/usr/share/gnu-smalltalk/kernel/Fraction.st is in gnu-smalltalk-common 3.2.5-1.
This file is owned by root:root, with mode 0o644.
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|
| Class Fraction Definitions
|
|
======================================================================"
"======================================================================
|
| Copyright 1992,94,95,99,2000,2001,2002,2008,2009
| Free Software Foundation, Inc.
| Written by David Duke.
| Slightly modified by Steve Byrne and Paolo Bonzini.
|
| This file is part of the GNU Smalltalk class library.
|
| The GNU Smalltalk class library is free software; you can redistribute it
| and/or modify it under the terms of the GNU Lesser General Public License
| as published by the Free Software Foundation; either version 2.1, or (at
| your option) any later version.
|
| The GNU Smalltalk class library is distributed in the hope that it will be
| useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser
| General Public License for more details.
|
| You should have received a copy of the GNU Lesser General Public License
| along with the GNU Smalltalk class library; see the file COPYING.LIB.
| If not, write to the Free Software Foundation, 59 Temple Place - Suite
| 330, Boston, MA 02110-1301, USA.
|
======================================================================"
Number subclass: Fraction [
| numerator denominator |
<category: 'Language-Data types'>
<comment: ' I represent rational numbers in the form (p/q) where p and q are integers.
The arithmetic operations *, +, -, /, on fractions, all return a reduced
fraction.'>
Zero := nil.
One := nil.
Fraction class >> coerce: aNumber [
"Answer aNumber converted to a Fraction"
<category: 'converting'>
^aNumber asExactFraction
]
Fraction class >> initialize [
"Initialize the receiver's class variables"
<category: 'instance creation'>
Zero := self numerator: 0 denominator: 1.
One := self numerator: 1 denominator: 1
]
Fraction class >> numerator: nInteger denominator: dInteger [
"Answer a new instance of fraction (nInteger/dInteger)"
<category: 'instance creation'>
^self new setNumerator: nInteger setDenominator: dInteger
]
denominator [
"Answer the receiver's denominator"
<category: 'accessing'>
^denominator
]
numerator [
"Answer the receiver's numerator"
<category: 'accessing'>
^numerator
]
* aNumber [
"Multiply two numbers and answer the result."
<category: 'arithmetic'>
| num den gcd |
aNumber generality = self generality
ifFalse: [^self retryMultiplicationCoercing: aNumber].
aNumber numerator = 0 ifTrue: [^aNumber].
self numerator = 0 ifTrue: [^self].
num := numerator * aNumber numerator.
den := denominator * aNumber denominator.
aNumber == self
ifFalse:
[gcd := (numerator gcd: aNumber denominator)
* (denominator gcd: aNumber numerator).
num := num divExact: gcd.
den := den divExact: gcd].
den = 1 ifTrue: [^num].
^Fraction numerator: num denominator: den
]
+ aNumber [
"Sum two numbers and answer the result."
<category: 'arithmetic'>
| gcd num den |
aNumber generality = self generality
ifFalse: [^self retrySumCoercing: aNumber].
gcd := denominator gcd: aNumber denominator.
gcd == 1
ifTrue:
[^Fraction numerator: numerator * aNumber denominator
+ (aNumber numerator * denominator)
denominator: denominator * aNumber denominator].
num := numerator * (aNumber denominator divExact: gcd)
+ (aNumber numerator * (denominator divExact: gcd)).
den := denominator * aNumber denominator divExact: gcd.
"Compute a GCD on smaller operands"
gcd := num gcd: den.
num := num divExact: gcd.
den := den divExact: gcd.
den = 1 ifTrue: [^num].
^Fraction numerator: num denominator: den
]
- aNumber [
"Subtract aNumber from the receiver and answer the result."
<category: 'arithmetic'>
| gcd num den |
aNumber generality = self generality
ifFalse: [^self retryDifferenceCoercing: aNumber].
gcd := denominator gcd: aNumber denominator.
gcd == 1
ifTrue:
[^Fraction numerator: numerator * aNumber denominator
- (aNumber numerator * denominator)
denominator: denominator * aNumber denominator].
num := numerator * (aNumber denominator divExact: gcd)
- (aNumber numerator * (denominator divExact: gcd)).
den := denominator * aNumber denominator divExact: gcd.
"Compute a GCD on smaller operands"
gcd := num gcd: den.
num := num divExact: gcd.
den := den divExact: gcd.
den = 1 ifTrue: [^num].
^Fraction numerator: num denominator: den
]
/ aNumber [
"Divide the receiver by aNumber and answer the result."
