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Double-width tower extension part 1 (#72)

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* Implement double-width field multiplication for double-width towering

* Fp2 mul acceleration via double-width lazy reduction (pure Nim)

* Inline assembly for basic add and sub

* Use 2 registers instead of 12+ for ASM conditional copy

* Prepare assembly for extended multiprecision multiplication support

* Add assembly for mul

* initial implementation of assembly reduction

* stash current progress of assembly reduction

* Fix clobbering issue, only P256 comparison remain buggy

* Fix asm montgomery reduction for NIST P256 as well

* MULX/ADCX/ADOX multi-precision multiplication

* MULX/ADCX/ADOX reduction v1

* Add (deactivated) assembly for double-width substraction + rework benches

* Add bench to nimble and deactivate double-width for now. slower than classic

* Fix x86-32 running out of registers for mul

* Clang needs to be at v9 to support flag output constraints (Xcode 11.4.2 / OSX Catalina)

* 32-bit doesn't have enough registers for ASM mul

* Fix again Travis Clang 9 issues

* LLVM 9 is not whitelisted in travis

* deactivated assembler with travis clang

* syntax error

* another

* ...

* missing space, yeah ...
This commit is contained in:
Mamy Ratsimbazafy 2020-08-20 10:21:39 +02:00 committed by GitHub
parent 5e8b1870a6
commit d41c653c8a
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GPG Key ID: 4AEE18F83AFDEB23
37 changed files with 1901 additions and 249 deletions
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25
.travis.yml
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@ -13,6 +13,7 @@ matrix:
# Build and test on both x86-64 and ARM64 # Build and test on both x86-64 and ARM64
# Ubuntu Bionic (18.04) is needed, it includes # Ubuntu Bionic (18.04) is needed, it includes
# GCC 7 codegen fixes to addcarry_u64. # GCC 7 codegen fixes to addcarry_u64.
# Clang 9 (and GCC-6) are needed for inline assembly "flag output constraints"
- dist: bionic - dist: bionic
arch: amd64 arch: amd64
env: env:
@ -33,9 +34,19 @@ matrix:
- ARCH=amd64 - ARCH=amd64
- CHANNEL=devel - CHANNEL=devel
compiler: clang compiler: clang
# addons:
# apt:
# sources:
# - ubuntu-toolchain-r-test
# - llvm-toolchain-bionic-9.0 # LLVM 9 repo is disallowed
# packages:
# - clang-9.0
# env:
# - MATRIX_EVAL="CC=clang-9.0 && CXX=clang++-9.0"
# On OSX we only test against clang (gcc is mapped to clang by default) # On OSX we only test against clang (gcc is mapped to clang by default)
- os: osx - os: osx
osx_image: xcode11.5 # Need xcode 11.4.2 min for Clang 9
arch: amd64 arch: amd64
env: env:
- ARCH=amd64 - ARCH=amd64
@ -98,9 +109,17 @@ before_script:
script: script:
- nimble refresh - nimble refresh
- nimble install gmp stew - nimble install gmp stew
- nimble test_parallel # Installing Clang9.0 or later is a pain in Travis
- if [[ "$ARCH" != "arm64" ]]; then # for inline assembly "flag output constraint"
nimble test_parallel_no_assembler; # Also MacOS build is timing out with 2 series of tests.
- |
if [[ "$TRAVIS_COMPILER" == "clang" ]]; then
nimble test_parallel_no_assembler
else
nimble test_parallel
if [[ "$ARCH" != "arm64" ]]; then
nimble test_parallel_no_assembler
fi
fi fi
branches: branches:
except: except:

2
azure-pipelines.yml
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@ -36,7 +36,7 @@ strategy:
# TEST_LANG: c # TEST_LANG: c
MacOS_devel_64bit: MacOS_devel_64bit:
VM: 'macOS-10.14' VM: 'macOS-10.15'
UCPU: amd64 UCPU: amd64
CHANNEL: devel CHANNEL: devel
TEST_LANG: c TEST_LANG: c

2
benchmarks/bench_elliptic_template.nim
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@ -61,7 +61,7 @@ echo "Optimization level => "
echo " no optimization: ", not defined(release) echo " no optimization: ", not defined(release)
echo " release: ", defined(release) echo " release: ", defined(release)
echo " danger: ", defined(danger) echo " danger: ", defined(danger)
echo " inline assembly: ", UseX86ASM echo " inline assembly: ", UseASM_X86_64
when (sizeof(int) == 4) or defined(Constantine32): when (sizeof(int) == 4) or defined(Constantine32):
echo "⚠️ Warning: using Constantine with 32-bit limbs" echo "⚠️ Warning: using Constantine with 32-bit limbs"

2
benchmarks/bench_fields_template.nim
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@ -58,7 +58,7 @@ echo "Optimization level => "
echo " no optimization: ", not defined(release) echo " no optimization: ", not defined(release)
echo " release: ", defined(release) echo " release: ", defined(release)
echo " danger: ", defined(danger) echo " danger: ", defined(danger)
echo " inline assembly: ", UseX86ASM echo " inline assembly: ", UseASM_X86_64
when (sizeof(int) == 4) or defined(Constantine32): when (sizeof(int) == 4) or defined(Constantine32):
echo "⚠️ Warning: using Constantine with 32-bit limbs" echo "⚠️ Warning: using Constantine with 32-bit limbs"

196
benchmarks/bench_fp_double_width.nim Normal file
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@ -0,0 +1,196 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
# ############################################################
#
# Benchmark of finite fields
#
# ############################################################
import
# Internals
../constantine/config/[curves, common],
../constantine/arithmetic,
../constantine/towers,
# Helpers
../helpers/[prng_unsafe, static_for],
./platforms,
# Standard library
std/[monotimes, times, strformat, strutils, macros]
var rng: RngState
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
rng.seed(seed)
echo "bench xoshiro512** seed: ", seed
# warmup
proc warmup*() =
# Warmup - make sure cpu is on max perf
let start = cpuTime()
var foo = 123
for i in 0 ..< 300_000_000:
foo += i*i mod 456
foo = foo mod 789
# Compiler shouldn't optimize away the results as cpuTime rely on sideeffects
let stop = cpuTime()
echo &"Warmup: {stop - start:>4.4f} s, result {foo} (displayed to avoid compiler optimizing warmup away)\n"
warmup()
when defined(gcc):
echo "\nCompiled with GCC"
elif defined(clang):
echo "\nCompiled with Clang"
elif defined(vcc):
echo "\nCompiled with MSVC"
elif defined(icc):
echo "\nCompiled with ICC"
else:
echo "\nCompiled with an unknown compiler"
echo "Optimization level => "
echo " no optimization: ", not defined(release)
echo " release: ", defined(release)
echo " danger: ", defined(danger)
echo " inline assembly: ", UseASM_X86_64
when (sizeof(int) == 4) or defined(Constantine32):
echo "⚠️ Warning: using Constantine with 32-bit limbs"
else:
echo "Using Constantine with 64-bit limbs"
when SupportsCPUName:
echo "Running on ", cpuName(), ""
when SupportsGetTicks:
echo "\n⚠️ Cycles measurements are approximate and use the CPU nominal clock: Turbo-Boost and overclocking will skew them."
echo "i.e. a 20% overclock will be about 20% off (assuming no dynamic frequency scaling)"
echo "\n=================================================================================================================\n"
proc separator*() =
echo "-".repeat(145)
proc report(op, field: string, start, stop: MonoTime, startClk, stopClk: int64, iters: int) =
let ns = inNanoseconds((stop-start) div iters)
let throughput = 1e9 / float64(ns)
when SupportsGetTicks:
echo &"{op:<28} {field:<40} {throughput:>15.3f} ops/s {ns:>9} ns/op {(stopClk - startClk) div iters:>9} CPU cycles (approx)"
else:
echo &"{op:<28} {field:<40} {throughput:>15.3f} ops/s {ns:>9} ns/op"
proc notes*() =
echo "Notes:"
echo " - Compilers:"
echo " Compilers are severely limited on multiprecision arithmetic."
echo " Inline Assembly is used by default (nimble bench_fp)."
echo " Bench without assembly can use \"nimble bench_fp_gcc\" or \"nimble bench_fp_clang\"."
echo " GCC is significantly slower than Clang on multiprecision arithmetic due to catastrophic handling of carries."
echo " - The simplest operations might be optimized away by the compiler."
echo " - Fast Squaring and Fast Multiplication are possible if there are spare bits in the prime representation (i.e. the prime uses 254 bits out of 256 bits)"
template bench(op: string, desc: string, iters: int, body: untyped): untyped =
let start = getMonotime()
when SupportsGetTicks:
let startClk = getTicks()
for _ in 0 ..< iters:
body
when SupportsGetTicks:
let stopClk = getTicks()
let stop = getMonotime()
when not SupportsGetTicks:
let startClk = -1'i64
let stopClk = -1'i64
report(op, desc, start, stop, startClk, stopClk, iters)
func random_unsafe(rng: var RngState, a: var FpDbl, Base: typedesc) =
## Initialize a standalone Double-Width field element
## we don't reduce it modulo p², this is only used for benchmark
let aHi = rng.random_unsafe(Base)
let aLo = rng.random_unsafe(Base)
for i in 0 ..< aLo.mres.limbs.len:
a.limbs2x[i] = aLo.mres.limbs[i]
for i in 0 ..< aHi.mres.limbs.len:
a.limbs2x[aLo.mres.limbs.len+i] = aHi.mres.limbs[i]
proc sumNoReduce(T: typedesc, iters: int) =
var r: T
let a = rng.random_unsafe(T)
let b = rng.random_unsafe(T)
bench("Addition no reduce", $T, iters):
r.sumNoReduce(a, b)
proc sum(T: typedesc, iters: int) =
var r: T
let a = rng.random_unsafe(T)
let b = rng.random_unsafe(T)
bench("Addition", $T, iters):
r.sum(a, b)
proc diffNoReduce(T: typedesc, iters: int) =
var r: T
let a = rng.random_unsafe(T)
let b = rng.random_unsafe(T)
bench("Substraction no reduce", $T, iters):
r.diffNoReduce(a, b)
proc diff(T: typedesc, iters: int) =
var r: T
let a = rng.random_unsafe(T)
let b = rng.random_unsafe(T)
bench("Substraction", $T, iters):
r.diff(a, b)
proc diff2xNoReduce(T: typedesc, iters: int) =
var r, a, b: doubleWidth(T)
rng.random_unsafe(r, T)
rng.random_unsafe(a, T)
rng.random_unsafe(b, T)
bench("Substraction 2x no reduce", $doubleWidth(T), iters):
r.diffNoReduce(a, b)
proc diff2x(T: typedesc, iters: int) =
var r, a, b: doubleWidth(T)
rng.random_unsafe(r, T)
rng.random_unsafe(a, T)
rng.random_unsafe(b, T)
bench("Substraction 2x", $doubleWidth(T), iters):
r.diff(a, b)
proc mul2xBench*(rLen, aLen, bLen: static int, iters: int) =
var r: BigInt[rLen]
let a = rng.random_unsafe(BigInt[aLen])
let b = rng.random_unsafe(BigInt[bLen])
bench("Multiplication", $rLen & " <- " & $aLen & " x " & $bLen, iters):
r.prod(a, b)
proc reduce2x*(T: typedesc, iters: int) =
var r: T
var t: doubleWidth(T)
rng.random_unsafe(t, T)
bench("Reduce 2x-width", $T & " <- " & $doubleWidth(T), iters):
r.reduce(t)
proc main() =
separator()
sumNoReduce(Fp[BLS12_381], iters = 10_000_000)
diffNoReduce(Fp[BLS12_381], iters = 10_000_000)
sum(Fp[BLS12_381], iters = 10_000_000)
diff(Fp[BLS12_381], iters = 10_000_000)
diff2x(Fp[BLS12_381], iters = 10_000_000)
diff2xNoReduce(Fp[BLS12_381], iters = 10_000_000)
mul2xBench(768, 384, 384, iters = 10_000_000)
reduce2x(Fp[BLS12_381], iters = 10_000_000)
separator()
main()
notes()

