diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt index 10058865e0378..f3d2cabb2c141 100644 --- a/libc/config/darwin/arm/entrypoints.txt +++ b/libc/config/darwin/arm/entrypoints.txt @@ -131,6 +131,7 @@ set(TARGET_LIBM_ENTRYPOINTS libc.src.math.erff libc.src.math.exp libc.src.math.expf + libc.src.math.exp10 libc.src.math.exp10f libc.src.math.exp2 libc.src.math.exp2f diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt index 7cd16df79a21c..e0bf9800ec881 100644 --- a/libc/config/linux/aarch64/entrypoints.txt +++ b/libc/config/linux/aarch64/entrypoints.txt @@ -245,6 +245,7 @@ set(TARGET_LIBM_ENTRYPOINTS libc.src.math.erff libc.src.math.exp libc.src.math.expf + libc.src.math.exp10 libc.src.math.exp10f libc.src.math.exp2 libc.src.math.exp2f diff --git a/libc/config/linux/riscv64/entrypoints.txt b/libc/config/linux/riscv64/entrypoints.txt index 4655744ebdcd0..2b2f2629f78ce 100644 --- a/libc/config/linux/riscv64/entrypoints.txt +++ b/libc/config/linux/riscv64/entrypoints.txt @@ -254,6 +254,7 @@ set(TARGET_LIBM_ENTRYPOINTS libc.src.math.erff libc.src.math.exp libc.src.math.expf + libc.src.math.exp10 libc.src.math.exp10f libc.src.math.exp2 libc.src.math.exp2f diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt index 4df1bf334c0c8..dcb8c6231432d 100644 --- a/libc/config/linux/x86_64/entrypoints.txt +++ b/libc/config/linux/x86_64/entrypoints.txt @@ -258,6 +258,7 @@ set(TARGET_LIBM_ENTRYPOINTS libc.src.math.erff libc.src.math.exp libc.src.math.expf + libc.src.math.exp10 libc.src.math.exp10f libc.src.math.exp2 libc.src.math.exp2f diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt index 15554b91eaf1c..26552fe7b07b5 100644 --- a/libc/config/windows/entrypoints.txt +++ b/libc/config/windows/entrypoints.txt @@ -130,6 +130,7 @@ set(TARGET_LIBM_ENTRYPOINTS libc.src.math.erff libc.src.math.exp libc.src.math.expf + libc.src.math.exp10 libc.src.math.exp10f libc.src.math.exp2 libc.src.math.exp2f diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst index 30c29252809b5..4e2ef031ab244 100644 --- a/libc/docs/math/index.rst +++ b/libc/docs/math/index.rst @@ -358,7 +358,7 @@ Higher Math Functions +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | expl | | | | | | | | | | | | | +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ -| exp10 | | | | | | | | | | | | | +| exp10 | |check| | |check| | | |check| | |check| | | | |check| | | | | | +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | exp10f | |check| | |check| | | |check| | |check| | | | |check| | | | | | +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ diff --git a/libc/spec/gnu_ext.td b/libc/spec/gnu_ext.td index a358caf4313b4..362add7283d6e 100644 --- a/libc/spec/gnu_ext.td +++ b/libc/spec/gnu_ext.td @@ -31,6 +31,7 @@ def GnuExtensions : StandardSpec<"GNUExtensions"> { RetValSpec, [ArgSpec, ArgSpec, ArgSpec] >, + FunctionSpec<"exp10", RetValSpec, [ArgSpec]>, FunctionSpec<"exp10f", RetValSpec, [ArgSpec]>, ] >; diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt index 79056fcb64b38..8b2021cac8239 100644 --- a/libc/src/math/CMakeLists.txt +++ b/libc/src/math/CMakeLists.txt @@ -85,6 +85,7 @@ add_math_entrypoint_object(expf) add_math_entrypoint_object(exp2) add_math_entrypoint_object(exp2f) +add_math_entrypoint_object(exp10) add_math_entrypoint_object(exp10f) add_math_entrypoint_object(expm1f) diff --git a/libc/src/math/exp10.h b/libc/src/math/exp10.h new file mode 100644 index 0000000000000..5afc95db2ce9c --- /dev/null +++ b/libc/src/math/exp10.h @@ -0,0 +1,18 @@ +//===-- Implementation header for