fp25519 passing tests

internal/examples/fp25519/fp.go

@@ -8,16 +8,28 @@ var p, _ = new(big.Int).SetString("578960446186580977117854925043439539266349923
 // Elt is an element of the field modulo 2^255-19.
 type Elt struct{ n big.Int }
 
-// Modp reduces z modulo p, ensuring it's in the range [0, p).
-func Modp(z *Elt) {
-	z.n.Mod(&z.n, p)
+func (z *Elt) SetInt(x *big.Int) *Elt {
+	z.n.Set(x)
+	return z.modp()
+}
+
+func (z *Elt) Int() *big.Int {
+	return new(big.Int).Set(&z.n)
 }
 
-// Mul computes z = x*y (mod p).
-func Mul(z, x, y *Elt) {
+// Mul computes z = x*y (mod p) and returns it.
+func (z *Elt) Mul(x, y *Elt) *Elt {
 	z.n.Mul(&x.n, &y.n)
-	Modp(z)
+	return z.modp()
 }
 
-// Sqr computes z = x^2 (mod p).
-func Sqr(z, x *Elt) { Mul(z, x, x) }
+// Sqr computes z = x^2 (mod p) and returns it.
+func (z *Elt) Sqr(x *Elt) *Elt {
+	return z.Mul(x, x)
+}
+
+// modp reduces z modulo p, ensuring it's in the range [0, p).
+func (z *Elt) modp() *Elt {
+	z.n.Mod(&z.n, p)
+	return z
+}

internal/examples/fp25519/fp_test.go

@@ -0,0 +1,31 @@
+package fp25519
+
+import (
+	"crypto/rand"
+	"math/big"
+	"testing"
+)
+
+func RandElt(t *testing.T) *Elt {
+	t.Helper()
+	one := new(big.Int).SetInt64(1)
+	max := new(big.Int).Sub(p, one)
+	x, err := rand.Int(rand.Reader, max)
+	if err != nil {
+		t.Fatal(err)
+	}
+	x.Add(x, one)
+	return new(Elt).SetInt(x)
+}
+
+func TestInv(t *testing.T) {
+	const trials = 1 << 12
+	for trial := 0; trial < trials; trial++ {
+		x := RandElt(t)
+		got := new(Elt).Inv(x)
+		expect := new(big.Int).ModInverse(x.Int(), p)
+		if got.Int().Cmp(expect) != 0 {
+			t.FailNow()
+		}
+	}
+}

internal/examples/fp25519/inv.go

@@ -1,85 +1,87 @@
 package fp25519
 
-func Inv(z, x *Elt) {
+func (z *Elt) Inv(x *Elt) *Elt {
 	var (
 		t0 = new(Elt)
 		t1 = new(Elt)
 		t2 = new(Elt)
 	)
 
-	Sqr(z, x)
+	z.Sqr(x)
 
-	Mul(z, x, z)
+	z.Mul(x, z)
 
-	Sqr(t0, z)
+	t0.Sqr(z)
 	for s := 1; s < 2; s++ {
-		Sqr(t0, t0)
+		t0.Sqr(t0)
 	}
 
-	Mul(t0, z, t0)
+	t0.Mul(z, t0)
 
-	Sqr(t1, t0)
+	t1.Sqr(t0)
 	for s := 1; s < 4; s++ {
-		Sqr(t1, t1)
+		t1.Sqr(t1)
 	}
 
-	Mul(t0, t0, t1)
+	t0.Mul(t0, t1)
 
 	for s := 0; s < 2; s++ {
-		Sqr(t0, t0)
+		t0.Sqr(t0)
 	}
 
-	Mul(t0, z, t0)
+	t0.Mul(z, t0)
 
-	Sqr(t1, t0)
+	t1.Sqr(t0)
 	for s := 1; s < 10; s++ {
-		Sqr(t1, t1)
+		t1.Sqr(t1)
 	}
 
