86 lines
3.0 KiB
C++
86 lines
3.0 KiB
C++
//===-- Implementation header for qsort utilities ---------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC_STDLIB_QSORT_PIVOT_H
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#define LLVM_LIBC_SRC_STDLIB_QSORT_PIVOT_H
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#include <stddef.h> // For size_t
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namespace LIBC_NAMESPACE_DECL {
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namespace internal {
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// Recursively select a pseudomedian if above this threshold.
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constexpr size_t PSEUDO_MEDIAN_REC_THRESHOLD = 64;
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// Selects a pivot from `array`. Algorithm taken from glidesort by Orson Peters.
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//
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// This chooses a pivot by sampling an adaptive amount of points, approximating
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// the quality of a median of sqrt(n) elements.
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template <typename A, typename F>
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size_t choose_pivot(const A &array, const F &is_less) {
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const size_t len = array.len();
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if (len < 8) {
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return 0;
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}
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const size_t len_div_8 = len / 8;
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const size_t a = 0; // [0, floor(n/8))
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const size_t b = len_div_8 * 4; // [4*floor(n/8), 5*floor(n/8))
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const size_t c = len_div_8 * 7; // [7*floor(n/8), 8*floor(n/8))
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if (len < PSEUDO_MEDIAN_REC_THRESHOLD)
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return median3(array, a, b, c, is_less);
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else
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return median3_rec(array, a, b, c, len_div_8, is_less);
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}
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// Calculates an approximate median of 3 elements from sections a, b, c, or
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// recursively from an approximation of each, if they're large enough. By
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// dividing the size of each section by 8 when recursing we have logarithmic
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// recursion depth and overall sample from f(n) = 3*f(n/8) -> f(n) =
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// O(n^(log(3)/log(8))) ~= O(n^0.528) elements.
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template <typename A, typename F>
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size_t median3_rec(const A &array, size_t a, size_t b, size_t c, size_t n,
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const F &is_less) {
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if (n * 8 >= PSEUDO_MEDIAN_REC_THRESHOLD) {
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const size_t n8 = n / 8;
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a = median3_rec(array, a, a + (n8 * 4), a + (n8 * 7), n8, is_less);
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b = median3_rec(array, b, b + (n8 * 4), b + (n8 * 7), n8, is_less);
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c = median3_rec(array, c, c + (n8 * 4), c + (n8 * 7), n8, is_less);
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}
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return median3(array, a, b, c, is_less);
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}
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/// Calculates the median of 3 elements.
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template <typename A, typename F>
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size_t median3(const A &array, size_t a, size_t b, size_t c, const F &is_less) {
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const void *a_ptr = array.get(a);
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const void *b_ptr = array.get(b);
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const void *c_ptr = array.get(c);
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const bool x = is_less(a_ptr, b_ptr);
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const bool y = is_less(a_ptr, c_ptr);
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if (x == y) {
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// If x=y=0 then b, c <= a. In this case we want to return max(b, c).
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// If x=y=1 then a < b, c. In this case we want to return min(b, c).
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// By toggling the outcome of b < c using XOR x we get this behavior.
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const bool z = is_less(b_ptr, c_ptr);
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return z ^ x ? c : b;
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} else {
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// Either c <= a < b or b <= a < c, thus a is our median.
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return a;
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}
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}
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} // namespace internal
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC_STDLIB_QSORT_PIVOT_H
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