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Perf: revisiting field extensions in std/ #1110

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merged 10 commits into from
May 4, 2024
Merged

Perf: revisiting field extensions in std/ #1110

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cae8d0b
wip: toom-cook-3x
yelhousni Apr 18, 2024
31b012b
perf(bw6): toom-cook-3x for Fp3 mul
yelhousni Apr 19, 2024
ff0cc83
Merge branch 'master' into perf/field-extensions
yelhousni Apr 22, 2024
42f32b2
perf(bw6): revisit tower extension
yelhousni Apr 22, 2024
0bd62d5
perf(bn254): revisit tower extension
yelhousni Apr 22, 2024
26c7d02
perf(bls12-381): revisit tower extension
yelhousni Apr 22, 2024
9b0c001
Merge branch 'master' into perf/field-extensions
yelhousni Apr 23, 2024
9431336
test: update stats
yelhousni Apr 23, 2024
994237b
Merge branch 'master' into perf/field-extensions
yelhousni Apr 24, 2024
5e84406
Merge branch 'master' into perf/field-extensions
yelhousni May 4, 2024
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7 changes: 3 additions & 4 deletions std/algebra/emulated/fields_bls12381/e12.go
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Original file line number Diff line number Diff line change
Expand Up @@ -49,8 +49,8 @@ func (e Ext12) Mul(x, y *E12) *E12 {
a = e.Ext6.Mul(a, b)
b = e.Ext6.Mul(&x.C0, &y.C0)
c := e.Ext6.Mul(&x.C1, &y.C1)
z1 := e.Ext6.Sub(a, b)
z1 = e.Ext6.Sub(z1, c)
d := e.Ext6.Add(c, b)
z1 := e.Ext6.Sub(a, d)
z0 := e.Ext6.MulByNonResidue(c)
z0 = e.Ext6.Add(z0, b)
return &E12{
Expand Down Expand Up @@ -101,8 +101,7 @@ func (e Ext12) IsZero(z *E12) frontend.Variable {
func (e Ext12) Square(x *E12) *E12 {
c0 := e.Ext6.Sub(&x.C0, &x.C1)
c3 := e.Ext6.MulByNonResidue(&x.C1)
c3 = e.Ext6.Neg(c3)
c3 = e.Ext6.Add(&x.C0, c3)
c3 = e.Ext6.Sub(&x.C0, c3)
c2 := e.Ext6.Mul(&x.C0, &x.C1)
c0 = e.Ext6.Mul(c0, c3)
c0 = e.Ext6.Add(c0, c2)
Expand Down
12 changes: 6 additions & 6 deletions std/algebra/emulated/fields_bls12381/e12_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -93,8 +93,8 @@ func (e *Ext12) MulBy014(z *E12, c0, c1 *E2) *E12 {

zC1 := e.Ext6.Add(&z.C1, &z.C0)
zC1 = e.Ext6.MulBy01(zC1, c0, d)
zC1 = e.Ext6.Sub(zC1, a)
zC1 = e.Ext6.Sub(zC1, &b)
tmp := e.Ext6.Add(&b, a)
zC1 = e.Ext6.Sub(zC1, tmp)
zC0 := e.Ext6.MulByNonResidue(&b)
zC0 = e.Ext6.Add(zC0, a)

Expand Down Expand Up @@ -124,8 +124,8 @@ func (e Ext12) Mul014By014(d0, d1, c0, c1 *E2) [5]*E2 {
tmp := e.Ext2.Add(c0, c1)
x01 := e.Ext2.Add(d0, d1)
x01 = e.Ext2.Mul(x01, tmp)
x01 = e.Ext2.Sub(x01, x0)
x01 = e.Ext2.Sub(x01, x1)
tmp = e.Ext2.Add(x1, x0)
x01 = e.Ext2.Sub(x01, tmp)
x14 := e.Ext2.Add(c1, d1)

