From 6db84dcfdcc0cd1b8556f145c39d230bf2a5ffef Mon Sep 17 00:00:00 2001
From: Filippo Valsorda <hi@filippo.io>
Date: Sat, 30 Nov 2019 22:46:35 -0400
Subject: [PATCH] internal/radix51: restructure according to
 golang.org/wiki/TargetSpecific

---
 internal/radix51/fe.go                        |  17 +-
 .../radix51/{fe_mul_amd64.go => fe_amd64.go}  |  11 +-
 .../radix51/{fe_mul_amd64.s => fe_amd64.s}    | 154 +++++++++++++++++-
 internal/radix51/{fe_mul.go => fe_generic.go} |  81 ++++++++-
 internal/radix51/fe_noasm.go                  |  11 ++
 internal/radix51/fe_square.go                 |  82 ----------
 internal/radix51/fe_square_amd64.go           |  16 --
 internal/radix51/fe_square_amd64.s            | 150 -----------------
 internal/radix51/mul.go                       |  18 --
 internal/radix51/mul_bits.go                  |   2 +-
 internal/radix51/mul_compat.go                |   2 +-
 11 files changed, 258 insertions(+), 286 deletions(-)
 rename internal/radix51/{fe_mul_amd64.go => fe_amd64.go} (60%)
 rename internal/radix51/{fe_mul_amd64.s => fe_amd64.s} (53%)
 rename internal/radix51/{fe_mul.go => fe_generic.go} (66%)
 create mode 100644 internal/radix51/fe_noasm.go
 delete mode 100644 internal/radix51/fe_square.go
 delete mode 100644 internal/radix51/fe_square_amd64.go
 delete mode 100644 internal/radix51/fe_square_amd64.s
 delete mode 100644 internal/radix51/mul.go

diff --git a/internal/radix51/fe.go b/internal/radix51/fe.go
index f9dd35b..09f36bc 100644
--- a/internal/radix51/fe.go
+++ b/internal/radix51/fe.go
@@ -3,8 +3,9 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// GF(2^255-19) field arithmetic in radix 2^51 representation. This code is a
-// port of the public domain amd64-51-30k version of ed25519 from SUPERCOP.
+// Package radix51 implements GF(2^255-19) field arithmetic in radix 2^51
+// representation. This code is a port of the public domain amd64-51-30k version
+// of ed25519 from SUPERCOP.
 //
 // The interface works similarly to math/big.Int, and all arguments and
 // receivers are allowed to alias.
@@ -360,3 +361,15 @@ func (v *FieldElement) IsNegative() int {
 func (v *FieldElement) Abs(u *FieldElement) *FieldElement {
 	return v.CondNeg(u, u.IsNegative())
 }
+
+// Mul sets v = x * y and returns v.
+func (v *FieldElement) Mul(x, y *FieldElement) *FieldElement {
+	feMul(v, x, y)
+	return v
+}
+
+// Square sets v = x * x and returns v.
+func (v *FieldElement) Square(x *FieldElement) *FieldElement {
+	feSquare(v, x)
+	return v
+}
diff --git a/internal/radix51/fe_mul_amd64.go b/internal/radix51/fe_amd64.go
similarity index 60%
rename from internal/radix51/fe_mul_amd64.go
rename to internal/radix51/fe_amd64.go
index 53b761c..8327caa 100644
--- a/internal/radix51/fe_mul_amd64.go
+++ b/internal/radix51/fe_amd64.go
@@ -2,15 +2,12 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// +build amd64,!noasm
+// +build amd64,!purego
 
 package radix51
 
-// Mul sets v = x * y and returns v.
