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gfp_invert_sqrt.go
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gfp_invert_sqrt.go
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// Code generated by addchain. DO NOT EDIT.
package bn256
// Invert sets e = 1/x, and returns e.
//
// If x == 0, Invert returns e = 0.
func (e *gfP) Invert(x *gfP) *gfP {
// Inversion is implemented as exponentiation with exponent p − 2.
// 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
// _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
// _1111011 = _110 + _1110101
// _10110110 = _111011 + _1111011
// i72 = ((_10110110 << 2 + 1) << 33 + _10101) << 8
// i94 = ((_11101 + i72) << 9 + _1101111) << 10 + _1110101
// i116 = ((2*i94 + 1) << 14 + _1110101) << 5
// i129 = 2*((_1101 + i116) << 9 + _1111011 + _100)
// i146 = ((1 + i129) << 5 + _1011) << 9 + _111011
// i174 = ((i146 << 8 + _11101) << 9 + _101001) << 9
// i194 = ((_11111 + i174) << 8 + _101001) << 9 + _1101001
// i220 = ((i194 << 8 + _1100011) << 8 + _1001111) << 8
// i237 = ((_1011101 + i220) << 7 + _1101101) << 7 + _1011111
// i260 = ((i237 << 8 + _101011) << 6 + _11111) << 7
// i279 = ((_11011 + i260) << 9 + _1001111) << 7 + _1100011
// i305 = ((i279 << 8 + _1010001) << 8 + _1000101) << 8
// return _1111011 + i305
//
var z = new(gfP).Set(e)
var t0 = new(gfP)
var t1 = new(gfP)
var t2 = new(gfP)
var t3 = new(gfP)
var t4 = new(gfP)
var t5 = new(gfP)
var t6 = new(gfP)
var t7 = new(gfP)
var t8 = new(gfP)
var t9 = new(gfP)
var t10 = new(gfP)
var t11 = new(gfP)
var t12 = new(gfP)
var t13 = new(gfP)
var t14 = new(gfP)
var t15 = new(gfP)
var t16 = new(gfP)
var t17 = new(gfP)
var t18 = new(gfP)
var t19 = new(gfP)
var t20 = new(gfP)
t17.Square(x, 1)
t15.Square(t17, 1)
z.Mul(t17, t15)
t2.Mul(t15, z)
t14.Mul(x, t2)
t16.Mul(t17, t14)
t0.Mul(z, t2)
t19.Mul(t2, t14)
t4.Mul(z, t19)
t12.Mul(t17, t4)
t5.Mul(t17, t12)
t11.Mul(t2, t5)
t6.Mul(t17, t11)
t13.Mul(t0, t6)
t0.Mul(t2, t13)
t3.Mul(t2, t0)
t1.Mul(t17, t3)
t2.Mul(t2, t1)
t9.Mul(t17, t2)
t7.Mul(t17, t9)
t2.Mul(t15, t7)
t10.Mul(z, t2)
t8.Mul(t15, t10)
t18.Mul(t17, t8)
t17.Mul(z, t18)
z.Mul(z, t17)
t20.Mul(t13, z)
t20.Square(t20, 2)
t20.Mul(x, t20)
t20.Square(t20, 33)
t19.Mul(t19, t20)
t19.Square(t19, 8)
t19.Mul(t12, t19)
t19.Square(t19, 9)
t18.Mul(t18, t19)
t18.Square(t18, 10)
t18.Mul(t17, t18)
t18.Square(t18, 1)
t18.Mul(x, t18)
t18.Square(t18, 14)
t17.Mul(t17, t18)
t17.Square(t17, 5)
t16.Mul(t16, t17)
t16.Square(t16, 9)
t16.Mul(z, t16)
t15.Mul(t15, t16)
t15.Square(t15, 1)
t15.Mul(x, t15)
t15.Square(t15, 5)
t14.Mul(t14, t15)
t14.Square(t14, 9)
t13.Mul(t13, t14)
t13.Square(t13, 8)
t12.Mul(t12, t13)
t12.Square(t12, 9)
t12.Mul(t11, t12)
t12.Square(t12, 9)
t12.Mul(t5, t12)
t12.Square(t12, 8)
t11.Mul(t11, t12)
t11.Square(t11, 9)
t10.Mul(t10, t11)
t10.Square(t10, 8)
t10.Mul(t2, t10)
t10.Square(t10, 8)
t10.Mul(t3, t10)
t10.Square(t10, 8)
t9.Mul(t9, t10)
t9.Square(t9, 7)
t8.Mul(t8, t9)
t8.Square(t8, 7)
t7.Mul(t7, t8)
t7.Square(t7, 8)
t6.Mul(t6, t7)
t6.Square(t6, 6)
t5.Mul(t5, t6)
t5.Square(t5, 7)
t4.Mul(t4, t5)
t4.Square(t4, 9)
t3.Mul(t3, t4)
t3.Square(t3, 7)
t2.Mul(t2, t3)
t2.Square(t2, 8)
t1.Mul(t1, t2)
t1.Square(t1, 8)
t0.Mul(t0, t1)
t0.Square(t0, 8)
z.Mul(z, t0)
return e.Set(z)
}
// Sqrt sets e to a square root of x. If x is not a square, Sqrt returns
// false and e is unchanged. e and x can overlap.
func Sqrt(e, x *gfP) (isSquare bool) {
candidate, b, i := &gfP{}, &gfP{}, &gfP{}
sqrtCandidate(candidate, x)
gfpMul(b, twoExpPMinus5Over8, candidate) // b=ta1
gfpMul(candidate, x, b) // a1=fb
gfpMul(i, two, candidate) // i=2(fb)
gfpMul(i, i, b) // i=2(fb)b
gfpSub(i, i, one) // i=2(fb)b-1
gfpMul(i, candidate, i) // i=(fb)(2(fb)b-1)
square := new(gfP).Square(i, 1)
if square.Equal(x) != 1 {
return false
}
e.Set(i)
return true
}
// sqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
func sqrtCandidate(z, x *gfP) {
// Since p = 8k+5, exponentiation by (p - 5) / 8 yields a square root candidate.
