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NPO2 slope span optimization
2020-10-21 21:31:28 +00:00
// libdivide.h - Optimized integer division
// https://libdivide.com
//
// Copyright (C) 2010 - 2019 ridiculous_fish, <libdivide@ridiculousfish.com>
// Copyright (C) 2016 - 2019 Kim Walisch, <kim.walisch@gmail.com>
//
// libdivide is dual-licensed under the Boost or zlib licenses.
// You may use libdivide under the terms of either of these.
Clarify license file mention in libdivide.h
2020-11-06 22:19:43 +00:00
// See LICENSE.txt in the libdivide source code repository for more details.
NPO2 slope span optimization
2020-10-21 21:31:28 +00:00
Clarify licensing-related text in libdivide.h
2020-10-31 14:39:05 +00:00
// NOTICE: This is an altered source version of libdivide.
// Libdivide is used here under the terms of the zlib license.
// Here is the zlib license text from https://github.com/ridiculousfish/libdivide/blob/master/LICENSE.txt
/*
zlib License
------------
Copyright (C) 2010 - 2019 ridiculous_fish, <libdivide@ridiculousfish.com>
Copyright (C) 2016 - 2019 Kim Walisch, <kim.walisch@gmail.com>
This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software
in a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/
// This version of libdivide has been modified for use with SRB2.
// Changes made include:
NPO2 slope span optimization
2020-10-21 21:31:28 +00:00
// - unused parts commented out (to avoid the need to fix C90 compilation issues with them)
// - C90 compilation issues fixed with used parts
// - use I_Error for errors
#ifndef LIBDIVIDE_H
#define LIBDIVIDE_H
#define LIBDIVIDE_VERSION "3.0"
#define LIBDIVIDE_VERSION_MAJOR 3
#define LIBDIVIDE_VERSION_MINOR 0
#include <stdint.h>
#if defined(__cplusplus)
#include <cstdlib>
#include <cstdio>
#include <type_traits>
#else
#include <stdlib.h>
#include <stdio.h>
#endif
#if defined(LIBDIVIDE_AVX512)
#include <immintrin.h>
#elif defined(LIBDIVIDE_AVX2)
#include <immintrin.h>
#elif defined(LIBDIVIDE_SSE2)
#include <emmintrin.h>
#endif
#if defined(_MSC_VER)
#include <intrin.h>
// disable warning C4146: unary minus operator applied
// to unsigned type, result still unsigned
#pragma warning(disable: 4146)
#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
#define LIBDIVIDE_ERROR(msg) \
I_Error("libdivide.h:%d: %s(): Error: %s\n", \
__LINE__, LIBDIVIDE_FUNCTION, msg);
#if defined(LIBDIVIDE_ASSERTIONS_ON)
#define LIBDIVIDE_ASSERT(x) \
if (!(x)) { \
I_Error("libdivide.h:%d: %s(): Assertion failed: %s\n", \
__LINE__, LIBDIVIDE_FUNCTION, #x); \
}
#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_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_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_32_SHIFT_MASK = 0x1F,
LIBDIVIDE_64_SHIFT_MASK = 0x3F,
LIBDIVIDE_ADD_MARKER = 0x40,
LIBDIVIDE_NEGATIVE_DIVISOR = 0x80
};
//static inline struct libdivide_s32_t libdivide_s32_gen(int32_t d);
static inline struct libdivide_u32_t libdivide_u32_gen(uint32_t d);
//static inline struct libdivide_s64_t libdivide_s64_gen(int64_t d);
//static inline struct libdivide_u64_t libdivide_u64_gen(uint64_t d);
/*static inline struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d);
static inline struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d);
static inline struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d);
static inline struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d);*/
//static inline int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom);
static inline uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom);
//static inline int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom);
//static inline uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom);
/*static inline int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom);
static inline uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom);
static inline int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom);
static inline uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom);*/
/*static inline int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom);
static inline uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom);
static inline int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom);
static inline uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom);*/
/*static inline int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom);
static inline uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom);
static inline int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom);
static inline uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom);*/
//////// Internal Utility Functions
static 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 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 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 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 inline int32_t libdivide_count_leading_zeros32(uint32_t val) {
#if 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 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_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 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 {u1, u0} by a 64-bit
// uint {v}. The result must fit in 64 bits.
// Returns the quotient directly and the remainder in *r
/*static uint64_t libdivide_128_div_64_to_64(uint64_t u1, uint64_t u0, uint64_t v, uint64_t *r) {
#if defined(LIBDIVIDE_X86_64) && \
defined(LIBDIVIDE_GCC_STYLE_ASM)
uint64_t result;
__asm__("divq %[v]"
: "=a"(result), "=d"(*r)
: [v] "r"(v), "a"(u0), "d"(u1)
);
return result;
#elif defined(HAS_INT128_T) && \
defined(HAS_INT128_DIV)
__uint128_t n = ((__uint128_t)u1 << 64) | u0;
uint64_t result = (uint64_t)(n / v);
*r = (uint64_t)(n - result * (__uint128_t)v);
return result;
#else
// Code taken from Hacker's Delight:
// http://www.hackersdelight.org/HDcode/divlu.c.
// License permits inclusion here per:
// http://www.hackersdelight.org/permissions.htm
const uint64_t b = (1ULL << 32); // Number base (32 bits)
uint64_t un1, un0; // Norm. dividend LSD's
uint64_t vn1, vn0; // Norm. divisor digits
uint64_t q1, q0; // Quotient digits
uint64_t un64, un21, un10; // Dividend digit pairs
uint64_t rhat; // A remainder
int32_t s; // Shift amount for norm
// If overflow, set rem. to an impossible value,
// and return the largest possible quotient
if (u1 >= v) {
*r = (uint64_t) -1;
return (uint64_t) -1;
}
// count leading zeros
s = libdivide_count_leading_zeros64(v);
if (s > 0) {
// Normalize divisor
v = v << s;
un64 = (u1 << s) | (u0 >> (64 - s));
un10 = u0 << s; // Shift dividend left
} else {
// Avoid undefined behavior of (u0 >> 64).