-func (v *FieldElement) Mul(x, y *FieldElement) *FieldElement {
-	feMul(v, x, y)
-	return v
-}
-
 //go:noescape
 func feMul(out, a, b *FieldElement)
+
+//go:noescape
+func feSquare(out, x *FieldElement)
diff --git a/internal/radix51/fe_mul_amd64.s b/internal/radix51/fe_amd64.s
similarity index 53%
rename from internal/radix51/fe_mul_amd64.s
rename to internal/radix51/fe_amd64.s
index a4cb3ad..dfc95e6 100644
--- a/internal/radix51/fe_mul_amd64.s
+++ b/internal/radix51/fe_amd64.s
@@ -2,13 +2,14 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// Based on assembly generated by PeachPy. Equivalent to the Go in fe_mul.go,
-// which was originally based on the amd64-51-30k assembly in SUPERCOP.
-
-// +build amd64,!noasm
+// +build amd64,!purego
 
 // func feMul(out, a, b *FieldElement)
 TEXT ·feMul(SB),$0-24
+	// Based on assembly generated by PeachPy. Equivalent to the Go in
+	// feMulGeneric, which was originally based on the amd64-51-30k
+	// assembly in SUPERCOP.
+
 	MOVQ out+0(FP), DI
 	MOVQ a+8(FP), BX
 	MOVQ b+16(FP), CX
@@ -200,3 +201,148 @@ TEXT ·feMul(SB),$0-24
 	MOVQ R12, 24(DI)
 	MOVQ R14, 32(DI)
 	RET
+
+// func feSquare(out, x *FieldElement)
+TEXT ·feSquare(SB),4,$0-16
+    MOVQ out+0(FP), DI
+    MOVQ x+8(FP), SI
+
+    // r0 = x0*x0 + x1*38*x4 + x2*38*x3
+    MOVQ 0(SI), AX
+    MULQ 0(SI)
+    MOVQ AX, CX // r00
+    MOVQ DX, R8 // r01
+
+    MOVQ 8(SI), DX
+    IMUL3Q $38, DX, AX
+    MULQ 32(SI)
+    ADDQ AX, CX
+    ADCQ DX, R8
+
+    MOVQ 16(SI), DX
+    IMUL3Q $38, DX, AX
+    MULQ 24(SI)
+    ADDQ AX, CX
+    ADCQ DX, R8
+
+    // r1 = x0*2*x1 + x2*38*x4 + x3*19*x3
+    MOVQ 0(SI), AX
+    SHLQ $1, AX
+    MULQ 8(SI)
+    MOVQ AX, R9  // r10
+    MOVQ DX, R10 // r11
+
+    MOVQ 16(SI), DX
+    IMUL3Q $38, DX, AX
+    MULQ 32(SI)
+    ADDQ AX, R9
+    ADCQ DX, R10
+
+    MOVQ 24(SI), DX
+    IMUL3Q $19, DX, AX
+    MULQ 24(SI)
+    ADDQ AX, R9
+    ADCQ DX, R10
+
+    // r2 = x0*2*x2 + x1*x1 + x3*38*x4
+    MOVQ 0(SI), AX
+    SHLQ $1, AX
+    MULQ 16(SI)
+    MOVQ AX, R11 // r20
+    MOVQ DX, R12 // r21
+
+    MOVQ 8(SI), AX
+    MULQ 8(SI)
+    ADDQ AX, R11
+    ADCQ DX, R12
+
+    MOVQ 24(SI), DX
+    IMUL3Q $38, DX, AX
+    MULQ 32(SI)
+    ADDQ AX, R11
+    ADCQ DX, R12
+
+    // r3 = x0*2*x3 + x1*2*x2 + x4*19*x4
+    MOVQ 0(SI), AX
+    SHLQ $1, AX
+    MULQ 24(SI)
+    MOVQ AX, R13 // r30
+    MOVQ DX, R14 // r31
+
+    MOVQ 8(SI), AX
+    SHLQ $1, AX
+    MULQ 16(SI)
+    ADDQ AX, R13
+    ADCQ DX, R14
+
+    MOVQ 32(SI), DX
+    IMUL3Q $19, DX, AX
+    MULQ 32(SI)
+    ADDQ AX, R13
+    ADCQ DX, R14
+
+    // r4 = x0*2*x4 + x1*2*x3 + x2*x2
+    MOVQ 0(SI), AX
+    SHLQ $1, AX
+    MULQ 32(SI)
+    MOVQ AX, R15 // r40
+    MOVQ DX, BX  // r41
+
+    MOVQ 8(SI), AX
+    SHLQ $1, AX