exp10 -------------------------*- C++ -*-===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_LIBC_SRC_MATH_EXP10_H +#define LLVM_LIBC_SRC_MATH_EXP10_H + +namespace __llvm_libc { + +double exp10(double x); + +} // namespace __llvm_libc + +#endif // LLVM_LIBC_SRC_MATH_EXP10_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index fa7a5ed0ad9d5..9b092c3d3e7e6 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -648,6 +648,33 @@ add_entrypoint_object( -O3 ) +add_entrypoint_object( + exp10 + SRCS + exp10.cpp + HDRS + ../exp10.h + DEPENDS + .common_constants + .explogxf + libc.src.__support.CPP.bit + libc.src.__support.CPP.optional + 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.nearest_integer + libc.src.__support.FPUtil.polyeval + libc.src.__support.FPUtil.rounding_mode + libc.src.__support.FPUtil.triple_double + libc.src.__support.macros.optimization + libc.include.errno + libc.src.errno.errno + libc.include.math + COMPILE_OPTIONS + -O3 +) + add_entrypoint_object( exp10f SRCS diff --git a/libc/src/math/generic/exp10.cpp b/libc/src/math/generic/exp10.cpp new file mode 100644 index 0000000000000..4a43259b3307d --- /dev/null +++ b/libc/src/math/generic/exp10.cpp @@ -0,0 +1,476 @@ +//===-- Double-precision 10^x function ------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#include "src/math/exp10.h" +#include "common_constants.h" // Lookup tables EXP2_MID1 and EXP_M2. +#include "explogxf.h" // ziv_test_denorm. +#include "src/__support/CPP/bit.h" +#include "src/__support/CPP/optional.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/FPUtil/nearest_integer.h" +#include "src/__support/FPUtil/rounding_mode.h" +#include "src/__support/FPUtil/triple_double.h" +#include "src/__support/common.h" +#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY + +#include + +namespace __llvm_libc { + +using fputil::DoubleDouble; +using fputil::TripleDouble; +using Float128 = typename fputil::DyadicFloat<128>; + +// log2(10) +constexpr double LOG2_10 = 0x1.a934f0979a371p+1; + +// -2^-12 * log10(2) +// > a = -2^-12 * log10(2); +// > b = round(a, 32, RN); +// > c = round(a - b, 32, RN); +// > d = round(a - b - c, D, RN); +// Errors < 1.5 * 2^-144 +constexpr double MLOG10_2_EXP2_M12_HI = -0x1.3441350ap-14; +constexpr double MLOG10_2_EXP2_M12_MID = 0x1.0c0219dc1da99p-51; +constexpr double MLOG10_2_EXP2_M12_MID_32 = 0x1.0c0219dcp-51; +constexpr double MLOG10_2_EXP2_M12_LO = 0x1.da994fd20dba2p-87; + +// Error bounds: +// Errors when using double precision. +constexpr double ERR_D = 0x1.8p-63; + +// Errors when using double-double precision. +constexpr double ERR_DD = 0x1.8p-99; + +// Polynomial approximations with double precision. Generated by Sollya with: +// > P = fpminimax((10^x - 1)/x, 3, [|D...|], [-2^-14, 2^-14]); +// > P; +// Error bounds: +// | output - (10^dx - 1) / dx | < 2^-52. +LIBC_INLINE double poly_approx_d(double dx) { + // dx^2 + double dx2 = dx * dx; + double c0 = + fputil::multiply_add(dx, 0x1.53524c73cea6ap+1, 0x1.26bb1bbb55516p+1); + double c1 = + fputil::multiply_add(dx, 0x1.2bd75cc6afc65p+0, 0x1.0470587aa264cp+1); + double p = fputil::multiply_add(dx2, c1, c0); + return p; +} + +// Polynomial approximation with double-double precision. Generated by Solya +// with: +// > P = fpminimax((10^x - 1)/x, 5, [|DD...