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/config.h" 22 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 23 24 #include <errno.h> 25 26 namespace LIBC_NAMESPACE_DECL { 27 namespace generic { 28 29 LIBC_INLINE float exp10f(float x) { 30 using FPBits = typename fputil::FPBits<float>; 31 FPBits xbits(x); 32 33 uint32_t x_u = xbits.uintval(); 34 uint32_t x_abs = x_u & 0x7fff'ffffU; 35 36 // When |x| >= log10(2^128), or x is nan 37 if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) { 38 // When x < log10(2^-150) or nan 39 if (x_u > 0xc234'9e35U) { 40 // exp(-Inf) = 0 41 if (xbits.is_inf()) 42 return 0.0f; 43 // exp(nan) = nan 44 if (xbits.is_nan()) 45 return x; 46 if (fputil::fenv_is_round_up()) 47 return FPBits::min_subnormal().get_val(); 48 fputil::set_errno_if_required(ERANGE); 49 fputil::raise_except_if_required(FE_UNDERFLOW); 50 return 0.0f; 51 } 52 // x >= log10(2^128) or nan 53 if (xbits.is_pos() && (x_u >= 0x421a'209bU)) { 54 // x is finite 55 if (x_u < 0x7f80'0000U) { 56 int rounding = fputil::quick_get_round(); 57 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) 58 return FPBits::max_normal().get_val(); 59 60 fputil::set_errno_if_required(ERANGE); 61 fputil::raise_except_if_required(FE_OVERFLOW); 62 } 63 // x is +inf or nan 64 return x + FPBits::inf().get_val(); 65 } 66 } 67 68 // When |x| <= log10(2)*2^-6 69 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) { 70 if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f 71 if (fputil::fenv_is_round_to_nearest()) 72 return 0x1.fffffep-1f; 73 } 74 // |x| < 2^-25 75 // 10^x ~ 1 + log(10) * x 76 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) { 77 return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f); 78 } 79 80 return static_cast<float>(Exp10Base::powb_lo(x)); 81 } 82 83 // Exceptional value. 84 if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f 85 if (fputil::fenv_is_round_up()) 86 return 0x1.1657c4p+0f; 87 } 88 89 // Exact outputs when x = 1, 2, ..., 10. 90 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f) 91 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) { 92 switch (x_u) { 93 case 0x3f800000U: // x = 1.0f 94 return 10.0f; 95 case 0x40000000U: // x = 2.0f 96 return 100.0f; 97 case 0x40400000U: // x = 3.0f 98 return 1'000.0f; 99 case 0x40800000U: // x = 4.0f 100 return 10'000.0f; 101 case 0x40a00000U: // x = 5.0f 102 return 100'000.0f; 103 case 0x40c00000U: // x = 6.0f 104 return 1'000'000.0f; 105 case 0x40e00000U: // x = 7.0f 106 return 10'000'000.0f; 107 case 0x41000000U: // x = 8.0f 108 return 100'000'000.0f; 109 case 0x41100000U: // x = 9.0f 110 return 1'000'000'000.0f; 111 case 0x41200000U: // x = 10.0f 112 return 10'000'000'000.0f; 113 } 114 } 115 116 // Range reduction: 10^x = 2^(mid + hi) * 10^lo 117 // rr = (2^(mid + hi), lo) 118 auto rr = exp_b_range_reduc<Exp10Base>(x); 119 120 // The low part is approximated by a degree-5 minimax polynomial. 121 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5 122 using fputil::multiply_add; 123 double lo2 = rr.lo * rr.lo; 124 // c0 = 1 + COEFFS[0] * lo 125 double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0); 126 // c1 = COEFFS[1] + COEFFS[2] * lo 127 double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]); 128 // c2 = COEFFS[3] + COEFFS[4] * lo 129 double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]); 130 // p = c1 + c2 * lo^2 131 // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3 132 double p = multiply_add(lo2, c2, c1); 133 // 10^lo ~ c0 + p * lo^2 134 // 10^x = 2^(mid + hi) * 10^lo 135 // ~ mh * (c0 + p * lo^2) 136 // = (mh * c0) + p * (mh * lo^2) 137 return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh)); 138 } 139 140 } // namespace generic 141 } // namespace LIBC_NAMESPACE_DECL 142 143 #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H 144