case class Real(hi: Double, lo: Double = 0.0) extends Fractional[Real] with Ordered[Real] with Product with Serializable
The Real class provides higher precision floating point numbers using the
Double Double technique, which supports 106 bits of precision.
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Code adapted from DoubleDouble.java:
- hi
the high portion of the real number
- lo
the low portion of the real number
- See also
oai.cwi.nl/oai/asset/9159/9159A.pdf -----------------------------------------------------------------------------
http://tsusiatsoftware.net/dd/main.html
- Alphabetic
- By Inheritance
- Real
- Product
- Equals
- Ordered
- Comparable
- Fractional
- Numeric
- Ordering
- PartialOrdering
- Equiv
- Serializable
- Serializable
- Comparator
- AnyRef
- Any
- Hide All
- Show All
- Public
- All
Instance Constructors
-
new
Real(hi: Double, lo: Double = 0.0)
- hi
the high portion of the real number
- lo
the low portion of the real number
Type Members
Value Members
-
def
!=~(y: Real): Boolean
Return whether two real numbers are not nearly equal.
Return whether two real numbers are not nearly equal.
- y
the compare 'this' with y
-
def
%(x: Real): Real
Compute the remainder of the 'this' divided by 'x', i.e., 'this mod x'.
Compute the remainder of the 'this' divided by 'x', i.e., 'this mod x'.
- x
the modulus
-
def
*(y: Real): Real
Multiply two real numbers.
Multiply two real numbers.
- y
multiply this times y
-
def
+(y: Real): Real
Add two real numbers.
Add two real numbers.
- y
add real y to this
-
def
-(y: Real): Real
Subtract two real numbers.
Subtract two real numbers.
- y
subtract y from this
-
def
/(y: Real): Real
Divide two real numbers.
Divide two real numbers.
- y
divide this by y
-
def
<(that: Real): Boolean
- Definition Classes
- Ordered
-
def
<=(that: Real): Boolean
- Definition Classes
- Ordered
-
def
=~(y: Real): Boolean
Return whether two real numbers are nearly equal.
Return whether two real numbers are nearly equal.
- y
the compare 'this' with y
-
def
>(that: Real): Boolean
- Definition Classes
- Ordered
-
def
>=(that: Real): Boolean
- Definition Classes
- Ordered
-
def
abs: Real
Return the absolute value of 'this' real number.
-
def
abs(x: Real): Real
- Definition Classes
- Numeric
-
def
ceil: Real
Return the 'ceil'ing (integer above) of 'this' real number.
-
def
compare(y: Real): Int
Compare 'this' real number with that real number 'y'.
Compare 'this' real number with that real number 'y'.
- y
that real number
- Definition Classes
- Real → Ordered
-
def
compare(x: Real, y: Real): Int
Compare two real numbers (negative for <, zero for ==, positive for >).
Compare two real numbers (negative for <, zero for ==, positive for >).
- x
the first real number to compare
- y
the second real number to compare
- Definition Classes
- Real → Ordering → Comparator
-
def
compareTo(that: Real): Int
- Definition Classes
- Ordered → Comparable
-
def
div(x: Real, y: Real): Real
- Definition Classes
- Real → Fractional
-
def
equals(x: Any): Boolean
Override equals to determine whether 'this' real number equals real 'y'.
Override equals to determine whether 'this' real number equals real 'y'.
- Definition Classes
- Real → Equals → Comparator → AnyRef → Any
-
def
equiv(x: Real, y: Real): Boolean
- Definition Classes
- Ordering → PartialOrdering → Equiv
-
def
floor: Real
Return the floor (integer below) of 'this' real number.
-
def
fromInt(x: Int): Real
Create a real number from an
Int.Create a real number from an
Int.- Definition Classes
- Real → Numeric
-
def
fromLong(x: Long): Real
Create a real number from an
Long. -
def
gt(x: Real, y: Real): Boolean
- Definition Classes
- Ordering → PartialOrdering
-
def
gteq(x: Real, y: Real): Boolean
- Definition Classes
- Ordering → PartialOrdering
-
def
hashCode(): Int
Must also override hashCode to be be compatible with equals.
Must also override hashCode to be be compatible with equals.
- Definition Classes
- Real → AnyRef → Any
- val hi: Double
-
def
in(set: Set[Real]): Boolean
Determine whether 'this' is in the given set.
-
def
in(lim: (Real, Real)): Boolean
Determine whether 'this' is within the given bounds
Determine whether 'this' is within the given bounds
- lim
the given (lower, upper) bounds
-
def
isInfinity: Boolean
Determine whether 'this' number "is Infinite".
-
def
isNaN: Boolean
Determine whether 'this' number "is Not a Number".
- val lo: Double
-
def
lt(x: Real, y: Real): Boolean
- Definition Classes
- Ordering → PartialOrdering
-
def
lteq(x: Real, y: Real): Boolean
- Definition Classes
- Ordering → PartialOrdering
-
def
max(y: Real): Real
Return the maximum of 'this' and that real numbers.
Return the maximum of 'this' and that real numbers.
- y
that real number to compare with this
-
def
max(x: Real, y: Real): Real
- Definition Classes
- Ordering
-
def
min(y: Real): Real
Return the minimum of 'this' and that real numbers.
Return the minimum of 'this' and that real numbers.