+    MULQ 24(SI)
+    ADDQ AX, R15
+    ADCQ DX, BX
+
+    MOVQ 16(SI), AX
+    MULQ 16(SI)
+    ADDQ AX, R15
+    ADCQ DX, BX
+
+    // Reduce
+    MOVQ $2251799813685247, AX // (1<<51) - 1
+    SHLQ $13, CX, R8     // r01 = shld with r00
+    ANDQ AX, CX          // r00 &= mask51
+    SHLQ $13, R9, R10    // r11 = shld with r10
+    ANDQ AX, R9          // r10 &= mask51
+    ADDQ R8, R9          // r10 += r01
+    SHLQ $13, R11, R12   // r21 = shld with r20
+    ANDQ AX, R11         // r20 &= mask51
+    ADDQ R10, R11        // r20 += r11
+    SHLQ $13, R13, R14   // r31 = shld with r30
+    ANDQ AX, R13         // r30 &= mask51
+    ADDQ R12, R13        // r30 += r21
+    SHLQ $13, R15, BX    // r41 = shld with r40
+    ANDQ AX, R15         // r40 &= mask51
+    ADDQ R14, R15        // r40 += r31
+    IMUL3Q $19, BX, DX   // r41 = r41*19
+    ADDQ DX, CX          // r00 += r41
+
+    MOVQ CX, DX          // rdx <-- r00
+    SHRQ $51, DX         // rdx <-- r00 >> 51
+    ADDQ DX, R9          // r10 += r00 >> 51
+    MOVQ R9, DX          // rdx <-- r10
+    SHRQ $51, DX         // rdx <-- r10 >> 51
+    ANDQ AX, CX          // r00 &= mask51
+    ADDQ DX, R11         // r20 += r10 >> 51
+    MOVQ R11, DX         // rdx <-- r20
+    SHRQ $51, DX         // rdx <-- r20 >> 51
+    ANDQ AX, R9          // r10 &= mask51
+    ADDQ DX, R13         // r30 += r20 >> 51
+    MOVQ R13, DX         // rdx <-- r30
+    SHRQ $51, DX         // rdx <-- r30 >> 51
+    ANDQ AX, R11         // r20 &= mask51
+    ADDQ DX, R15         // r40 += r30 >> 51
+    MOVQ R15, DX         // rdx <-- r40
+    SHRQ $51, DX         // rdx <-- r40 >> 51
+    ANDQ AX, R13         // r30 &= mask51
+    IMUL3Q $19, DX, DX   // rdx <-- (r40 >> 51) * 19
+    ADDQ DX, CX          // r00 += (r40 >> 51) *19
+    ANDQ AX, R15         // r40 &= mask51
+
+    MOVQ CX, 0(DI)
+    MOVQ R9, 8(DI)
+    MOVQ R11, 16(DI)
+    MOVQ R13, 24(DI)
+    MOVQ R15, 32(DI)
+    RET
diff --git a/internal/radix51/fe_mul.go b/internal/radix51/fe_generic.go
similarity index 66%
rename from internal/radix51/fe_mul.go
rename to internal/radix51/fe_generic.go
index 4296409..601d9e7 100644
--- a/internal/radix51/fe_mul.go
+++ b/internal/radix51/fe_generic.go
@@ -2,12 +2,9 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// +build !amd64 noasm
-
 package radix51
 
-// Mul sets v = x * y and returns v.
-func (v *FieldElement) Mul(x, y *FieldElement) *FieldElement {
+func feMulGeneric(v, x, y *FieldElement) {
 	x0 := x[0]
 	x1 := x[1]
 	x2 := x[2]
@@ -104,5 +101,79 @@ func (v *FieldElement) Mul(x, y *FieldElement) *FieldElement {
 	// finally from r_4 to r_0 . Each of these carries is done as one copy, one
 	// right shift by 51, one logical and with 2^51 − 1, and one addition.
