109 lines
3.4 KiB
Factor
109 lines
3.4 KiB
Factor
! Copyright (C) 2017 Jon Harper.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel kernel.private math math.functions
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math.functions.private math.private sequences.private ;
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IN: math.functions.integer-logs
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<PRIVATE
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GENERIC: (integer-log10) ( x -- n ) foldable
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! For 32 bits systems, we could reduce
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! this to the first 27 elements..
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CONSTANT: log10-guesses {
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0 0 0 0 1 1 1 2 2 2 3 3 3 3
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4 4 4 5 5 5 6 6 6 6 7 7 7 8
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8 8 9 9 9 9 10 10 10 11 11 11
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12 12 12 12 13 13 13 14 14 14
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15 15 15 15 16 16 16 17 17
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}
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! This table will hold a few unused bignums on 32 bits systems...
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! It could be reduced to the first 8 elements
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! Note that even though the 64 bits most-positive-fixnum
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! is hardcoded here this table also works (by chance) for 32bit systems.
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! This is because there is only one power of 2 greater than the
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! greatest power of 10 for 27 bit unsigned integers so we don't
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! need to hardcode the 32 bits most-positive-fixnum. See the
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! table below for powers of 2 and powers of 10 around the
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! most-positive-fixnum.
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!
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! 67108864 2^26 | 72057594037927936 2^56
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! 99999999 10^8 | 99999999999999999 10^17
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! 134217727 2^27-1 | 144115188075855872 2^57
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! | 288230376151711744 2^58
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! | 576460752303423487 2^59-1
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CONSTANT: log10-thresholds {
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9 99 999 9999 99999 999999
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9999999 99999999 999999999
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9999999999 99999999999
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999999999999 9999999999999
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99999999999999 999999999999999
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9999999999999999 99999999999999999
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576460752303423487
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}
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: fixnum-integer-log10 ( n -- x )
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dup (log2) { array-capacity } declare
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log10-guesses nth-unsafe { array-capacity } declare
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dup log10-thresholds nth-unsafe { fixnum } declare
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rot < [ 1 + ] when ; inline
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! bignum-integer-log10-find-down and bignum-integer-log10-find-up
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! work with very bad guesses, but in practice they will never loop
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! more than once.
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: bignum-integer-log10-find-down ( guess 10^guess n -- log10 )
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[ 2dup > ] [ [ [ 1 - ] [ 10 / ] bi* ] dip ] do while 2drop ;
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: bignum-integer-log10-find-up ( guess 10^guess n -- log10 )
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[ 10 * ] dip
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[ 2dup <= ] [ [ [ 1 + ] [ 10 * ] bi* ] dip ] while 2drop ;
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: bignum-integer-log10-guess ( n -- guess 10^guess )
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(log2) >integer log10-2 * >integer dup 10^ ;
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: bignum-integer-log10 ( n -- x )
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[ bignum-integer-log10-guess ] keep 2dup >
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[ bignum-integer-log10-find-down ]
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[ bignum-integer-log10-find-up ] if ; inline
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M: fixnum (integer-log10) fixnum-integer-log10 { fixnum } declare ; inline
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M: bignum (integer-log10) bignum-integer-log10 ; inline
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PRIVATE>
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ERROR: log-expects-positive x ;
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<PRIVATE
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GENERIC: (integer-log2) ( x -- n ) foldable
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M: integer (integer-log2) ( x -- n ) (log2) ; inline
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: ((ratio-integer-log)) ( ratio quot -- log )
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[ >integer ] dip call ; inline
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: (ratio-integer-log) ( ratio quot base -- log )
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pick 1 >=
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[ drop ((ratio-integer-log)) ] [
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[ recip ] 2dip
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[ drop ((ratio-integer-log)) ] [ nip pick ^ = ] 3bi
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[ 1 + ] unless neg
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] if ; inline
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M: ratio (integer-log2) ( r -- n ) [ (integer-log2) ] 2 (ratio-integer-log) ;
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M: ratio (integer-log10) ( r -- n ) [ (integer-log10) ] 10 (ratio-integer-log) ;
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: (integer-log) ( x quot -- n )
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[ dup 0 > ] dip [ log-expects-positive ] if ; inline
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PRIVATE>
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: integer-log10 ( x -- n )
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[ (integer-log10) ] (integer-log) ; inline
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: integer-log2 ( x -- n )
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[ (integer-log2) ] (integer-log) ; inline
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