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| 1 | +//===-- Implementation of exp10m1f 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 | +#include "src/math/exp10m1f.h" |
| 10 | +#include "src/__support/FPUtil/FEnvImpl.h" |
| 11 | +#include "src/__support/FPUtil/FPBits.h" |
| 12 | +#include "src/__support/FPUtil/PolyEval.h" |
| 13 | +#include "src/__support/FPUtil/except_value_utils.h" |
| 14 | +#include "src/__support/FPUtil/multiply_add.h" |
| 15 | +#include "src/__support/FPUtil/rounding_mode.h" |
| 16 | +#include "src/__support/common.h" |
| 17 | +#include "src/__support/macros/optimization.h" |
| 18 | +#include "src/errno/libc_errno.h" |
| 19 | + |
| 20 | +#include "explogxf.h" |
| 21 | + |
| 22 | +namespace LIBC_NAMESPACE { |
| 23 | + |
| 24 | +static constexpr size_t N_EXCEPTS_LO = 11; |
| 25 | + |
| 26 | +static constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP10M1F_EXCEPTS_LO = |
| 27 | + {{ |
| 28 | + // x = 0x1.0fe54ep-11, exp10m1f(x) = 0x1.3937eep-10 (RZ) |
| 29 | + {0x3a07'f2a7U, 0x3a9c'9bf7U, 1U, 0U, 1U}, |
| 30 | + // x = 0x1.80e6eap-11, exp10m1f(x) = 0x1.bb8272p-10 (RZ) |
| 31 | + {0x3a40'7375U, 0x3add'c139U, 1U, 0U, 1U}, |
| 32 | + // x = -0x1.2a33bcp-51, exp10m1f(x) = -0x1.57515ep-50 (RZ) |
| 33 | + {0xa615'19deU, 0xa6ab'a8afU, 0U, 1U, 0U}, |
| 34 | + // x = -0x0p+0, exp10m1f(x) = -0x0p+0 (RZ) |
| 35 | + {0x8000'0000U, 0x8000'0000U, 0U, 0U, 0U}, |
| 36 | + // x = -0x1.b59e08p-31, exp10m1f(x) = -0x1.f7d356p-30 (RZ) |
| 37 | + {0xb05a'cf04U, 0xb0fb'e9abU, 0U, 1U, 1U}, |
| 38 | + // x = -0x1.bf342p-12, exp10m1f(x) = -0x1.014e02p-10 (RZ) |
| 39 | + {0xb9df'9a10U, 0xba80'a701U, 0U, 1U, 0U}, |
| 40 | + // x = -0x1.6207fp-11, exp10m1f(x) = -0x1.9746cap-10 (RZ) |
| 41 | + {0xba31'03f8U, 0xbacb'a365U, 0U, 1U, 1U}, |
| 42 | + // x = -0x1.bd0c66p-11, exp10m1f(x) = -0x1.ffe168p-10 (RZ) |
| 43 | + {0xba5e'8633U, 0xbaff'f0b4U, 0U, 1U, 1U}, |
| 44 | + // x = -0x1.ffd84cp-10, exp10m1f(x) = -0x1.25faf2p-8 (RZ) |
| 45 | + {0xbaff'ec26U, 0xbb92'fd79U, 0U, 1U, 0U}, |
| 46 | + // x = -0x1.a74172p-9, exp10m1f(x) = -0x1.e57be2p-8 (RZ) |
| 47 | + {0xbb53'a0b9U, 0xbbf2'bdf1U, 0U, 1U, 1U}, |
| 48 | + // x = -0x1.cb694cp-9, exp10m1f(x) = -0x1.0764e4p-7 (RZ) |
| 49 | + {0xbb65'b4a6U, 0xbc03'b272U, 0U, 1U, 0U}, |
| 50 | + }}; |
| 51 | + |
| 52 | +static constexpr size_t N_EXCEPTS_HI = 19; |
| 53 | + |
| 54 | +static constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP10M1F_EXCEPTS_HI = |
| 55 | + {{ |
| 56 | + // (input, RZ output, RU offset, RD offset, RN offset) |
| 57 | + // x = 0x1.8d31eep-8, exp10m1f(x) = 0x1.cc7e4cp-7 (RZ) |
| 58 | + {0x3bc6'98f7U, 0x3c66'3f26U, 1U, 0U, 1U}, |
| 59 | + // x = 0x1.915fcep-8, exp10m1f(x) = 0x1.d15f72p-7 (RZ) |
| 60 | + {0x3bc8'afe7U, 0x3c68'afb9U, 1U, 0U, 0U}, |
| 61 | + // x = 0x1.bcf982p-8, exp10m1f(x) = 0x1.022928p-6 (RZ) |
| 62 | + {0x3bde'7cc1U, 0x3c81'1494U, 1U, 0U, 1U}, |
| 63 | + // x = 0x1.99ff0ap-7, exp10m1f(x) = 0x1.dee416p-6 (RZ) |
| 64 | + {0x3c4c'ff85U, 0x3cef'720bU, 1U, 0U, 0U}, |
| 65 | + // x = 0x1.75ea14p-6, exp10m1f(x) = 0x1.b9ff16p-5 (RZ) |
| 66 | + {0x3cba'f50aU, 0x3d5c'ff8bU, 1U, 0U, 0U}, |
| 67 | + // x = 0x1.f81b64p-6, exp10m1f(x) = 0x1.2cb6bcp-4 (RZ) |
| 68 | + {0x3cfc'0db2U, 0x3d96'5b5eU, 1U, 0U, 0U}, |
| 69 | + // x = 0x1.fafecp+3, exp10m1f(x) = 0x1.8c880ap+52 (RZ) |
