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2080 lines
78 KiB
C++
2080 lines
78 KiB
C++
// libdivide.h - Optimized integer division
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// https://libdivide.com
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//
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// Copyright (C) 2010 - 2019 ridiculous_fish, <libdivide@ridiculousfish.com>
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// Copyright (C) 2016 - 2019 Kim Walisch, <kim.walisch@gmail.com>
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//
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// libdivide is dual-licensed under the Boost or zlib licenses.
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// You may use libdivide under the terms of either of these.
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// See LICENSE.txt for more details.
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#ifndef LIBDIVIDE_H
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#define LIBDIVIDE_H
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#define LIBDIVIDE_VERSION "2.0"
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#define LIBDIVIDE_VERSION_MAJOR 2
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#define LIBDIVIDE_VERSION_MINOR 0
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#include <stdint.h>
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#if defined(__cplusplus)
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#include <cstdlib>
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#include <cstdio>
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#else
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#include <stdlib.h>
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#include <stdio.h>
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#endif
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#if defined(__x86_64__) || defined(_M_X64)
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#define LIBDIVIDE_X86_64
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#endif
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#if defined LIBDIVIDE_X86_64 || defined __SSE2__ || (defined _M_IX86_FP && _M_IX86_FP == 2)
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#define LIBDIVIDE_SSE2 1
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#endif
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#if defined(LIBDIVIDE_AVX512)
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#include <immintrin.h>
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#elif defined(LIBDIVIDE_AVX2)
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#include <immintrin.h>
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#elif defined(LIBDIVIDE_SSE2)
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#include <emmintrin.h>
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#endif
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#if defined(_MSC_VER)
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#include <intrin.h>
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// disable warning C4146: unary minus operator applied
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// to unsigned type, result still unsigned
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#pragma warning(disable: 4146)
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#define LIBDIVIDE_VC
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#endif
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#if !defined(__has_builtin)
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#define __has_builtin(x) 0
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#endif
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#if defined(__SIZEOF_INT128__)
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#define HAS_INT128_T
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// clang-cl on Windows does not yet support 128-bit division
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#if !(defined(__clang__) && defined(LIBDIVIDE_VC))
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#define HAS_INT128_DIV
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#endif
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#endif
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#if defined(__i386__)
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#define LIBDIVIDE_i386
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#endif
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#if defined(__GNUC__) || defined(__clang__)
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#define LIBDIVIDE_GCC_STYLE_ASM
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#endif
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#if defined(__cplusplus) || defined(LIBDIVIDE_VC)
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#define LIBDIVIDE_FUNCTION __FUNCTION__
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#else
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#define LIBDIVIDE_FUNCTION __func__
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#endif
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#if 0
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#define LIBDIVIDE_ERROR(msg) \
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do { \
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fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", \
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__LINE__, LIBDIVIDE_FUNCTION, msg); \
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exit(-1); \
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} while (0)
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#else
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#define LIBDIVIDE_ERROR(msg)
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#endif
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#if defined(LIBDIVIDE_ASSERTIONS_ON)
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#define LIBDIVIDE_ASSERT(x) \
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do { \
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if (!(x)) { \
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fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", \
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__LINE__, LIBDIVIDE_FUNCTION, #x); \
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exit(-1); \
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} \
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} while (0)
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#else
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#define LIBDIVIDE_ASSERT(x)
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#endif
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#ifdef __cplusplus
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namespace libdivide {
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#endif
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// pack divider structs to prevent compilers from padding.
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// This reduces memory usage by up to 43% when using a large
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// array of libdivide dividers and improves performance
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// by up to 10% because of reduced memory bandwidth.
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#pragma pack(push, 1)
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struct libdivide_u32_t {
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uint32_t magic;
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uint8_t more;
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};
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struct libdivide_s32_t {
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int32_t magic;
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uint8_t more;
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};
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struct libdivide_u64_t {
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uint64_t magic;
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uint8_t more;
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};
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struct libdivide_s64_t {
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int64_t magic;
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uint8_t more;
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};
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struct libdivide_u32_branchfree_t {
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uint32_t magic;
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uint8_t more;
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};
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struct libdivide_s32_branchfree_t {
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int32_t magic;
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uint8_t more;
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};
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struct libdivide_u64_branchfree_t {
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uint64_t magic;
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uint8_t more;
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};
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struct libdivide_s64_branchfree_t {
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int64_t magic;
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uint8_t more;
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};
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#pragma pack(pop)
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// Explanation of the "more" field:
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//
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// * Bits 0-5 is the shift value (for shift path or mult path).
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// * Bit 6 is the add indicator for mult path.
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// * Bit 7 is set if the divisor is negative. We use bit 7 as the negative
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// divisor indicator so that we can efficiently use sign extension to
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// create a bitmask with all bits set to 1 (if the divisor is negative)
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// or 0 (if the divisor is positive).
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//
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// u32: [0-4] shift value
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// [5] ignored
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// [6] add indicator
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// magic number of 0 indicates shift path
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//
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// s32: [0-4] shift value
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// [5] ignored
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// [6] add indicator
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// [7] indicates negative divisor
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// magic number of 0 indicates shift path
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//
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// u64: [0-5] shift value
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// [6] add indicator
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// magic number of 0 indicates shift path
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//
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// s64: [0-5] shift value
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// [6] add indicator
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// [7] indicates negative divisor
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// magic number of 0 indicates shift path
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//
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// In s32 and s64 branchfree modes, the magic number is negated according to
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// whether the divisor is negated. In branchfree strategy, it is not negated.
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enum {
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LIBDIVIDE_32_SHIFT_MASK = 0x1F,
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LIBDIVIDE_64_SHIFT_MASK = 0x3F,
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LIBDIVIDE_ADD_MARKER = 0x40,
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LIBDIVIDE_NEGATIVE_DIVISOR = 0x80
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};
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static inline struct libdivide_s32_t libdivide_s32_gen(int32_t d);
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static inline struct libdivide_u32_t libdivide_u32_gen(uint32_t d);
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static inline struct libdivide_s64_t libdivide_s64_gen(int64_t d);
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static inline struct libdivide_u64_t libdivide_u64_gen(uint64_t d);
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static inline struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d);
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static inline struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d);
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static inline struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d);
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static inline struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d);
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static inline int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom);
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static inline uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom);
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static inline int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom);
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static inline uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom);
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static inline int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom);
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static inline uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom);
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static inline int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom);
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static inline uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom);
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static inline int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom);
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static inline uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom);
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static inline int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom);
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static inline uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom);
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static inline int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom);
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static inline uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom);
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static inline int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom);
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static inline uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom);
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//////// Internal Utility Functions
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static inline uint32_t libdivide_mullhi_u32(uint32_t x, uint32_t y) {
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uint64_t xl = x, yl = y;
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uint64_t rl = xl * yl;
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return (uint32_t)(rl >> 32);
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}
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static inline int32_t libdivide_mullhi_s32(int32_t x, int32_t y) {
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int64_t xl = x, yl = y;
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int64_t rl = xl * yl;
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// needs to be arithmetic shift
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return (int32_t)(rl >> 32);
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}
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static inline uint64_t libdivide_mullhi_u64(uint64_t x, uint64_t y) {
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#if defined(LIBDIVIDE_VC) && \
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defined(LIBDIVIDE_X86_64)
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return __umulh(x, y);
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#elif defined(HAS_INT128_T)
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__uint128_t xl = x, yl = y;
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__uint128_t rl = xl * yl;
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return (uint64_t)(rl >> 64);
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#else
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// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
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uint32_t mask = 0xFFFFFFFF;
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uint32_t x0 = (uint32_t)(x & mask);
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uint32_t x1 = (uint32_t)(x >> 32);
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uint32_t y0 = (uint32_t)(y & mask);
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uint32_t y1 = (uint32_t)(y >> 32);
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uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
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uint64_t x0y1 = x0 * (uint64_t)y1;
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uint64_t x1y0 = x1 * (uint64_t)y0;
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uint64_t x1y1 = x1 * (uint64_t)y1;
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uint64_t temp = x1y0 + x0y0_hi;
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uint64_t temp_lo = temp & mask;
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uint64_t temp_hi = temp >> 32;
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return x1y1 + temp_hi + ((temp_lo + x0y1) >> 32);
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#endif
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}
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static inline int64_t libdivide_mullhi_s64(int64_t x, int64_t y) {
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#if defined(LIBDIVIDE_VC) && \
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defined(LIBDIVIDE_X86_64)
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return __mulh(x, y);
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#elif defined(HAS_INT128_T)
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__int128_t xl = x, yl = y;
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__int128_t rl = xl * yl;
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return (int64_t)(rl >> 64);
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#else
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// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
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uint32_t mask = 0xFFFFFFFF;
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uint32_t x0 = (uint32_t)(x & mask);
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uint32_t y0 = (uint32_t)(y & mask);
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int32_t x1 = (int32_t)(x >> 32);
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int32_t y1 = (int32_t)(y >> 32);
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uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
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int64_t t = x1 * (int64_t)y0 + x0y0_hi;
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int64_t w1 = x0 * (int64_t)y1 + (t & mask);
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return x1 * (int64_t)y1 + (t >> 32) + (w1 >> 32);
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#endif
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}
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static inline int32_t libdivide_count_leading_zeros32(uint32_t val) {
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#if defined(__GNUC__) || \
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__has_builtin(__builtin_clz)
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// Fast way to count leading zeros
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return __builtin_clz(val);
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#elif defined(LIBDIVIDE_VC)
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unsigned long result;
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if (_BitScanReverse(&result, val)) {
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return 31 - result;
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}
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return 0;
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#else
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int32_t result = 0;
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uint32_t hi = 1U << 31;
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for (; ~val & hi; hi >>= 1) {
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result++;
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}
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return result;
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#endif
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}
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static inline int32_t libdivide_count_leading_zeros64(uint64_t val) {
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#if defined(__GNUC__) || \
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__has_builtin(__builtin_clzll)
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// Fast way to count leading zeros
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return __builtin_clzll(val);
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#elif defined(LIBDIVIDE_VC) && defined(_WIN64)
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unsigned long result;
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if (_BitScanReverse64(&result, val)) {
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return 63 - result;
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}
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return 0;
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#else
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uint32_t hi = val >> 32;
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uint32_t lo = val & 0xFFFFFFFF;
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if (hi != 0) return libdivide_count_leading_zeros32(hi);
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return 32 + libdivide_count_leading_zeros32(lo);
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#endif
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}
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// libdivide_64_div_32_to_32: divides a 64-bit uint {u1, u0} by a 32-bit
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// uint {v}. The result must fit in 32 bits.
