element_exp.go

// Copyright 2020 ConsenSys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// Code generated by consensys/gnark-crypto DO NOT EDIT

package fp

// expBySqrtExp is equivalent to z.Exp(x, 680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaab)
//
// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
func (z *Element) expBySqrtExp(x Element) *Element {
	// addition chain:
	//
	//	_10       = 2*1
	//	_100      = 2*_10
	//	_1000     = 2*_100
	//	_1001     = 1 + _1000
	//	_1011     = _10 + _1001
	//	_1100     = 1 + _1011
	//	_10001    = _1000 + _1001
	//	_10100    = _1000 + _1100
	//	_10110    = _10 + _10100
	//	_11001    = _1000 + _10001
	//	_11010    = 1 + _11001
	//	_101011   = _10001 + _11010
	//	_110100   = _1001 + _101011
	//	_110111   = _1100 + _101011
	//	_1001101  = _10110 + _110111
	//	_1001111  = _10 + _1001101
	//	_1010101  = _1000 + _1001101
	//	_1011101  = _1000 + _1010101
	//	_1100111  = _11010 + _1001101
	//	_1101001  = _10 + _1100111
	//	_1110111  = _11010 + _1011101
	//	_1111011  = _100 + _1110111
	//	_10001001 = _110100 + _1010101
	//	_10010101 = _1100 + _10001001
	//	_10010111 = _10 + _10010101
	//	_10101001 = _10100 + _10010101
	//	_10110001 = _1000 + _10101001
	//	_10111111 = _10110 + _10101001
	//	_11000011 = _100 + _10111111
	//	_11010000 = _10001 + _10111111
	//	_11010111 = _10100 + _11000011
	//	_11100001 = _10001 + _11010000
	//	_11100101 = _100 + _11100001
	//	_11101011 = _10100 + _11010111
	//	_11110101 = _10100 + _11100001
	//	_11111111 = _10100 + _11101011
	//	i58       = ((_10111111 + _11100001) << 8 + _10001) << 11 + _11110101
	//	i86       = ((i58 << 11 + _11100101) << 8 + _11111111) << 7
	//	i108      = ((_1001101 + i86) << 9 + _1101001) << 10 + _10110001
	//	i132      = ((i108 << 7 + _1011101) << 9 + _1111011) << 6
	//	i155      = ((_11001 + i132) << 11 + _1101001) << 9 + _11101011
	//	i183      = ((i155 << 10 + _11010111) << 6 + _11001) << 10
	//	i206      = ((_1110111 + i183) << 9 + _10010111) << 11 + _1001111
	//	i236      = ((i206 << 10 + _11100001) << 9 + _10001001) << 9
	//	i257      = ((_10111111 + i236) << 8 + _1100111) << 10 + _11000011
	//	i285      = ((i257 << 9 + _10010101) << 12 + _1111011) << 5
	//	i306      = ((_1011 + i285) << 11 + _1111011) << 7 + _1001
	//	i338      = ((i306 << 13 + _11110101) << 9 + _10111111) << 8
	//	i360      = ((_11111111 + i338) << 8 + _11101011) << 11 + _10101001
	//	i384      = ((i360 << 8 + _11111111) << 8 + _11111111) << 6
	//	i406      = ((_110111 + i384) << 10 + _11111111) << 9 + _11111111
	//	i432      = ((i406 << 8 + _11111111) << 8 + _11111111) << 8
	//	return      ((_11111111 + i432) << 7 + _1010101) << 7 + _101011
	//
	// Operations: 373 squares 76 multiplies

	// Allocate Temporaries.
	var (
		t0  = new(Element)
		t1  = new(Element)
		t2  = new(Element)
		t3  = new(Element)
		t4  = new(Element)
		t5  = new(Element)
		t6  = new(Element)
		t7  = new(Element)
		t8  = new(Element)
		t9  = new(Element)
		t10 = new(Element)
		t11 = new(Element)
		t12 = new(Element)
		t13 = new(Element)
		t14 = new(Element)
		t15 = new(Element)
		t16 = new(Element)
		t17 = new(Element)
		t18 = new(Element)
		t19 = new(Element)
		t20 = new(Element)
		t21 = new(Element)
		t22 = new(Element)
		t23 = new(Element)
		t24 = new(Element)
		t25 = new(Element)
		t26 = new(Element)
	)

	// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26 Element
	// Step 1: t3 = x^0x2
	t3.Square(&x)

	// Step 2: t4 = x^0x4
	t4.Square(t3)

	// Step 3: t6 = x^0x8
	t6.Square(t4)

	// Step 4: t7 = x^0x9
	t7.Mul(&x, t6)

	// Step 5: t9 = x^0xb
	t9.Mul(t3, t7)

	// Step 6: t10 = x^0xc
	t10.Mul(&x, t9)

	// Step 7: t25 = x^0x11
	t25.Mul(t6, t7)

	// Step 8: t1 = x^0x14
	t1.Mul(t6, t10)

	// Step 9: t5 = x^0x16
	t5.Mul(t3, t1)

	// Step 10: t18 = x^0x19
	t18.Mul(t6, t25)

	// Step 11: t8 = x^0x1a
	t8.Mul(&x, t18)

	// Step 12: z = x^0x2b
	z.Mul(t25, t8)

	// Step 13: t11 = x^0x34
	t11.Mul(t7, z)

	// Step 14: t2 = x^0x37
	t2.Mul(t10, z)

	// Step 15: t23 = x^0x4d
	t23.Mul(t5, t2)

	// Step 16: t15 = x^0x4f
	t15.Mul(t3, t23)

	// Step 17: t0 = x^0x55
	t0.Mul(t6, t23)

	// Step 18: t21 = x^0x5d
	t21.Mul(t6, t0)

	// Step 19: t12 = x^0x67
	t12.Mul(t8, t23)

	// Step 20: t20 = x^0x69
	t20.Mul(t3, t12)

	// Step 21: t17 = x^0x77
	t17.Mul(t8, t21)

	// Step 22: t8 = x^0x7b
	t8.Mul(t4, t17)

	// Step 23: t13 = x^0x89
	t13.Mul(t11, t0)

	// Step 24: t10 = x^0x95
	t10.Mul(t10, t13)

	// Step 25: t16 = x^0x97
	t16.Mul(t3, t10)

	// Step 26: t3 = x^0xa9
	t3.Mul(t1, t10)

	// Step 27: t22 = x^0xb1
	t22.Mul(t6, t3)

	// Step 28: t5 = x^0xbf
	t5.Mul(t5, t3)

	// Step 29: t11 = x^0xc3
	t11.Mul(t4, t5)

	// Step 30: t6 = x^0xd0
	t6.Mul(t25, t5)

	// Step 31: t19 = x^0xd7
	t19.Mul(t1, t11)

	// Step 32: t14 = x^0xe1
	t14.Mul(t25, t6)

	// Step 33: t24 = x^0xe5
	t24.Mul(t4, t14)

	// Step 34: t4 = x^0xeb
	t4.Mul(t1, t19)

	// Step 35: t6 = x^0xf5
	t6.Mul(t1, t14)

	// Step 36: t1 = x^0xff
	t1.Mul(t1, t4)

	// Step 37: t26 = x^0x1a0
	t26.Mul(t5, t14)

	// Step 45: t26 = x^0x1a000
	for s := 0; s < 8; s++ {
		t26.Square(t26)
	}

	// Step 46: t25 = x^0x1a011
	t25.Mul(t25, t26)

	// Step 57: t25 = x^0xd008800
	for s := 0; s < 11; s++ {
		t25.Square(t25)
	}

	// Step 58: t25 = x^0xd0088f5
	t25.Mul(t6, t25)

	// Step 69: t25 = x^0x680447a800
	for s := 0; s < 11; s++ {
		t25.Square(t25)
	}

	// Step 70: t24 = x^0x680447a8e5
	t24.Mul(t24, t25)

	// Step 78: t24 = x^0x680447a8e500
	for s := 0; s < 8; s++ {
		t24.Square(t24)
	}

