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fix modmul 256-bit perf #156

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merged 1 commit into from
Jul 9, 2024
Merged

fix modmul 256-bit perf #156

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31 changes: 21 additions & 10 deletions benchmarks/bench.nim
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -23,8 +23,8 @@ let a = [123'u64, 123'u64, 123'u64, 123'u64]
let m = [456'u64, 456'u64, 456'u64, 45'u64]

proc add_stint(a, m: array[4, uint64]) =
let aU256 = cast[Stuint[256]](a)
let mU256 = cast[Stuint[256]](m)
let aU256 = cast[StUint[256]](a)
let mU256 = cast[StUint[256]](m)

bench "Add (stint)":
var foo = aU256
Expand All @@ -33,26 +33,37 @@ proc add_stint(a, m: array[4, uint64]) =
foo += aU256

proc mul_stint(a, m: array[4, uint64]) =
let aU256 = cast[Stuint[256]](a)
let mU256 = cast[Stuint[256]](m)
let aU256 = cast[StUint[256]](a)
let mU256 = cast[StUint[256]](m)

bench "Mul (stint)":
var foo = aU256
for i in 0 ..< 100_000_000:
foo += (foo * foo)

proc mod_stint(a, m: array[4, uint64]) =
let aU256 = cast[Stuint[256]](a)
let mU256 = cast[Stuint[256]](m)
let aU256 = cast[StUint[256]](a)
let mU256 = cast[StUint[256]](m)

bench "Mod (stint)":
var foo = aU256
for i in 0 ..< 100_000_000:
foo += (foo * foo) mod mU256

add_stint(a, m)
mul_stint(a, m)
mod_stint(a, m)
proc mulmod_stint(a, m: array[4, uint64]) =
let aU256 = cast[StUint[256]](a)
let mU256 = cast[StUint[256]](m)

bench "Modmul (stint)":
var foo = aU256
for i in 0 ..< 100_000_000:
foo += mulmod(aU256, aU256, mU256)

# add_stint(a, m)
# mul_stint(a, m)
# mod_stint(a, m)

mulmod_stint(a, m)

when defined(bench_ttmath):
# need C++
Expand Down Expand Up @@ -88,4 +99,4 @@ when defined(bench_ttmath):

add_ttmath(a, m)
mul_ttmath(a, m)
mod_ttmath(a, m)
mod_ttmath(a, m)
80 changes: 21 additions & 59 deletions stint/modular_arithmetic.nim
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Original file line number Diff line number Diff line change
Expand Up @@ -22,8 +22,9 @@ func addmod_internal(a, b, m: StUint): StUint {.inline.}=
let b_from_m = m - b

if a >= b_from_m:
return a - b_from_m
return m - b_from_m + a
a - b_from_m
else:
m - b_from_m + a

func submod_internal(a, b, m: StUint): StUint {.inline.}=
## Modular substraction
Expand All @@ -34,53 +35,9 @@ func submod_internal(a, b, m: StUint): StUint {.inline.}=

# We don't do a_m - b_m directly to avoid underflows
if a >= b:
return a - b
return m - b + a


func doublemod_internal(a, m: StUint): StUint {.inline.}=
## Double a modulo m. Assume a < m
## Internal proc - used in mulmod

doAssert a < m

result = a
if a >= m - a:
result -= m
result += a

func mulmod_internal(a, b, m: StUint): StUint {.inline.}=
## Does (a * b) mod m. Assume a < m and b < m
## Internal proc - used in powmod

doAssert a < m
doAssert b < m

var (a, b) = (a, b)

if b > a:
swap(a, b)

while not b.isZero:
if b.isOdd:
result = result.addmod_internal(a, m)
a = doublemod_internal(a, m)
b = b shr 1

func powmod_internal(a, b, m: StUint): StUint {.inline.}=
## Compute ``(a ^ b) mod m``, assume a < m
## Internal proc

doAssert a < m

var (a, b) = (a, b)
result = one(type a)

while not b.isZero:
if b.isOdd:
result = result.mulmod_internal(a, m)
b = b shr 1
a = mulmod_internal(a, a, m)
a - b
else:
m - b + a

func addmod*(a, b, m: StUint): StUint =
## Modular addition
Expand All @@ -90,7 +47,7 @@ func addmod*(a, b, m: StUint): StUint =
let b_m = if b < m: b
else: b mod m

result = addmod_internal(a_m, b_m, m)
addmod_internal(a_m, b_m, m)

func submod*(a, b, m: StUint): StUint =
## Modular substraction
Expand All @@ -100,24 +57,29 @@ func submod*(a, b, m: StUint): StUint =
let b_m = if b < m: b
else: b mod m

result = submod_internal(a_m, b_m, m)
submod_internal(a_m, b_m, m)

func mulmod*(a, b, m: StUint): StUint =
## Modular multiplication

let a_m = if a < m: a
else: a mod m
let b_m = if b < m: b
else: b mod m
let
ax = a.stuint(a.bits * 2)
bx = b.stuint(b.bits * 2)
mx = m.stuint(m.bits * 2)
px = ax * bx

result = mulmod_internal(a_m, b_m, m)
divmod(px, mx).rem.stuint(a.bits)

func powmod*(a, b, m: StUint): StUint =
## Modular exponentiation

let a_m = if a < m: a
else: a mod m
var (a, b) = (a, b)
result = one(type a)

result = powmod_internal(a_m, b, m)
while not b.isZero:
if b.isOdd:
result = result.mulmod(a, m)
b = b shr 1
a = mulmod(a, a, m)

{.pop.}
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