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gmsm/sm9/bn256/gfp2_sqrt.go
emmansun 13ddfad8e4 sm9: optimize generate and gfP2 sqrt
2023-04-29 13:33:44 +08:00

641 lines
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// Code generated by addchain. DO NOT EDIT.
package bn256
func (e *gfP2) expPMinus1Over4(x *gfP2) *gfP2 {
// The sequence of 53 multiplications and 249 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
// _10 = 2*1
// _100 = 2*_10
// _110 = _10 + _100
// _1010 = _100 + _110
// _1011 = 1 + _1010
// _1101 = _10 + _1011
// _10000 = _110 + _1010
// _10101 = _1010 + _1011
// _11011 = _110 + _10101
// _11101 = _10 + _11011
// _11111 = _10 + _11101
// _101001 = _1010 + _11111
// _101011 = _10 + _101001
// _111011 = _10000 + _101011
// _1000101 = _1010 + _111011
// _1001111 = _1010 + _1000101
// _1010001 = _10 + _1001111
// _1011011 = _1010 + _1010001
// _1011101 = _10 + _1011011
// _1011111 = _10 + _1011101
// _1100011 = _100 + _1011111
// _1101001 = _110 + _1100011
// _1101101 = _100 + _1101001
// _1101111 = _10 + _1101101
// _1110101 = _110 + _1101111
// i71 = ((_1011011 << 3 + 1) << 33 + _10101) << 8
// i93 = ((_11101 + i71) << 9 + _1101111) << 10 + _1110101
// i115 = ((2*i93 + 1) << 14 + _1110101) << 5
// i128 = 2*((_1101 + i115) << 9 + _1110101) + _10101
// i152 = ((i128 << 5 + _1011) << 9 + _111011) << 8
// i173 = ((_11101 + i152) << 9 + _101001) << 9 + _11111
// i200 = ((i173 << 8 + _101001) << 9 + _1101001) << 8
// i219 = ((_1100011 + i200) << 8 + _1001111) << 8 + _1011101
// i243 = ((i219 << 7 + _1101101) << 7 + _1011111) << 8
// i259 = ((_101011 + i243) << 6 + _11111) << 7 + _11011
// i285 = ((i259 << 9 + _1001111) << 7 + _1100011) << 8
// return ((_1010001 + i285) << 8 + _1000101) << 6 + _11111
//
var z = new(gfP2).Set(e)
var t0 = new(gfP2)
var t1 = new(gfP2)
var t2 = new(gfP2)
var t3 = new(gfP2)
var t4 = new(gfP2)
var t5 = new(gfP2)
var t6 = new(gfP2)
var t7 = new(gfP2)
var t8 = new(gfP2)
var t9 = new(gfP2)
var t10 = new(gfP2)
var t11 = new(gfP2)
var t12 = new(gfP2)
var t13 = new(gfP2)
var t14 = new(gfP2)
var t15 = new(gfP2)
var t16 = new(gfP2)
var t17 = new(gfP2)
var t18 = new(gfP2)
t17.Square(x)
t7.Square(t17)
t15.Mul(t17, t7)
t2.Mul(t7, t15)
t13.Mul(x, t2)
t16.Mul(t17, t13)
t0.Mul(t15, t2)
t14.Mul(t2, t13)
t4.Mul(t15, t14)
t11.Mul(t17, t4)
z.Mul(t17, t11)
t10.Mul(t2, z)
t5.Mul(t17, t10)
t12.Mul(t0, t5)
t0.Mul(t2, t12)
t3.Mul(t2, t0)
t1.Mul(t17, t3)
t18.Mul(t2, t1)
t8.Mul(t17, t18)
t6.Mul(t17, t8)
t2.Mul(t7, t6)
t9.Mul(t15, t2)
t7.Mul(t7, t9)
t17.Mul(t17, t7)