// The behavior is undefined if the right operand is
// negative, or greater than or equal to the length
// in bits of the promoted left operand.
un64 = u1;
un10 = u0;
}
// Break divisor up into two 32-bit digits
vn1 = v >> 32;
vn0 = v & 0xFFFFFFFF;
// Break right half of dividend into two digits
un1 = un10 >> 32;
un0 = un10 & 0xFFFFFFFF;
// Compute the first quotient digit, q1
q1 = un64 / vn1;
rhat = un64 - q1 * vn1;
while (q1 >= b || q1 * vn0 > b * rhat + un1) {
q1 = q1 - 1;
rhat = rhat + vn1;
if (rhat >= b)
break;
}
// Multiply and subtract
un21 = un64 * b + un1 - q1 * v;
// Compute the second quotient digit
q0 = un21 / vn1;
rhat = un21 - q0 * vn1;
while (q0 >= b || q0 * vn0 > b * rhat + un0) {
q0 = q0 - 1;
rhat = rhat + vn1;
if (rhat >= b)
break;
}
*r = (un21 * b + un0 - q0 * v) >> s;
return q1 * b + q0;
#endif
}*/
// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0)
static 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 uint64_t libdivide_128_div_128_to_64(uint64_t u_hi, uint64_t u_lo, uint64_t v_hi, uint64_t v_lo, uint64_t *r_hi, uint64_t *r_lo) {
#if defined(HAS_INT128_T) && \
defined(HAS_INT128_DIV)
__uint128_t ufull = u_hi;
__uint128_t vfull = v_hi;
ufull = (ufull << 64) | u_lo;
vfull = (vfull << 64) | v_lo;
uint64_t res = (uint64_t)(ufull / vfull);
__uint128_t remainder = ufull - (vfull * res);
*r_lo = (uint64_t)remainder;
*r_hi = (uint64_t)(remainder >> 64);
return res;
#else
// Adapted from "Unsigned Doubleword Division" in Hacker's Delight
// We want to compute u / v
typedef struct { uint64_t hi; uint64_t lo; } u128_t;
u128_t u = {u_hi, u_lo};
u128_t v = {v_hi, v_lo};
if (v.hi == 0) {
// divisor v is a 64 bit value, so we just need one 128/64 division
// Note that we are simpler than Hacker's Delight here, because we know
// the quotient fits in 64 bits whereas Hacker's Delight demands a full
// 128 bit quotient
*r_hi = 0;
return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo);
}
// Here v >= 2**64
// We know that v.hi != 0, so count leading zeros is OK
// We have 0 <= n <= 63
uint32_t n = libdivide_count_leading_zeros64(v.hi);
// Normalize the divisor so its MSB is 1
u128_t v1t = v;
libdivide_u128_shift(&v1t.hi, &v1t.lo, n);
uint64_t v1 = v1t.hi; // i.e. v1 = v1t >> 64
// To ensure no overflow
u128_t u1 = u;
libdivide_u128_shift(&u1.hi, &u1.lo, -1);
// Get quotient from divide unsigned insn.
uint64_t rem_ignored;
uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored);
// Undo normalization and division of u by 2.
u128_t q0 = {0, q1};
libdivide_u128_shift(&q0.hi, &q0.lo, n);
libdivide_u128_shift(&q0.hi, &q0.lo, -63);
// Make q0 correct or too small by 1
// Equivalent to `if (q0 != 0) q0 = q0 - 1;`
if (q0.hi != 0 || q0.lo != 0) {
q0.hi -= (q0.lo == 0); // borrow
q0.lo -= 1;
}
// Now q0 is correct.
// Compute q0 * v as q0v
// = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo)
// = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) +
// (q0.lo * v.hi << 64) + q0.lo * v.lo)
// Each term is 128 bit
// High half of full product (upper 128 bits!) are dropped
u128_t q0v = {0, 0};
q0v.hi = q0.hi*v.lo + q0.lo*v.hi + libdivide_mullhi_u64(q0.lo, v.lo);
q0v.lo = q0.lo*v.lo;
// Compute u - q0v as u_q0v
// This is the remainder
u128_t u_q0v = u;
u_q0v.hi -= q0v.hi + (u.lo < q0v.lo); // second term is borrow
u_q0v.lo -= q0v.lo;
// Check if u_q0v >= v
// This checks if our remainder is larger than the divisor
if ((u_q0v.hi > v.hi) ||
(u_q0v.hi == v.hi && u_q0v.lo >= v.lo)) {
// Increment q0
q0.lo += 1;
q0.hi += (q0.lo == 0); // carry
// Subtract v from remainder
u_q0v.hi -= v.hi + (u_q0v.lo < v.lo);
u_q0v.lo -= v.lo;
}
*r_hi = u_q0v.hi;
*r_lo = u_q0v.lo;
LIBDIVIDE_ASSERT(q0.hi == 0);
return q0.lo;
#endif
}*/
////////// UINT32
Suppress libdivide warnings in GCC/Clang
2023-05-29 12:38:22 +00:00
#if defined(__GNUC__) || defined(__clang__) // Suppress intentional compiler warnings
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Waggregate-return"
#endif
NPO2 slope span optimization
2020-10-21 21:31:28 +00:00
static inline struct libdivide_u32_t libdivide_internal_u32_gen(uint32_t d, int branchfree) {
struct libdivide_u32_t result;
uint32_t floor_log_2_d;
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
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;
uint32_t e;
proposed_m = libdivide_64_div_32_to_32(1U << floor_log_2_d, 0, d, &rem);
LIBDIVIDE_ASSERT(rem > 0 && rem < d);
e = d - rem;
// This power works if e < 2**floor_log_2_d.
if (!branchfree && (e < (1U << floor_log_2_d))) {
// This power works
more = floor_log_2_d;
} else {
// We have to use the general 33-bit algorithm. We need to compute
// (2**power) / d. However, we already have (2**(power-1))/d and
// its remainder. By doubling both, and then correcting the
// remainder, we can compute the larger division.
// don't care about overflow here - in fact, we expect it
const uint32_t twice_rem = rem + rem;
proposed_m += proposed_m;
if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
}
result.magic = 1 + proposed_m;
result.more = more;
// result.more's shift should in general be ceil_log_2_d. But if we
// used the smaller power, we subtract one from the shift because we're
// using the smaller power. If we're using the larger power, we
// subtract one from the shift because it's taken care of by the add
// indicator. So floor_log_2_d happens to be correct in both cases.
}
return result;
}
struct libdivide_u32_t libdivide_u32_gen(uint32_t d) {
return libdivide_internal_u32_gen(d, 0);
}
/*struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d) {
if (d == 1) {
LIBDIVIDE_ERROR("branchfree divider must be != 1");
}
struct libdivide_u32_t tmp = libdivide_internal_u32_gen(d, 1);
struct libdivide_u32_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_32_SHIFT_MASK)};
return ret;
}*/
Suppress libdivide warnings in GCC/Clang
2023-05-29 12:38:22 +00:00
#if defined(__GNUC__) || defined(__clang__) // Stop suppressing intentional compiler warnings
#pragma GCC diagnostic pop
#endif
NPO2 slope span optimization
2020-10-21 21:31:28 +00:00
uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return numer >> more;
}
else {
uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
uint32_t t = ((numer - q) >> 1) + q;
return t >> (more & LIBDIVIDE_32_SHIFT_MASK);
}
else {
// All upper bits are 0,
// don't need to mask them off.
return q >> more;
}
}
}
/*uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom) {
uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
uint32_t t = ((numer - q) >> 1) + q;
return t >> denom->more;
}
uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
if (!denom->magic) {
return 1U << shift;
} else if (!(more & LIBDIVIDE_ADD_MARKER)) {
// We compute q = n/d = n*m / 2^(32 + shift)
// Therefore we have d = 2^(32 + shift) / m
// We need to ceil it.