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// Returns the quotient directly and the remainder in *r
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static inline uint32_t libdivide_64_div_32_to_32(uint32_t u1, uint32_t u0, uint32_t v, uint32_t *r) {
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#if (defined(LIBDIVIDE_i386) || defined(LIBDIVIDE_X86_64)) && \
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defined(LIBDIVIDE_GCC_STYLE_ASM)
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uint32_t result;
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__asm__("divl %[v]"
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: "=a"(result), "=d"(*r)
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: [v] "r"(v), "a"(u0), "d"(u1)
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);
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return result;
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#else
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uint64_t n = ((uint64_t)u1 << 32) | u0;
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uint32_t result = (uint32_t)(n / v);
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*r = (uint32_t)(n - result * (uint64_t)v);
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return result;
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#endif
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}
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// libdivide_128_div_64_to_64: divides a 128-bit uint {u1, u0} by a 64-bit
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// uint {v}. The result must fit in 64 bits.
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// Returns the quotient directly and the remainder in *r
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static uint64_t libdivide_128_div_64_to_64(uint64_t u1, uint64_t u0, uint64_t v, uint64_t *r) {
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#if defined(LIBDIVIDE_X86_64) && \
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defined(LIBDIVIDE_GCC_STYLE_ASM)
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uint64_t result;
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__asm__("divq %[v]"
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: "=a"(result), "=d"(*r)
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: [v] "r"(v), "a"(u0), "d"(u1)
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);
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return result;
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#elif defined(HAS_INT128_T) && \
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defined(HAS_INT128_DIV)
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__uint128_t n = ((__uint128_t)u1 << 64) | u0;
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uint64_t result = (uint64_t)(n / v);
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*r = (uint64_t)(n - result * (__uint128_t)v);
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return result;
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#else
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// Code taken from Hacker's Delight:
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// http://www.hackersdelight.org/HDcode/divlu.c.
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// License permits inclusion here per:
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// http://www.hackersdelight.org/permissions.htm
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const uint64_t b = (1ULL << 32); // Number base (32 bits)
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uint64_t un1, un0; // Norm. dividend LSD's
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uint64_t vn1, vn0; // Norm. divisor digits
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uint64_t q1, q0; // Quotient digits
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uint64_t un64, un21, un10; // Dividend digit pairs
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uint64_t rhat; // A remainder
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int32_t s; // Shift amount for norm
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// If overflow, set rem. to an impossible value,
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// and return the largest possible quotient
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if (EDUKE32_PREDICT_FALSE(u1 >= v)) {
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*r = (uint64_t) -1;
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return (uint64_t) -1;
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}
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// count leading zeros
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s = libdivide_count_leading_zeros64(v);
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if (s > 0) {
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// Normalize divisor
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v = v << s;
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un64 = (u1 << s) | (u0 >> (64 - s));
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un10 = u0 << s; // Shift dividend left
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} else {
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// Avoid undefined behavior of (u0 >> 64).
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// The behavior is undefined if the right operand is
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// negative, or greater than or equal to the length
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// in bits of the promoted left operand.
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un64 = u1;
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un10 = u0;
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}
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// Break divisor up into two 32-bit digits
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vn1 = v >> 32;
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vn0 = v & 0xFFFFFFFF;
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// Break right half of dividend into two digits
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un1 = un10 >> 32;
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un0 = un10 & 0xFFFFFFFF;
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// Compute the first quotient digit, q1
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q1 = un64 / vn1;
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rhat = un64 - q1 * vn1;
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while (q1 >= b || q1 * vn0 > b * rhat + un1) {
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q1 = q1 - 1;
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rhat = rhat + vn1;
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if (rhat >= b)
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break;
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}
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// Multiply and subtract
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un21 = un64 * b + un1 - q1 * v;
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// Compute the second quotient digit
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q0 = un21 / vn1;
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rhat = un21 - q0 * vn1;
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while (q0 >= b || q0 * vn0 > b * rhat + un0) {
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q0 = q0 - 1;
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rhat = rhat + vn1;
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if (rhat >= b)
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break;
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}
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*r = (un21 * b + un0 - q0 * v) >> s;
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return q1 * b + q0;
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#endif
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}
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// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0)
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static inline void libdivide_u128_shift(uint64_t *u1, uint64_t *u0, int32_t signed_shift) {
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if (signed_shift > 0) {
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uint32_t shift = signed_shift;
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*u1 <<= shift;
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*u1 |= *u0 >> (64 - shift);
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*u0 <<= shift;
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}
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else if (signed_shift < 0) {
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uint32_t shift = -signed_shift;
|
|
*u0 >>= shift;
|
|
*u0 |= *u1 << (64 - shift);
|
|
*u1 >>= shift;
|
|
}
|
|
}
|
|
|
|
// Computes a 128 / 128 -> 64 bit division, with a 128 bit remainder.
|
|
static uint64_t libdivide_128_div_128_to_64(uint64_t u_hi, uint64_t u_lo, uint64_t v_hi, uint64_t v_lo, uint64_t *r_hi, uint64_t *r_lo) {
|
|
#if defined(HAS_INT128_T) && \
|
|
defined(HAS_INT128_DIV)
|
|
__uint128_t ufull = u_hi;
|
|
__uint128_t vfull = v_hi;
|
|
ufull = (ufull << 64) | u_lo;
|
|
vfull = (vfull << 64) | v_lo;
|
|
uint64_t res = (uint64_t)(ufull / vfull);
|
|
__uint128_t remainder = ufull - (vfull * res);
|
|
*r_lo = (uint64_t)remainder;
|
|
*r_hi = (uint64_t)(remainder >> 64);
|
|
return res;
|
|
#else
|
|
// Adapted from "Unsigned Doubleword Division" in Hacker's Delight
|
|
// We want to compute u / v
|
|
typedef struct { uint64_t hi; uint64_t lo; } u128_t;
|
|
u128_t u = {u_hi, u_lo};
|
|
u128_t v = {v_hi, v_lo};
|
|
|
|
if (v.hi == 0) {
|
|
// divisor v is a 64 bit value, so we just need one 128/64 division
|
|
// Note that we are simpler than Hacker's Delight here, because we know
|
|
// the quotient fits in 64 bits whereas Hacker's Delight demands a full
|
|
// 128 bit quotient
|
|
*r_hi = 0;
|
|
return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo);
|
|
}
|
|
// Here v >= 2**64
|
|
// We know that v.hi != 0, so count leading zeros is OK
|
|
// We have 0 <= n <= 63
|
|
uint32_t n = libdivide_count_leading_zeros64(v.hi);
|
|
|
|
// Normalize the divisor so its MSB is 1
|
|
u128_t v1t = v;
|
|
libdivide_u128_shift(&v1t.hi, &v1t.lo, n);
|
|
uint64_t v1 = v1t.hi; // i.e. v1 = v1t >> 64
|
|
|
|
// To ensure no overflow
|
|
u128_t u1 = u;
|
|
libdivide_u128_shift(&u1.hi, &u1.lo, -1);
|
|
|
|
// Get quotient from divide unsigned insn.
|
|
uint64_t rem_ignored;
|
|
uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored);
|
|
|
|
// Undo normalization and division of u by 2.
|
|
u128_t q0 = {0, q1};
|
|
libdivide_u128_shift(&q0.hi, &q0.lo, n);
|
|
libdivide_u128_shift(&q0.hi, &q0.lo, -63);
|
|
|
|
// Make q0 correct or too small by 1
|
|
// Equivalent to `if (q0 != 0) q0 = q0 - 1;`
|
|
if (q0.hi != 0 || q0.lo != 0) {
|
|
q0.hi -= (q0.lo == 0); // borrow
|
|
q0.lo -= 1;
|
|
}
|
|
|
|
// Now q0 is correct.