zC0B0 := e.Ext2.NonResidue()
Expand All @@ -148,8 +148,8 @@ func (e *Ext12) MulBy01245(z *E12, x [5]*E2) *E12 {
a = e.Ext6.Mul(a, b)
b = e.Ext6.Mul(&z.C0, c0)
c := e.Ext6.MulBy12(&z.C1, x[3], x[4])
z1 := e.Ext6.Sub(a, b)
z1 = e.Ext6.Sub(z1, c)
d := e.Ext6.Add(c, b)
z1 := e.Ext6.Sub(a, d)
z0 := e.Ext6.MulByNonResidue(c)
z0 = e.Ext6.Add(z0, b)
return &E12{
Expand Down
60 changes: 32 additions & 28 deletions std/algebra/emulated/fields_bls12381/e2.go
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Expand Up @@ -59,8 +59,8 @@ func NewExt2(api frontend.API) *Ext2 {
}

func (e Ext2) MulByElement(x *E2, y *baseEl) *E2 {
z0 := e.fp.MulMod(&x.A0, y)
z1 := e.fp.MulMod(&x.A1, y)
z0 := e.fp.Mul(&x.A0, y)
z1 := e.fp.Mul(&x.A1, y)
return &E2{
A0: *z0,
A1: *z1,
Expand Down Expand Up @@ -110,9 +110,9 @@ func (e Ext2) MulByNonResidue1Power1(x *E2) *E2 {
// MulByNonResidue1Power2 returns x*(1+u)^(2*(p^1-1)/6)
func (e Ext2) MulByNonResidue1Power2(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436")
a := e.fp.MulMod(&x.A1, &element)
a := e.fp.Mul(&x.A1, &element)
a = e.fp.Neg(a)
b := e.fp.MulMod(&x.A0, &element)
b := e.fp.Mul(&x.A0, &element)
return &E2{
A0: *a,
A1: *b,
Expand All @@ -128,8 +128,8 @@ func (e Ext2) MulByNonResidue1Power3(x *E2) *E2 {
func (e Ext2) MulByNonResidue1Power4(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

Expand All @@ -142,59 +142,62 @@ func (e Ext2) MulByNonResidue1Power5(x *E2) *E2 {
func (e Ext2) MulByNonResidue2Power1(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

// MulByNonResidue2Power2 returns x*(1+u)^(2*(p^2-1)/6)
func (e Ext2) MulByNonResidue2Power2(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

// MulByNonResidue2Power3 returns x*(1+u)^(3*(p^2-1)/6)
func (e Ext2) MulByNonResidue2Power3(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559786")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

// MulByNonResidue2Power4 returns x*(1+u)^(4*(p^2-1)/6)
func (e Ext2) MulByNonResidue2Power4(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

// MulByNonResidue2Power5 returns x*(1+u)^(5*(p^2-1)/6)
func (e Ext2) MulByNonResidue2Power5(x *E2) *E2 {
element := emulated.ValueOf[emulated.BLS12381Fp]("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437")
return &E2{
A0: *e.fp.MulMod(&x.A0, &element),
A1: *e.fp.MulMod(&x.A1, &element),
A0: *e.fp.Mul(&x.A0, &element),
A1: *e.fp.Mul(&x.A1, &element),
}
}

func (e Ext2) Mul(x, y *E2) *E2 {
a := e.fp.Add(&x.A0, &x.A1)
b := e.fp.Add(&y.A0, &y.A1)
a = e.fp.MulMod(a, b)
b = e.fp.MulMod(&x.A0, &y.A0)
c := e.fp.MulMod(&x.A1, &y.A1)
z1 := e.fp.Sub(a, b)
z1 = e.fp.Sub(z1, c)
z0 := e.fp.Sub(b, c)

v0 := e.fp.Mul(&x.A0, &y.A0)
v1 := e.fp.Mul(&x.A1, &y.A1)

b0 := e.fp.Sub(v0, v1)
b1 := e.fp.Add(&x.A0, &x.A1)
tmp := e.fp.Add(&y.A0, &y.A1)
b1 = e.fp.Mul(b1, tmp)
tmp = e.fp.Add(v0, v1)
b1 = e.fp.Sub(b1, tmp)

