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libdivide runtime cache
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fastdiv.cpp
// libdivide.h - Optimized integer division
// https://libdivide.com
//
// Copyright (C) 2010 - 2021 ridiculous_fish, <[email protected]>
// Copyright (C) 2016 - 2021 Kim Walisch, <[email protected]>
//
// libdivide is dual-licensed under the Boost or zlib licenses.
// You may use libdivide under the terms of either of these.
// See LICENSE.txt for more details.
#ifndef LIBDIVIDE_H
#define LIBDIVIDE_H
#define LIBDIVIDE_VERSION "5.0"
#define LIBDIVIDE_VERSION_MAJOR 5
#define LIBDIVIDE_VERSION_MINOR 0
#include <stdint.h>
#if !defined(__AVR__)
#include <stdio.h>
#include <stdlib.h>
#endif
#if defined(LIBDIVIDE_SSE2)
#include <emmintrin.h>
#endif
#if defined(LIBDIVIDE_AVX2) || defined(LIBDIVIDE_AVX512)
#include <immintrin.h>
#endif
#if defined(LIBDIVIDE_NEON)
#include <arm_neon.h>
#endif
#if defined(_MSC_VER)
#include <intrin.h>
#pragma warning(push)
// disable warning C4146: unary minus operator applied
// to unsigned type, result still unsigned
#pragma warning(disable : 4146)
// disable warning C4204: nonstandard extension used : non-constant aggregate
// initializer
//
// It's valid C99
#pragma warning(disable : 4204)
#define LIBDIVIDE_VC
#endif
#if !defined(__has_builtin)
#define __has_builtin(x) 0
#endif
#if defined(__SIZEOF_INT128__)
#define HAS_INT128_T
// clang-cl on Windows does not yet support 128-bit division
#if !(defined(__clang__) && defined(LIBDIVIDE_VC))
#define HAS_INT128_DIV
#endif
#endif
#if defined(__x86_64__) || defined(_M_X64)
#define LIBDIVIDE_X86_64
#endif
#if defined(__i386__)
#define LIBDIVIDE_i386
#endif
#if defined(__GNUC__) || defined(__clang__)
#define LIBDIVIDE_GCC_STYLE_ASM
#endif
#if defined(__cplusplus) || defined(LIBDIVIDE_VC)
#define LIBDIVIDE_FUNCTION __FUNCTION__
#else
#define LIBDIVIDE_FUNCTION __func__
#endif
// Set up forced inlining if possible.
// We need both the attribute and keyword to avoid "might not be inlineable" warnings.
#ifdef __has_attribute
#if __has_attribute(always_inline)
#define LIBDIVIDE_INLINE __attribute__((always_inline)) inline
#endif
#endif
#ifndef LIBDIVIDE_INLINE
#define LIBDIVIDE_INLINE inline
#endif
#if defined(__AVR__)
#define LIBDIVIDE_ERROR(msg)
#else
#define LIBDIVIDE_ERROR(msg) \
do { \
fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", __LINE__, LIBDIVIDE_FUNCTION, msg); \
abort(); \
} while (0)
#endif
#if defined(LIBDIVIDE_ASSERTIONS_ON) && !defined(__AVR__)
#define LIBDIVIDE_ASSERT(x) \
do { \
if (!(x)) { \
fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", __LINE__, \
LIBDIVIDE_FUNCTION, #x); \
abort(); \
} \
} while (0)
#else
#define LIBDIVIDE_ASSERT(x)
#endif
#ifdef __cplusplus
namespace libdivide {
#endif
// pack divider structs to prevent compilers from padding.
// This reduces memory usage by up to 43% when using a large
// array of libdivide dividers and improves performance
// by up to 10% because of reduced memory bandwidth.
#pragma pack(push, 1)
struct libdivide_u16_t {
uint16_t magic;
uint8_t more;
};
struct libdivide_s16_t {
int16_t magic;
uint8_t more;
};
struct libdivide_u32_t {
uint32_t magic;
uint8_t more;
};
struct libdivide_s32_t {
int32_t magic;
uint8_t more;
};
struct libdivide_u64_t {
uint64_t magic;
uint8_t more;
};
struct libdivide_s64_t {
int64_t magic;
uint8_t more;
};
struct libdivide_u16_branchfree_t {
uint16_t magic;
uint8_t more;
};
struct libdivide_s16_branchfree_t {
int16_t magic;
uint8_t more;
};
struct libdivide_u32_branchfree_t {
uint32_t magic;
uint8_t more;
};
struct libdivide_s32_branchfree_t {
int32_t magic;
uint8_t more;
};
struct libdivide_u64_branchfree_t {
uint64_t magic;
uint8_t more;
};
struct libdivide_s64_branchfree_t {
int64_t magic;
uint8_t more;
};
#pragma pack(pop)
// Explanation of the "more" field:
//
// * Bits 0-5 is the shift value (for shift path or mult path).
// * Bit 6 is the add indicator for mult path.
// * Bit 7 is set if the divisor is negative. We use bit 7 as the negative
// divisor indicator so that we can efficiently use sign extension to
// create a bitmask with all bits set to 1 (if the divisor is negative)
// or 0 (if the divisor is positive).
//
// u32: [0-4] shift value
// [5] ignored
// [6] add indicator
// magic number of 0 indicates shift path
//
// s32: [0-4] shift value
// [5] ignored
// [6] add indicator
// [7] indicates negative divisor
// magic number of 0 indicates shift path
//
// u64: [0-5] shift value
// [6] add indicator
// magic number of 0 indicates shift path
//
// s64: [0-5] shift value
// [6] add indicator
// [7] indicates negative divisor
// magic number of 0 indicates shift path
//
// In s32 and s64 branchfree modes, the magic number is negated according to
// whether the divisor is negated. In branchfree strategy, it is not negated.