|
|
// Compute q0 * v as q0v
|
|
// = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo)
|
|
// = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) +
|
|
// (q0.lo * v.hi << 64) + q0.lo * v.lo)
|
|
// Each term is 128 bit
|
|
// High half of full product (upper 128 bits!) are dropped
|
|
u128_t q0v = {0, 0};
|
|
q0v.hi = q0.hi*v.lo + q0.lo*v.hi + libdivide_mullhi_u64(q0.lo, v.lo);
|
|
q0v.lo = q0.lo*v.lo;
|
|
|
|
// Compute u - q0v as u_q0v
|
|
// This is the remainder
|
|
u128_t u_q0v = u;
|
|
u_q0v.hi -= q0v.hi + (u.lo < q0v.lo); // second term is borrow
|
|
u_q0v.lo -= q0v.lo;
|
|
|
|
// Check if u_q0v >= v
|
|
// This checks if our remainder is larger than the divisor
|
|
if ((u_q0v.hi > v.hi) ||
|
|
(u_q0v.hi == v.hi && u_q0v.lo >= v.lo)) {
|
|
// Increment q0
|
|
q0.lo += 1;
|
|
q0.hi += (q0.lo == 0); // carry
|
|
|
|
// Subtract v from remainder
|
|
u_q0v.hi -= v.hi + (u_q0v.lo < v.lo);
|
|
u_q0v.lo -= v.lo;
|
|
}
|
|
|
|
*r_hi = u_q0v.hi;
|
|
*r_lo = u_q0v.lo;
|
|
|
|
LIBDIVIDE_ASSERT(q0.hi == 0);
|
|
return q0.lo;
|
|
#endif
|
|
}
|
|
|
|
////////// UINT32
|
|
|
|
static inline struct libdivide_u32_t libdivide_internal_u32_gen(uint32_t d, int branchfree) {
|
|
if (d == 0) {
|
|
LIBDIVIDE_ERROR("divider must be != 0");
|
|
}
|
|
|
|
struct libdivide_u32_t result;
|
|
uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(d);
|
|
|
|
// Power of 2
|
|
if ((d & (d - 1)) == 0) {
|
|
// We need to subtract 1 from the shift value in case of an unsigned
|
|
// branchfree divider because there is a hardcoded right shift by 1
|
|
// in its division algorithm. Because of this we also need to add back
|
|
// 1 in its recovery algorithm.
|
|
result.magic = 0;
|
|
result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
|
|
} else {
|
|
uint8_t more;
|
|
uint32_t rem, proposed_m;
|
|
proposed_m = libdivide_64_div_32_to_32(1U << floor_log_2_d, 0, d, &rem);
|
|
|
|
LIBDIVIDE_ASSERT(rem > 0 && rem < d);
|
|
const uint32_t e = d - rem;
|
|
|
|
// This power works if e < 2**floor_log_2_d.
|
|
if (!branchfree && (e < (1U << floor_log_2_d))) {
|
|
// This power works
|
|
more = floor_log_2_d;
|
|
} else {
|
|
// We have to use the general 33-bit algorithm. We need to compute
|
|
// (2**power) / d. However, we already have (2**(power-1))/d and
|
|
// its remainder. By doubling both, and then correcting the
|
|
// remainder, we can compute the larger division.
|
|
// don't care about overflow here - in fact, we expect it
|
|
proposed_m += proposed_m;
|
|
const uint32_t twice_rem = rem + rem;
|
|
if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
|
|
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
|
|
}
|
|
result.magic = 1 + proposed_m;
|
|
result.more = more;
|
|
// result.more's shift should in general be ceil_log_2_d. But if we
|
|
// used the smaller power, we subtract one from the shift because we're
|
|
// using the smaller power. If we're using the larger power, we
|
|
// subtract one from the shift because it's taken care of by the add
|
|
// indicator. So floor_log_2_d happens to be correct in both cases.
|
|
}
|
|
return result;
|
|
}
|
|
|
|
struct libdivide_u32_t libdivide_u32_gen(uint32_t d) {
|
|
return libdivide_internal_u32_gen(d, 0);
|
|
}
|
|
|
|
struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d) {
|
|
if (d == 1) {
|
|
LIBDIVIDE_ERROR("branchfree divider must be != 1");
|
|
}
|
|
struct libdivide_u32_t tmp = libdivide_internal_u32_gen(d, 1);
|
|
struct libdivide_u32_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_32_SHIFT_MASK)};
|
|
return ret;
|
|
}
|
|
|
|
uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return numer >> more;
|
|
}
|
|
else {
|
|
uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
uint32_t t = ((numer - q) >> 1) + q;
|
|
return t >> (more & LIBDIVIDE_32_SHIFT_MASK);
|
|
}
|
|
else {
|
|
// All upper bits are 0,
|
|
// don't need to mask them off.
|
|
return q >> more;
|
|
}
|
|
}
|
|
}
|
|
|
|
uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom) {
|
|
uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
|
|
uint32_t t = ((numer - q) >> 1) + q;
|
|
return t >> denom->more;
|
|
}
|
|
|
|
uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
|
|
if (!denom->magic) {
|
|
return 1U << shift;
|
|
} else if (!(more & LIBDIVIDE_ADD_MARKER)) {
|
|
// We compute q = n/d = n*m / 2^(32 + shift)
|
|
// Therefore we have d = 2^(32 + shift) / m
|
|
// We need to ceil it.
|
|
// We know d is not a power of 2, so m is not a power of 2,
|
|
// so we can just add 1 to the floor
|
|
uint32_t hi_dividend = 1U << shift;
|
|
uint32_t rem_ignored;
|
|
return 1 + libdivide_64_div_32_to_32(hi_dividend, 0, denom->magic, &rem_ignored);
|
|
} else {
|
|
// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
|
|
// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
|
|
// Also note that shift may be as high as 31, so shift + 1 will
|
|
// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
|
|
// then double the quotient and remainder.
|
|
uint64_t half_n = 1ULL << (32 + shift);
|
|
uint64_t d = (1ULL << 32) | denom->magic;
|
|
// Note that the quotient is guaranteed <= 32 bits, but the remainder
|
|
// may need 33!
|
|
uint32_t half_q = (uint32_t)(half_n / d);
|
|
uint64_t rem = half_n % d;
|
|
// We computed 2^(32+shift)/(m+2^32)
|
|
// Need to double it, and then add 1 to the quotient if doubling th
|
|
// remainder would increase the quotient.
|
|
// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
|
|
uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
|
|
|
|
// We rounded down in gen (hence +1)
|
|
return full_q + 1;
|
|
}
|
|
}
|
|
|
|
uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
|
|
if (!denom->magic) {
|
|
return 1U << (shift + 1);
|
|
} else {
|
|
// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
|
|
// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
|
|
// Also note that shift may be as high as 31, so shift + 1 will
|
|
// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
|
|
// then double the quotient and remainder.
|
|
uint64_t half_n = 1ULL << (32 + shift);
|
|
uint64_t d = (1ULL << 32) | denom->magic;
|
|
// Note that the quotient is guaranteed <= 32 bits, but the remainder
|
|
// may need 33!
|
|
uint32_t half_q = (uint32_t)(half_n / d);
|
|
uint64_t rem = half_n % d;
|
|
// We computed 2^(32+shift)/(m+2^32)
|
|
// Need to double it, and then add 1 to the quotient if doubling th
|
|
// remainder would increase the quotient.
|
|
// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
|
|
uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
|
|
|
|
// We rounded down in gen (hence +1)
|
|
return full_q + 1;
|
|
}
|
|
}
|
|
|
|
/////////// UINT64
|
|
|
|
static inline struct libdivide_u64_t libdivide_internal_u64_gen(uint64_t d, int branchfree) {
|
|
if (d == 0) {
|
|
LIBDIVIDE_ERROR("divider must be != 0");
|
|
}
|
|
|
|
struct libdivide_u64_t result;
|
|
uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(d);
|
|
|
|
// Power of 2
|
|
if ((d & (d - 1)) == 0) {
|
|
// We need to subtract 1 from the shift value in case of an unsigned
|
|
// branchfree divider because there is a hardcoded right shift by 1
|
|
// in its division algorithm. Because of this we also need to add back
|
|
// 1 in its recovery algorithm.
|
|
result.magic = 0;
|
|
result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
|
|
} else {
|
|
uint64_t proposed_m, rem;
|
|
uint8_t more;
|
|
// (1 << (64 + floor_log_2_d)) / d
|
|
proposed_m = libdivide_128_div_64_to_64(1ULL << floor_log_2_d, 0, d, &rem);
|
|
|
|
LIBDIVIDE_ASSERT(rem > 0 && rem < d);
|
|
const uint64_t e = d - rem;
|
|
|
|
// This power works if e < 2**floor_log_2_d.
|
|
if (!branchfree && e < (1ULL << floor_log_2_d)) {
|
|
// This power works
|
|
more = floor_log_2_d;
|
|
} else {
|
|
// We have to use the general 65-bit algorithm. We need to compute
|
|
// (2**power) / d. However, we already have (2**(power-1))/d and
|
|
// its remainder. By doubling both, and then correcting the
|
|
// remainder, we can compute the larger division.
|
|
// don't care about overflow here - in fact, we expect it
|
|
proposed_m += proposed_m;
|
|
const uint64_t twice_rem = rem + rem;
|
|
if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
|
|
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
|
|
}
|
|
result.magic = 1 + proposed_m;
|
|
result.more = more;
|
|
// result.more's shift should in general be ceil_log_2_d. But if we
|
|
// used the smaller power, we subtract one from the shift because we're
|
|
// using the smaller power. If we're using the larger power, we
|
|
// subtract one from the shift because it's taken care of by the add
|
|
// indicator. So floor_log_2_d happens to be correct in both cases,
|
|
// which is why we do it outside of the if statement.
