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-rw-r--r--libc/src/math/generic/exp2f_impl.h167
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diff --git a/libc/src/math/generic/exp2f_impl.h b/libc/src/math/generic/exp2f_impl.h
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-//===-- Single-precision 2^x function -------------------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
-
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
-#include "src/__support/FPUtil/rounding_mode.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-#include "src/__support/macros/properties/cpu_features.h"
-#include "src/__support/math/exp10f_utils.h"
-
-namespace LIBC_NAMESPACE_DECL {
-namespace generic {
-
-LIBC_INLINE float exp2f(float x) {
- using FPBits = typename fputil::FPBits<float>;
- FPBits xbits(x);
-
- uint32_t x_u = xbits.uintval();
- uint32_t x_abs = x_u & 0x7fff'ffffU;
-
- // When |x| >= 128, or x is nan, or |x| <= 2^-5
- if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
- // |x| <= 2^-5
- if (x_abs <= 0x3d00'0000) {
- // |x| < 2^-25
- if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
- return 1.0f + x;
- }
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- constexpr uint32_t EXVAL1 = 0x3b42'9d37U;
- constexpr uint32_t EXVAL2 = 0xbcf3'a937U;
- constexpr uint32_t EXVAL_MASK = EXVAL1 & EXVAL2;
-
- // Check exceptional values.
- if (LIBC_UNLIKELY((x_u & EXVAL_MASK) == EXVAL_MASK)) {
- if (LIBC_UNLIKELY(x_u == EXVAL1)) { // x = 0x1.853a6ep-9f
- return fputil::round_result_slightly_down(0x1.00870ap+0f);
- } else if (LIBC_UNLIKELY(x_u == EXVAL2)) { // x = -0x1.e7526ep-6f
- return fputil::round_result_slightly_down(0x1.f58d62p-1f);
- }
- }
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- // Minimax polynomial generated by Sollya with:
- // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
- constexpr double COEFFS[] = {
- 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
- 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
- double xd = static_cast<double>(x);
- double xsq = xd * xd;
- double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
- double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
- double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
- double p = fputil::polyeval(xsq, c0, c1, c2);
- double r = fputil::multiply_add(p, xd, 1.0);
- return static_cast<float>(r);
- }
-
- // x >= 128
- if (xbits.is_pos()) {
- // x is finite
- if (x_u < 0x7f80'0000U) {
- int rounding = fputil::quick_get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return FPBits::max_normal().get_val();
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- }
- // x is +inf or nan
- return x + FPBits::inf().get_val();
- }
- // x <= -150
- if (x_u >= 0xc316'0000U) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0f;
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
- if (fputil::fenv_is_round_up())
- return FPBits::min_subnormal().get_val();
- if (x != 0.0f) {
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- }
- return 0.0f;
- }
- }
-
- // For -150 < x < 128, to compute 2^x, we perform the following range
- // reduction: find hi, mid, lo such that:
- // x = hi + mid + lo, in which
- // hi is an integer,
- // 0 <= mid * 2^5 < 32 is an integer
- // -2^(-6) <= lo <= 2^-6.
- // In particular,
- // hi + mid = round(x * 2^5) * 2^(-5).
- // Then,
- // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
- // 2^mid is stored in the lookup table of 32 elements.
- // 2^lo is computed using a degree-5 minimax polynomial
- // generated by Sollya.
- // We perform 2^hi * 2^mid by simply add hi to the exponent field
- // of 2^mid.
-
- // kf = (hi + mid) * 2^5 = round(x * 2^5)
- float kf;
- int k;
-#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
- kf = fputil::nearest_integer(x * 32.0f);
- k = static_cast<int>(kf);
-#else
- constexpr float HALF[2] = {0.5f, -0.5f};
- k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
- kf = static_cast<float>(k);
-#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
-
- // dx = lo = x - (hi + mid) = x - kf * 2^(-5)
- double dx = fputil::multiply_add(-0x1.0p-5f, kf, x);
-
- // hi = floor(kf * 2^(-4))
- // exp_hi = shift hi to the exponent field of double precision.
- int64_t exp_hi =
- static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
- << fputil::FPBits<double>::FRACTION_LEN);
- // mh = 2^hi * 2^mid
- // mh_bits = bit field of mh
- int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;
- double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
-
- // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
- // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
- constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
- 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
- 0x1.5d88091198529p-10};
- double dx_sq = dx * dx;
- double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0);
- double c2 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
- double c3 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
- double p = fputil::multiply_add(dx_sq, c3, c2);
- // 2^x = 2^(hi + mid + lo)
- // = 2^(hi + mid) * 2^lo
- // ~ mh * (1 + lo * P(lo))
- // = mh + (mh*lo) * P(lo)
- return static_cast<float>(fputil::multiply_add(p, dx_sq * mh, c1 * mh));
-}
-
-} // namespace generic
-} // namespace LIBC_NAMESPACE_DECL
-
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
generated by cgit v1.1 at 2025-10-07 15:56:08 +0000