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, 35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba88600000010a11)
//
// 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
	//	_11       = 1 + _10
	//	_100      = 1 + _11
	//	_101      = 1 + _100
	//	_111      = _10 + _101
	//	_1001     = _10 + _111
	//	_1011     = _10 + _1001
	//	_1111     = _100 + _1011
	//	_10001    = _10 + _1111
	//	_10011    = _10 + _10001
	//	_10111    = _100 + _10011
	//	_11011    = _100 + _10111
	//	_11101    = _10 + _11011
	//	_11111    = _10 + _11101
	//	_110100   = _10111 + _11101
	//	_11010000 = _110100 << 2
	//	_11010111 = _111 + _11010000
	//	i36       = 2*((_11010111 << 8 + _11101) << 7 + _10001)
	//	i50       = ((1 + i36) << 9 + _10111) << 2 + _11
	//	i71       = ((i50 << 6 + _101) << 4 + 1) << 9
	//	i84       = ((_11101 + i71) << 5 + _1011) << 5 + _11
	//	i105      = (2*(i84 << 8 + _11101) + 1) << 10
	//	i125      = ((_10111 + i105) << 12 + _11011) << 5 + _101
	//	i147      = ((i125 << 7 + _101) << 6 + _1001) << 7
	//	i158      = ((_11101 + i147) << 5 + _10001) << 3 + _101
	//	i181      = ((i158 << 8 + _10001) << 6 + _11011) << 7
	//	i200      = ((_11111 + i181) << 4 + _11) << 12 + _1111
	//	i219      = ((i200 << 4 + _101) << 8 + _10011) << 5
	//	i232      = ((_10001 + i219) << 3 + _111) << 7 + _1111
	//	i254      = ((i232 << 5 + _1111) << 7 + _11011) << 8
	//	i269      = ((_10001 + i254) << 6 + _11111) << 6 + _11101
	//	i304      = ((i269 << 9 + _1001) << 5 + _1001) << 19
	//	i321      = ((_10111 + i304) << 8 + _1011) << 6 + _10111
	//	i337      = ((i321 << 4 + _101) << 4 + 1) << 6
	//	i376      = ((_11 + i337) << 29 + 1) << 7 + _101
	//	return      i376 << 9 + _10001
	//
	// Operations: 325 squares 61 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)
	)

	// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11 Element
	// Step 1: t6 = x^0x2
	t6.Square(&x)

	// Step 2: t1 = x^0x3
	t1.Mul(&x, t6)

	// Step 3: t5 = x^0x4
	t5.Mul(&x, t1)

	// Step 4: t0 = x^0x5
	t0.Mul(&x, t5)

	// Step 5: t9 = x^0x7
	t9.Mul(t6, t0)

	// Step 6: t4 = x^0x9
	t4.Mul(t6, t9)

	// Step 7: t3 = x^0xb
	t3.Mul(t6, t4)

	// Step 8: t8 = x^0xf
	t8.Mul(t5, t3)

	// Step 9: z = x^0x11
	z.Mul(t6, t8)

	// Step 10: t10 = x^0x13
	t10.Mul(t6, z)

	// Step 11: t2 = x^0x17
	t2.Mul(t5, t10)

	// Step 12: t7 = x^0x1b
	t7.Mul(t5, t2)

	// Step 13: t5 = x^0x1d
	t5.Mul(t6, t7)

	// Step 14: t6 = x^0x1f
	t6.Mul(t6, t5)

	// Step 15: t11 = x^0x34
	t11.Mul(t2, t5)

	// Step 17: t11 = x^0xd0
	for s := 0; s < 2; s++ {
		t11.Square(t11)
	}

	// Step 18: t11 = x^0xd7
	t11.Mul(t9, t11)

	// Step 26: t11 = x^0xd700
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 27: t11 = x^0xd71d
	t11.Mul(t5, t11)

	// Step 34: t11 = x^0x6b8e80
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 35: t11 = x^0x6b8e91
	t11.Mul(z, t11)

	// Step 36: t11 = x^0xd71d22
	t11.Square(t11)

	// Step 37: t11 = x^0xd71d23
	t11.Mul(&x, t11)