|
|
}
|
|
return result;
|
|
}
|
|
|
|
struct libdivide_u64_t libdivide_u64_gen(uint64_t d) {
|
|
return libdivide_internal_u64_gen(d, 0);
|
|
}
|
|
|
|
struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d) {
|
|
if (d == 1) {
|
|
LIBDIVIDE_ERROR("branchfree divider must be != 1");
|
|
}
|
|
struct libdivide_u64_t tmp = libdivide_internal_u64_gen(d, 1);
|
|
struct libdivide_u64_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_64_SHIFT_MASK)};
|
|
return ret;
|
|
}
|
|
|
|
uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return numer >> more;
|
|
}
|
|
else {
|
|
uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
uint64_t t = ((numer - q) >> 1) + q;
|
|
return t >> (more & LIBDIVIDE_64_SHIFT_MASK);
|
|
}
|
|
else {
|
|
// All upper bits are 0,
|
|
// don't need to mask them off.
|
|
return q >> more;
|
|
}
|
|
}
|
|
}
|
|
|
|
uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom) {
|
|
uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
|
|
uint64_t t = ((numer - q) >> 1) + q;
|
|
return t >> denom->more;
|
|
}
|
|
|
|
uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
|
|
if (!denom->magic) {
|
|
return 1ULL << shift;
|
|
} else if (!(more & LIBDIVIDE_ADD_MARKER)) {
|
|
// We compute q = n/d = n*m / 2^(64 + shift)
|
|
// Therefore we have d = 2^(64 + shift) / m
|
|
// We need to ceil it.
|
|
// We know d is not a power of 2, so m is not a power of 2,
|
|
// so we can just add 1 to the floor
|
|
uint64_t hi_dividend = 1ULL << shift;
|
|
uint64_t rem_ignored;
|
|
return 1 + libdivide_128_div_64_to_64(hi_dividend, 0, denom->magic, &rem_ignored);
|
|
} else {
|
|
// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
|
|
// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
|
|
// libdivide_u32_recover for more on what we do here.
|
|
// TODO: do something better than 128 bit math
|
|
|
|
// Full n is a (potentially) 129 bit value
|
|
// half_n is a 128 bit value
|
|
// Compute the hi half of half_n. Low half is 0.
|
|
uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
|
|
// d is a 65 bit value. The high bit is always set to 1.
|
|
const uint64_t d_hi = 1, d_lo = denom->magic;
|
|
// Note that the quotient is guaranteed <= 64 bits,
|
|
// but the remainder may need 65!
|
|
uint64_t r_hi, r_lo;
|
|
uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
|
|
// We computed 2^(64+shift)/(m+2^64)
|
|
// Double the remainder ('dr') and check if that is larger than d
|
|
// Note that d is a 65 bit value, so r1 is small and so r1 + r1
|
|
// cannot overflow
|
|
uint64_t dr_lo = r_lo + r_lo;
|
|
uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
|
|
int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
|
|
uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
|
|
return full_q + 1;
|
|
}
|
|
}
|
|
|
|
uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
|
|
if (!denom->magic) {
|
|
return 1ULL << (shift + 1);
|
|
} else {
|
|
// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
|
|
// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
|
|
// libdivide_u32_recover for more on what we do here.
|
|
// TODO: do something better than 128 bit math
|
|
|
|
// Full n is a (potentially) 129 bit value
|
|
// half_n is a 128 bit value
|
|
// Compute the hi half of half_n. Low half is 0.
|
|
uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
|
|
// d is a 65 bit value. The high bit is always set to 1.
|
|
const uint64_t d_hi = 1, d_lo = denom->magic;
|
|
// Note that the quotient is guaranteed <= 64 bits,
|
|
// but the remainder may need 65!
|
|
uint64_t r_hi, r_lo;
|
|
uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
|
|
// We computed 2^(64+shift)/(m+2^64)
|
|
// Double the remainder ('dr') and check if that is larger than d
|
|
// Note that d is a 65 bit value, so r1 is small and so r1 + r1
|
|
// cannot overflow
|
|
uint64_t dr_lo = r_lo + r_lo;
|
|
uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
|
|
int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
|
|
uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
|
|
return full_q + 1;
|
|
}
|
|
}
|
|
|
|
/////////// SINT32
|
|
|
|
static inline struct libdivide_s32_t libdivide_internal_s32_gen(int32_t d, int branchfree) {
|
|
if (d == 0) {
|
|
LIBDIVIDE_ERROR("divider must be != 0");
|
|
}
|
|
|
|
struct libdivide_s32_t result;
|
|
|
|
// If d is a power of 2, or negative a power of 2, we have to use a shift.
|
|
// This is especially important because the magic algorithm fails for -1.
|
|
// To check if d is a power of 2 or its inverse, it suffices to check
|
|
// whether its absolute value has exactly one bit set. This works even for
|
|
// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
|
|
// and is a power of 2.
|
|
uint32_t ud = (uint32_t)d;
|
|
uint32_t absD = (d < 0) ? -ud : ud;
|
|
uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(absD);
|
|
// check if exactly one bit is set,
|
|
// don't care if absD is 0 since that's divide by zero
|
|
if ((absD & (absD - 1)) == 0) {
|
|
// Branchfree and normal paths are exactly the same
|
|
result.magic = 0;
|
|
result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
|
|
} else {
|
|
LIBDIVIDE_ASSERT(floor_log_2_d >= 1);
|
|
|
|
uint8_t more;
|
|
// the dividend here is 2**(floor_log_2_d + 31), so the low 32 bit word
|
|
// is 0 and the high word is floor_log_2_d - 1
|
|
uint32_t rem, proposed_m;
|
|
proposed_m = libdivide_64_div_32_to_32(1U << (floor_log_2_d - 1), 0, absD, &rem);
|
|
const uint32_t e = absD - rem;
|
|
|
|
// We are going to start with a power of floor_log_2_d - 1.
|
|
// This works if works if e < 2**floor_log_2_d.
|
|
if (!branchfree && e < (1U << floor_log_2_d)) {
|
|
// This power works
|
|
more = floor_log_2_d - 1;
|
|
} else {
|
|
// We need to go one higher. This should not make proposed_m
|
|
// overflow, but it will make it negative when interpreted as an
|
|
// int32_t.
|
|
proposed_m += proposed_m;
|
|
const uint32_t twice_rem = rem + rem;
|
|
if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
|
|
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
|
|
}
|
|
|
|
proposed_m += 1;
|
|
int32_t magic = (int32_t)proposed_m;
|
|
|
|
// Mark if we are negative. Note we only negate the magic number in the
|
|
// branchfull case.
|
|
if (d < 0) {
|
|
more |= LIBDIVIDE_NEGATIVE_DIVISOR;
|
|
if (!branchfree) {
|
|
magic = -magic;
|
|
}
|
|
}
|
|
|
|
result.more = more;
|
|
result.magic = magic;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
struct libdivide_s32_t libdivide_s32_gen(int32_t d) {
|
|
return libdivide_internal_s32_gen(d, 0);
|
|
}
|
|
|
|
struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d) {
|
|
struct libdivide_s32_t tmp = libdivide_internal_s32_gen(d, 1);
|
|
struct libdivide_s32_branchfree_t result = {tmp.magic, tmp.more};
|
|
return result;
|
|
}
|
|
|
|
int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
|
|
if (!denom->magic) {
|
|
uint32_t sign = (int8_t)more >> 7;
|
|
uint32_t mask = (1U << shift) - 1;
|
|
uint32_t uq = numer + ((numer >> 31) & mask);
|
|
int32_t q = (int32_t)uq;
|
|
q >>= shift;
|
|
q = (q ^ sign) - sign;
|
|
return q;
|
|
} else {
|
|
uint32_t uq = (uint32_t)libdivide_mullhi_s32(denom->magic, numer);
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift and then sign extend
|
|
int32_t sign = (int8_t)more >> 7;
|
|
// q += (more < 0 ? -numer : numer)
|
|
// cast required to avoid UB
|
|
uq += ((uint32_t)numer ^ sign) - sign;
|
|
}
|
|
int32_t q = (int32_t)uq;
|
|
q >>= shift;
|
|
q += (q < 0);
|
|
return q;
|
|
}
|
|
}
|
|
|
|
int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
// must be arithmetic shift and then sign extend
|
|
int32_t sign = (int8_t)more >> 7;
|
|
int32_t magic = denom->magic;
|
|
int32_t q = libdivide_mullhi_s32(magic, numer);
|
|
q += numer;
|
|
|
|
// If q is non-negative, we have nothing to do
|
|
// If q is negative, we want to add either (2**shift)-1 if d is a power of
|
|
// 2, or (2**shift) if it is not a power of 2
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
uint32_t q_sign = (uint32_t)(q >> 31);
|
|
q += q_sign & ((1U << shift) - is_power_of_2);
|
|
|
|
// Now arithmetic right shift
|
|
q >>= shift;
|
|
// Negate if needed
|
|
q = (q ^ sign) - sign;
|
|
|
|
return q;
|
|
}
|
|
|
|
int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
if (!denom->magic) {
|
|
uint32_t absD = 1U << shift;
|
|
if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
|
|
absD = -absD;
|
|
}
|
|
return (int32_t)absD;
|
|
} else {
|
|
// Unsigned math is much easier
|
|
// We negate the magic number only in the branchfull case, and we don't
|
|
// know which case we're in. However we have enough information to
|
|
// determine the correct sign of the magic number. The divisor was
|
|
// negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set,
|
|
// the magic number's sign is opposite that of the divisor.
