Number #

In general, machine learning algorithm tries to solve problems using numerical computations, in a continues field like real numbers $\mathbf{R}$ or complex numbers $\mathbf{C}$.

Using Go genetics, lets define a Number type that includes all built-in numbers.

// Number is a custom type set of constraints extending all number types
type Number interface {
    ~int | ~float32 | ~float64 | ~complex64 | ~complex128
}

However, some commonly used operations in machine learning, like Max assumes the numbers is directly comparable, but complex numbers are not. We define the OrderedNumber type by adding a cmp.Ordered constraint to all numbers.

type OrderedNumber interface {
    Number
    cmp.Ordered
}

Finally, the system types are limited by their size (bits), therefore have a limited precision. We can add BigNumber types provided by Go standard library.

type BigNumber interface {
    big.Float | big.Rat | big.Int
}

In addition to the fundamental arithmetic operations ($+,-,\times,\div$), it is advantageous to enumerate a collection of standard functions that are broadly applicable to the generic Number type, including but not limited to Sign, Abs, Exp, Sqrt, Sin, Cos, and Log.

func Sign[T Number](x T) T {
	switch v := any(x).(type) {
	case int:
		if v > 0 {
			return T(1)
		} else if v < 0 {
			return T(-1)
		}
		return T(0)

	case float32:
		if v > 0 {
			return T(1)
		} else if v < 0 {
			return T(-1)
		}
		return T(0)

	case float64:
		if v > 0 {
			return T(1)
		} else if v < 0 {
			return T(-1)
		}
		return T(0)

	case complex64:
		if v == 0 {
			return T(0)
		}
		abs := float32(cmplx.Abs(complex128(v)))
		return any(v / complex(abs, 0)).(T)

	case complex128:
		if v == 0 {
			return T(0)
		}
		return any(v / complex(cmplx.Abs(v), 0)).(T)

	default:
		panic("unsupported type")
	}
}