| 70 | + {0x417d'7f60U, 0x59c6'4405U, 1U, 0U, 0U}, |
| 71 | + // x = -0x1.3bf094p-8, exp10m1f(x) = -0x1.69ba4ap-7 (RZ) |
| 72 | + {0xbb9d'f84aU, 0xbc34'dd25U, 0U, 1U, 0U}, |
| 73 | + // x = -0x1.4558bcp-8, exp10m1f(x) = -0x1.746fb8p-7 (RZ) |
| 74 | + {0xbba2'ac5eU, 0xbc3a'37dcU, 0U, 1U, 1U}, |
| 75 | + // x = -0x1.4bb43p-8, exp10m1f(x) = -0x1.7babe4p-7 (RZ) |
| 76 | + {0xbba5'da18U, 0xbc3d'd5f2U, 0U, 1U, 1U}, |
| 77 | + // x = -0x1.776cc8p-8, exp10m1f(x) = -0x1.ad62c4p-7 (RZ) |
| 78 | + {0xbbbb'b664U, 0xbc56'b162U, 0U, 1U, 0U}, |
| 79 | + // x = -0x1.f024cp-8, exp10m1f(x) = -0x1.1b20d6p-6 (RZ) |
| 80 | + {0xbbf8'1260U, 0xbc8d'906bU, 0U, 1U, 1U}, |
| 81 | + // x = -0x1.f510eep-8, exp10m1f(x) = -0x1.1de9aap-6 (RZ) |
| 82 | + {0xbbfa'8877U, 0xbc8e'f4d5U, 0U, 1U, 0U}, |
| 83 | + // x = -0x1.0b43c4p-7, exp10m1f(x) = -0x1.30d418p-6 (RZ) |
| 84 | + {0xbc05'a1e2U, 0xbc98'6a0cU, 0U, 1U, 0U}, |
| 85 | + // x = -0x1.245ee4p-7, exp10m1f(x) = -0x1.4d2b86p-6 (RZ) |
| 86 | + {0xbc12'2f72U, 0xbca6'95c3U, 0U, 1U, 0U}, |
| 87 | + // x = -0x1.f9f2dap-7, exp10m1f(x) = -0x1.1e2186p-5 (RZ) |
| 88 | + {0xbc7c'f96dU, 0xbd0f'10c3U, 0U, 1U, 0U}, |
| 89 | + // x = -0x1.08e42p-6, exp10m1f(x) = -0x1.2b5c4p-5 (RZ) |
| 90 | + {0xbc84'7210U, 0xbd15'ae20U, 0U, 1U, 1U}, |
| 91 | + // x = -0x1.0cdc44p-5, exp10m1f(x) = -0x1.2a2152p-4 (RZ) |
| 92 | + {0xbd06'6e22U, 0xbd95'10a9U, 0U, 1U, 1U}, |
| 93 | + // x = -0x1.ca4322p-5, exp10m1f(x) = -0x1.ef073p-4 (RZ) |
| 94 | + {0xbd65'2191U, 0xbdf7'8398U, 0U, 1U, 1U}, |
| 95 | + }}; |
| 96 | + |
| 97 | +LLVM_LIBC_FUNCTION(float, exp10m1f, (float x)) { |
| 98 | + using FPBits = fputil::FPBits<float>; |
| 99 | + FPBits xbits(x); |
| 100 | + |
| 101 | + uint32_t x_u = xbits.uintval(); |
| 102 | + uint32_t x_abs = x_u & 0x7fff'ffffU; |
| 103 | + |
| 104 | + // When x >= log10(2^128), or x is nan |
| 105 | + if (LIBC_UNLIKELY(xbits.is_pos() && x_u >= 0x421a'209bU)) { |
| 106 | + if (xbits.is_finite()) { |
| 107 | + int rounding = fputil::quick_get_round(); |
| 108 | + if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) |
| 109 | + return FPBits::max_normal().get_val(); |
| 110 | + |
| 111 | + fputil::set_errno_if_required(ERANGE); |
| 112 | + fputil::raise_except_if_required(FE_OVERFLOW); |
| 113 | + } |
| 114 | + |
| 115 | + // x >= log10(2^128) and 10^x - 1 rounds to +inf, or x is +inf or nan |
| 116 | + return x + FPBits::inf().get_val(); |
| 117 | + } |
| 118 | + |
| 119 | + // When |x| <= log10(2) * 2^(-6) |
| 120 | + if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) { |
| 121 | + if (auto r = EXP10M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) |
| 122 | + return r.value(); |
| 123 | + |
| 124 | + double dx = x; |
| 125 | + double dx_sq = dx * dx; |
| 126 | + double c0 = dx * Exp10Base::COEFFS[0]; |
| 127 | + double c1 = |
| 128 | + fputil::multiply_add(dx, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]); |
| 129 | + double c2 = |
| 130 | + fputil::multiply_add(dx, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]); |
| 131 | + // 10^dx - 1 ~ (1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5) - 1 |
| 132 | + // = COEFFS[0] * dx + ... + COEFFS[4] * dx^5 |
| 133 | + return static_cast<float>(fputil::polyeval(dx_sq, c0, c1, c2)); |
| 134 | + } |
| 135 | + |
| 136 | + // When x <= log10(2^-25), or x is nan |