 	*v = FieldElement{r00, r10, r20, r30, r40}
-	return v.carryPropagate1().carryPropagate2()
+	v.carryPropagate1().carryPropagate2()
+}
+
+func feSquareGeneric(v, x *FieldElement) {
+	// Squaring needs only 15 mul instructions. Some inputs are multiplied by 2;
+	// this is combined with multiplication by 19 where possible. The coefficient
+	// reduction after squaring is the same as for multiplication.
+
+	x0 := x[0]
+	x1 := x[1]
+	x2 := x[2]
+	x3 := x[3]
+	x4 := x[4]
+
+	x0_2 := x0 << 1
+	x1_2 := x1 << 1
+
+	x1_38 := x1 * 38
+	x2_38 := x2 * 38
+	x3_38 := x3 * 38
+
+	x3_19 := x3 * 19
+	x4_19 := x4 * 19
+
+	// r0 = x0*x0 + x1*38*x4 + x2*38*x3
+	r00, r01 := madd64(0, 0, x0, x0)
+	r00, r01 = madd64(r00, r01, x1_38, x4)
+	r00, r01 = madd64(r00, r01, x2_38, x3)
+
+	// r1 = x0*2*x1 + x2*38*x4 + x3*19*x3
+	r10, r11 := madd64(0, 0, x0_2, x1)
+	r10, r11 = madd64(r10, r11, x2_38, x4)
+	r10, r11 = madd64(r10, r11, x3_19, x3)
+
+	// r2 = x0*2*x2 + x1*x1 + x3*38*x4
+	r20, r21 := madd64(0, 0, x0_2, x2)
+	r20, r21 = madd64(r20, r21, x1, x1)
+	r20, r21 = madd64(r20, r21, x3_38, x4)
+
+	// r3 = x0*2*x3 + x1*2*x2 + x4*19*x4
+	r30, r31 := madd64(0, 0, x0_2, x3)
+	r30, r31 = madd64(r30, r31, x1_2, x2)
+	r30, r31 = madd64(r30, r31, x4_19, x4)
+
+	// r4 = x0*2*x4 + x1*2*x3 + x2*x2
+	r40, r41 := madd64(0, 0, x0_2, x4)
+	r40, r41 = madd64(r40, r41, x1_2, x3)
+	r40, r41 = madd64(r40, r41, x2, x2)
+
+	// Same reduction
+
+	r01 = (r01 << 13) | (r00 >> 51)
+	r00 &= maskLow51Bits
+
+	r11 = (r11 << 13) | (r10 >> 51)
+	r10 &= maskLow51Bits
+	r10 += r01
+
+	r21 = (r21 << 13) | (r20 >> 51)
+	r20 &= maskLow51Bits
+	r20 += r11
+
+	r31 = (r31 << 13) | (r30 >> 51)
+	r30 &= maskLow51Bits
+	r30 += r21
+
+	r41 = (r41 << 13) | (r40 >> 51)
+	r40 &= maskLow51Bits
+	r40 += r31
+
+	r41 *= 19
+	r00 += r41
+
+	*v = FieldElement{r00, r10, r20, r30, r40}
+	v.carryPropagate1().carryPropagate2()
 }
diff --git a/internal/radix51/fe_noasm.go b/internal/radix51/fe_noasm.go
new file mode 100644
index 0000000..39cfa36
--- /dev/null
+++ b/internal/radix51/fe_noasm.go
@@ -0,0 +1,11 @@
+// Copyright (c) 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !amd64 purego
+
+package radix51
+
+func feMul(v, x, y *FieldElement) { feMulGeneric(v, x, y) }
+
+func feSquare(v, x *FieldElement) { feSquareGeneric(v, x) }
diff --git a/internal/radix51/fe_square.go b/internal/radix51/fe_square.go
deleted file mode 100644
index d795bd5..0000000
--- a/internal/radix51/fe_square.go
+++ /dev/null
@@ -1,82 +0,0 @@
-// Copyright (c) 2017 George Tankersley. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// +build !amd64 noasm
-
-package radix51
-
-// Square sets v = x * x and returns v.