- y
that real number to compare with this
-
def
min(x: Real, y: Real): Real
- Definition Classes
- Ordering
-
def
minus(x: Real, y: Real): Real
- Definition Classes
- Real → Numeric
-
implicit
def
mkNumericOps(lhs: Real): FractionalOps
- Definition Classes
- Fractional → Numeric
-
implicit
def
mkOrderingOps(lhs: Real): Real.Ops
- Definition Classes
- Ordering
- def near_eq(x: Real, y: Real): Boolean
-
def
negate(x: Real): Real
- Definition Classes
- Real → Numeric
-
def
not_in(set: Set[Real]): Boolean
Determine whether 'this' is not in the given set.
-
def
not_in(lim: (Real, Real)): Boolean
Determine whether 'this' is not within the given bounds
Determine whether 'this' is not within the given bounds
- lim
the given (lower, upper) bounds
-
def
on[U](f: (U) ⇒ Real): Ordering[U]
- Definition Classes
- Ordering
-
def
one: Real
- Definition Classes
- Numeric
-
def
plus(x: Real, y: Real): Real
- Definition Classes
- Real → Numeric
- def pow(x: Real, y: Real): Real
- def pow(x: Real, k: Int): Real
- def rem(x: Real, y: Real): Real
-
def
reverse: Ordering[Real]
- Definition Classes
- Ordering → PartialOrdering
-
def
reversed(): Comparator[Real]
- Definition Classes
- Comparator
-
def
round: Long
Return the 'round'ed (closest) integer to 'this' real number.
-
def
signum: Real
Return the signum of 'this' real number, 1, 0, -1 for >0, =0, <0.
-
def
signum(x: Real): Int
- Definition Classes
- Numeric
-
def
thenComparing[U <: Comparable[_ >: U]](arg0: Function[_ >: Real, _ <: U]): Comparator[Real]
- Definition Classes
- Comparator
-
def
thenComparing[U](arg0: Function[_ >: Real, _ <: U], arg1: Comparator[_ >: U]): Comparator[Real]
- Definition Classes
- Comparator
-
def
thenComparing(arg0: Comparator[_ >: Real]): Comparator[Real]
- Definition Classes
- Comparator
-
def
thenComparingDouble(arg0: ToDoubleFunction[_ >: Real]): Comparator[Real]
- Definition Classes
- Comparator
-
def
thenComparingInt(arg0: ToIntFunction[_ >: Real]): Comparator[Real]
- Definition Classes
- Comparator
-
def
thenComparingLong(arg0: ToLongFunction[_ >: Real]): Comparator[Real]
- Definition Classes
- Comparator
-
def
times(x: Real, y: Real): Real
- Definition Classes
- Real → Numeric
- def toDouble: Double
-
def
toDouble(x: Real): Double
Convert that/'this' real number to a
Double.Convert that/'this' real number to a
Double.- x
that real number to convert
- Definition Classes
- Real → Numeric
- def toFloat: Float
-
def
toFloat(x: Real): Float
Convert that/'this' real number to a
Float.Convert that/'this' real number to a
Float.- x
that real number to convert
- Definition Classes
- Real → Numeric
- def toInt: Int
-
def
toInt(x: Real): Int
Convert that/'this' real number to an
Int.Convert that/'this' real number to an
Int.- x
that real number to convert
- Definition Classes
- Real → Numeric
- def toLong: Long
-
def
toLong(x: Real): Long
Convert 'this' real number to a
Long. - def toReal: Real
-
def
toReal(x: Real): Real
Convert that/'this' real number to a
Real.Convert that/'this' real number to a
Real.- x
that real number to convert
-
def
toString(): String
Convert 'this' real number to a String in standard form "dd.dd".
Convert 'this' real number to a String in standard form "dd.dd". FIX: add support for scientific notation
- Definition Classes
- Real → AnyRef → Any
-
def
toString2: String
Convert 'this' real number to a String of the form "(hi, lo)".
-
def
tryCompare(x: Real, y: Real): Some[Int]
- Definition Classes
- Ordering → PartialOrdering
-
def
unary_-(): Real
Compute the unary minus (-).
-
val
val1: Double
General alias for the parts of a real number
-
val
val2: Double
General alias for the parts of a real number
-
def
zero: Real
- Definition Classes
- Numeric
-
def
~^(y: Real): Real
Raise a real number to the 'k'-th power.
Raise a real number to the 'k'-th power.
- y
the power/exponent (as a
Real)
-
def
~^(k: Int): Real
Raise a real number to the 'k'-th power.
Raise a real number to the 'k'-th power.
- k
the power/exponent (as a
Int)
- def ↑(y: Real): Real
- def ∈(set: Set[Real]): Boolean
- def ∈(lim: (Real, Real)): Boolean
- def ∉(set: Set[Real]): Boolean
- def ∉(lim: (Real, Real)): Boolean
- def ≈(y: Real): Boolean
- def ≉(y: Real): Boolean
-
def
≠(y: Real): Boolean
Compare 'this' real number with that real number 'y' for inequality.
Compare 'this' real number with that real number 'y' for inequality.
- y
that real number
-
def
≤(y: Real): Boolean
Compare 'this' real number with that real number 'y' for less than or equal to.
Compare 'this' real number with that real number 'y' for less than or equal to.
- y
that real number
-
def
≥(y: Real): Boolean
Compare 'this' real number with that real number 'y' for greater than or equal to.
Compare 'this' real number with that real number 'y' for greater than or equal to.
- y
that real number