|], [-2^-14, 2^-14]); +// Error bounds: +// | output - 10^(dx) | < 2^-101 +DoubleDouble poly_approx_dd(const DoubleDouble &dx) { + // Taylor polynomial. + constexpr DoubleDouble COEFFS[] = { + {0, 0x1p0}, + {-0x1.f48ad494e927bp-53, 0x1.26bb1bbb55516p1}, + {-0x1.e2bfab3191cd2p-53, 0x1.53524c73cea69p1}, + {0x1.80fb65ec3b503p-53, 0x1.0470591de2ca4p1}, + {0x1.338fc05e21e55p-54, 0x1.2bd7609fd98c4p0}, + {0x1.d4ea116818fbp-56, 0x1.1429ffd519865p-1}, + {-0x1.872a8ff352077p-57, 0x1.a7ed70847c8b3p-3}, + + }; + + DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2], + COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]); + return p; +} + +// Polynomial approximation with 128-bit precision: +// Return exp(dx) ~ 1 + a0 * dx + a1 * dx^2 + ... + a6 * dx^7 +// For |dx| < 2^-14: +// | output - 10^dx | < 1.5 * 2^-124. +Float128 poly_approx_f128(const Float128 &dx) { + using MType = typename Float128::MantissaType; + + constexpr Float128 COEFFS_128[]{ + {false, -127, MType({0, 0x8000000000000000})}, // 1.0 + {false, -126, MType({0xea56d62b82d30a2d, 0x935d8dddaaa8ac16})}, + {false, -126, MType({0x80a99ce75f4d5bdb, 0xa9a92639e753443a})}, + {false, -126, MType({0x6a4f9d7dbf6c9635, 0x82382c8ef1652304})}, + {false, -124, MType({0x345787019216c7af, 0x12bd7609fd98c44c})}, + {false, -127, MType({0xcc41ed7e0d27aee5, 0x450a7ff47535d889})}, + {false, -130, MType({0x8326bb91a6e7601d, 0xd3f6b844702d636b})}, + {false, -130, MType({0xfa7b46df314112a9, 0x45b937f0d05bb1cd})}, + }; + + Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2], + COEFFS_128[3], COEFFS_128[4], COEFFS_128[5], + COEFFS_128[6], COEFFS_128[7]); + return p; +} + +// Compute 10^(x) using 128-bit precision. +// TODO(lntue): investigate triple-double precision implementation for this +// step. +Float128 exp10_f128(double x, double kd, int idx1, int idx2) { + double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact + double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact + double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-144 + + Float128 dx = fputil::quick_add( + Float128(t1), fputil::quick_add(Float128(t2), Float128(t3))); + + // TODO: Skip recalculating exp_mid1 and exp_mid2. + Float128 exp_mid1 = + fputil::quick_add(Float128(EXP2_MID1[idx1].hi), + fputil::quick_add(Float128(EXP2_MID1[idx1].mid), + Float128(EXP2_MID1[idx1].lo))); + + Float128 exp_mid2 = + fputil::quick_add(Float128(EXP2_MID2[idx2].hi), + fputil::quick_add(Float128(EXP2_MID2[idx2].mid), + Float128(EXP2_MID2[idx2].lo))); + + Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2); + + Float128 p = poly_approx_f128(dx); + + Float128 r = fputil::quick_mul(exp_mid, p); + + r.exponent += static_cast(kd) >> 12; + + return r; +} + +// Compute 10^x with double-double precision. +DoubleDouble exp10_double_double(double x, double kd, + const DoubleDouble &exp_mid) { + // Recalculate dx: + // dx = x - k * 2^-12 * log10(2) + double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact + double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact + double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-140 + + DoubleDouble dx = fputil::exact_add(t1, t2); + dx.lo += t3; + + // Degree-6 polynomial approximation in double-double precision. + // | p - 10^x | < 2^-103. + DoubleDouble p = poly_approx_dd(dx); + + // Error bounds: 2^-102. + DoubleDouble r = fputil::quick_mult(exp_mid, p); + + return r; +} + +// When output is denormal. +double exp10_denorm(double x) { + // Range reduction. + double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21); + int k = static_cast(cpp::bit_cast(tmp) >> 19); + double kd = static_cast(k); + + uint32_t idx1 = (k >> 6) & 0x3f; + uint32_t idx2 = k & 0x3f; + + int hi = k >> 12; + + DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi}; + DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi}; + DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2); + + // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14 + double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact + double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h); + + double mid_lo = dx * exp_mid.hi; + + // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4. + double p = poly_approx_d(dx); + + double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo); + + if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D); + LIBC_LIKELY(r.has_value())) + return r.value(); + + // Use double-double + DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid); + + if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD); + LIBC_LIKELY(r.has_value())) + return r.value(); + + // Use 128-bit precision + Float128 r_f128 = exp10_f128(x, kd, idx1, idx2); + + return static_cast(r_f128); +} + +// Check for exceptional cases when: +// * log10(1 - 2^-54) < x < log10(1 + 2^-53) +// * x >= log10(2^1024) +// * x <= log10(2^-1022) +// * x is inf or nan +double set_exceptional(double x) { + using FPBits = typename fputil::FPBits; + using FloatProp = typename fputil::FloatProperties; + FPBits xbits(x); + + uint64_t x_u = xbits.uintval(); + uint64_t x_abs = x_u & FloatProp::EXP_MANT_MASK; + + // |x| < log10(1 + 2^-53) + if (x_abs <= 0x3c8bcb7b1526e50e) { + // 10^(x) ~ 1 + x/2 + return fputil::multiply_add(x, 0.5, 1.0); + } + + // x <= log10(2^-1022) || x >= log10(2^1024) or inf/nan. + if (x_u >= 0xc0733a7146f72a42) { + // x <= log10(2^-1075) or -inf/nan + if (x_u > 0xc07439b746e36b52) { + // exp(-Inf) = 0 + if (xbits.is_inf()) + return 0.0; + + // exp(nan) = nan + if (xbits.is_nan()) + return x; + + if (fputil::quick_get_round() == FE_UPWARD) + return static_cast(FPBits(FPBits::MIN_SUBNORMAL)); + fputil::set_errno_if_required(ERANGE); + fputil::raise_except_if_required(FE_UNDERFLOW); + return 0.0; + } + + return exp10_denorm(x); + } + + // x >= log10(2^1024) or +inf/nan + // x is finite + if (x_u < 0x7ff0'0000'0000'0000ULL) { + int rounding = fputil::quick_get_round(); + if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) + return static_cast(FPBits(FPBits::MAX_NORMAL)); + + fputil::set_errno_if_required(ERANGE); + fputil::raise_except_if_required(FE_OVERFLOW); + } + // x is +inf or nan + return x + static_cast(FPBits::inf()); +} + +LLVM_LIBC_FUNCTION(double, exp10, (double x)) { + using FPBits = typename fputil::FPBits; + using FloatProp = typename fputil::FloatProperties; + FPBits xbits(x); + + uint64_t x_u = xbits.uintval(); + + // x <= log10(2^-1022) or x >= log10(2^1024) or + // log10(1 - 2^-54) < x < log10(1 + 2^-53). + if (LIBC_UNLIKELY(x_u >= 0xc0733a7146f72a42 || + (x_u <= 0xbc7bcb7b1526e50e && x_u >= 0x40734413509f79ff) || + x_u < 0x3c8bcb7b1526e50e)) { + return set_exceptional(x); + } + + // Now log10(2^-1075) < x <= log10(1 - 2^-54) or + // log10(1 + 2^-53) < x < log10(2^1024) + + // Range reduction: + // Let x = log10(2) * (hi + mid1 + mid2) + lo + // in which: + // hi is an integer + // mid1 * 2^6 is an integer + // mid2 * 2^12 is an integer + // then: + // 10^(x) = 2^hi * 2^(mid1) * 2^(mid2) * 10^(lo). + // With this formula: + // - multiplying by 2^hi is exact and cheap, simply by adding the exponent + // field. + // - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables. + // - 10^(lo) ~ 1 + a0*lo + a1 * lo^2 + ... + // + // We compute (hi + mid1 + mid2) together by perform the rounding on + // x * log2(10) * 2^12. + // Since |x| < |log10(2^-1075)| < 