	// Step 46: t11 = x^0x1ae3a4600
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}

	// Step 47: t11 = x^0x1ae3a4617
	t11.Mul(t2, t11)

	// Step 49: t11 = x^0x6b8e9185c
	for s := 0; s < 2; s++ {
		t11.Square(t11)
	}

	// Step 50: t11 = x^0x6b8e9185f
	t11.Mul(t1, t11)

	// Step 56: t11 = x^0x1ae3a4617c0
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 57: t11 = x^0x1ae3a4617c5
	t11.Mul(t0, t11)

	// Step 61: t11 = x^0x1ae3a4617c50
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 62: t11 = x^0x1ae3a4617c51
	t11.Mul(&x, t11)

	// Step 71: t11 = x^0x35c748c2f8a200
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}

	// Step 72: t11 = x^0x35c748c2f8a21d
	t11.Mul(t5, t11)

	// Step 77: t11 = x^0x6b8e9185f1443a0
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 78: t11 = x^0x6b8e9185f1443ab
	t11.Mul(t3, t11)

	// Step 83: t11 = x^0xd71d230be2887560
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 84: t11 = x^0xd71d230be2887563
	t11.Mul(t1, t11)

	// Step 92: t11 = x^0xd71d230be288756300
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 93: t11 = x^0xd71d230be28875631d
	t11.Mul(t5, t11)

	// Step 94: t11 = x^0x1ae3a4617c510eac63a
	t11.Square(t11)

	// Step 95: t11 = x^0x1ae3a4617c510eac63b
	t11.Mul(&x, t11)

	// Step 105: t11 = x^0x6b8e9185f1443ab18ec00
	for s := 0; s < 10; s++ {
		t11.Square(t11)
	}

	// Step 106: t11 = x^0x6b8e9185f1443ab18ec17
	t11.Mul(t2, t11)

	// Step 118: t11 = x^0x6b8e9185f1443ab18ec17000
	for s := 0; s < 12; s++ {
		t11.Square(t11)
	}

	// Step 119: t11 = x^0x6b8e9185f1443ab18ec1701b
	t11.Mul(t7, t11)

	// Step 124: t11 = x^0xd71d230be28875631d82e0360
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 125: t11 = x^0xd71d230be28875631d82e0365
	t11.Mul(t0, t11)

	// Step 132: t11 = x^0x6b8e9185f1443ab18ec1701b280
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 133: t11 = x^0x6b8e9185f1443ab18ec1701b285
	t11.Mul(t0, t11)

	// Step 139: t11 = x^0x1ae3a4617c510eac63b05c06ca140
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 140: t11 = x^0x1ae3a4617c510eac63b05c06ca149
	t11.Mul(t4, t11)

	// Step 147: t11 = x^0xd71d230be28875631d82e03650a480
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 148: t11 = x^0xd71d230be28875631d82e03650a49d
	t11.Mul(t5, t11)

	// Step 153: t11 = x^0x1ae3a4617c510eac63b05c06ca1493a0
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 154: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1
	t11.Mul(z, t11)

	// Step 157: t11 = x^0xd71d230be28875631d82e03650a49d88
	for s := 0; s < 3; s++ {
		t11.Square(t11)
	}

	// Step 158: t11 = x^0xd71d230be28875631d82e03650a49d8d
	t11.Mul(t0, t11)

	// Step 166: t11 = x^0xd71d230be28875631d82e03650a49d8d00
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 167: t11 = x^0xd71d230be28875631d82e03650a49d8d11
	t11.Mul(z, t11)

	// Step 173: t11 = x^0x35c748c2f8a21d58c760b80d942927634440
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 174: t11 = x^0x35c748c2f8a21d58c760b80d94292763445b
	t11.Mul(t7, t11)

	// Step 181: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d80
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 182: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f
	t11.Mul(t6, t11)

	// Step 186: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f0
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 187: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f3
	t11.Mul(t1, t11)

	// Step 199: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f3000
	for s := 0; s < 12; s++ {
		t11.Square(t11)
	}

	// Step 200: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f
	t11.Mul(t8, t11)

	// Step 204: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f0
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 205: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5
	t11.Mul(t0, t11)

