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c++ source #1
Output
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Intel asm syntax
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Verbose demangling
Filters
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Debug intrinsics
Compiler
6502-c++ 11.1.0
ARM GCC 10.2.0
ARM GCC 10.3.0
ARM GCC 10.4.0
ARM GCC 10.5.0
ARM GCC 11.1.0
ARM GCC 11.2.0
ARM GCC 11.3.0
ARM GCC 11.4.0
ARM GCC 12.1.0
ARM GCC 12.2.0
ARM GCC 12.3.0
ARM GCC 12.4.0
ARM GCC 13.1.0
ARM GCC 13.2.0
ARM GCC 13.2.0 (unknown-eabi)
ARM GCC 13.3.0
ARM GCC 13.3.0 (unknown-eabi)
ARM GCC 14.1.0
ARM GCC 14.1.0 (unknown-eabi)
ARM GCC 14.2.0
ARM GCC 14.2.0 (unknown-eabi)
ARM GCC 4.5.4
ARM GCC 4.6.4
ARM GCC 5.4
ARM GCC 6.3.0
ARM GCC 6.4.0
ARM GCC 7.3.0
ARM GCC 7.5.0
ARM GCC 8.2.0
ARM GCC 8.5.0
ARM GCC 9.3.0
ARM GCC 9.4.0
ARM GCC 9.5.0
ARM GCC trunk
ARM gcc 10.2.1 (none)
ARM gcc 10.3.1 (2021.07 none)
ARM gcc 10.3.1 (2021.10 none)
ARM gcc 11.2.1 (none)
ARM gcc 5.4.1 (none)
ARM gcc 7.2.1 (none)
ARM gcc 8.2 (WinCE)
ARM gcc 8.3.1 (none)
ARM gcc 9.2.1 (none)
ARM msvc v19.0 (WINE)
ARM msvc v19.10 (WINE)
ARM msvc v19.14 (WINE)
ARM64 Morello gcc 10.1 Alpha 2
ARM64 gcc 10.2
ARM64 gcc 10.3
ARM64 gcc 10.4
ARM64 gcc 10.5.0
ARM64 gcc 11.1
ARM64 gcc 11.2
ARM64 gcc 11.3
ARM64 gcc 11.4.0
ARM64 gcc 12.1
ARM64 gcc 12.2.0
ARM64 gcc 12.3.0
ARM64 gcc 12.4.0
ARM64 gcc 13.1.0
ARM64 gcc 13.2.0
ARM64 gcc 13.3.0
ARM64 gcc 14.1.0
ARM64 gcc 14.2.0
ARM64 gcc 4.9.4
ARM64 gcc 5.4
ARM64 gcc 5.5.0
ARM64 gcc 6.3
ARM64 gcc 6.4
ARM64 gcc 7.3
ARM64 gcc 7.5
ARM64 gcc 8.2
ARM64 gcc 8.5
ARM64 gcc 9.3
ARM64 gcc 9.4
ARM64 gcc 9.5
ARM64 gcc trunk
ARM64 msvc v19.14 (WINE)
AVR gcc 10.3.0
AVR gcc 11.1.0
AVR gcc 12.1.0
AVR gcc 12.2.0
AVR gcc 12.3.0
AVR gcc 12.4.0
AVR gcc 13.1.0
AVR gcc 13.2.0
AVR gcc 13.3.0
AVR gcc 14.1.0
AVR gcc 14.2.0
AVR gcc 4.5.4
AVR gcc 4.6.4
AVR gcc 5.4.0
AVR gcc 9.2.0
AVR gcc 9.3.0
Arduino Mega (1.8.9)
Arduino Uno (1.8.9)
BPF clang (trunk)
BPF clang 13.0.0
BPF clang 14.0.0
BPF clang 15.0.0
BPF clang 16.0.0
BPF clang 17.0.1
BPF clang 18.1.0
BPF clang 19.1.0
BPF gcc 13.1.0
BPF gcc 13.2.0
BPF gcc 13.3.0
BPF gcc trunk
EDG (experimental reflection)
EDG 6.5
EDG 6.5 (GNU mode gcc 13)
EDG 6.6
EDG 6.6 (GNU mode gcc 13)
FRC 2019
FRC 2020
FRC 2023
HPPA gcc 14.2.0
KVX ACB 4.1.0 (GCC 7.5.0)
KVX ACB 4.1.0-cd1 (GCC 7.5.0)
KVX ACB 4.10.0 (GCC 10.3.1)
KVX ACB 4.11.1 (GCC 10.3.1)
KVX ACB 4.12.0 (GCC 11.3.0)
KVX ACB 4.2.0 (GCC 7.5.0)
KVX ACB 4.3.0 (GCC 7.5.0)
KVX ACB 4.4.0 (GCC 7.5.0)
KVX ACB 4.6.0 (GCC 9.4.1)
KVX ACB 4.8.0 (GCC 9.4.1)
KVX ACB 4.9.0 (GCC 9.4.1)
KVX ACB 5.0.0 (GCC 12.2.1)
LoongArch64 clang (trunk)
LoongArch64 clang 17.0.1
LoongArch64 clang 18.1.0
LoongArch64 clang 19.1.0
M68K gcc 13.1.0
M68K gcc 13.2.0
M68K gcc 13.3.0
M68K gcc 14.1.0
M68K gcc 14.2.0
M68k clang (trunk)
MRISC32 gcc (trunk)
MSP430 gcc 4.5.3
MSP430 gcc 5.3.0
MSP430 gcc 6.2.1
MinGW clang 14.0.3
MinGW clang 14.0.6
MinGW clang 15.0.7
MinGW clang 16.0.0
MinGW clang 16.0.2
MinGW gcc 11.3.0
MinGW gcc 12.1.0
MinGW gcc 12.2.0
MinGW gcc 13.1.0
RISC-V (32-bits) gcc (trunk)
RISC-V (32-bits) gcc 10.2.0
RISC-V (32-bits) gcc 10.3.0
RISC-V (32-bits) gcc 11.2.0
RISC-V (32-bits) gcc 11.3.0
RISC-V (32-bits) gcc 11.4.0
RISC-V (32-bits) gcc 12.1.0
RISC-V (32-bits) gcc 12.2.0
RISC-V (32-bits) gcc 12.3.0
RISC-V (32-bits) gcc 12.4.0
RISC-V (32-bits) gcc 13.1.0
RISC-V (32-bits) gcc 13.2.0
RISC-V (32-bits) gcc 13.3.0
RISC-V (32-bits) gcc 14.1.0
RISC-V (32-bits) gcc 14.2.0
RISC-V (32-bits) gcc 8.2.0
RISC-V (32-bits) gcc 8.5.0
RISC-V (32-bits) gcc 9.4.0
RISC-V (64-bits) gcc (trunk)
RISC-V (64-bits) gcc 10.2.0
RISC-V (64-bits) gcc 10.3.0
RISC-V (64-bits) gcc 11.2.0
RISC-V (64-bits) gcc 11.3.0
RISC-V (64-bits) gcc 11.4.0
RISC-V (64-bits) gcc 12.1.0
RISC-V (64-bits) gcc 12.2.0
RISC-V (64-bits) gcc 12.3.0
RISC-V (64-bits) gcc 12.4.0
RISC-V (64-bits) gcc 13.1.0
RISC-V (64-bits) gcc 13.2.0
RISC-V (64-bits) gcc 13.3.0
RISC-V (64-bits) gcc 14.1.0
RISC-V (64-bits) gcc 14.2.0
RISC-V (64-bits) gcc 8.2.0
RISC-V (64-bits) gcc 8.5.0
RISC-V (64-bits) gcc 9.4.0
RISC-V rv32gc clang (trunk)
RISC-V rv32gc clang 10.0.0
RISC-V rv32gc clang 10.0.1
RISC-V rv32gc clang 11.0.0
RISC-V rv32gc clang 11.0.1
RISC-V rv32gc clang 12.0.0
RISC-V rv32gc clang 12.0.1
RISC-V rv32gc clang 13.0.0
RISC-V rv32gc clang 13.0.1
RISC-V rv32gc clang 14.0.0
RISC-V rv32gc clang 15.0.0
RISC-V rv32gc clang 16.0.0
RISC-V rv32gc clang 17.0.1
RISC-V rv32gc clang 18.1.0
RISC-V rv32gc clang 19.1.0
RISC-V rv32gc clang 9.0.0
RISC-V rv32gc clang 9.0.1
RISC-V rv64gc clang (trunk)
RISC-V rv64gc clang 10.0.0
RISC-V rv64gc clang 10.0.1
RISC-V rv64gc clang 11.0.0
RISC-V rv64gc clang 11.0.1
RISC-V rv64gc clang 12.0.0
RISC-V rv64gc clang 12.0.1
RISC-V rv64gc clang 13.0.0
RISC-V rv64gc clang 13.0.1
RISC-V rv64gc clang 14.0.0
RISC-V rv64gc clang 15.0.0
RISC-V rv64gc clang 16.0.0
RISC-V rv64gc clang 17.0.1
RISC-V rv64gc clang 18.1.0
RISC-V rv64gc clang 19.1.0
RISC-V rv64gc clang 9.0.0
RISC-V rv64gc clang 9.0.1
Raspbian Buster
Raspbian Stretch
SPARC LEON gcc 12.2.0
SPARC LEON gcc 12.3.0
SPARC LEON gcc 12.4.0
SPARC LEON gcc 13.1.0
SPARC LEON gcc 13.2.0
SPARC LEON gcc 13.3.0
SPARC LEON gcc 14.1.0
SPARC LEON gcc 14.2.0
SPARC gcc 12.2.0
SPARC gcc 12.3.0
SPARC gcc 12.4.0
SPARC gcc 13.1.0
SPARC gcc 13.2.0
SPARC gcc 13.3.0
SPARC gcc 14.1.0
SPARC gcc 14.2.0
SPARC64 gcc 12.2.0
SPARC64 gcc 12.3.0
SPARC64 gcc 12.4.0
SPARC64 gcc 13.1.0
SPARC64 gcc 13.2.0
SPARC64 gcc 13.3.0
SPARC64 gcc 14.1.0
SPARC64 gcc 14.2.0
TI C6x gcc 12.2.0