|
|
// We want to compute the positive magic number.
|
|
int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
|
|
int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
|
|
? denom->magic > 0 : denom->magic < 0;
|
|
|
|
// Handle the power of 2 case (including branchfree)
|
|
if (denom->magic == 0) {
|
|
int32_t result = 1U << shift;
|
|
return negative_divisor ? -result : result;
|
|
}
|
|
|
|
uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic);
|
|
uint64_t n = 1ULL << (32 + shift); // this shift cannot exceed 30
|
|
uint32_t q = (uint32_t)(n / d);
|
|
int32_t result = (int32_t)q;
|
|
result += 1;
|
|
return negative_divisor ? -result : result;
|
|
}
|
|
}
|
|
|
|
int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom) {
|
|
return libdivide_s32_recover((const struct libdivide_s32_t *)denom);
|
|
}
|
|
|
|
///////////// SINT64
|
|
|
|
static inline struct libdivide_s64_t libdivide_internal_s64_gen(int64_t d, int branchfree) {
|
|
if (d == 0) {
|
|
LIBDIVIDE_ERROR("divider must be != 0");
|
|
}
|
|
|
|
struct libdivide_s64_t result;
|
|
|
|
// If d is a power of 2, or negative a power of 2, we have to use a shift.
|
|
// This is especially important because the magic algorithm fails for -1.
|
|
// To check if d is a power of 2 or its inverse, it suffices to check
|
|
// whether its absolute value has exactly one bit set. This works even for
|
|
// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
|
|
// and is a power of 2.
|
|
uint64_t ud = (uint64_t)d;
|
|
uint64_t absD = (d < 0) ? -ud : ud;
|
|
uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(absD);
|
|
// check if exactly one bit is set,
|
|
// don't care if absD is 0 since that's divide by zero
|
|
if ((absD & (absD - 1)) == 0) {
|
|
// Branchfree and non-branchfree cases are the same
|
|
result.magic = 0;
|
|
result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
|
|
} else {
|
|
// the dividend here is 2**(floor_log_2_d + 63), so the low 64 bit word
|
|
// is 0 and the high word is floor_log_2_d - 1
|
|
uint8_t more;
|
|
uint64_t rem, proposed_m;
|
|
proposed_m = libdivide_128_div_64_to_64(1ULL << (floor_log_2_d - 1), 0, absD, &rem);
|
|
const uint64_t e = absD - rem;
|
|
|
|
// We are going to start with a power of floor_log_2_d - 1.
|
|
// This works if works if e < 2**floor_log_2_d.
|
|
if (!branchfree && e < (1ULL << floor_log_2_d)) {
|
|
// This power works
|
|
more = floor_log_2_d - 1;
|
|
} else {
|
|
// We need to go one higher. This should not make proposed_m
|
|
// overflow, but it will make it negative when interpreted as an
|
|
// int32_t.
|
|
proposed_m += proposed_m;
|
|
const uint64_t twice_rem = rem + rem;
|
|
if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
|
|
// note that we only set the LIBDIVIDE_NEGATIVE_DIVISOR bit if we
|
|
// also set ADD_MARKER this is an annoying optimization that
|
|
// enables algorithm #4 to avoid the mask. However we always set it
|
|
// in the branchfree case
|
|
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
|
|
}
|
|
proposed_m += 1;
|
|
int64_t magic = (int64_t)proposed_m;
|
|
|
|
// Mark if we are negative
|
|
if (d < 0) {
|
|
more |= LIBDIVIDE_NEGATIVE_DIVISOR;
|
|
if (!branchfree) {
|
|
magic = -magic;
|
|
}
|
|
}
|
|
|
|
result.more = more;
|
|
result.magic = magic;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
struct libdivide_s64_t libdivide_s64_gen(int64_t d) {
|
|
return libdivide_internal_s64_gen(d, 0);
|
|
}
|
|
|
|
struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d) {
|
|
struct libdivide_s64_t tmp = libdivide_internal_s64_gen(d, 1);
|
|
struct libdivide_s64_branchfree_t ret = {tmp.magic, tmp.more};
|
|
return ret;
|
|
}
|
|
|
|
int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
|
|
if (!denom->magic) { // shift path
|
|
uint64_t mask = (1ULL << shift) - 1;
|
|
uint64_t uq = numer + ((numer >> 63) & mask);
|
|
int64_t q = (int64_t)uq;
|
|
q >>= shift;
|
|
// must be arithmetic shift and then sign-extend
|
|
int64_t sign = (int8_t)more >> 7;
|
|
q = (q ^ sign) - sign;
|
|
return q;
|
|
} else {
|
|
uint64_t uq = (uint64_t)libdivide_mullhi_s64(denom->magic, numer);
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift and then sign extend
|
|
int64_t sign = (int8_t)more >> 7;
|
|
// q += (more < 0 ? -numer : numer)
|
|
// cast required to avoid UB
|
|
uq += ((uint64_t)numer ^ sign) - sign;
|
|
}
|
|
int64_t q = (int64_t)uq;
|
|
q >>= shift;
|
|
q += (q < 0);
|
|
return q;
|
|
}
|
|
}
|
|
|
|
int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
// must be arithmetic shift and then sign extend
|
|
int64_t sign = (int8_t)more >> 7;
|
|
int64_t magic = denom->magic;
|
|
int64_t q = libdivide_mullhi_s64(magic, numer);
|
|
q += numer;
|
|
|
|
// If q is non-negative, we have nothing to do.
|
|
// If q is negative, we want to add either (2**shift)-1 if d is a power of
|
|
// 2, or (2**shift) if it is not a power of 2.
|
|
uint64_t is_power_of_2 = (magic == 0);
|
|
uint64_t q_sign = (uint64_t)(q >> 63);
|
|
q += q_sign & ((1ULL << shift) - is_power_of_2);
|
|
|
|
// Arithmetic right shift
|
|
q >>= shift;
|
|
// Negate if needed
|
|
q = (q ^ sign) - sign;
|
|
|
|
return q;
|
|
}
|
|
|
|
int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
if (denom->magic == 0) { // shift path
|
|
uint64_t absD = 1ULL << shift;
|
|
if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
|
|
absD = -absD;
|
|
}
|
|
return (int64_t)absD;
|
|
} else {
|
|
// Unsigned math is much easier
|
|
int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
|
|
int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
|
|
? denom->magic > 0 : denom->magic < 0;
|
|
|
|
uint64_t d = (uint64_t)(magic_was_negated ? -denom->magic : denom->magic);
|
|
uint64_t n_hi = 1ULL << shift, n_lo = 0;
|
|
uint64_t rem_ignored;
|
|
uint64_t q = libdivide_128_div_64_to_64(n_hi, n_lo, d, &rem_ignored);
|
|
int64_t result = (int64_t)(q + 1);
|
|
if (negative_divisor) {
|
|
result = -result;
|
|
}
|
|
return result;
|
|
}
|
|
}
|
|
|
|
int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom) {
|
|
return libdivide_s64_recover((const struct libdivide_s64_t *)denom);
|
|
}
|
|
|
|
#if defined(LIBDIVIDE_AVX512)
|
|
|
|
static inline __m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom);
|
|
static inline __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom);
|
|
static inline __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom);
|
|
static inline __m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom);
|
|
|
|
static inline __m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom);
|
|
static inline __m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom);
|
|
static inline __m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom);
|
|
static inline __m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom);
|
|
|
|
//////// Internal Utility Functions
|
|
|
|
static inline __m512i libdivide_s64_signbits(__m512i v) {;
|
|
return _mm512_srai_epi64(v, 63);
|
|
}
|
|
|
|
static inline __m512i libdivide_s64_shift_right_vector(__m512i v, int amt) {
|
|
return _mm512_srai_epi64(v, amt);
|
|
}
|
|
|
|
// Here, b is assumed to contain one 32-bit value repeated.
|
|
static inline __m512i libdivide_mullhi_u32_vector(__m512i a, __m512i b) {
|
|
__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epu32(a, b), 32);
|
|
__m512i a1X3X = _mm512_srli_epi64(a, 32);
|
|
__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
|
|
__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epu32(a1X3X, b), mask);
|
|
return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
|
|
}
|
|
|
|
// b is one 32-bit value repeated.
|
|
static inline __m512i libdivide_mullhi_s32_vector(__m512i a, __m512i b) {
|
|
__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epi32(a, b), 32);
|
|
__m512i a1X3X = _mm512_srli_epi64(a, 32);
|
|
__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
|
|
__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epi32(a1X3X, b), mask);
|
|
return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
|
|
}
|
|
|
|
// Here, y is assumed to contain one 64-bit value repeated.