enum {
LIBDIVIDE_16_SHIFT_MASK = 0x1F,
LIBDIVIDE_32_SHIFT_MASK = 0x1F,
LIBDIVIDE_64_SHIFT_MASK = 0x3F,
LIBDIVIDE_ADD_MARKER = 0x40,
LIBDIVIDE_NEGATIVE_DIVISOR = 0x80
};
static LIBDIVIDE_INLINE struct libdivide_s16_t libdivide_s16_gen(int16_t d);
static LIBDIVIDE_INLINE struct libdivide_u16_t libdivide_u16_gen(uint16_t d);
static LIBDIVIDE_INLINE struct libdivide_s32_t libdivide_s32_gen(int32_t d);
static LIBDIVIDE_INLINE struct libdivide_u32_t libdivide_u32_gen(uint32_t d);
static LIBDIVIDE_INLINE struct libdivide_s64_t libdivide_s64_gen(int64_t d);
static LIBDIVIDE_INLINE struct libdivide_u64_t libdivide_u64_gen(uint64_t d);
static LIBDIVIDE_INLINE struct libdivide_s16_branchfree_t libdivide_s16_branchfree_gen(int16_t d);
static LIBDIVIDE_INLINE struct libdivide_u16_branchfree_t libdivide_u16_branchfree_gen(uint16_t d);
static LIBDIVIDE_INLINE struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d);
static LIBDIVIDE_INLINE struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d);
static LIBDIVIDE_INLINE struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d);
static LIBDIVIDE_INLINE struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d);
static LIBDIVIDE_INLINE int16_t libdivide_s16_do_raw(
int16_t numer, int16_t magic, uint8_t more);
static LIBDIVIDE_INLINE int16_t libdivide_s16_do(
int16_t numer, const struct libdivide_s16_t* denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_do_raw(
uint16_t numer, uint16_t magic, uint8_t more);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_do(
uint16_t numer, const struct libdivide_u16_t* denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_do(
int32_t numer, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_do(
uint32_t numer, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_do(
int64_t numer, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_do(
uint64_t numer, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE int16_t libdivide_s16_branchfree_do(
int16_t numer, const struct libdivide_s16_branchfree_t* denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_branchfree_do(
uint16_t numer, const struct libdivide_u16_branchfree_t* denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_branchfree_do(
int32_t numer, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_branchfree_do(
uint32_t numer, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_branchfree_do(
int64_t numer, const struct libdivide_s64_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_branchfree_do(
uint64_t numer, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE int16_t libdivide_s16_recover(const struct libdivide_s16_t* denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_recover(const struct libdivide_u16_t* denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE int16_t libdivide_s16_branchfree_recover(
const struct libdivide_s16_branchfree_t* denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_branchfree_recover(
const struct libdivide_u16_branchfree_t* denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_branchfree_recover(
const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_branchfree_recover(
const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_branchfree_recover(
const struct libdivide_s64_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_branchfree_recover(
const struct libdivide_u64_branchfree_t *denom);
//////// Internal Utility Functions
static LIBDIVIDE_INLINE uint16_t libdivide_mullhi_u16(uint16_t x, uint16_t y) {
uint32_t xl = x, yl = y;
uint32_t rl = xl * yl;
return (uint16_t)(rl >> 16);
}
static LIBDIVIDE_INLINE int16_t libdivide_mullhi_s16(int16_t x, int16_t y) {
int32_t xl = x, yl = y;
int32_t rl = xl * yl;
// needs to be arithmetic shift
return (int16_t)(rl >> 16);
}
static LIBDIVIDE_INLINE uint32_t libdivide_mullhi_u32(uint32_t x, uint32_t y) {
uint64_t xl = x, yl = y;
uint64_t rl = xl * yl;
return (uint32_t)(rl >> 32);
}
static LIBDIVIDE_INLINE int32_t libdivide_mullhi_s32(int32_t x, int32_t y) {
int64_t xl = x, yl = y;
int64_t rl = xl * yl;
// needs to be arithmetic shift
return (int32_t)(rl >> 32);
}
static LIBDIVIDE_INLINE uint64_t libdivide_mullhi_u64(uint64_t x, uint64_t y) {
#if defined(LIBDIVIDE_VC) && defined(LIBDIVIDE_X86_64)
return __umulh(x, y);
#elif defined(HAS_INT128_T)
__uint128_t xl = x, yl = y;
__uint128_t rl = xl * yl;
return (uint64_t)(rl >> 64);
#else
// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
uint32_t mask = 0xFFFFFFFF;
uint32_t x0 = (uint32_t)(x & mask);
uint32_t x1 = (uint32_t)(x >> 32);
uint32_t y0 = (uint32_t)(y & mask);
uint32_t y1 = (uint32_t)(y >> 32);
uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
uint64_t x0y1 = x0 * (uint64_t)y1;
uint64_t x1y0 = x1 * (uint64_t)y0;
uint64_t x1y1 = x1 * (uint64_t)y1;
uint64_t temp = x1y0 + x0y0_hi;
uint64_t temp_lo = temp & mask;
uint64_t temp_hi = temp >> 32;
return x1y1 + temp_hi + ((temp_lo + x0y1) >> 32);
#endif
}
static LIBDIVIDE_INLINE int64_t libdivide_mullhi_s64(int64_t x, int64_t y) {
#if defined(LIBDIVIDE_VC) && defined(LIBDIVIDE_X86_64)
return __mulh(x, y);
#elif defined(HAS_INT128_T)
__int128_t xl = x, yl = y;
__int128_t rl = xl * yl;
return (int64_t)(rl >> 64);
#else
// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
uint32_t mask = 0xFFFFFFFF;
uint32_t x0 = (uint32_t)(x & mask);
uint32_t y0 = (uint32_t)(y & mask);
int32_t x1 = (int32_t)(x >> 32);
int32_t y1 = (int32_t)(y >> 32);
uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
int64_t t = x1 * (int64_t)y0 + x0y0_hi;
int64_t w1 = x0 * (int64_t)y1 + (t & mask);
return x1 * (int64_t)y1 + (t >> 32) + (w1 >> 32);
#endif
}
static LIBDIVIDE_INLINE int16_t libdivide_count_leading_zeros16(uint16_t val) {
#if defined(__AVR__)
// Fast way to count leading zeros
// On the AVR 8-bit architecture __builtin_clz() works on a int16_t.
return __builtin_clz(val);
#elif defined(__GNUC__) || __has_builtin(__builtin_clz)
// Fast way to count leading zeros
return __builtin_clz(val) - 16;
#elif defined(LIBDIVIDE_VC)
unsigned long result;
if (_BitScanReverse(&result, (unsigned long)val)) {
return (int16_t)(15 - result);
}
return 0;
#else
if (val == 0) return 16;
int16_t result = 4;
uint16_t hi = 0xFU << 12;
while ((val & hi) == 0) {
hi >>= 4;
result += 4;
}
while (val & hi) {
result -= 1;
hi <<= 1;
}
return result;
#endif
}
static LIBDIVIDE_INLINE int32_t libdivide_count_leading_zeros32(uint32_t val) {
#if defined(__AVR__)
// Fast way to count leading zeros
return __builtin_clzl(val);
#elif defined(__GNUC__) || __has_builtin(__builtin_clz)
// Fast way to count leading zeros
return __builtin_clz(val);
#elif defined(LIBDIVIDE_VC)
unsigned long result;
if (_BitScanReverse(&result, val)) {
return 31 - result;
}
return 0;
#else
if (val == 0) return 32;
int32_t result = 8;
uint32_t hi = 0xFFU << 24;
while ((val & hi) == 0) {
hi >>= 8;
result += 8;
}
while (val & hi) {
result -= 1;
hi <<= 1;
}
return result;
#endif
}
static LIBDIVIDE_INLINE int32_t libdivide_count_leading_zeros64(uint64_t val) {
#if defined(__GNUC__) || __has_builtin(__builtin_clzll)
// Fast way to count leading zeros
return __builtin_clzll(val);
#elif defined(LIBDIVIDE_VC) && defined(_WIN64)
unsigned long result;
if (_BitScanReverse64(&result, val)) {
return 63 - result;
}
return 0;
#else
uint32_t hi = val >> 32;
uint32_t lo = val & 0xFFFFFFFF;
if (hi != 0) return libdivide_count_leading_zeros32(hi);
return 32 + libdivide_count_leading_zeros32(lo);
#endif
}
// libdivide_32_div_16_to_16: divides a 32-bit uint {u1, u0} by a 16-bit
// uint {v}. The result must fit in 16 bits.
// Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint16_t libdivide_32_div_16_to_16(
uint16_t u1, uint16_t u0, uint16_t v, uint16_t* r) {
uint32_t n = ((uint32_t)u1 << 16) | u0;
uint16_t result = (uint16_t)(n / v);
*r = (uint16_t)(n - result * (uint32_t)v);
return result;
}
// libdivide_64_div_32_to_32: divides a 64-bit uint {u1, u0} by a 32-bit
// uint {v}. The result must fit in 32 bits.
// Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint32_t libdivide_64_div_32_to_32(
uint32_t u1, uint32_t u0, uint32_t v, uint32_t *r) {
#if (defined(LIBDIVIDE_i386) || defined(LIBDIVIDE_X86_64)) && defined(LIBDIVIDE_GCC_STYLE_ASM)
uint32_t result;
__asm__("divl %[v]" : "=a"(result), "=d"(*r) : [v] "r"(v), "a"(u0), "d"(u1));
return result;
#else
uint64_t n = ((uint64_t)u1 << 32) | u0;
uint32_t result = (uint32_t)(n / v);
*r = (uint32_t)(n - result * (uint64_t)v);
return result;
#endif
}
// libdivide_128_div_64_to_64: divides a 128-bit uint {numhi, numlo} by a 64-bit uint {den}. The
// result must fit in 64 bits. Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint64_t libdivide_128_div_64_to_64(
uint64_t numhi, uint64_t numlo, uint64_t den, uint64_t *r) {
// N.B. resist the temptation to use __uint128_t here.
// In LLVM compiler-rt, it performs a 128/128 -> 128 division which is many times slower than
// necessary. In gcc it's better but still slower than the divlu implementation, perhaps because
// it's not LIBDIVIDE_INLINEd.
