1*71db0c75SAndroid Build Coastguard Worker //===-- Half-precision 10^x function --------------------------------------===// 2*71db0c75SAndroid Build Coastguard Worker // 3*71db0c75SAndroid Build Coastguard Worker // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4*71db0c75SAndroid Build Coastguard Worker // See https://llvm.org/LICENSE.txt for license information. 5*71db0c75SAndroid Build Coastguard Worker // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6*71db0c75SAndroid Build Coastguard Worker // 7*71db0c75SAndroid Build Coastguard Worker //===----------------------------------------------------------------------===// 8*71db0c75SAndroid Build Coastguard Worker 9*71db0c75SAndroid Build Coastguard Worker #include "src/math/exp10f16.h" 10*71db0c75SAndroid Build Coastguard Worker #include "expxf16.h" 11*71db0c75SAndroid Build Coastguard Worker #include "hdr/errno_macros.h" 12*71db0c75SAndroid Build Coastguard Worker #include "hdr/fenv_macros.h" 13*71db0c75SAndroid Build Coastguard Worker #include "src/__support/CPP/array.h" 14*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/FEnvImpl.h" 15*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/FPBits.h" 16*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/PolyEval.h" 17*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/cast.h" 18*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/except_value_utils.h" 19*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/multiply_add.h" 20*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/nearest_integer.h" 21*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/rounding_mode.h" 22*71db0c75SAndroid Build Coastguard Worker #include "src/__support/common.h" 23*71db0c75SAndroid Build Coastguard Worker #include "src/__support/macros/config.h" 24*71db0c75SAndroid Build Coastguard Worker #include "src/__support/macros/optimization.h" 25*71db0c75SAndroid Build Coastguard Worker #include "src/__support/macros/properties/cpu_features.h" 26*71db0c75SAndroid Build Coastguard Worker 27*71db0c75SAndroid Build Coastguard Worker namespace LIBC_NAMESPACE_DECL { 28*71db0c75SAndroid Build Coastguard Worker 29*71db0c75SAndroid Build Coastguard Worker #ifdef LIBC_TARGET_CPU_HAS_FMA 30*71db0c75SAndroid Build Coastguard Worker static constexpr size_t N_EXP10F16_EXCEPTS = 5; 31*71db0c75SAndroid Build Coastguard Worker #else 32*71db0c75SAndroid Build Coastguard Worker static constexpr size_t N_EXP10F16_EXCEPTS = 8; 33*71db0c75SAndroid Build Coastguard Worker #endif 34*71db0c75SAndroid Build Coastguard Worker 35*71db0c75SAndroid Build Coastguard Worker static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS> 36*71db0c75SAndroid Build Coastguard Worker EXP10F16_EXCEPTS = {{ 37*71db0c75SAndroid Build Coastguard Worker // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ) 38*71db0c75SAndroid Build Coastguard Worker {0x363dU, 0x40e8U, 1U, 0U, 1U}, 39*71db0c75SAndroid Build Coastguard Worker // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ) 40*71db0c75SAndroid Build Coastguard Worker {0x3657U, 0x40fbU, 1U, 0U, 0U}, 41*71db0c75SAndroid Build Coastguard Worker // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ) 42*71db0c75SAndroid Build Coastguard Worker {0xac06U, 0x3aecU, 1U, 0U, 0U}, 43*71db0c75SAndroid Build Coastguard Worker // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ) 44*71db0c75SAndroid Build Coastguard Worker {0xbf0aU, 0x2473U, 1U, 0U, 0U}, 45*71db0c75SAndroid Build Coastguard Worker // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ) 46*71db0c75SAndroid Build Coastguard Worker {0xc387U, 0x09a5U, 1U, 0U, 0U}, 47*71db0c75SAndroid Build Coastguard Worker #ifndef LIBC_TARGET_CPU_HAS_FMA 48*71db0c75SAndroid Build Coastguard Worker // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ) 49*71db0c75SAndroid Build Coastguard Worker {0x4030U, 0x57c1U, 1U, 0U, 1U}, 50*71db0c75SAndroid Build Coastguard Worker // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ) 51*71db0c75SAndroid Build Coastguard Worker {0x406eU, 0x591fU, 1U, 0U, 1U}, 52*71db0c75SAndroid Build Coastguard Worker // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ) 53*71db0c75SAndroid Build Coastguard Worker {0x446eU, 0x7690U, 1U, 0U, 1U}, 54*71db0c75SAndroid Build Coastguard Worker #endif 55*71db0c75SAndroid Build Coastguard Worker }}; 56*71db0c75SAndroid Build Coastguard Worker 57*71db0c75SAndroid Build Coastguard Worker LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) { 58*71db0c75SAndroid Build Coastguard Worker using FPBits = fputil::FPBits<float16>; 59*71db0c75SAndroid Build Coastguard Worker FPBits x_bits(x); 60*71db0c75SAndroid Build Coastguard Worker 61*71db0c75SAndroid Build Coastguard