|
|
// https://stackoverflow.com/a/28827013
|
|
static inline __m512i libdivide_mullhi_u64_vector(__m512i x, __m512i y) {
|
|
__m512i lomask = _mm512_set1_epi64(0xffffffff);
|
|
__m512i xh = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM) 0xB1);
|
|
__m512i yh = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM) 0xB1);
|
|
__m512i w0 = _mm512_mul_epu32(x, y);
|
|
__m512i w1 = _mm512_mul_epu32(x, yh);
|
|
__m512i w2 = _mm512_mul_epu32(xh, y);
|
|
__m512i w3 = _mm512_mul_epu32(xh, yh);
|
|
__m512i w0h = _mm512_srli_epi64(w0, 32);
|
|
__m512i s1 = _mm512_add_epi64(w1, w0h);
|
|
__m512i s1l = _mm512_and_si512(s1, lomask);
|
|
__m512i s1h = _mm512_srli_epi64(s1, 32);
|
|
__m512i s2 = _mm512_add_epi64(w2, s1l);
|
|
__m512i s2h = _mm512_srli_epi64(s2, 32);
|
|
__m512i hi = _mm512_add_epi64(w3, s1h);
|
|
hi = _mm512_add_epi64(hi, s2h);
|
|
|
|
return hi;
|
|
}
|
|
|
|
// y is one 64-bit value repeated.
|
|
static inline __m512i libdivide_mullhi_s64_vector(__m512i x, __m512i y) {
|
|
__m512i p = libdivide_mullhi_u64_vector(x, y);
|
|
__m512i t1 = _mm512_and_si512(libdivide_s64_signbits(x), y);
|
|
__m512i t2 = _mm512_and_si512(libdivide_s64_signbits(y), x);
|
|
p = _mm512_sub_epi64(p, t1);
|
|
p = _mm512_sub_epi64(p, t2);
|
|
return p;
|
|
}
|
|
|
|
////////// UINT32
|
|
|
|
__m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm512_srli_epi32(numers, more);
|
|
}
|
|
else {
|
|
__m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
|
|
return _mm512_srli_epi32(t, shift);
|
|
}
|
|
else {
|
|
return _mm512_srli_epi32(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom) {
|
|
__m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
|
|
__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
|
|
return _mm512_srli_epi32(t, denom->more);
|
|
}
|
|
|
|
////////// UINT64
|
|
|
|
__m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm512_srli_epi64(numers, more);
|
|
}
|
|
else {
|
|
__m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
|
|
return _mm512_srli_epi64(t, shift);
|
|
}
|
|
else {
|
|
return _mm512_srli_epi64(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom) {
|
|
__m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
|
|
__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
|
|
return _mm512_srli_epi64(t, denom->more);
|
|
}
|
|
|
|
////////// SINT32
|
|
|
|
__m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
uint32_t mask = (1U << shift) - 1;
|
|
__m512i roundToZeroTweak = _mm512_set1_epi32(mask);
|
|
// q = numer + ((numer >> 31) & roundToZeroTweak);
|
|
__m512i q = _mm512_add_epi32(numers, _mm512_and_si512(_mm512_srai_epi32(numers, 31), roundToZeroTweak));
|
|
q = _mm512_srai_epi32(q, shift);
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm512_add_epi32(q, _mm512_sub_epi32(_mm512_xor_si512(numers, sign), sign));
|
|
}
|
|
// q >>= shift
|
|
q = _mm512_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
|
|
q = _mm512_add_epi32(q, _mm512_srli_epi32(q, 31)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom) {
|
|
int32_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
__m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(magic));
|
|
q = _mm512_add_epi32(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m512i q_sign = _mm512_srai_epi32(q, 31); // q_sign = q >> 31
|
|
__m512i mask = _mm512_set1_epi32((1U << shift) - is_power_of_2);
|
|
q = _mm512_add_epi32(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
|
|
q = _mm512_srai_epi32(q, shift); // q >>= shift
|
|
q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
|
|
return q;
|
|
}
|
|
|
|
////////// SINT64
|
|
|
|
__m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
int64_t magic = denom->magic;
|
|
if (magic == 0) { // shift path
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
uint64_t mask = (1ULL << shift) - 1;
|
|
__m512i roundToZeroTweak = _mm512_set1_epi64(mask);
|
|
// q = numer + ((numer >> 63) & roundToZeroTweak);
|
|
__m512i q = _mm512_add_epi64(numers, _mm512_and_si512(libdivide_s64_signbits(numers), roundToZeroTweak));
|
|
q = libdivide_s64_shift_right_vector(q, shift);
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm512_add_epi64(q, _mm512_sub_epi64(_mm512_xor_si512(numers, sign), sign));
|
|
}
|
|
// q >>= denom->mult_path.shift
|
|
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
|
|
q = _mm512_add_epi64(q, _mm512_srli_epi64(q, 63)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom) {
|
|
int64_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
|
|
|
|
// libdivide_mullhi_s64(numers, magic);
|
|
__m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
|
|
q = _mm512_add_epi64(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do.
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2.
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m512i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
|
|
__m512i mask = _mm512_set1_epi64((1ULL << shift) - is_power_of_2);
|
|
q = _mm512_add_epi64(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
|
|
q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
|
|
q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
|
|
return q;
|
|
}
|
|
|
|
#elif defined(LIBDIVIDE_AVX2)
|
|
|
|
static inline __m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom);
|
|
static inline __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom);
|
|
static inline __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom);
|
|
static inline __m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom);
|
|
|
|
static inline __m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom);
|
|
static inline __m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom);
|
|
static inline __m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom);
|
|
static inline __m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom);
|
|
|
|
//////// Internal Utility Functions
|
|
|
|
// Implementation of _mm256_srai_epi64(v, 63) (from AVX512).
|
|
static inline __m256i libdivide_s64_signbits(__m256i v) {
|
|
__m256i hiBitsDuped = _mm256_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
|
|
__m256i signBits = _mm256_srai_epi32(hiBitsDuped, 31);
|
|
return signBits;
|
|
}
|
|
|
|
// Implementation of _mm256_srai_epi64 (from AVX512).
|
|
static inline __m256i libdivide_s64_shift_right_vector(__m256i v, int amt) {
|
|
const int b = 64 - amt;
|
|
__m256i m = _mm256_set1_epi64x(1ULL << (b - 1));
|
|
__m256i x = _mm256_srli_epi64(v, amt);
|
|
__m256i result = _mm256_sub_epi64(_mm256_xor_si256(x, m), m);
|
|
return result;
|
|
}
|
|
|
|
// Here, b is assumed to contain one 32-bit value repeated.
|
|
static inline __m256i libdivide_mullhi_u32_vector(__m256i a, __m256i b) {
|
|
__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epu32(a, b), 32);
|
|
__m256i a1X3X = _mm256_srli_epi64(a, 32);
|
|
__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
|
|
__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epu32(a1X3X, b), mask);
|
|
return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
|
|
}
|
|
|
|
// b is one 32-bit value repeated.
|
|
static inline __m256i libdivide_mullhi_s32_vector(__m256i a, __m256i b) {
|
|
__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epi32(a, b), 32);
|
|
__m256i a1X3X = _mm256_srli_epi64(a, 32);
|
|
__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
|
|
__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epi32(a1X3X, b), mask);
|
|
return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
|
|
}
|
|
|
|
// Here, y is assumed to contain one 64-bit value repeated.
|
|
// https://stackoverflow.com/a/28827013
|
|
static inline __m256i libdivide_mullhi_u64_vector(__m256i x, __m256i y) {
|
|
__m256i lomask = _mm256_set1_epi64x(0xffffffff);
|
|
__m256i xh = _mm256_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h
|
|
__m256i yh = _mm256_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h
|
|
__m256i w0 = _mm256_mul_epu32(x, y); // x0l*y0l, x1l*y1l
|
|
__m256i w1 = _mm256_mul_epu32(x, yh); // x0l*y0h, x1l*y1h
|
|
__m256i w2 = _mm256_mul_epu32(xh, y); // x0h*y0l, x1h*y0l
|
|
__m256i w3 = _mm256_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h
|
|
__m256i w0h = _mm256_srli_epi64(w0, 32);
|
|
__m256i s1 = _mm256_add_epi64(w1, w0h);
|
|
__m256i s1l = _mm256_and_si256(s1, lomask);
|
|
__m256i s1h = _mm256_srli_epi64(s1, 32);
|
|
__m256i s2 = _mm256_add_epi64(w2, s1l);
|
|
__m256i s2h = _mm256_srli_epi64(s2, 32);
|
|
__m256i hi = _mm256_add_epi64(w3, s1h);
|
|
hi = _mm256_add_epi64(hi, s2h);
|
|
|
|
return hi;
|
|
}
|
|
|
|
// y is one 64-bit value repeated.