	// Step 79: t24 = x^0x680447a8e5ff
	t24.Mul(t1, t24)

	// Step 86: t24 = x^0x340223d472ff80
	for s := 0; s < 7; s++ {
		t24.Square(t24)
	}

	// Step 87: t23 = x^0x340223d472ffcd
	t23.Mul(t23, t24)

	// Step 96: t23 = x^0x680447a8e5ff9a00
	for s := 0; s < 9; s++ {
		t23.Square(t23)
	}

	// Step 97: t23 = x^0x680447a8e5ff9a69
	t23.Mul(t20, t23)

	// Step 107: t23 = x^0x1a0111ea397fe69a400
	for s := 0; s < 10; s++ {
		t23.Square(t23)
	}

	// Step 108: t22 = x^0x1a0111ea397fe69a4b1
	t22.Mul(t22, t23)

	// Step 115: t22 = x^0xd0088f51cbff34d25880
	for s := 0; s < 7; s++ {
		t22.Square(t22)
	}

	// Step 116: t21 = x^0xd0088f51cbff34d258dd
	t21.Mul(t21, t22)

	// Step 125: t21 = x^0x1a0111ea397fe69a4b1ba00
	for s := 0; s < 9; s++ {
		t21.Square(t21)
	}

	// Step 126: t21 = x^0x1a0111ea397fe69a4b1ba7b
	t21.Mul(t8, t21)

	// Step 132: t21 = x^0x680447a8e5ff9a692c6e9ec0
	for s := 0; s < 6; s++ {
		t21.Square(t21)
	}

	// Step 133: t21 = x^0x680447a8e5ff9a692c6e9ed9
	t21.Mul(t18, t21)

	// Step 144: t21 = x^0x340223d472ffcd3496374f6c800
	for s := 0; s < 11; s++ {
		t21.Square(t21)
	}

	// Step 145: t20 = x^0x340223d472ffcd3496374f6c869
	t20.Mul(t20, t21)

	// Step 154: t20 = x^0x680447a8e5ff9a692c6e9ed90d200
	for s := 0; s < 9; s++ {
		t20.Square(t20)
	}

	// Step 155: t20 = x^0x680447a8e5ff9a692c6e9ed90d2eb
	t20.Mul(t4, t20)

	// Step 165: t20 = x^0x1a0111ea397fe69a4b1ba7b6434bac00
	for s := 0; s < 10; s++ {
		t20.Square(t20)
	}

	// Step 166: t19 = x^0x1a0111ea397fe69a4b1ba7b6434bacd7
	t19.Mul(t19, t20)

	// Step 172: t19 = x^0x680447a8e5ff9a692c6e9ed90d2eb35c0
	for s := 0; s < 6; s++ {
		t19.Square(t19)
	}

	// Step 173: t18 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d9
	t18.Mul(t18, t19)

	// Step 183: t18 = x^0x1a0111ea397fe69a4b1ba7b6434bacd76400
	for s := 0; s < 10; s++ {
		t18.Square(t18)
	}

	// Step 184: t17 = x^0x1a0111ea397fe69a4b1ba7b6434bacd76477
	t17.Mul(t17, t18)

	// Step 193: t17 = x^0x340223d472ffcd3496374f6c869759aec8ee00
	for s := 0; s < 9; s++ {
		t17.Square(t17)
	}

	// Step 194: t16 = x^0x340223d472ffcd3496374f6c869759aec8ee97
	t16.Mul(t16, t17)

	// Step 205: t16 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b800
	for s := 0; s < 11; s++ {
		t16.Square(t16)
	}

	// Step 206: t15 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f
	t15.Mul(t15, t16)

	// Step 216: t15 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13c00
	for s := 0; s < 10; s++ {
		t15.Square(t15)
	}

	// Step 217: t14 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce1
	t14.Mul(t14, t15)

	// Step 226: t14 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c200
	for s := 0; s < 9; s++ {
		t14.Square(t14)
	}

	// Step 227: t13 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c289
	t13.Mul(t13, t14)

	// Step 236: t13 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f3851200
	for s := 0; s < 9; s++ {
		t13.Square(t13)
	}