-func (v *FieldElement) Square(x *FieldElement) *FieldElement {
-	// Squaring needs only 15 mul instructions. Some inputs are multiplied by 2;
-	// this is combined with multiplication by 19 where possible. The coefficient
-	// reduction after squaring is the same as for multiplication.
-
-	x0 := x[0]
-	x1 := x[1]
-	x2 := x[2]
-	x3 := x[3]
-	x4 := x[4]
-
-	x0_2 := x0 << 1
-	x1_2 := x1 << 1
-
-	x1_38 := x1 * 38
-	x2_38 := x2 * 38
-	x3_38 := x3 * 38
-
-	x3_19 := x3 * 19
-	x4_19 := x4 * 19
-
-	// r0 = x0*x0 + x1*38*x4 + x2*38*x3
-	r00, r01 := madd64(0, 0, x0, x0)
-	r00, r01 = madd64(r00, r01, x1_38, x4)
-	r00, r01 = madd64(r00, r01, x2_38, x3)
-
-	// r1 = x0*2*x1 + x2*38*x4 + x3*19*x3
-	r10, r11 := madd64(0, 0, x0_2, x1)
-	r10, r11 = madd64(r10, r11, x2_38, x4)
-	r10, r11 = madd64(r10, r11, x3_19, x3)
-
-	// r2 = x0*2*x2 + x1*x1 + x3*38*x4
-	r20, r21 := madd64(0, 0, x0_2, x2)
-	r20, r21 = madd64(r20, r21, x1, x1)
-	r20, r21 = madd64(r20, r21, x3_38, x4)
-
-	// r3 = x0*2*x3 + x1*2*x2 + x4*19*x4
-	r30, r31 := madd64(0, 0, x0_2, x3)
-	r30, r31 = madd64(r30, r31, x1_2, x2)
-	r30, r31 = madd64(r30, r31, x4_19, x4)
-
-	// r4 = x0*2*x4 + x1*2*x3 + x2*x2
-	r40, r41 := madd64(0, 0, x0_2, x4)
-	r40, r41 = madd64(r40, r41, x1_2, x3)
-	r40, r41 = madd64(r40, r41, x2, x2)
-
-	// Same reduction
-
-	r01 = (r01 << 13) | (r00 >> 51)
-	r00 &= maskLow51Bits
-
-	r11 = (r11 << 13) | (r10 >> 51)
-	r10 &= maskLow51Bits
-	r10 += r01
-
-	r21 = (r21 << 13) | (r20 >> 51)
-	r20 &= maskLow51Bits
-	r20 += r11
-
-	r31 = (r31 << 13) | (r30 >> 51)
-	r30 &= maskLow51Bits
-	r30 += r21
-
-	r41 = (r41 << 13) | (r40 >> 51)
-	r40 &= maskLow51Bits
-	r40 += r31
-
-	r41 *= 19
-	r00 += r41
-
-	*v = FieldElement{r00, r10, r20, r30, r40}
-	return v.carryPropagate1().carryPropagate2()
-}
diff --git a/internal/radix51/fe_square_amd64.go b/internal/radix51/fe_square_amd64.go
deleted file mode 100644
index afa1295..0000000
--- a/internal/radix51/fe_square_amd64.go
+++ /dev/null
@@ -1,16 +0,0 @@
-// Copyright (c) 2017 George Tankersley. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// +build amd64,!noasm
-
-package radix51
-
-// Square sets v = x * x and returns v.