t15.Mul(t15, t17)
for s := 0; s < 3; s++ {
t18.Square(t18)
}
t18.Mul(x, t18)
for s := 0; s < 33; s++ {
t18.Square(t18)
}
t18.Mul(t14, t18)
for s := 0; s < 8; s++ {
t18.Square(t18)
}
t18.Mul(t11, t18)
for s := 0; s < 9; s++ {
t18.Square(t18)
}
t17.Mul(t17, t18)
for s := 0; s < 10; s++ {
t17.Square(t17)
}
t17.Mul(t15, t17)
t17.Square(t17)
t17.Mul(x, t17)
for s := 0; s < 14; s++ {
t17.Square(t17)
}
t17.Mul(t15, t17)
for s := 0; s < 5; s++ {
t17.Square(t17)
}
t16.Mul(t16, t17)
for s := 0; s < 9; s++ {
t16.Square(t16)
}
t15.Mul(t15, t16)
t15.Square(t15)
t14.Mul(t14, t15)
for s := 0; s < 5; s++ {
t14.Square(t14)
}
t13.Mul(t13, t14)
for s := 0; s < 9; s++ {
t13.Square(t13)
}
t12.Mul(t12, t13)
for s := 0; s < 8; s++ {
t12.Square(t12)
}
t11.Mul(t11, t12)
for s := 0; s < 9; s++ {
t11.Square(t11)
}
t11.Mul(t10, t11)
for s := 0; s < 9; s++ {
t11.Square(t11)
}
t11.Mul(z, t11)
for s := 0; s < 8; s++ {
t11.Square(t11)
}
t10.Mul(t10, t11)
for s := 0; s < 9; s++ {
t10.Square(t10)
}
t9.Mul(t9, t10)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t9.Mul(t2, t9)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t9.Mul(t3, t9)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t8.Mul(t8, t9)
for s := 0; s < 7; s++ {
t8.Square(t8)
}
t7.Mul(t7, t8)
for s := 0; s < 7; s++ {
t7.Square(t7)
}
t6.Mul(t6, t7)
for s := 0; s < 8; s++ {
t6.Square(t6)
}
t5.Mul(t5, t6)
for s := 0; s < 6; s++ {
t5.Square(t5)
}
t5.Mul(z, t5)
for s := 0; s < 7; s++ {
t5.Square(t5)
}
t4.Mul(t4, t5)
for s := 0; s < 9; s++ {
t4.Square(t4)
}
t3.Mul(t3, t4)
for s := 0; s < 7; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
for s := 0; s < 8; s++ {
t2.Square(t2)
}
t1.Mul(t1, t2)
for s := 0; s < 8; s++ {
t1.Square(t1)
}
t0.Mul(t0, t1)
for s := 0; s < 6; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
return e.Set(z)
}
func (e *gfP2) expP(x *gfP2) *gfP2 {
// The sequence of 56 multiplications and 250 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
// _10 = 2*1
// _11 = 1 + _10
// _100 = 1 + _11
// _101 = 1 + _100
// _1000 = _11 + _101
// _1001 = 1 + _1000
// _1011 = _10 + _1001
// _1101 = _10 + _1011
// _10101 = _1000 + _1101
// _11001 = _100 + _10101
// _11101 = _100 + _11001
// _11111 = _10 + _11101
// _100011 = _100 + _11111
// _100101 = _10 + _100011
// _101001 = _100 + _100101
// _101011 = _10 + _101001
// _101101 = _10 + _101011
// _101111 = _10 + _101101
// _110011 = _100 + _101111
// _110101 = _10 + _110011
// _110111 = _10 + _110101
// _111011 = _100 + _110111
// _111101 = _10 + _111011
// _111111 = _10 + _111101