return &E2{
A0: *z0,
A1: *z1,
A0: *b0,
A1: *b1,
}
}

Expand Down Expand Up @@ -242,6 +245,7 @@ func (e Ext2) Zero() *E2 {
A1: *z1,
}
}

func (e Ext2) IsZero(z *E2) frontend.Variable {
a0 := e.fp.IsZero(&z.A0)
a1 := e.fp.IsZero(&z.A1)
Expand All @@ -260,8 +264,8 @@ func (e Ext2) NonResidue() *E2 {
func (e Ext2) Square(x *E2) *E2 {
a := e.fp.Add(&x.A0, &x.A1)
b := e.fp.Sub(&x.A0, &x.A1)
a = e.fp.MulMod(a, b)
b = e.fp.MulMod(&x.A0, &x.A1)
a = e.fp.Mul(a, b)
b = e.fp.Mul(&x.A0, &x.A1)
b = e.fp.MulConst(b, big.NewInt(2))
return &E2{
A0: *a,
Expand Down
28 changes: 17 additions & 11 deletions std/algebra/emulated/fields_bls12381/e6.go
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Original file line number Diff line number Diff line change
Expand Up @@ -86,22 +86,22 @@ func (e Ext6) Mul(x, y *E6) *E6 {
c0 := e.Ext2.Add(&x.B1, &x.B2)
tmp := e.Ext2.Add(&y.B1, &y.B2)
c0 = e.Ext2.Mul(c0, tmp)
c0 = e.Ext2.Sub(c0, t1)
c0 = e.Ext2.Sub(c0, t2)
tmp = e.Ext2.Add(t2, t1)
c0 = e.Ext2.Sub(c0, tmp)
c0 = e.Ext2.MulByNonResidue(c0)
c0 = e.Ext2.Add(c0, t0)
c1 := e.Ext2.Add(&x.B0, &x.B1)
tmp = e.Ext2.Add(&y.B0, &y.B1)
c1 = e.Ext2.Mul(c1, tmp)
c1 = e.Ext2.Sub(c1, t0)
c1 = e.Ext2.Sub(c1, t1)
tmp = e.Ext2.Add(t0, t1)
c1 = e.Ext2.Sub(c1, tmp)
tmp = e.Ext2.MulByNonResidue(t2)
c1 = e.Ext2.Add(c1, tmp)
tmp = e.Ext2.Add(&x.B0, &x.B2)
c2 := e.Ext2.Add(&y.B0, &y.B2)
c2 = e.Ext2.Mul(c2, tmp)
c2 = e.Ext2.Sub(c2, t0)
c2 = e.Ext2.Sub(c2, t2)
tmp = e.Ext2.Add(t0, t2)
c2 = e.Ext2.Sub(c2, tmp)
c2 = e.Ext2.Add(c2, t1)
return &E6{
B0: *c0,
Expand Down Expand Up @@ -166,8 +166,8 @@ func (e Ext6) MulBy12(x *E6, b1, b2 *E2) *E6 {
c0 := e.Ext2.Add(&x.B1, &x.B2)
tmp := e.Ext2.Add(b1, b2)
c0 = e.Ext2.Mul(c0, tmp)
c0 = e.Ext2.Sub(c0, t1)
c0 = e.Ext2.Sub(c0, t2)
tmp = e.Ext2.Add(t1, t2)
c0 = e.Ext2.Sub(c0, tmp)
c0 = e.Ext2.MulByNonResidue(c0)
c1 := e.Ext2.Add(&x.B0, &x.B1)
c1 = e.Ext2.Mul(c1, b1)
Expand Down Expand Up @@ -207,7 +207,13 @@ func (e Ext6) MulBy0(z *E6, c0 *E2) *E6 {
}
}

