================ @@ -0,0 +1,162 @@ +//===-- Half-precision 10^x - 1 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/exp10m1f16.h" +#include "expxf16.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/except_value_utils.h" +#include "src/__support/FPUtil/multiply_add.h" +#include "src/__support/FPUtil/rounding_mode.h" +#include "src/__support/common.h" +#include "src/__support/macros/config.h" +#include "src/__support/macros/optimization.h" +#include "src/__support/macros/properties/cpu_features.h" + +namespace LIBC_NAMESPACE_DECL { + +static constexpr fputil::ExceptValues<float16, 3> EXP10M1F16_EXCEPTS_LO = {{ + // (input, RZ output, RU offset, RD offset, RN offset) + // x = 0x1.5c4p-4, exp10m1f16(x) = 0x1.bacp-3 (RZ) + {0x2d71U, 0x32ebU, 1U, 0U, 0U}, + // x = -0x1.5ep-13, exp10m1f16(x) = -0x1.92cp-12 (RZ) + {0x8978U, 0x8e4bU, 0U, 1U, 0U}, + // x = -0x1.e2p-10, exp10m1f16(x) = -0x1.14cp-8 (RZ) + {0x9788U, 0x9c53U, 0U, 1U, 0U}, +}}; + +#ifdef LIBC_TARGET_CPU_HAS_FMA +static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 3; +#else +static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 6; +#endif + +static constexpr fputil::ExceptValues<float16, N_EXP10M1F16_EXCEPTS_HI> + EXP10M1F16_EXCEPTS_HI = {{ + // (input, RZ output, RU offset, RD offset, RN offset) + // x = 0x1.8f4p-2, exp10m1f16(x) = 0x1.744p+0 (RZ) + {0x363dU, 0x3dd1U, 1U, 0U, 0U}, + // x = 0x1.95cp-2, exp10m1f16(x) = 0x1.7d8p+0 (RZ) + {0x3657U, 0x3df6U, 1U, 0U, 0U}, + // x = 0x1.d04p-2, exp10m1f16(x) = 0x1.d7p+0 (RZ) + {0x3741U, 0x3f5cU, 1U, 0U, 1U}, +#ifndef LIBC_TARGET_CPU_HAS_FMA + // x = 0x1.0cp+1, exp10m1f16(x) = 0x1.ec4p+6 (RZ) + {0x4030U, 0x57b1U, 1U, 0U, 1U}, + // x = 0x1.1b8p+1, exp10m1f16(x) = 0x1.45cp+7 (RZ) + {0x406eU, 0x5917U, 1U, 0U, 1U}, + // x = 0x1.2f4p+2, exp10m1f16(x) = 0x1.ab8p+15 (RZ) + {0x44bdU, 0x7aaeU, 1U, 0U, 1U}, +#endif + }}; + +LLVM_LIBC_FUNCTION(float16, exp10m1f16, (float16 x)) { + using FPBits = fputil::FPBits<float16>; + FPBits x_bits(x); + + uint16_t x_u = x_bits.uintval(); + uint16_t x_abs = x_u & 0x7fffU; + + // When |x| <= 2^(-3), or |x| >= 11 * log10(2), or x is NaN. + if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x429fU)) { + // exp10m1(NaN) = NaN + if (x_bits.is_nan()) { + if (x_bits.is_signaling_nan()) { + fputil::raise_except_if_required(FE_INVALID); + return FPBits::quiet_nan().get_val(); + } + + return x; + } + + // When x >= 16 * log10(2). + if (x_u >= 0x44d1U && x_bits.is_pos()) { + // exp10m1(+inf) = +inf + if (x_bits.is_inf()) + return FPBits::inf().get_val(); + + switch (fputil::quick_get_round()) { + case FE_TONEAREST: + case FE_UPWARD: + fputil::set_errno_if_required(ERANGE); + fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT); + return FPBits::inf().get_val(); + default: + return FPBits::max_normal().get_val(); + } + } + + // When x < -11 * log10(2). + if (x_u > 0xc29fU) { + // exp10m1(-inf) = -1 + if (x_bits.is_inf()) + return FPBits::one(Sign::NEG).get_val(); + + // When x >= -0x1.ce4p+1, round(10^x - 1, HP, RN) = -0x1.ffcp-1. + if (x_u <= 0xc339U) { + return fputil::round_result_slightly_down( + static_cast<float16>(-0x1.ffcp-1)); + } + + // When x < -0x1.ce4p+1, round(10^x - 1, HP, RN) = -1. + switch (fputil::quick_get_round()) { + case FE_TONEAREST: + case FE_DOWNWARD: + return FPBits::one(Sign::NEG).get_val(); + default: + return static_cast<float16>(-0x1.ffcp-1); + } + } + + // When |x| <= 2^(-3). + if (x_abs <= 0x3000U) { + if (auto r = EXP10M1F16_EXCEPTS_LO.lookup(x_u); + LIBC_UNLIKELY(r.has_value())) + return r.value(); + + float xf = x; + // Degree-5 minimax polynomial generated by Sollya with the following + // commands: + // > display = hexadecimal; + // > P = fpminimax((10^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]); + // > x * P; + return static_cast<float16>( + xf * fputil::polyeval(xf, 0x1.26bb1cp+1f, 0x1.5351c8p+1f, + 0x1.04704p+1f, 0x1.2ce084p+0f, 0x1.14a6bep-1f)); + } + } + + // When x is 1, 2, or 3. These are hard-to-round cases with exact results. + // 10^4 - 1 = 9'999 is not exactly representable as a float16, but luckily the ---------------- lntue wrote:
It's actually not luck, because the relative error of `9'999` to the nearest half-precision is: ``` > (9999 - round(9999, HP, RN)) / 9999; 0x1.a37...p-14 ``` while the relative error of the relative errors from the approximation is: ``` > dirtyinfnorm(((10^x - 1) - x*P)/(10^x - 1), [-2^-3, 2^-3]); 0x1.9d5...p-23 ``` https://github.com/llvm/llvm-project/pull/105706 _______________________________________________ llvm-branch-commits mailing list llvm-branch-commits@lists.llvm.org https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-branch-commits
