2^3 - Float128 x2_3 = - fputil::quick_mul(fputil::quick_mul(x2_f128, x2_f128), x2_f128); - // a^2 - Float128 a_sq_f128 = fputil::quick_mul(Float128(a), Float128(a)); - // x2^3 * a^2 - Float128 x2_3_a_sq = fputil::quick_mul(x2_3, a_sq_f128); - // h2 = x2^3 * a^2 - 1 - Float128 h2_f128 = fputil::quick_add(x2_3_a_sq, Float128(-1.0)); - double h2 = static_cast<double>(h2_f128); - // t2 = 1 - h2 / 3 - Float128 t2 = - fputil::quick_add(Float128(1.0), Float128(h2 * (-0x1.5555555555555p-2))); - // x3 = x2 * (1 - h2 / 3) ~ a^(-2/3) - Float128 x3 = fputil::quick_mul(x2_f128, t2); - // r3 = a * x3 ~ a * a^(-2/3) = a^(1/3) - Float128 r3 = fputil::quick_mul(Float128(a), x3); - - // Check for exact cases: - Float128::MantissaType rounding_bits = - r3.mantissa & 0x0000'0000'0000'03FF'FFFF'FFFF'FFFF'FFFF_u128; - - double result = static_cast<double>(r3); - if ((rounding_bits < 0x0000'0000'0000'0000'0000'0000'0000'000F_u128) || - (rounding_bits >= 0x0000'0000'0000'03FF'FFFF'FFFF'FFFF'FFF0_u128)) { - // Output is exact. - r3.mantissa &= 0xFFFF'FFFF'FFFF'FFFF'FFFF'FFFF'FFFF'FFF0_u128; - - if (rounding_bits >= 0x0000'0000'0000'03FF'FFFF'FFFF'FFFF'FFF0_u128) { - Float128 tmp{r3.sign, r3.exponent - 123, - 0x8000'0000'0000'0000'0000'0000'0000'0000_u128}; - Float128 r4 = fputil::quick_add(r3, tmp); - result = static_cast<double>(r4); - } else { - result = static_cast<double>(r3); - } - - fputil::clear_except_if_required(FE_INEXACT); - } - - return update_exponent(result); -#endif // LIBC_MATH_CBRT_SKIP_ACCURATE_PASS -} +LLVM_LIBC_FUNCTION(double, cbrt, (double x)) { return math::cbrt(x); } } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp index 42e3ff0..2a15df2 100644 --- a/libc/src/math/generic/common_constants.cpp +++ b/libc/src/math/generic/common_constants.cpp @@ -12,84 +12,6 @@ namespace LIBC_NAMESPACE_DECL { -// Lookup table for logf(f) = logf(1 + n*2^(-7)) where n = 0..127, -// computed and stored as float precision constants. -// Generated by Sollya with the following commands: -// display = hexadecimal; -// for n from 0 to 127 do { print(single(1 / (1 + n / 128.0))); }; -const float ONE_OVER_F_FLOAT[128] = { - 0x1p0f, 0x1.fc07fp-1f, 0x1.f81f82p-1f, 0x1.f4465ap-1f, - 0x1.f07c2p-1f, 0x1.ecc07cp-1f, 0x1.e9131ap-1f, 0x1.e573acp-1f, - 0x1.e1e1e2p-1f, 0x1.de5d6ep-1f, 0x1.dae608p-1f, 0x1.d77b66p-1f, - 0x1.d41d42p-1f, 0x1.d0cb58p-1f, 0x1.cd8568p-1f, 0x1.ca4b3p-1f, - 0x1.c71c72p-1f, 0x1.c3f8fp-1f, 0x1.c0e07p-1f, 0x1.bdd2b8p-1f, - 0x1.bacf92p-1f, 0x1.b7d6c4p-1f, 0x1.b4e81cp-1f, 0x1.b20364p-1f, - 0x1.af286cp-1f, 0x1.ac5702p-1f, 0x1.a98ef6p-1f, 0x1.a6d01ap-1f, - 0x1.a41a42p-1f, 0x1.a16d4p-1f, 0x1.9ec8eap-1f, 0x1.9c2d14p-1f, - 0x1.99999ap-1f, 0x1.970e5p-1f, 0x1.948b1p-1f, 0x1.920fb4p-1f, - 0x1.8f9c18p-1f, 0x1.8d3018p-1f, 0x1.8acb9p-1f, 0x1.886e6p-1f, - 0x1.861862p-1f, 0x1.83c978p-1f, 0x1.818182p-1f, 0x1.7f406p-1f, - 0x1.7d05f4p-1f, 0x1.7ad22p-1f, 0x1.78a4c8p-1f, 0x1.767dcep-1f, - 0x1.745d18p-1f, 0x1.724288p-1f, 0x1.702e06p-1f, 0x1.6e1f76p-1f, - 0x1.6c16c2p-1f, 0x1.6a13cep-1f, 0x1.681682p-1f, 0x1.661ec6p-1f, - 0x1.642c86p-1f, 0x1.623fa8p-1f, 0x1.605816p-1f, 0x1.5e75bcp-1f, - 0x1.5c9882p-1f, 0x1.5ac056p-1f, 