// We know d is not a power of 2, so m is not a power of 2,
// so we can just add 1 to the floor
uint32_t hi_dividend = 1U << shift;
uint32_t rem_ignored;
return 1 + libdivide_64_div_32_to_32(hi_dividend, 0, denom->magic, &rem_ignored);
} else {
// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
// Also note that shift may be as high as 31, so shift + 1 will
// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
// then double the quotient and remainder.
uint64_t half_n = 1ULL << (32 + shift);
uint64_t d = (1ULL << 32) | denom->magic;
// Note that the quotient is guaranteed <= 32 bits, but the remainder
// may need 33!
uint32_t half_q = (uint32_t)(half_n / d);
uint64_t rem = half_n % d;
// We computed 2^(32+shift)/(m+2^32)
// Need to double it, and then add 1 to the quotient if doubling th
// remainder would increase the quotient.
// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
// We rounded down in gen (hence +1)
return full_q + 1;
}
}
uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
if (!denom->magic) {
return 1U << (shift + 1);
} else {
// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
// Also note that shift may be as high as 31, so shift + 1 will
// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
// then double the quotient and remainder.
uint64_t half_n = 1ULL << (32 + shift);
uint64_t d = (1ULL << 32) | denom->magic;
// Note that the quotient is guaranteed <= 32 bits, but the remainder
// may need 33!
uint32_t half_q = (uint32_t)(half_n / d);
uint64_t rem = half_n % d;
// We computed 2^(32+shift)/(m+2^32)
// Need to double it, and then add 1 to the quotient if doubling th
// remainder would increase the quotient.
// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
// We rounded down in gen (hence +1)
return full_q + 1;
}
}*/
/////////// UINT64
/*static inline struct libdivide_u64_t libdivide_internal_u64_gen(uint64_t d, int branchfree) {
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
struct libdivide_u64_t result;
uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(d);
// Power of 2
if ((d & (d - 1)) == 0) {
// We need to subtract 1 from the shift value in case of an unsigned
// branchfree divider because there is a hardcoded right shift by 1
// in its division algorithm. Because of this we also need to add back
// 1 in its recovery algorithm.
result.magic = 0;
result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
} else {
uint64_t proposed_m, rem;
uint8_t more;
// (1 << (64 + floor_log_2_d)) / d
proposed_m = libdivide_128_div_64_to_64(1ULL << floor_log_2_d, 0, d, &rem);
LIBDIVIDE_ASSERT(rem > 0 && rem < d);
const uint64_t e = d - rem;
// This power works if e < 2**floor_log_2_d.
if (!branchfree && e < (1ULL << floor_log_2_d)) {
// This power works
more = floor_log_2_d;
} else {
// We have to use the general 65-bit algorithm. We need to compute
// (2**power) / d. However, we already have (2**(power-1))/d and
// its remainder. By doubling both, and then correcting the
// remainder, we can compute the larger division.
// don't care about overflow here - in fact, we expect it
proposed_m += proposed_m;
const uint64_t twice_rem = rem + rem;
if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
}
result.magic = 1 + proposed_m;
result.more = more;
// result.more's shift should in general be ceil_log_2_d. But if we
// used the smaller power, we subtract one from the shift because we're
// using the smaller power. If we're using the larger power, we
// subtract one from the shift because it's taken care of by the add
// indicator. So floor_log_2_d happens to be correct in both cases,
// which is why we do it outside of the if statement.
}
return result;
}
struct libdivide_u64_t libdivide_u64_gen(uint64_t d) {
return libdivide_internal_u64_gen(d, 0);
}
struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d) {
if (d == 1) {
LIBDIVIDE_ERROR("branchfree divider must be != 1");
}
struct libdivide_u64_t tmp = libdivide_internal_u64_gen(d, 1);
struct libdivide_u64_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_64_SHIFT_MASK)};
return ret;
}
uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return numer >> more;
}
else {
uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
uint64_t t = ((numer - q) >> 1) + q;
return t >> (more & LIBDIVIDE_64_SHIFT_MASK);
}
else {
// All upper bits are 0,
// don't need to mask them off.
return q >> more;
}
}
}
uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom) {
uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
uint64_t t = ((numer - q) >> 1) + q;
return t >> denom->more;
}
uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
if (!denom->magic) {
return 1ULL << shift;
} else if (!(more & LIBDIVIDE_ADD_MARKER)) {
// We compute q = n/d = n*m / 2^(64 + shift)
// Therefore we have d = 2^(64 + shift) / m
// We need to ceil it.
// We know d is not a power of 2, so m is not a power of 2,
// so we can just add 1 to the floor
uint64_t hi_dividend = 1ULL << shift;
uint64_t rem_ignored;
return 1 + libdivide_128_div_64_to_64(hi_dividend, 0, denom->magic, &rem_ignored);
} else {
// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
// libdivide_u32_recover for more on what we do here.
// TODO: do something better than 128 bit math
// Full n is a (potentially) 129 bit value
// half_n is a 128 bit value
// Compute the hi half of half_n. Low half is 0.
uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
// d is a 65 bit value. The high bit is always set to 1.
const uint64_t d_hi = 1, d_lo = denom->magic;
// Note that the quotient is guaranteed <= 64 bits,
// but the remainder may need 65!
uint64_t r_hi, r_lo;
uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
// We computed 2^(64+shift)/(m+2^64)
// Double the remainder ('dr') and check if that is larger than d
// Note that d is a 65 bit value, so r1 is small and so r1 + r1
// cannot overflow
uint64_t dr_lo = r_lo + r_lo;
uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
return full_q + 1;
}
}
uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
if (!denom->magic) {
return 1ULL << (shift + 1);
} else {
// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
// libdivide_u32_recover for more on what we do here.
// TODO: do something better than 128 bit math
// Full n is a (potentially) 129 bit value
// half_n is a 128 bit value
// Compute the hi half of half_n. Low half is 0.
uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
// d is a 65 bit value. The high bit is always set to 1.
const uint64_t d_hi = 1, d_lo = denom->magic;
// Note that the quotient is guaranteed <= 64 bits,
// but the remainder may need 65!
uint64_t r_hi, r_lo;
uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
// We computed 2^(64+shift)/(m+2^64)
// Double the remainder ('dr') and check if that is larger than d
// Note that d is a 65 bit value, so r1 is small and so r1 + r1
// cannot overflow
uint64_t dr_lo = r_lo + r_lo;
uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
return full_q + 1;
}
}*/
/////////// SINT32
/*static inline struct libdivide_s32_t libdivide_internal_s32_gen(int32_t d, int branchfree) {
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
struct libdivide_s32_t result;
// If d is a power of 2, or negative a power of 2, we have to use a shift.
