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90 lines
1.8 KiB
Go
90 lines
1.8 KiB
Go
// 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 *P521Element) Invert(x *P521Element) *P521Element {
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// Inversion is implemented as exponentiation with exponent p − 2.
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// The sequence of 13 multiplications and 520 squarings is derived from the
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// following addition chain generated with github.com/mmcloughlin/addchain v0.3.0.
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//
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// _10 = 2*1
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// _11 = 1 + _10
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// _1100 = _11 << 2
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// _1111 = _11 + _1100
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// _11110000 = _1111 << 4
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// _11111111 = _1111 + _11110000
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// x16 = _11111111 << 8 + _11111111
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// x32 = x16 << 16 + x16
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// x64 = x32 << 32 + x32
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// x65 = 2*x64 + 1
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// x129 = x65 << 64 + x64
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// x130 = 2*x129 + 1
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// x259 = x130 << 129 + x129
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// x260 = 2*x259 + 1
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// x519 = x260 << 259 + x259
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// return x519 << 2 + 1
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//
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var z = new(P521Element).Set(e)
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var t0 = new(P521Element)
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z.Square(x)
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z.Mul(x, z)
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t0.Square(z)
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for s := 1; s < 2; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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for s := 1; s < 4; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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for s := 1; s < 8; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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for s := 1; s < 16; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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for s := 1; s < 32; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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t0.Mul(x, t0)
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for s := 0; s < 64; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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t0.Mul(x, t0)
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for s := 0; s < 129; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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t0.Square(z)
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t0.Mul(x, t0)
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for s := 0; s < 259; s++ {
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t0.Square(t0)
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}
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z.Mul(z, t0)
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for s := 0; s < 2; s++ {
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z.Square(z)
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}
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z.Mul(x, z)
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return e.Set(z)
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}
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