| //===-- Single-precision log(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 |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #include "src/math/logf.h" |
| #include "src/__support/math/logf.h" // Lookup table for (1/f) and log(f) |
| |
| // This is an algorithm for log(x) in single precision which is correctly |
| // rounded for all rounding modes, based on the implementation of log(x) from |
| // the RLIBM project at: |
| // https://people.cs.rutgers.edu/~sn349/rlibm |
| |
| // Step 1 - Range reduction: |
| // For x = 2^m * 1.mant, log(x) = m * log(2) + log(1.m) |
| // If x is denormal, we normalize it by multiplying x by 2^23 and subtracting |
| // m by 23. |
| |
| // Step 2 - Another range reduction: |
| // To compute log(1.mant), let f be the highest 8 bits including the hidden |
| // bit, and d be the difference (1.mant - f), i.e. the remaining 16 bits of the |
| // mantissa. Then we have the following approximation formula: |
| // log(1.mant) = log(f) + log(1.mant / f) |
| // = log(f) + log(1 + d/f) |
| // ~ log(f) + P(d/f) |
| // since d/f is sufficiently small. |
| // log(f) and 1/f are then stored in two 2^7 = 128 entries look-up tables. |
| |
| // Step 3 - Polynomial approximation: |
| // To compute P(d/f), we use a single degree-5 polynomial in double precision |
| // which provides correct rounding for all but few exception values. |
| // For more detail about how this polynomial is obtained, please refer to the |
| // paper: |
| // Lim, J. and Nagarakatte, S., "One Polynomial Approximation to Produce |
| // Correctly Rounded Results of an Elementary Function for Multiple |
| // Representations and Rounding Modes", Proceedings of the 49th ACM SIGPLAN |
| // Symposium on Principles of Programming Languages (POPL-2022), Philadelphia, |
| // USA, January 16-22, 2022. |
| // https://people.cs.rutgers.edu/~sn349/papers/rlibmall-popl-2022.pdf |
| |
| namespace LIBC_NAMESPACE_DECL { |
| |
| LLVM_LIBC_FUNCTION(float, logf, (float x)) { return math::logf(x); } |
| |
| } // namespace LIBC_NAMESPACE_DECL |
