88 lines
1.8 KiB
Go
88 lines
1.8 KiB
Go
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// Copyright 2021 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Code generated by addchain. DO NOT EDIT.
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package fiat
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// Invert sets e = 1/x, and returns e.
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//
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// If x == 0, Invert returns e = 0.
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func (e *P224Element) Invert(x *P224Element) *P224Element {
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// Inversion is implemented as exponentiation with exponent p − 2.
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// The sequence of 11 multiplications and 223 squarings is derived from the
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// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
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//
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// _10 = 2*1
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// _11 = 1 + _10
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// _110 = 2*_11
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// _111 = 1 + _110
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// _111000 = _111 << 3
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// _111111 = _111 + _111000
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// x12 = _111111 << 6 + _111111
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// x14 = x12 << 2 + _11
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// x17 = x14 << 3 + _111
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// x31 = x17 << 14 + x14
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// x48 = x31 << 17 + x17
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// x96 = x48 << 48 + x48
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// x127 = x96 << 31 + x31
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// return x127 << 97 + x96
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//
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var z = new(P224Element).Set(e)
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var t0 = new(P224Element)
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var t1 = new(P224Element)
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var t2 = new(P224Element)
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z.Square(x)
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t0.Mul(x, z)
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z.Square(t0)
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z.Mul(x, z)
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t1.Square(z)
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for s := 1; s < 3; s++ {
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t1.Square(t1)
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}
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t1.Mul(z, t1)
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t2.Square(t1)
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for s := 1; s < 6; s++ {
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t2.Square(t2)
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}
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t1.Mul(t1, t2)
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for s := 0; s < 2; s++ {
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t1.Square(t1)
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}
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t0.Mul(t0, t1)
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t1.Square(t0)
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for s := 1; s < 3; s++ {
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t1.Square(t1)
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}
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z.Mul(z, t1)
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t1.Square(z)
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for s := 1; s < 14; s++ {
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t1.Square(t1)
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}
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t0.Mul(t0, t1)
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t1.Square(t0)
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for s := 1; s < 17; s++ {
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t1.Square(t1)
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}
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z.Mul(z, t1)
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t1.Square(z)
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for s := 1; s < 48; s++ {
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t1.Square(t1)
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}
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z.Mul(z, t1)
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t1.Square(z)
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for s := 1; s < 31; s++ {
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t1.Square(t1)
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}
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t0.Mul(t0, t1)
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for s := 0; s < 97; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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return e.Set(z)
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}
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