TI C6x gcc 12.3.0
TI C6x gcc 12.4.0
TI C6x gcc 13.1.0
TI C6x gcc 13.2.0
TI C6x gcc 13.3.0
TI C6x gcc 14.1.0
TI C6x gcc 14.2.0
TI CL430 21.6.1
VAX gcc NetBSDELF 10.4.0
VAX gcc NetBSDELF 10.5.0 (Nov 15 03:50:22 2023)
WebAssembly clang (trunk)
Xtensa ESP32 gcc 11.2.0 (2022r1)
Xtensa ESP32 gcc 12.2.0 (20230208)
Xtensa ESP32 gcc 8.2.0 (2019r2)
Xtensa ESP32 gcc 8.2.0 (2020r1)
Xtensa ESP32 gcc 8.2.0 (2020r2)
Xtensa ESP32 gcc 8.4.0 (2020r3)
Xtensa ESP32 gcc 8.4.0 (2021r1)
Xtensa ESP32 gcc 8.4.0 (2021r2)
Xtensa ESP32-S2 gcc 11.2.0 (2022r1)
Xtensa ESP32-S2 gcc 12.2.0 (20230208)
Xtensa ESP32-S2 gcc 8.2.0 (2019r2)
Xtensa ESP32-S2 gcc 8.2.0 (2020r1)
Xtensa ESP32-S2 gcc 8.2.0 (2020r2)
Xtensa ESP32-S2 gcc 8.4.0 (2020r3)
Xtensa ESP32-S2 gcc 8.4.0 (2021r1)
Xtensa ESP32-S2 gcc 8.4.0 (2021r2)
Xtensa ESP32-S3 gcc 11.2.0 (2022r1)
Xtensa ESP32-S3 gcc 12.2.0 (20230208)
Xtensa ESP32-S3 gcc 8.4.0 (2020r3)
Xtensa ESP32-S3 gcc 8.4.0 (2021r1)
Xtensa ESP32-S3 gcc 8.4.0 (2021r2)
arm64 msvc v19.20 VS16.0
arm64 msvc v19.21 VS16.1
arm64 msvc v19.22 VS16.2
arm64 msvc v19.23 VS16.3
arm64 msvc v19.24 VS16.4
arm64 msvc v19.25 VS16.5
arm64 msvc v19.27 VS16.7
arm64 msvc v19.28 VS16.8
arm64 msvc v19.28 VS16.9
arm64 msvc v19.29 VS16.10
arm64 msvc v19.29 VS16.11
arm64 msvc v19.30 VS17.0
arm64 msvc v19.31 VS17.1
arm64 msvc v19.32 VS17.2
arm64 msvc v19.33 VS17.3
arm64 msvc v19.34 VS17.4
arm64 msvc v19.35 VS17.5
arm64 msvc v19.36 VS17.6
arm64 msvc v19.37 VS17.7
arm64 msvc v19.38 VS17.8
arm64 msvc v19.39 VS17.9
arm64 msvc v19.40 VS17.10
arm64 msvc v19.latest
armv7-a clang (trunk)
armv7-a clang 10.0.0
armv7-a clang 10.0.1
armv7-a clang 11.0.0
armv7-a clang 11.0.1
armv7-a clang 12.0.0
armv7-a clang 12.0.1
armv7-a clang 13.0.0
armv7-a clang 13.0.1
armv7-a clang 14.0.0
armv7-a clang 15.0.0
armv7-a clang 16.0.0
armv7-a clang 17.0.1
armv7-a clang 18.1.0
armv7-a clang 19.1.0
armv7-a clang 9.0.0
armv7-a clang 9.0.1
armv8-a clang (all architectural features, trunk)
armv8-a clang (trunk)
armv8-a clang 10.0.0
armv8-a clang 10.0.1
armv8-a clang 11.0.0
armv8-a clang 11.0.1
armv8-a clang 12.0.0
armv8-a clang 13.0.0
armv8-a clang 14.0.0
armv8-a clang 15.0.0
armv8-a clang 16.0.0
armv8-a clang 17.0.1
armv8-a clang 18.1.0
armv8-a clang 19.1.0
armv8-a clang 9.0.0
armv8-a clang 9.0.1
ellcc 0.1.33
ellcc 0.1.34
ellcc 2017-07-16
hexagon-clang 16.0.5
llvm-mos atari2600-3e
llvm-mos atari2600-4k
llvm-mos atari2600-common
llvm-mos atari5200-supercart
llvm-mos atari8-cart-megacart
llvm-mos atari8-cart-std
llvm-mos atari8-cart-xegs
llvm-mos atari8-common
llvm-mos atari8-dos
llvm-mos c128
llvm-mos c64
llvm-mos commodore
llvm-mos cpm65
llvm-mos cx16
llvm-mos dodo
llvm-mos eater
llvm-mos mega65
llvm-mos nes
llvm-mos nes-action53
llvm-mos nes-cnrom
llvm-mos nes-gtrom
llvm-mos nes-mmc1
llvm-mos nes-mmc3
llvm-mos nes-nrom
llvm-mos nes-unrom
llvm-mos nes-unrom-512
llvm-mos osi-c1p
llvm-mos pce
llvm-mos pce-cd
llvm-mos pce-common
llvm-mos pet
llvm-mos rp6502
llvm-mos rpc8e
llvm-mos supervision
llvm-mos vic20
loongarch64 gcc 12.2.0
loongarch64 gcc 12.3.0
loongarch64 gcc 12.4.0
loongarch64 gcc 13.1.0
loongarch64 gcc 13.2.0
loongarch64 gcc 13.3.0
loongarch64 gcc 14.1.0
loongarch64 gcc 14.2.0
mips clang 13.0.0
mips clang 14.0.0
mips clang 15.0.0
mips clang 16.0.0
mips clang 17.0.1
mips clang 18.1.0
mips clang 19.1.0
mips gcc 11.2.0
mips gcc 12.1.0
mips gcc 12.2.0
mips gcc 12.3.0
mips gcc 12.4.0
mips gcc 13.1.0
mips gcc 13.2.0
mips gcc 13.3.0
mips gcc 14.1.0
mips gcc 14.2.0
mips gcc 4.9.4
mips gcc 5.4
mips gcc 5.5.0
mips gcc 9.3.0 (codescape)
mips gcc 9.5.0
mips64 (el) gcc 12.1.0
mips64 (el) gcc 12.2.0
mips64 (el) gcc 12.3.0
mips64 (el) gcc 12.4.0
mips64 (el) gcc 13.1.0
mips64 (el) gcc 13.2.0
mips64 (el) gcc 13.3.0
mips64 (el) gcc 14.1.0
mips64 (el) gcc 14.2.0
mips64 (el) gcc 4.9.4
mips64 (el) gcc 5.4.0
mips64 (el) gcc 5.5.0
mips64 (el) gcc 9.5.0
mips64 clang 13.0.0
mips64 clang 14.0.0
mips64 clang 15.0.0
mips64 clang 16.0.0
mips64 clang 17.0.1
mips64 clang 18.1.0
mips64 clang 19.1.0
mips64 gcc 11.2.0
mips64 gcc 12.1.0
mips64 gcc 12.2.0
mips64 gcc 12.3.0
mips64 gcc 12.4.0
mips64 gcc 13.1.0
mips64 gcc 13.2.0
mips64 gcc 13.3.0
mips64 gcc 14.1.0
mips64 gcc 14.2.0
mips64 gcc 4.9.4
mips64 gcc 5.4.0
mips64 gcc 5.5.0
mips64 gcc 9.5.0
mips64el clang 13.0.0
mips64el clang 14.0.0
mips64el clang 15.0.0
mips64el clang 16.0.0
mips64el clang 17.0.1
mips64el clang 18.1.0
mips64el clang 19.1.0
mipsel clang 13.0.0
mipsel clang 14.0.0
mipsel clang 15.0.0
mipsel clang 16.0.0
mipsel clang 17.0.1
mipsel clang 18.1.0
mipsel clang 19.1.0
mipsel gcc 12.1.0
mipsel gcc 12.2.0
mipsel gcc 12.3.0
mipsel gcc 12.4.0
mipsel gcc 13.1.0
mipsel gcc 13.2.0
mipsel gcc 13.3.0
mipsel gcc 14.1.0
mipsel gcc 14.2.0
mipsel gcc 4.9.4
mipsel gcc 5.4.0
mipsel gcc 5.5.0
mipsel gcc 9.5.0
nanoMIPS gcc 6.3.0 (mtk)
power gcc 11.2.0
power gcc 12.1.0
power gcc 12.2.0
power gcc 12.3.0
power gcc 12.4.0
power gcc 13.1.0
power gcc 13.2.0
power gcc 13.3.0
power gcc 14.1.0
power gcc 14.2.0
power gcc 4.8.5
power64 AT12.0 (gcc8)
power64 AT13.0 (gcc9)
power64 gcc 11.2.0
power64 gcc 12.1.0
power64 gcc 12.2.0
power64 gcc 12.3.0
power64 gcc 12.4.0
power64 gcc 13.1.0
power64 gcc 13.2.0
power64 gcc 13.3.0
power64 gcc 14.1.0
power64 gcc 14.2.0
power64 gcc trunk
power64le AT12.0 (gcc8)
power64le AT13.0 (gcc9)
power64le clang (trunk)
power64le gcc 11.2.0
power64le gcc 12.1.0
power64le gcc 12.2.0
power64le gcc 12.3.0
power64le gcc 12.4.0
power64le gcc 13.1.0
power64le gcc 13.2.0
power64le gcc 13.3.0
power64le gcc 14.1.0
power64le gcc 14.2.0
