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package spire.algebra

import spire.math.{ Complex, Trig, Fractional }
import spire.macrosk.Ops

import scala.{ specialized => spec }

trait InnerProductSpace[V, @spec(Int, Long, Float, Double) F] extends NormedVectorSpace[V, F] {
  implicit def nroot: NRoot[F]

  def norm(v: V): F = nroot.sqrt(dot(v, v))
  def dot(v: V, w: V): F
}

object InnerProductSpace {
  implicit def Tuple2IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple2IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def Tuple3IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple3IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def Tuple4IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple4IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def Tuple5IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple5IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def Tuple6IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple6IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def Tuple7IsInnerProductSpace[@spec(Int,Long,Float,Double) A](implicit
      scalar0: Field[A], nroot0: NRoot[A]) = new Tuple7IsInnerProductSpace[A] {
    val scalar = scalar0
    val nroot = nroot0
  }

  implicit def ComplexIsInnerProductSpace[@spec(Float, Double) A](implicit
      f0: Fractional[A], t0: Trig[A]) = new ComplexIsInnerProductSpace[A] {
    def scalar = f0
    def nroot = f0
    def f = f0
    def t = t0
  }
}

final class InnerProductSpaceOps[V](lhs: V) {
  def dot[F](rhs: V)(implicit ev: InnerProductSpace[V, F]): F =
    macro Ops.binopWithEv[V, InnerProductSpace[V, F], F]
  def ⋅[F](rhs: V)(implicit ev: InnerProductSpace[V, F]): F =
    macro Ops.binopWithEv[V, InnerProductSpace[V, F], F]
}

trait ComplexIsInnerProductSpace[@spec(Float, Double) A] extends ComplexIsField[A]
with InnerProductSpace[Complex[A], A] with RingAlgebra[Complex[A], A] {
  def timesl(r: A, v: Complex[A]): Complex[A] = Complex(r, scalar.zero) * v
  override def norm(x: Complex[A]): A = x.abs
  def dot(x: Complex[A], y: Complex[A]): A =
    scalar.plus(scalar.times(x.real, y.real), scalar.times(x.imag, y.imag))
}

trait Tuple2IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A), A] with Tuple2IsModule[A] {
  def dot(v: (A, A), w: (A, A)): A =
    scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2))
}

trait Tuple3IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A, A), A] with Tuple3IsModule[A] {
  def dot(v: (A, A, A), w: (A, A, A)): A =
    scalar.plus(scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2)), scalar.times(v._3, w._3))
}

trait Tuple4IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A, A, A), A] with Tuple4IsModule[A] {
  def dot(v: (A, A, A, A), w: (A, A, A, A)): A =
    scalar.plus(scalar.plus(scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2)), scalar.times(v._3, w._3)), scalar.times(v._4, w._4))
}

trait Tuple5IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A, A, A, A), A] with Tuple5IsModule[A] {
  def dot(v: (A, A, A, A, A), w: (A, A, A, A, A)): A =
    scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2)), scalar.times(v._3, w._3)), scalar.times(v._4, w._4)), scalar.times(v._5, w._5))
}

trait Tuple6IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A, A, A, A, A), A] with Tuple6IsModule[A] {
  def dot(v: (A, A, A, A, A, A), w: (A, A, A, A, A, A)): A =
    scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2)), scalar.times(v._3, w._3)), scalar.times(v._4, w._4)), scalar.times(v._5, w._5)), scalar.times(v._6, w._6))
}

trait Tuple7IsInnerProductSpace[@spec(Int,Long,Float,Double) A]
extends InnerProductSpace[(A, A, A, A, A, A, A), A] with Tuple7IsModule[A] {
  def dot(v: (A, A, A, A, A, A, A), w: (A, A, A, A, A, A, A)): A =
    scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.plus(scalar.times(v._1, w._1), scalar.times(v._2, w._2)), scalar.times(v._3, w._3)), scalar.times(v._4, w._4)), scalar.times(v._5, w._5)), scalar.times(v._6, w._6)), scalar.times(v._7, w._7))
}