Worker uint16_t x_u = x_bits.uintval(); 62*71db0c75SAndroid Build Coastguard Worker uint16_t x_abs = x_u & 0x7fffU; 63*71db0c75SAndroid Build Coastguard Worker 64*71db0c75SAndroid Build Coastguard Worker // When |x| >= 5, or x is NaN. 65*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_abs >= 0x4500U)) { 66*71db0c75SAndroid Build Coastguard Worker // exp10(NaN) = NaN 67*71db0c75SAndroid Build Coastguard Worker if (x_bits.is_nan()) { 68*71db0c75SAndroid Build Coastguard Worker if (x_bits.is_signaling_nan()) { 69*71db0c75SAndroid Build Coastguard Worker fputil::raise_except_if_required(FE_INVALID); 70*71db0c75SAndroid Build Coastguard Worker return FPBits::quiet_nan().get_val(); 71*71db0c75SAndroid Build Coastguard Worker } 72*71db0c75SAndroid Build Coastguard Worker 73*71db0c75SAndroid Build Coastguard Worker return x; 74*71db0c75SAndroid Build Coastguard Worker } 75*71db0c75SAndroid Build Coastguard Worker 76*71db0c75SAndroid Build Coastguard Worker // When x >= 5. 77*71db0c75SAndroid Build Coastguard Worker if (x_bits.is_pos()) { 78*71db0c75SAndroid Build Coastguard Worker // exp10(+inf) = +inf 79*71db0c75SAndroid Build Coastguard Worker if (x_bits.is_inf()) 80*71db0c75SAndroid Build Coastguard Worker return FPBits::inf().get_val(); 81*71db0c75SAndroid Build Coastguard Worker 82*71db0c75SAndroid Build Coastguard Worker switch (fputil::quick_get_round()) { 83*71db0c75SAndroid Build Coastguard Worker case FE_TONEAREST: 84*71db0c75SAndroid Build Coastguard Worker case FE_UPWARD: 85*71db0c75SAndroid Build Coastguard Worker fputil::set_errno_if_required(ERANGE); 86*71db0c75SAndroid Build Coastguard Worker fputil::raise_except_if_required(FE_OVERFLOW); 87*71db0c75SAndroid Build Coastguard Worker return FPBits::inf().get_val(); 88*71db0c75SAndroid Build Coastguard Worker default: 89*71db0c75SAndroid Build Coastguard Worker return FPBits::max_normal().get_val(); 90*71db0c75SAndroid Build Coastguard Worker } 91*71db0c75SAndroid Build Coastguard Worker } 92*71db0c75SAndroid Build Coastguard Worker 93*71db0c75SAndroid Build Coastguard Worker // When x <= -8. 94*71db0c75SAndroid Build Coastguard Worker if (x_u >= 0xc800U) { 95*71db0c75SAndroid Build Coastguard Worker // exp10(-inf) = +0 96*71db0c75SAndroid Build Coastguard Worker if (x_bits.is_inf()) 97*71db0c75SAndroid Build Coastguard Worker return FPBits::zero().get_val(); 98*71db0c75SAndroid Build Coastguard Worker 99*71db0c75SAndroid Build Coastguard Worker fputil::set_errno_if_required(ERANGE); 100*71db0c75SAndroid Build Coastguard Worker fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); 101*71db0c75SAndroid Build Coastguard Worker 102*71db0c75SAndroid Build Coastguard Worker if (fputil::fenv_is_round_up()) 103*71db0c75SAndroid Build Coastguard Worker return FPBits::min_subnormal().get_val(); 104*71db0c75SAndroid Build Coastguard Worker return FPBits::zero().get_val(); 105*71db0c75SAndroid Build Coastguard Worker } 106*71db0c75SAndroid Build Coastguard Worker } 107*71db0c75SAndroid Build Coastguard Worker 108*71db0c75SAndroid Build Coastguard Worker // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results. 109*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) { 110*71db0c75SAndroid Build Coastguard Worker switch (x_u) { 111*71db0c75SAndroid Build Coastguard Worker case 0x3c00U: // x = 1.0f16 112*71db0c75SAndroid Build Coastguard Worker return fputil::cast<float16>(10.0); 113*71db0c75SAndroid Build Coastguard Worker case 0x4000U: // x = 2.0f16 114*71db0c75SAndroid Build Coastguard Worker return fputil::cast<float16>(100.0); 115*71db0c75SAndroid Build Coastguard Worker case 0x4200U: // x = 3.0f16 116*71db0c75SAndroid Build Coastguard Worker return fputil::cast<float16>(1'000.0); 117*71db0c75SAndroid Build Coastguard Worker case 0x4400U: // x = 4.0f16 118*71db0c75SAndroid Build Coastguard Worker return fputil::cast<float16>(10'000.0); 119*71db0c75SAndroid Build Coastguard Worker } 120*71db0c75SAndroid Build Coastguard Worker } 121*71db0c75SAndroid Build Coastguard Worker 122*71db0c75SAndroid Build Coastguard Worker if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 123*71db0c75SAndroid Build Coastguard Worker return r.value(); 124*71db0c75SAndroid Build Coastguard Worker 125*71db0c75SAndroid Build Coastguard Worker // 10^x = 2^((hi + mid) * log2(10)) * 10^lo 126*71db0c75SAndroid Build Coastguard Worker auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x); 127*71db0c75SAndroid Build Coastguard Worker return fputil::cast<float16>(exp2_hi_mid * exp10_lo); 128*71db0c75SAndroid Build Coastguard Worker } 129*71db0c75SAndroid Build Coastguard Worker 130*71db0c75SAndroid Build Coastguard Worker } // namespace LIBC_NAMESPACE_DECL 131