power64le gcc 6.3.0
power64le gcc trunk
powerpc64 clang (trunk)
s390x gcc 11.2.0
s390x gcc 12.1.0
s390x gcc 12.2.0
s390x gcc 12.3.0
s390x gcc 12.4.0
s390x gcc 13.1.0
s390x gcc 13.2.0
s390x gcc 13.3.0
s390x gcc 14.1.0
s390x gcc 14.2.0
sh gcc 12.2.0
sh gcc 12.3.0
sh gcc 12.4.0
sh gcc 13.1.0
sh gcc 13.2.0
sh gcc 13.3.0
sh gcc 14.1.0
sh gcc 14.2.0
sh gcc 4.9.4
sh gcc 9.5.0
vast (trunk)
x64 msvc v19.0 (WINE)
x64 msvc v19.10 (WINE)
x64 msvc v19.14 (WINE)
x64 msvc v19.20 VS16.0
x64 msvc v19.21 VS16.1
x64 msvc v19.22 VS16.2
x64 msvc v19.23 VS16.3
x64 msvc v19.24 VS16.4
x64 msvc v19.25 VS16.5
x64 msvc v19.27 VS16.7
x64 msvc v19.28 VS16.8
x64 msvc v19.28 VS16.9
x64 msvc v19.29 VS16.10
x64 msvc v19.29 VS16.11
x64 msvc v19.30 VS17.0
x64 msvc v19.31 VS17.1
x64 msvc v19.32 VS17.2
x64 msvc v19.33 VS17.3
x64 msvc v19.34 VS17.4
x64 msvc v19.35 VS17.5
x64 msvc v19.36 VS17.6
x64 msvc v19.37 VS17.7
x64 msvc v19.38 VS17.8
x64 msvc v19.39 VS17.9
x64 msvc v19.40 VS17.10
x64 msvc v19.latest
x86 djgpp 4.9.4
x86 djgpp 5.5.0
x86 djgpp 6.4.0
x86 djgpp 7.2.0
x86 msvc v19.0 (WINE)
x86 msvc v19.10 (WINE)
x86 msvc v19.14 (WINE)
x86 msvc v19.20 VS16.0
x86 msvc v19.21 VS16.1
x86 msvc v19.22 VS16.2
x86 msvc v19.23 VS16.3
x86 msvc v19.24 VS16.4
x86 msvc v19.25 VS16.5
x86 msvc v19.27 VS16.7
x86 msvc v19.28 VS16.8
x86 msvc v19.28 VS16.9
x86 msvc v19.29 VS16.10
x86 msvc v19.29 VS16.11
x86 msvc v19.30 VS17.0
x86 msvc v19.31 VS17.1
x86 msvc v19.32 VS17.2
x86 msvc v19.33 VS17.3
x86 msvc v19.34 VS17.4
x86 msvc v19.35 VS17.5
x86 msvc v19.36 VS17.6
x86 msvc v19.37 VS17.7
x86 msvc v19.38 VS17.8
x86 msvc v19.39 VS17.9
x86 msvc v19.40 VS17.10
x86 msvc v19.latest
x86 nvc++ 22.11
x86 nvc++ 22.7
x86 nvc++ 22.9
x86 nvc++ 23.1
x86 nvc++ 23.11
x86 nvc++ 23.3
x86 nvc++ 23.5
x86 nvc++ 23.7
x86 nvc++ 23.9
x86 nvc++ 24.1
x86 nvc++ 24.3
x86 nvc++ 24.5
x86 nvc++ 24.7
x86-64 Zapcc 190308
x86-64 clang (EricWF contracts)
x86-64 clang (amd-staging)
x86-64 clang (assertions trunk)
x86-64 clang (clangir)
x86-64 clang (dascandy contracts)
x86-64 clang (experimental -Wlifetime)
x86-64 clang (experimental P1061)
x86-64 clang (experimental P1144)
x86-64 clang (experimental P1221)
x86-64 clang (experimental P2996)
x86-64 clang (experimental P3068)
x86-64 clang (experimental P3309)
x86-64 clang (experimental P3367)
x86-64 clang (experimental P3372)
x86-64 clang (experimental metaprogramming - P2632)
x86-64 clang (old concepts branch)
x86-64 clang (p1974)
x86-64 clang (pattern matching - P2688)
x86-64 clang (reflection)
x86-64 clang (resugar)
x86-64 clang (thephd.dev)
x86-64 clang (trunk)
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Source code
// libdivide.h // Copyright 2010 - 2019 ridiculous_fish // // 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 "2.0" #define LIBDIVIDE_VERSION_MAJOR 2 #define LIBDIVIDE_VERSION_MINOR 0 #include <stdint.h> #if defined(__cplusplus) #include <cstdlib> #include <cstdio> #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(__has_builtin) #define __has_builtin(x) 0 #endif #if defined(__SIZEOF_INT128__) #define HAS_INT128_T #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 #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 // _udiv128() is available in Visual Studio 2019 // or later on the x64 CPU architecture #if defined(LIBDIVIDE_X86_64) && _MSC_VER >= 1920 #if !defined(__has_include) #include <immintrin.h> #define LIBDIVIDE_VC_UDIV128 #elif __has_include(<immintrin.h>) #include <immintrin.h> #define LIBDIVIDE_VC_UDIV128 #endif #endif #endif #define LIBDIVIDE_ERROR(msg) \ do { \ fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", \ __LINE__, LIBDIVIDE_FUNCTION, msg); \ exit(-1); \ } while (0) #if defined(LIBDIVIDE_ASSERTIONS_ON) #define LIBDIVIDE_ASSERT(x) \ do { \ if (!(x)) { \ fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", \ __LINE__, LIBDIVIDE_FUNCTION, #x); \ exit(-1); \ } \ } while (0) #else #define LIBDIVIDE_ASSERT(x) #endif #ifdef __cplusplus // We place libdivide within the libdivide namespace, and that goes in an // anonymous namespace so that the functions are only visible to files that // #include this header and don't get external linkage. At least that's the // theory. namespace { namespace libdivide { #endif // Explanation of "more" field: bit 6 is whether to use shift path. If we are // using the shift path, bit 7 is whether the divisor is negative in the signed // case; in the unsigned case it is 0. Bits 0-4 is shift value (for shift // path or mult path). In 32 bit case, bit 5 is always 0. We use bit 7 as the // "negative divisor indicator" so that we can use sign extension to // efficiently go to a full-width -1. // // u32: [0-4] shift value // [5] ignored // [6] add indicator // [7] shift path // // s32: [0-4] shift value // [5] shift path // [6] add indicator // [7] indicates negative divisor // // u64: [0-5] shift value // [6] add indicator // [7] shift path // // s64: [0-5] shift value // [6] add indicator // [7] indicates negative divisor // magic number of 0 indicates shift path (we ran out of bits!) // // 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_ONE_MARKER = 0x40, LIBDIVIDE_U32_SHIFT_PATH = 0x80, LIBDIVIDE_U64_SHIFT_PATH = 0x80, LIBDIVIDE_S32_SHIFT_PATH = 0x20, LIBDIVIDE_NEGATIVE_DIVISOR = 0x80 }; // 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) #ifndef LIBDIVIDE_API #ifdef __cplusplus // In C++, we don't want our public functions to be static, because // they are arguments to templates and static functions can't do that. // They