0x1.58ed24p-1f, 0x1.571ed4p-1f, - 0x1.555556p-1f, 0x1.539094p-1f, 0x1.51d07ep-1f, 0x1.501502p-1f, - 0x1.4e5e0ap-1f, 0x1.4cab88p-1f, 0x1.4afd6ap-1f, 0x1.49539ep-1f, - 0x1.47ae14p-1f, 0x1.460cbcp-1f, 0x1.446f86p-1f, 0x1.42d662p-1f, - 0x1.414142p-1f, 0x1.3fb014p-1f, 0x1.3e22ccp-1f, 0x1.3c995ap-1f, - 0x1.3b13b2p-1f, 0x1.3991c2p-1f, 0x1.381382p-1f, 0x1.3698ep-1f, - 0x1.3521dp-1f, 0x1.33ae46p-1f, 0x1.323e34p-1f, 0x1.30d19p-1f, - 0x1.2f684cp-1f, 0x1.2e025cp-1f, 0x1.2c9fb4p-1f, 0x1.2b404ap-1f, - 0x1.29e412p-1f, 0x1.288b02p-1f, 0x1.27350cp-1f, 0x1.25e228p-1f, - 0x1.24924ap-1f, 0x1.234568p-1f, 0x1.21fb78p-1f, 0x1.20b47p-1f, - 0x1.1f7048p-1f, 0x1.1e2ef4p-1f, 0x1.1cf06ap-1f, 0x1.1bb4a4p-1f, - 0x1.1a7b96p-1f, 0x1.194538p-1f, 0x1.181182p-1f, 0x1.16e068p-1f, - 0x1.15b1e6p-1f, 0x1.1485fp-1f, 0x1.135c82p-1f, 0x1.12358ep-1f, - 0x1.111112p-1f, 0x1.0fef02p-1f, 0x1.0ecf56p-1f, 0x1.0db20ap-1f, - 0x1.0c9714p-1f, 0x1.0b7e6ep-1f, 0x1.0a681p-1f, 0x1.0953f4p-1f, - 0x1.08421p-1f, 0x1.07326p-1f, 0x1.0624dep-1f, 0x1.05198p-1f, - 0x1.041042p-1f, 0x1.03091cp-1f, 0x1.020408p-1f, 0x1.010102p-1f}; - -// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127, -// computed and stored as float precision constants. -// Generated by Sollya with the following commands: -// display = hexadecimal; -// for n from 0 to 127 do { print(single(log(1 + n / 128.0))); }; -const float LOG_F_FLOAT[128] = { - 0.0f, 0x1.fe02a6p-8f, 0x1.fc0a8cp-7f, 0x1.7b91bp-6f, - 0x1.f829bp-6f, 0x1.39e87cp-5f, 0x1.77459p-5f, 0x1.b42dd8p-5f, - 0x1.f0a30cp-5f, 0x1.16536ep-4f, 0x1.341d7ap-4f, 0x1.51b074p-4f, - 0x1.6f0d28p-4f, 0x1.8c345ep-4f, 0x1.a926d4p-4f, 0x1.c5e548p-4f, - 0x1.e27076p-4f, 0x1.fec914p-4f, 0x1.0d77e8p-3f, 0x1.1b72aep-3f, - 0x1.29553p-3f, 0x1.371fc2p-3f, 0x1.44d2b6p-3f, 0x1.526e5ep-3f, - 0x1.5ff308p-3f, 0x1.6d60fep-3f, 0x1.7ab89p-3f, 0x1.87fa06p-3f, - 0x1.9525aap-3f, 0x1.a23bc2p-3f, 0x1.af3c94p-3f, 0x1.bc2868p-3f, - 0x1.c8ff7cp-3f, 0x1.d5c216p-3f, 0x1.e27076p-3f, 0x1.ef0adcp-3f, - 0x1.fb9186p-3f, 0x1.04025ap-2f, 0x1.0a324ep-2f, 0x1.1058cp-2f, - 0x1.1675cap-2f, 0x1.1c898cp-2f, 0x1.22942p-2f, 0x1.2895a2p-2f, - 0x1.2e8e2cp-2f, 0x1.347ddap-2f, 0x1.3a64c6p-2f, 0x1.404308p-2f, - 0x1.4618bcp-2f, 0x1.4be5fap-2f, 0x1.51aad8p-2f, 0x1.576772p-2f, - 0x1.5d1bdcp-2f, 0x1.62c83p-2f, 0x1.686c82p-2f, 0x1.6e08eap-2f, - 0x1.739d8p-2f, 0x1.792a56p-2f, 0x1.7eaf84p-2f, 0x1.842d1ep-2f, - 0x1.89a338p-2f, 0x1.8f11e8p-2f, 0x1.947942p-2f, 0x1.99d958p-2f, - 0x1.9f323ep-2f, 0x1.a4840ap-2f, 0x1.a9cecap-2f, 0x1.af1294p-2f, - 0x1.b44f78p-2f, 0x1.b9858ap-2f, 0x1.beb4dap-2f, 0x1.c3dd7ap-2f, - 0x1.c8ff7cp-2f, 0x1.ce1afp-2f, 0x1.d32fe8p-2f, 0x1.d83e72p-2f, - 0x1.dd46ap-2f, 0x1.e24882p-2f, 0x1.e74426p-2f, 0x1.ec399ep-2f, - 0x1.f128f6p-2f, 0x1.f6124p-2f, 0x1.faf588p-2f, 0x1.ffd2ep-2f, - 0x1.02552ap-1f, 0x1.04bdfap-1f, 0x1.0723e6p-1f, 0x1.0986f4p-1f, - 0x1.0be72ep-1f, 0x1.0e4498p-1f, 0x1.109f3ap-1f, 0x1.12f71ap-1f, - 0x1.154c3ep-1f, 0x1.179eacp-1f, 0x1.19ee6cp-1f, 0x1.1c3b82p-1f, - 0x1.1e85f6p-1f, 0x1.20cdcep-1f, 0x1.23130ep-1f, 0x1.2555bcp-1f, - 0x1.2795e2p-1f, 0x1.29d38p-1f, 0x1.2c0e9ep-1f, 0x1.2e4744p-1f, - 0x1.307d74p-1f, 0x1.32b134p-1f, 0x1.34e28ap-1f, 0x1.37117cp-1f, - 0x1.393e0ep-1f, 