<category: 'arithmetic'>
| num den gcd |
aNumber generality = self generality
ifFalse: [^self retryDivisionCoercing: aNumber].
aNumber numerator = 0 ifTrue: [^self zeroDivide].
self numerator = 0 ifTrue: [^self].
num := numerator * aNumber denominator.
den := denominator * aNumber numerator.
gcd := (numerator gcd: aNumber numerator)
* (denominator gcd: aNumber denominator).
num := num divExact: gcd.
den := den divExact: gcd.
den = 1 ifTrue: [^num].
^Fraction numerator: num denominator: den
]
// aNumber [
"Return the integer quotient of dividing the receiver by aNumber with
truncation towards negative infinity."
<category: 'arithmetic'>
^(self / aNumber) floor
]
\\ aNumber [
"Return the remainder from dividing the receiver by aNumber, (using //)."
<category: 'arithmetic'>
^self - (self // aNumber * aNumber)
]
estimatedLog [
"Answer an estimate of (self abs floorLog: 10)"
<category: 'arithmetic'>
^numerator estimatedLog - denominator estimatedLog
]
zero [
"Coerce 0 to the receiver's class"
<category: 'coercing'>
^Zero
]
unity [
"Coerce 1 to the receiver's class"
<category: 'coercing'>
^One
]
coerce: aNumber [
"Coerce aNumber to the receiver's class"
<category: 'coercing'>
^aNumber asExactFraction
]
generality [
"Return the receiver's generality"
<category: 'coercing'>
^300
]
floor [
"Truncate the receiver towards negative infinity
and return the truncated result"
<category: 'coercing'>
^numerator // denominator
]
ceiling [
"Truncate the receiver towards positive infinity
and return the truncated result"
<category: 'coercing'>
^(numerator + denominator - 1) // denominator
]
truncated [
"Truncate the receiver and return the truncated result"
<category: 'coercing'>
^numerator quo: denominator
]
< arg [
"Test if the receiver is less than arg."
<category: 'comparing'>
arg generality = self generality
ifFalse: [^self retryRelationalOp: #< coercing: arg].
^(self compare: arg) < 0
]
<= arg [
"Test if the receiver is less than or equal to arg."
<category: 'comparing'>
arg generality = self generality
ifFalse: [^self retryRelationalOp: #<= coercing: arg].
^(self compare: arg) <= 0
]
> arg [
"Test if the receiver is more than arg."
<category: 'comparing'>
arg generality = self generality
ifFalse: [^self retryRelationalOp: #> coercing: arg].
^(self compare: arg) > 0
]
>= arg [
"Test if the receiver is greater than or equal to arg."
<category: 'comparing'>
arg generality = self generality
ifFalse: [^self retryRelationalOp: #>= coercing: arg].
^(self compare: arg) >= 0
]
= arg [
"Test if the receiver equals arg."
<category: 'comparing'>
(arg isKindOf: Number) ifFalse: [^false].
arg generality = self generality
ifFalse: [^self retryEqualityCoercing: arg].
^self numerator = arg numerator and: [self denominator = arg denominator]
]
hash [
"Answer an hash value for the receiver"
<category: 'comparing'>
denominator = 1 ifTrue: [^numerator hash].
^self asFloatD hash
]
compare: arg [
"Answer an integer <, >, = 0 depending on the ordering
between the receiver and arg."
<category: 'private - comparing'>
"Comparing numbers with different signs, we just care about that;
canonical form further restricts the check to the numerator."
| n1 n2 delta |
self numerator sign = arg numerator sign
ifFalse: [^numerator sign - arg numerator sign].
n1 := numerator abs.
n2 := arg numerator abs.
"The first line is (n1 * d2) highBit +/- 1, and similarly for the second."
delta := numerator abs highBit + arg denominator highBit
- arg numerator abs highBit - denominator highBit.
delta < -1 ifTrue: [^delta * numerator sign].
delta > 1 ifTrue: [^delta * numerator sign].
"Cross multiply and compare. Sending #* to the denominators is
faster because they cannot be LargeNegativeIntegers."
^(arg denominator * numerator - (denominator * arg numerator)) sign
]
isRational [
"Answer whether the receiver is rational - true"
<category: 'testing'>
^true
]
integerPart [
"Answer the integer part of the receiver, expressed as a Fraction"
<category: 'converting'>
^Fraction numerator: self truncated denominator: 1
]
asCNumber [
"Convert the receiver to a kind of number that is understood by
the C call-out mechanism."