get internal linkage through virtue of the anonymous namespace. // In C, they should be static. #define LIBDIVIDE_API #else #define LIBDIVIDE_API static inline #endif #endif LIBDIVIDE_API struct libdivide_s32_t libdivide_s32_gen(int32_t y); LIBDIVIDE_API struct libdivide_u32_t libdivide_u32_gen(uint32_t y); LIBDIVIDE_API struct libdivide_s64_t libdivide_s64_gen(int64_t y); LIBDIVIDE_API struct libdivide_u64_t libdivide_u64_gen(uint64_t y); LIBDIVIDE_API struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t y); LIBDIVIDE_API struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t y); LIBDIVIDE_API struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t y); LIBDIVIDE_API struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t y); LIBDIVIDE_API int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom); LIBDIVIDE_API uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom); LIBDIVIDE_API int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom); LIBDIVIDE_API uint64_t libdivide_u64_do(uint64_t y, const struct libdivide_u64_t *denom); LIBDIVIDE_API int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom); LIBDIVIDE_API uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom); LIBDIVIDE_API int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom); LIBDIVIDE_API uint64_t libdivide_u64_branchfree_do(uint64_t y, const struct libdivide_u64_branchfree_t *denom); LIBDIVIDE_API int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom); LIBDIVIDE_API uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom); LIBDIVIDE_API int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom); LIBDIVIDE_API uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom); LIBDIVIDE_API int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom); LIBDIVIDE_API uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom); LIBDIVIDE_API int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom); LIBDIVIDE_API 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 int32_t result = 0; uint32_t hi = 1U << 31; for (; ~val & hi; hi >>= 1) { result++; } 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_VC_UDIV128) return _udiv128(u1, u0, v, r); #elif 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) __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 { 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) __uint128_t ufull = u_hi; __uint128_t vfull = v_hi; ufull = (ufull << 64) | u_lo; vfull = (vfull << 64) | v_lo; uint64_t res = (uint64_t)(ufull / vfull); __uint128_t remainder = ufull - (vfull * res); *r_lo = (uint64_t)remainder; *r_hi = (uint64_t)(remainder >> 64); return res; #else // Adapted from "Unsigned Doubleword Division" in Hacker's Delight // We want to compute u / v typedef struct { uint64_t hi; uint64_t lo; } u128_t; u128_t u = {u_hi, u_lo}; u128_t v = {v_hi, v_lo}; if (v.hi == 0) { // divisor v is a 64 bit value, so we just need one 128/64 division // Note that we are simpler than Hacker's Delight here, because we know // the quotient fits in 64 bits whereas Hacker's Delight demands a full // 128 bit quotient *r_hi = 0; return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo); } // Here v >= 2**64 // We know that v.hi != 0, so count leading zeros is OK // We have 0 <= n <= 63 uint32_t n = libdivide_count_leading_zeros64(v.hi); // Normalize the divisor so its MSB is 1 u128_t v1t = v; libdivide_u128_shift(&v1t.hi, &v1t.lo, n); uint64_t v1 = v1t.hi; // i.e. v1 = v1t >> 64 // To ensure no overflow u128_t u1 = u; libdivide_u128_shift(&u1.hi, &u1.lo, -1); // Get quotient from divide unsigned insn. uint64_t rem_ignored; uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored); // Undo normalization and division of u by 2. u128_t q0 = {0, q1}; libdivide_u128_shift(&q0.hi, &q0.lo, n); libdivide_u128_shift(&q0.hi, &q0.lo, -63); // Make q0 correct or too small by 1 // Equivalent to `if (q0 != 0) q0 = q0 - 1;` if (q0.hi != 0 || q0.lo != 0) { q0.hi -= (q0.lo == 0); // borrow q0.lo -= 1; } // Now q0 is correct. // Compute q0 * v as q0v // = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo) // = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) + // (q0.lo * v.hi << 64) + q0.lo * v.lo) // Each term is 128 bit // High half of full product (upper 128 bits!) are dropped u128_t q0v = {0, 0}; q0v.hi = q0.hi*v.lo + q0.lo*v.hi + libdivide_mullhi_u64(q0.lo, v.lo); q0v.lo = q0.lo*v.lo; // Compute u - q0v as u_q0v // This is the remainder u128_t u_q0v = u; u_q0v.hi -= q0v.hi + (u.lo < q0v.lo); // second term is borrow u_q0v.lo -= q0v.lo; // Check if u_q0v >= v // This checks if our remainder is larger than the divisor if ((u_q0v.hi > v.hi) || (u_q0v.hi == v.hi && u_q0v.lo >= v.lo)) { // Increment q0 q0.lo += 1; q0.hi += (q0.lo == 0); // carry // Subtract v from remainder u_q0v.hi -= v.hi + (u_q0v.lo < v.lo); u_q0v.lo -= v.lo; } *r_hi = u_q0v.hi; *r_lo = u_q0v.lo; LIBDIVIDE_ASSERT(q0.hi == 0); return q0.lo; #endif } ////////// UINT32 static inline struct libdivide_u32_t libdivide_internal_u32_gen(uint32_t d, int branchfree) { if (d == 0) { LIBDIVIDE_ERROR("divider must be != 0"); } struct libdivide_u32_t result; uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(d); if ((d & (d - 1)) == 0) { // Power of 2 if (! branchfree) { result.magic = 0; result.more = (uint8_t)(floor_log_2_d | LIBDIVIDE_U32_SHIFT_PATH); } else { // We want a magic number of 2**32 and a shift of floor_log_2_d // but one of the shifts is taken up by LIBDIVIDE_ADD_MARKER, // so we subtract 1 from the