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