// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

//go:build (amd64 || arm64) && !purego

package nistec

import "errors"

// Montgomery multiplication modulo org(G). Sets res = in1 * in2 * R⁻¹.
//
//go:noescape
func p256OrdMul(res, in1, in2 *p256OrdElement)

// Montgomery square modulo org(G), repeated n times (n >= 1).
//
//go:noescape

			h1, c = bits.Add64(h1, binary.LittleEndian.Uint64(buf[8:16]), c)
			h2 += c

			msg = nil
		}

		// Multiplication of big number limbs is similar to elementary school
		// columnar multiplication. Instead of digits, there are 64-bit limbs.
		//
		// We are multiplying a 3 limbs number, h, by a 2 limbs number, r.
		//
		//                        h2    h1    h0  x

// 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.

	HasASIMD    bool // Advanced SIMD (always available)
	HasEVTSTRM  bool // Event stream support
	HasAES      bool // AES hardware implementation
	HasPMULL    bool // Polynomial multiplication instruction set
	HasSHA1     bool // SHA1 hardware implementation
	HasSHA2     bool // SHA2 hardware implementation
	HasCRC32    bool // CRC32 hardware implementation

		hash ^= sum64a(c)
		hash *= prime64
	}
	*s = hash
	return len(data), nil
}

func (s *sum128) Write(data []byte) (int, error) {
	for _, c := range data {
		// Compute the multiplication
		s0, s1 := bits.Mul64(prime128Lower, s[1])
		s0 += s[1]<<prime128Shift + prime128Lower*s[0]
		// Update the values
		s[1] = s1
		s[0] = s0
		s[1] ^= uint64(c)
	}
	return len(data), nil
}

which can be handled without a recursive call. That is, the algorithm uses two
full iterations, each using an n-by-n/2-digit division and an n/2-by-n/2-digit
multiplication, along with a few n-digit additions and subtractions. The standard
n-by-n-digit multiplication algorithm requires O(n²) time, making the overall
algorithm require time T(n) where

	T(n) = 2T(n/2) + O(n) + O(n²)

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:
	//

package ssa

import (
	"math/big"
	"math/bits"
)

// So you want to compute x / c for some constant c?
// Machine division instructions are slow, so we try to
// compute this division with a multiplication + a few
// other cheap instructions instead.
// (We assume here that c != 0, +/- 1, or +/- 2^i.  Those
// cases are easy to handle in different ways).

// Technique from https://gmplib.org/~tege/divcnst-pldi94.pdf

	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.