1//===-- Common utils for exp10f16 -------------------------------*- C++ -*-===//
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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_H
10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_H
11
12#include "include/llvm-libc-macros/float16-macros.h"
13
14#ifdef LIBC_TYPES_HAS_FLOAT16
15
16#include "exp10_float16_constants.h"
17#include "expf16_utils.h"
18#include "src/__support/FPUtil/FPBits.h"
19
20namespace LIBC_NAMESPACE_DECL {
21
22LIBC_INLINE ExpRangeReduction exp10_range_reduction(float16 x) {
23 // For -8 < x < 5, to compute 10^x, we perform the following range reduction:
24 // find hi, mid, lo, such that:
25 // x = (hi + mid) * log2(10) + lo, in which
26 // hi is an integer,
27 // mid * 2^3 is an integer,
28 // -2^(-4) <= lo < 2^(-4).
29 // In particular,
30 // hi + mid = round(x * 2^3) * 2^(-3).
31 // Then,
32 // 10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo
33 // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
34 // by adding hi to the exponent field of 2^mid. 10^lo is computed using a
35 // degree-4 minimax polynomial generated by Sollya.
36
37 float xf = x;
38 float kf = fputil::nearest_integer(x: xf * (LOG2F_10 * 0x1.0p+3f));
39 int x_hi_mid = static_cast<int>(kf);
40 unsigned x_hi = static_cast<unsigned>(x_hi_mid) >> 3;
41 unsigned x_mid = static_cast<unsigned>(x_hi_mid) & 0x7;
42 // lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x
43 float lo = fputil::multiply_add(x: kf, y: LOG10F_2 * -0x1.0p-3f, z: xf);
44
45 uint32_t exp2_hi_mid_bits =
46 EXP2_MID_BITS[x_mid] +
47 static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
48 float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
49 // Degree-4 minimax polynomial generated by Sollya with the following
50 // commands:
51 // > display = hexadecimal;
52 // > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]);
53 // > 1 + x * P;
54 float exp10_lo = fputil::polyeval(x: lo, a0: 0x1p+0f, a: 0x1.26bb14p+1f, a: 0x1.53526p+1f,
55 a: 0x1.04b434p+1f, a: 0x1.2bcf9ep+0f);
56 return {.exp_hi_mid: exp2_hi_mid, .exp_lo: exp10_lo};
57}
58
59} // namespace LIBC_NAMESPACE_DECL
60
61#endif // LIBC_TYPES_HAS_FLOAT16
62
63#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_H
64