	// Step 213: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f500
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 214: t10 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f513
	t10.Mul(t10, t11)

	// Step 219: t10 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea260
	for s := 0; s < 5; s++ {
		t10.Square(t10)
	}

	// Step 220: t10 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271
	t10.Mul(z, t10)

	// Step 223: t10 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f51388
	for s := 0; s < 3; s++ {
		t10.Square(t10)
	}

	// Step 224: t9 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f
	t9.Mul(t9, t10)

	// Step 231: t9 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c780
	for s := 0; s < 7; s++ {
		t9.Square(t9)
	}

	// Step 232: t9 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f
	t9.Mul(t8, t9)

	// Step 237: t9 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1e0
	for s := 0; s < 5; s++ {
		t9.Square(t9)
	}

	// Step 238: t8 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef
	t8.Mul(t8, t9)

	// Step 245: t8 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f780
	for s := 0; s < 7; s++ {
		t8.Square(t8)
	}

	// Step 246: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b
	t7.Mul(t7, t8)

	// Step 254: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b00
	for s := 0; s < 8; s++ {
		t7.Square(t7)
	}

	// Step 255: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b11
	t7.Mul(z, t7)

	// Step 261: t7 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c440
	for s := 0; s < 6; s++ {
		t7.Square(t7)
	}

	// Step 262: t6 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f
	t6.Mul(t6, t7)

	// Step 268: t6 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117c0
	for s := 0; s < 6; s++ {
		t6.Square(t6)
	}

	// Step 269: t5 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117dd
	t5.Mul(t5, t6)

	// Step 278: t5 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba00
	for s := 0; s < 9; s++ {
		t5.Square(t5)
	}

	// Step 279: t5 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09
	t5.Mul(t4, t5)

	// Step 284: t5 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f74120
	for s := 0; s < 5; s++ {
		t5.Square(t5)
	}

	// Step 285: t4 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f74129
	t4.Mul(t4, t5)

	// Step 304: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09480000
	for s := 0; s < 19; s++ {
		t4.Square(t4)
	}

	// Step 305: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09480017
	t4.Mul(t2, t4)

	// Step 313: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba0948001700
	for s := 0; s < 8; s++ {
		t4.Square(t4)
	}

	// Step 314: t3 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b
	t3.Mul(t3, t4)

	// Step 320: t3 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2c0
	for s := 0; s < 6; s++ {
		t3.Square(t3)
	}

	// Step 321: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d7
	t2.Mul(t2, t3)

	// Step 325: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d70
	for s := 0; s < 4; s++ {
		t2.Square(t2)
	}

	// Step 326: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d75
	t2.Mul(t0, t2)

	// Step 330: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d750
	for s := 0; s < 4; s++ {
		t2.Square(t2)
	}

	// Step 331: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d751
	t2.Mul(&x, t2)

	// Step 337: t2 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d440
	for s := 0; s < 6; s++ {
		t2.Square(t2)
	}

	// Step 338: t1 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443
	t1.Mul(t1, t2)

	// Step 367: t1 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba8860000000
	for s := 0; s < 29; s++ {
		t1.Square(t1)
	}

	// Step 368: t1 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba8860000001
	t1.Mul(&x, t1)

	// Step 375: t1 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443000000080
	for s := 0; s < 7; s++ {
		t1.Square(t1)
	}

	// Step 376: t0 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443000000085
	t0.Mul(t0, t1)

	// Step 385: t0 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba88600000010a00
	for s := 0; s < 9; s++ {
		t0.Square(t0)
	}

	// Step 386: z = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba88600000010a11
	z.Mul(z, t0)

