-! Copyright (C) 2004, 2008 Slava Pestov.
+! Copyright (C) 2004, 2010 Slava Pestov.
! See http://factorcode.org/license.txt for BSD license.
USING: math kernel math.constants math.private math.bits
-math.libm combinators math.order sequences ;
+math.libm combinators fry math.order sequences ;
IN: math.functions
: >fraction ( a/b -- a b )
GENERIC: sqrt ( x -- y ) foldable
M: real sqrt
- >float dup 0.0 < [ neg fsqrt 0.0 swap rect> ] [ fsqrt ] if ;
+ >float dup 0.0 <
+ [ neg fsqrt [ 0.0 ] dip rect> ] [ fsqrt ] if ; inline
: factor-2s ( n -- r s )
#! factor an integer into 2^r * s
dup 0 = [ 1 ] [
- 0 swap [ dup even? ] [ [ 1 + ] [ 2/ ] bi* ] while
+ [ 0 ] dip [ dup even? ] [ [ 1 + ] [ 2/ ] bi* ] while
] if ; inline
<PRIVATE
GENERIC# ^n 1 ( z w -- z^w ) foldable
: (^n) ( z w -- z^w )
- make-bits 1 [ [ dupd * ] when [ sq ] dip ] reduce nip ; inline
+ make-bits 1 [ [ over * ] when [ sq ] dip ] reduce nip ; inline
M: integer ^n
[ factor-2s ] dip [ (^n) ] keep rot * shift ;
M: ratio ^n
- [ >fraction ] dip [ ^n ] curry bi@ / ;
+ [ >fraction ] dip '[ _ ^n ] bi@ / ;
M: float ^n (^n) ;
M: complex ^n (^n) ;
: integer^ ( x y -- z )
- dup 0 > [ ^n ] [ neg ^n recip ] if ; inline
+ dup 0 >= [ ^n ] [ [ recip ] dip neg ^n ] if ; inline
PRIVATE>
: >polar ( z -- abs arg )
>float-rect [ [ sq ] bi@ + fsqrt ] [ swap fatan2 ] 2bi ; inline
-: cis ( arg -- z ) dup fcos swap fsin rect> ; inline
+: cis ( arg -- z ) >float [ fcos ] [ fsin ] bi rect> ; inline
: polar> ( abs arg -- z ) cis * ; inline
+GENERIC: exp ( x -- y )
+
+M: float exp fexp ; inline
+
+M: real exp >float exp ; inline
+
+M: complex exp >rect [ exp ] dip polar> ; inline
+
<PRIVATE
: ^mag ( w abs arg -- magnitude )
- [ >float-rect swap ] [ swap fpow ] [ rot * fexp /f ] tri* ; inline
+ [ >float-rect swap ]
+ [ >float swap >float fpow ]
+ [ rot * exp /f ]
+ tri* ; inline
: ^theta ( w abs arg -- theta )
[ >float-rect ] [ flog * swap ] [ * + ] tri* ; inline
: real^? ( x y -- ? )
2dup [ real? ] both? [ drop 0 >= ] [ 2drop f ] if ; inline
-: 0^ ( x -- z )
- dup zero? [ drop 0/0. ] [ 0 < 1/0. 0 ? ] if ; inline
+: 0^ ( zero x -- z )
+ swap [ 0/0. ] swap '[ 0 < 1/0. _ ? ] if-zero ; inline
-: (^mod) ( n x y -- z )
- make-bits 1 [
- [ dupd * pick mod ] when [ sq over mod ] dip
- ] reduce 2nip ; inline
+: (^mod) ( x y n -- z )
+ [ make-bits 1 ] dip dup
+ '[ [ over * _ mod ] when [ sq _ mod ] dip ] reduce nip ; inline
: (gcd) ( b a x y -- a d )
over zero? [
2nip
] [
swap [ /mod [ over * swapd - ] dip ] keep (gcd)
- ] if ;
+ ] if ; inline recursive
PRIVATE>
: ^ ( x y -- z )
{