// This is especially important because the magic algorithm fails for -1.
// To check if d is a power of 2 or its inverse, it suffices to check
// whether its absolute value has exactly one bit set. This works even for
// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
// and is a power of 2.
uint32_t ud = (uint32_t)d;
uint32_t absD = (d < 0) ? -ud : ud;
uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(absD);
// check if exactly one bit is set,
// don't care if absD is 0 since that's divide by zero
if ((absD & (absD - 1)) == 0) {
// Branchfree and normal paths are exactly the same
result.magic = 0;
result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
} else {
LIBDIVIDE_ASSERT(floor_log_2_d >= 1);
uint8_t more;
// the dividend here is 2**(floor_log_2_d + 31), so the low 32 bit word
// is 0 and the high word is floor_log_2_d - 1
uint32_t rem, proposed_m;
proposed_m = libdivide_64_div_32_to_32(1U << (floor_log_2_d - 1), 0, absD, &rem);
const uint32_t e = absD - rem;
// We are going to start with a power of floor_log_2_d - 1.
// This works if works if e < 2**floor_log_2_d.
if (!branchfree && e < (1U << floor_log_2_d)) {
// This power works
more = floor_log_2_d - 1;
} else {
// We need to go one higher. This should not make proposed_m
// overflow, but it will make it negative when interpreted as an
// int32_t.
proposed_m += proposed_m;
const uint32_t twice_rem = rem + rem;
if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
}
proposed_m += 1;
int32_t magic = (int32_t)proposed_m;
// Mark if we are negative. Note we only negate the magic number in the
// branchfull case.
if (d < 0) {
more |= LIBDIVIDE_NEGATIVE_DIVISOR;
if (!branchfree) {
magic = -magic;
}
}
result.more = more;
result.magic = magic;
}
return result;
}
struct libdivide_s32_t libdivide_s32_gen(int32_t d) {
return libdivide_internal_s32_gen(d, 0);
}
struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d) {
struct libdivide_s32_t tmp = libdivide_internal_s32_gen(d, 1);
struct libdivide_s32_branchfree_t result = {tmp.magic, tmp.more};
return result;
}
int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
if (!denom->magic) {
uint32_t sign = (int8_t)more >> 7;
uint32_t mask = (1U << shift) - 1;
uint32_t uq = numer + ((numer >> 31) & mask);
int32_t q = (int32_t)uq;
q >>= shift;
q = (q ^ sign) - sign;
return q;
} else {
uint32_t uq = (uint32_t)libdivide_mullhi_s32(denom->magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift and then sign extend
int32_t sign = (int8_t)more >> 7;
// q += (more < 0 ? -numer : numer)
// cast required to avoid UB
uq += ((uint32_t)numer ^ sign) - sign;
}
int32_t q = (int32_t)uq;
q >>= shift;
q += (q < 0);
return q;
}
}
int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
// must be arithmetic shift and then sign extend
int32_t sign = (int8_t)more >> 7;
int32_t magic = denom->magic;
int32_t q = libdivide_mullhi_s32(magic, numer);
q += numer;
// If q is non-negative, we have nothing to do
// If q is negative, we want to add either (2**shift)-1 if d is a power of
// 2, or (2**shift) if it is not a power of 2
uint32_t is_power_of_2 = (magic == 0);
uint32_t q_sign = (uint32_t)(q >> 31);
q += q_sign & ((1U << shift) - is_power_of_2);
// Now arithmetic right shift
q >>= shift;
// Negate if needed
q = (q ^ sign) - sign;
return q;
}
int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
if (!denom->magic) {
uint32_t absD = 1U << shift;
if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
absD = -absD;
}
return (int32_t)absD;
} else {
// Unsigned math is much easier
// We negate the magic number only in the branchfull case, and we don't
// know which case we're in. However we have enough information to
// determine the correct sign of the magic number. The divisor was
// negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set,
// the magic number's sign is opposite that of the divisor.
// We want to compute the positive magic number.
int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
? denom->magic > 0 : denom->magic < 0;
// Handle the power of 2 case (including branchfree)
if (denom->magic == 0) {
int32_t result = 1U << shift;
return negative_divisor ? -result : result;
}
uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic);
uint64_t n = 1ULL << (32 + shift); // this shift cannot exceed 30
uint32_t q = (uint32_t)(n / d);
int32_t result = (int32_t)q;
result += 1;
return negative_divisor ? -result : result;
}
}
int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom) {
return libdivide_s32_recover((const struct libdivide_s32_t *)denom);
}*/
///////////// SINT64
/*static inline struct libdivide_s64_t libdivide_internal_s64_gen(int64_t d, int branchfree) {
if (d == 0) {
LIBDIVIDE_ERROR("divider must be != 0");
}
struct libdivide_s64_t result;
// If d is a power of 2, or negative a power of 2, we have to use a shift.
// This is especially important because the magic algorithm fails for -1.
// To check if d is a power of 2 or its inverse, it suffices to check
// whether its absolute value has exactly one bit set. This works even for
// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
// and is a power of 2.
uint64_t ud = (uint64_t)d;
uint64_t absD = (d < 0) ? -ud : ud;
uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(absD);
// check if exactly one bit is set,
// don't care if absD is 0 since that's divide by zero
if ((absD & (absD - 1)) == 0) {
// Branchfree and non-branchfree cases are the same
result.magic = 0;
result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
} else {
// the dividend here is 2**(floor_log_2_d + 63), so the low 64 bit word
// is 0 and the high word is floor_log_2_d - 1
uint8_t more;
uint64_t rem, proposed_m;
proposed_m = libdivide_128_div_64_to_64(1ULL << (floor_log_2_d - 1), 0, absD, &rem);
const uint64_t e = absD - rem;
// We are going to start with a power of floor_log_2_d - 1.
// This works if works if e < 2**floor_log_2_d.
if (!branchfree && e < (1ULL << floor_log_2_d)) {
// This power works
more = floor_log_2_d - 1;
} else {
// We need to go one higher. This should not make proposed_m
// overflow, but it will make it negative when interpreted as an
// int32_t.
