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bluepython508 committed 2026-10-22 12:27:19 +01:00
1 parent 3530afb854
commit 6903fcff27
2146 files changed
+112256 -190703
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vendor/filippo.io/edwards25519/field/fe_generic.go
Generated Vendored
+88 -82
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@@ -12,20 +12,42 @@ type uint128 struct {
lo, hi uint64
}
// mul64 returns a * b.
func mul64(a, b uint64) uint128 {
// mul returns a * b.
func mul(a, b uint64) uint128 {
hi, lo := bits.Mul64(a, b)
return uint128{lo, hi}
}
// addMul64 returns v + a * b.
func addMul64(v uint128, a, b uint64) uint128 {
// addMul returns v + a * b.
func addMul(v uint128, a, b uint64) uint128 {
hi, lo := bits.Mul64(a, b)
lo, c := bits.Add64(lo, v.lo, 0)
hi, _ = bits.Add64(hi, v.hi, c)
return uint128{lo, hi}
}
// mul19 returns v * 19.
func mul19(v uint64) uint64 {
// Using this approach seems to yield better optimizations than *19.
return v + (v+v<<3)<<1
}
// addMul19 returns v + 19 * a * b, where a and b are at most 52 bits.
func addMul19(v uint128, a, b uint64) uint128 {
hi, lo := bits.Mul64(mul19(a), b)
lo, c := bits.Add64(lo, v.lo, 0)
hi, _ = bits.Add64(hi, v.hi, c)
return uint128{lo, hi}
}
// addMul38 returns v + 38 * a * b, where a and b are at most 52 bits.
func addMul38(v uint128, a, b uint64) uint128 {
hi, lo := bits.Mul64(mul19(a), b*2)
lo, c := bits.Add64(lo, v.lo, 0)
hi, _ = bits.Add64(hi, v.hi, c)
return uint128{lo, hi}
}
// shiftRightBy51 returns a >> 51. a is assumed to be at most 115 bits.
func shiftRightBy51(a uint128) uint64 {
return (a.hi << (64 - 51)) | (a.lo >> 51)
@@ -76,45 +98,40 @@ func feMulGeneric(v, a, b *Element) {
//
// Finally we add up the columns into wide, overlapping limbs.
a1_19 := a1 * 19
a2_19 := a2 * 19
a3_19 := a3 * 19
a4_19 := a4 * 19
// r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
r0 := mul64(a0, b0)
r0 = addMul64(r0, a1_19, b4)
r0 = addMul64(r0, a2_19, b3)
r0 = addMul64(r0, a3_19, b2)
r0 = addMul64(r0, a4_19, b1)
r0 := mul(a0, b0)
r0 = addMul19(r0, a1, b4)
r0 = addMul19(r0, a2, b3)
r0 = addMul19(r0, a3, b2)
r0 = addMul19(r0, a4, b1)
// r1 = a0×b1 + a1×b0 + 19×(a2×b4 + a3×b3 + a4×b2)
r1 := mul64(a0, b1)
r1 = addMul64(r1, a1, b0)
r1 = addMul64(r1, a2_19, b4)
r1 = addMul64(r1, a3_19, b3)
r1 = addMul64(r1, a4_19, b2)
