// n = len(m.nat.limbs).
//
// Faster Montgomery multiplication replaces standard modular multiplication for
// numbers in this representation.
//
// This assumes that x is already reduced mod m.
func (x *Nat) montgomeryRepresentation(m *Modulus) *Nat {
	// A Montgomery multiplication (which computes a * b / R) by R * R works out
	// to a multiplication by R, which takes the value out of the Montgomery domain.

func karatsuba(z, x, y nat) {
	n := len(y)

	// Switch to basic multiplication if numbers are odd or small.
	// (n is always even if karatsubaThreshold is even, but be
	// conservative)
	if n&1 != 0 || n < karatsubaThreshold || n < 2 {
		basicMul(z, x, y)
		return
	}
	// n&1 == 0 && n >= karatsubaThreshold && n >= 2

	// Karatsuba multiplication is based on the observation that
	// for two numbers x and y with:
	//

	var overflow bool
	var lenmem, newlenmem, capmem uintptr
	// Specialize for common values of et.Size.
	// For 1 we don't need any division/multiplication.
	// For goarch.PtrSize, compiler will optimize division/multiplication into a shift by a constant.
	// For powers of 2, use a variable shift.
	noscan := !et.Pointers()
	switch {
	case et.Size_ == 1:
		lenmem = uintptr(oldLen)

        return self.bias_fn() and self.bias_size != self.filters.shape[-1]

      @def_function.function
      def matmul(self, input_tensor: core.Tensor) -> Mapping[str, core.Tensor]:
        """Performs a matrix multiplication.

        Depending on self.bias_fn and self.activation_fn, it may add a bias
        term or go through the activaction function.

        Args:
          input_tensor: Input tensor to matmul with the filter.

// The following assembly functions are implemented in p256_asm_*.s

// Montgomery multiplication. Sets res = in1 * in2 * R⁻¹ mod p.
//
//go:noescape
func p256Mul(res, in1, in2 *p256Element)

// Montgomery square, repeated n times (n >= 1).
//
//go:noescape
func p256Sqr(res, in *p256Element, n int)

// Montgomery multiplication by R⁻¹, or 1 outside the domain.

	//
	// We want to compute
	// 	hi, lo := bits.Mul64(r.Uint64(), n)
	// In terms of 32-bit halves, this is:
	// 	x1:x0 := r.Uint64()
	// 	0:hi, lo1:lo0 := bits.Mul64(x1:x0, 0:n)
	// Writing out the multiplication in terms of bits.Mul32 allows
	// using direct hardware instructions and avoiding
	// the computations involving these zeros.
	x := r.Uint64()
	lo1a, lo0 := bits.Mul32(uint32(x), n)

	r := a - (b + a)
	return r
}

func AddAddSubSimplify(a, b, c int) int {
	// amd64:-"SUBQ"
	// ppc64x:-"SUB"
	r := a + (b + (c - a))
	return r
}

// -------------------- //
//    Multiplication    //
// -------------------- //

func Pow2Muls(n1, n2 int) (int, int) {
	// amd64:"SHLQ\t[$]5",-"IMULQ"
	// 386:"SHLL\t[$]5",-"IMULL"
	// arm:"SLL\t[$]5",-"MUL"
	// arm64:"LSL\t[$]5",-"MUL"

func (g *gcm) mul(y *gcmFieldElement) {
	var z gcmFieldElement

	for i := 0; i < 2; i++ {
		word := y.high
		if i == 1 {
			word = y.low
		}

		// Multiplication works by multiplying z by 16 and adding in
		// one of the precomputed multiples of H.
		for j := 0; j < 64; j += 4 {
			msw := z.high & 0xf
			z.high >>= 4
			z.high |= z.low << 60
			z.low >>= 4

		z.form = zero
		z.neg = false
		return
	}
	// len(z.mant) > 0

	z.setExpAndRound(ex+int64(len(z.mant))*_W-fnorm(z.mant), 0)
}

// z = x * y, ignoring signs of x and y for the multiplication
// but using the sign of z for rounding the result.
// x and y must have a non-empty mantissa and valid exponent.
func (z *Float) umul(x, y *Float) {
	if debugFloat {
		validateBinaryOperands(x, y)
	}

	// can interpret x as the sum of three shorter values a, b, and c.
	//
	//    x = a + b * 2^168 + c * 2^336  mod l
	//
	// We then precompute 2^168 and 2^336 modulo l, and perform the reduction
	// with two multiplications and two additions.

	s.setShortBytes(x[:21])
	t := new(Scalar).setShortBytes(x[21:42])
	s.Add(s, t.Multiply(t, scalarTwo168))
	t.setShortBytes(x[42:])
	s.Add(s, t.Multiply(t, scalarTwo336))