proposed_m += proposed_m;
const uint64_t twice_rem = rem + rem;
if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
// note that we only set the LIBDIVIDE_NEGATIVE_DIVISOR bit if we
// also set ADD_MARKER this is an annoying optimization that
// enables algorithm #4 to avoid the mask. However we always set it
// in the branchfree case
more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
}
proposed_m += 1;
int64_t magic = (int64_t)proposed_m;
// Mark if we are negative
if (d < 0) {
more |= LIBDIVIDE_NEGATIVE_DIVISOR;
if (!branchfree) {
magic = -magic;
}
}
result.more = more;
result.magic = magic;
}
return result;
}
struct libdivide_s64_t libdivide_s64_gen(int64_t d) {
return libdivide_internal_s64_gen(d, 0);
}
struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d) {
struct libdivide_s64_t tmp = libdivide_internal_s64_gen(d, 1);
struct libdivide_s64_branchfree_t ret = {tmp.magic, tmp.more};
return ret;
}
int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
if (!denom->magic) { // shift path
uint64_t mask = (1ULL << shift) - 1;
uint64_t uq = numer + ((numer >> 63) & mask);
int64_t q = (int64_t)uq;
q >>= shift;
// must be arithmetic shift and then sign-extend
int64_t sign = (int8_t)more >> 7;
q = (q ^ sign) - sign;
return q;
} else {
uint64_t uq = (uint64_t)libdivide_mullhi_s64(denom->magic, numer);
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift and then sign extend
int64_t sign = (int8_t)more >> 7;
// q += (more < 0 ? -numer : numer)
// cast required to avoid UB
uq += ((uint64_t)numer ^ sign) - sign;
}
int64_t q = (int64_t)uq;
q >>= shift;
q += (q < 0);
return q;
}
}
int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
// must be arithmetic shift and then sign extend
int64_t sign = (int8_t)more >> 7;
int64_t magic = denom->magic;
int64_t q = libdivide_mullhi_s64(magic, numer);
q += numer;
// If q is non-negative, we have nothing to do.
// If q is negative, we want to add either (2**shift)-1 if d is a power of
// 2, or (2**shift) if it is not a power of 2.
uint64_t is_power_of_2 = (magic == 0);
uint64_t q_sign = (uint64_t)(q >> 63);
q += q_sign & ((1ULL << shift) - is_power_of_2);
// Arithmetic right shift
q >>= shift;
// Negate if needed
q = (q ^ sign) - sign;
return q;
}
int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
if (denom->magic == 0) { // shift path
uint64_t absD = 1ULL << shift;
if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
absD = -absD;
}
return (int64_t)absD;
} else {
// Unsigned math is much easier
int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
? denom->magic > 0 : denom->magic < 0;
uint64_t d = (uint64_t)(magic_was_negated ? -denom->magic : denom->magic);
uint64_t n_hi = 1ULL << shift, n_lo = 0;
uint64_t rem_ignored;
uint64_t q = libdivide_128_div_64_to_64(n_hi, n_lo, d, &rem_ignored);
int64_t result = (int64_t)(q + 1);
if (negative_divisor) {
result = -result;
}
return result;
}
}
int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom) {
return libdivide_s64_recover((const struct libdivide_s64_t *)denom);
}*/
#if defined(LIBDIVIDE_AVX512)
static inline __m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom);
static inline __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom);
static inline __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom);
static inline __m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom);
static inline __m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom);
static inline __m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom);
static inline __m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom);
static inline __m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
static inline __m512i libdivide_s64_signbits(__m512i v) {;
return _mm512_srai_epi64(v, 63);
}
static inline __m512i libdivide_s64_shift_right_vector(__m512i v, int amt) {
return _mm512_srai_epi64(v, amt);
}
// Here, b is assumed to contain one 32-bit value repeated.
static inline __m512i libdivide_mullhi_u32_vector(__m512i a, __m512i b) {
__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epu32(a, b), 32);
__m512i a1X3X = _mm512_srli_epi64(a, 32);
__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epu32(a1X3X, b), mask);
return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
}
// b is one 32-bit value repeated.
static inline __m512i libdivide_mullhi_s32_vector(__m512i a, __m512i b) {
__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epi32(a, b), 32);
__m512i a1X3X = _mm512_srli_epi64(a, 32);
__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epi32(a1X3X, b), mask);
return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
}
// Here, y is assumed to contain one 64-bit value repeated.
// https://stackoverflow.com/a/28827013
static inline __m512i libdivide_mullhi_u64_vector(__m512i x, __m512i y) {
__m512i lomask = _mm512_set1_epi64(0xffffffff);
__m512i xh = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM) 0xB1);
__m512i yh = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM) 0xB1);
__m512i w0 = _mm512_mul_epu32(x, y);
__m512i w1 = _mm512_mul_epu32(x, yh);
__m512i w2 = _mm512_mul_epu32(xh, y);
__m512i w3 = _mm512_mul_epu32(xh, yh);
__m512i w0h = _mm512_srli_epi64(w0, 32);
__m512i s1 = _mm512_add_epi64(w1, w0h);
__m512i s1l = _mm512_and_si512(s1, lomask);
__m512i s1h = _mm512_srli_epi64(s1, 32);
__m512i s2 = _mm512_add_epi64(w2, s1l);
__m512i s2h = _mm512_srli_epi64(s2, 32);
__m512i hi = _mm512_add_epi64(w3, s1h);
hi = _mm512_add_epi64(hi, s2h);
return hi;
}
// y is one 64-bit value repeated.
static inline __m512i libdivide_mullhi_s64_vector(__m512i x, __m512i y) {
__m512i p = libdivide_mullhi_u64_vector(x, y);
__m512i t1 = _mm512_and_si512(libdivide_s64_signbits(x), y);
__m512i t2 = _mm512_and_si512(libdivide_s64_signbits(y), x);
p = _mm512_sub_epi64(p, t1);
p = _mm512_sub_epi64(p, t2);
return p;
}
////////// UINT32
__m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm512_srli_epi32(numers, more);
}
else {
__m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
return _mm512_srli_epi32(t, shift);
}
else {
return _mm512_srli_epi32(q, more);
}
}
}
__m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom) {
__m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
return _mm512_srli_epi32(t, denom->more);
}
////////// UINT64
__m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm512_srli_epi64(numers, more);
}
else {
__m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
return _mm512_srli_epi64(t, shift);
}
else {
return _mm512_srli_epi64(q, more);
}
}
}
__m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom) {
__m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
return _mm512_srli_epi64(t, denom->more);
}
////////// SINT32
__m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
uint32_t mask = (1U << shift) - 1;
__m512i roundToZeroTweak = _mm512_set1_epi32(mask);
// q = numer + ((numer >> 31) & roundToZeroTweak);
__m512i q = _mm512_add_epi32(numers, _mm512_and_si512(_mm512_srai_epi32(numers, 31), roundToZeroTweak));
q = _mm512_srai_epi32(q, shift);
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign);
return q;
}
else {
__m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm512_add_epi32(q, _mm512_sub_epi32(_mm512_xor_si512(numers, sign), sign));
}
// q >>= shift
q = _mm512_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
q = _mm512_add_epi32(q, _mm512_srli_epi32(q, 31)); // q += (q < 0)
return q;
}
}
__m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom) {
int32_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
// must be arithmetic shift
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
__m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(magic));
q = _mm512_add_epi32(q, numers); // q += numers
// If q is non-negative, we have nothing to do
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2
uint32_t is_power_of_2 = (magic == 0);
__m512i q_sign = _mm512_srai_epi32(q, 31); // q_sign = q >> 31
__m512i mask = _mm512_set1_epi32((1U << shift) - is_power_of_2);
q = _mm512_add_epi32(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
q = _mm512_srai_epi32(q, shift); // q >>= shift
q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
////////// SINT64
__m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
int64_t magic = denom->magic;
if (magic == 0) { // shift path
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
uint64_t mask = (1ULL << shift) - 1;
__m512i roundToZeroTweak = _mm512_set1_epi64(mask);
// q = numer + ((numer >> 63) & roundToZeroTweak);
__m512i q = _mm512_add_epi64(numers, _mm512_and_si512(libdivide_s64_signbits(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vector(q, shift);
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign);
return q;
}
else {
__m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm512_add_epi64(q, _mm512_sub_epi64(_mm512_xor_si512(numers, sign), sign));
}
// q >>= denom->mult_path.shift
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
q = _mm512_add_epi64(q, _mm512_srli_epi64(q, 63)); // q += (q < 0)
return q;
}
}
__m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom) {
int64_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
// must be arithmetic shift
__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
// libdivide_mullhi_s64(numers, magic);
__m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
q = _mm512_add_epi64(q, numers); // q += numers
// If q is non-negative, we have nothing to do.