// _1011010 = _11101 + _111101
// i71 = ((_1011010 << 3 + _1001) << 33 + _10101) << 8
// i88 = ((_11101 + i71) << 8 + _110111) << 6 + _100011
// i115 = ((i88 << 6 + _101011) << 12 + _11101) << 7
// i128 = ((_101101 + i115) << 8 + _111111) << 2 + _11
// i152 = ((i128 << 5 + _1011) << 9 + _111011) << 8
// i173 = ((_11101 + i152) << 9 + _101001) << 9 + _11111
// i195 = ((i173 << 8 + _101001) << 6 + _1101) << 6
// i213 = ((_1011 + i195) << 7 + _1101) << 8 + _111101
// i234 = ((i213 << 7 + _111011) << 6 + _101101) << 6
// i250 = ((_101111 + i234) << 6 + _100101) << 7 + _110111
// i272 = ((i250 << 6 + _110011) << 6 + _11001) << 8
// i290 = ((_111111 + i272) << 9 + _110101) << 6 + _101
// return (i290 << 9 + _101011) << 5 + _11101
//
var z = new(gfP2).Set(e)
var t0 = new(gfP2)
var t1 = new(gfP2)
var t2 = new(gfP2)
var t3 = new(gfP2)
var t4 = new(gfP2)
var t5 = new(gfP2)
var t6 = new(gfP2)
var t7 = new(gfP2)
var t8 = new(gfP2)
var t9 = new(gfP2)
var t10 = new(gfP2)
var t11 = new(gfP2)
var t12 = new(gfP2)
var t13 = new(gfP2)
var t14 = new(gfP2)
var t15 = new(gfP2)
var t16 = new(gfP2)
var t17 = new(gfP2)
var t18 = new(gfP2)
var t19 = new(gfP2)
var t20 = new(gfP2)
t3.Square(x)
t16.Mul(x, t3)
t10.Mul(x, t16)
t1.Mul(x, t10)
z.Mul(t16, t1)
t19.Mul(x, z)
t13.Mul(t3, t19)
t12.Mul(t3, t13)
t18.Mul(z, t12)
t4.Mul(t10, t18)
z.Mul(t10, t4)
t15.Mul(t3, z)
t17.Mul(t10, t15)
t7.Mul(t3, t17)
t14.Mul(t10, t7)
t0.Mul(t3, t14)
t9.Mul(t3, t0)
t8.Mul(t3, t9)
t5.Mul(t10, t8)
t2.Mul(t3, t5)
t6.Mul(t3, t2)
t10.Mul(t10, t6)
t11.Mul(t3, t10)
t3.Mul(t3, t11)
t20.Mul(z, t11)
for s := 0; s < 3; s++ {
t20.Square(t20)
}
t19.Mul(t19, t20)
for s := 0; s < 33; s++ {
t19.Square(t19)
}
t18.Mul(t18, t19)
for s := 0; s < 8; s++ {
t18.Square(t18)
}
t18.Mul(z, t18)
for s := 0; s < 8; s++ {
t18.Square(t18)
}
t18.Mul(t6, t18)
for s := 0; s < 6; s++ {
t18.Square(t18)
}
t17.Mul(t17, t18)
for s := 0; s < 6; s++ {
t17.Square(t17)
}
t17.Mul(t0, t17)
for s := 0; s < 12; s++ {
t17.Square(t17)
}
t17.Mul(z, t17)
for s := 0; s < 7; s++ {
t17.Square(t17)
}
t17.Mul(t9, t17)
for s := 0; s < 8; s++ {
t17.Square(t17)
}
t17.Mul(t3, t17)
for s := 0; s < 2; s++ {
t17.Square(t17)
}
t16.Mul(t16, t17)
for s := 0; s < 5; s++ {
t16.Square(t16)
}
t16.Mul(t13, t16)
for s := 0; s < 9; s++ {
t16.Square(t16)
}
t16.Mul(t10, t16)
for s := 0; s < 8; s++ {
t16.Square(t16)
}
t16.Mul(z, t16)
for s := 0; s < 9; s++ {
t16.Square(t16)
}
t16.Mul(t14, t16)
for s := 0; s < 9; s++ {
t16.Square(t16)
}
t15.Mul(t15, t16)
for s := 0; s < 8; s++ {
t15.Square(t15)
}
t14.Mul(t14, t15)
for s := 0; s < 6; s++ {