-func (v *FieldElement) Square(x *FieldElement) *FieldElement {
-	feSquare(v, x)
-	return v
-}
-
-//go:noescape
-func feSquare(out, x *FieldElement)
diff --git a/internal/radix51/fe_square_amd64.s b/internal/radix51/fe_square_amd64.s
deleted file mode 100644
index 953c7bb..0000000
--- a/internal/radix51/fe_square_amd64.s
+++ /dev/null
@@ -1,150 +0,0 @@
-// Copyright (c) 2017 George Tankersley. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// +build amd64,!noasm
-
-// func feSquare(out, x *FieldElement)
-TEXT ·feSquare(SB),4,$0-16
-    MOVQ out+0(FP), DI
-    MOVQ x+8(FP), SI
-
-    // r0 = x0*x0 + x1*38*x4 + x2*38*x3
-    MOVQ 0(SI), AX
-    MULQ 0(SI)
-    MOVQ AX, CX // r00
-    MOVQ DX, R8 // r01
-
-    MOVQ 8(SI), DX
-    IMUL3Q $38, DX, AX
-    MULQ 32(SI)
-    ADDQ AX, CX
-    ADCQ DX, R8
-
-    MOVQ 16(SI), DX
-    IMUL3Q $38, DX, AX
-    MULQ 24(SI)
-    ADDQ AX, CX
-    ADCQ DX, R8
-
-    // r1 = x0*2*x1 + x2*38*x4 + x3*19*x3
-    MOVQ 0(SI), AX
-    SHLQ $1, AX
-    MULQ 8(SI)
-    MOVQ AX, R9  // r10
-    MOVQ DX, R10 // r11
-
-    MOVQ 16(SI), DX
-    IMUL3Q $38, DX, AX
-    MULQ 32(SI)
-    ADDQ AX, R9
-    ADCQ DX, R10
-
-    MOVQ 24(SI), DX
-    IMUL3Q $19, DX, AX
-    MULQ 24(SI)
-    ADDQ AX, R9
-    ADCQ DX, R10
-
-    // r2 = x0*2*x2 + x1*x1 + x3*38*x4
-    MOVQ 0(SI), AX
-    SHLQ $1, AX
-    MULQ 16(SI)
-    MOVQ AX, R11 // r20
-    MOVQ DX, R12 // r21
-
-    MOVQ 8(SI), AX
-    MULQ 8(SI)
-    ADDQ AX, R11
-    ADCQ DX, R12
-
-    MOVQ 24(SI), DX
-    IMUL3Q $38, DX, AX
-    MULQ 32(SI)
-    ADDQ AX, R11
-    ADCQ DX, R12
-
-    // r3 = x0*2*x3 + x1*2*x2 + x4*19*x4
-    MOVQ 0(SI), AX
-    SHLQ $1, AX
-    MULQ 24(SI)
-    MOVQ AX, R13 // r30
-    MOVQ DX, R14 // r31
-
-    MOVQ 8(SI), AX
-    SHLQ $1, AX
-    MULQ 16(SI)
-    ADDQ AX, R13
-    ADCQ DX, R14
-
-    MOVQ 32(SI), DX
-    IMUL3Q $19, DX, AX
-    MULQ 32(SI)
-    ADDQ AX, R13
-    ADCQ DX, R14
-
-    // r4 = x0*2*x4 + x1*2*x3 + x2*x2
-    MOVQ 0(SI), AX
-    SHLQ $1, AX
-    MULQ 32(SI)
-    MOVQ AX, R15 // r40
-    MOVQ DX, BX  // r41
-
-    MOVQ 8(SI), AX
-    SHLQ $1, AX
-    MULQ 24(SI)
-    ADDQ AX, R15
-    ADCQ DX, BX
-
-    MOVQ 16(SI), AX
-    MULQ 16(SI)
-    ADDQ AX, R15
-    ADCQ DX, BX
-
-    // Reduce
-    MOVQ $2251799813685247, AX // (1<<51) - 1
-    SHLQ $13, CX, R8     // r01 = shld with r00
-    ANDQ AX, CX          // r00 &= mask51
-    SHLQ $13, R9, R10    // r11 = shld with r10
-    ANDQ AX, R9          // r10 &= mask51
-    ADDQ R8, R9          // r10 += r01
-    SHLQ $13, R11, R12   // r21 = shld with r20
-    ANDQ AX, R11         // r20 &= mask51
-    ADDQ R10, R11        // r20 += r11
-    SHLQ $13, R13, R14   // r31 = shld with r30
