p224_invert.mx raw

   1  // Copyright 2021 The Go Authors. All rights reserved.
   2  // Use of this source code is governed by a BSD-style
   3  // license that can be found in the LICENSE file.
   4  
   5  // Code generated by addchain. DO NOT EDIT.
   6  
   7  package fiat
   8  
   9  // Invert sets e = 1/x, and returns e.
  10  //
  11  // If x == 0, Invert returns e = 0.
  12  func (e *P224Element) Invert(x *P224Element) *P224Element {
  13  	// Inversion is implemented as exponentiation with exponent p − 2.
  14  	// The sequence of 11 multiplications and 223 squarings is derived from the
  15  	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
  16  	//
  17  	//	_10     = 2*1
  18  	//	_11     = 1 + _10
  19  	//	_110    = 2*_11
  20  	//	_111    = 1 + _110
  21  	//	_111000 = _111 << 3
  22  	//	_111111 = _111 + _111000
  23  	//	x12     = _111111 << 6 + _111111
  24  	//	x14     = x12 << 2 + _11
  25  	//	x17     = x14 << 3 + _111
  26  	//	x31     = x17 << 14 + x14
  27  	//	x48     = x31 << 17 + x17
  28  	//	x96     = x48 << 48 + x48
  29  	//	x127    = x96 << 31 + x31
  30  	//	return    x127 << 97 + x96
  31  	//
  32  
  33  	var z = (&P224Element{}).Set(e)
  34  	var t0 = &P224Element{}
  35  	var t1 = &P224Element{}
  36  	var t2 = &P224Element{}
  37  
  38  	z.Square(x)
  39  	t0.Mul(x, z)
  40  	z.Square(t0)
  41  	z.Mul(x, z)
  42  	t1.Square(z)
  43  	for s := 1; s < 3; s++ {
  44  		t1.Square(t1)
  45  	}
  46  	t1.Mul(z, t1)
  47  	t2.Square(t1)
  48  	for s := 1; s < 6; s++ {
  49  		t2.Square(t2)
  50  	}
  51  	t1.Mul(t1, t2)
  52  	for s := 0; s < 2; s++ {
  53  		t1.Square(t1)
  54  	}
  55  	t0.Mul(t0, t1)
  56  	t1.Square(t0)
  57  	for s := 1; s < 3; s++ {
  58  		t1.Square(t1)
  59  	}
  60  	z.Mul(z, t1)
  61  	t1.Square(z)
  62  	for s := 1; s < 14; s++ {
  63  		t1.Square(t1)
  64  	}
  65  	t0.Mul(t0, t1)
  66  	t1.Square(t0)
  67  	for s := 1; s < 17; s++ {
  68  		t1.Square(t1)
  69  	}
  70  	z.Mul(z, t1)
  71  	t1.Square(z)
  72  	for s := 1; s < 48; s++ {
  73  		t1.Square(t1)
  74  	}
  75  	z.Mul(z, t1)
  76  	t1.Square(z)
  77  	for s := 1; s < 31; s++ {
  78  		t1.Square(t1)
  79  	}
  80  	t0.Mul(t0, t1)
  81  	for s := 0; s < 97; s++ {
  82  		t0.Square(t0)
  83  	}
  84  	z.Mul(z, t0)
  85  
  86  	return e.Set(z)
  87  }
  88