|
|
static inline __m256i libdivide_mullhi_s64_vector(__m256i x, __m256i y) {
|
|
__m256i p = libdivide_mullhi_u64_vector(x, y);
|
|
__m256i t1 = _mm256_and_si256(libdivide_s64_signbits(x), y);
|
|
__m256i t2 = _mm256_and_si256(libdivide_s64_signbits(y), x);
|
|
p = _mm256_sub_epi64(p, t1);
|
|
p = _mm256_sub_epi64(p, t2);
|
|
return p;
|
|
}
|
|
|
|
////////// UINT32
|
|
|
|
__m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm256_srli_epi32(numers, more);
|
|
}
|
|
else {
|
|
__m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
|
|
return _mm256_srli_epi32(t, shift);
|
|
}
|
|
else {
|
|
return _mm256_srli_epi32(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom) {
|
|
__m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
|
|
__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
|
|
return _mm256_srli_epi32(t, denom->more);
|
|
}
|
|
|
|
////////// UINT64
|
|
|
|
__m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm256_srli_epi64(numers, more);
|
|
}
|
|
else {
|
|
__m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
|
|
return _mm256_srli_epi64(t, shift);
|
|
}
|
|
else {
|
|
return _mm256_srli_epi64(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom) {
|
|
__m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
|
|
__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
|
|
return _mm256_srli_epi64(t, denom->more);
|
|
}
|
|
|
|
////////// SINT32
|
|
|
|
__m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
uint32_t mask = (1U << shift) - 1;
|
|
__m256i roundToZeroTweak = _mm256_set1_epi32(mask);
|
|
// q = numer + ((numer >> 31) & roundToZeroTweak);
|
|
__m256i q = _mm256_add_epi32(numers, _mm256_and_si256(_mm256_srai_epi32(numers, 31), roundToZeroTweak));
|
|
q = _mm256_srai_epi32(q, shift);
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm256_add_epi32(q, _mm256_sub_epi32(_mm256_xor_si256(numers, sign), sign));
|
|
}
|
|
// q >>= shift
|
|
q = _mm256_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
|
|
q = _mm256_add_epi32(q, _mm256_srli_epi32(q, 31)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom) {
|
|
int32_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
__m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(magic));
|
|
q = _mm256_add_epi32(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m256i q_sign = _mm256_srai_epi32(q, 31); // q_sign = q >> 31
|
|
__m256i mask = _mm256_set1_epi32((1U << shift) - is_power_of_2);
|
|
q = _mm256_add_epi32(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
|
|
q = _mm256_srai_epi32(q, shift); // q >>= shift
|
|
q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
|
|
return q;
|
|
}
|
|
|
|
////////// SINT64
|
|
|
|
__m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
int64_t magic = denom->magic;
|
|
if (magic == 0) { // shift path
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
uint64_t mask = (1ULL << shift) - 1;
|
|
__m256i roundToZeroTweak = _mm256_set1_epi64x(mask);
|
|
// q = numer + ((numer >> 63) & roundToZeroTweak);
|
|
__m256i q = _mm256_add_epi64(numers, _mm256_and_si256(libdivide_s64_signbits(numers), roundToZeroTweak));
|
|
q = libdivide_s64_shift_right_vector(q, shift);
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm256_add_epi64(q, _mm256_sub_epi64(_mm256_xor_si256(numers, sign), sign));
|
|
}
|
|
// q >>= denom->mult_path.shift
|
|
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
|
|
q = _mm256_add_epi64(q, _mm256_srli_epi64(q, 63)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom) {
|
|
int64_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
|
|
|
|
// libdivide_mullhi_s64(numers, magic);
|
|
__m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
|
|
q = _mm256_add_epi64(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do.
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2.
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m256i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
|
|
__m256i mask = _mm256_set1_epi64x((1ULL << shift) - is_power_of_2);
|
|
q = _mm256_add_epi64(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
|
|
q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
|
|
q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
|
|
return q;
|
|
}
|
|
|
|
#elif defined(LIBDIVIDE_SSE2)
|
|
|
|
static inline __m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom);
|
|
static inline __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom);
|
|
static inline __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom);
|
|
static inline __m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom);
|
|
|
|
static inline __m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom);
|
|
static inline __m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom);
|
|
static inline __m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom);
|
|
static inline __m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom);
|
|
|
|
//////// Internal Utility Functions
|
|
|
|
// Implementation of _mm_srai_epi64(v, 63) (from AVX512).
|
|
static inline __m128i libdivide_s64_signbits(__m128i v) {
|
|
__m128i hiBitsDuped = _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
|
|
__m128i signBits = _mm_srai_epi32(hiBitsDuped, 31);
|
|
return signBits;
|
|
}
|
|
|
|
// Implementation of _mm_srai_epi64 (from AVX512).
|
|
static inline __m128i libdivide_s64_shift_right_vector(__m128i v, int amt) {
|
|
const int b = 64 - amt;
|
|
__m128i m = _mm_set1_epi64x(1ULL << (b - 1));
|
|
__m128i x = _mm_srli_epi64(v, amt);
|
|
__m128i result = _mm_sub_epi64(_mm_xor_si128(x, m), m);
|
|
return result;
|
|
}
|
|
|
|
// Here, b is assumed to contain one 32-bit value repeated.
|
|
static inline __m128i libdivide_mullhi_u32_vector(__m128i a, __m128i b) {
|
|
__m128i hi_product_0Z2Z = _mm_srli_epi64(_mm_mul_epu32(a, b), 32);
|
|
__m128i a1X3X = _mm_srli_epi64(a, 32);
|
|
__m128i mask = _mm_set_epi32(-1, 0, -1, 0);
|
|
__m128i hi_product_Z1Z3 = _mm_and_si128(_mm_mul_epu32(a1X3X, b), mask);
|
|
return _mm_or_si128(hi_product_0Z2Z, hi_product_Z1Z3);
|
|
}
|
|
|
|
// SSE2 does not have a signed multiplication instruction, but we can convert
|
|
// unsigned to signed pretty efficiently. Again, b is just a 32 bit value
|
|
// repeated four times.
|
|
static inline __m128i libdivide_mullhi_s32_vector(__m128i a, __m128i b) {
|
|
__m128i p = libdivide_mullhi_u32_vector(a, b);
|
|
// t1 = (a >> 31) & y, arithmetic shift
|
|
__m128i t1 = _mm_and_si128(_mm_srai_epi32(a, 31), b);
|
|
__m128i t2 = _mm_and_si128(_mm_srai_epi32(b, 31), a);
|
|
p = _mm_sub_epi32(p, t1);
|
|
p = _mm_sub_epi32(p, t2);
|
|
return p;
|
|
}
|
|
|
|
// Here, y is assumed to contain one 64-bit value repeated.
|
|
// https://stackoverflow.com/a/28827013
|
|
static inline __m128i libdivide_mullhi_u64_vector(__m128i x, __m128i y) {
|
|
__m128i lomask = _mm_set1_epi64x(0xffffffff);
|
|
__m128i xh = _mm_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h
|
|
__m128i yh = _mm_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h
|
|
__m128i w0 = _mm_mul_epu32(x, y); // x0l*y0l, x1l*y1l
|
|
__m128i w1 = _mm_mul_epu32(x, yh); // x0l*y0h, x1l*y1h
|
|
__m128i w2 = _mm_mul_epu32(xh, y); // x0h*y0l, x1h*y0l
|
|
__m128i w3 = _mm_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h
|
|
__m128i w0h = _mm_srli_epi64(w0, 32);
|
|
__m128i s1 = _mm_add_epi64(w1, w0h);
|
|
__m128i s1l = _mm_and_si128(s1, lomask);
|
|
__m128i s1h = _mm_srli_epi64(s1, 32);
|
|
__m128i s2 = _mm_add_epi64(w2, s1l);
|
|
__m128i s2h = _mm_srli_epi64(s2, 32);
|
|
__m128i hi = _mm_add_epi64(w3, s1h);
|
|
hi = _mm_add_epi64(hi, s2h);
|
|
|
|
return hi;
|
|
}
|
|
|
|
// y is one 64-bit value repeated.