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2.
uint32_t is_power_of_2 = (magic == 0);
__m512i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
__m512i mask = _mm512_set1_epi64((1ULL << shift) - is_power_of_2);
q = _mm512_add_epi64(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#elif defined(LIBDIVIDE_AVX2)
static inline __m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom);
static inline __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom);
static inline __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom);
static inline __m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom);
static inline __m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom);
static inline __m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom);
static inline __m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom);
static inline __m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
// Implementation of _mm256_srai_epi64(v, 63) (from AVX512).
static inline __m256i libdivide_s64_signbits(__m256i v) {
__m256i hiBitsDuped = _mm256_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
__m256i signBits = _mm256_srai_epi32(hiBitsDuped, 31);
return signBits;
}
// Implementation of _mm256_srai_epi64 (from AVX512).
static inline __m256i libdivide_s64_shift_right_vector(__m256i v, int amt) {
const int b = 64 - amt;
__m256i m = _mm256_set1_epi64x(1ULL << (b - 1));
__m256i x = _mm256_srli_epi64(v, amt);
__m256i result = _mm256_sub_epi64(_mm256_xor_si256(x, m), m);
return result;
}
// Here, b is assumed to contain one 32-bit value repeated.
static inline __m256i libdivide_mullhi_u32_vector(__m256i a, __m256i b) {
__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epu32(a, b), 32);
__m256i a1X3X = _mm256_srli_epi64(a, 32);
__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epu32(a1X3X, b), mask);
return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
}
// b is one 32-bit value repeated.
static inline __m256i libdivide_mullhi_s32_vector(__m256i a, __m256i b) {
__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epi32(a, b), 32);
__m256i a1X3X = _mm256_srli_epi64(a, 32);
__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epi32(a1X3X, b), mask);
return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
}
// Here, y is assumed to contain one 64-bit value repeated.
// https://stackoverflow.com/a/28827013
static inline __m256i libdivide_mullhi_u64_vector(__m256i x, __m256i y) {
__m256i lomask = _mm256_set1_epi64x(0xffffffff);
__m256i xh = _mm256_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h
__m256i yh = _mm256_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h
__m256i w0 = _mm256_mul_epu32(x, y); // x0l*y0l, x1l*y1l
__m256i w1 = _mm256_mul_epu32(x, yh); // x0l*y0h, x1l*y1h
__m256i w2 = _mm256_mul_epu32(xh, y); // x0h*y0l, x1h*y0l
__m256i w3 = _mm256_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h
__m256i w0h = _mm256_srli_epi64(w0, 32);
__m256i s1 = _mm256_add_epi64(w1, w0h);
__m256i s1l = _mm256_and_si256(s1, lomask);
__m256i s1h = _mm256_srli_epi64(s1, 32);
__m256i s2 = _mm256_add_epi64(w2, s1l);
__m256i s2h = _mm256_srli_epi64(s2, 32);
__m256i hi = _mm256_add_epi64(w3, s1h);
hi = _mm256_add_epi64(hi, s2h);
return hi;
}
// y is one 64-bit value repeated.
static inline __m256i libdivide_mullhi_s64_vector(__m256i x, __m256i y) {
__m256i p = libdivide_mullhi_u64_vector(x, y);
__m256i t1 = _mm256_and_si256(libdivide_s64_signbits(x), y);
__m256i t2 = _mm256_and_si256(libdivide_s64_signbits(y), x);
p = _mm256_sub_epi64(p, t1);
p = _mm256_sub_epi64(p, t2);
return p;
}
////////// UINT32
__m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm256_srli_epi32(numers, more);
}
else {
__m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
return _mm256_srli_epi32(t, shift);
}
else {
return _mm256_srli_epi32(q, more);
}
}
}
__m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom) {
__m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
return _mm256_srli_epi32(t, denom->more);
}
////////// UINT64
__m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm256_srli_epi64(numers, more);
}
else {
__m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
return _mm256_srli_epi64(t, shift);
}
else {
return _mm256_srli_epi64(q, more);
}
}
}
__m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom) {
__m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
return _mm256_srli_epi64(t, denom->more);
}
////////// SINT32
__m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
uint32_t mask = (1U << shift) - 1;
__m256i roundToZeroTweak = _mm256_set1_epi32(mask);
// q = numer + ((numer >> 31) & roundToZeroTweak);
__m256i q = _mm256_add_epi32(numers, _mm256_and_si256(_mm256_srai_epi32(numers, 31), roundToZeroTweak));
q = _mm256_srai_epi32(q, shift);
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign);
return q;
}
else {
__m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm256_add_epi32(q, _mm256_sub_epi32(_mm256_xor_si256(numers, sign), sign));
}
// q >>= shift
q = _mm256_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
q = _mm256_add_epi32(q, _mm256_srli_epi32(q, 31)); // q += (q < 0)
return q;
}
}
__m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom) {
int32_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
// must be arithmetic shift
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
__m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(magic));
q = _mm256_add_epi32(q, numers); // q += numers
// If q is non-negative, we have nothing to do
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2
uint32_t is_power_of_2 = (magic == 0);
__m256i q_sign = _mm256_srai_epi32(q, 31); // q_sign = q >> 31
__m256i mask = _mm256_set1_epi32((1U << shift) - is_power_of_2);
q = _mm256_add_epi32(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
q = _mm256_srai_epi32(q, shift); // q >>= shift
q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
////////// SINT64
__m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
int64_t magic = denom->magic;
if (magic == 0) { // shift path
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
uint64_t mask = (1ULL << shift) - 1;
__m256i roundToZeroTweak = _mm256_set1_epi64x(mask);
// q = numer + ((numer >> 63) & roundToZeroTweak);
__m256i q = _mm256_add_epi64(numers, _mm256_and_si256(libdivide_s64_signbits(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vector(q, shift);
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign);
return q;
}
else {
__m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm256_add_epi64(q, _mm256_sub_epi64(_mm256_xor_si256(numers, sign), sign));
}
// q >>= denom->mult_path.shift
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
q = _mm256_add_epi64(q, _mm256_srli_epi64(q, 63)); // q += (q < 0)
return q;
}
}
__m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom) {
int64_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
// must be arithmetic shift
__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
// libdivide_mullhi_s64(numers, magic);
__m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
q = _mm256_add_epi64(q, numers); // q += numers
// If q is non-negative, we have nothing to do.