59
constantine.nimble
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@ -35,6 +35,8 @@ const testDesc: seq[tuple[path: string, useGMP: bool]] = @[
("tests/t_finite_fields_vs_gmp.nim", true), ("tests/t_finite_fields_vs_gmp.nim", true),
# Precompute # Precompute
("tests/t_precomputed", false), ("tests/t_precomputed", false),
# Double-width finite fields
("tests/t_finite_fields_double_width.nim", false),
# Towers of extension fields # Towers of extension fields
("tests/t_fp2.nim", false), ("tests/t_fp2.nim", false),
("tests/t_fp2_sqrt.nim", false), ("tests/t_fp2_sqrt.nim", false),
@ -100,13 +102,15 @@ proc test(flags, path: string, commandFile = false) =
# commandFile.writeLine command # commandFile.writeLine command
exec "echo \'" & command & "\' >> " & buildParallel exec "echo \'" & command & "\' >> " & buildParallel
proc runBench(benchName: string, compiler = "") = proc runBench(benchName: string, compiler = "", useAsm = true) =
if not dirExists "build": if not dirExists "build":
mkDir "build" mkDir "build"
var cc = "" var cc = ""
if compiler != "": if compiler != "":
cc = "--cc:" & compiler & " -d:ConstantineASM=false" cc = "--cc:" & compiler
if not useAsm:
cc &= " -d:ConstantineASM=false"
exec "nim c " & cc & exec "nim c " & cc &
" -d:danger --verbosity:0 -o:build/" & benchName & "_" & compiler & " -d:danger --verbosity:0 -o:build/" & benchName & "_" & compiler &
" -r --hints:off --warnings:off benchmarks/" & benchName & ".nim" " -r --hints:off --warnings:off benchmarks/" & benchName & ".nim"
@ -298,6 +302,27 @@ task bench_fp_gcc, "Run benchmark 𝔽p with gcc":
task bench_fp_clang, "Run benchmark 𝔽p with clang": task bench_fp_clang, "Run benchmark 𝔽p with clang":
runBench("bench_fp", "clang") runBench("bench_fp", "clang")
task bench_fp_gcc_noasm, "Run benchmark 𝔽p with gcc - no Assembly":
runBench("bench_fp", "gcc", useAsm = false)
task bench_fp_clang_noasm, "Run benchmark 𝔽p with clang - no Assembly":
runBench("bench_fp", "clang", useAsm = false)
task bench_fpdbl, "Run benchmark 𝔽pDbl with your default compiler":
runBench("bench_fp_double_width")
task bench_fpdbl_gcc, "Run benchmark 𝔽p with gcc":
runBench("bench_fp_double_width", "gcc")
task bench_fpdbl_clang, "Run benchmark 𝔽p with clang":
runBench("bench_fp_double_width", "clang")
task bench_fpdbl_gcc_noasm, "Run benchmark 𝔽p with gcc - no Assembly":
runBench("bench_fp_double_width", "gcc", useAsm = false)
task bench_fpdbl_clang_noasm, "Run benchmark 𝔽p with clang - no Assembly":
runBench("bench_fp_double_width", "clang", useAsm = false)
task bench_fp2, "Run benchmark with 𝔽p2 your default compiler": task bench_fp2, "Run benchmark with 𝔽p2 your default compiler":
runBench("bench_fp2") runBench("bench_fp2")
@ -307,6 +332,12 @@ task bench_fp2_gcc, "Run benchmark 𝔽p2 with gcc":
task bench_fp2_clang, "Run benchmark 𝔽p2 with clang": task bench_fp2_clang, "Run benchmark 𝔽p2 with clang":
runBench("bench_fp2", "clang") runBench("bench_fp2", "clang")
task bench_fp2_gcc_noasm, "Run benchmark 𝔽p2 with gcc - no Assembly":
runBench("bench_fp2", "gcc", useAsm = false)
task bench_fp2_clang_noasm, "Run benchmark 𝔽p2 with clang - no Assembly":
runBench("bench_fp2", "clang", useAsm = false)
task bench_fp6, "Run benchmark with 𝔽p6 your default compiler": task bench_fp6, "Run benchmark with 𝔽p6 your default compiler":
runBench("bench_fp6") runBench("bench_fp6")
@ -316,6 +347,12 @@ task bench_fp6_gcc, "Run benchmark 𝔽p6 with gcc":
task bench_fp6_clang, "Run benchmark 𝔽p6 with clang": task bench_fp6_clang, "Run benchmark 𝔽p6 with clang":
runBench("bench_fp6", "clang") runBench("bench_fp6", "clang")
task bench_fp6_gcc_noasm, "Run benchmark 𝔽p6 with gcc - no Assembly":
runBench("bench_fp6", "gcc", useAsm = false)
task bench_fp6_clang_noasm, "Run benchmark 𝔽p6 with clang - no Assembly":
runBench("bench_fp6", "clang", useAsm = false)
task bench_fp12, "Run benchmark with 𝔽p12 your default compiler": task bench_fp12, "Run benchmark with 𝔽p12 your default compiler":
runBench("bench_fp12") runBench("bench_fp12")
@ -325,6 +362,12 @@ task bench_fp12_gcc, "Run benchmark 𝔽p12 with gcc":
task bench_fp12_clang, "Run benchmark 𝔽p12 with clang": task bench_fp12_clang, "Run benchmark 𝔽p12 with clang":
runBench("bench_fp12", "clang") runBench("bench_fp12", "clang")
task bench_fp12_gcc_noasm, "Run benchmark 𝔽p12 with gcc - no Assembly":
runBench("bench_fp12", "gcc", useAsm = false)
task bench_fp12_clang_noasm, "Run benchmark 𝔽p12 with clang - no Assembly":
runBench("bench_fp12", "clang", useAsm = false)
task bench_ec_g1, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - GCC": task bench_ec_g1, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - GCC":
runBench("bench_ec_g1") runBench("bench_ec_g1")
@ -334,6 +377,12 @@ task bench_ec_g1_gcc, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weier
task bench_ec_g1_clang, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - Clang": task bench_ec_g1_clang, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - Clang":
runBench("bench_ec_g1", "clang") runBench("bench_ec_g1", "clang")
task bench_ec_g1_gcc_noasm, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - GCC no Assembly":
runBench("bench_ec_g1", "gcc", useAsm = false)
task bench_ec_g1_clang_noasm, "Run benchmark on Elliptic Curve group 𝔾1 - Short Weierstrass with Projective Coordinates - Clang no Assembly":
runBench("bench_ec_g1", "clang", useAsm = false)
task bench_ec_g2, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - GCC": task bench_ec_g2, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - GCC":
runBench("bench_ec_g2") runBench("bench_ec_g2")
@ -342,3 +391,9 @@ task bench_ec_g2_gcc, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weier
task bench_ec_g2_clang, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - Clang": task bench_ec_g2_clang, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - Clang":
runBench("bench_ec_g2", "clang") runBench("bench_ec_g2", "clang")
task bench_ec_g2_gcc_noasm, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - GCC no Assembly":
runBench("bench_ec_g2", "gcc", useAsm = false)
task bench_ec_g2_clang_noasm, "Run benchmark on Elliptic Curve group 𝔾2 - Short Weierstrass with Projective Coordinates - Clang no Assembly":
runBench("bench_ec_g2", "clang", useAsm = false)

4
constantine/arithmetic.nim
View File

@ -8,8 +8,8 @@
import import
arithmetic/bigints, arithmetic/bigints,
arithmetic/[finite_fields, finite_fields_inversion] arithmetic/[finite_fields, finite_fields_inversion, finite_fields_double_width]
export export
bigints, bigints,
finite_fields, finite_fields_inversion finite_fields, finite_fields_inversion, finite_fields_double_width

18
constantine/arithmetic/bigints.nim
View File

@ -9,13 +9,10 @@
import import
../config/[common, type_bigint], ../config/[common, type_bigint],
../primitives, ../primitives,
./limbs_generic, ./limbs,
./limbs_generic_modular, ./limbs_generic_modular,
./limbs_montgomery ./limbs_montgomery
when UseX86ASM:
import ./limbs_asm_x86
export BigInt export BigInt
# ############################################################ # ############################################################
@ -85,10 +82,7 @@ func ccopy*(a: var BigInt, b: BigInt, ctl: SecretBool) =
## If ctl is true: b is copied into a ## If ctl is true: b is copied into a
## if ctl is false: b is not copied and a is untouched ## if ctl is false: b is not copied and a is untouched
## Time and memory accesses are the same whether a copy occurs or not ## Time and memory accesses are the same whether a copy occurs or not
when UseX86ASM: ccopy(a.limbs, b.limbs, ctl)
ccopy_asm(a.limbs, b.limbs, ctl)
else:
ccopy(a.limbs, b.limbs, ctl)
func cswap*(a, b: var BigInt, ctl: CTBool) = func cswap*(a, b: var BigInt, ctl: CTBool) =
## Swap ``a`` and ``b`` if ``ctl`` is true ## Swap ``a`` and ``b`` if ``ctl`` is true
@ -245,6 +239,14 @@ func prod*[rBits, aBits, bBits](r: var BigInt[rBits], a: BigInt[aBits], b: BigIn
## It will be truncated if it cannot fit in r limbs. ## It will be truncated if it cannot fit in r limbs.
r.limbs.prod(a.limbs, b.limbs) r.limbs.prod(a.limbs, b.limbs)
func mul*[aBits, bBits](a: var BigInt[aBits], b: BigInt[bBits]) =
## Multi-precision multiplication
## a <- a*b
## `a`, `b`, can have different sizes
var t{.noInit.}: typeof(a)
t.limbs.prod(a.limbs, b.limbs)
a = t
func prod_high_words*[rBits, aBits, bBits](r: var BigInt[rBits], a: BigInt[aBits], b: BigInt[bBits], lowestWordIndex: static int) = func prod_high_words*[rBits, aBits, bBits](r: var BigInt[rBits], a: BigInt[aBits], b: BigInt[bBits], lowestWordIndex: static int) =
## Multi-precision multiplication keeping only high words ## Multi-precision multiplication keeping only high words
## r <- a*b >> (2^WordBitWidth)^lowestWordIndex ## r <- a*b >> (2^WordBitWidth)^lowestWordIndex

41
constantine/arithmetic/finite_fields.nim
View File

@ -29,7 +29,7 @@ import
../config/[common, type_fp, curves], ../config/[common, type_fp, curves],
./bigints, ./limbs_montgomery ./bigints, ./limbs_montgomery
when UseX86ASM: when UseASM_X86_64:
import ./limbs_asm_modular_x86 import ./limbs_asm_modular_x86
export Fp export Fp
@ -120,7 +120,7 @@ func setOne*(a: var Fp) {.inline.} =
func `+=`*(a: var Fp, b: Fp) {.inline.} = func `+=`*(a: var Fp, b: Fp) {.inline.} =
## In-place addition modulo p ## In-place addition modulo p
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
addmod_asm(a.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs) addmod_asm(a.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs)
else: else:
var overflowed = add(a.mres, b.mres) var overflowed = add(a.mres, b.mres)
@ -129,7 +129,7 @@ func `+=`*(a: var Fp, b: Fp) {.inline.} =
func `-=`*(a: var Fp, b: Fp) {.inline.} = func `-=`*(a: var Fp, b: Fp) {.inline.} =
## In-place substraction modulo p ## In-place substraction modulo p
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
submod_asm(a.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs) submod_asm(a.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs)
else: else:
let underflowed = sub(a.mres, b.mres) let underflowed = sub(a.mres, b.mres)
@ -137,7 +137,7 @@ func `-=`*(a: var Fp, b: Fp) {.inline.} =
func double*(a: var Fp) {.inline.} = func double*(a: var Fp) {.inline.} =
## Double ``a`` modulo p ## Double ``a`` modulo p
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
addmod_asm(a.mres.limbs, a.mres.limbs, Fp.C.Mod.limbs) addmod_asm(a.mres.limbs, a.mres.limbs, Fp.C.Mod.limbs)
else: else:
var overflowed = double(a.mres) var overflowed = double(a.mres)
@ -145,9 +145,9 @@ func double*(a: var Fp) {.inline.} =
discard csub(a.mres, Fp.C.Mod, overflowed) discard csub(a.mres, Fp.C.Mod, overflowed)
func sum*(r: var Fp, a, b: Fp) {.inline.} = func sum*(r: var Fp, a, b: Fp) {.inline.} =
## Sum ``a`` and ``b`` into ``r`` module p ## Sum ``a`` and ``b`` into ``r`` modulo p
## r is initialized/overwritten ## r is initialized/overwritten
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
r = a r = a
addmod_asm(r.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs) addmod_asm(r.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs)
else: else:
@ -155,21 +155,42 @@ func sum*(r: var Fp, a, b: Fp) {.inline.} =
overflowed = overflowed or not(r.mres < Fp.C.Mod) overflowed = overflowed or not(r.mres < Fp.C.Mod)
discard csub(r.mres, Fp.C.Mod, overflowed) discard csub(r.mres, Fp.C.Mod, overflowed)
func sumNoReduce*(r: var Fp, a, b: Fp) {.inline.} =
## Sum ``a`` and ``b`` into ``r`` without reduction
discard r.mres.sum(a.mres, b.mres)
func diff*(r: var Fp, a, b: Fp) {.inline.} = func diff*(r: var Fp, a, b: Fp) {.inline.} =
## Substract `b` from `a` and store the result into `r`. ## Substract `b` from `a` and store the result into `r`.
## `r` is initialized/overwritten ## `r` is initialized/overwritten
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling ## Requires r != b
var t = a # Handle aliasing r == b when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
r = a
submod_asm(r.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs)
else:
var underflowed = r.mres.diff(a.mres, b.mres)
discard cadd(r.mres, Fp.C.Mod, underflowed)
func diffAlias*(r: var Fp, a, b: Fp) {.inline.} =
## Substract `b` from `a` and store the result into `r`.
## `r` is initialized/overwritten
## Handles r == b
when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
var t = a
submod_asm(t.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs) submod_asm(t.mres.limbs, b.mres.limbs, Fp.C.Mod.limbs)
r = t r = t
else: else:
var underflowed = r.mres.diff(a.mres, b.mres) var underflowed = r.mres.diff(a.mres, b.mres)
discard cadd(r.mres, Fp.C.Mod, underflowed) discard cadd(r.mres, Fp.C.Mod, underflowed)
func diffNoReduce*(r: var Fp, a, b: Fp) {.inline.} =
## Substract `b` from `a` and store the result into `r`
## without reduction
discard r.mres.diff(a.mres, b.mres)
func double*(r: var Fp, a: Fp) {.inline.} = func double*(r: var Fp, a: Fp) {.inline.} =
## Double ``a`` into ``r`` ## Double ``a`` into ``r``
## `r` is initialized/overwritten ## `r` is initialized/overwritten
when UseX86ASM and a.mres.limbs.len <= 6: # TODO: handle spilling when UseASM_X86_64 and a.mres.limbs.len <= 6: # TODO: handle spilling
r = a r = a
addmod_asm(r.mres.limbs, a.mres.limbs, Fp.C.Mod.limbs) addmod_asm(r.mres.limbs, a.mres.limbs, Fp.C.Mod.limbs)
else: else:
@ -188,7 +209,7 @@ func square*(r: var Fp, a: Fp) {.inline.} =
func neg*(r: var Fp, a: Fp) {.inline.} = func neg*(r: var Fp, a: Fp) {.inline.} =
## Negate modulo p ## Negate modulo p
when UseX86ASM and defined(gcc): when UseASM_X86_64 and defined(gcc):
# Clang and every compiler besides GCC # Clang and every compiler besides GCC
# can cleanly optimized this # can cleanly optimized this
# especially on Fp2 # especially on Fp2

72
constantine/arithmetic/finite_fields_double_width.nim Normal file
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@ -0,0 +1,72 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
../config/[common, curves, type_bigint, type_fp],
../primitives,
./bigints,
./finite_fields,
./limbs,
./limbs_double_width
when UseASM_X86_64:
import limbs_asm_modular_dbl_width_x86
type FpDbl*[C: static Curve] = object
## Double-width Fp element
## This allows saving on reductions
# We directly work with double the number of limbs
limbs2x*: matchingLimbs2x(C)
template doubleWidth*(T: typedesc[Fp]): typedesc =
## Return the double-width type matching with Fp
FpDbl[T.C]
func mulNoReduce*(r: var FpDbl, a, b: Fp) {.inline.} =
## Store the product of ``a`` by ``b`` into ``r``
r.limbs2x.prod(a.mres.limbs, b.mres.limbs)
func reduce*(r: var Fp, a: FpDbl) {.inline.} =
## Reduce a double-width field element into r
const N = r.mres.limbs.len
montyRed(
r.mres.limbs,
a.limbs2x,
Fp.C.Mod.limbs,
Fp.C.getNegInvModWord(),
Fp.C.canUseNoCarryMontyMul()
)
func diffNoInline(r: var FpDbl, a, b: FpDbl): Borrow =
r.limbs2x.diff(a.limbs2x, b.limbs2x)
func diffNoReduce*(r: var FpDbl, a, b: FpDbl) =
## Double-width substraction without reduction
discard diffNoInline(r, a, b)
func diff*(r: var FpDbl, a, b: FpDbl) =
## Double-width modular substraction
when false: # TODO slower
r = a
sub2x_asm(r.limbs2x, b.limbs2x, FpDbl.C.Mod.limbs)
else:
var underflowed = SecretBool diffNoInline(r, a, b)
const N = r.limbs2x.len div 2
const M = FpDbl.C.Mod
var carry = Carry(0)
var sum: SecretWord
for i in 0 ..< N:
addC(carry, sum, r.limbs2x[i+N], M.limbs[i], carry)
underflowed.ccopy(r.limbs2x[i+N], sum)
func `-=`*(a: var FpDbl, b: FpDbl) =
when false: # TODO slower
sub2x_asm(a.limbs2x, b.limbs2x, FpDbl.C.Mod.limbs)
else:
a.diff(a, b)