#if defined(LIBDIVIDE_X86_64) && defined(LIBDIVIDE_GCC_STYLE_ASM)
uint64_t result;
__asm__("divq %[v]" : "=a"(result), "=d"(*r) : [v] "r"(den), "a"(numlo), "d"(numhi));
return result;
#else
// We work in base 2**32.
// A uint32 holds a single digit. A uint64 holds two digits.
// Our numerator is conceptually [num3, num2, num1, num0].
// Our denominator is [den1, den0].
const uint64_t b = ((uint64_t)1 << 32);
// The high and low digits of our computed quotient.
uint32_t q1;
uint32_t q0;
// The normalization shift factor.
int shift;
// The high and low digits of our denominator (after normalizing).
// Also the low 2 digits of our numerator (after normalizing).
uint32_t den1;
uint32_t den0;
uint32_t num1;
uint32_t num0;
// A partial remainder.
uint64_t rem;
// The estimated quotient, and its corresponding remainder (unrelated to true remainder).
uint64_t qhat;
uint64_t rhat;
// Variables used to correct the estimated quotient.
uint64_t c1;
uint64_t c2;
// Check for overflow and divide by 0.
if (numhi >= den) {
if (r != NULL) *r = ~0ull;
return ~0ull;
}
// Determine the normalization factor. We multiply den by this, so that its leading digit is at
// least half b. In binary this means just shifting left by the number of leading zeros, so that
// there's a 1 in the MSB.
// We also shift numer by the same amount. This cannot overflow because numhi < den.
// The expression (-shift & 63) is the same as (64 - shift), except it avoids the UB of shifting
// by 64. The funny bitwise 'and' ensures that numlo does not get shifted into numhi if shift is
// 0. clang 11 has an x86 codegen bug here: see LLVM bug 50118. The sequence below avoids it.
shift = libdivide_count_leading_zeros64(den);
den <<= shift;
numhi <<= shift;
numhi |= (numlo >> (-shift & 63)) & (-(int64_t)shift >> 63);
numlo <<= shift;
// Extract the low digits of the numerator and both digits of the denominator.
num1 = (uint32_t)(numlo >> 32);
num0 = (uint32_t)(numlo & 0xFFFFFFFFu);
den1 = (uint32_t)(den >> 32);
den0 = (uint32_t)(den & 0xFFFFFFFFu);
// We wish to compute q1 = [n3 n2 n1] / [d1 d0].
// Estimate q1 as [n3 n2] / [d1], and then correct it.
// Note while qhat may be 2 digits, q1 is always 1 digit.
qhat = numhi / den1;
rhat = numhi % den1;
c1 = qhat * den0;
c2 = rhat * b + num1;
if (c1 > c2) qhat -= (c1 - c2 > den) ? 2 : 1;
q1 = (uint32_t)qhat;
// Compute the true (partial) remainder.
rem = numhi * b + num1 - q1 * den;
// We wish to compute q0 = [rem1 rem0 n0] / [d1 d0].
// Estimate q0 as [rem1 rem0] / [d1] and correct it.
qhat = rem / den1;
rhat = rem % den1;
c1 = qhat * den0;
c2 = rhat * b + num0;
if (c1 > c2) qhat -= (c1 - c2 > den) ? 2 : 1;
q0 = (uint32_t)qhat;
// Return remainder if requested.
if (r != NULL) *r = (rem * b + num0 - q0 * den) >> shift;
return ((uint64_t)q1 << 32) | q0;
#endif
}
// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0)
static LIBDIVIDE_INLINE void libdivide_u128_shift(
uint64_t *u1, uint64_t *u0, int32_t signed_shift) {
if (signed_shift > 0) {
uint32_t shift = signed_shift;
*u1 <<= shift;
*u1 |= *u0 >> (64 - shift);
*u0 <<= shift;
} else if (signed_shift < 0) {
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 LIBDIVIDE_INLINE 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
}
////////// UINT16
static LIBDIVIDE_INLINE struct libdivide_u16_t libdivide_internal_u16_gen(
uint16_t d, int branchfree) {
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
struct libdivide_u16_t result;
uint8_t floor_log_2_d = (uint8_t)(15 - libdivide_count_leading_zeros16(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;
uint16_t rem, proposed_m;
proposed_m = libdivide_32_div_16_to_16((uint16_t)1 << floor_log_2_d, 0, d, &rem);
LIBDIVIDE_ASSERT(rem > 0 && rem < d);
const uint16_t e = d - rem;
// This power works if e < 2**floor_log_2_d.
if (!branchfree && (e < ((uint16_t)1 << floor_log_2_d))) {
// This power works
more = floor_log_2_d;
}
else {
// We have to use the general 17-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 uint16_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_u16_t libdivide_u16_gen(uint16_t d) {
return libdivide_internal_u16_gen(d, 0);
}
struct libdivide_u16_branchfree_t libdivide_u16_branchfree_gen(uint16_t d) {
if (d == 1) {
LIBDIVIDE_ERROR("branchfree divider must be != 1");
}
struct libdivide_u16_t tmp = libdivide_internal_u16_gen(d, 1);
struct libdivide_u16_branchfree_t ret = {
tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_16_SHIFT_MASK) };
return ret;
}
// The original libdivide_u16_do takes a const pointer. However, this cannot be used
// with a compile time constant libdivide_u16_t: it will generate a warning about
// taking the address of a temporary. Hence this overload.
uint16_t libdivide_u16_do_raw(uint16_t numer, uint16_t magic, uint8_t more) {
if (!magic) {
return numer >> more;
}
else {
uint16_t q = libdivide_mullhi_u16(magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
uint16_t t = ((numer - q) >> 1) + q;
return t >> (more & LIBDIVIDE_16_SHIFT_MASK);
}
else {
// All upper bits are 0,
// don't need to mask them off.
return q >> more;
}
}
}
uint16_t libdivide_u16_do(uint16_t numer, const struct libdivide_u16_t* denom) {
return libdivide_u16_do_raw(numer, denom->magic, denom->more);
}
uint16_t libdivide_u16_branchfree_do(
uint16_t numer, const struct libdivide_u16_branchfree_t* denom) {
uint16_t q = libdivide_mullhi_u16(denom->magic, numer);
uint16_t t = ((numer - q) >> 1) + q;
return t >> denom->more;
}
uint16_t libdivide_u16_recover(const struct libdivide_u16_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
if (!denom->magic) {
return (uint16_t)1 << shift;
} else if (!(more & LIBDIVIDE_ADD_MARKER)) {
// We compute q = n/d = n*m / 2^(16 + shift)
// Therefore we have d = 2^(16 + 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
uint16_t hi_dividend = (uint16_t)1 << shift;
uint16_t rem_ignored;
return 1 + libdivide_32_div_16_to_16(hi_dividend, 0, denom->magic, &rem_ignored);
} else {
// Here we wish to compute d = 2^(16+shift+1)/(m+2^16).
// Notice (m + 2^16) is a 17 bit number. Use 32 bit division for now
// Also note that shift may be as high as 15, so shift + 1 will
// overflow. So we have to compute it as 2^(16+shift)/(m+2^16), and
// then double the quotient and remainder.
uint32_t half_n = (uint32_t)1 << (16 + shift);
uint32_t d = ( (uint32_t)1 << 16) | denom->magic;
// Note that the quotient is guaranteed <= 16 bits, but the remainder
// may need 17!
uint16_t half_q = (uint16_t)(half_n / d);
uint32_t rem = half_n % d;
// We computed 2^(16+shift)/(m+2^16)
// 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 17 bits
uint16_t full_q = half_q + half_q + ((rem << 1) >= d);
// We rounded down in gen (hence +1)
return full_q + 1;
}
}
uint16_t libdivide_u16_branchfree_recover(const struct libdivide_u16_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
if (!denom->magic) {
return (uint16_t)1 << (shift + 1);
} else {
// Here we wish to compute d = 2^(16+shift+1)/(m+2^16).
