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[libc][math][c23] Add expm1f16 C23 math function
Part of #95250.
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| //===-- Implementation header for expm1f16 ----------------------*- 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_EXPM1F16_H | ||
| #define LLVM_LIBC_SRC_MATH_EXPM1F16_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 expm1f16(float16 x); | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LLVM_LIBC_SRC_MATH_EXPM1F16_H |
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| //===-- Half-precision e^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/expm1f16.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" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| static constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{ | ||
| // (input, RZ output, RU offset, RD offset, RN offset) | ||
| // x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ) | ||
| {0x2959U, 0x2975U, 1U, 0U, 1U}, | ||
| }}; | ||
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| #ifdef LIBC_TARGET_CPU_HAS_FMA | ||
| static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2; | ||
| #else | ||
| static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3; | ||
| #endif | ||
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| static constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI> | ||
| EXPM1F16_EXCEPTS_HI = {{ | ||
| // (input, RZ output, RU offset, RD offset, RN offset) | ||
| // x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ) | ||
| {0x3f0dU, 0x44d3U, 1U, 0U, 1U}, | ||
| // x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ) | ||
| {0xb38aU, 0xb2b7U, 0U, 1U, 1U}, | ||
| #ifndef LIBC_TARGET_CPU_HAS_FMA | ||
| // x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ) | ||
| {0x3282U, 0x3337U, 1U, 0U, 0U}, | ||
| #endif | ||
| }}; | ||
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| LLVM_LIBC_FUNCTION(float16, expm1f16, (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 * log(2), or x is NaN. | ||
| if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) { | ||
| // expm1(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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| // expm1(+/-0) = +/-0 | ||
| if (x_abs == 0) | ||
| return x; | ||
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| // When x >= 12. | ||
| if (x_bits.is_pos() && x_abs >= 0x4a00U) { | ||
| // expm1(+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 <= -11 * log(2). | ||
| if (x_u >= 0xc7a0U) { | ||
| // expm1(-inf) = -1 | ||
| if (x_bits.is_inf()) | ||
| return FPBits::one(Sign::NEG).get_val(); | ||
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| fputil::set_errno_if_required(ERANGE); | ||
| fputil::raise_except_if_required(FE_INEXACT); | ||
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| switch (fputil::quick_get_round()) { | ||
| case FE_UPWARD: | ||
| case FE_TOWARDZERO: | ||
| return static_cast<float16>(-0x1.ffcp-1); | ||
| case FE_TONEAREST: | ||
| if (x_u > 0xc828U) | ||
| return FPBits::one(Sign::NEG).get_val(); | ||
| return static_cast<float16>(-0x1.ffcp-1); | ||
| default: | ||
| return FPBits::one(Sign::NEG).get_val(); | ||
| } | ||
| } | ||
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| // When 0 < |x| <= 2^(-3). | ||
| if (x_abs <= 0x3000U && !x_bits.is_zero()) { | ||
| if (auto r = EXPM1F16_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(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]); | ||
| // > x * P; | ||
| return static_cast<float16>( | ||
| xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f, | ||
| 0x1.55905ep-5f, 0x1.1124c2p-7f)); | ||
| } | ||
| } | ||
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| if (auto r = EXPM1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
| return r.value(); | ||
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| // exp(x) = exp(hi + mid) * exp(lo) | ||
| auto [exp_hi_mid, exp_lo] = exp_range_reduction(x); | ||
| // expm1(x) = exp(hi + mid) * exp(lo) - 1 | ||
| return static_cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f)); | ||
| } | ||
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| } // namespace LIBC_NAMESPACE_DECL |
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