gmsm/internal/sm2ec/fiat/sm2p256_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 *SM2P256Element) Invert(x *SM2P256Element) *SM2P256Element {
	// Inversion is implemented as exponentiation with exponent p − 2.
	// The sequence of 14 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
	//	_1111110 = 2*_111111
	//	_1111111 = 1 + _1111110
	//	x12      = _1111110 << 5 + _111111
	//	x24      = x12 << 12 + x12
	//	x31      = x24 << 7 + _1111111
	//	i39      = x31 << 2
	//	i68      = i39 << 29
	//	x62      = x31 + i68
	//	i71      = i68 << 2
	//	x64      = i39 + i71 + _11
	//	i265     = ((i71 << 32 + x64) << 64 + x64) << 94
	//	return     (x62 + i265) << 2 + 1
	//
	var z = new(SM2P256Element).Set(e)
	var t0 = new(SM2P256Element)
	var t1 = new(SM2P256Element)
	var t2 = new(SM2P256Element)

	z.Square(x)
	t0.Mul(x, z)
	z.Square(t0)
	z.Mul(x, z)
	t1.Square(z)
	for s := 1; s < 3; s++ {
		t1.Square(t1)
	}
	t1.Mul(z, t1)
	t2.Square(t1)
	z.Mul(x, t2)
	for s := 0; s < 5; s++ {
		t2.Square(t2)
	}
	t1.Mul(t1, t2)
	t2.Square(t1)
	for s := 1; s < 12; s++ {
		t2.Square(t2)
	}
	t1.Mul(t1, t2)
	for s := 0; s < 7; s++ {
		t1.Square(t1)
	}
	z.Mul(z, t1)
	t2.Square(z)
	for s := 1; s < 2; s++ {
		t2.Square(t2)
	}
	t1.Square(t2)
	for s := 1; s < 29; s++ {
		t1.Square(t1)
	}
	z.Mul(z, t1)
	for s := 0; s < 2; s++ {
		t1.Square(t1)
	}
	t2.Mul(t2, t1)
	t0.Mul(t0, t2)
	for s := 0; s < 32; s++ {
		t1.Square(t1)
	}
	t1.Mul(t0, t1)
	for s := 0; s < 64; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 94; 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)
}