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 7package fiat 8 9// Invert sets e = 1/x, and returns e. 10// 11// If x == 0, Invert returns e = 0. 12func (e *P521Element) Invert(x *P521Element) *P521Element { 13 // Inversion is implemented as exponentiation with exponent p − 2. 14 // The sequence of 13 multiplications and 520 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 // _1100 = _11 << 2 20 // _1111 = _11 + _1100 21 // _11110000 = _1111 << 4 22 // _11111111 = _1111 + _11110000 23 // x16 = _11111111 << 8 + _11111111 24 // x32 = x16 << 16 + x16 25 // x64 = x32 << 32 + x32 26 // x65 = 2*x64 + 1 27 // x129 = x65 << 64 + x64 28 // x130 = 2*x129 + 1 29 // x259 = x130 << 129 + x129 30 // x260 = 2*x259 + 1 31 // x519 = x260 << 259 + x259 32 // return x519 << 2 + 1 33 // 34 35 var z = new(P521Element).Set(e) 36 var t0 = new(P521Element) 37 38 z.Square(x) 39 z.Mul(x, z) 40 t0.Square(z) 41 for s := 1; s < 2; s++ { 42 t0.Square(t0) 43 } 44 z.Mul(z, t0) 45 t0.Square(z) 46 for s := 1; s < 4; s++ { 47 t0.Square(t0) 48 } 49 z.Mul(z, t0) 50 t0.Square(z) 51 for s := 1; s < 8; s++ { 52 t0.Square(t0) 53 } 54 z.Mul(z, t0) 55 t0.Square(z) 56 for s := 1; s < 16; s++ { 57 t0.Square(t0) 58 } 59 z.Mul(z, t0) 60 t0.Square(z) 61 for s := 1; s < 32; s++ { 62 t0.Square(t0) 63 } 64 z.Mul(z, t0) 65 t0.Square(z) 66 t0.Mul(x, t0) 67 for s := 0; s < 64; s++ { 68 t0.Square(t0) 69 } 70 z.Mul(z, t0) 71 t0.Square(z) 72 t0.Mul(x, t0) 73 for s := 0; s < 129; s++ { 74 t0.Square(t0) 75 } 76 z.Mul(z, t0) 77 t0.Square(z) 78 t0.Mul(x, t0) 79 for s := 0; s < 259; s++ { 80 t0.Square(t0) 81 } 82 z.Mul(z, t0) 83 for s := 0; s < 2; s++ { 84 z.Square(z) 85 } 86 z.Mul(x, z) 87 88 return e.Set(z) 89} 90