factor/basis/math/functions/integer-logs/integer-logs.factor

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Factor

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