6.104 Number

Defined in namespace Smalltalk

Category: Language-Data types

I am an abstract class that provides operations on numbers, both floating point and integer. I provide some generic predicates, and supply the implicit type coercing code for binary operations.

6.104.1 Number class: converting		(class)
6.104.2 Number class: testing		(class)
6.104.3 Number: arithmetic		(instance)
6.104.4 Number: converting		(instance)
6.104.5 Number: copying		(instance)
6.104.6 Number: error raising		(instance)
6.104.7 Number: Intervals & iterators		(instance)
6.104.8 Number: misc math		(instance)
6.104.9 Number: point creation		(instance)
6.104.10 Number: retrying		(instance)
6.104.11 Number: testing		(instance)
6.104.12 Number: truncation and round off		(instance)

6.104.1 Number class: converting

coerce: aNumber

Answer aNumber - whatever class it belongs to, it is good

readFrom: aStream

Answer the number read from the rest of aStream, converted to an instance of the receiver. If the receiver is number, the class of the result is undefined -- but the result is good.

6.104.2 Number class: testing

isImmediate

Answer whether, if x is an instance of the receiver, x copy == x

6.104.3 Number: arithmetic

* aNumber

Subtract the receiver and aNumber, answer the result

+ aNumber

Sum the receiver and aNumber, answer the result

- aNumber

Subtract aNumber from the receiver, answer the result

/ aNumber

Divide the receiver by aNumber, answer the result (no loss of precision)

// aNumber

Divide the receiver by aNumber, answer the result truncated towards -infinity

\\ aNumber

Divide the receiver by aNumber truncating towards -infinity, answer the remainder

quo: aNumber

Return the integer quotient of dividing the receiver by aNumber with truncation towards zero.

reciprocal

Return the reciprocal of the receiver

rem: aNumber

Return the remainder of dividing the receiver by aNumber with truncation towards zero.

6.104.4 Number: converting

asFloat

This method's functionality should be implemented by subclasses of Number

asFloatD

This is mandated by the ANSI standard; since GNU Smalltalk currently does not support different floating-point classes, simply convert the receiver to a Float.

asFloatE

This is mandated by the ANSI standard; since GNU Smalltalk currently does not support different floating-point classes, simply convert the receiver to a Float.

asFloatQ

This is mandated by the ANSI standard; since GNU Smalltalk currently does not support different floating-point classes, simply convert the receiver to a Float.

asRectangle

Answer an empty rectangle whose origin is (self asPoint)

asScaledDecimal: n

Answer the receiver, converted to a ScaledDecimal object.

coerce: aNumber

Answer aNumber - whatever class it belongs to, it is good

degreesToRadians

Convert the receiver to radians

generality

Answer the receiver's generality

radiansToDegrees

Convert the receiver from radians to degrees

unity

Coerce 1 to the receiver's class. The default implementation works, but is inefficient

zero

Coerce 0 to the receiver's class. The default implementation works, but is inefficient

6.104.5 Number: copying

deepCopy

Return the receiver - it's an immediate (immutable) object

shallowCopy

Return the receiver - it's an immediate (immutable) object

6.104.6 Number: error raising

arithmeticError: msg

Raise an ArithmeticError exception having msg as its message text.

zeroDivide

Raise a division-by-zero (ZeroDivide) exception whose dividend is the receiver.

6.104.7 Number: Intervals & iterators

to: stop

Return an interval going from the receiver to stop by 1

to: stop by: step

Return an interval going from the receiver to stop with the given step

to: stop by: step do: aBlock

Evaluate aBlock for each value in the interval going from the receiver to stop with the given step. Compiled in-line for integer literal steps, and for one-argument aBlocks without temporaries, and therefore not overridable.

to: stop do: aBlock

Evaluate aBlock for each value in the interval going from the receiver to stop by 1. Compiled in-line for one-argument aBlocks without temporaries, and therefore not overridable.

6.104.8 Number: misc math

abs

Answer the absolute value of the receiver

arcCos

return the arc cosine of the receiver

arcSin

return the arc sine of the receiver

arcTan

return the arc tangent of the receiver

cos

return the cosine of the receiver

estimatedLog

Answer an estimate of (self abs floorLog: 10). This method should be overridden by subclasses, but Number's implementation does not raise errors - simply, it gives a correct result, so it is slow.

exp

return e raised to the receiver

floorLog: radix

return (self log: radix) floor. Optimized to answer an integer.

ln

return log base e of the receiver

log

return log base aNumber of the receiver

log: aNumber

return log base aNumber of the receiver

negated

Answer the negated of the receiver

raisedTo: aNumber

Return self raised to aNumber power

raisedToInteger: anInteger

Return self raised to the anInteger-th power

sin

return the sine of the receiver

sqrt

return the square root of the receiver

squared

Answer the square of the receiver

tan

return the tangent of the receiver

6.104.9 Number: point creation

@ y

Answer a new point whose x is the receiver and whose y is y

asPoint

Answer a new point, self @ self

6.104.10 Number: retrying

retry: aSymbol coercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling aSymbol. aSymbol is supposed not to be #= or #~= (since those don't fail if aNumber is not a Number).

retryDifferenceCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #-.

retryDivisionCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #/.

retryEqualityCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #=.

retryError

Raise an error--a retrying method was called with two arguments having the same generality.

retryInequalityCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #~=.

retryMultiplicationCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #*.

retryRelationalOp: aSymbol coercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling aSymbol (<, <=, >, >=).

retrySumCoercing: aNumber

Coerce to the other number's class the one number between the receiver and aNumber which has the lowest, and retry calling #+.

6.104.11 Number: testing

closeTo: num

Answer whether the receiver can be considered sufficiently close to num (this is done by checking equality if num is not a number, and by checking with 0.01% tolerance if num is a number).

even

Returns true if self is divisible by 2

isNumber

Answer `true'.

isRational

Answer whether the receiver is rational - false by default

negative

Answer whether the receiver is < 0

odd

Returns true if self is not divisible by 2

positive

Answer whether the receiver is >= 0

sign

Returns the sign of the receiver.

strictlyPositive

Answer whether the receiver is > 0

6.104.12 Number: truncation and round off

asInteger

Answer the receiver, rounded to the nearest integer

floor

Return the integer nearest the receiver toward negative infinity.

fractionPart

Answer a number which, summed to the #integerPart of the receiver, gives the receiver itself.

integerPart

Answer the receiver, truncated towards zero

rounded

Returns the integer nearest the receiver

roundTo: aNumber

Answer the receiver, truncated to the nearest multiple of aNumber

truncated

Answer the receiver, truncated towards zero

truncateTo: aNumber

Answer the receiver, truncated towards zero to a multiple of aNumber