1 //===-- Utilities for trigonometric functions -------------------*- 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_MATH_GENERIC_RANGE_REDUCTION_H
10 #define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H
11
12 #include "src/__support/FPUtil/FPBits.h"
13 #include "src/__support/FPUtil/multiply_add.h"
14 #include "src/__support/FPUtil/nearest_integer.h"
15 #include "src/__support/common.h"
16 #include "src/__support/macros/config.h"
17
18 namespace LIBC_NAMESPACE_DECL {
19
20 namespace generic {
21
22 static constexpr uint32_t FAST_PASS_BOUND = 0x4a80'0000U; // 2^22
23
24 static constexpr int N_ENTRIES = 8;
25
26 // We choose to split bits of 32/pi into 28-bit precision pieces, so that the
27 // product of x * THIRTYTWO_OVER_PI_28[i] is exact.
28 // These are generated by Sollya with:
29 // > a1 = D(round(32/pi, 28, RN)); a1;
30 // > a2 = D(round(32/pi - a1, 28, RN)); a2;
31 // > a3 = D(round(32/pi - a1 - a2, 28, RN)); a3;
32 // > a4 = D(round(32/pi - a1 - a2 - a3, 28, RN)); a4;
33 // ...
34 static constexpr double THIRTYTWO_OVER_PI_28[N_ENTRIES] = {
35 0x1.45f306ep+3, -0x1.b1bbeaep-28, 0x1.3f84ebp-57, -0x1.7056592p-87,
36 0x1.c0db62ap-116, -0x1.4cd8778p-145, -0x1.bef806cp-174, 0x1.63abdecp-204};
37
38 // Exponents of the least significant bits of the corresponding entries in
39 // THIRTYTWO_OVER_PI_28.
40 static constexpr int THIRTYTWO_OVER_PI_28_LSB_EXP[N_ENTRIES] = {
41 -24, -55, -81, -114, -143, -170, -200, -230};
42
43 // Return k and y, where
44 // k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
small_range_reduction(double x,double & y)45 LIBC_INLINE int64_t small_range_reduction(double x, double &y) {
46 double prod = x * THIRTYTWO_OVER_PI_28[0];
47 double kd = fputil::nearest_integer(prod);
48 y = prod - kd;
49 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[1], y);
50 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[2], y);
51 return static_cast<int64_t>(kd);
52 }
53
54 // Return k and y, where
55 // k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
56 // For large range, there are at most 2 parts of THIRTYTWO_OVER_PI_28
57 // contributing to the lowest 6 binary digits (k & 63). If the least
58 // significant bit of x * the least significant bit of THIRTYTWO_OVER_PI_28[i]
59 // >= 64, we can completely ignore THIRTYTWO_OVER_PI_28[i].
60 LIBC_INLINE int64_t large_range_reduction(double x, int x_exp, double &y) {
61 int idx = 0;
62 y = 0;
63 int x_lsb_exp_m4 = x_exp - fputil::FPBits<float>::FRACTION_LEN;
64
65 // Skipping the first parts of 32/pi such that:
66 // LSB of x * LSB of THIRTYTWO_OVER_PI_28[i] >= 32.
67 while (x_lsb_exp_m4 + THIRTYTWO_OVER_PI_28_LSB_EXP[idx] > 5)
68 ++idx;
69
70 double prod_hi = x * THIRTYTWO_OVER_PI_28[idx];
71 // Get the integral part of x * THIRTYTWO_OVER_PI_28[idx]
72 double k_hi = fputil::nearest_integer(prod_hi);
73 // Get the fractional part of x * THIRTYTWO_OVER_PI_28[idx]
74 double frac = prod_hi - k_hi;
75 double prod_lo = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 1], frac);
76 double k_lo = fputil::nearest_integer(prod_lo);
77
78 // Now y is the fractional parts.
79 y = prod_lo - k_lo;
80 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 2], y);
81 y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 3], y);
82
83 return static_cast<int64_t>(k_hi) + static_cast<int64_t>(k_lo);
84 }
85
86 } // namespace generic
87
88 } // namespace LIBC_NAMESPACE_DECL
89
90 #endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H
91