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| 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 |
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