t14.Square(t14)
}
t14.Mul(t12, t14)
for s := 0; s < 6; s++ {
t14.Square(t14)
}
t13.Mul(t13, t14)
for s := 0; s < 7; s++ {
t13.Square(t13)
}
t12.Mul(t12, t13)
for s := 0; s < 8; s++ {
t12.Square(t12)
}
t11.Mul(t11, t12)
for s := 0; s < 7; s++ {
t11.Square(t11)
}
t10.Mul(t10, t11)
for s := 0; s < 6; s++ {
t10.Square(t10)
}
t9.Mul(t9, t10)
for s := 0; s < 6; s++ {
t9.Square(t9)
}
t8.Mul(t8, t9)
for s := 0; s < 6; s++ {
t8.Square(t8)
}
t7.Mul(t7, t8)
for s := 0; s < 7; s++ {
t7.Square(t7)
}
t6.Mul(t6, t7)
for s := 0; s < 6; s++ {
t6.Square(t6)
}
t5.Mul(t5, t6)
for s := 0; s < 6; s++ {
t5.Square(t5)
}
t4.Mul(t4, t5)
for s := 0; s < 8; s++ {
t4.Square(t4)
}
t3.Mul(t3, t4)
for s := 0; s < 9; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
for s := 0; s < 6; s++ {
t2.Square(t2)
}
t1.Mul(t1, t2)
for s := 0; s < 9; s++ {
t1.Square(t1)
}
t0.Mul(t0, t1)
for s := 0; s < 5; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
return e.Set(z)
}
func (e *gfP2) expPMinus1Over2(x *gfP2) *gfP2 {
// The sequence of 53 multiplications and 250 squarings is derived from the
// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
//
// _10 = 2*1
// _100 = 2*_10
// _110 = _10 + _100
// _1010 = _100 + _110
// _1011 = 1 + _1010
// _1101 = _10 + _1011
// _10000 = _110 + _1010
// _10101 = _1010 + _1011
// _11011 = _110 + _10101
// _11101 = _10 + _11011
// _11111 = _10 + _11101
// _101001 = _1010 + _11111
// _101011 = _10 + _101001
// _111011 = _10000 + _101011
// _1000101 = _1010 + _111011
// _1001111 = _1010 + _1000101
// _1010001 = _10 + _1001111
// _1011011 = _1010 + _1010001
// _1011101 = _10 + _1011011
// _1011111 = _10 + _1011101
// _1100011 = _100 + _1011111
// _1101001 = _110 + _1100011
// _1101101 = _100 + _1101001
// _1101111 = _10 + _1101101
// _1110101 = _110 + _1101111
// i71 = ((_1011011 << 3 + 1) << 33 + _10101) << 8
// i93 = ((_11101 + i71) << 9 + _1101111) << 10 + _1110101
// i115 = ((2*i93 + 1) << 14 + _1110101) << 5
// i128 = 2*((_1101 + i115) << 9 + _1110101) + _10101
// i152 = ((i128 << 5 + _1011) << 9 + _111011) << 8
// i173 = ((_11101 + i152) << 9 + _101001) << 9 + _11111
// i200 = ((i173 << 8 + _101001) << 9 + _1101001) << 8
// i219 = ((_1100011 + i200) << 8 + _1001111) << 8 + _1011101
// i243 = ((i219 << 7 + _1101101) << 7 + _1011111) << 8
// i259 = ((_101011 + i243) << 6 + _11111) << 7 + _11011
// i285 = ((i259 << 9 + _1001111) << 7 + _1100011) << 8
// i302 = ((_1010001 + i285) << 8 + _1000101) << 6 + _11111
// return 2*i302
//
var z = new(gfP2).Set(e)
var t0 = new(gfP2)
var t1 = new(gfP2)