shift result.magic = 0; result.more = (uint8_t)((floor_log_2_d-1) | LIBDIVIDE_ADD_MARKER); } } else { uint8_t more; uint32_t rem, proposed_m; proposed_m = libdivide_64_div_32_to_32(1U << floor_log_2_d, 0, d, &rem); LIBDIVIDE_ASSERT(rem > 0 && rem < d); const uint32_t e = d - rem; // This power works if e < 2**floor_log_2_d. if (!branchfree && (e < (1U << floor_log_2_d))) { // This power works more = floor_log_2_d; } else { // We have to use the general 33-bit algorithm. We need to compute // (2**power) / d. However, we already have (2**(power-1))/d and // its remainder. By doubling both, and then correcting the // remainder, we can compute the larger division. // don't care about overflow here - in fact, we expect it proposed_m += proposed_m; const uint32_t twice_rem = rem + rem; if (twice_rem >= d || twice_rem < rem) proposed_m += 1; more = floor_log_2_d | LIBDIVIDE_ADD_MARKER; } result.magic = 1 + proposed_m; result.more = more; // result.more's shift should in general be ceil_log_2_d. But if we // used the smaller power, we subtract one from the shift because we're // using the smaller power. If we're using the larger power, we // subtract one from the shift because it's taken care of by the add // indicator. So floor_log_2_d happens to be correct in both cases. } return result; } struct libdivide_u32_t libdivide_u32_gen(uint32_t d) { return libdivide_internal_u32_gen(d, 0); } struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d) { if (d == 1) { struct libdivide_u32_branchfree_t ret1 = {0, LIBDIVIDE_ONE_MARKER}; return ret1; } 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 (more & LIBDIVIDE_U32_SHIFT_PATH) { return numer >> (more & LIBDIVIDE_32_SHIFT_MASK); } 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); q += (denom->more == LIBDIVIDE_ONE_MARKER) ? numer : 0; 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 (more & LIBDIVIDE_U32_SHIFT_PATH) { 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 unless we're a power of 2 (i.e. in branchfree case) // We can detect that by looking at m. If m zero, we're a power of 2 return full_q + (denom->magic != 0); } } uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom) { if (denom->more == LIBDIVIDE_ONE_MARKER) return 1; struct libdivide_u32_t denom_u32 = {denom->magic, (uint8_t)(denom->more | LIBDIVIDE_ADD_MARKER)}; return libdivide_u32_recover(&denom_u32); } /////////// 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); if ((d & (d - 1)) == 0) { // Power of 2 if (! branchfree) { result.magic = 0; result.more = floor_log_2_d | LIBDIVIDE_U64_SHIFT_PATH; } else { // We want a magic number of 2**64 and a shift of floor_log_2_d // but one of the shifts is taken up by LIBDIVIDE_ADD_MARKER, // so we subtract 1 from the shift. result.magic = 0; result.more = (floor_log_2_d-1) | LIBDIVIDE_ADD_MARKER; } } 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) { struct libdivide_u64_branchfree_t ret1 = {0, LIBDIVIDE_ONE_MARKER}; return ret1; } 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 (more & LIBDIVIDE_U64_SHIFT_PATH) { return numer >> (more & LIBDIVIDE_64_SHIFT_MASK); } 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); q += (denom->more == LIBDIVIDE_ONE_MARKER) ? numer : 0; 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 (more & LIBDIVIDE_U64_SHIFT_PATH) { 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 // Hack: if d is not a power of 2, this is a 128/128->64 divide // If d is a power of 2, this may be a bigger divide // However we can optimize that easily if (denom->magic == 0) { // 2^(64 + shift + 1) / (2^64) == 2^(shift + 1) return 1ULL << (shift + 1); } // 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) { if (denom->more == LIBDIVIDE_ONE_MARKER) return 1; struct libdivide_u64_t denom_u64 = {denom->magic, (uint8_t)(denom->more | LIBDIVIDE_ADD_MARKER)}; return libdivide_u64_recover(&denom_u64); } /////////// 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) | LIBDIVIDE_S32_SHIFT_PATH; } 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; if (more & LIBDIVIDE_S32_SHIFT_PATH) { uint32_t sign = (int8_t)more >> 7; uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; uint32_t mask = (1U << shift) - 1; uint32_t uq = numer + ((numer >> 31) & mask); int32_t q = (int32_t)uq; q = 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), casts to avoid UB uq += ((uint32_t)numer ^ sign) - sign; } int32_t q = (int32_t)uq; q >>= more & LIBDIVIDE_32_SHIFT_MASK; 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 = !!(more & LIBDIVIDE_S32_SHIFT_PATH); uint32_t q_sign = (uint32_t)(q >> 31); q += q_sign & ((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 (more & LIBDIVIDE_S32_SHIFT_PATH) { 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 = 1 << 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; int64_t magic = denom->magic; if (magic == 0) { //shift path uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; uint64_t mask = (1ULL << shift) - 1; uint64_t uq = numer + ((numer >> 63) & mask); int64_t q = (int64_t)uq; q = q >> shift; // must be arithmetic shift and then sign-extend int64_t shiftMask = (int8_t)more >> 7; q = (q ^ shiftMask) - shiftMask; return q; } else { uint64_t uq = (uint64_t)libdivide_mullhi_s64(magic, numer); if (more & LIBDIVIDE_ADD_MARKER) { // must be arithmetic shift and then sign extend int64_t sign = (int8_t)more >> 7; uq += ((uint64_t)numer ^ sign) - sign; } int64_t q = (int64_t)uq; q >>= more & LIBDIVIDE_64_SHIFT_MASK; 