	return z
}

// expByLegendreExp is equivalent to z.Exp(x, d71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117dd04a4000b85aea2180000004284600000000000)
//
// 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
	//	_11       = 1 + _10
	//	_100      = 1 + _11
	//	_101      = 1 + _100
	//	_111      = _10 + _101
	//	_1001     = _10 + _111
	//	_1011     = _10 + _1001
	//	_1111     = _100 + _1011
	//	_10001    = _10 + _1111
	//	_10011    = _10 + _10001
	//	_10111    = _100 + _10011
	//	_11011    = _100 + _10111
	//	_11101    = _10 + _11011
	//	_11111    = _10 + _11101
	//	_110100   = _10111 + _11101
	//	_11010000 = _110100 << 2
	//	_11010111 = _111 + _11010000
	//	i36       = 2*((_11010111 << 8 + _11101) << 7 + _10001)
	//	i50       = ((1 + i36) << 9 + _10111) << 2 + _11
	//	i71       = ((i50 << 6 + _101) << 4 + 1) << 9
	//	i84       = ((_11101 + i71) << 5 + _1011) << 5 + _11
	//	i105      = (2*(i84 << 8 + _11101) + 1) << 10
	//	i125      = ((_10111 + i105) << 12 + _11011) << 5 + _101
	//	i147      = ((i125 << 7 + _101) << 6 + _1001) << 7
	//	i158      = ((_11101 + i147) << 5 + _10001) << 3 + _101
	//	i181      = ((i158 << 8 + _10001) << 6 + _11011) << 7
	//	i200      = ((_11111 + i181) << 4 + _11) << 12 + _1111
	//	i219      = ((i200 << 4 + _101) << 8 + _10011) << 5
	//	i232      = ((_10001 + i219) << 3 + _111) << 7 + _1111
	//	i254      = ((i232 << 5 + _1111) << 7 + _11011) << 8
	//	i269      = ((_10001 + i254) << 6 + _11111) << 6 + _11101
	//	i304      = ((i269 << 9 + _1001) << 5 + _1001) << 19
	//	i321      = ((_10111 + i304) << 8 + _1011) << 6 + _10111
	//	i337      = ((i321 << 4 + _101) << 4 + 1) << 6
	//	i376      = ((_11 + i337) << 29 + 1) << 7 + _101
	//	return      (2*(i376 << 9 + _10001) + 1) << 45
	//
	// Operations: 371 squares 62 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)
	)

	// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11 Element
	// Step 1: t6 = x^0x2
	t6.Square(&x)

	// Step 2: t1 = x^0x3
	t1.Mul(&x, t6)

	// Step 3: t5 = x^0x4
	t5.Mul(&x, t1)

	// Step 4: t0 = x^0x5
	t0.Mul(&x, t5)

	// Step 5: t9 = x^0x7
	t9.Mul(t6, t0)

	// Step 6: t4 = x^0x9
	t4.Mul(t6, t9)

	// Step 7: t3 = x^0xb
	t3.Mul(t6, t4)

	// Step 8: t8 = x^0xf
	t8.Mul(t5, t3)

	// Step 9: z = x^0x11
	z.Mul(t6, t8)

	// Step 10: t10 = x^0x13
	t10.Mul(t6, z)

	// Step 11: t2 = x^0x17
	t2.Mul(t5, t10)

	// Step 12: t7 = x^0x1b
	t7.Mul(t5, t2)

	// Step 13: t5 = x^0x1d
	t5.Mul(t6, t7)

	// Step 14: t6 = x^0x1f
	t6.Mul(t6, t5)

	// Step 15: t11 = x^0x34
	t11.Mul(t2, t5)

	// Step 17: t11 = x^0xd0
	for s := 0; s < 2; s++ {
		t11.Square(t11)
	}

	// Step 18: t11 = x^0xd7
	t11.Mul(t9, t11)

	// Step 26: t11 = x^0xd700
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 27: t11 = x^0xd71d
	t11.Mul(t5, t11)

	// Step 34: t11 = x^0x6b8e80
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 35: t11 = x^0x6b8e91
	t11.Mul(z, t11)

	// Step 36: t11 = x^0xd71d22
	t11.Square(t11)

	// Step 37: t11 = x^0xd71d23
	t11.Mul(&x, t11)

	// Step 46: t11 = x^0x1ae3a4600
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}

	// Step 47: t11 = x^0x1ae3a4617
	t11.Mul(t2, t11)

	// Step 49: t11 = x^0x6b8e9185c
	for s := 0; s < 2; s++ {
		t11.Square(t11)
	}

	// Step 50: t11 = x^0x6b8e9185f
	t11.Mul(t1, t11)

