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[libc][math][c23] Add exp10f16 C23 math function (#101588)
Part of #95250.
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| Original file line number | Diff line number | Diff line change |
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| //===-- Implementation header for exp10f16 ----------------------*- 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #ifndef LLVM_LIBC_SRC_MATH_EXP10F16_H | ||
| #define LLVM_LIBC_SRC_MATH_EXP10F16_H | ||
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| #include "src/__support/macros/config.h" | ||
| #include "src/__support/macros/properties/types.h" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| float16 exp10f16(float16 x); | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LLVM_LIBC_SRC_MATH_EXP10F16_H |
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| Original file line number | Diff line number | Diff line change |
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| //===-- 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #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" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| #ifdef LIBC_TARGET_CPU_HAS_FMA | ||
| static constexpr size_t N_EXP10F16_EXCEPTS = 5; | ||
| #else | ||
| static constexpr size_t N_EXP10F16_EXCEPTS = 8; | ||
| #endif | ||
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| 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 | ||
| }}; | ||
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| // Generated by Sollya with the following commands: | ||
| // > display = hexadecimal; | ||
| // > round(log2(10), SG, RN); | ||
| static constexpr float LOG2F_10 = 0x1.a934fp+1f; | ||
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| // Generated by Sollya with the following commands: | ||
| // > display = hexadecimal; | ||
| // > round(log10(2), SG, RN); | ||
| static constexpr float LOG10F_2 = 0x1.344136p-2f; | ||
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| LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) { | ||
| using FPBits = fputil::FPBits<float16>; | ||
| FPBits x_bits(x); | ||
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| uint16_t x_u = x_bits.uintval(); | ||
| uint16_t x_abs = x_u & 0x7fffU; | ||
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| // 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(); | ||
| } | ||
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| return x; | ||
| } | ||
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| // When x >= 5. | ||
| if (x_bits.is_pos()) { | ||
| // exp10(+inf) = +inf | ||
| if (x_bits.is_inf()) | ||
| return FPBits::inf().get_val(); | ||
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| 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(); | ||
| } | ||
| } | ||
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| // When x <= -8. | ||
| if (x_u >= 0xc800U) { | ||
| // exp10(-inf) = +0 | ||
| if (x_bits.is_inf()) | ||
| return FPBits::zero().get_val(); | ||
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| fputil::set_errno_if_required(ERANGE); | ||
| fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); | ||
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| if (fputil::fenv_is_round_up()) | ||
| return FPBits::min_subnormal().get_val(); | ||
| return FPBits::zero().get_val(); | ||
| } | ||
| } | ||
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| // 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); | ||
| } | ||
| } | ||
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| if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
| return r.value(); | ||
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| // 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. | ||
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| 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); | ||
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| 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); | ||
| } | ||
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| } // namespace LIBC_NAMESPACE_DECL |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,28 @@ | ||
| //===-- Common utilities for half-precision exponential functions ---------===// | ||
| // | ||
| // 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H | ||
| #define LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H | ||
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| #include "src/__support/CPP/array.h" | ||
| #include "src/__support/macros/config.h" | ||
| #include <stdint.h> | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| // Generated by Sollya with the following commands: | ||
| // > display = hexadecimal; | ||
| // > for i from 0 to 7 do printsingle(round(2^(i * 2^-3), SG, RN)); | ||
| constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = { | ||
| 0x3f80'0000U, 0x3f8b'95c2U, 0x3f98'37f0U, 0x3fa5'fed7U, | ||
| 0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U, | ||
| }; | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H |
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