4e5f8b4d8d
Use expm1f(x) = exp(x) - 1 for |x| > ln(2). For |x| <= ln(2), divide it into 3 subintervals: [-ln2, -1/8], [-1/8, 1/8], [1/8, ln2] and use a degree-6 polynomial approximation generated by Sollya's fpminmax for each interval. Errors < 1.5 ULPs when we use fma to evaluate the polynomials. Differential Revision: https://reviews.llvm.org/D101134
55 lines
1.5 KiB
C++
55 lines
1.5 KiB
C++
//===-- Common header for PolyEval implementations --------------*- C++ -*-===//
|
|
//
|
|
// 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_UTILS_FPUTIL_POLYEVAL_H
|
|
#define LLVM_LIBC_UTILS_FPUTIL_POLYEVAL_H
|
|
|
|
#include "utils/CPP/TypeTraits.h"
|
|
|
|
// Evaluate polynomial using Horner's Scheme:
|
|
// With polyeval(x, a_0, a_1, ..., a_n) = a_n * x^n + ... + a_1 * x + a_0, we
|
|
// evaluated it as: a_0 + x * (a_1 + x * ( ... (a_(n-1) + x * a_n) ... ) ) ).
|
|
// We will use fma instructions if available.
|
|
// Example: to evaluate x^3 + 2*x^2 + 3*x + 4, call
|
|
// polyeval( x, 4.0, 3.0, 2.0, 1.0 )
|
|
|
|
#if defined(__x86_64__) || defined(__aarch64__)
|
|
#include "FMA.h"
|
|
|
|
namespace __llvm_libc {
|
|
namespace fputil {
|
|
|
|
template <typename T> static inline T polyeval(T x, T a0) { return a0; }
|
|
|
|
template <typename T, typename... Ts>
|
|
static inline T polyeval(T x, T a0, Ts... a) {
|
|
return fma(x, polyeval(x, a...), a0);
|
|
}
|
|
|
|
} // namespace fputil
|
|
} // namespace __llvm_libc
|
|
|
|
#else
|
|
|
|
namespace __llvm_libc {
|
|
namespace fputil {
|
|
|
|
template <typename T> static inline T polyeval(T x, T a0) { return a0; }
|
|
|
|
template <typename T, typename... Ts>
|
|
static inline T polyeval(T x, T a0, Ts... a) {
|
|
return x * polyeval(x, a...) + a0;
|
|
}
|
|
|
|
} // namespace fputil
|
|
} // namespace __llvm_libc
|
|
|
|
#endif
|
|
|
|
#endif // LLVM_LIBC_UTILS_FPUTIL_FMA_H
|