r1 := mul(a0, b1)
r1 = addMul(r1, a1, b0)
r1 = addMul19(r1, a2, b4)
r1 = addMul19(r1, a3, b3)
r1 = addMul19(r1, a4, b2)
// r2 = a0×b2 + a1×b1 + a2×b0 + 19×(a3×b4 + a4×b3)
r2 := mul64(a0, b2)
r2 = addMul64(r2, a1, b1)
r2 = addMul64(r2, a2, b0)
r2 = addMul64(r2, a3_19, b4)
r2 = addMul64(r2, a4_19, b3)
r2 := mul(a0, b2)
r2 = addMul(r2, a1, b1)
r2 = addMul(r2, a2, b0)
r2 = addMul19(r2, a3, b4)
r2 = addMul19(r2, a4, b3)
// r3 = a0×b3 + a1×b2 + a2×b1 + a3×b0 + 19×a4×b4
r3 := mul64(a0, b3)
r3 = addMul64(r3, a1, b2)
r3 = addMul64(r3, a2, b1)
r3 = addMul64(r3, a3, b0)
r3 = addMul64(r3, a4_19, b4)
r3 := mul(a0, b3)
r3 = addMul(r3, a1, b2)
r3 = addMul(r3, a2, b1)
r3 = addMul(r3, a3, b0)
r3 = addMul19(r3, a4, b4)
// r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
r4 := mul64(a0, b4)
r4 = addMul64(r4, a1, b3)
r4 = addMul64(r4, a2, b2)
r4 = addMul64(r4, a3, b1)
r4 = addMul64(r4, a4, b0)
r4 := mul(a0, b4)
r4 = addMul(r4, a1, b3)
r4 = addMul(r4, a2, b2)
r4 = addMul(r4, a3, b1)
r4 = addMul(r4, a4, b0)
// After the multiplication, we need to reduce (carry) the five coefficients
// to obtain a result with limbs that are at most slightly larger than 2⁵¹,
@@ -149,7 +166,7 @@ func feMulGeneric(v, a, b *Element) {
c3 := shiftRightBy51(r3)
c4 := shiftRightBy51(r4)
rr0 := r0.lo&maskLow51Bits + c4*19
rr0 := r0.lo&maskLow51Bits + mul19(c4)
rr1 := r1.lo&maskLow51Bits + c0
rr2 := r2.lo&maskLow51Bits + c1
rr3 := r3.lo&maskLow51Bits + c2
@@ -158,8 +175,12 @@ func feMulGeneric(v, a, b *Element) {
// Now all coefficients fit into 64-bit registers but are still too large to
// be passed around as an Element. We therefore do one last carry chain,
// where the carries will be small enough to fit in the wiggle room above 2⁵¹.
*v = Element{rr0, rr1, rr2, rr3, rr4}
v.carryPropagate()
v.l0 = rr0&maskLow51Bits + mul19(rr4>>51)
v.l1 = rr1&maskLow51Bits + rr0>>51
v.l2 = rr2&maskLow51Bits + rr1>>51
v.l3 = rr3&maskLow51Bits + rr2>>51
v.l4 = rr4&maskLow51Bits + rr3>>51
}
func feSquareGeneric(v, a *Element) {
@@ -190,44 +211,31 @@ func feSquareGeneric(v, a *Element) {
// l0l4 19×l4l4 19×l3l4 19×l2l4 19×l1l4 =
// --------------------------------------
// r4 r3 r2 r1 r0
//
// With precomputed 2×, 19×, and 2×19× terms, we can compute each limb with
// only three Mul64 and four Add64, instead of five and eight.