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; uint32_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. uint32_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) LIBDIVIDE_API __m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom); LIBDIVIDE_API __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom); LIBDIVIDE_API __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom); LIBDIVIDE_API __m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom); LIBDIVIDE_API __m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom); LIBDIVIDE_API __m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom); LIBDIVIDE_API __m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom); LIBDIVIDE_API __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 (more & LIBDIVIDE_U32_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; return _mm512_srli_epi32(numers, shift); } 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); } } } LIBDIVIDE_API __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)); q = _mm512_add_epi32(q, _mm512_maskz_mov_epi32((denom->more == LIBDIVIDE_ONE_MARKER) ? 0xffff : 0, numers)); __m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q); return _mm512_srli_epi32(t, denom->more & LIBDIVIDE_32_SHIFT_MASK); } ////////// UINT64 __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_U64_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; return _mm512_srli_epi64(numers, shift); } 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)); q = _mm512_add_epi64(q, _mm512_maskz_mov_epi64((denom->more == LIBDIVIDE_ONE_MARKER) ? 0xffff : 0, numers)); __m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q); return _mm512_srli_epi64(t, denom->more & LIBDIVIDE_64_SHIFT_MASK); } ////////// SINT32 __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_S32_SHIFT_PATH) { 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); // set all bits of shift mask = to the sign bit of more __m512i shiftMask = _mm512_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm512_sub_epi32(_mm512_xor_si512(q, shiftMask), shiftMask); 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((int32_t)(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((int32_t)(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((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_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 shiftMask = _mm512_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm512_sub_epi64(_mm512_xor_si512(q, shiftMask), shiftMask); 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((int32_t)((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((int32_t)(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) LIBDIVIDE_API __m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom); LIBDIVIDE_API __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom); LIBDIVIDE_API __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom); LIBDIVIDE_API __m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom); LIBDIVIDE_API __m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom); LIBDIVIDE_API __m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom); LIBDIVIDE_API __m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom); LIBDIVIDE_API __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 (more & LIBDIVIDE_U32_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; return _mm256_srli_epi32(numers, shift); } 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); } } } LIBDIVIDE_API __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)); q = _mm256_add_epi32(q, _mm256_maskz_mov_epi32((denom->more == LIBDIVIDE_ONE_MARKER) ? 0xff : 0, numers)); __m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q); return _mm256_srli_epi32(t, denom->more & LIBDIVIDE_32_SHIFT_MASK); } ////////// UINT64 __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_U64_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; return _mm256_srli_epi64(numers, shift); } 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)); q = _mm256_add_epi64(q, _mm256_maskz_mov_epi64((denom->more == LIBDIVIDE_ONE_MARKER) ? 0xffff : 0, numers)); __m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q); return _mm256_srli_epi64(t, denom->more & LIBDIVIDE_64_SHIFT_MASK); } ////////// SINT32 __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_S32_SHIFT_PATH) { 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); // set all bits of shift mask = to the sign bit of more __m256i shiftMask = _mm256_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm256_sub_epi32(_mm256_xor_si256(q, shiftMask), shiftMask); 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((int32_t)(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((int32_t)(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((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_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 shiftMask = _mm256_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm256_sub_epi64(_mm256_xor_si256(q, shiftMask), shiftMask); 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((int32_t)((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((int32_t)(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) LIBDIVIDE_API __m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom); LIBDIVIDE_API __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom); LIBDIVIDE_API __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom); LIBDIVIDE_API __m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom); LIBDIVIDE_API __m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom); LIBDIVIDE_API __m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom); LIBDIVIDE_API __m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom); LIBDIVIDE_API __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 (more & LIBDIVIDE_U32_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; return _mm_srli_epi32(numers, shift); } 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); } } } LIBDIVIDE_API __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)); q = _mm_add_epi32(q, (denom->more == LIBDIVIDE_ONE_MARKER) ? numers : _mm_set1_epi32(0)); __m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q); return _mm_srli_epi32(t, denom->more & LIBDIVIDE_32_SHIFT_MASK); } ////////// UINT64 __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_U64_SHIFT_PATH) { uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; return _mm_srli_epi64(numers, shift); } 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)); q = _mm_add_epi32(q, (denom->more == LIBDIVIDE_ONE_MARKER) ? numers : _mm_set1_epi32(0)); __m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q); return _mm_srli_epi64(t, denom->more & LIBDIVIDE_64_SHIFT_MASK); } ////////// SINT32 __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom) { uint8_t more = denom->more; if (more & LIBDIVIDE_S32_SHIFT_PATH) { 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); // set all bits of shift mask = to the sign bit of more __m128i shiftMask = _mm_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm_sub_epi32(_mm_xor_si128(q, shiftMask), shiftMask); 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((int32_t)(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((int32_t)(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((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_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 shiftMask = _mm_set1_epi32((int32_t)((int8_t)more >> 7)); // q = (q ^ shiftMask) - shiftMask; q = _mm_sub_epi64(_mm_xor_si128(q, shiftMask), shiftMask); 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((int32_t)((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((int32_t)(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 // Our divider struct is templated on both a type (like uint64_t) and an // algorithm index. BRANCHFULL is the default algorithm, BRANCHFREE is the // branchfree variant. enum { BRANCHFULL, BRANCHFREE }; namespace libdivide_internal { #if defined(__GNUC__) && \ __GNUC__ >= 6 && \ (defined(LIBDIVIDE_AVX512) || \ defined(LIBDIVIDE_AVX2) || \ defined(LIBDIVIDE_SSE2)) // Using vector functions as template arguments causes many // -Wignored-attributes compiler warnings with GCC 9. // These warnings can safely be turned off. #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wignored-attributes" #endif #if defined(LIBDIVIDE_AVX512) #define MAYBE_VECTOR(X) X #define MAYBE_VECTOR_PARAM(X) __m512i vector_func(__m512i, const X *) #elif defined(LIBDIVIDE_AVX2) #define MAYBE_VECTOR(X) X #define MAYBE_VECTOR_PARAM(X) __m256i vector_func(__m256i, const X *) #elif defined(LIBDIVIDE_SSE2) #define MAYBE_VECTOR(X) X #define MAYBE_VECTOR_PARAM(X) __m128i vector_func(__m128i, const X *) #else #define MAYBE_VECTOR(X) 0 #define MAYBE_VECTOR_PARAM(X) int unused #endif // The following convenience macros are used to build a type of the base // divider class and give it as template arguments the C functions // related to the macro name and the macro type paramaters. #define BRANCHFULL_DIVIDER(INT, TYPE) \ typedef base<INT, \ libdivide_##TYPE##_t, \ libdivide_##TYPE##_gen, \ libdivide_##TYPE##_do, \ MAYBE_VECTOR(libdivide_##TYPE##_do_vector)> #define BRANCHFREE_DIVIDER(INT, TYPE) \ typedef base<INT, \ libdivide_##TYPE##_branchfree_t, \ libdivide_##TYPE##_branchfree_gen, \ libdivide_##TYPE##_branchfree_do, \ MAYBE_VECTOR(libdivide_##TYPE##_branchfree_do_vector)> // Base divider, provides storage for the actual divider. // @T: e.g. uint32_t // @DenomType: e.g. libdivide_u32_t // @gen_func(): e.g. libdivide_u32_gen // @do_func(): e.g. libdivide_u32_do // @MAYBE_VECTOR_PARAM: e.g. libdivide_u32_do_vector template<typename T, typename DenomType, DenomType gen_func(T), T do_func(T, const DenomType *), MAYBE_VECTOR_PARAM(DenomType)> struct base { // Storage for the actual divider DenomType denom; // Constructor that takes a divisor value, and applies the gen function base(T d) : denom(gen_func(d)) { } // Default constructor to allow uninitialized uses in e.g. arrays base() {} T perform_divide(T val) const { return do_func(val, &denom); } #if defined(LIBDIVIDE_AVX512) __m512i perform_divide_vector(__m512i val) const { return vector_func(val, &denom); } #elif defined(LIBDIVIDE_AVX2) __m256i perform_divide_vector(__m256i val) const { return vector_func(val, &denom); } #elif defined(LIBDIVIDE_SSE2) __m128i perform_divide_vector(__m128i val) const { return vector_func(val, &denom); } #endif }; template<typename T, int ALGO> struct dispatcher { }; // Templated dispatch using partial specialization template<> struct dispatcher<int32_t, BRANCHFULL> { BRANCHFULL_DIVIDER(int32_t, s32) divider; }; template<> struct dispatcher<int32_t, BRANCHFREE> { BRANCHFREE_DIVIDER(int32_t, s32) divider; }; template<> struct dispatcher<uint32_t, BRANCHFULL> { BRANCHFULL_DIVIDER(uint32_t, u32) divider; }; template<> struct dispatcher<uint32_t, BRANCHFREE> { BRANCHFREE_DIVIDER(uint32_t, u32) divider; }; template<> struct