	// Step 237: t13 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf
	t13.Mul(t5, t13)

	// Step 245: t13 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf00
	for s := 0; s < 8; s++ {
		t13.Square(t13)
	}

	// Step 246: t12 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf67
	t12.Mul(t12, t13)

	// Step 256: t12 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9c00
	for s := 0; s < 10; s++ {
		t12.Square(t12)
	}

	// Step 257: t11 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc3
	t11.Mul(t11, t12)

	// Step 266: t11 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398600
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}

	// Step 267: t10 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398695
	t10.Mul(t10, t11)

	// Step 279: t10 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398695000
	for s := 0; s < 12; s++ {
		t10.Square(t10)
	}

	// Step 280: t10 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b
	t10.Mul(t8, t10)

	// Step 285: t10 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f60
	for s := 0; s < 5; s++ {
		t10.Square(t10)
	}

	// Step 286: t9 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b
	t9.Mul(t9, t10)

	// Step 297: t9 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b5800
	for s := 0; s < 11; s++ {
		t9.Square(t9)
	}

	// Step 298: t8 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b
	t8.Mul(t8, t9)

	// Step 305: t8 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d80
	for s := 0; s < 7; s++ {
		t8.Square(t8)
	}

	// Step 306: t7 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d89
	t7.Mul(t7, t8)

	// Step 319: t7 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b12000
	for s := 0; s < 13; s++ {
		t7.Square(t7)
	}

	// Step 320: t6 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f5
	t6.Mul(t6, t7)

	// Step 329: t6 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241ea00
	for s := 0; s < 9; s++ {
		t6.Square(t6)
	}

	// Step 330: t5 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabf
	t5.Mul(t5, t6)

	// Step 338: t5 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabf00
	for s := 0; s < 8; s++ {
		t5.Square(t5)
	}

	// Step 339: t5 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfff
	t5.Mul(t1, t5)

	// Step 347: t5 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfff00
	for s := 0; s < 8; s++ {
		t5.Square(t5)
	}

	// Step 348: t4 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb
	t4.Mul(t4, t5)

	// Step 359: t4 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff5800
	for s := 0; s < 11; s++ {
		t4.Square(t4)
	}

	// Step 360: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9
	t3.Mul(t3, t4)

	// Step 368: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a900
	for s := 0; s < 8; s++ {
		t3.Square(t3)
	}

	// Step 369: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ff
	t3.Mul(t1, t3)

	// Step 377: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ff00
	for s := 0; s < 8; s++ {
		t3.Square(t3)
	}

	// Step 378: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffff
	t3.Mul(t1, t3)

	// Step 384: t3 = x^0x340223d472ffcd3496374f6c869759aec8ee9709e70a257ece61a541ed61ec483d57fffd62a7fffc0
	for s := 0; s < 6; s++ {
		t3.Square(t3)
	}

	// Step 385: t2 = x^0x340223d472ffcd3496374f6c869759aec8ee9709e70a257ece61a541ed61ec483d57fffd62a7ffff7
	t2.Mul(t2, t3)

	// Step 395: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdc00
	for s := 0; s < 10; s++ {
		t2.Square(t2)
	}

	// Step 396: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff
	t2.Mul(t1, t2)

	// Step 405: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9fe00
	for s := 0; s < 9; s++ {
		t2.Square(t2)
	}

	// Step 406: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feff
	t2.Mul(t1, t2)

	// Step 414: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feff00
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}

	// Step 415: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffff
	t2.Mul(t1, t2)

	// Step 423: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffff00
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}

	// Step 424: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffff
	t2.Mul(t1, t2)

	// Step 432: t2 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffff00
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}

	// Step 433: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffff
	t1.Mul(t1, t2)

	// Step 440: t1 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffff80
	for s := 0; s < 7; s++ {
		t1.Square(t1)
	}

	// Step 441: t0 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd5
	t0.Mul(t0, t1)

	// Step 448: t0 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffea80
	for s := 0; s < 7; s++ {
		t0.Square(t0)
	}

