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[libc][math][c23] Add exp2m1f16 C23 math function (#105690)
Part of #95250.
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| Original file line number | Diff line number | Diff line change |
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| //===-- Implementation header for exp2m1f16 ---------------------*- 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_EXP2M1F16_H | ||
| #define LLVM_LIBC_SRC_MATH_EXP2M1F16_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 exp2m1f16(float16 x); | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LLVM_LIBC_SRC_MATH_EXP2M1F16_H |
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| Original file line number | Diff line number | Diff line change |
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| //===-- Half-precision 2^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/exp2m1f16.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, 6> EXP2M1F16_EXCEPTS_LO = {{ | ||
| // (input, RZ output, RU offset, RD offset, RN offset) | ||
| // x = 0x1.cf4p-13, exp2m1f16(x) = 0x1.41p-13 (RZ) | ||
| {0x0b3dU, 0x0904U, 1U, 0U, 1U}, | ||
| // x = 0x1.4fcp-12, exp2m1f16(x) = 0x1.d14p-13 (RZ) | ||
| {0x0d3fU, 0x0b45U, 1U, 0U, 1U}, | ||
| // x = 0x1.63p-11, exp2m1f16(x) = 0x1.ec4p-12 (RZ) | ||
| {0x118cU, 0x0fb1U, 1U, 0U, 0U}, | ||
| // x = 0x1.6fp-7, exp2m1f16(x) = 0x1.fe8p-8 (RZ) | ||
| {0x21bcU, 0x1ffaU, 1U, 0U, 1U}, | ||
| // x = -0x1.c6p-10, exp2m1f16(x) = -0x1.3a8p-10 (RZ) | ||
| {0x9718U, 0x94eaU, 0U, 1U, 0U}, | ||
| // x = -0x1.cfcp-10, exp2m1f16(x) = -0x1.414p-10 (RZ) | ||
| {0x973fU, 0x9505U, 0U, 1U, 0U}, | ||
| }}; | ||
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| #ifdef LIBC_TARGET_CPU_HAS_FMA | ||
| static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 6; | ||
| #else | ||
| static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 7; | ||
| #endif | ||
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| static constexpr fputil::ExceptValues<float16, N_EXP2M1F16_EXCEPTS_HI> | ||
| EXP2M1F16_EXCEPTS_HI = {{ | ||
| // (input, RZ output, RU offset, RD offset, RN offset) | ||
| // x = 0x1.e58p-3, exp2m1f16(x) = 0x1.6dcp-3 (RZ) | ||
| {0x3396U, 0x31b7U, 1U, 0U, 0U}, | ||
| #ifndef LIBC_TARGET_CPU_HAS_FMA | ||
| // x = 0x1.2e8p-2, exp2m1f16(x) = 0x1.d14p-3 (RZ) | ||
| {0x34baU, 0x3345U, 1U, 0U, 0U}, | ||
| #endif | ||
| // x = 0x1.ad8p-2, exp2m1f16(x) = 0x1.598p-2 (RZ) | ||
| {0x36b6U, 0x3566U, 1U, 0U, 0U}, | ||
| #ifdef LIBC_TARGET_CPU_HAS_FMA | ||
| // x = 0x1.edcp-2, exp2m1f16(x) = 0x1.964p-2 (RZ) | ||
| {0x37b7U, 0x3659U, 1U, 0U, 1U}, | ||
| #endif | ||
| // x = -0x1.804p-3, exp2m1f16(x) = -0x1.f34p-4 (RZ) | ||
| {0xb201U, 0xafcdU, 0U, 1U, 1U}, | ||
| // x = -0x1.f3p-3, exp2m1f16(x) = -0x1.3e4p-3 (RZ) | ||
| {0xb3ccU, 0xb0f9U, 0U, 1U, 0U}, | ||
| // x = -0x1.294p-1, exp2m1f16(x) = -0x1.53p-2 (RZ) | ||
| {0xb8a5U, 0xb54cU, 0U, 1U, 1U}, | ||
| #ifndef LIBC_TARGET_CPU_HAS_FMA | ||
| // x = -0x1.a34p-1, exp2m1f16(x) = -0x1.bb4p-2 (RZ) | ||
| {0xba8dU, 0xb6edU, 0U, 1U, 1U}, | ||
| #endif | ||
| }}; | ||
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| LLVM_LIBC_FUNCTION(float16, exp2m1f16, (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, or x is NaN. | ||
| if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x4980U)) { | ||
| // exp2m1(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. | ||
| if (x_u >= 0x4c00 && x_bits.is_pos()) { | ||
| // exp2m1(+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. | ||
| if (x_u > 0xc980U) { | ||
| // exp2m1(-inf) = -1 | ||
| if (x_bits.is_inf()) | ||
| return FPBits::one(Sign::NEG).get_val(); | ||
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| // When -12 < x < -11, round(2^x - 1, HP, RN) = -0x1.ffcp-1. | ||
| if (x_u < 0xca00U) | ||
| return fputil::round_result_slightly_down( | ||
| fputil::cast<float16>(-0x1.ffcp-1)); | ||
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| // When x <= -12, round(2^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 -0x1.ffcp-1; | ||
| } | ||
| } | ||
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| // When |x| <= 2^(-3). | ||
| if (x_abs <= 0x3000U) { | ||
| if (auto r = EXP2M1F16_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((2^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]); | ||
| // > x * P; | ||
| return fputil::cast<float16>( | ||
| xf * fputil::polyeval(xf, 0x1.62e43p-1f, 0x1.ebfbdep-3f, | ||
| 0x1.c6af88p-5f, 0x1.3b45d6p-7f, | ||
| 0x1.641e7cp-10f)); | ||
| } | ||
| } | ||
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| if (auto r = EXP2M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
| return r.value(); | ||
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| // exp2(x) = exp2(hi + mid) * exp2(lo) | ||
| auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x); | ||
| // exp2m1(x) = exp2(hi + mid) * exp2(lo) - 1 | ||
| return fputil::cast<float16>( | ||
| fputil::multiply_add(exp2_hi_mid, exp2_lo, -1.0f)); | ||
| } | ||
|
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| } // namespace LIBC_NAMESPACE_DECL |
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