p384_invert.go

     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 *P384Element) Invert(x *P384Element) *P384Element {
    13  	// Inversion is implemented as exponentiation with exponent p − 2.
    14  	// The sequence of 15 multiplications and 383 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  	//	x24     = x12 << 12 + x12
    25  	//	x30     = x24 << 6 + _111111
    26  	//	x31     = 2*x30 + 1
    27  	//	x32     = 2*x31 + 1
    28  	//	x63     = x32 << 31 + x31
    29  	//	x126    = x63 << 63 + x63
    30  	//	x252    = x126 << 126 + x126
    31  	//	x255    = x252 << 3 + _111
    32  	//	i397    = ((x255 << 33 + x32) << 94 + x30) << 2
    33  	//	return    1 + i397
    34  	//
    35  
    36  	var z = new(P384Element).Set(e)
    37  	var t0 = new(P384Element)
    38  	var t1 = new(P384Element)
    39  	var t2 = new(P384Element)
    40  	var t3 = new(P384Element)
    41  
    42  	z.Square(x)
    43  	z.Mul(x, z)
    44  	z.Square(z)
    45  	t1.Mul(x, z)
    46  	z.Square(t1)
    47  	for s := 1; s < 3; s++ {
    48  		z.Square(z)
    49  	}
    50  	z.Mul(t1, z)
    51  	t0.Square(z)
    52  	for s := 1; s < 6; s++ {
    53  		t0.Square(t0)
    54  	}
    55  	t0.Mul(z, t0)
    56  	t2.Square(t0)
    57  	for s := 1; s < 12; s++ {
    58  		t2.Square(t2)
    59  	}
    60  	t0.Mul(t0, t2)
    61  	for s := 0; s < 6; s++ {
    62  		t0.Square(t0)
    63  	}
    64  	z.Mul(z, t0)
    65  	t0.Square(z)
    66  	t2.Mul(x, t0)
    67  	t0.Square(t2)
    68  	t0.Mul(x, t0)
    69  	t3.Square(t0)
    70  	for s := 1; s < 31; s++ {
    71  		t3.Square(t3)
    72  	}
    73  	t2.Mul(t2, t3)
    74  	t3.Square(t2)
    75  	for s := 1; s < 63; s++ {
    76  		t3.Square(t3)
    77  	}
    78  	t2.Mul(t2, t3)
    79  	t3.Square(t2)
    80  	for s := 1; s < 126; s++ {
    81  		t3.Square(t3)
    82  	}
    83  	t2.Mul(t2, t3)
    84  	for s := 0; s < 3; s++ {
    85  		t2.Square(t2)
    86  	}
    87  	t1.Mul(t1, t2)
    88  	for s := 0; s < 33; s++ {
    89  		t1.Square(t1)
    90  	}
    91  	t0.Mul(t0, t1)
    92  	for s := 0; s < 94; s++ {
    93  		t0.Square(t0)
    94  	}
    95  	z.Mul(z, t0)
    96  	for s := 0; s < 2; s++ {
    97  		z.Square(z)
    98  	}
    99  	z.Mul(x, z)
   100  
   101  	return e.Set(z)
   102  }
   103
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