2^9, + // |x * 2^12| < 2^9 * 2^12 < 2^21, + // So we can fit the rounded result round(x * 2^12) in int32_t. + // Thus, the goal is to be able to use an additional addition and fixed width + // shift to get an int32_t representing round(x * 2^12). + // + // Assuming int32_t using 2-complement representation, since the mantissa part + // of a double precision is unsigned with the leading bit hidden, if we add an + // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^23 to the product, the + // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be + // considered as a proper 2-complement representations of x*2^12. + // + // One small problem with this approach is that the sum (x*2^12 + C) in + // double precision is rounded to the least significant bit of the dorminant + // factor C. In order to minimize the rounding errors from this addition, we + // want to minimize e1. Another constraint that we want is that after + // shifting the mantissa so that the least significant bit of int32_t + // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without + // any adjustment. So combining these 2 requirements, we can choose + // C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence + // after right shifting the mantissa, the resulting int32_t has correct sign. + // With this choice of C, the number of mantissa bits we need to shift to the + // right is: 52 - 33 = 19. + // + // Moreover, since the integer right shifts are equivalent to rounding down, + // we can add an extra 0.5 so that it will become round-to-nearest, tie-to- + // +infinity. So in particular, we can compute: + // hmm = x * 2^12 + C, + // where C = 2^33 + 2^32 + 2^-1, then if + // k = int32_t(lower 51 bits of double(x * 2^12 + C) >> 19), + // the reduced argument: + // lo = x - log10(2) * 2^-12 * k is bounded by: + // |lo| = |x - log10(2) * 2^-12 * k| + // = log10(2) * 2^-12 * | x * log2(10) * 2^12 - k | + // <= log10(2) * 2^-12 * (2^-1 + 2^-19) + // < 1.5 * 2^-2 * (2^-13 + 2^-31) + // = 1.5 * (2^-15 * 2^-31) + // + // Finally, notice that k only uses the mantissa of x * 2^12, so the + // exponent 2^12 is not needed. So we can simply define + // C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and + // k = int32_t(lower 51 bits of double(x + C) >> 19). + + // Rounding errors <= 2^-31. + double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21); + int k = static_cast(cpp::bit_cast(tmp) >> 19); + double kd = static_cast(k); + + uint32_t idx1 = (k >> 6) & 0x3f; + uint32_t idx2 = k & 0x3f; + + int hi = k >> 12; + + DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi}; + DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi}; + DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2); + + // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14 + double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact + double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h); + + // We use the degree-4 polynomial to approximate 10^(lo): + // 10^(lo) ~ 1 + a0 * lo + a1 * lo^2 + a2 * lo^3 + a3 * lo^4 + // = 1 + lo * P(lo) + // So that the errors are bounded by: + // |P(lo) - (10^lo - 1)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58 + // Let P_ be an evaluation of P where all intermediate computations are in + // double precision. Using either Horner's or Estrin's schemes, the evaluated + // errors can be bounded by: + // |P_(lo) - P(lo)| < 2^-51 + // => |lo * P_(lo) - (2^lo - 1) | < 2^-65 + // => 2^(mid1 + mid2) * |lo * P_(lo) - expm1(lo)| < 2^-64. + // Since we approximate + // 