-	Mul(t1, t0, t1)
+	t1.Mul(t0, t1)
 
 	for s := 0; s < 10; s++ {
-		Sqr(t1, t1)
+		t1.Sqr(t1)
 	}
 
-	Mul(t1, t0, t1)
+	t1.Mul(t0, t1)
 
-	Sqr(t2, t1)
+	t2.Sqr(t1)
 	for s := 1; s < 30; s++ {
-		Sqr(t2, t2)
+		t2.Sqr(t2)
 	}
 
-	Mul(t1, t1, t2)
+	t1.Mul(t1, t2)
 
-	Sqr(t2, t1)
+	t2.Sqr(t1)
 	for s := 1; s < 60; s++ {
-		Sqr(t2, t2)
+		t2.Sqr(t2)
 	}
 
-	Mul(t1, t1, t2)
+	t1.Mul(t1, t2)
 
-	Sqr(t2, t1)
+	t2.Sqr(t1)
 	for s := 1; s < 120; s++ {
-		Sqr(t2, t2)
+		t2.Sqr(t2)
 	}
 
-	Mul(t1, t1, t2)
+	t1.Mul(t1, t2)
 
 	for s := 0; s < 10; s++ {
-		Sqr(t1, t1)
+		t1.Sqr(t1)
 	}
 
-	Mul(t0, t0, t1)
+	t0.Mul(t0, t1)
 
 	for s := 0; s < 2; s++ {
-		Sqr(t0, t0)
+		t0.Sqr(t0)
 	}
 
-	Mul(t0, x, t0)
+	t0.Mul(x, t0)
 
 	for s := 0; s < 3; s++ {
-		Sqr(t0, t0)
+		t0.Sqr(t0)
 	}
 
-	Mul(z, z, t0)
+	z.Mul(z, t0)
+
+	return z
 }

internal/examples/fp25519/inv.tmpl

@@ -1,30 +1,31 @@
 package fp25519
 
-func Inv(z, x *Elt) {
-var (
-{{- range .Program.Temporaries }}
-	{{ . }} = new(Elt)
-{{- end -}}
-)
+func (z *Elt) Inv(x *Elt) *Elt {
+	var (
+		{{- range .Program.Temporaries }}
+		{{ . }} = new(Elt)
+		{{- end -}}
+	)
 
-{{ range $i := .Program.Instructions -}}
-{{- with add $i.Op }}
-Mul({{ $i.Output }}, {{ .X }}, {{ .Y }})
-{{ end -}}
+	{{ range $i := .Program.Instructions -}}
+	{{- with add $i.Op }}
+	{{ $i.Output }}.Mul({{ .X }}, {{ .Y }})
+	{{ end -}}
 
-{{- with double $i.Op }}
-Sqr({{ $i.Output }}, {{ .X }})
-{{ end -}}
+	{{- with double $i.Op }}
+	{{ $i.Output }}.Sqr({{ .X }})
+	{{ end -}}
 
-{{- with shift $i.Op -}}
-{{- $first := 0 -}}
-{{- if ne $i.Output.Identifier .X.Identifier }}
-Sqr({{ $i.Output }}, {{ .X }})
-{{- $first = 1 -}}
-{{- end }}
-for s := {{ $first }}; s < {{ .S }}; s++ {
-	Sqr({{ $i.Output }}, {{ $i.Output }})
-}
-{{ end -}}
-{{- end -}}
+	{{- with shift $i.Op -}}
+	{{- $first := 0 -}}
+	{{- if ne $i.Output.Identifier .X.Identifier }}
+	{{ $i.Output }}.Sqr({{ .X }})
+	{{- $first = 1 -}}
+	{{- end }}
+	for s := {{ $first }}; s < {{ .S }}; s++ {
+		{{ $i.Output }}.Sqr({{ $i.Output }})
+	}
+	{{ end -}}
+	{{- end }}
+	return z
 }