109 lines
3.7 KiB
C++
109 lines
3.7 KiB
C++
//===-- Single-precision e^x function -------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#include "src/math/expf.h"
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#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
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#include "src/__support/FPUtil/BasicOperations.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/nearest_integer.h"
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#include "src/__support/FPUtil/rounding_mode.h"
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#include "src/__support/common.h"
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#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
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#include <errno.h>
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namespace LIBC_NAMESPACE {
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LLVM_LIBC_FUNCTION(float, expf, (float x)) {
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using FPBits = typename fputil::FPBits<float>;
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FPBits xbits(x);
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uint32_t x_u = xbits.uintval();
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uint32_t x_abs = x_u & 0x7fff'ffffU;
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// Exceptional values
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if (LIBC_UNLIKELY(x_u == 0xc236'bd8cU)) { // x = -0x1.6d7b18p+5f
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return 0x1.108a58p-66f - x * 0x1.0p-95f;
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}
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// When |x| >= 89, |x| < 2^-25, or x is nan
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if (LIBC_UNLIKELY(x_abs >= 0x42b2'0000U || x_abs <= 0x3280'0000U)) {
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// |x| < 2^-25
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if (xbits.get_biased_exponent() <= 101) {
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return 1.0f + x;
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}
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// When x < log(2^-150) or nan
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if (xbits.uintval() >= 0xc2cf'f1b5U) {
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// exp(-Inf) = 0
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if (xbits.is_inf())
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return 0.0f;
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// exp(nan) = nan
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if (xbits.is_nan())
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return x;
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if (fputil::fenv_is_round_up())
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return FPBits::min_denormal();
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_UNDERFLOW);
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return 0.0f;
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}
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// x >= 89 or nan
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if (xbits.is_pos() && (xbits.uintval() >= 0x42b2'0000)) {
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// x is finite
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if (xbits.uintval() < 0x7f80'0000U) {
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int rounding = fputil::quick_get_round();
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if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
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return FPBits::max_normal();
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_OVERFLOW);
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}
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// x is +inf or nan
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return x + static_cast<float>(FPBits::inf());
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}
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}
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// For -104 < x < 89, to compute exp(x), we perform the following range
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// reduction: find hi, mid, lo such that:
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// x = hi + mid + lo, in which
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// hi is an integer,
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// mid * 2^7 is an integer
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// -2^(-8) <= lo < 2^-8.
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// In particular,
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// hi + mid = round(x * 2^7) * 2^(-7).
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// Then,
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// exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
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// We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
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// respectively. exp(lo) is computed using a degree-4 minimax polynomial
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// generated by Sollya.
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// x_hi = (hi + mid) * 2^7 = round(x * 2^7).
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float kf = fputil::nearest_integer(x * 0x1.0p7f);
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// Subtract (hi + mid) from x to get lo.
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double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x));
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int x_hi = static_cast<int>(kf);
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x_hi += 104 << 7;
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// hi = x_hi >> 7
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double exp_hi = EXP_M1[x_hi >> 7];
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// mid * 2^7 = x_hi & 0x0000'007fU;
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double exp_mid = EXP_M2[x_hi & 0x7f];
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// Degree-4 minimax polynomial generated by Sollya with the following
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// commands:
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// > display = hexadecimal;
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// > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);
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// > Q;
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double exp_lo =
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fputil::polyeval(xd, 0x1p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1,
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0x1.555566668e5e7p-3, 0x1.55555555ef243p-5);
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return static_cast<float>(exp_hi * exp_mid * exp_lo);
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}
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} // namespace LIBC_NAMESPACE
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