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo, + // We use the expression: + // (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~ + // ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo) + // with errors bounded by 2^-64. + + double mid_lo = dx * exp_mid.hi; + + // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4. + double p = poly_approx_d(dx); + + double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo); + + double upper = exp_mid.hi + (lo + ERR_D); + double lower = exp_mid.hi + (lo - ERR_D); + + if (LIBC_LIKELY(upper == lower)) { + // To multiply by 2^hi, a fast way is to simply add hi to the exponent + // field. + int64_t exp_hi = static_cast(hi) << FloatProp::MANTISSA_WIDTH; + double r = cpp::bit_cast(exp_hi + cpp::bit_cast(upper)); + return r; + } + + // Exact outputs when x = 1, 2, ..., 22 + hard to round with x = 23. + // Quick check mask: 0x800f'ffffU = ~(bits of 1.0 | ... | bits of 23.0) + if (LIBC_UNLIKELY((x_u & 0x8000'ffff'ffff'ffffULL) == 0ULL)) { + switch (x_u) { + case 0x3ff0000000000000: // x = 1.0 + return 10.0; + case 0x4000000000000000: // x = 2.0 + return 100.0; + case 0x4008000000000000: // x = 3.0 + return 1'000.0; + case 0x4010000000000000: // x = 4.0 + return 10'000.0; + case 0x4014000000000000: // x = 5.0 + return 100'000.0; + case 0x4018000000000000: // x = 6.0 + return 1'000'000.0; + case 0x401c000000000000: // x = 7.0 + return 10'000'000.0; + case 0x4020000000000000: // x = 8.0 + return 100'000'000.0; + case 0x4022000000000000: // x = 9.0 + return 1'000'000'000.0; + case 0x4024000000000000: // x = 10.0 + return 10'000'000'000.0; + case 0x4026000000000000: // x = 11.0 + return 100'000'000'000.0; + case 0x4028000000000000: // x = 12.0 + return 1'000'000'000'000.0; + case 0x402a000000000000: // x = 13.0 + return 10'000'000'000'000.0; + case 0x402c000000000000: // x = 14.0 + return 100'000'000'000'000.0; + case 0x402e000000000000: // x = 15.0 + return 1'000'000'000'000'000.0; + case 0x4030000000000000: // x = 16.0 + return 10'000'000'000'000'000.0; + case 0x4031000000000000: // x = 17.0 + return 100'000'000'000'000'000.0; + case 0x4032000000000000: // x = 18.0 + return 1'000'000'000'000'000'000.0; + case 0x4033000000000000: // x = 19.0 + return 10'000'000'000'000'000'000.0; + case 0x4034000000000000: // x = 20.0 + return 100'000'000'000'000'000'000.0; + case 0x4035000000000000: // x = 21.0 + return 1'000'000'000'000'000'000'000.0; + case 0x4036000000000000: // x = 22.0 + return 10'000'000'000'000'000'000'000.0; + case 0x4037000000000000: // x = 23.0 + return 0x1.52d02c7e14af6p76 + x; + } + } + + // Use double-double + DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid); + + double upper_dd = r_dd.hi + (r_dd.lo + ERR_DD); + double lower_dd = r_dd.hi + (r_dd.lo - ERR_DD); + + if (LIBC_LIKELY(upper_dd == lower_dd)) { + // To multiply by 2^hi, a fast way is to simply add hi to the exponent + // field. + int64_t exp_hi = static_cast(hi) << FloatProp::MANTISSA_WIDTH; + double r = cpp::bit_cast(exp_hi + cpp::bit_cast(upper_dd)); + return r; + } + + // Use 128-bit precision + Float128 r_f128 = exp10_f128(x, kd, idx1, idx2); + + return static_cast(r_f128); +} + +} // namespace __llvm_libc diff --git a/libc/src/math/generic/exp2.cpp b/libc/src/math/generic/exp2.cpp index 6b66e95aef590..96710c7d53706 100644 --- a/libc/src/math/generic/exp2.cpp +++ b/libc/src/math/generic/exp2.cpp @@ -104,7 +104,7 @@ Float128 poly_approx_f128(const Float128 &dx) { return p; } -// Compute exp(x) using 128-bit precision. +// Compute 2^(x) using 