121
constantine/arithmetic/limbs_generic.nim → constantine/arithmetic/limbs.nim
View File

@ -8,8 +8,13 @@
import import
../config/common, ../config/common,
../primitives, ../primitives
../../helpers/static_for
when UseASM_X86_32:
import ./limbs_asm_x86
when UseASM_X86_64:
import ./limbs_asm_mul_x86
import ./limbs_asm_mul_x86_adx_bmi2
# ############################################################ # ############################################################
# #
@ -37,39 +42,9 @@ import
# The limb-endianess is little-endian, less significant limb is at index 0. # The limb-endianess is little-endian, less significant limb is at index 0.
# The word-endianness is native-endian. # The word-endianness is native-endian.
type Limbs*[N: static int] = array[N, SecretWord]
## Limbs-type
## Should be distinct type to avoid builtins to use non-constant time
## implementation, for example for comparison.
##
## but for unknown reason, it prevents semchecking `bits`
# No exceptions allowed # No exceptions allowed
{.push raises: [].} {.push raises: [].}
# ############################################################
#
# Accessors
#
# ############################################################
#
# Commented out since we don't use a distinct type
# template `[]`[N](v: Limbs[N], idx: int): SecretWord =
# (array[N, SecretWord])(v)[idx]
#
# template `[]`[N](v: var Limbs[N], idx: int): var SecretWord =
# (array[N, SecretWord])(v)[idx]
#
# template `[]=`[N](v: Limbs[N], idx: int, val: SecretWord) =
# (array[N, SecretWord])(v)[idx] = val
# ############################################################
#
# Checks and debug/test only primitives
#
# ############################################################
# ############################################################ # ############################################################
# #
# Limbs Primitives # Limbs Primitives
@ -104,8 +79,11 @@ func ccopy*(a: var Limbs, b: Limbs, ctl: SecretBool) =
## If ctl is true: b is copied into a ## If ctl is true: b is copied into a
## if ctl is false: b is not copied and a is untouched ## if ctl is false: b is not copied and a is untouched
## Time and memory accesses are the same whether a copy occurs or not ## Time and memory accesses are the same whether a copy occurs or not
for i in 0 ..< a.len: when UseASM_X86_32:
ctl.ccopy(a[i], b[i]) ccopy_asm(a, b, ctl)
else:
for i in 0 ..< a.len:
ctl.ccopy(a[i], b[i])
func cswap*(a, b: var Limbs, ctl: CTBool) = func cswap*(a, b: var Limbs, ctl: CTBool) =
## Swap ``a`` and ``b`` if ``ctl`` is true ## Swap ``a`` and ``b`` if ``ctl`` is true
@ -190,9 +168,12 @@ func shiftRight*(a: var Limbs, k: int) {.inline.}=
func add*(a: var Limbs, b: Limbs): Carry = func add*(a: var Limbs, b: Limbs): Carry =
## Limbs addition ## Limbs addition
## Returns the carry ## Returns the carry
result = Carry(0) when UseASM_X86_32:
for i in 0 ..< a.len: result = add_asm(a, a, b)
addC(result, a[i], a[i], b[i], result) else:
result = Carry(0)
for i in 0 ..< a.len:
addC(result, a[i], a[i], b[i], result)
func add*(a: var Limbs, w: SecretWord): Carry = func add*(a: var Limbs, w: SecretWord): Carry =
## Limbs addition, add a number that fits in a word ## Limbs addition, add a number that fits in a word
@ -222,16 +203,22 @@ func sum*(r: var Limbs, a, b: Limbs): Carry =
## `r` is initialized/overwritten ## `r` is initialized/overwritten
## ##
## Returns the carry ## Returns the carry
result = Carry(0) when UseASM_X86_32:
for i in 0 ..< a.len: result = add_asm(r, a, b)
addC(result, r[i], a[i], b[i], result) else:
result = Carry(0)
for i in 0 ..< a.len:
addC(result, r[i], a[i], b[i], result)
func sub*(a: var Limbs, b: Limbs): Borrow = func sub*(a: var Limbs, b: Limbs): Borrow =
## Limbs substraction ## Limbs substraction
## Returns the borrow ## Returns the borrow
result = Borrow(0) when UseASM_X86_32:
for i in 0 ..< a.len: result = sub_asm(a, a, b)
subB(result, a[i], a[i], b[i], result) else:
result = Borrow(0)
for i in 0 ..< a.len:
subB(result, a[i], a[i], b[i], result)
func sub*(a: var Limbs, w: SecretWord): Borrow = func sub*(a: var Limbs, w: SecretWord): Borrow =
## Limbs substraction, sub a number that fits in a word ## Limbs substraction, sub a number that fits in a word
@ -272,9 +259,12 @@ func diff*(r: var Limbs, a, b: Limbs): Borrow =
## `r` is initialized/overwritten ## `r` is initialized/overwritten
## ##
## Returns the borrow ## Returns the borrow
result = Borrow(0) when UseASM_X86_32:
for i in 0 ..< a.len: result = sub_asm(r, a, b)
subB(result, r[i], a[i], b[i], result) else:
result = Borrow(0)
for i in 0 ..< a.len:
subB(result, r[i], a[i], b[i], result)
func cneg*(a: var Limbs, ctl: CTBool) = func cneg*(a: var Limbs, ctl: CTBool) =
## Conditional negation. ## Conditional negation.
@ -301,7 +291,7 @@ func cneg*(a: var Limbs, ctl: CTBool) =
# Multiplication # Multiplication
# ------------------------------------------------------------ # ------------------------------------------------------------
func prod*[rLen, aLen, bLen](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) = func prod*[rLen, aLen, bLen: static int](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
## Multi-precision multiplication ## Multi-precision multiplication
## r <- a*b ## r <- a*b
## ##
@ -309,23 +299,34 @@ func prod*[rLen, aLen, bLen](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen])
## if `r`.limbs.len < a.limbs.len + b.limbs.len ## if `r`.limbs.len < a.limbs.len + b.limbs.len
## The result will be truncated, i.e. it will be ## The result will be truncated, i.e. it will be
## a * b (mod (2^WordBitwidth)^r.limbs.len) ## a * b (mod (2^WordBitwidth)^r.limbs.len)
##
## `r` must not alias ``a`` or ``b``
# We use Product Scanning / Comba multiplication when UseASM_X86_64 and aLen <= 6:
var t, u, v = SecretWord(0) if ({.noSideEffect.}: hasBmi2()) and ({.noSideEffect.}: hasAdx()):
var z: Limbs[rLen] # zero-init, ensure on stack and removes in-place problems mul_asm_adx_bmi2(r, a, b)
else:
mul_asm(r, a, b)
elif UseASM_X86_64:
mul_asm(r, a, b)
else:
# We use Product Scanning / Comba multiplication
var t, u, v = SecretWord(0)
staticFor i, 0, min(a.len+b.len, r.len): staticFor i, 0, min(a.len+b.len, r.len):
const ib = min(b.len-1, i) const ib = min(b.len-1, i)
const ia = i - ib const ia = i - ib
staticFor j, 0, min(a.len - ia, ib+1): staticFor j, 0, min(a.len - ia, ib+1):
mulAcc(t, u, v, a[ia+j], b[ib-j]) mulAcc(t, u, v, a[ia+j], b[ib-j])
z[i] = v r[i] = v
v = u v = u
u = t u = t
t = SecretWord(0) t = SecretWord(0)
r = z if aLen+bLen < rLen:
for i in aLen+bLen ..< rLen:
r[i] = SecretWord 0
func prod_high_words*[rLen, aLen, bLen]( func prod_high_words*[rLen, aLen, bLen](
r: var Limbs[rLen], r: var Limbs[rLen],

84
constantine/arithmetic/limbs_asm_modular_dbl_width_x86.nim Normal file
View File

@ -0,0 +1,84 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/macros,
# Internal
../config/common,
../primitives
# ############################################################
#
# Assembly implementation of FpDbl
#
# ############################################################
static: doAssert UseASM_X86_64
{.localPassC:"-fomit-frame-pointer".} # Needed so that the compiler finds enough registers
# TODO slower than intrinsics
# Substraction
# ------------------------------------------------------------
macro sub2x_gen[N: static int](a: var Limbs[N], b: Limbs[N], M: Limbs[N div 2]): untyped =
## Generate an optimized out-of-place double-width substraction kernel
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
N2 = N div 2
arrA = init(OperandArray, nimSymbol = a, N, PointerInReg, InputOutput)
# We reuse the reg used for B for overflow detection
arrB = init(OperandArray, nimSymbol = b, N, PointerInReg, InputOutput)
# We could force M as immediate by specializing per moduli
arrM = init(OperandArray, nimSymbol = M, N, PointerInReg, Input)
# If N is too big, we need to spill registers. TODO.
arrT = init(OperandArray, nimSymbol = ident"t", N2, ElemsInReg, Output_EarlyClobber)
arrTadd = init(OperandArray, nimSymbol = ident"tadd", N2, ElemsInReg, Output_EarlyClobber)
# Substraction
for i in 0 ..< N:
ctx.mov arrT[i mod N2], arrA[i]
if i == 0:
ctx.sub arrT[0], arrB[0]
else:
ctx.sbb arrT[i mod N2], arrB[i]
ctx.mov arrA[i], arrT[i mod N2]
# Interleaved copy the modulus to hide SBB latencies
if i < N2:
ctx.mov arrTadd[i], arrM[i]
# Mask: underflowed contains 0xFFFF or 0x0000
let underflowed = arrB.reuseRegister()
ctx.sbb underflowed, underflowed
# Now mask the adder, with 0 or the modulus limbs
for i in 0 ..< N2:
ctx.`and` arrTadd[i], underflowed
# Add the masked modulus
for i in 0 ..< N2:
if i == 0:
ctx.add arrT[0], arrTadd[0]
else:
ctx.adc arrT[i], arrTadd[i]
ctx.mov arrA[i+N2], arrT[i]
let t = arrT.nimSymbol
let tadd = arrTadd.nimSymbol
result.add quote do:
var `t`{.noinit.}, `tadd` {.noInit.}: typeof(`a`)
result.add ctx.generate
func sub2x_asm*[N: static int](a: var Limbs[N], b: Limbs[N], M: Limbs[N div 2]) =
## Constant-time double-width substraction
sub2x_gen(a, b, M)

7
constantine/arithmetic/limbs_asm_modular_x86.nim
View File

@ -12,7 +12,7 @@ import
# Internal # Internal
../config/common, ../config/common,
../primitives, ../primitives,
./limbs_generic ./limbs
# ############################################################ # ############################################################
# #
@ -25,7 +25,7 @@ import
# They are nice to let the compiler deals with mov # They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves. # but too constraining so we move things ourselves.
static: doAssert UseX86ASM static: doAssert UseASM_X86_64
{.localPassC:"-fomit-frame-pointer".} # Needed so that the compiler finds enough registers {.localPassC:"-fomit-frame-pointer".} # Needed so that the compiler finds enough registers
@ -64,6 +64,7 @@ macro addmod_gen[N: static int](a: var Limbs[N], b, M: Limbs[N]): untyped =
ctx.mov arrTsub[i], arrT[i] ctx.mov arrTsub[i], arrT[i]
# Mask: overflowed contains 0xFFFF or 0x0000 # Mask: overflowed contains 0xFFFF or 0x0000
# TODO: unnecessary if MSB never set, i.e. "canUseNoCarryMontyMul"
let overflowed = arrB.reuseRegister() let overflowed = arrB.reuseRegister()
ctx.sbb overflowed, overflowed ctx.sbb overflowed, overflowed
@ -118,7 +119,7 @@ macro submod_gen[N: static int](a: var Limbs[N], b, M: Limbs[N]): untyped =
arrT = init(OperandArray, nimSymbol = ident"t", N, ElemsInReg, Output_EarlyClobber) arrT = init(OperandArray, nimSymbol = ident"t", N, ElemsInReg, Output_EarlyClobber)
arrTadd = init(OperandArray, nimSymbol = ident"tadd", N, ElemsInReg, Output_EarlyClobber) arrTadd = init(OperandArray, nimSymbol = ident"tadd", N, ElemsInReg, Output_EarlyClobber)
# Addition # Substraction
for i in 0 ..< N: for i in 0 ..< N:
ctx.mov arrT[i], arrA[i] ctx.mov arrT[i], arrA[i]
if i == 0: if i == 0:

29
constantine/arithmetic/limbs_asm_montmul_x86.nim
View File

@ -12,7 +12,8 @@ import
# Internal # Internal
../config/common, ../config/common,
../primitives, ../primitives,
./limbs_generic ./limbs,
./limbs_asm_montred_x86
# ############################################################ # ############################################################
# #
@ -25,7 +26,7 @@ import
# They are nice to let the compiler deals with mov # They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves. # but too constraining so we move things ourselves.
static: doAssert UseX86ASM static: doAssert UseASM_X86_64
# Necessary for the compiler to find enough registers (enabled at -O1) # Necessary for the compiler to find enough registers (enabled at -O1)
{.localPassC:"-fomit-frame-pointer".} {.localPassC:"-fomit-frame-pointer".}
@ -33,28 +34,6 @@ static: doAssert UseX86ASM
# Montgomery multiplication # Montgomery multiplication
# ------------------------------------------------------------ # ------------------------------------------------------------
# Fallback when no ADX and BMI2 support (MULX, ADCX, ADOX) # Fallback when no ADX and BMI2 support (MULX, ADCX, ADOX)
proc finalSub*(
ctx: var Assembler_x86,
r: Operand or OperandArray,
t, M, scratch: OperandArray
) =
## Reduce `t` into `r` modulo `M`
let N = M.len
ctx.comment "Final substraction"
for i in 0 ..< N:
ctx.mov scratch[i], t[i]
if i == 0:
ctx.sub scratch[i], M[i]
else:
ctx.sbb scratch[i], M[i]
# If we borrowed it means that we were smaller than
# the modulus and we don't need "scratch"
for i in 0 ..< N:
ctx.cmovnc t[i], scratch[i]
ctx.mov r[i], t[i]
macro montMul_CIOS_nocarry_gen[N: static int](r_MM: var Limbs[N], a_MM, b_MM, M_MM: Limbs[N], m0ninv_MM: BaseType): untyped = macro montMul_CIOS_nocarry_gen[N: static int](r_MM: var Limbs[N], a_MM, b_MM, M_MM: Limbs[N], m0ninv_MM: BaseType): untyped =
## Generate an optimized Montgomery Multiplication kernel ## Generate an optimized Montgomery Multiplication kernel
## using the CIOS method ## using the CIOS method
@ -211,7 +190,7 @@ macro montMul_CIOS_nocarry_gen[N: static int](r_MM: var Limbs[N], a_MM, b_MM, M_
ctx.mov rRDX, r ctx.mov rRDX, r
let r2 = rRDX.asArrayAddr(len = N) let r2 = rRDX.asArrayAddr(len = N)
ctx.finalSub( ctx.finalSubNoCarry(
r2, t, M, r2, t, M,
scratch scratch
) )

79
constantine/arithmetic/limbs_asm_montmul_x86_adx_bmi2.nim
View File

@ -12,8 +12,8 @@ import
# Internal # Internal
../config/common, ../config/common,
../primitives, ../primitives,
./limbs_generic, ./limbs,
./limbs_asm_montmul_x86 ./limbs_asm_montred_x86
# ############################################################ # ############################################################
# #
@ -26,7 +26,7 @@ import
# They are nice to let the compiler deals with mov # They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves. # but too constraining so we move things ourselves.
static: doAssert UseX86ASM static: doAssert UseASM_X86_64
# MULX/ADCX/ADOX # MULX/ADCX/ADOX
{.localPassC:"-madx -mbmi2".} {.localPassC:"-madx -mbmi2".}
@ -37,53 +37,58 @@ static: doAssert UseX86ASM
# ------------------------------------------------------------ # ------------------------------------------------------------
proc mulx_by_word( proc mulx_by_word(
ctx: var Assembler_x86, ctx: var Assembler_x86,
C: Operand, hi: Operand,
t: OperandArray, t: OperandArray,
a: Operand, # Pointer in scratchspace a: Operand, # Pointer in scratchspace
word: Operand, word0: Operand,
S, rRDX: Operand lo, rRDX: Operand
) = ) =
## Multiply the `a[0..<N]` by `word` and store in `t[0..<N]` ## Multiply the `a[0..<N]` by `word` and store in `t[0..<N]`
## and carry register `C` (t[N]) ## and carry register `C` (t[N])
## `t` and `C` overwritten ## `t` and `C` overwritten
## `S` is a scratchspace carry register ## `S` is a scratchspace carry register
## `rRDX` is the RDX register descriptor ## `rRDX` is the RDX register descriptor
let N = t.len let N = min(a.len, t.len)
doAssert N >= 2, "The Assembly-optimized montgomery multiplication requires at least 2 limbs."
ctx.comment " Outer loop i = 0" ctx.comment " Outer loop i = 0"
ctx.`xor` rRDX, rRDX # Clear flags - TODO: necessary?
ctx.mov rRDX, word
# for j=0 to N-1 # for j=0 to N-1
# (C,t[j]) := t[j] + a[j]*b[i] + C # (C,t[j]) := t[j] + a[j]*b[i] + C
# First limb # First limb
ctx.mulx t[1], t[0], a[0], rdx ctx.mov rRDX, word0
if N > 1:
ctx.mulx t[1], t[0], a[0], rdx
ctx.`xor` hi, hi # Clear flags - TODO: necessary?
else:
ctx.mulx hi, t[0], a[0], rdx
return
# Steady state # Steady state
for j in 1 ..< N-1: for j in 1 ..< N-1:
ctx.mulx t[j+1], S, a[j], rdx ctx.mulx t[j+1], lo, a[j], rdx
ctx.adox t[j], S # TODO, we probably can use ADC here if j == 1:
ctx.add t[j], lo
else:
ctx.adc t[j], lo
# Last limb # Last limb
ctx.mulx C, S, a[N-1], rdx ctx.comment " Outer loop i = 0, last limb"
ctx.adox t[N-1], S ctx.mulx hi, lo, a[N-1], rdx
ctx.adc t[N-1], lo
# Final carries # Final carries
ctx.comment " Mul carries i = 0" ctx.comment " Accumulate last carries in hi word"
ctx.mov rRDX, 0 # Set to 0 without clearing flags ctx.adc hi, 0
ctx.adcx C, rRDX
ctx.adox C, rRDX
proc mulaccx_by_word( proc mulaccx_by_word(
ctx: var Assembler_x86, ctx: var Assembler_x86,
C: Operand, hi: Operand,
t: OperandArray, t: OperandArray,
a: Operand, # Pointer in scratchspace a: Operand, # Pointer in scratchspace
i: int, i: int,
word: Operand, word: Operand,
S, rRDX: Operand lo, rRDX: Operand
) = ) =
## Multiply the `a[0..<N]` by `word` ## Multiply the `a[0..<N]` by `word`
## and accumulate in `t[0..<N]` ## and accumulate in `t[0..<N]`
@ -91,33 +96,33 @@ proc mulaccx_by_word(
## `t` and `C` are multiply-accumulated ## `t` and `C` are multiply-accumulated
## `S` is a scratchspace register ## `S` is a scratchspace register
## `rRDX` is the RDX register descriptor ## `rRDX` is the RDX register descriptor
let N = t.len let N = min(a.len, t.len)
doAssert N >= 2, "The Assembly-optimized montgomery multiplication requires at least 2 limbs."
doAssert i != 0 doAssert i != 0
ctx.comment " Outer loop i = " & $i ctx.comment " Outer loop i = " & $i & ", j in [0, " & $N & ")"
ctx.`xor` rRDX, rRDX # Clear flags - TODO: necessary?
ctx.mov rRDX, word ctx.mov rRDX, word
ctx.`xor` hi, hi # Clear flags - TODO: necessary?
# for j=0 to N-1 # for j=0 to N-1
# (C,t[j]) := t[j] + a[j]*b[i] + C # (C,t[j]) := t[j] + a[j]*b[i] + C
# Steady state # Steady state
for j in 0 ..< N-1: for j in 0 ..< N-1:
ctx.mulx C, S, a[j], rdx ctx.mulx hi, lo, a[j], rdx
ctx.adox t[j], S ctx.adox t[j], lo
ctx.adcx t[j+1], C ctx.adcx t[j+1], hi
# Last limb # Last limb
ctx.mulx C, S, a[N-1], rdx ctx.comment " Outer loop i = " & $i & ", last limb"
ctx.adox t[N-1], S ctx.mulx hi, lo, a[N-1], rdx
ctx.adox t[N-1], lo
# Final carries # Final carries
ctx.comment " Mul carries i = " & $i ctx.comment " Accumulate last carries in hi word"
ctx.mov rRDX, 0 # Set to 0 without clearing flags ctx.mov rRDX, 0 # Set to 0 without clearing flags
ctx.adcx C, rRDX ctx.adcx hi, rRDX
ctx.adox C, rRDX ctx.adox hi, rRDX
proc partialRedx( proc partialRedx(
ctx: var Assembler_x86, ctx: var Assembler_x86,
@ -163,7 +168,7 @@ proc partialRedx(
ctx.adox t[j-1], S ctx.adox t[j-1], S
# Last carries # Last carries
# t[N-1} = S + C # t[N-1] = S + C
ctx.comment " Reduction carry " ctx.comment " Reduction carry "
ctx.mov S, 0 ctx.mov S, 0
ctx.adcx t[N-1], S ctx.adcx t[N-1], S
@ -182,13 +187,13 @@ macro montMul_CIOS_nocarry_adx_bmi2_gen[N: static int](r_MM: var Limbs[N], a_MM,
let let
scratchSlots = max(N, 6) scratchSlots = max(N, 6)
r = init(OperandArray, nimSymbol = r_MM, N, PointerInReg, InputOutput) r = init(OperandArray, nimSymbol = r_MM, N, PointerInReg, InputOutput_EnsureClobber)
# We could force M as immediate by specializing per moduli # We could force M as immediate by specializing per moduli
M = init(OperandArray, nimSymbol = M_MM, N, PointerInReg, Input) M = init(OperandArray, nimSymbol = M_MM, N, PointerInReg, Input)
# If N is too big, we need to spill registers. TODO. # If N is too big, we need to spill registers. TODO.
t = init(OperandArray, nimSymbol = ident"t", N, ElemsInReg, Output_EarlyClobber) t = init(OperandArray, nimSymbol = ident"t", N, ElemsInReg, Output_EarlyClobber)
# MultiPurpose Register slots # MultiPurpose Register slots
scratch = init(OperandArray, nimSymbol = ident"scratch", scratchSlots, ElemsInReg, InputOutput) scratch = init(OperandArray, nimSymbol = ident"scratch", scratchSlots, ElemsInReg, InputOutput_EnsureClobber)
# MULX requires RDX # MULX requires RDX
rRDX = Operand( rRDX = Operand(
@ -270,7 +275,7 @@ macro montMul_CIOS_nocarry_adx_bmi2_gen[N: static int](r_MM: var Limbs[N], a_MM,
lo, C, rRDX lo, C, rRDX
) )
ctx.finalSub( ctx.finalSubNoCarry(
r, t, M, r, t, M,
scratch scratch
) )

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# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/macros,
# Internal
../config/common,
../primitives,
./limbs
# ############################################################
#
# Assembly implementation of finite fields
#
# ############################################################
static: doAssert UseASM_X86_32
# Necessary for the compiler to find enough registers (enabled at -O1)
{.localPassC:"-fomit-frame-pointer".}
proc finalSubNoCarry*(
ctx: var Assembler_x86,
r: Operand or OperandArray,
t, M, scratch: OperandArray
) =
## Reduce `t` into `r` modulo `M`
let N = M.len
ctx.comment "Final substraction (no carry)"
for i in 0 ..< N:
ctx.mov scratch[i], t[i]
if i == 0:
ctx.sub scratch[i], M[i]
else:
ctx.sbb scratch[i], M[i]
# If we borrowed it means that we were smaller than
# the modulus and we don't need "scratch"
for i in 0 ..< N:
ctx.cmovnc t[i], scratch[i]
ctx.mov r[i], t[i]
proc finalSubCanOverflow*(
ctx: var Assembler_x86,
r: Operand or OperandArray,
t, M, scratch: OperandArray,
overflowReg: Operand
) =
## Reduce `t` into `r` modulo `M`
## To be used when the final substraction can
## also depend on the carry flag
## This is in particular possible when the MSB
## is set for the prime modulus
## `overflowReg` should be a register that will be used
## to store the carry flag
ctx.sbb overflowReg, overflowReg
let N = M.len
ctx.comment "Final substraction (may carry)"
for i in 0 ..< N:
ctx.mov scratch[i], t[i]
if i == 0:
ctx.sub scratch[i], M[i]
else:
ctx.sbb scratch[i], M[i]
ctx.sbb overflowReg, 0
# If we borrowed it means that we were smaller than
# the modulus and we don't need "scratch"
for i in 0 ..< N:
ctx.cmovnc t[i], scratch[i]
ctx.mov r[i], t[i]
# Montgomery reduction
# ------------------------------------------------------------
macro montyRed_gen[N: static int](
r_MR: var array[N, SecretWord],
t_MR: array[N*2, SecretWord],
M_MR: array[N, SecretWord],
m0ninv_MR: BaseType,
canUseNoCarryMontyMul: static bool
) =
# TODO, slower than Clang, in particular due to the shadowing
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
# We could force M as immediate by specializing per moduli
M = init(OperandArray, nimSymbol = M_MR, N, PointerInReg, Input)
# MUL requires RAX and RDX
rRAX = Operand(
desc: OperandDesc(
asmId: "[rax]",
nimSymbol: ident"rax",
rm: RAX,
constraint: InputOutput_EnsureClobber,
cEmit: "rax"
)
)
rRDX = Operand(
desc: OperandDesc(
asmId: "[rdx]",
nimSymbol: ident"rdx",
rm: RDX,
constraint: Output_EarlyClobber,
cEmit: "rdx"
)
)
m0ninv = Operand(
desc: OperandDesc(
asmId: "[m0ninv]",
nimSymbol: m0ninv_MR,
rm: Reg,
constraint: Input,
cEmit: "m0ninv"
)
)
let scratchSlots = N+2
var scratch = init(OperandArray, nimSymbol = ident"scratch", scratchSlots, ElemsInReg, InputOutput_EnsureClobber)
# Prologue
let eax = rRAX.desc.nimSymbol
let edx = rRDX.desc.nimSymbol
let scratchSym = scratch.nimSymbol
result.add quote do:
static: doAssert: sizeof(SecretWord) == sizeof(ByteAddress)
var `eax`{.noInit.}, `edx`{.noInit.}: BaseType
var `scratchSym` {.noInit.}: Limbs[`scratchSlots`]
# Algorithm
# ---------------------------------------------------------
# for i in 0 .. n-1:
# hi <- 0
# m <- t[i] * m0ninv mod 2^w (i.e. simple multiplication)
# for j in 0 .. n-1:
# (hi, lo) <- t[i+j] + m * M[j] + hi
# t[i+j] <- lo
# t[i+n] += hi
# for i in 0 .. n-1:
# r[i] = t[i+n]
# if r >= M:
# r -= M
# No register spilling handling
doAssert N <= 6, "The Assembly-optimized montgomery multiplication requires at most 6 limbs."
result.add quote do:
`eax` = BaseType `t_MR`[0]
`scratchSym`[1 .. `N`-1] = `t_MR`.toOpenArray(1, `N`-1)
ctx.mov scratch[N], rRAX
ctx.imul rRAX, m0ninv # m <- t[i] * m0ninv mod 2^w
ctx.mov scratch[0], rRAX
# scratch: [t[0] * m0, t[1], t[2], t[3], t[0]] for 4 limbs
for i in 0 ..< N:
ctx.comment ""
let hi = scratch[N]
let next = scratch[N+1]
ctx.mul rdx, rax, M[0], rax
ctx.add hi, rRAX # Guaranteed to be zero
ctx.mov rRAX, scratch[0]
ctx.adc hi, rRDX
for j in 1 ..< N-1:
ctx.comment ""
ctx.mul rdx, rax, M[j], rax
ctx.add scratch[j], rRAX
ctx.mov rRAX, scratch[0]
ctx.adc rRDX, 0
ctx.add scratch[j], hi
ctx.adc rRDX, 0
ctx.mov hi, rRDX
# Next load
if i < N-1:
ctx.comment ""
ctx.mov next, scratch[1]
ctx.imul scratch[1], m0ninv
ctx.comment ""
# Last limb
ctx.comment ""
ctx.mul rdx, rax, M[N-1], rax
ctx.add scratch[N-1], rRAX
ctx.mov rRAX, scratch[1] # Contains next * m0
ctx.adc rRDX, 0
ctx.add scratch[N-1], hi
ctx.adc rRDX, 0
ctx.mov hi, rRDX
scratch.rotateLeft()
# Code generation
result.add ctx.generate()
# New codegen
ctx = init(Assembler_x86, BaseType)
let r = init(OperandArray, nimSymbol = r_MR, N, PointerInReg, InputOutput_EnsureClobber)
let t = init(OperandArray, nimSymbol = t_MR, N*2, PointerInReg, Input)
let extraRegNeeded = N-2
let tsub = init(OperandArray, nimSymbol = ident"tsub", extraRegNeeded, ElemsInReg, InputOutput_EnsureClobber)
let tsubsym = tsub.nimSymbol
result.add quote do:
var `tsubsym` {.noInit.}: Limbs[`extraRegNeeded`]
# This does t[i+n] += hi
# but in a separate carry chain, fused with the
# copy "r[i] = t[i+n]"
for i in 0 ..< N:
if i == 0:
ctx.add scratch[i], t[i+N]
else:
ctx.adc scratch[i], t[i+N]
let reuse = repackRegisters(tsub, scratch[N], scratch[N+1])
if canUseNoCarryMontyMul:
ctx.finalSubNoCarry(r, scratch, M, reuse)
else:
ctx.finalSubCanOverflow(r, scratch, M, reuse, rRAX)
# Code generation
result.add ctx.generate()
func montRed_asm*[N: static int](
r: var array[N, SecretWord],
t: array[N*2, SecretWord],
M: array[N, SecretWord],
m0ninv: BaseType,
canUseNoCarryMontyMul: static bool
) =
## Constant-time Montgomery reduction
montyRed_gen(r, t, M, m0ninv, canUseNoCarryMontyMul)