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2.
uint32_t is_power_of_2 = (magic == 0);
__m256i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
__m256i mask = _mm256_set1_epi64x((1ULL << shift) - is_power_of_2);
q = _mm256_add_epi64(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
#elif defined(LIBDIVIDE_SSE2)
static inline __m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom);
static inline __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom);
static inline __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom);
static inline __m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom);
static inline __m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom);
static inline __m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom);
static inline __m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom);
static inline __m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom);
//////// Internal Utility Functions
// Implementation of _mm_srai_epi64(v, 63) (from AVX512).
static inline __m128i libdivide_s64_signbits(__m128i v) {
__m128i hiBitsDuped = _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
__m128i signBits = _mm_srai_epi32(hiBitsDuped, 31);
return signBits;
}
// Implementation of _mm_srai_epi64 (from AVX512).
static inline __m128i libdivide_s64_shift_right_vector(__m128i v, int amt) {
const int b = 64 - amt;
__m128i m = _mm_set1_epi64x(1ULL << (b - 1));
__m128i x = _mm_srli_epi64(v, amt);
__m128i result = _mm_sub_epi64(_mm_xor_si128(x, m), m);
return result;
}
// Here, b is assumed to contain one 32-bit value repeated.
static inline __m128i libdivide_mullhi_u32_vector(__m128i a, __m128i b) {
__m128i hi_product_0Z2Z = _mm_srli_epi64(_mm_mul_epu32(a, b), 32);
__m128i a1X3X = _mm_srli_epi64(a, 32);
__m128i mask = _mm_set_epi32(-1, 0, -1, 0);
__m128i hi_product_Z1Z3 = _mm_and_si128(_mm_mul_epu32(a1X3X, b), mask);
return _mm_or_si128(hi_product_0Z2Z, hi_product_Z1Z3);
}
// SSE2 does not have a signed multiplication instruction, but we can convert
// unsigned to signed pretty efficiently. Again, b is just a 32 bit value
// repeated four times.
static inline __m128i libdivide_mullhi_s32_vector(__m128i a, __m128i b) {
__m128i p = libdivide_mullhi_u32_vector(a, b);
// t1 = (a >> 31) & y, arithmetic shift
__m128i t1 = _mm_and_si128(_mm_srai_epi32(a, 31), b);
__m128i t2 = _mm_and_si128(_mm_srai_epi32(b, 31), a);
p = _mm_sub_epi32(p, t1);
p = _mm_sub_epi32(p, t2);
return p;
}
// Here, y is assumed to contain one 64-bit value repeated.
// https://stackoverflow.com/a/28827013
static inline __m128i libdivide_mullhi_u64_vector(__m128i x, __m128i y) {
__m128i lomask = _mm_set1_epi64x(0xffffffff);
__m128i xh = _mm_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h
__m128i yh = _mm_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h
__m128i w0 = _mm_mul_epu32(x, y); // x0l*y0l, x1l*y1l
__m128i w1 = _mm_mul_epu32(x, yh); // x0l*y0h, x1l*y1h
__m128i w2 = _mm_mul_epu32(xh, y); // x0h*y0l, x1h*y0l
__m128i w3 = _mm_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h
__m128i w0h = _mm_srli_epi64(w0, 32);
__m128i s1 = _mm_add_epi64(w1, w0h);
__m128i s1l = _mm_and_si128(s1, lomask);
__m128i s1h = _mm_srli_epi64(s1, 32);
__m128i s2 = _mm_add_epi64(w2, s1l);
__m128i s2h = _mm_srli_epi64(s2, 32);
__m128i hi = _mm_add_epi64(w3, s1h);
hi = _mm_add_epi64(hi, s2h);
return hi;
}
// y is one 64-bit value repeated.
static inline __m128i libdivide_mullhi_s64_vector(__m128i x, __m128i y) {
__m128i p = libdivide_mullhi_u64_vector(x, y);
__m128i t1 = _mm_and_si128(libdivide_s64_signbits(x), y);
__m128i t2 = _mm_and_si128(libdivide_s64_signbits(y), x);
p = _mm_sub_epi64(p, t1);
p = _mm_sub_epi64(p, t2);
return p;
}
////////// UINT32
__m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm_srli_epi32(numers, more);
}
else {
__m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
return _mm_srli_epi32(t, shift);
}
else {
return _mm_srli_epi32(q, more);
}
}
}
__m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom) {
__m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
return _mm_srli_epi32(t, denom->more);
}
////////// UINT64
__m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
return _mm_srli_epi64(numers, more);
}
else {
__m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// uint32_t t = ((numer - q) >> 1) + q;
// return t >> denom->shift;
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
return _mm_srli_epi64(t, shift);
}
else {
return _mm_srli_epi64(q, more);
}
}
}
__m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom) {
__m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
return _mm_srli_epi64(t, denom->more);
}
////////// SINT32
__m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom) {
uint8_t more = denom->more;
if (!denom->magic) {
uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
uint32_t mask = (1U << shift) - 1;
__m128i roundToZeroTweak = _mm_set1_epi32(mask);
// q = numer + ((numer >> 31) & roundToZeroTweak);
__m128i q = _mm_add_epi32(numers, _mm_and_si128(_mm_srai_epi32(numers, 31), roundToZeroTweak));
q = _mm_srai_epi32(q, shift);
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign);
return q;
}
else {
__m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(denom->magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm_add_epi32(q, _mm_sub_epi32(_mm_xor_si128(numers, sign), sign));
}
// q >>= shift
q = _mm_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
q = _mm_add_epi32(q, _mm_srli_epi32(q, 31)); // q += (q < 0)
return q;
}
}
__m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom) {
int32_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
// must be arithmetic shift
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
__m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(magic));
q = _mm_add_epi32(q, numers); // q += numers
// If q is non-negative, we have nothing to do
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2
uint32_t is_power_of_2 = (magic == 0);
__m128i q_sign = _mm_srai_epi32(q, 31); // q_sign = q >> 31
__m128i mask = _mm_set1_epi32((1U << shift) - is_power_of_2);
q = _mm_add_epi32(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
q = _mm_srai_epi32(q, shift); // q >>= shift
q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
return q;
}
////////// SINT64
__m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom) {
uint8_t more = denom->more;
int64_t magic = denom->magic;
if (magic == 0) { // shift path
uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
uint64_t mask = (1ULL << shift) - 1;
__m128i roundToZeroTweak = _mm_set1_epi64x(mask);
// q = numer + ((numer >> 63) & roundToZeroTweak);
__m128i q = _mm_add_epi64(numers, _mm_and_si128(libdivide_s64_signbits(numers), roundToZeroTweak));
q = libdivide_s64_shift_right_vector(q, shift);
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
// q = (q ^ sign) - sign;
q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign);
return q;
}
else {
__m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
if (more & LIBDIVIDE_ADD_MARKER) {
// must be arithmetic shift
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
// q += ((numer ^ sign) - sign);
q = _mm_add_epi64(q, _mm_sub_epi64(_mm_xor_si128(numers, sign), sign));
}
// q >>= denom->mult_path.shift
q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
q = _mm_add_epi64(q, _mm_srli_epi64(q, 63)); // q += (q < 0)
return q;
}
}
__m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom) {
int64_t magic = denom->magic;
uint8_t more = denom->more;
uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
// must be arithmetic shift
__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
// libdivide_mullhi_s64(numers, magic);
__m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
q = _mm_add_epi64(q, numers); // q += numers
// If q is non-negative, we have nothing to do.
