p256_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 *P256Element) Invert(x *P256Element) *P256Element {
    13  	// Inversion is implemented as exponentiation with exponent p − 2.
    14  	// The sequence of 12 multiplications and 255 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  	//	x15     = x12 << 3 + _111
    25  	//	x16     = 2*x15 + 1
    26  	//	x32     = x16 << 16 + x16
    27  	//	i53     = x32 << 15
    28  	//	x47     = x15 + i53
    29  	//	i263    = ((i53 << 17 + 1) << 143 + x47) << 47
    30  	//	return    (x47 + i263) << 2 + 1
    31  	//
    32  
    33  	var z = new(P256Element).Set(e)
    34  	var t0 = new(P256Element)
    35  	var t1 = new(P256Element)
    36  
    37  	z.Square(x)
    38  	z.Mul(x, z)
    39  	z.Square(z)
    40  	z.Mul(x, z)
    41  	t0.Square(z)
    42  	for s := 1; s < 3; s++ {
    43  		t0.Square(t0)
    44  	}
    45  	t0.Mul(z, t0)
    46  	t1.Square(t0)
    47  	for s := 1; s < 6; s++ {
    48  		t1.Square(t1)
    49  	}
    50  	t0.Mul(t0, t1)
    51  	for s := 0; s < 3; s++ {
    52  		t0.Square(t0)
    53  	}
    54  	z.Mul(z, t0)
    55  	t0.Square(z)
    56  	t0.Mul(x, t0)
    57  	t1.Square(t0)
    58  	for s := 1; s < 16; s++ {
    59  		t1.Square(t1)
    60  	}
    61  	t0.Mul(t0, t1)
    62  	for s := 0; s < 15; s++ {
    63  		t0.Square(t0)
    64  	}
    65  	z.Mul(z, t0)
    66  	for s := 0; s < 17; s++ {
    67  		t0.Square(t0)
    68  	}
    69  	t0.Mul(x, t0)
    70  	for s := 0; s < 143; s++ {
    71  		t0.Square(t0)
    72  	}
    73  	t0.Mul(z, t0)
    74  	for s := 0; s < 47; s++ {
    75  		t0.Square(t0)
    76  	}
    77  	z.Mul(z, t0)
    78  	for s := 0; s < 2; s++ {
    79  		z.Square(z)
    80  	}
    81  	z.Mul(x, z)
    82  
    83  	return e.Set(z)
    84  }
    85
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