var t2 = new(gfP2)
var t3 = new(gfP2)
var t4 = new(gfP2)
var t5 = new(gfP2)
var t6 = new(gfP2)
var t7 = new(gfP2)
var t8 = new(gfP2)
var t9 = new(gfP2)
var t10 = new(gfP2)
var t11 = new(gfP2)
var t12 = new(gfP2)
var t13 = new(gfP2)
var t14 = new(gfP2)
var t15 = new(gfP2)
var t16 = new(gfP2)
var t17 = new(gfP2)
var t18 = new(gfP2)
t17.Square(x)
t7.Square(t17)
t15.Mul(t17, t7)
t2.Mul(t7, t15)
t13.Mul(x, t2)
t16.Mul(t17, t13)
t0.Mul(t15, t2)
t14.Mul(t2, t13)
t4.Mul(t15, t14)
t11.Mul(t17, t4)
z.Mul(t17, t11)
t10.Mul(t2, z)
t5.Mul(t17, t10)
t12.Mul(t0, t5)
t0.Mul(t2, t12)
t3.Mul(t2, t0)
t1.Mul(t17, t3)
t18.Mul(t2, t1)
t8.Mul(t17, t18)
t6.Mul(t17, t8)
t2.Mul(t7, t6)
t9.Mul(t15, t2)
t7.Mul(t7, t9)
t17.Mul(t17, t7)
t15.Mul(t15, t17)
for s := 0; s < 3; s++ {
t18.Square(t18)
}
t18.Mul(x, t18)
for s := 0; s < 33; s++ {
t18.Square(t18)
}
t18.Mul(t14, t18)
for s := 0; s < 8; s++ {
t18.Square(t18)
}
t18.Mul(t11, t18)
for s := 0; s < 9; s++ {
t18.Square(t18)
}
t17.Mul(t17, t18)
for s := 0; s < 10; s++ {
t17.Square(t17)
}
t17.Mul(t15, t17)
t17.Square(t17)
t17.Mul(x, t17)
for s := 0; s < 14; s++ {
t17.Square(t17)
}
t17.Mul(t15, t17)
for s := 0; s < 5; s++ {
t17.Square(t17)
}
t16.Mul(t16, t17)
for s := 0; s < 9; s++ {
t16.Square(t16)
}
t15.Mul(t15, t16)
t15.Square(t15)
t14.Mul(t14, t15)
for s := 0; s < 5; s++ {
t14.Square(t14)
}
t13.Mul(t13, t14)
for s := 0; s < 9; s++ {
t13.Square(t13)
}
t12.Mul(t12, t13)
for s := 0; s < 8; s++ {
t12.Square(t12)
}
t11.Mul(t11, t12)
for s := 0; s < 9; s++ {
t11.Square(t11)
}
t11.Mul(t10, t11)
for s := 0; s < 9; s++ {
t11.Square(t11)
}
t11.Mul(z, t11)
for s := 0; s < 8; s++ {
t11.Square(t11)
}
t10.Mul(t10, t11)
for s := 0; s < 9; s++ {
t10.Square(t10)
}
t9.Mul(t9, t10)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t9.Mul(t2, t9)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t9.Mul(t3, t9)
for s := 0; s < 8; s++ {
t9.Square(t9)
}
t8.Mul(t8, t9)
for s := 0; s < 7; s++ {
t8.Square(t8)
}
t7.Mul(t7, t8)
for s := 0; s < 7; s++ {
t7.Square(t7)
}
t6.Mul(t6, t7)
for s := 0; s < 8; s++ {
t6.Square(t6)
}
t5.Mul(t5, t6)
for s := 0; s < 6; s++ {
t5.Square(t5)
}
t5.Mul(z, t5)
for s := 0; s < 7; s++ {
t5.Square(t5)
}
t4.Mul(t4, t5)
for s := 0; s < 9; s++ {
t4.Square(t4)
}
t3.Mul(t3, t4)
for s := 0; s < 7; s++ {
t3.Square(t3)
}
t2.Mul(t2, t3)
for s := 0; s < 8; s++ {
t2.Square(t2)
}
t1.Mul(t1, t2)
for s := 0; s < 8; s++ {
t1.Square(t1)
}
t0.Mul(t0, t1)
for s := 0; s < 6; s++ {
t0.Square(t0)
}
z.Mul(z, t0)
z.Square(z)
return e.Set(z)
}
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