// MulBy01 multiplication by sparse element (c0,c1,0)
// MulBy01 multiplies z by an E6 sparse element of the form
//
// E6{
// B0: c0,
// B1: c1,
// B2: 0,
// }
func (e Ext6) MulBy01(z *E6, c0, c1 *E2) *E6 {
a := e.Ext2.Mul(&z.B0, c0)
b := e.Ext2.Mul(&z.B1, c1)
Expand All @@ -224,8 +230,8 @@ func (e Ext6) MulBy01(z *E6, c0, c1 *E2) *E6 {
t1 := e.Ext2.Add(c0, c1)
tmp = e.Ext2.Add(&z.B0, &z.B1)
t1 = e.Ext2.Mul(t1, tmp)
t1 = e.Ext2.Sub(t1, a)
t1 = e.Ext2.Sub(t1, b)
tmp = e.Ext2.Add(a, b)
t1 = e.Ext2.Sub(t1, tmp)
return &E6{
B0: *t0,
B1: *t1,
Expand Down
7 changes: 3 additions & 4 deletions std/algebra/emulated/fields_bn254/e12.go
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Expand Up @@ -49,8 +49,8 @@ func (e Ext12) Mul(x, y *E12) *E12 {
a = e.Ext6.Mul(a, b)
b = e.Ext6.Mul(&x.C0, &y.C0)
c := e.Ext6.Mul(&x.C1, &y.C1)
z1 := e.Ext6.Sub(a, b)
z1 = e.Ext6.Sub(z1, c)
d := e.Ext6.Add(c, b)
z1 := e.Ext6.Sub(a, d)
z0 := e.Ext6.MulByNonResidue(c)
z0 = e.Ext6.Add(z0, b)
return &E12{
Expand Down Expand Up @@ -101,8 +101,7 @@ func (e Ext12) IsZero(z *E12) frontend.Variable {
func (e Ext12) Square(x *E12) *E12 {
c0 := e.Ext6.Sub(&x.C0, &x.C1)
c3 := e.Ext6.MulByNonResidue(&x.C1)
c3 = e.Ext6.Neg(c3)
c3 = e.Ext6.Add(&x.C0, c3)
c3 = e.Ext6.Sub(&x.C0, c3)
c2 := e.Ext6.Mul(&x.C0, &x.C1)
c0 = e.Ext6.Mul(c0, c3)
c0 = e.Ext6.Add(c0, c2)
Expand Down
12 changes: 6 additions & 6 deletions std/algebra/emulated/fields_bn254/e12_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -154,8 +154,8 @@ func (e *Ext12) Mul034By034(d3, d4, c3, c4 *E2) [5]*E2 {
tmp := e.Ext2.Add(c3, c4)
x34 := e.Ext2.Add(d3, d4)
x34 = e.Ext2.Mul(x34, tmp)
x34 = e.Ext2.Sub(x34, x3)
x34 = e.Ext2.Sub(x34, x4)
tmp = e.Ext2.Add(x4, x3)
x34 = e.Ext2.Sub(x34, tmp)

zC0B0 := e.Ext2.MulByNonResidue(x4)
zC0B0 = e.Ext2.Add(zC0B0, e.Ext2.One())
Expand All @@ -181,8 +181,8 @@ func (e *Ext12) MulBy01234(z *E12, x [5]*E2) *E12 {
a = e.Ext6.Mul(a, b)
b = e.Ext6.Mul(&z.C0, c0)
c := e.Ext6.MulBy01(&z.C1, x[3], x[4])
z1 := e.Ext6.Sub(a, b)
z1 = e.Ext6.Sub(z1, c)
d := e.Ext6.Add(c, b)
z1 := e.Ext6.Sub(a, d)
z0 := e.Ext6.MulByNonResidue(c)
z0 = e.Ext6.Add(z0, b)
return &E12{
Expand Down Expand Up @@ -211,8 +211,8 @@ func (e *Ext12) Mul01234By034(x [5]*E2, z3, z4 *E2) *E12 {
b := e.Ext6.Add(c0, c1)
a = e.Ext6.Mul(a, b)
c := e.Ext6.Mul01By01(z3, z4, x[3], x[4])
z1 := e.Ext6.Sub(a, c0)
z1 = e.Ext6.Sub(z1, c)
b = e.Ext6.Add(c0, c)
z1 := e.Ext6.Sub(a, b)
z0 := e.Ext6.MulByNonResidue(c)
z0 = e.Ext6.Add(z0, c0)
return &E12{
Expand Down