// Notice (m + 2^16) is a 17 bit number. Use 32 bit division for now
// Also note that shift may be as high as 15, so shift + 1 will
// overflow. So we have to compute it as 2^(16+shift)/(m+2^16), and
// then double the quotient and remainder.
uint32_t half_n = (uint32_t)1 << (16 + shift);
uint32_t d = ((uint32_t)1 << 16) | denom->magic;
// Note that the quotient is guaranteed <= 16 bits, but the remainder
// may need 17!
uint16_t half_q = (uint16_t)(half_n / d);
uint32_t rem = half_n % d;
// We computed 2^(16+shift)/(m+2^16)
// 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
uint16_t full_q = half_q + half_q + ((rem << 1) >= d);
// We rounded down in gen (hence +1)
return full_q + 1;
}
}
////////// UINT32
static LIBDIVIDE_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((uint32_t)1 << 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 < ((uint32_t)1 << floor_log_2_d))) {
// This power works
more = (uint8_t)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 = (uint8_t)(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 (uint32_t)1 << 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 = (uint32_t)1 << 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 = (uint64_t)1 << (32 + shift);
uint64_t d = ((uint64_t)1 << 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 (uint32_t)1 << (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 = (uint64_t)1 << (32 + shift);
uint64_t d = ((uint64_t)1 << 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 LIBDIVIDE_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((uint64_t)1 << 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 < ((uint64_t)1 << floor_log_2_d)) {
// This power works
more = (uint8_t)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 = (uint8_t)(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 (uint64_t)1 << 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 = (uint64_t)1 << 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 = (uint64_t)1 << 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 (uint64_t)1 << (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 = (uint64_t)1 << 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;
}
}
/////////// SINT16
static LIBDIVIDE_INLINE struct libdivide_s16_t libdivide_internal_s16_gen(
int16_t d, int branchfree) {
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
struct libdivide_s16_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.
uint16_t ud = (uint16_t)d;
uint16_t absD = (d < 0) ? -ud : ud;
uint16_t floor_log_2_d = 15 - libdivide_count_leading_zeros16(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 = (uint8_t)(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 16 bit word
// is 0 and the high word is floor_log_2_d - 1
uint16_t rem, proposed_m;
proposed_m = libdivide_32_div_16_to_16((uint16_t)1 << (floor_log_2_d - 1), 0, absD, &rem);
const uint16_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 < ((uint16_t)1 << floor_log_2_d)) {
// This power works
more = (uint8_t)(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
// int16_t.
proposed_m += proposed_m;
const uint16_t twice_rem = rem + rem;
if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
}
proposed_m += 1;
int16_t magic = (int16_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_s16_t libdivide_s16_gen(int16_t d) {
return libdivide_internal_s16_gen(d, 0);
}
struct libdivide_s16_branchfree_t libdivide_s16_branchfree_gen(int16_t d) {
struct libdivide_s16_t tmp = libdivide_internal_s16_gen(d, 1);
struct libdivide_s16_branchfree_t result = {tmp.magic, tmp.more};
return result;
}
// The original libdivide_s16_do takes a const pointer. However, this cannot be used
// with a compile time constant libdivide_s16_t: it will generate a warning about
// taking the address of a temporary. Hence this overload.
int16_t libdivide_s16_do_raw(int16_t numer, int16_t magic, uint8_t more) {
uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
if (!magic) {
uint16_t sign = (int8_t)more >> 7;
uint16_t mask = ((uint16_t)1 << shift) - 1;
uint16_t uq = numer + ((numer >> 15) & mask);
int16_t q = (int16_t)uq;
q >>= shift;
q = (q ^ sign) - sign;
return q;
} else {
uint16_t uq = (uint16_t)libdivide_mullhi_s16(magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift and then sign extend
int16_t sign = (int8_t)more >> 7;
// q += (more < 0 ? -numer : numer)
// cast required to avoid UB
uq += ((uint16_t)numer ^ sign) - sign;
}
int16_t q = (int16_t)uq;
q >>= shift;
q += (q < 0);
return q;
}
}
int16_t libdivide_s16_do(int16_t numer, const struct libdivide_s16_t *denom) {
return libdivide_s16_do_raw(numer, denom->magic, denom->more);
}
int16_t libdivide_s16_branchfree_do(int16_t numer, const struct libdivide_s16_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
// must be arithmetic shift and then sign extend
int16_t sign = (int8_t)more >> 7;
int16_t magic = denom->magic;
int16_t q = libdivide_mullhi_s16(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
uint16_t is_power_of_2 = (magic == 0);
uint16_t q_sign = (uint16_t)(q >> 15);
q += q_sign & (((uint16_t)1 << shift) - is_power_of_2);
// Now arithmetic right shift
q >>= shift;
// Negate if needed
q = (q ^ sign) - sign;
return q;
}
int16_t libdivide_s16_recover(const struct libdivide_s16_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
if (!denom->magic) {
uint16_t absD = (uint16_t)1 << shift;
if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
absD = -absD;
}
return (int16_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) {
int16_t result = (uint16_t)1 << shift;
return negative_divisor ? -result : result;
}
uint16_t d = (uint16_t)(magic_was_negated ? -denom->magic : denom->magic);
uint32_t n = (uint32_t)1 << (16 + shift); // this shift cannot exceed 30
uint16_t q = (uint16_t)(n / d);
int16_t result = (int16_t)q;
result += 1;
return negative_divisor ? -result : result;
}
}
int16_t libdivide_s16_branchfree_recover(const struct libdivide_s16_branchfree_t *denom) {
return libdivide_s16_recover((const struct libdivide_s16_t *)denom);
}
/////////// SINT32
static LIBDIVIDE_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 = (uint8_t)(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((uint32_t)1 << (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 < ((uint32_t)1 << floor_log_2_d)) {
// This power works
more = (uint8_t)(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 = (uint8_t)(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 = ((uint32_t)1 << 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 & (((uint32_t)1 << 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 = (uint32_t)1 << 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 = (uint32_t)1 << shift;
return negative_divisor ? -result : result;
}
uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic);
uint64_t n = (uint64_t)1 << (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 LIBDIVIDE_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 = (uint8_t)(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((uint64_t)1 << (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 < ((uint64_t)1 << floor_log_2_d)) {
// This power works
more = (uint8_t)(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 = (uint8_t)(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 = ((uint64_t)1 << 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 & (((uint64_t)1 << 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 = (uint64_t)1 << 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 = (uint64_t)1 << 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);
}
// Simplest possible vector type division: treat the vector type as an array
// of underlying native type.
#define SIMPLE_VECTOR_DIVISION(IntT, VecT, Algo) \
const size_t count = sizeof(VecT) / sizeof(IntT); \
VecT result; \
IntT *pSource = (IntT *)&numers; \
IntT *pTarget = (IntT *)&result; \
for (size_t loop=0; loop<count; ++loop) { \
pTarget[loop] = libdivide_##Algo##_do(pSource[loop], denom); \
} \
return result; \
#if defined(LIBDIVIDE_NEON)
static LIBDIVIDE_INLINE uint16x8_t libdivide_u16_do_vec128(
uint16x8_t numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE int16x8_t libdivide_s16_do_vec128(
int16x8_t numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_do_vec128(
uint32x4_t numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_do_vec128(
int32x4_t numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_do_vec128(
uint64x2_t numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_do_vec128(
int64x2_t numers, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE uint16x8_t libdivide_u16_branchfree_do_vec128(
uint16x8_t numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE int16x8_t libdivide_s16_branchfree_do_vec128(
int16x8_t numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_branchfree_do_vec128(
uint32x4_t numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_branchfree_do_vec128(
int32x4_t numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_branchfree_do_vec128(
uint64x2_t numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_branchfree_do_vec128(
int64x2_t numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
// Logical right shift by runtime value.
// NEON implements right shift as left shits by negative values.
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_neon_srl(uint32x4_t v, uint8_t amt) {
int32_t wamt = (int32_t)(amt);
return vshlq_u32(v, vdupq_n_s32(-wamt));
}
static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_neon_srl(uint64x2_t v, uint8_t amt) {
int64_t wamt = (int64_t)(amt);
return vshlq_u64(v, vdupq_n_s64(-wamt));
}
// Arithmetic right shift by runtime value.