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# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/macros,
# Internal
../config/common,
../primitives,
./limbs,
./limbs_asm_montred_x86
# ############################################################
#
# Assembly implementation of finite fields
#
# ############################################################
# TODO, MCL has an implementation about 14% faster
static: doAssert UseASM_X86_64
# MULX/ADCX/ADOX
{.localPassC:"-madx -mbmi2".}
# Necessary for the compiler to find enough registers (enabled at -O1)
{.localPassC:"-fomit-frame-pointer".}
# Montgomery reduction
# ------------------------------------------------------------
macro montyRedx_gen[N: static int](
r_MR: var array[N, SecretWord],
t_MR: array[N*2, SecretWord],
M_MR: array[N, SecretWord],
m0ninv_MR: BaseType,
canUseNoCarryMontyMul: static bool
) =
# TODO, slower than Clang, in particular due to the shadowing
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
# We could force M as immediate by specializing per moduli
M = init(OperandArray, nimSymbol = M_MR, N, PointerInReg, Input)
hi = Operand(
desc: OperandDesc(
asmId: "[hi]",
nimSymbol: ident"hi",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "hi"
)
)
lo = Operand(
desc: OperandDesc(
asmId: "[lo]",
nimSymbol: ident"lo",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "lo"
)
)
rRDX = Operand(
desc: OperandDesc(
asmId: "[rdx]",
nimSymbol: ident"rdx",
rm: RDX,
constraint: InputOutput_EnsureClobber,
cEmit: "rdx"
)
)
m0ninv = Operand(
desc: OperandDesc(
asmId: "[m0ninv]",
nimSymbol: m0ninv_MR,
rm: Reg,
constraint: Input,
cEmit: "m0ninv"
)
)
let scratchSlots = N+1
var scratch = init(OperandArray, nimSymbol = ident"scratch", scratchSlots, ElemsInReg, InputOutput_EnsureClobber)
# Prologue
let edx = rRDX.desc.nimSymbol
let hisym = hi.desc.nimSymbol
let losym = lo.desc.nimSymbol
let scratchSym = scratch.nimSymbol
result.add quote do:
static: doAssert: sizeof(SecretWord) == sizeof(ByteAddress)
var `hisym`{.noInit.}, `losym`{.noInit.}, `edx`{.noInit.}: BaseType
var `scratchSym` {.noInit.}: Limbs[`scratchSlots`]
# Algorithm
# ---------------------------------------------------------
# for i in 0 .. n-1:
# hi <- 0
# m <- t[i] * m0ninv mod 2^w (i.e. simple multiplication)
# for j in 0 .. n-1:
# (hi, lo) <- t[i+j] + m * M[j] + hi
# t[i+j] <- lo
# t[i+n] += hi
# for i in 0 .. n-1:
# r[i] = t[i+n]
# if r >= M:
# r -= M
# No register spilling handling
doAssert N <= 6, "The Assembly-optimized montgomery multiplication requires at most 6 limbs."
result.add quote do:
`edx` = BaseType(`m0ninv_MR`)
`scratchSym`[0 .. `N`-1] = `t_MR`.toOpenArray(0, `N`-1)
for i in 0 ..< N:
# RDX contains m0ninv at the start of each loop
ctx.comment ""
ctx.imul rRDX, scratch[0] # m <- t[i] * m0ninv mod 2^w
ctx.comment "---- Reduction " & $i
ctx.`xor` scratch[N], scratch[N]
for j in 0 ..< N-1:
ctx.comment ""
ctx.mulx hi, lo, M[j], rdx
ctx.adcx scratch[j], lo
ctx.adox scratch[j+1], hi
# Last limb
ctx.comment ""
ctx.mulx hi, lo, M[N-1], rdx
ctx.mov rRDX, m0ninv # Reload m0ninv for next iter
ctx.adcx scratch[N-1], lo
ctx.adox hi, scratch[N]
ctx.adcx scratch[N], hi
scratch.rotateLeft()
# Code generation
result.add ctx.generate()
# New codegen
ctx = init(Assembler_x86, BaseType)
let r = init(OperandArray, nimSymbol = r_MR, N, PointerInReg, InputOutput_EnsureClobber)
let t = init(OperandArray, nimSymbol = t_MR, N*2, PointerInReg, Input)
let extraRegNeeded = N-1
let tsub = init(OperandArray, nimSymbol = ident"tsub", extraRegNeeded, ElemsInReg, InputOutput_EnsureClobber)
let tsubsym = tsub.nimSymbol
result.add quote do:
var `tsubsym` {.noInit.}: Limbs[`extraRegNeeded`]
# This does t[i+n] += hi
# but in a separate carry chain, fused with the
# copy "r[i] = t[i+n]"
for i in 0 ..< N:
if i == 0:
ctx.add scratch[i], t[i+N]
else:
ctx.adc scratch[i], t[i+N]
let reuse = repackRegisters(tsub, scratch[N])
if canUseNoCarryMontyMul:
ctx.finalSubNoCarry(r, scratch, M, reuse)
else:
ctx.finalSubCanOverflow(r, scratch, M, reuse, hi)
# Code generation
result.add ctx.generate()
func montRed_asm_adx_bmi2*[N: static int](
r: var array[N, SecretWord],
t: array[N*2, SecretWord],
M: array[N, SecretWord],
m0ninv: BaseType,
canUseNoCarryMontyMul: static bool
) =
## Constant-time Montgomery reduction
montyRedx_gen(r, t, M, m0ninv, canUseNoCarryMontyMul)

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# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/macros,
# Internal
../config/common,
../primitives
# ############################################################
#
# Assembly implementation of bigint multiplication
#
# ############################################################
# Note: We can refer to at most 30 registers in inline assembly
# and "InputOutput" registers count double
# They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves.
# TODO: verify that assembly generated works for small arrays
# that are passed by values
static: doAssert UseASM_X86_64 # Need 8 registers just for mul
# and 32-bit only has 8 max.
macro mul_gen[rLen, aLen, bLen: static int](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
## Comba multiplication generator
## `a`, `b`, `r` can have a different number of limbs
## if `r`.limbs.len < a.limbs.len + b.limbs.len
## The result will be truncated, i.e. it will be
## a * b (mod (2^WordBitwidth)^r.limbs.len)
##
## Assumes r doesn't aliases a or b
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
arrR = init(OperandArray, nimSymbol = r, rLen, PointerInReg, InputOutput_EnsureClobber)
arrA = init(OperandArray, nimSymbol = a, aLen, PointerInReg, Input)
arrB = init(OperandArray, nimSymbol = b, bLen, PointerInReg, Input)
t = Operand(
desc: OperandDesc(
asmId: "[t]",
nimSymbol: ident"t",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t"
)
)
u = Operand(
desc: OperandDesc(
asmId: "[u]",
nimSymbol: ident"u",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "u"
)
)
v = Operand(
desc: OperandDesc(
asmId: "[v]",
nimSymbol: ident"v",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "v"
)
)
# MUL requires RAX and RDX
rRAX = Operand(
desc: OperandDesc(
asmId: "[rax]",
nimSymbol: ident"rax",
rm: RAX,
constraint: Output_EarlyClobber,
cEmit: "rax"
)
)
rRDX = Operand(
desc: OperandDesc(
asmId: "[rdx]",
nimSymbol: ident"rdx",
rm: RDX,
constraint: Output_EarlyClobber,
cEmit: "rdx"
)
)
# Prologue
let tsym = t.desc.nimSymbol
let usym = u.desc.nimSymbol
let vsym = v.desc.nimSymbol
let eax = rRAX.desc.nimSymbol
let edx = rRDX.desc.nimSymbol
result.add quote do:
var `tsym`{.noInit.}, `usym`{.noInit.}, `vsym`{.noInit.}: BaseType # zero-init
var `eax`{.noInit.}, `edx`{.noInit.}: BaseType
# Algorithm
ctx.`xor` u, u
ctx.`xor` v, v
ctx.`xor` t, t
for i in 0 ..< min(aLen+bLen, rLen):
let ib = min(bLen-1, i)
let ia = i - ib
for j in 0 ..< min(aLen - ia, ib+1):
# (t, u, v) <- (t, u, v) + a[ia+j] * b[ib-j]
ctx.mov rRAX, arrB[ib-j]
ctx.mul rdx, rax, arrA[ia+j], rax
ctx.add v, rRAX
ctx.adc u, rRDX
ctx.adc t, 0
ctx.mov arrR[i], v
if i != min(aLen+bLen, rLen) - 1:
ctx.mov v, u
ctx.mov u, t
ctx.`xor` t, t
if aLen+bLen < rLen:
ctx.`xor` rRAX, rRAX
for i in aLen+bLen ..< rLen:
ctx.mov arrR[i], rRAX
# Codegen
result.add ctx.generate
func mul_asm*[rLen, aLen, bLen: static int](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
## Multi-precision Multiplication
## Assumes r doesn't alias a or b
mul_gen(r, a, b)

197
constantine/arithmetic/limbs_asm_mul_x86_adx_bmi2.nim Normal file
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@ -0,0 +1,197 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/macros,
# Internal
../config/common,
../primitives
# ############################################################
#
# Assembly implementation of finite fields
#
# ############################################################
# Note: We can refer to at most 30 registers in inline assembly
# and "InputOutput" registers count double
# They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves.
static: doAssert UseASM_X86_64
# MULX/ADCX/ADOX
{.localPassC:"-madx -mbmi2".}
# Necessary for the compiler to find enough registers (enabled at -O1)
# {.localPassC:"-fomit-frame-pointer".}
# Multiplication
# ------------------------------------------------------------
proc mulx_by_word(
ctx: var Assembler_x86,
r0: Operand,
a, t: OperandArray,
word0: Operand,
rRAX, rRDX: Operand
) =
## Multiply the `a[0..<N]` by `word`
## and store in `[t:r0]`
## with [t:r0] = tn, tn-1, ... t1, r0
doAssert a.len + 1 == t.len
let N = a.len
ctx.comment " Outer loop i = 0, j=0 to " & $N
# for j=0 to N-1
# (C,t[j]) := t[j] + a[j]*b[i] + C
# First limb
ctx.mov rRDX, word0
ctx.`xor` rRAX, rRAX # Clear flags (important if steady state is skipped)
ctx.mulx t[0], rRAX, a[0], rdx
ctx.mov r0, rRAX
# Steady state
for j in 1 ..< N:
ctx.mulx t[j], rRAX, a[j], rdx
if j == 1:
ctx.add t[j-1], rRAX
else:
ctx.adc t[j-1], rRAX
# Final carries
ctx.comment " Accumulate last carries in hi word"
ctx.adc t[N-1], 0
proc mulaccx_by_word(
ctx: var Assembler_x86,
r: OperandArray,
i: int,
a, t: OperandArray,
word: Operand,
rRAX, rRDX: Operand
) =
## Multiply the `a[0..<N]` by `word`
## and store in `[t:r0]`
## with [t:r0] = tn, tn-1, ... t1, r0
doAssert a.len + 1 == t.len
let N = min(a.len, r.len)
let hi = t[a.len]
doAssert i != 0
ctx.comment " Outer loop i = " & $i & ", j in [0, " & $N & ")"
ctx.mov rRDX, word
ctx.`xor` rRAX, rRAX # Clear flags
# for j=0 to N-1
# (C,t[j]) := t[j] + a[j]*b[i] + C
# Steady state
for j in 0 ..< N:
ctx.mulx hi, rRAX, a[j], rdx
ctx.adox t[j], rRAX
if j == 0:
ctx.mov r[i], t[j]
if j == N-1:
break
ctx.adcx t[j+1], hi
# Final carries
ctx.comment " Accumulate last carries in hi word"
ctx.mov rRDX, 0 # Set to 0 without clearing flags
ctx.adcx hi, rRDX
ctx.adox hi, rRDX
macro mulx_gen[rLen, aLen, bLen: static int](rx: var Limbs[rLen], ax: Limbs[aLen], bx: Limbs[bLen]) =
## `a`, `b`, `r` can have a different number of limbs
## if `r`.limbs.len < a.limbs.len + b.limbs.len
## The result will be truncated, i.e. it will be
## a * b (mod (2^WordBitwidth)^r.limbs.len)
##
## Assumes r doesn't aliases a or b
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
r = init(OperandArray, nimSymbol = rx, rLen, PointerInReg, InputOutput_EnsureClobber)
a = init(OperandArray, nimSymbol = ax, aLen, PointerInReg, Input)
b = init(OperandArray, nimSymbol = bx, bLen, PointerInReg, Input)
# MULX requires RDX
rRDX = Operand(
desc: OperandDesc(
asmId: "[rdx]",
nimSymbol: ident"rdx",
rm: RDX,
constraint: Output_EarlyClobber,
cEmit: "rdx"
)
)
rRAX = Operand(
desc: OperandDesc(
asmId: "[rax]",
nimSymbol: ident"rax",
rm: RAX,
constraint: Output_EarlyClobber,
cEmit: "rax"
)
)
tSlots = aLen+1 # Extra for high word
var # If aLen is too big, we need to spill registers. TODO.
t = init(OperandArray, nimSymbol = ident"t", tSlots, ElemsInReg, Output_EarlyClobber)
# Prologue
let tsym = t.nimSymbol
let eax = rRAX.desc.nimSymbol
let edx = rRDX.desc.nimSymbol
result.add quote do:
var `tsym`{.noInit.}: array[`tSlots`, BaseType]
var `edx`{.noInit.}, `eax`{.noInit.}: BaseType
for i in 0 ..< min(rLen, bLen):
if i == 0:
ctx.mulx_by_word(
r[0],
a, t,
b[0],
rRAX, rRDX,
)
else:
ctx.mulaccx_by_word(
r, i,
a, t,
b[i],
rRAX, rRDX
)
t.rotateLeft()
# Copy upper-limbs to result
for i in b.len ..< min(a.len+b.len, rLen):
ctx.mov r[i], t[i-b.len]
# Zero the extra
if aLen+bLen < rLen:
ctx.`xor` rRAX, rRAX
for i in aLen+bLen ..< rLen:
ctx.mov r[i], rRAX
# Codegen
result.add ctx.generate
func mul_asm_adx_bmi2*[rLen, aLen, bLen: static int](r: var Limbs[rLen], a: Limbs[aLen], b: Limbs[bLen]) =
## Multi-precision Multiplication
## Assumes r doesn't alias a or b
mulx_gen(r, a, b)

