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| 1 | +//===-- Half-precision 10^x - 1 function ----------------------------------===// |
| 2 | +// |
| 3 | +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| 4 | +// See https://llvm.org/LICENSE.txt for license information. |
| 5 | +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| 6 | +// |
| 7 | +//===----------------------------------------------------------------------===// |
| 8 | + |
| 9 | +#include "src/math/exp10m1f16.h" |
| 10 | +#include "expxf16.h" |
| 11 | +#include "hdr/errno_macros.h" |
| 12 | +#include "hdr/fenv_macros.h" |
| 13 | +#include "src/__support/FPUtil/FEnvImpl.h" |
| 14 | +#include "src/__support/FPUtil/FPBits.h" |
| 15 | +#include "src/__support/FPUtil/PolyEval.h" |
| 16 | +#include "src/__support/FPUtil/cast.h" |
| 17 | +#include "src/__support/FPUtil/except_value_utils.h" |
| 18 | +#include "src/__support/FPUtil/multiply_add.h" |
| 19 | +#include "src/__support/FPUtil/rounding_mode.h" |
| 20 | +#include "src/__support/common.h" |
| 21 | +#include "src/__support/macros/config.h" |
| 22 | +#include "src/__support/macros/optimization.h" |
| 23 | +#include "src/__support/macros/properties/cpu_features.h" |
| 24 | + |
| 25 | +namespace LIBC_NAMESPACE_DECL { |
| 26 | + |
| 27 | +static constexpr fputil::ExceptValues<float16, 3> EXP10M1F16_EXCEPTS_LO = {{ |
| 28 | + // (input, RZ output, RU offset, RD offset, RN offset) |
| 29 | + // x = 0x1.5c4p-4, exp10m1f16(x) = 0x1.bacp-3 (RZ) |
| 30 | + {0x2d71U, 0x32ebU, 1U, 0U, 0U}, |
| 31 | + // x = -0x1.5ep-13, exp10m1f16(x) = -0x1.92cp-12 (RZ) |
| 32 | + {0x8978U, 0x8e4bU, 0U, 1U, 0U}, |
| 33 | + // x = -0x1.e2p-10, exp10m1f16(x) = -0x1.14cp-8 (RZ) |
| 34 | + {0x9788U, 0x9c53U, 0U, 1U, 0U}, |
| 35 | +}}; |
| 36 | + |
| 37 | +#ifdef LIBC_TARGET_CPU_HAS_FMA |
| 38 | +static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 3; |
| 39 | +#else |
| 40 | +static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 6; |
| 41 | +#endif |
| 42 | + |
| 43 | +static constexpr fputil::ExceptValues<float16, N_EXP10M1F16_EXCEPTS_HI> |
| 44 | + EXP10M1F16_EXCEPTS_HI = {{ |
| 45 | + // (input, RZ output, RU offset, RD offset, RN offset) |
| 46 | + // x = 0x1.8f4p-2, exp10m1f16(x) = 0x1.744p+0 (RZ) |
| 47 | + {0x363dU, 0x3dd1U, 1U, 0U, 0U}, |
| 48 | + // x = 0x1.95cp-2, exp10m1f16(x) = 0x1.7d8p+0 (RZ) |
| 49 | + {0x3657U, 0x3df6U, 1U, 0U, 0U}, |
| 50 | + // x = 0x1.d04p-2, exp10m1f16(x) = 0x1.d7p+0 (RZ) |
| 51 | + {0x3741U, 0x3f5cU, 1U, 0U, 1U}, |
| 52 | +#ifndef LIBC_TARGET_CPU_HAS_FMA |
| 53 | + // x = 0x1.0cp+1, exp10m1f16(x) = 0x1.ec4p+6 (RZ) |
| 54 | + {0x4030U, 0x57b1U, 1U, 0U, 1U}, |
| 55 | + // x = 0x1.1b8p+1, exp10m1f16(x) = 0x1.45cp+7 (RZ) |
| 56 | + {0x406eU, 0x5917U, 1U, 0U, 1U}, |
| 57 | + // x = 0x1.2f4p+2, exp10m1f16(x) = 0x1.ab8p+15 (RZ) |
| 58 | + {0x44bdU, 0x7aaeU, 1U, 0U, 1U}, |
| 59 | +#endif |
| 60 | + }}; |
| 61 | + |
| 62 | +LLVM_LIBC_FUNCTION(float16, exp10m1f16, (float16 x)) { |
| 63 | + using FPBits = fputil::FPBits<float16>; |
| 64 | + FPBits x_bits(x); |
| 65 | + |
| 66 | + uint16_t x_u = x_bits.uintval(); |
| 67 | + uint16_t x_abs = x_u & 0x7fffU; |
| 68 | + |
| 69 | + // When |x| <= 2^(-3), or |x| >= 11 * log10(2), or x is NaN. |
| 70 | + if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x429fU)) { |
| 71 | + // exp10m1(NaN) = NaN |
| 72 | + if (x_bits.is_nan()) { |
| 73 | + if (x_bits.is_signaling_nan()) { |
| 74 | + fputil::raise_except_if_required(FE_INVALID); |