| 137 | + if (LIBC_UNLIKELY(x <= -0x1.e1a5e2p+2f)) { |
| 138 | + // exp10m1(-inf) = -1 |
| 139 | + if (xbits.is_inf()) |
| 140 | + return -1.0f; |
| 141 | + // exp10m1(nan) = nan |
| 142 | + if (xbits.is_nan()) |
| 143 | + return x; |
| 144 | + |
| 145 | + int rounding = fputil::quick_get_round(); |
| 146 | + if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO || |
| 147 | + (rounding == FE_TONEAREST && x == -0x1.e1a5e2p+2f)) |
| 148 | + return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f |
| 149 | +
|
| 150 | + fputil::set_errno_if_required(ERANGE); |
| 151 | + fputil::raise_except_if_required(FE_UNDERFLOW); |
| 152 | + return -1.0f; |
| 153 | + } |
| 154 | +
|
| 155 | + // Exact outputs when x = 1, 2, ..., 10. |
| 156 | + // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f) |
| 157 | + if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) { |
| 158 | + switch (x_u) { |
| 159 | + case 0x3f800000U: // x = 1.0f |
| 160 | + return 9.0f; |
| 161 | + case 0x40000000U: // x = 2.0f |
| 162 | + return 99.0f; |
| 163 | + case 0x40400000U: // x = 3.0f |
| 164 | + return 999.0f; |
| 165 | + case 0x40800000U: // x = 4.0f |
| 166 | + return 9'999.0f; |
| 167 | + case 0x40a00000U: // x = 5.0f |
| 168 | + return 99'999.0f; |
| 169 | + case 0x40c00000U: // x = 6.0f |
| 170 | + return 999'999.0f; |
| 171 | + case 0x40e00000U: // x = 7.0f |
| 172 | + return 9'999'999.0f; |
| 173 | + case 0x41000000U: { // x = 8.0f |
| 174 | + int rounding = fputil::quick_get_round(); |
| 175 | + if (rounding == FE_UPWARD || rounding == FE_TONEAREST) |
| 176 | + return 100'000'000.0f; |
| 177 | + return 99'999'992.0f; |
| 178 | + } |
| 179 | + case 0x41100000U: { // x = 9.0f |
| 180 | + int rounding = fputil::quick_get_round(); |
| 181 | + if (rounding == FE_UPWARD || rounding == FE_TONEAREST) |
| 182 | + return 1'000'000'000.0f; |
| 183 | + return 999'999'936.0f; |
| 184 | + } |
| 185 | + case 0x41200000U: { // x = 10.0f |
| 186 | + int rounding = fputil::quick_get_round(); |
| 187 | + if (rounding == FE_UPWARD || rounding == FE_TONEAREST) |
| 188 | + return 10'000'000'000.0f; |
| 189 | + return 9'999'998'976.0f; |
| 190 | + } |
| 191 | + } |
| 192 | + } |
| 193 | + |
| 194 | + if (auto r = EXP10M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) |
| 195 | + return r.value(); |
| 196 | + |
| 197 | + // Range reduction: 10^x = 2^(mid + hi) * 10^lo |
| 198 | + // rr = (2^(mid + hi), lo) |
| 199 | + auto rr = exp_b_range_reduc<Exp10Base>(x); |
| 200 | + |
| 201 | + // The low part is approximated by a degree-5 minimax polynomial. |
| 202 | + // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5 |
| 203 | + double lo_sq = rr.lo * rr.lo; |
| 204 | + double c0 = fputil::multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0); |
| 205 | + double c1 = |
| 206 | + fputil::multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]); |
| 207 | + double c2 = |
| 208 | + fputil::multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]); |
| 209 | + double exp10_lo = fputil::polyeval(lo_sq, c0, c1, c2); |
| 210 | + // 10^x - 1 = 2^(mid + hi) * 10^lo - 1 |
| 211 | + // ~ mh * exp10_lo - 1 |
| 212 | + return static_cast<float>(fputil::multiply_add(exp10_lo, rr.mh, -1.0)); |
| 213 | +} |
| 214 | + |
| 215 | +} // namespace LIBC_NAMESPACE |
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