// If q is negative, we want to add either (2**shift)-1 if d is
// a power of 2, or (2**shift) if it is not a power of 2.
uint32_t is_power_of_2 = (magic == 0);
__m128i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
__m128i mask = _mm_set1_epi64x((1ULL << shift) - is_power_of_2);
q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
q = libdivide_s64_shift_right_vector(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
// The C++ divider class is templated on both an integer type
// (like uint64_t) and an algorithm type.
// * BRANCHFULL is the default algorithm type.
// * BRANCHFREE is the branchfree algorithm type.
enum {
BRANCHFULL,
BRANCHFREE
};
#if defined(LIBDIVIDE_AVX512)
#define LIBDIVIDE_VECTOR_TYPE __m512i
#elif defined(LIBDIVIDE_AVX2)
#define LIBDIVIDE_VECTOR_TYPE __m256i
#elif defined(LIBDIVIDE_SSE2)
#define LIBDIVIDE_VECTOR_TYPE __m128i
#endif
#if !defined(LIBDIVIDE_VECTOR_TYPE)
#define LIBDIVIDE_DIVIDE_VECTOR(ALGO)
#else
#define LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const { \
return libdivide_##ALGO##_do_vector(n, &denom); \
}
#endif
// The DISPATCHER_GEN() macro generates C++ methods (for the given integer
// and algorithm types) that redirect to libdivide's C API.
#define DISPATCHER_GEN(T, ALGO) \
libdivide_##ALGO##_t denom; \
dispatcher() { } \
dispatcher(T d) \
: denom(libdivide_##ALGO##_gen(d)) \
{ } \
T divide(T n) const { \
return libdivide_##ALGO##_do(n, &denom); \
} \
LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
T recover() const { \
return libdivide_##ALGO##_recover(&denom); \
}
// The dispatcher selects a specific division algorithm for a given
// type and ALGO using partial template specialization.
template<bool IS_INTEGRAL, bool IS_SIGNED, int SIZEOF, int ALGO> struct dispatcher { };
template<> struct dispatcher<true, true, sizeof(int32_t), BRANCHFULL> { DISPATCHER_GEN(int32_t, s32) };
template<> struct dispatcher<true, true, sizeof(int32_t), BRANCHFREE> { DISPATCHER_GEN(int32_t, s32_branchfree) };
template<> struct dispatcher<true, false, sizeof(uint32_t), BRANCHFULL> { DISPATCHER_GEN(uint32_t, u32) };
template<> struct dispatcher<true, false, sizeof(uint32_t), BRANCHFREE> { DISPATCHER_GEN(uint32_t, u32_branchfree) };
template<> struct dispatcher<true, true, sizeof(int64_t), BRANCHFULL> { DISPATCHER_GEN(int64_t, s64) };
template<> struct dispatcher<true, true, sizeof(int64_t), BRANCHFREE> { DISPATCHER_GEN(int64_t, s64_branchfree) };
template<> struct dispatcher<true, false, sizeof(uint64_t), BRANCHFULL> { DISPATCHER_GEN(uint64_t, u64) };
template<> struct dispatcher<true, false, sizeof(uint64_t), BRANCHFREE> { DISPATCHER_GEN(uint64_t, u64_branchfree) };
// This is the main divider class for use by the user (C++ API).
// The actual division algorithm is selected using the dispatcher struct
// based on the integer and algorithm template parameters.
template<typename T, int ALGO = BRANCHFULL>
class divider {
public:
// We leave the default constructor empty so that creating
// an array of dividers and then initializing them
// later doesn't slow us down.
divider() { }
// Constructor that takes the divisor as a parameter
divider(T d) : div(d) { }
// Divides n by the divisor
T divide(T n) const {
return div.divide(n);
}
// Recovers the divisor, returns the value that was
// used to initialize this divider object.
T recover() const {
return div.recover();
}
bool operator==(const divider<T, ALGO>& other) const {
return div.denom.magic == other.denom.magic &&
div.denom.more == other.denom.more;
}
bool operator!=(const divider<T, ALGO>& other) const {
return !(*this == other);
}
#if defined(LIBDIVIDE_VECTOR_TYPE)
// Treats the vector as packed integer values with the same type as
// the divider (e.g. s32, u32, s64, u64) and divides each of
// them by the divider, returning the packed quotients.
LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const {
return div.divide(n);
}
#endif
private:
// Storage for the actual divisor
dispatcher<std::is_integral<T>::value,
std::is_signed<T>::value, sizeof(T), ALGO> div;
};
// Overload of operator / for scalar division
template<typename T, int ALGO>
T operator/(T n, const divider<T, ALGO>& div) {
return div.divide(n);
}
// Overload of operator /= for scalar division
template<typename T, int ALGO>
T& operator/=(T& n, const divider<T, ALGO>& div) {
n = div.divide(n);
return n;
}
#if defined(LIBDIVIDE_VECTOR_TYPE)
// Overload of operator / for vector division
template<typename T, int ALGO>
LIBDIVIDE_VECTOR_TYPE operator/(LIBDIVIDE_VECTOR_TYPE n, const divider<T, ALGO>& div) {
return div.divide(n);
}
// Overload of operator /= for vector division
template<typename T, int ALGO>
LIBDIVIDE_VECTOR_TYPE& operator/=(LIBDIVIDE_VECTOR_TYPE& n, const divider<T, ALGO>& div) {
n = div.divide(n);
return n;
}
#endif
// libdivdie::branchfree_divider<T>
template <typename T>
using branchfree_divider = divider<T, BRANCHFREE>;
} // namespace libdivide
#endif // __cplusplus
#endif // LIBDIVIDE_H
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