	// Step 56: t11 = x^0x1ae3a4617c0
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 57: t11 = x^0x1ae3a4617c5
	t11.Mul(t0, t11)

	// Step 61: t11 = x^0x1ae3a4617c50
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 62: t11 = x^0x1ae3a4617c51
	t11.Mul(&x, t11)

	// Step 71: t11 = x^0x35c748c2f8a200
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}

	// Step 72: t11 = x^0x35c748c2f8a21d
	t11.Mul(t5, t11)

	// Step 77: t11 = x^0x6b8e9185f1443a0
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 78: t11 = x^0x6b8e9185f1443ab
	t11.Mul(t3, t11)

	// Step 83: t11 = x^0xd71d230be2887560
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 84: t11 = x^0xd71d230be2887563
	t11.Mul(t1, t11)

	// Step 92: t11 = x^0xd71d230be288756300
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 93: t11 = x^0xd71d230be28875631d
	t11.Mul(t5, t11)

	// Step 94: t11 = x^0x1ae3a4617c510eac63a
	t11.Square(t11)

	// Step 95: t11 = x^0x1ae3a4617c510eac63b
	t11.Mul(&x, t11)

	// Step 105: t11 = x^0x6b8e9185f1443ab18ec00
	for s := 0; s < 10; s++ {
		t11.Square(t11)
	}

	// Step 106: t11 = x^0x6b8e9185f1443ab18ec17
	t11.Mul(t2, t11)

	// Step 118: t11 = x^0x6b8e9185f1443ab18ec17000
	for s := 0; s < 12; s++ {
		t11.Square(t11)
	}

	// Step 119: t11 = x^0x6b8e9185f1443ab18ec1701b
	t11.Mul(t7, t11)

	// Step 124: t11 = x^0xd71d230be28875631d82e0360
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 125: t11 = x^0xd71d230be28875631d82e0365
	t11.Mul(t0, t11)

	// Step 132: t11 = x^0x6b8e9185f1443ab18ec1701b280
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 133: t11 = x^0x6b8e9185f1443ab18ec1701b285
	t11.Mul(t0, t11)

	// Step 139: t11 = x^0x1ae3a4617c510eac63b05c06ca140
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 140: t11 = x^0x1ae3a4617c510eac63b05c06ca149
	t11.Mul(t4, t11)

	// Step 147: t11 = x^0xd71d230be28875631d82e03650a480
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 148: t11 = x^0xd71d230be28875631d82e03650a49d
	t11.Mul(t5, t11)

	// Step 153: t11 = x^0x1ae3a4617c510eac63b05c06ca1493a0
	for s := 0; s < 5; s++ {
		t11.Square(t11)
	}

	// Step 154: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1
	t11.Mul(z, t11)

	// Step 157: t11 = x^0xd71d230be28875631d82e03650a49d88
	for s := 0; s < 3; s++ {
		t11.Square(t11)
	}

	// Step 158: t11 = x^0xd71d230be28875631d82e03650a49d8d
	t11.Mul(t0, t11)

	// Step 166: t11 = x^0xd71d230be28875631d82e03650a49d8d00
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 167: t11 = x^0xd71d230be28875631d82e03650a49d8d11
	t11.Mul(z, t11)

	// Step 173: t11 = x^0x35c748c2f8a21d58c760b80d942927634440
	for s := 0; s < 6; s++ {
		t11.Square(t11)
	}

	// Step 174: t11 = x^0x35c748c2f8a21d58c760b80d94292763445b
	t11.Mul(t7, t11)

	// Step 181: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d80
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}

	// Step 182: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f
	t11.Mul(t6, t11)

	// Step 186: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f0
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 187: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f3
	t11.Mul(t1, t11)

	// Step 199: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f3000
	for s := 0; s < 12; s++ {
		t11.Square(t11)
	}

	// Step 200: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f
	t11.Mul(t8, t11)

	// Step 204: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f0
	for s := 0; s < 4; s++ {
		t11.Square(t11)
	}

	// Step 205: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5
	t11.Mul(t0, t11)

	// Step 213: t11 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f500
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}

	// Step 214: t10 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f513
	t10.Mul(t10, t11)