0x1.3b6844p-1f, 0x1.3d9026p-1f, 0x1.3fb5b8p-1f, - 0x1.41d8fep-1f, 0x1.43f9fep-1f, 0x1.4618bcp-1f, 0x1.48353ep-1f, - 0x1.4a4f86p-1f, 0x1.4c679ap-1f, 0x1.4e7d82p-1f, 0x1.50913cp-1f, - 0x1.52a2d2p-1f, 0x1.54b246p-1f, 0x1.56bf9ep-1f, 0x1.58cadcp-1f, - 0x1.5ad404p-1f, 0x1.5cdb1ep-1f, 0x1.5ee02ap-1f, 0x1.60e33p-1f}; - // Range reduction constants for logarithms. // r(0) = 1, r(127) = 0.5 // r(k) = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + k*2^-7)) diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h index 72b1d564..9ee31f0 100644 --- a/libc/src/math/generic/common_constants.h +++ b/libc/src/math/generic/common_constants.h @@ -17,14 +17,6 @@ namespace LIBC_NAMESPACE_DECL { -// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127, -// computed and stored as float precision constants. -extern const float ONE_OVER_F_FLOAT[128]; - -// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127, -// computed and stored as float precision constants. -extern const float LOG_F_FLOAT[128]; - // Lookup table for range reduction constants r for logarithms. extern const float R[128]; diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h index a2a6d60..72f8da8 100644 --- a/libc/src/math/generic/explogxf.h +++ b/libc/src/math/generic/explogxf.h @@ -121,49 +121,6 @@ template <bool is_sinh> LIBC_INLINE double exp_pm_eval(float x) { return r; } -// x should be positive, normal finite value -// TODO: Simplify range reduction and polynomial degree for float16. -// See issue #137190. -LIBC_INLINE static float log_eval_f(float x) { - // For x = 2^ex * (1 + mx), logf(x) = ex * logf(2) + logf(1 + mx). - using FPBits = fputil::FPBits<float>; - FPBits xbits(x); - - float ex = static_cast<float>(xbits.get_exponent()); - // p1 is the leading 7 bits of mx, i.e. - // p1 * 2^(-7) <= m_x < (p1 + 1) * 2^(-7). - int p1 = static_cast<int>(xbits.get_mantissa() >> (FPBits::FRACTION_LEN - 7)); - - // Set bits to (1 + (mx - p1*2^(-7))) - xbits.set_uintval(xbits.uintval() & (FPBits::FRACTION_MASK >> 7)); - xbits.set_biased_exponent(FPBits::EXP_BIAS); - // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)). - float dx = (xbits.get_val() - 1.0f) * ONE_OVER_F_FLOAT[p1]; - - // Minimax polynomial for log(1 + dx), generated using Sollya: - // > P = fpminimax(log(1 + x)/x, 6, [|SG...|], [0, 2^-7]); - // > Q = (P - 1) / x; - // > for i from 0 to degree(Q) do print(coeff(Q, i)); - constexpr float COEFFS[6] = {-0x1p-1f, 0x1.555556p-2f, -0x1.00022ep-2f, - 0x1.9ea056p-3f, -0x1.e50324p-2f, 0x1.c018fp3f}; - - float dx2 = dx * dx; - - float c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]); - float c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]); - float c3 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]); - - float p = fputil::polyeval(dx2, dx, c1, c2, c3); - - // Generated by Sollya with the following commands: - // > display = hexadecimal; - // > round(log(2), SG, RN); - constexpr float LOGF_2 = 0x1.62e43p-1f; - - float result = fputil::multiply_add(ex, LOGF_2, LOG_F_FLOAT[p1] + p); - return result; -} - } // namespace LIBC_NAMESPACE_DECL #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H |