1 //===-- Single-precision 10^x 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 #ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H 10 #define LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H 11 12 #include "explogxf.h" 13 #include "src/__support/FPUtil/BasicOperations.h" 14 #include "src/__support/FPUtil/FEnvImpl.h" 15 #include "src/__support/FPUtil/FPBits.h" 16 #include "src/__support/FPUtil/PolyEval.h" 17 #include "src/__support/FPUtil/multiply_add.h" 18 #include "src/__support/FPUtil/nearest_integer.h" 19 #include "src/__support/FPUtil/rounding_mode.h" 20 #include "src/__support/common.h" 21 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 22 #include "src/math/exp10f.h" 23 24 #include <errno.h> 25 26 namespace LIBC_NAMESPACE::generic { 27 28 LIBC_INLINE float exp10f(float x) { 29 using FPBits = typename fputil::FPBits<float>; 30 FPBits xbits(x); 31 32 uint32_t x_u = xbits.uintval(); 33 uint32_t x_abs = x_u & 0x7fff'ffffU; 34 35 // When |x| >= log10(2^128), or x is nan 36 if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) { 37 // When x < log10(2^-150) or nan 38 if (x_u > 0xc234'9e35U) { 39 // exp(-Inf) = 0 40 if (xbits.is_inf()) 41 return 0.0f; 42 // exp(nan) = nan 43 if (xbits.is_nan()) 44 return x; 45 if (fputil::fenv_is_round_up()) 46 return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL)); 47 fputil::set_errno_if_required(ERANGE); 48 fputil::raise_except_if_required(FE_UNDERFLOW); 49 return 0.0f; 50 } 51 // x >= log10(2^128) or nan 52 if (!xbits.get_sign() && (x_u >= 0x421a'209bU)) { 53 // x is finite 54 if (x_u < 0x7f80'0000U) { 55 int rounding = fputil::quick_get_round(); 56 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) 57 return static_cast<float>(FPBits(FPBits::MAX_NORMAL)); 58 59 fputil::set_errno_if_required(ERANGE); 60 fputil::raise_except_if_required(FE_OVERFLOW); 61 } 62 // x is +inf or nan 63 return x + static_cast<float>(FPBits::inf()); 64 } 65 } 66 67 // When |x| <= log10(2)*2^-6 68 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) { 69 if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f 70 if (fputil::fenv_is_round_to_nearest()) 71 return 0x1.fffffep-1f; 72 } 73 // |x| < 2^-25 74 // 10^x ~ 1 + log(10) * x 75 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) { 76 return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f); 77 } 78 79 return static_cast<float>(Exp10Base::powb_lo(x)); 80 } 81 82 // Exceptional value. 83 if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f 84 if (fputil::fenv_is_round_up()) 85 return 0x1.1657c4p+0f; 86 } 87 88 // Exact outputs when x = 1, 2, ..., 10. 89 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f) 90 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) { 91 switch (x_u) { 92 case 0x3f800000U: // x = 1.0f 93 return 10.0f; 94 case 0x40000000U: // x = 2.0f 95 return 100.0f; 96 case 0x40400000U: // x = 3.0f 97 return 1'000.0f; 98 case 0x40800000U: // x = 4.0f 99 return 10'000.0f; 100 case 0x40a00000U: // x = 5.0f 101 return 100'000.0f; 102 case 0x40c00000U: // x = 6.0f 103 return 1'000'000.0f; 104 case 0x40e00000U: // x = 7.0f 105 return 10'000'000.0f; 106 case 0x41000000U: // x = 8.0f 107 return 100'000'000.0f; 108 case 0x41100000U: // x = 9.0f 109 return 1'000'000'000.0f; 110 case 0x41200000U: // x = 10.0f 111 return 10'000'000'000.0f; 112 } 113 } 114 115 // Range reduction: 10^x = 2^(mid + hi) * 10^lo 116 // rr = (2^(mid + hi), lo) 117 auto rr = exp_b_range_reduc<Exp10Base>(x); 118 119 // The low part is approximated by a degree-5 minimax polynomial. 120 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5 121 using fputil::multiply_add; 122 double lo2 = rr.lo * rr.lo; 123 // c0 = 1 + COEFFS[0] * lo 124 double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0); 125 // c1 = COEFFS[1] + COEFFS[2] * lo 126 double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]); 127 // c2 = COEFFS[3] + COEFFS[4] * lo 128 double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]); 129 // p = c1 + c2 * lo^2 130 // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3 131 double p = multiply_add(lo2, c2, c1); 132 // 10^lo ~ c0 + p * lo^2 133 // 10^x = 2^(mid + hi) * 10^lo 134 // ~ mh * (c0 + p * lo^2) 135 // = (mh * c0) + p * (mh * lo^2) 136 return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh)); 137 } 138 139 } // namespace LIBC_NAMESPACE::generic 140 141 #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H 142