spire.algebra.Field.scala Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of spire_2.10 Show documentation

core

The newest version!

package spire
package algebra

import java.lang.Double.{ isInfinite, isNaN, doubleToLongBits }
import java.lang.Long.{ numberOfTrailingZeros }

trait Field[@sp(Byte, Short, Int, Long, Float, Double) A] extends Any with EuclideanRing[A] with MultiplicativeAbGroup[A] {

  /**
   * This is implemented in terms of basic Field ops. However, this is
   * probably significantly less efficient than can be done with a specific
   * type. So, it is recommended that this method is overriden.
   *
   * This is possible because a Double is a rational number.
   */
  def fromDouble(a: Double): A = if (a == 0.0) {
    fromInt(0)
  } else {
    require(!isInfinite(a) && !isNaN(a),
            "Double must be representable as a fraction.")

    val bits = doubleToLongBits(a)
    val m = bits & 0x000FFFFFFFFFFFFFL | 0x0010000000000000L
    val zeros = numberOfTrailingZeros(m)
    val value = m >>> zeros
    val exp = ((bits >> 52) & 0x7FF).toInt - 1075 + zeros // 1023 + 52

    val high = times(fromInt((value >>> 30).toInt), fromInt(1 << 30))
    val low = fromInt((value & 0x3FFFFFFF).toInt)
    val num = plus(high, low)
    val unsigned = if (exp > 0) {
      times(num, pow(fromInt(2), exp))
    } else if (exp < 0) {
      div(num, pow(fromInt(2), -exp))
    } else {
      num
    }

    if (a < 0) negate(unsigned) else unsigned
  }
}

object Field {
  @inline final def apply[A](implicit f: Field[A]): Field[A] = f
}