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_neon_sra(int32x4_t v, uint8_t amt) {
int32_t wamt = (int32_t)(amt);
return vshlq_s32(v, vdupq_n_s32(-wamt));
}
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_neon_sra(int64x2_t v, uint8_t amt) {
int64_t wamt = (int64_t)(amt);
return vshlq_s64(v, vdupq_n_s64(-wamt));
}
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_signbits(int64x2_t v) { return vshrq_n_s64(v, 63); }
static LIBDIVIDE_INLINE uint32x4_t libdivide_mullhi_u32_vec128(uint32x4_t a, uint32_t b) {
// Desire is [x0, x1, x2, x3]
uint32x4_t w1 = vreinterpretq_u32_u64(vmull_n_u32(vget_low_u32(a), b)); // [_, x0, _, x1]
uint32x4_t w2 = vreinterpretq_u32_u64(vmull_high_n_u32(a, b)); //[_, x2, _, x3]
return vuzp2q_u32(w1, w2); // [x0, x1, x2, x3]
}
static LIBDIVIDE_INLINE int32x4_t libdivide_mullhi_s32_vec128(int32x4_t a, int32_t b) {
int32x4_t w1 = vreinterpretq_s32_s64(vmull_n_s32(vget_low_s32(a), b)); // [_, x0, _, x1]
int32x4_t w2 = vreinterpretq_s32_s64(vmull_high_n_s32(a, b)); //[_, x2, _, x3]
return vuzp2q_s32(w1, w2); // [x0, x1, x2, x3]
}
static LIBDIVIDE_INLINE uint64x2_t libdivide_mullhi_u64_vec128(uint64x2_t x, uint64_t sy) {
// full 128 bits product is:
// x0*y0 + (x0*y1 << 32) + (x1*y0 << 32) + (x1*y1 << 64)
// Note x0,y0,x1,y1 are all conceptually uint32, products are 32x32->64.
// Get low and high words. x0 contains low 32 bits, x1 is high 32 bits.
uint64x2_t y = vdupq_n_u64(sy);
uint32x2_t x0 = vmovn_u64(x);
uint32x2_t y0 = vmovn_u64(y);
uint32x2_t x1 = vshrn_n_u64(x, 32);
uint32x2_t y1 = vshrn_n_u64(y, 32);
// Compute x0*y0.
uint64x2_t x0y0 = vmull_u32(x0, y0);
uint64x2_t x0y0_hi = vshrq_n_u64(x0y0, 32);
// Compute other intermediate products.
uint64x2_t temp = vmlal_u32(x0y0_hi, x1, y0); // temp = x0y0_hi + x1*y0;
// We want to split temp into its low 32 bits and high 32 bits, both
// in the low half of 64 bit registers.
// Use shifts to avoid needing a reg for the mask.
uint64x2_t temp_lo = vshrq_n_u64(vshlq_n_u64(temp, 32), 32); // temp_lo = temp & 0xFFFFFFFF;
uint64x2_t temp_hi = vshrq_n_u64(temp, 32); // temp_hi = temp >> 32;
temp_lo = vmlal_u32(temp_lo, x0, y1); // temp_lo += x0*y0
temp_lo = vshrq_n_u64(temp_lo, 32); // temp_lo >>= 32
temp_hi = vmlal_u32(temp_hi, x1, y1); // temp_hi += x1*y1
uint64x2_t result = vaddq_u64(temp_hi, temp_lo);
return result;
}
static LIBDIVIDE_INLINE int64x2_t libdivide_mullhi_s64_vec128(int64x2_t x, int64_t sy) {
int64x2_t p = vreinterpretq_s64_u64(
libdivide_mullhi_u64_vec128(vreinterpretq_u64_s64(x), (uint64_t)(sy)));
int64x2_t y = vdupq_n_s64(sy);
int64x2_t t1 = vandq_s64(libdivide_s64_signbits(x), y);
int64x2_t t2 = vandq_s64(libdivide_s64_signbits(y), x);
p = vsubq_s64(p, t1);
p = vsubq_s64(p, t2);
return p;
}
////////// UINT16
uint16x8_t libdivide_u16_do_vec128(uint16x8_t numers, const struct libdivide_u16_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, uint16x8_t, u16)
}
uint16x8_t libdivide_u16_branchfree_do_vec128(uint16x8_t numers, const struct libdivide_u16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, uint16x8_t, u16_branchfree)
}
////////// UINT32
uint32x4_t libdivide_u32_do_vec128(uint32x4_t numers, const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return libdivide_u32_neon_srl(numers, more);
} else {
uint32x4_t q = libdivide_mullhi_u32_vec128(numers, denom->magic);
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
// Note we can use halving-subtract to avoid the shift.
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
uint32x4_t t = vaddq_u32(vhsubq_u32(numers, q), q);
return libdivide_u32_neon_srl(t, shift);
} else {
return libdivide_u32_neon_srl(q, more);
}
}
}
uint32x4_t libdivide_u32_branchfree_do_vec128(
uint32x4_t numers, const struct libdivide_u32_branchfree_t *denom) {
uint32x4_t q = libdivide_mullhi_u32_vec128(numers, denom->magic);
uint32x4_t t = vaddq_u32(vhsubq_u32(numers, q), q);
return libdivide_u32_neon_srl(t, denom->more);
}
////////// UINT64
uint64x2_t libdivide_u64_do_vec128(uint64x2_t numers, const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return libdivide_u64_neon_srl(numers, more);
} else {
uint64x2_t q = libdivide_mullhi_u64_vec128(numers, denom->magic);
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
// No 64-bit halving subtracts in NEON :(
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
uint64x2_t t = vaddq_u64(vshrq_n_u64(vsubq_u64(numers, q), 1), q);
return libdivide_u64_neon_srl(t, shift);
} else {
return libdivide_u64_neon_srl(q, more);
}
}
}
uint64x2_t libdivide_u64_branchfree_do_vec128(
uint64x2_t numers, const struct libdivide_u64_branchfree_t *denom) {
uint64x2_t q = libdivide_mullhi_u64_vec128(numers, denom->magic);
uint64x2_t t = vaddq_u64(vshrq_n_u64(vsubq_u64(numers, q), 1), q);
return libdivide_u64_neon_srl(t, denom->more);
}
////////// SINT16
int16x8_t libdivide_s16_do_vec128(int16x8_t numers, const struct libdivide_s16_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, int16x8_t, s16)
}
int16x8_t libdivide_s16_branchfree_do_vec128(int16x8_t numers, const struct libdivide_s16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, int16x8_t, s16_branchfree)
}
////////// SINT32
int32x4_t libdivide_s32_do_vec128(int32x4_t numers, const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
uint32_t mask = ((uint32_t)1 << shift) - 1;
int32x4_t roundToZeroTweak = vdupq_n_s32((int)mask);
// q = numer + ((numer >> 31) & roundToZeroTweak);
int32x4_t q = vaddq_s32(numers, vandq_s32(vshrq_n_s32(numers, 31), roundToZeroTweak));
q = libdivide_s32_neon_sra(q, shift);
int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = vsubq_s32(veorq_s32(q, sign), sign);
return q;
} else {
int32x4_t q = libdivide_mullhi_s32_vec128(numers, denom->magic);
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = vaddq_s32(q, vsubq_s32(veorq_s32(numers, sign), sign));
}
// q >>= shift
q = libdivide_s32_neon_sra(q, more & LIBDIVIDE_32_SHIFT_MASK);
q = vaddq_s32(
q, vreinterpretq_s32_u32(vshrq_n_u32(vreinterpretq_u32_s32(q), 31))); // q += (q < 0)
return q;
}
}
int32x4_t libdivide_s32_branchfree_do_vec128(
int32x4_t 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
int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
int32x4_t q = libdivide_mullhi_s32_vec128(numers, magic);
q = vaddq_s32(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);
int32x4_t q_sign = vshrq_n_s32(q, 31); // q_sign = q >> 31
int32x4_t mask = vdupq_n_s32(((uint32_t)1 << shift) - is_power_of_2);
q = vaddq_s32(q, vandq_s32(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s32_neon_sra(q, shift); // q >>= shift
q = vsubq_s32(veorq_s32(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
////////// SINT64
int64x2_t libdivide_s64_do_vec128(int64x2_t numers, const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
int64_t magic = denom->magic;
if (magic == 0) { // shift path
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
uint64_t mask = ((uint64_t)1 << shift) - 1;
int64x2_t roundToZeroTweak = vdupq_n_s64(mask); // TODO: no need to sign extend
// q = numer + ((numer >> 63) & roundToZeroTweak);
int64x2_t q =
vaddq_s64(numers, vandq_s64(libdivide_s64_signbits(numers), roundToZeroTweak));
q = libdivide_s64_neon_sra(q, shift);
// q = (q ^ sign) - sign;
int64x2_t sign = vreinterpretq_s64_s8(vdupq_n_s8((int8_t)more >> 7));
q = vsubq_s64(veorq_s64(q, sign), sign);
return q;
} else {
int64x2_t q = libdivide_mullhi_s64_vec128(numers, magic);
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
int64x2_t sign = vdupq_n_s64((int8_t)more >> 7); // TODO: no need to widen
// q += ((numer ^ sign) - sign);
q = vaddq_s64(q, vsubq_s64(veorq_s64(numers, sign), sign));
}
// q >>= denom->mult_path.shift
q = libdivide_s64_neon_sra(q, more & LIBDIVIDE_64_SHIFT_MASK);
q = vaddq_s64(