168
constantine/arithmetic/limbs_asm_x86.nim
View File

@ -11,8 +11,7 @@ import
std/macros, std/macros,
# Internal # Internal
../config/common, ../config/common,
../primitives, ../primitives
./limbs_generic
# ############################################################ # ############################################################
# #
@ -25,9 +24,10 @@ import
# They are nice to let the compiler deals with mov # They are nice to let the compiler deals with mov
# but too constraining so we move things ourselves. # but too constraining so we move things ourselves.
static: doAssert UseX86ASM # TODO: verify that assembly generated works for small arrays
# that are passed by values
{.localPassC:"-fomit-frame-pointer".} # Needed so that the compiler finds enough registers static: doAssert UseASM_X86_32
# Copy # Copy
# ------------------------------------------------------------ # ------------------------------------------------------------
@ -40,8 +40,6 @@ macro ccopy_gen[N: static int](a: var Limbs[N], b: Limbs[N], ctl: SecretBool): u
let let
arrA = init(OperandArray, nimSymbol = a, N, PointerInReg, InputOutput) arrA = init(OperandArray, nimSymbol = a, N, PointerInReg, InputOutput)
arrB = init(OperandArray, nimSymbol = b, N, PointerInReg, Input) arrB = init(OperandArray, nimSymbol = b, N, PointerInReg, Input)
# If N is too big, we need to spill registers. TODO.
arrT = init(OperandArray, nimSymbol = ident"t", N, ElemsInReg, Output_EarlyClobber)
control = Operand( control = Operand(
desc: OperandDesc( desc: OperandDesc(
@ -53,16 +51,42 @@ macro ccopy_gen[N: static int](a: var Limbs[N], b: Limbs[N], ctl: SecretBool): u
) )
) )
var # Swappable registers to break dependency chains
t0 = Operand(
desc: OperandDesc(
asmId: "[t0]",
nimSymbol: ident"t0",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t0"
)
)
t1 = Operand(
desc: OperandDesc(
asmId: "[t1]",
nimSymbol: ident"t1",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t1"
)
)
# Prologue
let t0sym = t0.desc.nimSymbol
let t1sym = t1.desc.nimSymbol
result.add quote do:
var `t0sym`{.noinit.}, `t1sym`{.noinit.}: BaseType
# Algorithm
ctx.test control, control ctx.test control, control
for i in 0 ..< N: for i in 0 ..< N:
ctx.mov arrT[i], arrA[i] ctx.mov t0, arrA[i]
ctx.cmovnz arrT[i], arrB[i] ctx.cmovnz t0, arrB[i]
ctx.mov arrA[i], arrT[i] ctx.mov arrA[i], t0
swap(t0, t1)
let t = arrT.nimSymbol # Codegen
let c = control.desc.nimSymbol
result.add quote do:
var `t` {.noInit.}: typeof(`a`)
result.add ctx.generate() result.add ctx.generate()
func ccopy_asm*(a: var Limbs, b: Limbs, ctl: SecretBool) {.inline.}= func ccopy_asm*(a: var Limbs, b: Limbs, ctl: SecretBool) {.inline.}=
@ -71,3 +95,121 @@ func ccopy_asm*(a: var Limbs, b: Limbs, ctl: SecretBool) {.inline.}=
## if ctl is false: b is not copied and a is untouched ## if ctl is false: b is not copied and a is untouched
## Time and memory accesses are the same whether a copy occurs or not ## Time and memory accesses are the same whether a copy occurs or not
ccopy_gen(a, b, ctl) ccopy_gen(a, b, ctl)
# Addition
# ------------------------------------------------------------
macro add_gen[N: static int](carry: var Carry, r: var Limbs[N], a, b: Limbs[N]): untyped =
## Generate an optimized out-of-place addition kernel
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
arrR = init(OperandArray, nimSymbol = r, N, PointerInReg, InputOutput)
arrA = init(OperandArray, nimSymbol = a, N, PointerInReg, Input)
arrB = init(OperandArray, nimSymbol = b, N, PointerInReg, Input)
var # Swappable registers to break dependency chains
t0 = Operand(
desc: OperandDesc(
asmId: "[t0]",
nimSymbol: ident"t0",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t0"
)
)
t1 = Operand(
desc: OperandDesc(
asmId: "[t1]",
nimSymbol: ident"t1",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t1"
)
)
# Prologue
let t0sym = t0.desc.nimSymbol
let t1sym = t1.desc.nimSymbol
result.add quote do:
var `t0sym`{.noinit.}, `t1sym`{.noinit.}: BaseType
# Algorithm
for i in 0 ..< N:
ctx.mov t0, arrA[i]
if i == 0:
ctx.add t0, arrB[0]
else:
ctx.adc t0, arrB[i]
ctx.mov arrR[i], t0
swap(t0, t1)
ctx.setToCarryFlag(carry)
# Codegen
result.add ctx.generate
func add_asm*(r: var Limbs, a, b: Limbs): Carry {.inline.}=
## Constant-time addition
add_gen(result, r, a, b)
# Substraction
# ------------------------------------------------------------
macro sub_gen[N: static int](borrow: var Borrow, r: var Limbs[N], a, b: Limbs[N]): untyped =
## Generate an optimized out-of-place substraction kernel
result = newStmtList()
var ctx = init(Assembler_x86, BaseType)
let
arrR = init(OperandArray, nimSymbol = r, N, PointerInReg, InputOutput)
arrA = init(OperandArray, nimSymbol = a, N, PointerInReg, Input)
arrB = init(OperandArray, nimSymbol = b, N, PointerInReg, Input)
var # Swappable registers to break dependency chains
t0 = Operand(
desc: OperandDesc(
asmId: "[t0]",
nimSymbol: ident"t0",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t0"
)
)
t1 = Operand(
desc: OperandDesc(
asmId: "[t1]",
nimSymbol: ident"t1",
rm: Reg,
constraint: Output_EarlyClobber,
cEmit: "t1"
)
)
# Prologue
let t0sym = t0.desc.nimSymbol
let t1sym = t1.desc.nimSymbol
result.add quote do:
var `t0sym`{.noinit.}, `t1sym`{.noinit.}: BaseType
# Algorithm
for i in 0 ..< N:
ctx.mov t0, arrA[i]
if i == 0:
ctx.sub t0, arrB[0]
else:
ctx.sbb t0, arrB[i]
ctx.mov arrR[i], t0
swap(t0, t1)
ctx.setToCarryFlag(borrow)
# Codegen
result.add ctx.generate
func sub_asm*(r: var Limbs, a, b: Limbs): Borrow {.inline.}=
## Constant-time substraction
sub_gen(result, r, a, b)

101
constantine/arithmetic/limbs_double_width.nim Normal file
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@ -0,0 +1,101 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
../config/common,
../primitives,
./limbs
when UseASM_X86_32:
import ./limbs_asm_montred_x86
when UseASM_X86_64:
import ./limbs_asm_montred_x86_adx_bmi2
# ############################################################
#
# Limbs raw representation and operations
#
# ############################################################
# No exceptions allowed
{.push raises: [].}
# Montgomery Reduction
# ------------------------------------------------------------
# This is the reduction part of SOS (Separated Operand Scanning) modular multiplication technique
# TODO upstream, using Limbs[N] breaks semcheck
func montyRed*[N: static int](
r: var array[N, SecretWord],
t: array[N*2, SecretWord],
M: array[N, SecretWord],
m0ninv: BaseType, canUseNoCarryMontyMul: static bool) =
## Montgomery reduce a double-width bigint modulo M
# - Analyzing and Comparing Montgomery Multiplication Algorithms
# Cetin Kaya Koc and Tolga Acar and Burton S. Kaliski Jr.
# http://pdfs.semanticscholar.org/5e39/41ff482ec3ee41dc53c3298f0be085c69483.pdf
#
# - Arithmetic of Finite Fields
# Chapter 5 of Guide to Pairing-Based Cryptography
# Jean Luc Beuchat, Luis J. Dominguez Perez, Sylvain Duquesne, Nadia El Mrabet, Laura Fuentes-Castañeda, Francisco Rodríguez-Henríquez, 2017
# https://www.researchgate.net/publication/319538235_Arithmetic_of_Finite_Fields
#
# Algorithm
# Inputs:
# - N number of limbs
# - t[0 ..< 2N] (double-width input to reduce)
# - M[0 ..< N] The field modulus (must be odd for Montgomery reduction)
# - m0ninv: Montgomery Reduction magic number = -1/M[0]
# Output:
# - r[0 ..< N], in the Montgomery domain
# Parameters:
# - w, the word width usually 64 on 64-bit platforms or 32 on 32-bit
#
# for i in 0 .. n-1:
# C <- 0
# m <- t[i] * m0ninv mod 2^w (i.e. simple multiplication)
# for j in 0 .. n-1:
# (C, S) <- t[i+j] + m * M[j] + C
# t[i+j] <- S
# t[i+n] += C
# for i in 0 .. n-1:
# r[i] = t[i+n]
# if r >= M:
# r -= M
#
# Important note: `t[i+n] += C` should propagate the carry
# to the higher limb if any, thank you "implementation detail"
# missing from paper.
when UseASM_X86_64 and r.len <= 6:
if ({.noSideEffect.}: hasBmi2()) and ({.noSideEffect.}: hasAdx()):
montRed_asm_adx_bmi2(r, t, M, m0ninv, canUseNoCarryMontyMul)
else:
montRed_asm(r, t, M, m0ninv, canUseNoCarryMontyMul)
elif UseASM_X86_32 and r.len <= 6:
# TODO: Assembly faster than GCC but slower than Clang
montRed_asm(r, t, M, m0ninv, canUseNoCarryMontyMul)
else:
var t = t # Copy "t" for mutation and ensure on stack
var res: typeof(r) # Accumulator
staticFor i, 0, N:
var C = Zero
let m = t[i] * SecretWord(m0ninv)
staticFor j, 0, N:
muladd2(C, t[i+j], m, M[j], t[i+j], C)
res[i] = C
# This does t[i+n] += C
# but in a separate carry chain, fused with the
# copy "r[i] = t[i+n]"
var carry = Carry(0)
staticFor i, 0, N:
addC(carry, res[i], t[i+N], res[i], carry)
# Final substraction
discard res.csub(M, SecretWord(carry).isNonZero() or not(res < M))
r = res

2
constantine/arithmetic/limbs_generic_modular.nim
View File

@ -9,7 +9,7 @@
import import
../config/common, ../config/common,
../primitives, ../primitives,
./limbs_generic ./limbs
# No exceptions allowed # No exceptions allowed
{.push raises: [].} {.push raises: [].}

