} else {
		y1 = Pow(x, x-0.5) / y1
	}
	return y1, SqrtTwoPi * w * y2
}

// Gamma returns the Gamma function of x.
//
// Special cases are:
//
//	Gamma(+Inf) = +Inf
//	Gamma(+0) = +Inf
//	Gamma(-0) = -Inf
//	Gamma(x) = NaN for integer x < 0
//	Gamma(-Inf) = NaN
//	Gamma(NaN) = NaN
func Gamma(x float64) float64 {
	const Euler = 0.57721566490153286060651209008240243104215933593992 // A001620

	-1.63092934096575273989e-03, // 0xBF5AB89D0B9E43E4
}

// Lgamma returns the natural logarithm and sign (-1 or +1) of [Gamma](x).
//
// Special cases are:
//
//	Lgamma(+Inf) = +Inf
//	Lgamma(0) = +Inf
//	Lgamma(-integer) = +Inf
//	Lgamma(-Inf) = -Inf
//	Lgamma(NaN) = NaN
func Lgamma(x float64) (lgamma float64, sign int) {
	const (
		Ymin  = 1.461632144968362245

            "Rsqrt", "Sigmoid", "Sign", "Sinh", "Softplus", "Softsign", "Sqrt",
            "Square", "Tan", "Tanh", "Real", "Imag", "Erf", "Erfc", "Erfinv",
            "Lgamma", "Digamma",
            // Binary
            "Add", "AddV2", "Sub", "Mul", "Div", "Atan2", "Complex", "DivNoNan",
            "MulNoNan", "FloorDiv", "Xlogy", "Xlog1py", "Xdivy", "FloorMod",

Alexander Zielenski <******@****.***> 1697824555 -0700

	for i := 0; i < len(vf); i++ {
		if f, s := Lgamma(vf[i]); !close(lgamma[i].f, f) || lgamma[i].i != s {
			t.Errorf("Lgamma(%g) = %g, %d, want %g, %d", vf[i], f, s, lgamma[i].f, lgamma[i].i)
		}
	}
	for i := 0; i < len(vflgammaSC); i++ {
		if f, s := Lgamma(vflgammaSC[i]); !alike(lgammaSC[i].f, f) || lgammaSC[i].i != s {
			t.Errorf("Lgamma(%g) = %g, %d, want %g, %d", vflgammaSC[i], f, s, lgammaSC[i].f, lgammaSC[i].i)

		}
	}
}

func TestGammas(t *testing.T) {
	ζ := big.NewInt(17)
	q := big.NewInt(q)
	for k, gamma := range gammas {
		// ζ^2BitRev7(i)+1
		exp := new(big.Int).Exp(ζ, big.NewInt(int64(BitRev7(uint8(k)))*2+1), q)
		if big.NewInt(int64(gamma)).Cmp(exp) != 0 {
			t.Errorf("gammas[%d] = %v, expected %v", k, gamma, exp)
		}
	}
}

func TestRoundTrip(t *testing.T) {
	dk, err := GenerateKey()
	if err != nil {

    // Compute the reflected value, used when x < 0.5:
    //
    //   lgamma(x) = log(pi) - lgamma(1-x) - log(abs(sin(pi * x))).
    //
    // (The abs is because lgamma is the log of the absolute value of the gamma
    // function.)
    //
    // We have to be careful when computing the final term above. gamma(x) goes
    // to +/-inf at every integer x < 0, and this is controlled by the

          task alpha {
            description = 'ALPHA from sub project'
          }
          task beta {
            description = 'BETA from sub project'
          }
          task gamma {
            description = 'GAMMA from sub'
          }
        '''

        when:
        def buildInvocations = withConnection { ProjectConnection connection ->
            connection.getModel(BuildInvocations.class)
        }

	z3.Mul(z3, z3)
	z3.Sub(z3, gamma)
	if z3.Sign() == -1 {
		z3.Add(z3, curve.P)
	}
	z3.Sub(z3, delta)
	if z3.Sign() == -1 {
		z3.Add(z3, curve.P)
	}
	z3.Mod(z3, curve.P)

	beta.Lsh(beta, 2)
	beta.Sub(beta, x3)
	if beta.Sign() == -1 {
		beta.Add(beta, curve.P)
	}
	y3 := alpha.Mul(alpha, beta)

	gamma.Mul(gamma, gamma)
	gamma.Lsh(gamma, 3)
	gamma.Mod(gamma, curve.P)

    value {
      s: "res5a_branch1/kernel"
    }
  }
}
node {
  name: "bn5a_branch1/gamma"
  op: "VarHandleOp"
  device: "/job:localhost/replica:0/task:0/device:GPU:0"
  attr {
    key: "_class"
    value {
      list {
        s: "loc:@training/SGD/bn5a_branch1/gamma/momentum"
      }
    }
  }
  attr {
    key: "container"
    value {
      s: ""