q, vreinterpretq_s64_u64(vshrq_n_u64(vreinterpretq_u64_s64(q), 63))); // q += (q < 0)
return q;
}
}
int64x2_t libdivide_s64_branchfree_do_vec128(
int64x2_t 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
int64x2_t sign = vdupq_n_s64((int8_t)more >> 7); // TODO: avoid sign extend
// libdivide_mullhi_s64(numers, magic);
int64x2_t q = libdivide_mullhi_s64_vec128(numers, magic);
q = vaddq_s64(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);
int64x2_t q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
int64x2_t mask = vdupq_n_s64(((uint64_t)1 << shift) - is_power_of_2);
q = vaddq_s64(q, vandq_s64(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s64_neon_sra(q, shift); // q >>= shift
q = vsubq_s64(veorq_s64(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#endif
#if defined(LIBDIVIDE_AVX512)
static LIBDIVIDE_INLINE __m512i libdivide_u16_do_vec512(
__m512i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s16_do_vec512(
__m512i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u32_do_vec512(
__m512i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s32_do_vec512(
__m512i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u64_do_vec512(
__m512i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s64_do_vec512(
__m512i numers, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u16_branchfree_do_vec512(
__m512i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s16_branchfree_do_vec512(
__m512i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u32_branchfree_do_vec512(
__m512i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s32_branchfree_do_vec512(
__m512i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u64_branchfree_do_vec512(
__m512i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s64_branchfree_do_vec512(
__m512i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
static LIBDIVIDE_INLINE __m512i libdivide_s64_signbits_vec512(__m512i v) {
;
return _mm512_srai_epi64(v, 63);
}
static LIBDIVIDE_INLINE __m512i libdivide_s64_shift_right_vec512(__m512i v, int amt) {
return _mm512_srai_epi64(v, amt);
}
// Here, b is assumed to contain one 32-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_u32_vec512(__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 LIBDIVIDE_INLINE __m512i libdivide_mullhi_s32_vec512(__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.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_u64_vec512(__m512i x, __m512i y) {
// see m128i variant for comments.
__m512i x0y0 = _mm512_mul_epu32(x, y);
__m512i x0y0_hi = _mm512_srli_epi64(x0y0, 32);
__m512i x1 = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM)_MM_SHUFFLE(3, 3, 1, 1));
__m512i y1 = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM)_MM_SHUFFLE(3, 3, 1, 1));
__m512i x0y1 = _mm512_mul_epu32(x, y1);
__m512i x1y0 = _mm512_mul_epu32(x1, y);
__m512i x1y1 = _mm512_mul_epu32(x1, y1);
__m512i mask = _mm512_set1_epi64(0xFFFFFFFF);
__m512i temp = _mm512_add_epi64(x1y0, x0y0_hi);
__m512i temp_lo = _mm512_and_si512(temp, mask);
__m512i temp_hi = _mm512_srli_epi64(temp, 32);
temp_lo = _mm512_srli_epi64(_mm512_add_epi64(temp_lo, x0y1), 32);
temp_hi = _mm512_add_epi64(x1y1, temp_hi);
return _mm512_add_epi64(temp_lo, temp_hi);
}
// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_s64_vec512(__m512i x, __m512i y) {
__m512i p = libdivide_mullhi_u64_vec512(x, y);
__m512i t1 = _mm512_and_si512(libdivide_s64_signbits_vec512(x), y);
__m512i t2 = _mm512_and_si512(libdivide_s64_signbits_vec512(y), x);
p = _mm512_sub_epi64(p, t1);
p = _mm512_sub_epi64(p, t2);
return p;
}
////////// UINT16
__m512i libdivide_u16_do_vec512(__m512i numers, const struct libdivide_u16_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m512i, u16)
}
__m512i libdivide_u16_branchfree_do_vec512(__m512i numers, const struct libdivide_u16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m512i, u16_branchfree)
}
////////// UINT32
__m512i libdivide_u32_do_vec512(__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_vec512(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_vec512(
__m512i numers, const struct libdivide_u32_branchfree_t *denom) {
__m512i q = libdivide_mullhi_u32_vec512(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_vec512(__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_vec512(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_vec512(
__m512i numers, const struct libdivide_u64_branchfree_t *denom) {
__m512i q = libdivide_mullhi_u64_vec512(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);
}
////////// SINT16
__m512i libdivide_s16_do_vec512(__m512i numers, const struct libdivide_s16_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m512i, s16)
}
__m512i libdivide_s16_branchfree_do_vec512(__m512i numers, const struct libdivide_s16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m512i, s16_branchfree)
}
////////// SINT32
__m512i libdivide_s32_do_vec512(__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 = ((uint32_t)1 << 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_vec512(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_vec512(
__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_vec512(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(((uint32_t)1 << 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_vec512(__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 = ((uint64_t)1 << 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_vec512(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vec512(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_vec512(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_vec512(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_vec512(
__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_vec512(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_vec512(q); // q_sign = q >> 63
__m512i mask = _mm512_set1_epi64(((uint64_t)1 << 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_vec512(q, shift); // q >>= shift
q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#endif
#if defined(LIBDIVIDE_AVX2)
static LIBDIVIDE_INLINE __m256i libdivide_u16_do_vec256(
__m256i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s16_do_vec256(
__m256i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u32_do_vec256(
__m256i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s32_do_vec256(
__m256i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u64_do_vec256(
__m256i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s64_do_vec256(
__m256i numers, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u16_branchfree_do_vec256(
__m256i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s16_branchfree_do_vec256(
__m256i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u32_branchfree_do_vec256(
__m256i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s32_branchfree_do_vec256(
__m256i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u64_branchfree_do_vec256(
__m256i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s64_branchfree_do_vec256(
__m256i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
// Implementation of _mm256_srai_epi64(v, 63) (from AVX512).
static LIBDIVIDE_INLINE __m256i libdivide_s64_signbits_vec256(__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 LIBDIVIDE_INLINE __m256i libdivide_s64_shift_right_vec256(__m256i v, int amt) {
const int b = 64 - amt;
__m256i m = _mm256_set1_epi64x((uint64_t)1 << (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 LIBDIVIDE_INLINE __m256i libdivide_mullhi_u32_vec256(__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 LIBDIVIDE_INLINE __m256i libdivide_mullhi_s32_vec256(__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.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_u64_vec256(__m256i x, __m256i y) {
// see m128i variant for comments.