	// Step 449: z = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaab
	z.Mul(z, t0)

	return z
}

// expByLegendreExp is equivalent to z.Exp(x, d0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd555)
//
// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
func (z *Element) expByLegendreExp(x Element) *Element {
	// addition chain:
	//
	//	_10       = 2*1
	//	_100      = 2*_10
	//	_1000     = 2*_100
	//	_1001     = 1 + _1000
	//	_1011     = _10 + _1001
	//	_1101     = _10 + _1011
	//	_10001    = _100 + _1101
	//	_10100    = _1001 + _1011
	//	_11001    = _1000 + _10001
	//	_11010    = 1 + _11001
	//	_110100   = 2*_11010
	//	_110110   = _10 + _110100
	//	_110111   = 1 + _110110
	//	_1001101  = _11001 + _110100
	//	_1001111  = _10 + _1001101
	//	_1010101  = _1000 + _1001101
	//	_1011101  = _1000 + _1010101
	//	_1100111  = _11010 + _1001101
	//	_1101001  = _10 + _1100111
	//	_1110111  = _11010 + _1011101
	//	_1111011  = _100 + _1110111
	//	_10001001 = _110100 + _1010101
	//	_10010101 = _11010 + _1111011
	//	_10010111 = _10 + _10010101
	//	_10101001 = _10100 + _10010101
	//	_10110001 = _1000 + _10101001
	//	_10111111 = _110110 + _10001001
	//	_11000011 = _100 + _10111111
	//	_11010000 = _1101 + _11000011
	//	_11010111 = _10100 + _11000011
	//	_11100001 = _10001 + _11010000
	//	_11100101 = _100 + _11100001
	//	_11101011 = _10100 + _11010111
	//	_11110101 = _10100 + _11100001
	//	_11111111 = _10100 + _11101011
	//	i57       = ((_10111111 + _11100001) << 8 + _10001) << 11 + _11110101
	//	i85       = ((i57 << 11 + _11100101) << 8 + _11111111) << 7
	//	i107      = ((_1001101 + i85) << 9 + _1101001) << 10 + _10110001
	//	i131      = ((i107 << 7 + _1011101) << 9 + _1111011) << 6
	//	i154      = ((_11001 + i131) << 11 + _1101001) << 9 + _11101011
	//	i182      = ((i154 << 10 + _11010111) << 6 + _11001) << 10
	//	i205      = ((_1110111 + i182) << 9 + _10010111) << 11 + _1001111
	//	i235      = ((i205 << 10 + _11100001) << 9 + _10001001) << 9
	//	i256      = ((_10111111 + i235) << 8 + _1100111) << 10 + _11000011
	//	i284      = ((i256 << 9 + _10010101) << 12 + _1111011) << 5
	//	i305      = ((_1011 + i284) << 11 + _1111011) << 7 + _1001
	//	i337      = ((i305 << 13 + _11110101) << 9 + _10111111) << 8
	//	i359      = ((_11111111 + i337) << 8 + _11101011) << 11 + _10101001
	//	i383      = ((i359 << 8 + _11111111) << 8 + _11111111) << 6
	//	i405      = ((_110111 + i383) << 10 + _11111111) << 9 + _11111111
	//	i431      = ((i405 << 8 + _11111111) << 8 + _11111111) << 8
	//	return      ((_11111111 + i431) << 7 + _1010101) << 8 + _1010101
	//
	// Operations: 375 squares 74 multiplies

	// Allocate Temporaries.
	var (
		t0  = new(Element)
		t1  = new(Element)
		t2  = new(Element)
		t3  = new(Element)
		t4  = new(Element)
		t5  = new(Element)
		t6  = new(Element)
		t7  = new(Element)
		t8  = new(Element)
		t9  = new(Element)
		t10 = new(Element)
		t11 = new(Element)
		t12 = new(Element)
		t13 = new(Element)
		t14 = new(Element)
		t15 = new(Element)
		t16 = new(Element)
		t17 = new(Element)
		t18 = new(Element)
		t19 = new(Element)
		t20 = new(Element)
		t21 = new(Element)
		t22 = new(Element)
		t23 = new(Element)
		t24 = new(Element)
		t25 = new(Element)
	)

	// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25 Element
	// Step 1: t2 = x^0x2
	t2.Square(&x)

	// Step 2: t3 = x^0x4
	t3.Square(t2)

	// Step 3: t10 = x^0x8
	t10.Square(t3)

	// Step 4: t6 = x^0x9
	t6.Mul(&x, t10)

	// Step 5: t8 = x^0xb
	t8.Mul(t2, t6)

	// Step 6: t5 = x^0xd
	t5.Mul(t2, t8)

	// Step 7: t24 = x^0x11
	t24.Mul(t3, t5)

	// Step 8: t0 = x^0x14
	t0.Mul(t6, t8)

	// Step 9: t17 = x^0x19
	t17.Mul(t10, t24)

	// Step 10: t9 = x^0x1a
	t9.Mul(&x, t17)

	// Step 11: t12 = x^0x34
	t12.Square(t9)

	// Step 12: t4 = x^0x36
	t4.Mul(t2, t12)

	// Step 13: t1 = x^0x37
	t1.Mul(&x, t4)

	// Step 14: t22 = x^0x4d
	t22.Mul(t17, t12)

	// Step 15: t14 = x^0x4f
	t14.Mul(t2, t22)

	// Step 16: z = x^0x55
	z.Mul(t10, t22)

	// Step 17: t20 = x^0x5d
	t20.Mul(t10, z)

	// Step 18: t11 = x^0x67
	t11.Mul(t9, t22)

	// Step 19: t19 = x^0x69
	t19.Mul(t2, t11)

	// Step 20: t16 = x^0x77
	t16.Mul(t9, t20)

	// Step 21: t7 = x^0x7b
	t7.Mul(t3, t16)

	// Step 22: t12 = x^0x89
	t12.Mul(t12, z)

	// Step 23: t9 = x^0x95
	t9.Mul(t9, t7)

	// Step 24: t15 = x^0x97
	t15.Mul(t2, t9)

	// Step 25: t2 = x^0xa9
	t2.Mul(t0, t9)

	// Step 26: t21 = x^0xb1
	t21.Mul(t10, t2)

	// Step 27: t4 = x^0xbf
	t4.Mul(t4, t12)

	// Step 28: t10 = x^0xc3
	t10.Mul(t3, t4)

	// Step 29: t5 = x^0xd0
	t5.Mul(t5, t10)

	// Step 30: t18 = x^0xd7
	t18.Mul(t0, t10)

	// Step 31: t13 = x^0xe1
	t13.Mul(t24, t5)

	// Step 32: t23 = x^0xe5
	t23.Mul(t3, t13)

	// Step 33: t3 = x^0xeb
	t3.Mul(t0, t18)

	// Step 34: t5 = x^0xf5
	t5.Mul(t0, t13)

	// Step 35: t0 = x^0xff
	t0.Mul(t0, t3)

	// Step 36: t25 = x^0x1a0
	t25.Mul(t4, t13)

	// Step 44: t25 = x^0x1a000
	for s := 0; s < 8; s++ {
		t25.Square(t25)
	}

	// Step 45: t24 = x^0x1a011
	t24.Mul(t24, t25)

	// Step 56: t24 = x^0xd008800
	for s := 0; s < 11; s++ {
		t24.Square(t24)
	}

	// Step 57: t24 = x^0xd0088f5
	t24.Mul(t5, t24)

	// Step 68: t24 = x^0x680447a800
	for s := 0; s < 11; s++ {
		t24.Square(t24)
	}

	// Step 69: t23 = x^0x680447a8e5
	t23.Mul(t23, t24)

	// Step 77: t23 = x^0x680447a8e500
	for s := 0; s < 8; s++ {
		t23.Square(t23)
	}

	// Step 78: t23 = x^0x680447a8e5ff
	t23.Mul(t0, t23)

	// Step 85: t23 = x^0x340223d472ff80
	for s := 0; s < 7; s++ {
		t23.Square(t23)
	}

