1 //===-- Implementation header for expf --------------------------*- C++ -*-===// 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___SUPPORT_MATH_EXPF_H 10 #define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H 11 12 #include "exp_float_constants.h" // Lookup tables EXP_M1 and EXP_M2. 13 #include "src/__support/FPUtil/FEnvImpl.h" 14 #include "src/__support/FPUtil/FPBits.h" 15 #include "src/__support/FPUtil/PolyEval.h" 16 #include "src/__support/FPUtil/multiply_add.h" 17 #include "src/__support/FPUtil/nearest_integer.h" 18 #include "src/__support/FPUtil/rounding_mode.h" 19 #include "src/__support/common.h" 20 #include "src/__support/macros/config.h" 21 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 22 23 namespace LIBC_NAMESPACE_DECL { 24 25 namespace math { 26 27 static constexpr float expf(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 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS 35 // Exceptional values 36 if (LIBC_UNLIKELY(x_u == 0xc236'bd8cU)) { // x = -0x1.6d7b18p+5f 37 return 0x1.108a58p-66f - x * 0x1.0p-95f; 38 } 39 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 40 41 // When |x| >= 89, |x| < 2^-25, or x is nan 42 if (LIBC_UNLIKELY(x_abs >= 0x42b2'0000U || x_abs <= 0x3280'0000U)) { 43 // |x| < 2^-25 44 if (xbits.get_biased_exponent() <= 101) { 45 return 1.0f + x; 46 } 47 48 // When x < log(2^-150) or nan 49 if (xbits.uintval() >= 0xc2cf'f1b5U) { 50 // exp(-Inf) = 0 51 if (xbits.is_inf()) 52 return 0.0f; 53 // exp(nan) = nan 54 if (xbits.is_nan()) 55 return x; 56 if (fputil::fenv_is_round_up()) 57 return FPBits::min_subnormal().get_val(); 58 fputil::set_errno_if_required(ERANGE); 59 fputil::raise_except_if_required(FE_UNDERFLOW); 60 return 0.0f; 61 } 62 // x >= 89 or nan 63 if (xbits.is_pos() && (xbits.uintval() >= 0x42b2'0000)) { 64 // x is finite 65 if (xbits.uintval() < 0x7f80'0000U) { 66 int rounding = fputil::quick_get_round(); 67 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) 68 return FPBits::max_normal().get_val(); 69 70 fputil::set_errno_if_required(ERANGE); 71 fputil::raise_except_if_required(FE_OVERFLOW); 72 } 73 // x is +inf or nan 74 return x + FPBits::inf().get_val(); 75 } 76 } 77 // For -104 < x < 89, to compute exp(x), we perform the following range 78 // reduction: find hi, mid, lo such that: 79 // x = hi + mid + lo, in which 80 // hi is an integer, 81 // mid * 2^7 is an integer 82 // -2^(-8) <= lo < 2^-8. 83 // In particular, 84 // hi + mid = round(x * 2^7) * 2^(-7). 85 // Then, 86 // exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo). 87 // We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2 88 // respectively. exp(lo) is computed using a degree-4 minimax polynomial 89 // generated by Sollya. 90 91 // x_hi = (hi + mid) * 2^7 = round(x * 2^7). 92 float kf = fputil::nearest_integer(x * 0x1.0p7f); 93 // Subtract (hi + mid) from x to get lo. 94 double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x)); 95 int x_hi = static_cast<int>(kf); 96 x_hi += 104 << 7; 97 // hi = x_hi >> 7 98 double exp_hi = EXP_M1[x_hi >> 7]; 99 // mid * 2^7 = x_hi & 0x0000'007fU; 100 double exp_mid = EXP_M2[x_hi & 0x7f]; 101 // Degree-4 minimax polynomial generated by Sollya with the following 102 // commands: 103 // > display = hexadecimal; 104 // > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]); 105 // > Q; 106 double exp_lo = 107 fputil::polyeval(xd, 0x1p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1, 108 0x1.555566668e5e7p-3, 0x1.55555555ef243p-5); 109 return static_cast<float>(exp_hi * exp_mid * exp_lo); 110 } 111 112 } // namespace math 113 114 } // namespace LIBC_NAMESPACE_DECL 115 116 #endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H 117