|
|
static inline __m128i libdivide_mullhi_s64_vector(__m128i x, __m128i y) {
|
|
__m128i p = libdivide_mullhi_u64_vector(x, y);
|
|
__m128i t1 = _mm_and_si128(libdivide_s64_signbits(x), y);
|
|
__m128i t2 = _mm_and_si128(libdivide_s64_signbits(y), x);
|
|
p = _mm_sub_epi64(p, t1);
|
|
p = _mm_sub_epi64(p, t2);
|
|
return p;
|
|
}
|
|
|
|
////////// UINT32
|
|
|
|
__m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm_srli_epi32(numers, more);
|
|
}
|
|
else {
|
|
__m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
|
|
return _mm_srli_epi32(t, shift);
|
|
}
|
|
else {
|
|
return _mm_srli_epi32(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom) {
|
|
__m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
|
|
__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
|
|
return _mm_srli_epi32(t, denom->more);
|
|
}
|
|
|
|
////////// UINT64
|
|
|
|
__m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
return _mm_srli_epi64(numers, more);
|
|
}
|
|
else {
|
|
__m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// uint32_t t = ((numer - q) >> 1) + q;
|
|
// return t >> denom->shift;
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
|
|
return _mm_srli_epi64(t, shift);
|
|
}
|
|
else {
|
|
return _mm_srli_epi64(q, more);
|
|
}
|
|
}
|
|
}
|
|
|
|
__m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom) {
|
|
__m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
|
|
__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
|
|
return _mm_srli_epi64(t, denom->more);
|
|
}
|
|
|
|
////////// SINT32
|
|
|
|
__m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom) {
|
|
uint8_t more = denom->more;
|
|
if (!denom->magic) {
|
|
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
uint32_t mask = (1U << shift) - 1;
|
|
__m128i roundToZeroTweak = _mm_set1_epi32(mask);
|
|
// q = numer + ((numer >> 31) & roundToZeroTweak);
|
|
__m128i q = _mm_add_epi32(numers, _mm_and_si128(_mm_srai_epi32(numers, 31), roundToZeroTweak));
|
|
q = _mm_srai_epi32(q, shift);
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(denom->magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm_add_epi32(q, _mm_sub_epi32(_mm_xor_si128(numers, sign), sign));
|
|
}
|
|
// q >>= shift
|
|
q = _mm_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
|
|
q = _mm_add_epi32(q, _mm_srli_epi32(q, 31)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom) {
|
|
int32_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
__m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(magic));
|
|
q = _mm_add_epi32(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m128i q_sign = _mm_srai_epi32(q, 31); // q_sign = q >> 31
|
|
__m128i mask = _mm_set1_epi32((1U << shift) - is_power_of_2);
|
|
q = _mm_add_epi32(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
|
|
q = _mm_srai_epi32(q, shift); // q >>= shift
|
|
q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
|
|
return q;
|
|
}
|
|
|
|
////////// SINT64
|
|
|
|
__m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom) {
|
|
uint8_t more = denom->more;
|
|
int64_t magic = denom->magic;
|
|
if (magic == 0) { // shift path
|
|
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
uint64_t mask = (1ULL << shift) - 1;
|
|
__m128i roundToZeroTweak = _mm_set1_epi64x(mask);
|
|
// q = numer + ((numer >> 63) & roundToZeroTweak);
|
|
__m128i q = _mm_add_epi64(numers, _mm_and_si128(libdivide_s64_signbits(numers), roundToZeroTweak));
|
|
q = libdivide_s64_shift_right_vector(q, shift);
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
// q = (q ^ sign) - sign;
|
|
q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign);
|
|
return q;
|
|
}
|
|
else {
|
|
__m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
|
|
if (more & LIBDIVIDE_ADD_MARKER) {
|
|
// must be arithmetic shift
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
// q += ((numer ^ sign) - sign);
|
|
q = _mm_add_epi64(q, _mm_sub_epi64(_mm_xor_si128(numers, sign), sign));
|
|
}
|
|
// q >>= denom->mult_path.shift
|
|
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
|
|
q = _mm_add_epi64(q, _mm_srli_epi64(q, 63)); // q += (q < 0)
|
|
return q;
|
|
}
|
|
}
|
|
|
|
__m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom) {
|
|
int64_t magic = denom->magic;
|
|
uint8_t more = denom->more;
|
|
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
|
|
// must be arithmetic shift
|
|
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
|
|
|
|
// libdivide_mullhi_s64(numers, magic);
|
|
__m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
|
|
q = _mm_add_epi64(q, numers); // q += numers
|
|
|
|
// If q is non-negative, we have nothing to do.
|
|
// If q is negative, we want to add either (2**shift)-1 if d is
|
|
// a power of 2, or (2**shift) if it is not a power of 2.
|
|
uint32_t is_power_of_2 = (magic == 0);
|
|
__m128i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
|
|
__m128i mask = _mm_set1_epi64x((1ULL << shift) - is_power_of_2);
|
|
q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
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q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
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q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
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return q;
|
|
}
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|
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#endif
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/////////// C++ stuff
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|
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#ifdef __cplusplus
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|
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// The C++ divider class is templated on both an integer type
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// (like uint64_t) and an algorithm type.
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|
// * BRANCHFULL is the default algorithm type.
|
|
// * BRANCHFREE is the branchfree algorithm type.
|
|
enum {
|
|
BRANCHFULL,
|
|
BRANCHFREE
|
|
};
|
|
|
|
#if defined(LIBDIVIDE_AVX512)
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|
#define LIBDIVIDE_VECTOR_TYPE __m512i
|
|
#elif defined(LIBDIVIDE_AVX2)
|
|
#define LIBDIVIDE_VECTOR_TYPE __m256i
|
|
#elif defined(LIBDIVIDE_SSE2)
|
|
#define LIBDIVIDE_VECTOR_TYPE __m128i
|
|
#endif
|
|
|
|
#if !defined(LIBDIVIDE_VECTOR_TYPE)
|
|
#define LIBDIVIDE_DIVIDE_VECTOR(ALGO)
|
|
#else
|
|
#define LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
|
|
LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const { \
|
|
return libdivide_##ALGO##_do_vector(n, &denom); \
|
|
}
|
|
#endif
|
|
|
|
// The DISPATCHER_GEN() macro generates C++ methods (for the given integer
|
|
// and algorithm types) that redirect to libdivide's C API.
|
|
#define DISPATCHER_GEN(T, ALGO) \
|
|
libdivide_##ALGO##_t denom; \
|
|
dispatcher() { } \
|
|
dispatcher(T d) \
|
|
: denom(libdivide_##ALGO##_gen(d)) \
|
|
{ } \
|
|
T divide(T n) const { \
|
|
return libdivide_##ALGO##_do(n, &denom); \
|
|
} \
|
|
LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
|
|
T recover() const { \
|
|
return libdivide_##ALGO##_recover(&denom); \
|
|
}
|
|
|
|
// The dispatcher selects a specific division algorithm for a given
|
|
// type and ALGO using partial template specialization.
|
|
template<typename T, int ALGO> struct dispatcher { };
|
|
|
|
template<> struct dispatcher<int32_t, BRANCHFULL> { DISPATCHER_GEN(int32_t, s32) };
|
|
template<> struct dispatcher<int32_t, BRANCHFREE> { DISPATCHER_GEN(int32_t, s32_branchfree) };
|
|
template<> struct dispatcher<uint32_t, BRANCHFULL> { DISPATCHER_GEN(uint32_t, u32) };
|
|
template<> struct dispatcher<uint32_t, BRANCHFREE> { DISPATCHER_GEN(uint32_t, u32_branchfree) };
|
|
template<> struct dispatcher<int64_t, BRANCHFULL> { DISPATCHER_GEN(int64_t, s64) };
|
|
template<> struct dispatcher<int64_t, BRANCHFREE> { DISPATCHER_GEN(int64_t, s64_branchfree) };
|
|
template<> struct dispatcher<uint64_t, BRANCHFULL> { DISPATCHER_GEN(uint64_t, u64) };
|
|
template<> struct dispatcher<uint64_t, BRANCHFREE> { DISPATCHER_GEN(uint64_t, u64_branchfree) };
|
|
|
|
// This is the main divider class for use by the user (C++ API).
|
|
// The actual division algorithm is selected using the dispatcher struct
|
|
// based on the integer and algorithm template parameters.
|
|
template<typename T, int ALGO = BRANCHFULL>
|
|
class divider {
|
|
public:
|
|
// We leave the default constructor empty so that creating
|
|
// an array of dividers and then initializing them
|
|
// later doesn't slow us down.
|
|
divider() { }
|
|
|
|
// Constructor that takes the divisor as a parameter
|
|
divider(T d) : div(d) { }
|
|
|
|
// Divides n by the divisor
|
|
T divide(T n) const {
|
|
return div.divide(n);
|
|
}
|
|
|
|
// Recovers the divisor, returns the value that was
|
|
// used to initialize this divider object.
|
|
T recover() const {
|
|
return div.recover();
|
|
}
|
|
|
|
bool operator==(const divider<T, ALGO>& other) const {
|
|
return div.denom.magic == other.denom.magic &&
|
|
div.denom.more == other.denom.more;
|
|
}
|
|
|
|
bool operator!=(const divider<T, ALGO>& other) const {
|
|
return !(*this == other);
|
|
}
|
|
|
|
#if defined(LIBDIVIDE_VECTOR_TYPE)
|
|
// Treats the vector as packed integer values with the same type as
|
|
// the divider (e.g. s32, u32, s64, u64) and divides each of
|
|
// them by the divider, returning the packed quotients.
|
|
LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const {
|
|
return div.divide(n);
|
|
}
|
|
#endif
|
|
private:
|
|
// Storage for the actual divisor
|
|
dispatcher<T, ALGO> div;
|
|
};
|
|
|
|
// Overload of operator / for scalar division
|
|
template<typename T, int ALGO>
|
|
T operator/(T n, const divider<T, ALGO>& div) {
|
|
return div.divide(n);
|
|
}
|
|
|
|
// Overload of operator /= for scalar division
|
|
template<typename T, int ALGO>
|
|
T& operator/=(T& n, const divider<T, ALGO>& div) {
|
|
n = div.divide(n);
|
|
return n;
|
|
}
|
|
|
|
#if defined(LIBDIVIDE_VECTOR_TYPE)
|
|
// Overload of operator / for vector division
|
|
template<typename T, int ALGO>
|
|
LIBDIVIDE_VECTOR_TYPE operator/(LIBDIVIDE_VECTOR_TYPE n, const divider<T, ALGO>& div) {
|
|
return div.divide(n);
|
|
}
|
|
// Overload of operator /= for vector division
|
|
template<typename T, int ALGO>
|
|
LIBDIVIDE_VECTOR_TYPE& operator/=(LIBDIVIDE_VECTOR_TYPE& n, const divider<T, ALGO>& div) {
|
|
n = div.divide(n);
|
|
return n;
|
|
}
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L || \
|
|
(defined(_MSC_VER) && _MSC_VER >= 1800)
|
|
// libdivdie::branchfree_divider<T>
|
|
template <typename T>
|
|
using branchfree_divider = divider<T, BRANCHFREE>;
|
|
#endif
|
|
|
|
} // namespace libdivide
|
|
|
|
#endif // __cplusplus
|
|
|
|
#endif // LIBDIVIDE_H
|