56
constantine/arithmetic/limbs_montgomery.nim
View File

@ -12,9 +12,9 @@ import
# Internal # Internal
../config/common, ../config/common,
../primitives, ../primitives,
./limbs_generic ./limbs
when UseX86ASM: when UseASM_X86_64:
import import
./limbs_asm_montmul_x86, ./limbs_asm_montmul_x86,
./limbs_asm_montmul_x86_adx_bmi2 ./limbs_asm_montmul_x86_adx_bmi2
@ -37,55 +37,7 @@ when UseX86ASM:
# - pairing final exponentiation # - pairing final exponentiation
# are bottlenecked by Montgomery multiplications or squarings # are bottlenecked by Montgomery multiplications or squarings
# #
# Unfortunately, the fastest implementation of Montgomery Multiplication # Hence we use inline assembly where possible
# on x86 is impossible without resorting to assembly (probably 15~30% faster)
#
# It requires implementing 2 parallel pipelines of carry-chains (via instruction-level parallelism)
# of MULX, ADCX and ADOX instructions, according to Intel paper:
# https://www.intel.cn/content/dam/www/public/us/en/documents/white-papers/ia-large-integer-arithmetic-paper.pdf
# and the code generation of MCL
# https://github.com/herumi/mcl
#
# A generic implementation would require implementing a mini-compiler as macro
# significantly sacrificing code readability, portability, auditability and maintainability.
#
# This would however save significant hardware or cloud resources.
# An example inline assembly compiler for add-with-carry is available in
# primitives/research/addcarry_subborrow_compiler.nim
#
# Instead we follow the optimized high-level implementation of Goff
# which skips a significant amount of additions for moduli
# that have their the most significant bit unset.
# Loop unroller
# ------------------------------------------------------------
proc replaceNodes(ast: NimNode, what: NimNode, by: NimNode): NimNode =
# Replace "what" ident node by "by"
proc inspect(node: NimNode): NimNode =
case node.kind:
of {nnkIdent, nnkSym}:
if node.eqIdent(what):
return by
return node
of nnkEmpty:
return node
of nnkLiterals:
return node
else:
var rTree = node.kind.newTree()
for child in node:
rTree.add inspect(child)
return rTree
result = inspect(ast)
macro staticFor(idx: untyped{nkIdent}, start, stopEx: static int, body: untyped): untyped =
result = newStmtList()
for i in start ..< stopEx:
result.add nnkBlockStmt.newTree(
ident("unrolledIter_" & $idx & $i),
body.replaceNodes(idx, newLit i)
)
# No exceptions allowed # No exceptions allowed
{.push raises: [].} {.push raises: [].}
@ -348,7 +300,7 @@ func montyMul*(
# - specialize/duplicate code for m0ninv == 1 (especially if only 1 curve is needed) # - specialize/duplicate code for m0ninv == 1 (especially if only 1 curve is needed)
# - keep it generic and optimize code size # - keep it generic and optimize code size
when canUseNoCarryMontyMul: when canUseNoCarryMontyMul:
when UseX86ASM and a.len in {2 .. 6}: # TODO: handle spilling when UseASM_X86_64 and a.len in {2 .. 6}: # TODO: handle spilling
if ({.noSideEffect.}: hasBmi2()) and ({.noSideEffect.}: hasAdx()): if ({.noSideEffect.}: hasBmi2()) and ({.noSideEffect.}: hasAdx()):
montMul_CIOS_nocarry_asm_adx_bmi2(r, a, b, M, m0ninv) montMul_CIOS_nocarry_asm_adx_bmi2(r, a, b, M, m0ninv)
else: else:

11
constantine/config/common.nim
View File

@ -30,6 +30,14 @@ type
SecretBool* = CTBool[SecretWord] SecretBool* = CTBool[SecretWord]
Limbs*[N: static int] = array[N, SecretWord]
## Limbs-type
## Should be distinct type to avoid builtins to use non-constant time
## implementation, for example for comparison.
##
## but for unknown reason, it prevents semchecking `bits`
const const
WordBitWidth* = sizeof(SecretWord) * 8 WordBitWidth* = sizeof(SecretWord) * 8
## Logical word size ## Logical word size
@ -44,7 +52,8 @@ const
# TODO, we restrict assembly to 64-bit words # TODO, we restrict assembly to 64-bit words
# We need to support register spills for large limbs # We need to support register spills for large limbs
const ConstantineASM {.booldefine.} = true const ConstantineASM {.booldefine.} = true
const UseX86ASM* = WordBitWidth == 64 and ConstantineASM and X86 and GCC_Compatible const UseASM_X86_32* = ConstantineASM and X86 and GCC_Compatible
const UseASM_X86_64* = WordBitWidth == 64 and UseASM_X86_32
# ############################################################ # ############################################################
# #

12
constantine/config/curves.nim
View File

@ -27,15 +27,19 @@ macro Mod*(C: static Curve): untyped =
## Get the Modulus associated to a curve ## Get the Modulus associated to a curve
result = bindSym($C & "_Modulus") result = bindSym($C & "_Modulus")
func getCurveBitwidth*(C: static Curve): static int = template getCurveBitwidth*(C: Curve): int =
## Returns the number of bits taken by the curve modulus ## Returns the number of bits taken by the curve modulus
result = static(CurveBitWidth[C]) CurveBitWidth[C]
template matchingBigInt*(C: static Curve): untyped = template matchingBigInt*(C: static Curve): untyped =
BigInt[CurveBitWidth[C]] BigInt[CurveBitWidth[C]]
func family*(C: static Curve): CurveFamily = template family*(C: Curve): CurveFamily =
result = static(CurveFamilies[C]) CurveFamilies[C]
template matchingLimbs2x*(C: Curve): untyped =
const N2 = wordsRequired(getCurveBitwidth(C)) * 2 # TODO upstream, not precomputing N2 breaks semcheck
array[N2, SecretWord] # TODO upstream, using Limbs[N2] breaks semcheck
# ############################################################ # ############################################################
# #

2
constantine/config/type_bigint.nim
View File

@ -31,8 +31,6 @@ type
debug: debug:
import std/strutils import std/strutils
type Limbs[N: static int] = array[N, SecretWord]
func toString*(a: Limbs): string = func toString*(a: Limbs): string =
result = "[" result = "["
result.add " 0x" & toHex(BaseType(a[0])) result.add " 0x" & toHex(BaseType(a[0]))

1
constantine/elliptic/ec_endomorphism_accel.nim
View File

@ -10,7 +10,6 @@ import
# Standard Library # Standard Library
std/typetraits, std/typetraits,
# Internal # Internal
../../helpers/static_for,
../primitives, ../primitives,
../config/[common, curves, type_bigint], ../config/[common, curves, type_bigint],
../arithmetic, ../arithmetic,

1
constantine/elliptic/ec_endomorphism_params.nim
View File

@ -8,7 +8,6 @@
import import
# Internal # Internal
../../helpers/static_for,
../primitives, ../primitives,
../config/[common, curves, type_bigint], ../config/[common, curves, type_bigint],
../arithmetic, ../arithmetic,

4
constantine/elliptic/ec_weierstrass_projective.nim
View File

@ -190,7 +190,7 @@ func sum*[F](
r.y.sum(Q.x, Q.z) # 15. Y3 <- X2 + Z2 r.y.sum(Q.x, Q.z) # 15. Y3 <- X2 + Z2
r.x *= r.y # 16. X3 <- X3 Y3 X3 = (X1 Z1)(X2 Z2) r.x *= r.y # 16. X3 <- X3 Y3 X3 = (X1 Z1)(X2 Z2)
r.y.sum(t0, t2) # 17. Y3 <- t0 + t2 Y3 = X1 X2 + Z1 Z2 r.y.sum(t0, t2) # 17. Y3 <- t0 + t2 Y3 = X1 X2 + Z1 Z2
r.y.diff(r.x, r.y) # 18. Y3 <- X3 - Y3 Y3 = (X1 + Z1)(X2 + Z2) - (X1 X2 + Z1 Z2) = X1 Z2 + X2 Z1 r.y.diffAlias(r.x, r.y) # 18. Y3 <- X3 - Y3 Y3 = (X1 + Z1)(X2 + Z2) - (X1 X2 + Z1 Z2) = X1 Z2 + X2 Z1
when F is Fp2 and F.C.getSexticTwist() == D_Twist: when F is Fp2 and F.C.getSexticTwist() == D_Twist:
t0 *= SexticNonResidue t0 *= SexticNonResidue
t1 *= SexticNonResidue t1 *= SexticNonResidue
@ -206,7 +206,7 @@ func sum*[F](
r.y *= SexticNonResidue r.y *= SexticNonResidue
r.x.prod(t4, r.y) # 25. X3 <- t4 Y3 X3 = 3b(Y1 Z2 + Y2 Z1)(X1 Z2 + X2 Z1) r.x.prod(t4, r.y) # 25. X3 <- t4 Y3 X3 = 3b(Y1 Z2 + Y2 Z1)(X1 Z2 + X2 Z1)
t2.prod(t3, t1) # 26. t2 <- t3 t1 t2 = (X1 Y2 + X2 Y1) (Y1 Y2 - 3b Z1 Z2) t2.prod(t3, t1) # 26. t2 <- t3 t1 t2 = (X1 Y2 + X2 Y1) (Y1 Y2 - 3b Z1 Z2)
r.x.diff(t2, r.x) # 27. X3 <- t2 - X3 X3 = (X1 Y2 + X2 Y1) (Y1 Y2 - 3b Z1 Z2) - 3b(Y1 Z2 + Y2 Z1)(X1 Z2 + X2 Z1) r.x.diffAlias(t2, r.x) # 27. X3 <- t2 - X3 X3 = (X1 Y2 + X2 Y1) (Y1 Y2 - 3b Z1 Z2) - 3b(Y1 Z2 + Y2 Z1)(X1 Z2 + X2 Z1)
r.y *= t0 # 28. Y3 <- Y3 t0 Y3 = 9b X1 X2 (X1 Z2 + X2 Z1) r.y *= t0 # 28. Y3 <- Y3 t0 Y3 = 9b X1 X2 (X1 Z2 + X2 Z1)
t1 *= r.z # 29. t1 <- t1 Z3 t1 = (Y1 Y2 - 3b Z1 Z2)(Y1 Y2 + 3b Z1 Z2) t1 *= r.z # 29. t1 <- t1 Z3 t1 = (Y1 Y2 - 3b Z1 Z2)(Y1 Y2 + 3b Z1 Z2)
r.y += t1 # 30. Y3 <- t1 + Y3 Y3 = (Y1 Y2 + 3b Z1 Z2)(Y1 Y2 - 3b Z1 Z2) + 9b X1 X2 (X1 Z2 + X2 Z1) r.y += t1 # 30. Y3 <- t1 + Y3 Y3 = (Y1 Y2 + 3b Z1 Z2)(Y1 Y2 - 3b Z1 Z2) + 9b X1 X2 (X1 Z2 + X2 Z1)

6
constantine/primitives.nim
View File

@ -12,7 +12,8 @@ import
primitives/multiplexers, primitives/multiplexers,
primitives/addcarry_subborrow, primitives/addcarry_subborrow,
primitives/extended_precision, primitives/extended_precision,
primitives/bithacks primitives/bithacks,
primitives/static_for
export export
constant_time_types, constant_time_types,
@ -20,7 +21,8 @@ export
multiplexers, multiplexers,
addcarry_subborrow, addcarry_subborrow,
extended_precision, extended_precision,
bithacks bithacks,
staticFor
when X86 and GCC_Compatible: when X86 and GCC_Compatible:
import primitives/[cpuinfo_x86, macro_assembler_x86] import primitives/[cpuinfo_x86, macro_assembler_x86]

42
constantine/primitives/macro_assembler_x86.nim
View File

@ -6,7 +6,7 @@
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). # * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms. # at your option. This file may not be copied, modified, or distributed except according to those terms.
import std/[macros, strutils, sets, hashes] import std/[macros, strutils, sets, hashes, algorithm]
# A compile-time inline assembler # A compile-time inline assembler
@ -33,6 +33,9 @@ type
RAX = "a" RAX = "a"
# Flags
CarryFlag = "@ccc"
Register* = enum Register* = enum
rbx, rdx, r8, rax rbx, rdx, r8, rax
@ -98,6 +101,12 @@ func hash(od: OperandDesc): Hash =
func len*(opArray: OperandArray): int = func len*(opArray: OperandArray): int =
opArray.buf.len opArray.buf.len
func len*(opArray: Operand): int =
opArray.buf.len
func rotateLeft*(opArray: var OperandArray) =
opArray.buf.rotateLeft(1)
proc `[]`*(opArray: OperandArray, index: int): Operand = proc `[]`*(opArray: OperandArray, index: int): Operand =
opArray.buf[index] opArray.buf[index]
@ -181,6 +190,25 @@ func asArrayAddr*(op: Operand, len: int): Operand =
# Code generation # Code generation
# ------------------------------------------------------------------------------------------------------------ # ------------------------------------------------------------------------------------------------------------
func setToCarryFlag*(a: var Assembler_x86, carry: NimNode) =
# We need to dereference the hidden pointer of var param
let isHiddenDeref = carry.kind == nnkHiddenDeref
let nimSymbol = if isHiddenDeref: carry[0]
else: carry
{.noSideEffect.}:
let symStr = $nimSymbol
let desc = OperandDesc(
asmId: "",
nimSymbol: ident(symStr),
rm: CarryFlag,
constraint: Output_Overwrite,
cEmit: symStr
)
a.operands.incl(desc)
func generate*(a: Assembler_x86): NimNode = func generate*(a: Assembler_x86): NimNode =
## Generate the inline assembly code from ## Generate the inline assembly code from
## the desired instruction ## the desired instruction
@ -527,7 +555,7 @@ func cmovc*(a: var Assembler_x86, dst, src: Operand) =
func cmovnc*(a: var Assembler_x86, dst, src: Operand) = func cmovnc*(a: var Assembler_x86, dst, src: Operand) =
## Does: dst <- src if the carry flag is not set ## Does: dst <- src if the carry flag is not set
doAssert dst.desc.rm in {Reg, ElemsInReg}, "The destination operand must be a register: " & $dst.repr doAssert dst.desc.rm in {Reg, ElemsInReg}, "The destination operand must be a register: " & $dst.repr
doAssert dst.desc.constraint in {Output_EarlyClobber, InputOutput, Output_Overwrite}, $dst.repr doAssert dst.desc.constraint in OutputReg, $dst.repr
a.codeFragment("cmovnc", src, dst) a.codeFragment("cmovnc", src, dst)
# No clobber # No clobber
@ -566,7 +594,7 @@ func mul*(a: var Assembler_x86, dHi, dLo: Register, src0: Operand, src1: Registe
func imul*(a: var Assembler_x86, dst, src: Operand) = func imul*(a: var Assembler_x86, dst, src: Operand) =
## Does dst <- dst * src, keeping only the low half ## Does dst <- dst * src, keeping only the low half
doAssert dst.desc.rm in {Reg, ElemsInReg}, "The destination operand must be a register: " & $dst.repr doAssert dst.desc.rm in {Reg, ElemsInReg}+SpecificRegisters, "The destination operand must be a register: " & $dst.repr
doAssert dst.desc.constraint in OutputReg, $dst.repr doAssert dst.desc.constraint in OutputReg, $dst.repr
a.codeFragment("imul", src, dst) a.codeFragment("imul", src, dst)
@ -574,9 +602,9 @@ func imul*(a: var Assembler_x86, dst, src: Operand) =
func mulx*(a: var Assembler_x86, dHi, dLo, src0: Operand, src1: Register) = func mulx*(a: var Assembler_x86, dHi, dLo, src0: Operand, src1: Register) =
## Does (dHi, dLo) <- src0 * src1 ## Does (dHi, dLo) <- src0 * src1
doAssert src1 == rdx, "MULX requires the RDX register" doAssert src1 == rdx, "MULX requires the RDX register"
doAssert dHi.desc.rm in {Reg, ElemsInReg} or dHi.desc.rm in SpecificRegisters, doAssert dHi.desc.rm in {Reg, ElemsInReg}+SpecificRegisters,
"The destination operand must be a register " & $dHi.repr "The destination operand must be a register " & $dHi.repr
doAssert dLo.desc.rm in {Reg, ElemsInReg} or dLo.desc.rm in SpecificRegisters, doAssert dLo.desc.rm in {Reg, ElemsInReg}+SpecificRegisters,
"The destination operand must be a register " & $dLo.repr "The destination operand must be a register " & $dLo.repr
doAssert dHi.desc.constraint in OutputReg doAssert dHi.desc.constraint in OutputReg
doAssert dLo.desc.constraint in OutputReg doAssert dLo.desc.constraint in OutputReg
@ -595,7 +623,7 @@ func adcx*(a: var Assembler_x86, dst, src: Operand) =
## Does: dst <- dst + src + carry ## Does: dst <- dst + src + carry
## and only sets the carry flag ## and only sets the carry flag
doAssert dst.desc.constraint in OutputReg, $dst.repr doAssert dst.desc.constraint in OutputReg, $dst.repr
doAssert dst.desc.rm in {Reg, ElemsInReg}, "The destination operand must be a register: " & $dst.repr doAssert dst.desc.rm in {Reg, ElemsInReg}+SpecificRegisters, "The destination operand must be a register: " & $dst.repr
a.codeFragment("adcx", src, dst) a.codeFragment("adcx", src, dst)
a.areFlagsClobbered = true a.areFlagsClobbered = true
@ -603,7 +631,7 @@ func adox*(a: var Assembler_x86, dst, src: Operand) =
## Does: dst <- dst + src + overflow ## Does: dst <- dst + src + overflow
## and only sets the overflow flag ## and only sets the overflow flag
doAssert dst.desc.constraint in OutputReg, $dst.repr doAssert dst.desc.constraint in OutputReg, $dst.repr
doAssert dst.desc.rm in {Reg, ElemsInReg}, "The destination operand must be a register: " & $dst.repr doAssert dst.desc.rm in {Reg, ElemsInReg}+SpecificRegisters, "The destination operand must be a register: " & $dst.repr
a.codeFragment("adox", src, dst) a.codeFragment("adox", src, dst)
a.areFlagsClobbered = true a.areFlagsClobbered = true