	// Step 219: t10 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea260
	for s := 0; s < 5; s++ {
		t10.Square(t10)
	}

	// Step 220: t10 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271
	t10.Mul(z, t10)

	// Step 223: t10 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f51388
	for s := 0; s < 3; s++ {
		t10.Square(t10)
	}

	// Step 224: t9 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f
	t9.Mul(t9, t10)

	// Step 231: t9 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c780
	for s := 0; s < 7; s++ {
		t9.Square(t9)
	}

	// Step 232: t9 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f
	t9.Mul(t8, t9)

	// Step 237: t9 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1e0
	for s := 0; s < 5; s++ {
		t9.Square(t9)
	}

	// Step 238: t8 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef
	t8.Mul(t8, t9)

	// Step 245: t8 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f780
	for s := 0; s < 7; s++ {
		t8.Square(t8)
	}

	// Step 246: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b
	t7.Mul(t7, t8)

	// Step 254: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b00
	for s := 0; s < 8; s++ {
		t7.Square(t7)
	}

	// Step 255: t7 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b11
	t7.Mul(z, t7)

	// Step 261: t7 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c440
	for s := 0; s < 6; s++ {
		t7.Square(t7)
	}

	// Step 262: t6 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f
	t6.Mul(t6, t7)

	// Step 268: t6 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117c0
	for s := 0; s < 6; s++ {
		t6.Square(t6)
	}

	// Step 269: t5 = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117dd
	t5.Mul(t5, t6)

	// Step 278: t5 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba00
	for s := 0; s < 9; s++ {
		t5.Square(t5)
	}

	// Step 279: t5 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09
	t5.Mul(t4, t5)

	// Step 284: t5 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f74120
	for s := 0; s < 5; s++ {
		t5.Square(t5)
	}

	// Step 285: t4 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f74129
	t4.Mul(t4, t5)

	// Step 304: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09480000
	for s := 0; s < 19; s++ {
		t4.Square(t4)
	}

	// Step 305: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba09480017
	t4.Mul(t2, t4)

	// Step 313: t4 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba0948001700
	for s := 0; s < 8; s++ {
		t4.Square(t4)
	}

	// Step 314: t3 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b
	t3.Mul(t3, t4)

	// Step 320: t3 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2c0
	for s := 0; s < 6; s++ {
		t3.Square(t3)
	}

	// Step 321: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d7
	t2.Mul(t2, t3)

	// Step 325: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d70
	for s := 0; s < 4; s++ {
		t2.Square(t2)
	}

	// Step 326: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d75
	t2.Mul(t0, t2)

	// Step 330: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d750
	for s := 0; s < 4; s++ {
		t2.Square(t2)
	}

	// Step 331: t2 = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d751
	t2.Mul(&x, t2)

	// Step 337: t2 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d440
	for s := 0; s < 6; s++ {
		t2.Square(t2)
	}

	// Step 338: t1 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443
	t1.Mul(t1, t2)

	// Step 367: t1 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba8860000000
	for s := 0; s < 29; s++ {
		t1.Square(t1)
	}

	// Step 368: t1 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba8860000001
	t1.Mul(&x, t1)

	// Step 375: t1 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443000000080
	for s := 0; s < 7; s++ {
		t1.Square(t1)
	}

	// Step 376: t0 = x^0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d443000000085
	t0.Mul(t0, t1)

	// Step 385: t0 = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba88600000010a00
	for s := 0; s < 9; s++ {
		t0.Square(t0)
	}

	// Step 386: z = x^0x35c748c2f8a21d58c760b80d94292763445b3e601ea271e3de6c45f741290002e16ba88600000010a11
	z.Mul(z, t0)

	// Step 387: z = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d7510c00000021422
	z.Square(z)

	// Step 388: z = x^0x6b8e9185f1443ab18ec1701b28524ec688b67cc03d44e3c7bcd88bee82520005c2d7510c00000021423
	z.Mul(&x, z)

	// Step 433: z = x^0xd71d230be28875631d82e03650a49d8d116cf9807a89c78f79b117dd04a4000b85aea2180000004284600000000000
	for s := 0; s < 45; s++ {
		z.Square(z)
	}

	return z
}