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Diffstat (limited to 'libc/src/math/generic/exp10f16.cpp')
| -rw-r--r-- | libc/src/math/generic/exp10f16.cpp | 170 |
1 files changed, 170 insertions, 0 deletions
diff --git a/libc/src/math/generic/exp10f16.cpp b/libc/src/math/generic/exp10f16.cpp new file mode 100644 index 000000000000..9959f7450b59 --- /dev/null +++ b/libc/src/math/generic/exp10f16.cpp @@ -0,0 +1,170 @@ +//===-- Half-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/exp10f16.h" +#include "expxf16.h" +#include "hdr/errno_macros.h" +#include "hdr/fenv_macros.h" +#include "src/__support/CPP/array.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/nearest_integer.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 { + +#ifdef LIBC_TARGET_CPU_HAS_FMA +static constexpr size_t N_EXP10F16_EXCEPTS = 5; +#else +static constexpr size_t N_EXP10F16_EXCEPTS = 8; +#endif + +static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS> + EXP10F16_EXCEPTS = {{ + // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ) + {0x363dU, 0x40e8U, 1U, 0U, 1U}, + // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ) + {0x3657U, 0x40fbU, 1U, 0U, 0U}, + // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ) + {0xac06U, 0x3aecU, 1U, 0U, 0U}, + // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ) + {0xbf0aU, 0x2473U, 1U, 0U, 0U}, + // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ) + {0xc387U, 0x09a5U, 1U, 0U, 0U}, +#ifndef LIBC_TARGET_CPU_HAS_FMA + // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ) + {0x4030U, 0x57c1U, 1U, 0U, 1U}, + // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ) + {0x406eU, 0x591fU, 1U, 0U, 1U}, + // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ) + {0x446eU, 0x7690U, 1U, 0U, 1U}, +#endif + }}; + +// Generated by Sollya with the following commands: +// > display = hexadecimal; +// > round(log2(10), SG, RN); +static constexpr float LOG2F_10 = 0x1.a934fp+1f; + +// Generated by Sollya with the following commands: +// > display = hexadecimal; +// > round(log10(2), SG, RN); +static constexpr float LOG10F_2 = 0x1.344136p-2f; + +LLVM_LIBC_FUNCTION(float16, exp10f16, (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| >= 5, or x is NaN. + if (LIBC_UNLIKELY(x_abs >= 0x4500U)) { + // exp10(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 >= 5. + if (x_bits.is_pos()) { + // exp10(+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); + return FPBits::inf().get_val(); + default: + return FPBits::max_normal().get_val(); + } + } + + // When x <= -8. + if (x_u >= 0xc800U) { + // exp10(-inf) = +0 + if (x_bits.is_inf()) + return FPBits::zero().get_val(); + + fputil::set_errno_if_required(ERANGE); + fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); + + if (fputil::fenv_is_round_up()) + return FPBits::min_subnormal().get_val(); + return FPBits::zero().get_val(); + } + } + + // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results. + if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) { + switch (x_u) { + case 0x3c00U: // x = 1.0f16 + return static_cast<float16>(10.0); + case 0x4000U: // x = 2.0f16 + return static_cast<float16>(100.0); + case 0x4200U: // x = 3.0f16 + return static_cast<float16>(1'000.0); + case 0x4400U: // x = 4.0f16 + return static_cast<float16>(10'000.0); + } + } + + if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) + return r.value(); + + // For -8 < x < 5, to compute 10^x, we perform the following range reduction: + // find hi, mid, lo, such that: + // x = (hi + mid) * log2(10) + lo, in which + // hi is an integer, + // mid * 2^3 is an integer, + // -2^(-4) <= lo < 2^(-4). + // In particular, + // hi + mid = round(x * 2^3) * 2^(-3). + // Then, + // 10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo + // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid + // by adding hi to the exponent field of 2^mid. 10^lo is computed using a + // degree-4 minimax polynomial generated by Sollya. + + float xf = x; + float kf = fputil::nearest_integer(xf * (LOG2F_10 * 0x1.0p+3f)); + int x_hi_mid = static_cast<int>(kf); + int x_hi = x_hi_mid >> 3; + int x_mid = x_hi_mid & 0x7; + // lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x + float lo = fputil::multiply_add(kf, LOG10F_2 * -0x1.0p-3f, xf); + + uint32_t exp2_hi_mid_bits = + EXP2_MID_BITS[x_mid] + + static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN); + float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val(); + // Degree-4 minimax polynomial generated by Sollya with the following + // commands: + // > display = hexadecimal; + // > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]); + // > 1 + x * P; + float exp10_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.26bb14p+1f, 0x1.53526p+1f, + 0x1.04b434p+1f, 0x1.2bcf9ep+0f); + return static_cast<float16>(exp2_hi_mid * exp10_lo); +} + +} // namespace LIBC_NAMESPACE_DECL |