-    ANDQ AX, R13         // r30 &= mask51
-    ADDQ R12, R13        // r30 += r21
-    SHLQ $13, R15, BX    // r41 = shld with r40
-    ANDQ AX, R15         // r40 &= mask51
-    ADDQ R14, R15        // r40 += r31
-    IMUL3Q $19, BX, DX   // r41 = r41*19
-    ADDQ DX, CX          // r00 += r41
-
-    MOVQ CX, DX          // rdx <-- r00
-    SHRQ $51, DX         // rdx <-- r00 >> 51
-    ADDQ DX, R9          // r10 += r00 >> 51
-    MOVQ R9, DX          // rdx <-- r10
-    SHRQ $51, DX         // rdx <-- r10 >> 51
-    ANDQ AX, CX          // r00 &= mask51
-    ADDQ DX, R11         // r20 += r10 >> 51
-    MOVQ R11, DX         // rdx <-- r20
-    SHRQ $51, DX         // rdx <-- r20 >> 51
-    ANDQ AX, R9          // r10 &= mask51
-    ADDQ DX, R13         // r30 += r20 >> 51
-    MOVQ R13, DX         // rdx <-- r30
-    SHRQ $51, DX         // rdx <-- r30 >> 51
-    ANDQ AX, R11         // r20 &= mask51
-    ADDQ DX, R15         // r40 += r30 >> 51
-    MOVQ R15, DX         // rdx <-- r40
-    SHRQ $51, DX         // rdx <-- r40 >> 51
-    ANDQ AX, R13         // r30 &= mask51
-    IMUL3Q $19, DX, DX   // rdx <-- (r40 >> 51) * 19
-    ADDQ DX, CX          // r00 += (r40 >> 51) *19
-    ANDQ AX, R15         // r40 &= mask51
-
-    MOVQ CX, 0(DI)
-    MOVQ R9, 8(DI)
-    MOVQ R11, 16(DI)
-    MOVQ R13, 24(DI)
-    MOVQ R15, 32(DI)
-    RET
diff --git a/internal/radix51/mul.go b/internal/radix51/mul.go
deleted file mode 100644
index c196d9d..0000000
--- a/internal/radix51/mul.go
+++ /dev/null
@@ -1,18 +0,0 @@
-// Copyright (c) 2017 George Tankersley. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package radix51
-
-import "unsafe"
-
-// mul64x64 multiples two 64-bit numbers and adds them to two accumulators.
-// This function is written to ensure it inlines. I am so sorry.
-func mul64x64(lo, hi, a, b uint64) (ol uint64, oh uint64) {
-	t1 := (a>>32)*(b&0xFFFFFFFF) + ((a & 0xFFFFFFFF) * (b & 0xFFFFFFFF) >> 32)
-	t2 := (a&0xFFFFFFFF)*(b>>32) + (t1 & 0xFFFFFFFF)
-	ol = (a * b) + lo
-	cmp := ol < lo
-	oh = hi + (a>>32)*(b>>32) + t1>>32 + t2>>32 + uint64(*(*byte)(unsafe.Pointer(&cmp)))
-	return
-}
diff --git a/internal/radix51/mul_bits.go b/internal/radix51/mul_bits.go
index 0965d03..bf10590 100644
--- a/internal/radix51/mul_bits.go
+++ b/internal/radix51/mul_bits.go
@@ -2,7 +2,7 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// +build go1.12
+// +build go1.13
 
 package radix51
 
diff --git a/internal/radix51/mul_compat.go b/internal/radix51/mul_compat.go
index 3ffb93b..59d5b75 100644
--- a/internal/radix51/mul_compat.go
+++ b/internal/radix51/mul_compat.go
@@ -2,7 +2,7 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// +build !go1.12
+// +build !go1.13
 
 package radix51