	// Step 86: t22 = x^0x340223d472ffcd
	t22.Mul(t22, t23)

	// Step 95: t22 = x^0x680447a8e5ff9a00
	for s := 0; s < 9; s++ {
		t22.Square(t22)
	}

	// Step 96: t22 = x^0x680447a8e5ff9a69
	t22.Mul(t19, t22)

	// Step 106: t22 = x^0x1a0111ea397fe69a400
	for s := 0; s < 10; s++ {
		t22.Square(t22)
	}

	// Step 107: t21 = x^0x1a0111ea397fe69a4b1
	t21.Mul(t21, t22)

	// Step 114: t21 = x^0xd0088f51cbff34d25880
	for s := 0; s < 7; s++ {
		t21.Square(t21)
	}

	// Step 115: t20 = x^0xd0088f51cbff34d258dd
	t20.Mul(t20, t21)

	// Step 124: t20 = x^0x1a0111ea397fe69a4b1ba00
	for s := 0; s < 9; s++ {
		t20.Square(t20)
	}

	// Step 125: t20 = x^0x1a0111ea397fe69a4b1ba7b
	t20.Mul(t7, t20)

	// Step 131: t20 = x^0x680447a8e5ff9a692c6e9ec0
	for s := 0; s < 6; s++ {
		t20.Square(t20)
	}

	// Step 132: t20 = x^0x680447a8e5ff9a692c6e9ed9
	t20.Mul(t17, t20)

	// Step 143: t20 = x^0x340223d472ffcd3496374f6c800
	for s := 0; s < 11; s++ {
		t20.Square(t20)
	}

	// Step 144: t19 = x^0x340223d472ffcd3496374f6c869
	t19.Mul(t19, t20)

	// Step 153: t19 = x^0x680447a8e5ff9a692c6e9ed90d200
	for s := 0; s < 9; s++ {
		t19.Square(t19)
	}

	// Step 154: t19 = x^0x680447a8e5ff9a692c6e9ed90d2eb
	t19.Mul(t3, t19)

	// Step 164: t19 = x^0x1a0111ea397fe69a4b1ba7b6434bac00
	for s := 0; s < 10; s++ {
		t19.Square(t19)
	}

	// Step 165: t18 = x^0x1a0111ea397fe69a4b1ba7b6434bacd7
	t18.Mul(t18, t19)

	// Step 171: t18 = x^0x680447a8e5ff9a692c6e9ed90d2eb35c0
	for s := 0; s < 6; s++ {
		t18.Square(t18)
	}

	// Step 172: t17 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d9
	t17.Mul(t17, t18)

	// Step 182: t17 = x^0x1a0111ea397fe69a4b1ba7b6434bacd76400
	for s := 0; s < 10; s++ {
		t17.Square(t17)
	}

	// Step 183: t16 = x^0x1a0111ea397fe69a4b1ba7b6434bacd76477
	t16.Mul(t16, t17)

	// Step 192: t16 = x^0x340223d472ffcd3496374f6c869759aec8ee00
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}

	// Step 193: t15 = x^0x340223d472ffcd3496374f6c869759aec8ee97
	t15.Mul(t15, t16)

	// Step 204: t15 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b800
	for s := 0; s < 11; s++ {
		t15.Square(t15)
	}

	// Step 205: t14 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f
	t14.Mul(t14, t15)

	// Step 215: t14 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13c00
	for s := 0; s < 10; s++ {
		t14.Square(t14)
	}

	// Step 216: t13 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce1
	t13.Mul(t13, t14)

	// Step 225: t13 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c200
	for s := 0; s < 9; s++ {
		t13.Square(t13)
	}

	// Step 226: t12 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c289
	t12.Mul(t12, t13)

	// Step 235: t12 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f3851200
	for s := 0; s < 9; s++ {
		t12.Square(t12)
	}

	// Step 236: t12 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf
	t12.Mul(t4, t12)

	// Step 244: t12 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf00
	for s := 0; s < 8; s++ {
		t12.Square(t12)
	}

	// Step 245: t11 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf67
	t11.Mul(t11, t12)