__m256i x0y0 = _mm256_mul_epu32(x, y);
__m256i x0y0_hi = _mm256_srli_epi64(x0y0, 32);
__m256i x1 = _mm256_shuffle_epi32(x, _MM_SHUFFLE(3, 3, 1, 1));
__m256i y1 = _mm256_shuffle_epi32(y, _MM_SHUFFLE(3, 3, 1, 1));
__m256i x0y1 = _mm256_mul_epu32(x, y1);
__m256i x1y0 = _mm256_mul_epu32(x1, y);
__m256i x1y1 = _mm256_mul_epu32(x1, y1);
__m256i mask = _mm256_set1_epi64x(0xFFFFFFFF);
__m256i temp = _mm256_add_epi64(x1y0, x0y0_hi);
__m256i temp_lo = _mm256_and_si256(temp, mask);
__m256i temp_hi = _mm256_srli_epi64(temp, 32);
temp_lo = _mm256_srli_epi64(_mm256_add_epi64(temp_lo, x0y1), 32);
temp_hi = _mm256_add_epi64(x1y1, temp_hi);
return _mm256_add_epi64(temp_lo, temp_hi);
}
// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_s64_vec256(__m256i x, __m256i y) {
__m256i p = libdivide_mullhi_u64_vec256(x, y);
__m256i t1 = _mm256_and_si256(libdivide_s64_signbits_vec256(x), y);
__m256i t2 = _mm256_and_si256(libdivide_s64_signbits_vec256(y), x);
p = _mm256_sub_epi64(p, t1);
p = _mm256_sub_epi64(p, t2);
return p;
}
////////// UINT16
__m256i libdivide_u16_do_vec256(__m256i numers, const struct libdivide_u16_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m256i, u16)
}
__m256i libdivide_u16_branchfree_do_vec256(__m256i numers, const struct libdivide_u16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m256i, u16_branchfree)
}
////////// UINT32
__m256i libdivide_u32_do_vec256(__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_vec256(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_vec256(
__m256i numers, const struct libdivide_u32_branchfree_t *denom) {
__m256i q = libdivide_mullhi_u32_vec256(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_vec256(__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_vec256(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_vec256(
__m256i numers, const struct libdivide_u64_branchfree_t *denom) {
__m256i q = libdivide_mullhi_u64_vec256(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);
}
////////// SINT16
__m256i libdivide_s16_do_vec256(__m256i numers, const struct libdivide_s16_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m256i, s16)
}
__m256i libdivide_s16_branchfree_do_vec256(__m256i numers, const struct libdivide_s16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m256i, s16_branchfree)
}
////////// SINT32
__m256i libdivide_s32_do_vec256(__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 = ((uint32_t)1 << 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_vec256(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_vec256(
__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_vec256(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(((uint32_t)1 << 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_vec256(__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 = ((uint64_t)1 << 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_vec256(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vec256(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_vec256(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_vec256(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_vec256(
__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_vec256(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_vec256(q); // q_sign = q >> 63
__m256i mask = _mm256_set1_epi64x(((uint64_t)1 << 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_vec256(q, shift); // q >>= shift
q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#endif
#if defined(LIBDIVIDE_SSE2)
static LIBDIVIDE_INLINE __m128i libdivide_u16_do_vec128(
__m128i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s16_do_vec128(
__m128i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u32_do_vec128(
__m128i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s32_do_vec128(
__m128i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u64_do_vec128(
__m128i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s64_do_vec128(
__m128i numers, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u16_branchfree_do_vec128(
__m128i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s16_branchfree_do_vec128(
__m128i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u32_branchfree_do_vec128(
__m128i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s32_branchfree_do_vec128(
__m128i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u64_branchfree_do_vec128(
__m128i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s64_branchfree_do_vec128(
__m128i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
// Implementation of _mm_srai_epi64(v, 63) (from AVX512).
static LIBDIVIDE_INLINE __m128i libdivide_s64_signbits_vec128(__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 LIBDIVIDE_INLINE __m128i libdivide_s64_shift_right_vec128(__m128i v, int amt) {
const int b = 64 - amt;
__m128i m = _mm_set1_epi64x((uint64_t)1 << (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 LIBDIVIDE_INLINE __m128i libdivide_mullhi_u32_vec128(__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 LIBDIVIDE_INLINE __m128i libdivide_mullhi_s32_vec128(__m128i a, __m128i b) {
__m128i p = libdivide_mullhi_u32_vec128(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.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_u64_vec128(__m128i x, __m128i y) {
// full 128 bits product is:
// x0*y0 + (x0*y1 << 32) + (x1*y0 << 32) + (x1*y1 << 64)
// Note x0,y0,x1,y1 are all conceptually uint32, products are 32x32->64.
// Compute x0*y0.
// Note x1, y1 are ignored by mul_epu32.
__m128i x0y0 = _mm_mul_epu32(x, y);
__m128i x0y0_hi = _mm_srli_epi64(x0y0, 32);
// Get x1, y1 in the low bits.
// We could shuffle or right shift. Shuffles are preferred as they preserve
// the source register for the next computation.
__m128i x1 = _mm_shuffle_epi32(x, _MM_SHUFFLE(3, 3, 1, 1));
__m128i y1 = _mm_shuffle_epi32(y, _MM_SHUFFLE(3, 3, 1, 1));
// No need to mask off top 32 bits for mul_epu32.
__m128i x0y1 = _mm_mul_epu32(x, y1);
__m128i x1y0 = _mm_mul_epu32(x1, y);
__m128i x1y1 = _mm_mul_epu32(x1, y1);
// Mask here selects low bits only.
__m128i mask = _mm_set1_epi64x(0xFFFFFFFF);
__m128i temp = _mm_add_epi64(x1y0, x0y0_hi);
__m128i temp_lo = _mm_and_si128(temp, mask);
__m128i temp_hi = _mm_srli_epi64(temp, 32);
temp_lo = _mm_srli_epi64(_mm_add_epi64(temp_lo, x0y1), 32);
temp_hi = _mm_add_epi64(x1y1, temp_hi);
return _mm_add_epi64(temp_lo, temp_hi);
}
// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_s64_vec128(__m128i x, __m128i y) {
__m128i p = libdivide_mullhi_u64_vec128(x, y);
__m128i t1 = _mm_and_si128(libdivide_s64_signbits_vec128(x), y);
__m128i t2 = _mm_and_si128(libdivide_s64_signbits_vec128(y), x);
p = _mm_sub_epi64(p, t1);
p = _mm_sub_epi64(p, t2);
return p;
}
////////// UINT26
__m128i libdivide_u16_do_vec128(__m128i numers, const struct libdivide_u16_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m128i, u16)
}
__m128i libdivide_u16_branchfree_do_vec128(__m128i numers, const struct libdivide_u16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(uint16_t, __m128i, u16_branchfree)
}
////////// UINT32
__m128i libdivide_u32_do_vec128(__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_vec128(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_vec128(
__m128i numers, const struct libdivide_u32_branchfree_t *denom) {
__m128i q = libdivide_mullhi_u32_vec128(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_vec128(__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_vec128(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_vec128(
__m128i numers, const struct libdivide_u64_branchfree_t *denom) {
__m128i q = libdivide_mullhi_u64_vec128(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);
}
////////// SINT16
__m128i libdivide_s16_do_vec128(__m128i numers, const struct libdivide_s16_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m128i, s16)
}
__m128i libdivide_s16_branchfree_do_vec128(__m128i numers, const struct libdivide_s16_branchfree_t *denom) {
SIMPLE_VECTOR_DIVISION(int16_t, __m128i, s16_branchfree)
}
////////// SINT32
__m128i libdivide_s32_do_vec128(__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 = ((uint32_t)1 << 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_vec128(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_vec128(
__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_vec128(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(((uint32_t)1 << 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_vec128(__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 = ((uint64_t)1 << 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_vec128(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vec128(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_vec128(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_vec128(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_vec128(
__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_vec128(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_vec128(q); // q_sign = q >> 63
__m128i mask = _mm_set1_epi64x(((uint64_t)1 << shift) - is_power_of_2);
q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s64_shift_right_vec128(q, shift); // q >>= shift
q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#endif
/////////// C++ stuff
#ifdef __cplusplus
enum Branching {
BRANCHFULL, // use branching algorithms
BRANCHFREE // use branchfree algorithms
};
#if defined(LIBDIVIDE_NEON)
// Helper to deduce NEON vector type for integral type.
template <typename T>
struct NeonVecFor {};
template <>
struct NeonVecFor<uint16_t> {
typedef uint16x8_t type;
};
template <>
struct NeonVecFor<int16_t> {
typedef int16x8_t type;
};
template <>
struct NeonVecFor<uint32_t> {
typedef uint32x4_t type;
};
template <>
struct NeonVecFor<int32_t> {
typedef int32x4_t type;
};
template <>
struct NeonVecFor<uint64_t> {
typedef uint64x2_t type;
};
template <>
struct NeonVecFor<int64_t> {
typedef int64x2_t type;
};
#endif
// Versions of our algorithms for SIMD.
