src/crypto/internal/nistec/fiat/p256_invert.go

// Copyright 2021 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.

// Code generated by addchain. DO NOT EDIT.

package fiat

// Invert sets e = 1/x, and returns e.
//
// If x == 0, Invert returns e = 0.
func (e *P256Element) Invert(x *P256Element) *P256Element {
	// Inversion is implemented as exponentiation with exponent p − 2.
	// The sequence of 12 multiplications and 255 squarings is derived from the
	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
	//
	//	_10     = 2*1
	//	_11     = 1 + _10
	//	_110    = 2*_11
	//	_111    = 1 + _110
	//	_111000 = _111 << 3
	//	_111111 = _111 + _111000
	//	x12     = _111111 << 6 + _111111
	//	x15     = x12 << 3 + _111
	//	x16     = 2*x15 + 1
	//	x32     = x16 << 16 + x16
	//	i53     = x32 << 15
	//	x47     = x15 + i53
	//	i263    = ((i53 << 17 + 1) << 143 + x47) << 47
	//	return    (x47 + i263) << 2 + 1
	//

	var z = new(P256Element).Set(e)
	var t0 = new(P256Element)
	var t1 = new(P256Element)

	z.Square(x)
	z.Mul(x, z)
	z.Square(z)
	z.Mul(x, z)
	t0.Square(z)
	for s := 1; s < 3; s++ {
		t0.Square(t0)
	}
	t0.Mul(z, t0)
	t1.Square(t0)
	for s := 1; s < 6; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 3; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	t0.Square(z)
	t0.Mul(x, t0)
	t1.Square(t0)
	for s := 1; s < 16; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 15; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	for s := 0; s < 17; s++ {
		t0.Square(t0)
	}
	t0.Mul(x, t0)
	for s := 0; s < 143; s++ {
		t0.Square(t0)
	}
	t0.Mul(z, t0)
	for s := 0; s < 47; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	for s := 0; s < 2; s++ {
		z.Square(z)
	}
	z.Mul(x, z)

	return e.Set(z)
}