- { [ over 0 = ] [ nip 0^ ] }
+ { [ over zero? ] [ 0^ ] }
{ [ dup integer? ] [ integer^ ] }
- { [ 2dup real^? ] [ fpow ] }
+ { [ 2dup real^? ] [ [ >float ] bi@ fpow ] }
[ ^complex ]
} cond ; inline
+: nth-root ( n x -- y ) swap recip ^ ; inline
+
: gcd ( x y -- a d )
- [ 0 1 ] 2dip (gcd) dup 0 < [ neg ] when ; foldable
+ [ 0 1 ] 2dip (gcd) dup 0 < [ neg ] when ; inline
: lcm ( a b -- c )
[ * ] 2keep gcd nip /i ; foldable
: divisor? ( m n -- ? )
- mod 0 = ;
+ mod 0 = ; inline
ERROR: non-trivial-divisor n ;
[ non-trivial-divisor ] if ; foldable
: ^mod ( x y n -- z )
- over 0 < [
- [ [ neg ] dip ^mod ] keep mod-inv
- ] [
- -rot (^mod)
- ] if ; foldable
-
-: 10^ ( n -- n' ) 10 swap ^ ; inline
+ over 0 <
+ [ [ [ neg ] dip ^mod ] keep mod-inv ] [ (^mod) ] if ; foldable
GENERIC: absq ( x -- y ) foldable
-M: real absq sq ;
+M: real absq sq ; inline
: ~abs ( x y epsilon -- ? )
[ - abs ] dip < ;
: ~rel ( x y epsilon -- ? )
- [ [ - abs ] 2keep [ abs ] bi@ + ] dip * < ;
+ [ [ - abs ] 2keep [ abs ] bi@ + ] dip * <= ;
: ~ ( x y epsilon -- ? )
{
- { [ 2over [ fp-nan? ] either? ] [ 3drop f ] }
{ [ dup zero? ] [ drop number= ] }
- { [ dup 0 < ] [ ~rel ] }
+ { [ dup 0 < ] [ neg ~rel ] }
[ ~abs ]
} cond ;
: >=1? ( x -- ? )
dup complex? [ drop f ] [ 1 >= ] if ; inline
-GENERIC: exp ( x -- y )
+GENERIC: frexp ( x -- y exp )
-M: real exp fexp ;
+M: float frexp
+ dup fp-special? [ dup zero? ] unless* [ 0 ] [
+ double>bits
+ [ 0x800f,ffff,ffff,ffff bitand 0.5 double>bits bitor bits>double ]
+ [ -52 shift 0x7ff bitand 1022 - ] bi
+ ] if ; inline
-M: complex exp >rect swap fexp swap polar> ;
+M: integer frexp
+ [ 0.0 0 ] [
+ dup 0 > [ 1 ] [ abs -1 ] if swap dup log2 [
+ 52 swap - shift 0x000f,ffff,ffff,ffff bitand
+ 0.5 double>bits bitor bits>double
+ ] [ 1 + ] bi [ * ] dip
+ ] if-zero ; inline
GENERIC: log ( x -- y )
-M: real log dup 0.0 >= [ flog ] [ 0.0 rect> log ] if ;
+M: float log dup 0.0 >= [ flog ] [ 0.0 rect> log ] if ; inline
+
+M: real log >float log ; inline
+
+M: complex log >polar [ flog ] dip rect> ; inline
+
+<PRIVATE
-M: complex log >polar swap flog swap rect> ;
+: most-negative-finite-float ( -- x )
+ -0x1.ffff,ffff,ffff,fp1023 >integer ; inline
+: most-positive-finite-float ( -- x )
+ 0x1.ffff,ffff,ffff,fp1023 >integer ; inline
+CONSTANT: log-2 0x1.62e42fefa39efp-1
+CONSTANT: log10-2 0x1.34413509f79ffp-2
+
+: (representable-as-float?) ( x -- ? )
+ most-negative-finite-float
+ most-positive-finite-float between? ; inline
+
+: (bignum-log) ( n log-quot: ( x -- y ) log-2 -- log )
+ [ dup ] dip '[
+ dup (representable-as-float?)
