spire.math.fpf

FastMaybeFloat

object FastMaybeFloat

A Long encoded version of MaybeDouble, geared for unboxed speed. This is significantly less accurate, but may provide good speed gains in common cases.

The values approx and measure are both truncated floats with the full 8 bit exponent, but only 16 bit mantissa. Since the measure is always positive, we only need 2 * (16 + 8) + 1 = 49 bits for these 2 numbers, which leaves 15 bits for the index. These sizes were chosen so that worst case relative error, ind * eps, has a value less than 1. In our case, with worst case ind = -1 >>> 17, we have ind * eps =~ 0.5.

This was inspired by Erik Osheim's awesome FastComplex, which encodes the imaginary and real parts as 2 Floats in the a single Long.

TODO: Perhaps, if we've only used + or *, we could store a higher precision float instead, since we don't need measure. Use 1 bit to handle the switching, taken from the index.

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  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. final val Invalid: Long(-1L)

  7. def apply(x: Rational): Long

  8. def apply(x: BigDecimal): Long

  9. def apply(x: BigInt): Long

  10. def apply(x: Long): Long

  11. def apply(x: Int): Long

  12. def apply(x: Double): Long

  13. def apply(x: Float): Long

  14. final def approx(mf: Long): Float

  15. def asFloat(x: Long): Float

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    @inline()

  16. final def asInstanceOf[T0]: T0

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  17. def clone(): AnyRef

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  18. final def div(a: Long, b: Long): Long

  19. final val eps: Float

  20. final def eq(arg0: AnyRef): Boolean

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  21. def equals(arg0: Any): Boolean

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  22. final def error(mf: Long): Float

  23. def finalize(): Unit

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  24. final def getClass(): Class[_]

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  25. def hashCode(): Int

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  26. final def index(mf: Long): Int

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    @inline()

  27. def invalid(a: Long): Boolean

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  28. final def isInstanceOf[T0]: Boolean

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  29. def max(a: Int, b: Int): Int

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    @inline()

  30. final def measure(mf: Long): Float

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    @inline()

  31. def min(a: Int, b: Int): Int

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  32. final def minus(a: Long, b: Long): Long

  33. final def ne(arg0: AnyRef): Boolean

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  34. final def notify(): Unit

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  35. final def notifyAll(): Unit

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  36. def nroot(a: Long, n: Int): Long

  37. final def plus(a: Long, b: Long): Long

  38. def pow(a: Long, k: Int): Long

  39. def sqrt(a: Long): Long

  40. final def synchronized[T0](arg0: ⇒ T0): T0

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  41. final def times(a: Long, b: Long): Long

  42. def toString(): String

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  43. final def wait(): Unit

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  44. final def wait(arg0: Long, arg1: Int): Unit

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  45. final def wait(arg0: Long): Unit

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