128-bit precision. // TODO(lntue): investigate triple-double precision implementation for this // step. Float128 exp2_f128(double x, int hi, int idx1, int idx2) { @@ -192,7 +192,7 @@ double exp2_denorm(double x) { // Check for exceptional cases when: // * log2(1 - 2^-54) < x < log2(1 + 2^-53) // * x >= 1024 -// * x <= -1075 +// * x <= -1022 // * x is inf or nan double set_exceptional(double x) { using FPBits = typename fputil::FPBits; @@ -208,9 +208,9 @@ double set_exceptional(double x) { return fputil::multiply_add(x, 0.5, 1.0); } - // x <= 2^-1075 || x >= 1024 or inf/nan. + // x <= -1022 || x >= 1024 or inf/nan. if (x_u > 0xc08ff00000000000) { - // x <= 2^-1075 or -inf/nan + // x <= -1075 or -inf/nan if (x_u >= 0xc090cc0000000000) { // exp(-Inf) = 0 if (xbits.is_inf()) diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt index ca55496b3244d..04b1256e09b46 100644 --- a/libc/test/src/math/CMakeLists.txt +++ b/libc/test/src/math/CMakeLists.txt @@ -647,6 +647,20 @@ add_fp_unittest( libc.src.__support.FPUtil.fp_bits ) +add_fp_unittest( + exp10_test + NEED_MPFR + SUITE + libc_math_unittests + SRCS + exp10_test.cpp + DEPENDS + libc.src.errno.errno + libc.include.math + libc.src.math.exp10 + libc.src.__support.FPUtil.fp_bits +) + add_fp_unittest( copysign_test SUITE diff --git a/libc/test/src/math/exp10_test.cpp b/libc/test/src/math/exp10_test.cpp new file mode 100644 index 0000000000000..2b4c5ccc13f5d --- /dev/null +++ b/libc/test/src/math/exp10_test.cpp @@ -0,0 +1,150 @@ +//===-- Unittests for 10^x ------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#include "src/__support/FPUtil/FPBits.h" +#include "src/errno/libc_errno.h" +#include "src/math/exp10.h" +#include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" +#include "utils/MPFRWrapper/MPFRUtils.h" +#include + +#include +#include + +namespace mpfr = __llvm_libc::testing::mpfr; +using __llvm_libc::testing::tlog; + +DECLARE_SPECIAL_CONSTANTS(double) + +TEST(LlvmLibcExp10Test, SpecialNumbers) { + EXPECT_FP_EQ(aNaN, __llvm_libc::exp10(aNaN)); + EXPECT_FP_EQ(inf, __llvm_libc::exp10(inf)); + EXPECT_FP_EQ_ALL_ROUNDING(zero, __llvm_libc::exp10(neg_inf)); + EXPECT_FP_EQ_WITH_EXCEPTION(zero, __llvm_libc::exp10(-0x1.0p20), + FE_UNDERFLOW); + EXPECT_FP_EQ_WITH_EXCEPTION(inf, __llvm_libc::exp10(0x1.0p20), FE_OVERFLOW); + EXPECT_FP_EQ_ALL_ROUNDING(1.0, __llvm_libc::exp10(0.0)); + EXPECT_FP_EQ_ALL_ROUNDING(1.0, __llvm_libc::exp10(-0.0)); +} + +TEST(LlvmLibcExp10Test, TrickyInputs) { + constexpr int N = 41; + constexpr uint64_t INPUTS[N] = { + 0x40033093317082F8, 0x3FD79289C6E6A5C0, + 0x3FD05DE80A173EA0, // 0x1.05de80a173eap-2 + 0xbf1eb7a4cb841fcc, // -0x1.eb7a4cb841fccp-14 + 0xbf19a61fb925970d, + 0x3fda7b764e2cf47a, // 0x1.a7b764e2cf47ap-2 + 0xc04757852a4b93aa, // -0x1.757852a4b93aap+5 + 0x4044c19e5712e377, // x=0x1.4c19e5712e377p+5 + 0xbf19a61fb925970d, // x=-0x1.9a61fb925970dp-14 + 0xc039a74cdab36c28, // x=-0x1.9a74cdab36c28p+4 + 0xc085b3e4e2e3bba9, // x=-0x1.5b3e4e2e3bba9p+9 + 0xc086960d591aec34, // x=-0x1.6960d591aec34p+9 + 0xc086232c09d58d91, // x=-0x1.6232c09d58d91p+9 + 0xc0874910d52d3051, // x=-0x1.74910d52d3051p9 + 0xc0867a172ceb0990, // x=-0x1.67a172ceb099p+9 + 0xc08ff80000000000, // x=-0x1.ff8p+9 + 0xbc971547652b82fe, // x=-0x1.71547652b82fep-54 + 0x0000000000000000, // x = 0 + 0x3ff0000000000000, // x = 1 + 0x4000000000000000, // x = 2 + 0x4008000000000000, // x = 3 + 0x4010000000000000, // x = 4 + 0x4014000000000000, // x = 5 + 0x4018000000000000, // x = 6 + 0x401c000000000000, // x = 7 + 0x4020000000000000, // x = 8 + 0x4022000000000000, // x = 9 + 0x4024000000000000, // x = 10 + 0x4026000000000000, // x = 11 + 0x4028000000000000, // x = 12 + 0x402a000000000000, // x = 13 + 0x402c000000000000, // x = 14 + 0x402e000000000000, // x = 15 + 0x4030000000000000, // x = 16 + 0x4031000000000000, // x = 17 + 0x4032000000000000, // x = 18 + 0x4033000000000000, // x = 19 + 0x4034000000000000, // x = 20 + 0x4035000000000000, // x = 21 + 0x4036000000000000, // x = 22 + 0x4037000000000000, // x = 23 + }; + for (int i = 0; i < N; ++i) { + double x = double(FPBits(INPUTS[i])); + EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp10, x, + __llvm_libc::exp10(x), 0.5); + } +} + +TEST(LlvmLibcExp10Test, InDoubleRange) { + constexpr uint64_t COUNT = 1'231; + uint64_t START = __llvm_libc::fputil::FPBits(0.25).uintval(); + uint64_t STOP = __llvm_libc::fputil::FPBits(4.0).uintval(); + uint64_t STEP = (STOP - START) / COUNT; + + auto test = [&](mpfr::RoundingMode rounding_mode) { + mpfr::ForceRoundingMode __r(rounding_mode); + if (!__r.success) + return; + + uint64_t fails = 0; + uint64_t count = 0; + uint64_t cc = 0; + double mx, mr = 0.0; + double tol = 0.5; + + for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) { + double x = FPBits(v).get_val(); + if (isnan(x) || isinf(x) || x < 0.0) + continue; + libc_errno = 0; + double result = __llvm_libc::exp10(x); + ++cc; + if (isnan(result) || isinf(result)) + continue; + + ++count; + + if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Exp10, x, result, + 0.5, rounding_mode)) { + ++fails; + while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Exp10, x, + result, tol, rounding_mode)) { + mx = x; + mr = result; + + if (tol > 1000.0) + break; + + tol *= 2.0; + } + } + } + tlog << " Exp10 failed: " << fails << "/" << count << "/" << cc + << " tests.\n"; + tlog << " Max ULPs is at most: " << static_cast(tol) << ".\n"; + if (fails) { + EXPECT_MPFR_MATCH(mpfr::Operation::Exp10, mx, mr, 0.5, rounding_mode); + } + }; + + tlog << " Test Rounding To Nearest...\n"; + test(mpfr::RoundingMode::Nearest); + + tlog << " Test Rounding Downward...\n"; + test(mpfr::RoundingMode::Downward); + + tlog << " Test Rounding Upward...\n"; + test(mpfr::RoundingMode::Upward); + + tlog << " Test Rounding Toward Zero...\n"; + test(mpfr::RoundingMode::TowardZero); +} diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel index 54b7dce3e7884..a25e83691c98c 100644 --- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel +++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel @@ -1246,6 +1246,22 @@ libc_math_function( ], ) +libc_math_function( + name = "exp10", + additional_deps = [ + ":__support_fputil_double_double", + ":__support_fputil_dyadic_float", + ":__support_fputil_multiply_add", + ":__support_fputil_nearest_integer", + ":__support_fputil_polyeval", + ":__support_fputil_rounding_mode", + ":__support_fputil_triple_double", + ":__support_macros_optimization", + ":common_constants", + ":explogxf", + ], +) + libc_math_function( name = "exp10f", additional_deps = [ diff --git a/utils/bazel/llvm-project-overlay/libc/test/src/math/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/test/src/math/BUILD.bazel index bfada56419994..76b884714cfa9 100644 --- a/utils/bazel/llvm-project-overlay/libc/test/src/math/BUILD.bazel +++ b/utils/bazel/llvm-project-overlay/libc/test/src/math/BUILD.bazel @@ -755,6 +755,13 @@ math_test( ], ) +math_test( + name = "exp10", + deps = [ + "//libc/utils/MPFRWrapper:mpfr_wrapper", + ], +) + math_test( name = "fmod", hdrs = ["FModTest.h"],