36
constantine/primitives/static_for.nim Normal file
View File

@ -0,0 +1,36 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import std/macros
proc replaceNodes(ast: NimNode, what: NimNode, by: NimNode): NimNode =
# Replace "what" ident node by "by"
proc inspect(node: NimNode): NimNode =
case node.kind:
of {nnkIdent, nnkSym}:
if node.eqIdent(what):
return by
return node
of nnkEmpty:
return node
of nnkLiterals:
return node
else:
var rTree = node.kind.newTree()
for child in node:
rTree.add inspect(child)
return rTree
result = inspect(ast)
macro staticFor*(idx: untyped{nkIdent}, start, stopEx: static int, body: untyped): untyped =
result = newStmtList()
for i in start ..< stopEx:
result.add nnkBlockStmt.newTree(
ident("unrolledIter_" & $idx & $i),
body.replaceNodes(idx, newLit i)
)

60
constantine/tower_field_extensions/quadratic_extensions.nim
View File

@ -84,17 +84,59 @@ func prod_complex(r: var QuadraticExt, a, b: QuadraticExt) =
mixin fromComplexExtension mixin fromComplexExtension
static: doAssert r.fromComplexExtension() static: doAssert r.fromComplexExtension()
var a0b0 {.noInit.}, a1b1 {.noInit.}: typeof(r.c0) # TODO: GCC is adding an unexplainable 30 cycles tax to this function (~10% slow down)
a0b0.prod(a.c0, b.c0) # [1 Mul] # for seemingly no reason
a1b1.prod(a.c1, b.c1) # [2 Mul]
r.c0.sum(a.c0, a.c1) # r0 = (a0 + a1) # [2 Mul, 1 Add] when true: # Single-width implementation
r.c1.sum(b.c0, b.c1) # r1 = (b0 + b1) # [2 Mul, 2 Add] # Clang 330 cycles on i9-9980XE @4.1 GHz
r.c1 *= r.c0 # r1 = (b0 + b1)(a0 + a1) # [3 Mul, 2 Add] - 𝔽p temporary var a0b0 {.noInit.}, a1b1 {.noInit.}: typeof(r.c0)
a0b0.prod(a.c0, b.c0) # [1 Mul]
a1b1.prod(a.c1, b.c1) # [2 Mul]
r.c0.diff(a0b0, a1b1) # r0 = a0 b0 - a1 b1 # [3 Mul, 2 Add, 1 Sub] r.c0.sum(a.c0, a.c1) # r0 = (a0 + a1) # [2 Mul, 1 Add]
r.c1 -= a0b0 # r1 = (b0 + b1)(a0 + a1) - a0b0 # [3 Mul, 2 Add, 2 Sub] r.c1.sum(b.c0, b.c1) # r1 = (b0 + b1) # [2 Mul, 2 Add]
r.c1 -= a1b1 # r1 = (b0 + b1)(a0 + a1) - a0b0 - a1b1 # [3 Mul, 2 Add, 3 Sub] r.c1 *= r.c0 # r1 = (b0 + b1)(a0 + a1) # [3 Mul, 2 Add] - 𝔽p temporary
r.c0.diff(a0b0, a1b1) # r0 = a0 b0 - a1 b1 # [3 Mul, 2 Add, 1 Sub]
r.c1 -= a0b0 # r1 = (b0 + b1)(a0 + a1) - a0b0 # [3 Mul, 2 Add, 2 Sub]
r.c1 -= a1b1 # r1 = (b0 + b1)(a0 + a1) - a0b0 - a1b1 # [3 Mul, 2 Add, 3 Sub]
else: # Double-width implementation with lazy reduction
# Deactivated for now Clang 360 cycles on i9-9980XE @4.1 GHz
var a0b0 {.noInit.}, a1b1 {.noInit.}: doubleWidth(typeof(r.c0))
var d {.noInit.}: doubleWidth(typeof(r.c0))
const msbSet = r.c0.typeof.C.canUseNoCarryMontyMul()
a0b0.mulNoReduce(a.c0, b.c0) # 44 cycles - cumul 44
a1b1.mulNoReduce(a.c1, b.c1) # 44 cycles - cumul 88
when msbSet:
r.c0.sum(a.c0, a.c1)
r.c1.sum(b.c0, b.c1)
else:
r.c0.sumNoReduce(a.c0, a.c1) # 5 cycles - cumul 93
r.c1.sumNoReduce(b.c0, b.c1) # 5 cycles - cumul 98
d.mulNoReduce(r.c0, r.c1) # 44 cycles - cumul 142
when msbSet:
d -= a0b0
d -= a1b1
else:
d.diffNoReduce(d, a0b0) # 10 cycles - cumul 152
d.diffNoReduce(d, a1b1) # 10 cycles - cumul 162
a0b0.diff(a0b0, a1b1) # 18 cycles - cumul 170
r.c0.reduce(a0b0) # 68 cycles - cumul 248
r.c1.reduce(d) # 68 cycles - cumul 316
# Single-width [3 Mul, 2 Add, 3 Sub]
# 3*81 + 2*14 + 3*12 = 307 theoretical cycles
# 330 measured
# Double-Width
# 316 theoretical cycles
# 365 measured
# Reductions can be 2x10 faster using MCL algorithm
# but there are still unexplained 50 cycles diff between theo and measured
# and unexplained 30 cycles between Clang and GCC
# - Function calls?
# - push/pop stack?
# Commutative ring implementation for generic quadratic extension fields # Commutative ring implementation for generic quadratic extension fields
# ------------------------------------------------------------------- # -------------------------------------------------------------------

13
constantine/tower_field_extensions/tower_common.nim
View File

@ -154,6 +154,19 @@ func diff*(r: var CubicExt, a, b: CubicExt) =
r.c1.diff(a.c1, b.c1) r.c1.diff(a.c1, b.c1)
r.c2.diff(a.c2, b.c2) r.c2.diff(a.c2, b.c2)
func diffAlias*(r: var QuadraticExt, a, b: QuadraticExt) =
## Diff ``a`` and ``b`` into ``r``
## Handles r and b aliasing
r.c0.diffAlias(a.c0, b.c0)
r.c1.diffAlias(a.c1, b.c1)
func diffAlias*(r: var CubicExt, a, b: CubicExt) =
## Diff ``a`` and ``b`` into ``r``
## Handles r and b aliasing
r.c0.diffAlias(a.c0, b.c0)
r.c1.diffAlias(a.c1, b.c1)
r.c2.diffAlias(a.c2, b.c2)
# Multiplication by a small integer known at compile-time # Multiplication by a small integer known at compile-time
# ------------------------------------------------------------------- # -------------------------------------------------------------------

6
tests/t_bigints.nim
View File

@ -145,6 +145,7 @@ proc mainArith() =
discard a.add(SecretWord 1) discard a.add(SecretWord 1)
check: bool(a == expected) check: bool(a == expected)
proc mainMul() =
suite "Multi-precision multiplication" & " [" & $WordBitwidth & "-bit mode]": suite "Multi-precision multiplication" & " [" & $WordBitwidth & "-bit mode]":
test "Same size operand into double size result": test "Same size operand into double size result":
block: block:
@ -185,6 +186,7 @@ proc mainArith() =
r.prod(b, a) r.prod(b, a)
check: bool(r == expected) check: bool(r == expected)
proc mainMulHigh() =
suite "Multi-precision multiplication keeping only high words" & " [" & $WordBitwidth & "-bit mode]": suite "Multi-precision multiplication keeping only high words" & " [" & $WordBitwidth & "-bit mode]":
test "Same size operand into double size result - discard first word": test "Same size operand into double size result - discard first word":
block: block:
@ -270,6 +272,7 @@ proc mainArith() =
r.prod_high_words(b, a, 2) r.prod_high_words(b, a, 2)
check: bool(r == expected) check: bool(r == expected)
proc mainModular() =
suite "Modular operations - small modulus" & " [" & $WordBitwidth & "-bit mode]": suite "Modular operations - small modulus" & " [" & $WordBitwidth & "-bit mode]":
# Vectors taken from Stint - https://github.com/status-im/nim-stint # Vectors taken from Stint - https://github.com/status-im/nim-stint
test "100 mod 13": test "100 mod 13":
@ -619,6 +622,9 @@ proc mainModularInverse() =
check: bool(r == expected) check: bool(r == expected)
mainArith() mainArith()
mainMul()
mainMulHigh()
mainModular()
mainNeg() mainNeg()
mainCopySwap() mainCopySwap()
mainModularInverse() mainModularInverse()

97
tests/t_finite_fields_double_width.nim Normal file
View File

@ -0,0 +1,97 @@
# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/[unittest, times],
# Internal
../constantine/arithmetic,
../constantine/io/[io_bigints, io_fields],
../constantine/config/[curves, common, type_bigint],
# Test utilities
../helpers/prng_unsafe
const Iters = 128
var rng: RngState
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
rng.seed(seed)
echo "\n------------------------------------------------------\n"
echo "test_finite_fields_double_width xoshiro512** seed: ", seed
proc randomCurve(C: static Curve) =
let a = rng.random_unsafe(Fp[C])
let b = rng.random_unsafe(Fp[C])
var r_fp, r_fpDbl: Fp[C]
var tmpDbl: FpDbl[C]
r_fp.prod(a, b)
tmpDbl.mulNoReduce(a, b)
r_fpDbl.reduce(tmpDbl)
doAssert bool(r_fp == r_fpDbl)
proc randomHighHammingWeight(C: static Curve) =
let a = rng.random_highHammingWeight(Fp[C])
let b = rng.random_highHammingWeight(Fp[C])
var r_fp, r_fpDbl: Fp[C]
var tmpDbl: FpDbl[C]
r_fp.prod(a, b)
tmpDbl.mulNoReduce(a, b)
r_fpDbl.reduce(tmpDbl)
doAssert bool(r_fp == r_fpDbl)
proc random_long01Seq(C: static Curve) =
let a = rng.random_long01Seq(Fp[C])
let b = rng.random_long01Seq(Fp[C])
var r_fp, r_fpDbl: Fp[C]
var tmpDbl: FpDbl[C]
r_fp.prod(a, b)
tmpDbl.mulNoReduce(a, b)
r_fpDbl.reduce(tmpDbl)
doAssert bool(r_fp == r_fpDbl)
suite "Field Multiplication via double-width field elements is consistent with single-width." & " [" & $WordBitwidth & "-bit mode]":
test "With P-224 field modulus":
for _ in 0 ..< Iters:
randomCurve(P224)
for _ in 0 ..< Iters:
randomHighHammingWeight(P224)
for _ in 0 ..< Iters:
random_long01Seq(P224)
test "With P-256 field modulus":
for _ in 0 ..< Iters:
randomCurve(P256)
for _ in 0 ..< Iters:
randomHighHammingWeight(P256)
for _ in 0 ..< Iters:
random_long01Seq(P256)
test "With BN254_Snarks field modulus":
for _ in 0 ..< Iters:
randomCurve(BN254_Snarks)
for _ in 0 ..< Iters:
randomHighHammingWeight(BN254_Snarks)
for _ in 0 ..< Iters:
random_long01Seq(BN254_Snarks)
test "With BLS12_381 field modulus":
for _ in 0 ..< Iters:
randomCurve(BLS12_381)
for _ in 0 ..< Iters:
randomHighHammingWeight(BLS12_381)
for _ in 0 ..< Iters:
random_long01Seq(BLS12_381)

2
tests/t_precomputed.nim
View File

@ -25,7 +25,7 @@ proc checkCubeRootOfUnity(curve: static Curve) =
test $curve & " cube root of unity (mod r)": test $curve & " cube root of unity (mod r)":
var cru: BigInt[3 * curve.getCurveOrderBitwidth()] var cru: BigInt[3 * curve.getCurveOrderBitwidth()]
cru.prod(curve.getCubicRootOfUnity_mod_r(), curve.getCubicRootOfUnity_mod_r()) cru.prod(curve.getCubicRootOfUnity_mod_r(), curve.getCubicRootOfUnity_mod_r())
cru.prod(cru, curve.getCubicRootOfUnity_mod_r()) cru.mul(curve.getCubicRootOfUnity_mod_r())
var r: BigInt[curve.getCurveOrderBitwidth()] var r: BigInt[curve.getCurveOrderBitwidth()]
r.reduce(cru, curve.getCurveOrder) r.reduce(cru, curve.getCurveOrder)