l0_2 := l0 * 2
l1_2 := l1 * 2
l1_38 := l1 * 38
l2_38 := l2 * 38
l3_38 := l3 * 38
l3_19 := l3 * 19
l4_19 := l4 * 19
// r0 = l0×l0 + 19×(l1×l4 + l2×l3 + l3×l2 + l4×l1) = l0×l0 + 19×2×(l1×l4 + l2×l3)
r0 := mul64(l0, l0)
r0 = addMul64(r0, l1_38, l4)
r0 = addMul64(r0, l2_38, l3)
r0 := mul(l0, l0)
r0 = addMul38(r0, l1, l4)
r0 = addMul38(r0, l2, l3)
// r1 = l0×l1 + l1×l0 + 19×(l2×l4 + l3×l3 + l4×l2) = 2×l0×l1 + 19×2×l2×l4 + 19×l3×l3
r1 := mul64(l0_2, l1)
r1 = addMul64(r1, l2_38, l4)
r1 = addMul64(r1, l3_19, l3)
r1 := mul(l0*2, l1)
r1 = addMul38(r1, l2, l4)
r1 = addMul19(r1, l3, l3)
// r2 = l0×l2 + l1×l1 + l2×l0 + 19×(l3×l4 + l4×l3) = 2×l0×l2 + l1×l1 + 19×2×l3×l4
r2 := mul64(l0_2, l2)
r2 = addMul64(r2, l1, l1)
r2 = addMul64(r2, l3_38, l4)
r2 := mul(l0*2, l2)
r2 = addMul(r2, l1, l1)
r2 = addMul38(r2, l3, l4)
// r3 = l0×l3 + l1×l2 + l2×l1 + l3×l0 + 19×l4×l4 = 2×l0×l3 + 2×l1×l2 + 19×l4×l4
r3 := mul64(l0_2, l3)
r3 = addMul64(r3, l1_2, l2)
r3 = addMul64(r3, l4_19, l4)
r3 := mul(l0*2, l3)
r3 = addMul(r3, l1*2, l2)
r3 = addMul19(r3, l4, l4)
// r4 = l0×l4 + l1×l3 + l2×l2 + l3×l1 + l4×l0 = 2×l0×l4 + 2×l1×l3 + l2×l2
r4 := mul64(l0_2, l4)
r4 = addMul64(r4, l1_2, l3)
r4 = addMul64(r4, l2, l2)
r4 := mul(l0*2, l4)
r4 = addMul(r4, l1*2, l3)
r4 = addMul(r4, l2, l2)
c0 := shiftRightBy51(r0)
c1 := shiftRightBy51(r1)
@@ -235,32 +243,30 @@ func feSquareGeneric(v, a *Element) {
c3 := shiftRightBy51(r3)
c4 := shiftRightBy51(r4)
rr0 := r0.lo&maskLow51Bits + c4*19
rr0 := r0.lo&maskLow51Bits + mul19(c4)
rr1 := r1.lo&maskLow51Bits + c0
rr2 := r2.lo&maskLow51Bits + c1
rr3 := r3.lo&maskLow51Bits + c2
rr4 := r4.lo&maskLow51Bits + c3
*v = Element{rr0, rr1, rr2, rr3, rr4}
v.carryPropagate()
v.l0 = rr0&maskLow51Bits + mul19(rr4>>51)
v.l1 = rr1&maskLow51Bits + rr0>>51
v.l2 = rr2&maskLow51Bits + rr1>>51
v.l3 = rr3&maskLow51Bits + rr2>>51
v.l4 = rr4&maskLow51Bits + rr3>>51
}
// carryPropagateGeneric brings the limbs below 52 bits by applying the reduction
// carryPropagate brings the limbs below 52 bits by applying the reduction
// identity (a * 2²⁵⁵ + b = a * 19 + b) to the l4 carry.
func (v *Element) carryPropagateGeneric() *Element {
c0 := v.l0 >> 51
c1 := v.l1 >> 51
c2 := v.l2 >> 51
c3 := v.l3 >> 51
c4 := v.l4 >> 51
// c4 is at most 64 - 51 = 13 bits, so c4*19 is at most 18 bits, and
func (v *Element) carryPropagate() *Element {
// (l4>>51) is at most 64 - 51 = 13 bits, so (l4>>51)*19 is at most 18 bits, and
// the final l0 will be at most 52 bits. Similarly for the rest.
v.l0 = v.l0&maskLow51Bits + c4*19
v.l1 = v.l1&maskLow51Bits + c0
v.l2 = v.l2&maskLow51Bits + c1
v.l3 = v.l3&maskLow51Bits + c2
v.l4 = v.l4&maskLow51Bits + c3
l0 := v.l0
v.l0 = v.l0&maskLow51Bits + mul19(v.l4>>51)
v.l4 = v.l4&maskLow51Bits + v.l3>>51
v.l3 = v.l3&maskLow51Bits + v.l2>>51
v.l2 = v.l2&maskLow51Bits + v.l1>>51
v.l1 = v.l1&maskLow51Bits + l0>>51
return v
}