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95 lines
2.0 KiB
Go
95 lines
2.0 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 *SM2P256Element) Invert(x *SM2P256Element) *SM2P256Element {
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// Inversion is implemented as exponentiation with exponent p − 2.
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// The sequence of 14 multiplications and 255 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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// _1111110 = 2*_111111
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// _1111111 = 1 + _1111110
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// x12 = _1111110 << 5 + _111111
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// x24 = x12 << 12 + x12
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// x31 = x24 << 7 + _1111111
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// i39 = x31 << 2
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// i68 = i39 << 29
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// x62 = x31 + i68
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// i71 = i68 << 2
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// x64 = i39 + i71 + _11
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// i265 = ((i71 << 32 + x64) << 64 + x64) << 94
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// return (x62 + i265) << 2 + 1
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//
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var z = new(SM2P256Element).Set(e)
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var t0 = new(SM2P256Element)
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var t1 = new(SM2P256Element)
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var t2 = new(SM2P256Element)
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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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z.Mul(x, t2)
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for s := 0; s < 5; s++ {
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t2.Square(t2)
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}
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t1.Mul(t1, t2)
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t2.Square(t1)
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for s := 1; s < 12; 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 < 7; s++ {
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t1.Square(t1)
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}
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z.Mul(z, t1)
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t2.Square(z)
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for s := 1; s < 2; s++ {
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t2.Square(t2)
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}
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t1.Square(t2)
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for s := 1; s < 29; s++ {
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t1.Square(t1)
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}
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z.Mul(z, t1)
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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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t2.Mul(t2, t1)
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t0.Mul(t0, t2)
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for s := 0; s < 32; s++ {
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t1.Square(t1)
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}
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t1.Mul(t0, t1)
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for s := 0; s < 64; 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 < 94; 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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