<category: 'coercion'>
^self asFloat: FloatD
]
asFloatD [
"Answer the receiver converted to a FloatD"
<category: 'converting'>
^self asFloat: FloatD
]
asFloatE [
"Answer the receiver converted to a FloatD"
<category: 'converting'>
^self asFloat: FloatE
]
asFloatQ [
"Answer the receiver converted to a FloatD"
<category: 'converting'>
^self asFloat: FloatQ
]
asExactFraction [
"Answer the receiver, it is already a Fraction"
<category: 'converting'>
^self
]
asFraction [
"Answer the receiver, it is already a Fraction"
<category: 'converting'>
^self
]
printOn: aStream [
"Print a representation of the receiver on aStream"
<category: 'printing'>
aStream
print: numerator;
nextPut: $/;
print: denominator
]
storeOn: aStream [
"Store Smalltalk code compiling to the receiver on aStream"
<category: 'printing'>
aStream
nextPutAll: '(Fraction numerator: ';
store: numerator;
nextPutAll: ' denominator: ';
store: denominator;
nextPut: $)
]
asFloat: characterization [
"Answer the receiver converted to a Float"
"Answer the receiver converted to a Float"
<category: 'private'>
| n d sign hn hd hq nBits q q1 r exponent floatExponent |
sign := numerator sign * denominator sign.
n := numerator abs.
d := denominator abs.
hn := n highBit.
hd := d highBit.
"If both numerator and denominator are represented exactly in floating
point number, then fastest thing to do is to use hardwired float division"
nBits := characterization precision + 1.
(hn < nBits and: [hd < nBits])
ifTrue:
[^(characterization coerce: numerator)
/ (characterization coerce: denominator)].
"Try and obtain a mantissa with characterization precision + 1 bits by integer division.
Additional bit is a helper for rounding mode.
First guess is rough, we might get one more bit or one less"
exponent := hn - hd - nBits.
exponent > 0
ifTrue: [d := d bitShift: exponent]
ifFalse: [n := n bitShift: exponent negated].
q := n quo: d.
r := n - (q * d).
hq := q highBit.
"check for gradual underflow, in which case we should use less bits"
floatExponent := exponent + hq.
floatExponent >= (characterization emin - 1)
ifFalse: [nBits := nBits + floatExponent - characterization emin + 1].
"Use exactly nBits"
hq > nBits
ifTrue:
[exponent := exponent + hq - nBits.
r := (q bitAnd: (1 bitShift: hq - nBits) - 1) * d + r.
q := q bitShift: nBits - hq].
hq < nBits
ifTrue:
[exponent := exponent + hq - nBits.
q1 := (r bitShift: nBits - hq) quo: d.
q := (q bitShift: nBits - hq) bitAnd: q1.
r := (r bitShift: nBits - hq) - (q1 * d)].
"check if we should round upward.
The case of exact half (q bitAnd: 1) = 1 & (r = 0)
will be handled by Integer>>asFloat:"
((q bitAnd: 1) = 0 or: [r = 0]) ifFalse: [q := q + 1].
"build the Float"
^(sign > 0
ifTrue: [characterization coerce: q]
ifFalse: [(characterization coerce: q) negated]) timesTwoPower: exponent
]
reduce [
"Reduce the fraction."
<category: 'private'>
| gcd |
numerator = 1 ifTrue: [^self].
denominator = 1 ifTrue: [^numerator].
numerator = 0 ifTrue: [^0].
numerator = denominator ifTrue: [^1].
gcd := numerator gcd: denominator.
gcd = 1 ifTrue: [^self].
denominator = gcd ifTrue: [^numerator divExact: gcd].
numerator := numerator divExact: gcd.
denominator := denominator divExact: gcd.
^self
]
setNumerator: numInteger setDenominator: denInteger [
"Set the fraction's numerator and denominator"
<category: 'private'>
denInteger = 0 ifTrue: [^numInteger zeroDivide].
denInteger < 0
ifTrue:
[numerator := numInteger negated.
denominator := denInteger negated]
ifFalse:
[numerator := numInteger.
denominator := denInteger]
]
negated [
"Return the receiver, with its sign changed."
<category: 'optimized cases'>
^Fraction numerator: 0 - numerator denominator: denominator
]
raisedToInteger: anInteger [
"Return self raised to the anInteger-th power."
"No need to reduce"
<category: 'optimized cases'>
anInteger < 0 ifTrue: [^self reciprocal raisedToInteger: 0 - anInteger].
^Fraction numerator: (numerator raisedToInteger: anInteger)
denominator: (denominator raisedToInteger: anInteger)
]
reciprocal [
"Return the reciprocal of the receiver"
<category: 'optimized cases'>
denominator < 0
ifTrue:
[^Fraction numerator: denominator negated denominator: numerator negated]
ifFalse: [^Fraction numerator: denominator denominator: numerator]
]
sqrt [
"Return the square root of the receiver."
<category: 'optimized cases'>
| n d |
n := numerator sqrt.
d := denominator sqrt.
"If both are integers the gcd is known to be 1, don't use n/d straight."
(n isInteger and: [ d isInteger ]) ifFalse: [ ^n / d ].
^Fraction numerator: n denominator: d
]
squared [
"Return the square of the receiver."
<category: 'optimized cases'>
^Fraction numerator: numerator squared denominator: denominator squared
]
]
|