//
// The sequence of 54 multiplications and 248 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
// _1111 = _10 + _1101
// _10000 = 1 + _1111
// _10101 = _110 + _1111
// _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
// i72 = ((_1011011 << 3 + 1) << 33 + _10101) << 8
// i94 = ((_11101 + i72) << 9 + _1101111) << 10 + _1110101
// i116 = ((2*i94 + 1) << 14 + _1110101) << 5
// i129 = 2*((_1101 + i116) << 9 + _1110101) + _10101
// i153 = ((i129 << 5 + _1011) << 9 + _111011) << 8
// i174 = ((_11101 + i153) << 9 + _101001) << 9 + _11111
// i201 = ((i174 << 8 + _101001) << 9 + _1101001) << 8
// i220 = ((_1100011 + i201) << 8 + _1001111) << 8 + _1011101
// i244 = ((i220 << 7 + _1101101) << 7 + _1011111) << 8
// i260 = ((_101011 + i244) << 6 + _11111) << 7 + _11011
// i286 = ((i260 << 9 + _1001111) << 7 + _1100011) << 8
// return ((_1010001 + i286) << 8 + _1000101) << 5 + _1111
//
var t0 = new(gfP)
var t1 = new(gfP)
var t2 = new(gfP)
var t3 = new(gfP)
var t4 = new(gfP)
var t5 = new(gfP)
var t6 = new(gfP)
var t7 = new(gfP)
var t8 = new(gfP)
var t9 = new(gfP)
var t10 = new(gfP)
var t11 = new(gfP)
var t12 = new(gfP)
var t13 = new(gfP)
var t14 = new(gfP)
var t15 = new(gfP)
var t16 = new(gfP)
var t17 = new(gfP)
var t18 = new(gfP)
var t19 = new(gfP)
t18.Square(x, 1)
t8.Square(t18, 1)
t16.Mul(t18, t8)
t2.Mul(t8, t16)
t14.Mul(x, t2)
t17.Mul(t18, t14)
z.Mul(t18, t17)
t0.Mul(x, z)
t15.Mul(t16, z)
t4.Mul(t16, t15)
t12.Mul(t18, t4)
t5.Mul(t18, t12)
t11.Mul(t2, t5)
t6.Mul(t18, t11)
t13.Mul(t0, t6)
t0.Mul(t2, t13)
t3.Mul(t2, t0)
t1.Mul(t18, t3)
t19.Mul(t2, t1)
t9.Mul(t18, t19)
t7.Mul(t18, t9)
t2.Mul(t8, t7)
t10.Mul(t16, t2)
t8.Mul(t8, t10)
t18.Mul(t18, t8)
t16.Mul(t16, t18)
t19.Square(t19, 3)
t19.Mul(x, t19)
t19.Square(t19, 33)
t19.Mul(t15, t19)
t19.Square(t19, 8)
t19.Mul(t12, t19)
t19.Square(t19, 9)
t18.Mul(t18, t19)
t18.Square(t18, 10)
t18.Mul(t16, t18)
t18.Square(t18, 1)
t18.Mul(x, t18)
t18.Square(t18, 14)
t18.Mul(t16, t18)
t18.Square(t18, 5)
t17.Mul(t17, t18)
t17.Square(t17, 9)
t16.Mul(t16, t17)
t16.Square(t16, 1)
t15.Mul(t15, t16)
t15.Square(t15, 5)
t14.Mul(t14, t15)
t14.Square(t14, 9)
t13.Mul(t13, t14)
t13.Square(t13, 8)
t12.Mul(t12, t13)
t12.Square(t12, 9)
t12.Mul(t11, t12)
t12.Square(t12, 9)
t12.Mul(t5, t12)
t12.Square(t12, 8)
t11.Mul(t11, t12)
t11.Square(t11, 9)
t10.Mul(t10, t11)
t10.Square(t10, 8)
t10.Mul(t2, t10)
t10.Square(t10, 8)
t10.Mul(t3, t10)
t10.Square(t10, 8)
t9.Mul(t9, t10)
t9.Square(t9, 7)
t8.Mul(t8, t9)
t8.Square(t8, 7)
t7.Mul(t7, t8)
t7.Square(t7, 8)
t6.Mul(t6, t7)
t6.Square(t6, 6)
t5.Mul(t5, t6)
t5.Square(t5, 7)
t4.Mul(t4, t5)
t4.Square(t4, 9)
t3.Mul(t3, t4)
t3.Square(t3, 7)
t2.Mul(t2, t3)
t2.Square(t2, 8)
t1.Mul(t1, t2)
t1.Square(t1, 8)
t0.Mul(t0, t1)
t0.Square(t0, 5)
z.Mul(z, t0)
}