#if defined(LIBDIVIDE_NEON)
#define LIBDIVIDE_DIVIDE_NEON(ALGO, INT_TYPE) \
LIBDIVIDE_INLINE typename NeonVecFor<INT_TYPE>::type divide( \
typename NeonVecFor<INT_TYPE>::type n) const { \
return libdivide_##ALGO##_do_vec128(n, &denom); \
}
#else
#define LIBDIVIDE_DIVIDE_NEON(ALGO, INT_TYPE)
#endif
#if defined(LIBDIVIDE_SSE2)
#define LIBDIVIDE_DIVIDE_SSE2(ALGO) \
LIBDIVIDE_INLINE __m128i divide(__m128i n) const { \
return libdivide_##ALGO##_do_vec128(n, &denom); \
}
#else
#define LIBDIVIDE_DIVIDE_SSE2(ALGO)
#endif
#if defined(LIBDIVIDE_AVX2)
#define LIBDIVIDE_DIVIDE_AVX2(ALGO) \
LIBDIVIDE_INLINE __m256i divide(__m256i n) const { \
return libdivide_##ALGO##_do_vec256(n, &denom); \
}
#else
#define LIBDIVIDE_DIVIDE_AVX2(ALGO)
#endif
#if defined(LIBDIVIDE_AVX512)
#define LIBDIVIDE_DIVIDE_AVX512(ALGO) \
LIBDIVIDE_INLINE __m512i divide(__m512i n) const { \
return libdivide_##ALGO##_do_vec512(n, &denom); \
}
#else
#define LIBDIVIDE_DIVIDE_AVX512(ALGO)
#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; \
LIBDIVIDE_INLINE dispatcher() {} \
LIBDIVIDE_INLINE dispatcher(T d) : denom(libdivide_##ALGO##_gen(d)) {} \
LIBDIVIDE_INLINE T divide(T n) const { return libdivide_##ALGO##_do(n, &denom); } \
LIBDIVIDE_INLINE T recover() const { return libdivide_##ALGO##_recover(&denom); } \
LIBDIVIDE_DIVIDE_NEON(ALGO, T) \
LIBDIVIDE_DIVIDE_SSE2(ALGO) \
LIBDIVIDE_DIVIDE_AVX2(ALGO) \
LIBDIVIDE_DIVIDE_AVX512(ALGO)
// The dispatcher selects a specific division algorithm for a given
// type and ALGO using partial template specialization.
template <typename _IntT, Branching ALGO>
struct dispatcher {};
template <>
struct dispatcher<int16_t, BRANCHFULL> {
DISPATCHER_GEN(int16_t, s16)
};
template <>
struct dispatcher<int16_t, BRANCHFREE> {
DISPATCHER_GEN(int16_t, s16_branchfree)
};
template <>
struct dispatcher<uint16_t, BRANCHFULL> {
DISPATCHER_GEN(uint16_t, u16)
};
template <>
struct dispatcher<uint16_t, BRANCHFREE> {
DISPATCHER_GEN(uint16_t, u16_branchfree)
};
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, Branching ALGO = BRANCHFULL>
class divider {
private:
typedef dispatcher<T, ALGO> dispatcher_t;
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
LIBDIVIDE_INLINE divider(T d) : div(d) {}
// Divides n by the divisor
LIBDIVIDE_INLINE 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); }
// Vector variants treat the input 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.
#if defined(LIBDIVIDE_SSE2)
LIBDIVIDE_INLINE __m128i divide(__m128i n) const { return div.divide(n); }
#endif
#if defined(LIBDIVIDE_AVX2)
LIBDIVIDE_INLINE __m256i divide(__m256i n) const { return div.divide(n); }
#endif
#if defined(LIBDIVIDE_AVX512)
LIBDIVIDE_INLINE __m512i divide(__m512i n) const { return div.divide(n); }
#endif
#if defined(LIBDIVIDE_NEON)
LIBDIVIDE_INLINE typename NeonVecFor<T>::type divide(typename NeonVecFor<T>::type n) const {
return div.divide(n);
}
#endif
private:
// Storage for the actual divisor
dispatcher_t div;
};
// Overload of operator / for scalar division
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE T operator/(T n, const divider<T, ALGO> &div) {
return div.divide(n);
}
// Overload of operator /= for scalar division
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE T &operator/=(T &n, const divider<T, ALGO> &div) {
n = div.divide(n);
return n;
}
// Overloads for vector types.
#if defined(LIBDIVIDE_SSE2)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m128i operator/(__m128i n, const divider<T, ALGO> &div) {
return div.divide(n);
}
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m128i operator/=(__m128i &n, const divider<T, ALGO> &div) {
n = div.divide(n);
return n;
}
#endif
#if defined(LIBDIVIDE_AVX2)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m256i operator/(__m256i n, const divider<T, ALGO> &div) {
return div.divide(n);
}
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m256i operator/=(__m256i &n, const divider<T, ALGO> &div) {
n = div.divide(n);
return n;
}
#endif
#if defined(LIBDIVIDE_AVX512)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m512i operator/(__m512i n, const divider<T, ALGO> &div) {
return div.divide(n);
}
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m512i operator/=(__m512i &n, const divider<T, ALGO> &div) {
n = div.divide(n);
return n;
}
#endif
#if defined(LIBDIVIDE_NEON)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE typename NeonVecFor<T>::type operator/(typename NeonVecFor<T>::type n, const divider<T, ALGO> &div) {
return div.divide(n);
}
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE typename NeonVecFor<T>::type operator/=(typename NeonVecFor<T>::type &n, const divider<T, ALGO> &div) {
n = div.divide(n);
return n;
}
#endif
#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
// libdivide::branchfree_divider<T>
template <typename T>
using branchfree_divider = divider<T, BRANCHFREE>;
#endif
} // namespace libdivide
#endif // __cplusplus
#if defined(_MSC_VER)
#pragma warning(pop)
#endif
#endif // LIBDIVIDE_H
#define ENTRIES 1024
template <typename T>
static unsigned fasthash(T den) {
return den * 0xBF58476D1CE4E5B9;
}
static unsigned fastrand() {
static __thread unsigned i = 0;
return fasthash(i++);
}
template <typename T>
T __div__(T num, T den) {
static __thread int disable = 0;
if (disable > 0) {
disable--;
skip:
return num/den;
}
static __thread struct {
T den;
libdivide::divider<T> fastdiv;
} fastdivs[ENTRIES] = {};
static __thread int lastidx = 0;
if (fastdivs[lastidx].den == den && den != 0) {
if (disable > -10000) disable--;
return num / fastdivs[lastidx].fastdiv;
}
unsigned idx = fasthash(den) % ENTRIES;
if (fastdivs[idx].den == den && den != 0) {
if (disable > -10000) disable--;
} else if (den != 0 && (fastdivs[idx].den == 0 || fastrand() % 16 == 0)) {
if (disable < 10000 && fastdivs[idx].den != 0) disable += 100;
fastdivs[idx].fastdiv = libdivide::divider<T>(den);
fastdivs[idx].den = den;
} else {
goto skip;
}
lastidx = idx;
return num / fastdivs[idx].fastdiv;
}
template int __div__(int num, int den);
template unsigned __div__(unsigned num, unsigned den);
template long __div__(long num, long den);
template unsigned long __div__(unsigned long num, unsigned long den);
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