	// Step 255: t11 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9c00
	for s := 0; s < 10; s++ {
		t11.Square(t11)
	}

	// Step 256: t10 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc3
	t10.Mul(t10, t11)

	// Step 265: t10 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398600
	for s := 0; s < 9; s++ {
		t10.Square(t10)
	}

	// Step 266: t9 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398695
	t9.Mul(t9, t10)

	// Step 278: t9 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb398695000
	for s := 0; s < 12; s++ {
		t9.Square(t9)
	}

	// Step 279: t9 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b
	t9.Mul(t7, t9)

	// Step 284: t9 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f60
	for s := 0; s < 5; s++ {
		t9.Square(t9)
	}

	// Step 285: t8 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b
	t8.Mul(t8, t9)

	// Step 296: t8 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b5800
	for s := 0; s < 11; s++ {
		t8.Square(t8)
	}

	// Step 297: t7 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b
	t7.Mul(t7, t8)

	// Step 304: t7 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d80
	for s := 0; s < 7; s++ {
		t7.Square(t7)
	}

	// Step 305: t6 = x^0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d89
	t6.Mul(t6, t7)

	// Step 318: t6 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b12000
	for s := 0; s < 13; s++ {
		t6.Square(t6)
	}

	// Step 319: t5 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f5
	t5.Mul(t5, t6)

	// Step 328: t5 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241ea00
	for s := 0; s < 9; s++ {
		t5.Square(t5)
	}

	// Step 329: t4 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabf
	t4.Mul(t4, t5)

	// Step 337: t4 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabf00
	for s := 0; s < 8; s++ {
		t4.Square(t4)
	}

	// Step 338: t4 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfff
	t4.Mul(t0, t4)

	// Step 346: t4 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfff00
	for s := 0; s < 8; s++ {
		t4.Square(t4)
	}

	// Step 347: t3 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb
	t3.Mul(t3, t4)

	// Step 358: t3 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff5800
	for s := 0; s < 11; s++ {
		t3.Square(t3)
	}

	// Step 359: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9
	t2.Mul(t2, t3)

	// Step 367: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a900
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}

	// Step 368: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ff
	t2.Mul(t0, t2)

	// Step 376: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ff00
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}

	// Step 377: t2 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffff
	t2.Mul(t0, t2)

	// Step 383: t2 = x^0x340223d472ffcd3496374f6c869759aec8ee9709e70a257ece61a541ed61ec483d57fffd62a7fffc0
	for s := 0; s < 6; s++ {
		t2.Square(t2)
	}

	// Step 384: t1 = x^0x340223d472ffcd3496374f6c869759aec8ee9709e70a257ece61a541ed61ec483d57fffd62a7ffff7
	t1.Mul(t1, t2)

	// Step 394: t1 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdc00
	for s := 0; s < 10; s++ {
		t1.Square(t1)
	}

	// Step 395: t1 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff
	t1.Mul(t0, t1)

	// Step 404: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9fe00
	for s := 0; s < 9; s++ {
		t1.Square(t1)
	}

	// Step 405: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feff
	t1.Mul(t0, t1)

	// Step 413: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feff00
	for s := 0; s < 8; s++ {
		t1.Square(t1)
	}

	// Step 414: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffff
	t1.Mul(t0, t1)

	// Step 422: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffff00
	for s := 0; s < 8; s++ {
		t1.Square(t1)
	}

	// Step 423: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffff
	t1.Mul(t0, t1)

	// Step 431: t1 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffff00
	for s := 0; s < 8; s++ {
		t1.Square(t1)
	}

	// Step 432: t0 = x^0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffff
	t0.Mul(t0, t1)

	// Step 439: t0 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffff80
	for s := 0; s < 7; s++ {
		t0.Square(t0)
	}

	// Step 440: t0 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd5
	t0.Mul(z, t0)

	// Step 448: t0 = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd500
	for s := 0; s < 8; s++ {
		t0.Square(t0)
	}

	// Step 449: z = x^0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd555
	z.Mul(z, t0)

	return z
}