| 75 | + return FPBits::quiet_nan().get_val(); |
| 76 | + } |
| 77 | + |
| 78 | + return x; |
| 79 | + } |
| 80 | + |
| 81 | + // When x >= 16 * log10(2). |
| 82 | + if (x_u >= 0x44d1U && x_bits.is_pos()) { |
| 83 | + // exp10m1(+inf) = +inf |
| 84 | + if (x_bits.is_inf()) |
| 85 | + return FPBits::inf().get_val(); |
| 86 | + |
| 87 | + switch (fputil::quick_get_round()) { |
| 88 | + case FE_TONEAREST: |
| 89 | + case FE_UPWARD: |
| 90 | + fputil::set_errno_if_required(ERANGE); |
| 91 | + fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT); |
| 92 | + return FPBits::inf().get_val(); |
| 93 | + default: |
| 94 | + return FPBits::max_normal().get_val(); |
| 95 | + } |
| 96 | + } |
| 97 | + |
| 98 | + // When x < -11 * log10(2). |
| 99 | + if (x_u > 0xc29fU) { |
| 100 | + // exp10m1(-inf) = -1 |
| 101 | + if (x_bits.is_inf()) |
| 102 | + return FPBits::one(Sign::NEG).get_val(); |
| 103 | + |
| 104 | + // When x >= -0x1.ce4p+1, round(10^x - 1, HP, RN) = -0x1.ffcp-1. |
| 105 | + if (x_u <= 0xc339U) { |
| 106 | + return fputil::round_result_slightly_down( |
| 107 | + fputil::cast<float16>(-0x1.ffcp-1)); |
| 108 | + } |
| 109 | + |
| 110 | + // When x < -0x1.ce4p+1, round(10^x - 1, HP, RN) = -1. |
| 111 | + switch (fputil::quick_get_round()) { |
| 112 | + case FE_TONEAREST: |
| 113 | + case FE_DOWNWARD: |
| 114 | + return FPBits::one(Sign::NEG).get_val(); |
| 115 | + default: |
| 116 | + return fputil::cast<float16>(-0x1.ffcp-1); |
| 117 | + } |
| 118 | + } |
| 119 | + |
| 120 | + // When |x| <= 2^(-3). |
| 121 | + if (x_abs <= 0x3000U) { |
| 122 | + if (auto r = EXP10M1F16_EXCEPTS_LO.lookup(x_u); |
| 123 | + LIBC_UNLIKELY(r.has_value())) |
| 124 | + return r.value(); |
| 125 | + |
| 126 | + float xf = x; |
| 127 | + // Degree-5 minimax polynomial generated by Sollya with the following |
| 128 | + // commands: |
| 129 | + // > display = hexadecimal; |
| 130 | + // > P = fpminimax((10^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]); |
| 131 | + // > x * P; |
| 132 | + return fputil::cast<float16>( |
| 133 | + xf * fputil::polyeval(xf, 0x1.26bb1cp+1f, 0x1.5351c8p+1f, |
| 134 | + 0x1.04704p+1f, 0x1.2ce084p+0f, 0x1.14a6bep-1f)); |
| 135 | + } |
| 136 | + } |
| 137 | + |
| 138 | + // When x is 1, 2, or 3. These are hard-to-round cases with exact results. |
| 139 | + // 10^4 - 1 = 9'999 is not exactly representable as a float16, but luckily the |
| 140 | + // polynomial approximation gives the correct result for x = 4 in all |
| 141 | + // rounding modes. |
| 142 | + if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) { |
| 143 | + switch (x_u) { |
| 144 | + case 0x3c00U: // x = 1.0f16 |
| 145 | + return fputil::cast<float16>(9.0); |
| 146 | + case 0x4000U: // x = 2.0f16 |
| 147 | + return fputil::cast<float16>(99.0); |
| 148 | + case 0x4200U: // x = 3.0f16 |
| 149 | + return fputil::cast<float16>(999.0); |
| 150 | + } |
| 151 | + } |
| 152 | + |
| 153 | + if (auto r = EXP10M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) |
| 154 | + return r.value(); |
| 155 | + |
| 156 | + // exp10(x) = exp2((hi + mid) * log2(10)) * exp10(lo) |
| 157 | + auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x); |
| 158 | + // exp10m1(x) = exp2((hi + mid) * log2(lo)) * exp10(lo) - 1 |
| 159 | + return fputil::cast<float16>( |
| 160 | + fputil::multiply_add(exp2_hi_mid, exp10_lo, -1.0f)); |
| 161 | +} |
| 162 | + |
| 163 | +} // namespace LIBC_NAMESPACE_DECL |
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