[libc][math][c23] Add exp10m1f16 C23 math function #105706
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| Original file line number | Diff line number | Diff line change |
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| //===-- Implementation header for exp10m1f16 --------------------*- 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_EXP10M1F16_H | ||
| #define LLVM_LIBC_SRC_MATH_EXP10M1F16_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 exp10m1f16(float16 x); | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LLVM_LIBC_SRC_MATH_EXP10M1F16_H |
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| Original file line number | Diff line number | Diff line change |
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| //===-- 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #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/cast.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" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| 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}, | ||
| }}; | ||
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| #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 | ||
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| 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 | ||
| }}; | ||
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| LLVM_LIBC_FUNCTION(float16, exp10m1f16, (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| <= 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(); | ||
| } | ||
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| return x; | ||
| } | ||
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| // 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(); | ||
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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 | FE_INEXACT); | ||
| return FPBits::inf().get_val(); | ||
| default: | ||
| return FPBits::max_normal().get_val(); | ||
| } | ||
| } | ||
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| // When x < -11 * log10(2). | ||
| if (x_u > 0xc29fU) { | ||
| // exp10m1(-inf) = -1 | ||
| if (x_bits.is_inf()) | ||
| return FPBits::one(Sign::NEG).get_val(); | ||
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| // When x >= -0x1.ce4p+1, round(10^x - 1, HP, RN) = -0x1.ffcp-1. | ||
| if (x_u <= 0xc339U) { | ||
| return fputil::round_result_slightly_down( | ||
| fputil::cast<float16>(-0x1.ffcp-1)); | ||
| } | ||
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| // 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 fputil::cast<float16>(-0x1.ffcp-1); | ||
| } | ||
| } | ||
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| // 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(); | ||
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| 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 fputil::cast<float16>( | ||
| xf * fputil::polyeval(xf, 0x1.26bb1cp+1f, 0x1.5351c8p+1f, | ||
| 0x1.04704p+1f, 0x1.2ce084p+0f, 0x1.14a6bep-1f)); | ||
| } | ||
| } | ||
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| // 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 | ||
|
There was a problem hiding this comment. It's actually not luck, because the relative error of while the relative error of the relative errors from the approximation is: |
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| // polynomial approximation gives the correct result for x = 4 in all | ||
| // rounding modes. | ||
| if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) { | ||
| switch (x_u) { | ||
| case 0x3c00U: // x = 1.0f16 | ||
| return fputil::cast<float16>(9.0); | ||
| case 0x4000U: // x = 2.0f16 | ||
| return fputil::cast<float16>(99.0); | ||
| case 0x4200U: // x = 3.0f16 | ||
| return fputil::cast<float16>(999.0); | ||
| } | ||
| } | ||
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| if (auto r = EXP10M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
| return r.value(); | ||
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| // exp10(x) = exp2((hi + mid) * log2(10)) * exp10(lo) | ||
| auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x); | ||
| // exp10m1(x) = exp2((hi + mid) * log2(lo)) * exp10(lo) - 1 | ||
| return fputil::cast<float16>( | ||
| fputil::multiply_add(exp2_hi_mid, exp10_lo, -1.0f)); | ||
| } | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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also update new header gen.
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Will make a single PR to update newhdrgen for all the new
float16functions later as discussed.