+ [ >float @ ] [ frexp [ @ ] [ _ * ] bi* + ] if
+ ] call ; inline
+
+PRIVATE>
+
+M: bignum log [ log ] log-2 (bignum-log) ;
+
+GENERIC: log1+ ( x -- y )
+
+M: object log1+ 1 + log ; inline
+
+M: float log1+ dup -1.0 >= [ flog1+ ] [ 1.0 + 0.0 rect> log ] if ; inline
+
+: 10^ ( x -- y ) 10 swap ^ ; inline
+
+GENERIC: log10 ( x -- y ) foldable
+
+M: real log10 >float flog10 ; inline
+
+M: complex log10 log 10 log / ; inline
+
+M: bignum log10 [ log10 ] log10-2 (bignum-log) ;
GENERIC: cos ( x -- y ) foldable
[ [ fcos ] [ fcosh ] bi* * ]
[ [ fsin neg ] [ fsinh ] bi* * ] 2bi rect> ;
-M: real cos fcos ;
+M: float cos fcos ; inline
+
+M: real cos >float cos ; inline
: sec ( x -- y ) cos recip ; inline
[ [ fcosh ] [ fcos ] bi* * ]
[ [ fsinh ] [ fsin ] bi* * ] 2bi rect> ;
-M: real cosh fcosh ;
+M: float cosh fcosh ; inline
+
+M: real cosh >float cosh ; inline
: sech ( x -- y ) cosh recip ; inline
[ [ fsin ] [ fcosh ] bi* * ]
[ [ fcos ] [ fsinh ] bi* * ] 2bi rect> ;
-M: real sin fsin ;
+M: float sin fsin ; inline
+
+M: real sin >float sin ; inline
: cosec ( x -- y ) sin recip ; inline
[ [ fsinh ] [ fcos ] bi* * ]
[ [ fcosh ] [ fsin ] bi* * ] 2bi rect> ;
-M: real sinh fsinh ;
+M: float sinh fsinh ; inline
+
+M: real sinh >float sinh ; inline
: cosech ( x -- y ) sinh recip ; inline
M: complex tan [ sin ] [ cos ] bi / ;
-M: real tan ftan ;
+M: float tan ftan ; inline
+
+M: real tan >float tan ; inline
GENERIC: tanh ( x -- y ) foldable
M: complex tanh [ sinh ] [ cosh ] bi / ;
-M: real tanh ftanh ;
+M: float tanh ftanh ; inline
+
+M: real tanh >float tanh ; inline
: cot ( x -- y ) tan recip ; inline
: -i* ( x -- y ) >rect swap neg rect> ;
: asin ( x -- y )
- dup [-1,1]? [ fasin ] [ i* asinh -i* ] if ; inline
+ dup [-1,1]? [ >float fasin ] [ i* asinh -i* ] if ; inline
: acos ( x -- y )
- dup [-1,1]? [ facos ] [ asin pi 2 / swap - ] if ;
+ dup [-1,1]? [ >float facos ] [ asin pi 2 / swap - ] if ;
inline
GENERIC: atan ( x -- y ) foldable
-M: complex atan i* atanh i* ;
+M: complex atan i* atanh i* ; inline
-M: real atan fatan ;
+M: float atan fatan ; inline
+
+M: real atan >float atan ; inline
: asec ( x -- y ) recip acos ; inline
: round ( x -- y ) dup sgn 2 / + truncate ; inline
: floor ( x -- y )
- dup 1 mod dup zero?
- [ drop ] [ dup 0 < [ - 1 - ] [ - ] if ] if ; foldable
+ dup 1 mod
+ [ ] [ dup 0 < [ - 1 - ] [ - ] if ] if-zero ; foldable
: ceiling ( x -- y ) neg floor neg ; foldable
: floor-to ( x step -- y )
- dup zero? [ drop ] [ [ / floor ] [ * ] bi ] if ;
+ [ [ / floor ] [ * ] bi ] unless-zero ;
: lerp ( a b t -- a_t ) [ over - ] dip * + ; inline
-
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