//===-- 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 // //===----------------------------------------------------------------------===// #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" namespace LIBC_NAMESPACE_DECL { #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS static constexpr fputil::ExceptValues 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}, }}; #ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 6; #else static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 7; #endif static constexpr fputil::ExceptValues 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_FLOAT // 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_FLOAT // 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_FLOAT // x = -0x1.a34p-1, exp2m1f16(x) = -0x1.bb4p-2 (RZ) {0xba8dU, 0xb6edU, 0U, 1U, 1U}, #endif }}; #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS LLVM_LIBC_FUNCTION(float16, exp2m1f16, (float16 x)) { using FPBits = fputil::FPBits; FPBits x_bits(x); uint16_t x_u = x_bits.uintval(); uint16_t x_abs = x_u & 0x7fffU; // 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(); } return x; } // When x >= 16. if (x_u >= 0x4c00 && x_bits.is_pos()) { // exp2m1(+inf) = +inf if (x_bits.is_inf()) return FPBits::inf().get_val(); 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(); } } // When x < -11. if (x_u > 0xc980U) { // exp2m1(-inf) = -1 if (x_bits.is_inf()) return FPBits::one(Sign::NEG).get_val(); // 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(-0x1.ffcp-1)); // 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 fputil::cast(-0x1.ffcp-1); } } // When |x| <= 2^(-3). if (x_abs <= 0x3000U) { #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS if (auto r = EXP2M1F16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) return r.value(); #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 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( xf * fputil::polyeval(xf, 0x1.62e43p-1f, 0x1.ebfbdep-3f, 0x1.c6af88p-5f, 0x1.3b45d6p-7f, 0x1.641e7cp-10f)); } } #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS if (auto r = EXP2M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) return r.value(); #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS // 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( fputil::multiply_add(exp2_hi_mid, exp2_lo, -1.0f)); } } // namespace LIBC_NAMESPACE_DECL