dispatcher<int64_t, BRANCHFULL> { BRANCHFULL_DIVIDER(int64_t, s64) divider; }; template<> struct dispatcher<int64_t, BRANCHFREE> { BRANCHFREE_DIVIDER(int64_t, s64) divider; }; template<> struct dispatcher<uint64_t, BRANCHFULL> { BRANCHFULL_DIVIDER(uint64_t, u64) divider; }; template<> struct dispatcher<uint64_t, BRANCHFREE> { BRANCHFREE_DIVIDER(uint64_t, u64) divider; }; #if defined(__GNUC__) && \ __GNUC__ >= 6 && \ (defined(LIBDIVIDE_AVX512) || \ defined(LIBDIVIDE_AVX2) || \ defined(LIBDIVIDE_SSE2)) #pragma GCC diagnostic pop #endif // Overloads that don't depend on the algorithm inline int32_t recover(const libdivide_s32_t *s) { return libdivide_s32_recover(s); } inline uint32_t recover(const libdivide_u32_t *s) { return libdivide_u32_recover(s); } inline int64_t recover(const libdivide_s64_t *s) { return libdivide_s64_recover(s); } inline uint64_t recover(const libdivide_u64_t *s) { return libdivide_u64_recover(s); } inline int32_t recover(const libdivide_s32_branchfree_t *s) { return libdivide_s32_branchfree_recover(s); } inline uint32_t recover(const libdivide_u32_branchfree_t *s) { return libdivide_u32_branchfree_recover(s); } inline int64_t recover(const libdivide_s64_branchfree_t *s) { return libdivide_s64_branchfree_recover(s); } inline uint64_t recover(const libdivide_u64_branchfree_t *s) { return libdivide_u64_branchfree_recover(s); } } // namespace libdivide_internal // This is the main divider class for use by the user (C++ API). // The divider itself is stored in the div variable who's // type is chosen by the dispatcher based on the template paramaters. template<typename T, int ALGO = BRANCHFULL> class divider { private: // Here's the actual divider typedef typename libdivide_internal::dispatcher<T, ALGO>::divider div_t; div_t div; public: // Constructor that takes the divisor as a parameter divider(T n) : div(n) { } // Default constructor. We leave this deliberately undefined so that // creating an array of divider and then initializing them // doesn't slow us down. divider() { } // Divides the parameter by the divisor, returning the quotient T perform_divide(T val) const { return div.perform_divide(val); } // Recovers the divisor that was used to initialize the divider T recover_divisor() const { return libdivide_internal::recover(&div.denom); } #if defined(LIBDIVIDE_AVX512) // Treats the vector as either 8 or 16 packed values (depending on the // size), and divides each of them by the divisor, // returning the packed quotients. __m512i perform_divide_vector(__m512i val) const { return div.perform_divide_vector(val); } #elif defined(LIBDIVIDE_AVX2) // Treats the vector as either 4 or 8 packed values (depending on the // size), and divides each of them by the divisor, // returning the packed quotients. __m256i perform_divide_vector(__m256i val) const { return div.perform_divide_vector(val); } #elif defined(LIBDIVIDE_SSE2) // Treats the vector as either 2 or 4 packed values (depending on the // size), and divides each of them by the divisor, // returning the packed quotients. __m128i perform_divide_vector(__m128i val) const { return div.perform_divide_vector(val); } #endif bool operator==(const divider<T, ALGO>& him) const { return div.denom.magic == him.div.denom.magic && div.denom.more == him.div.denom.more; } bool operator!=(const divider<T, ALGO>& him) const { return !(*this == him); } }; #if __cplusplus >= 201103L || \ (defined(_MSC_VER) && _MSC_VER >= 1800) // libdivdie::branchfree_divider<T> template <typename T> using branchfree_divider = divider<T, BRANCHFREE>; #endif // Overload of the / operator for scalar division template<typename T, int ALGO> T operator/(T numer, const divider<T, ALGO>& denom) { return denom.perform_divide(numer); } // Overload of the /= operator for scalar division template<typename T, int ALGO> T operator/=(T& numer, const divider<T, ALGO>& denom) { numer = denom.perform_divide(numer); return numer; } #if defined(LIBDIVIDE_AVX512) // Overload of the / operator for vector division template<typename T, int ALGO> __m512i operator/(__m512i numer, const divider<T, ALGO>& denom) { return denom.perform_divide_vector(numer); } // Overload of the /= operator for vector division template<typename T, int ALGO> __m512i operator/=(__m512i& numer, const divider<T, ALGO>& denom) { numer = denom.perform_divide_vector(numer); return numer; } #elif defined(LIBDIVIDE_AVX2) // Overload of the / operator for vector division template<typename T, int ALGO> __m256i operator/(__m256i numer, const divider<T, ALGO>& denom) { return denom.perform_divide_vector(numer); } // Overload of the /= operator for vector division template<typename T, int ALGO> __m256i operator/=(__m256i& numer, const divider<T, ALGO>& denom) { numer = denom.perform_divide_vector(numer); return numer; } #elif defined(LIBDIVIDE_SSE2) // Overload of the / operator for vector division template<typename T, int ALGO> __m128i operator/(__m128i numer, const divider<T, ALGO>& denom) { return denom.perform_divide_vector(numer); } // Overload of the /= operator for vector division template<typename T, int ALGO> __m128i operator/=(__m128i& numer, const divider<T, ALGO>& denom) { numer = denom.perform_divide_vector(numer); return numer; } #endif } // namespace libdivide } // anonymous namespace #endif // __cplusplus #endif // LIBDIVIDE_H uint64_t divide(uint64_t x, void* divider) { auto& fast_d = *((libdivide::branchfree_divider<uint64_t>*) divider); return x / fast_d; }
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