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