\ High level floating point 14jan94py
\ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009,2010,2011,2012 Free Software Foundation, Inc.
\ This file is part of Gforth.
\ Gforth is free software; you can redistribute it and/or
\ modify it under the terms of the GNU General Public License
\ as published by the Free Software Foundation, either version 3
\ of the License, or (at your option) any later version.
\ This program 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 General Public License for more details.
\ You should have received a copy of the GNU General Public License
\ along with this program. If not, see http://www.gnu.org/licenses/.
\ 1 cells 4 = [IF]
\ ' cells Alias sfloats
\ ' cell+ Alias sfloat+
\ ' align Alias sfalign
\ ' aligned Alias sfaligned
\ [ELSE]
\ : sfloats 2* 2* ;
\ : sfloat+ 4 + ;
\ : sfaligned ( addr -- addr' ) 3 + -4 and ;
\ : sfalign ( -- ) here dup sfaligned swap ?DO bl c, LOOP ;
\ [THEN]
\ 1 floats 8 = [IF]
\ ' floats Alias dfloats
\ ' float+ Alias dfloat+
\ ' falign Alias dfalign
\ ' faligned Alias dfaligned
\ [ELSE]
\ : dfloats 2* 2* 2* ;
\ : dfloat+ 8 + ;
\ : dfaligned ( addr -- addr' ) 7 + -8 and ;
\ : dfalign ( -- ) here dup dfaligned swap ?DO bl c, LOOP ;
\ [THEN]
: sfalign ( -- ) \ float-ext s-f-align
\G If the data-space pointer is not single-float-aligned, reserve
\G enough space to align it.
here dup sfaligned swap ?DO bl c, LOOP ;
: dfalign ( -- ) \ float-ext d-f-align
\G If the data-space pointer is not double-float-aligned, reserve
\G enough space to align it.
here dup dfaligned swap ?DO bl c, LOOP ;
(Field) sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
\G @code{1 sfloats +}.
1 sfloats ,
(Field) dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
\G @code{1 dfloats +}.
1 dfloats ,
: f, ( f -- ) \ gforth
\G Reserve data space for one floating-point number and store
\G @i{f} in the space.
here 1 floats allot f! ;
: fconstant ( r "name" -- ) \ float f-constant
Create f,
DOES> ( -- r )
f@ ;
: fdepth ( -- +n ) \ float f-depth
\G @i{+n} is the current number of (floating-point) values on the
\G floating-point stack.
fp0 @ fp@ - [ 1 floats ] Literal / ;
: FLiteral ( compilation r -- ; run-time -- r ) \ float f-literal
\G Compile appropriate code such that, at run-time, @i{r} is placed
\G on the (floating-point) stack. Interpretation semantics are undefined.
BEGIN here cell+ cell+ dup faligned <> WHILE postpone noop REPEAT
postpone ahead here >r f, postpone then
r> postpone literal postpone f@ ; immediate
&15 Value precision ( -- u ) \ float-ext
\G @i{u} is the number of significant digits currently used by
\G @code{F.} @code{FE.} and @code{FS.}
: set-precision ( u -- ) \ float-ext
\G Set the number of significant digits currently used by
\G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
to precision ;
: scratch ( -- addr len )
pad precision - precision ;
: zeros ( n -- ) 0 max 0 ?DO '0 emit LOOP ;
: -zeros ( addr u -- addr' u' )
BEGIN dup WHILE 1- 2dup + c@ '0 <> UNTIL 1+ THEN ;
: f$ ( f -- n ) scratch represent 0=
IF 2drop scratch 3 min type rdrop EXIT THEN
IF '- emit THEN ;
: f. ( r -- ) \ float-ext f-dot
\G Display (the floating-point number) @i{r} without exponent,
\G followed by a space.
f$ dup >r 0<=
IF '0 emit
ELSE scratch r@ min type r@ precision - zeros THEN
'. emit r@ negate zeros
scratch r> 0 max /string 0 max -zeros type space ;
\ I'm afraid this does not really implement ansi semantics wrt precision.
\ Shouldn't precision indicate the number of places shown after the point?
\ Why do you think so? ANS Forth appears ambiguous on this point. -anton.
: fe. ( r -- ) \ float-ext f-e-dot
\G Display @i{r} using engineering notation (with exponent dividable
\G by 3), followed by a space.
f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
scratch r@ tuck min tuck - >r type r> zeros
'. emit scratch r> /string type
'E emit r> . ;
: fs. ( r -- ) \ float-ext f-s-dot
\G Display @i{r} using scientific notation (with exponent), followed
\G by a space.
f$ 1-
scratch over c@ emit '. emit 1 /string type
'E emit . ;
[IFDEF] fp-char
: sfnumber ( c-addr u -- r true | false )
fp-char @ >float1 ;
Create si-prefixes ," PTGMk munpf"
si-prefixes count bl scan drop Constant zero-exp
: prefix-number ( c-addr u -- r true | false )
si-prefixes count bounds DO
2dup I c@ scan nip dup 0<> IF
1 = IF 1- fp-char @ ELSE I c@ THEN
>float1
dup IF 1000 s>f zero-exp I - s>f f** f* THEN
UNLOOP EXIT THEN drop
LOOP
sfnumber ;
[ELSE]
: sfnumber ( c-addr u -- r true | false )
>float ;
: prefix-number sfnumber ;
[THEN]
[ifdef] recognizer:
[IFDEF] 2lit,
: flit, postpone Fliteral ;
:noname ['] noop ;
:noname ['] flit, ;
[ELSE]
' noop
:noname postpone Fliteral ;
[THEN]
dup
recognizer: r:fnumber
: fnum-recognizer ( addr u -- float int-table | addr u r:fail )
2dup prefix-number
IF
2drop r:fnumber EXIT
THEN
r:fail ;
' fnum-recognizer
forth-recognizer get-recognizers
1+ forth-recognizer set-recognizers
[else]
[ifundef] compiler-notfound1
defer compiler-notfound1
' no.extensions IS compiler-notfound1
:noname compiler-notfound1 execute ; is compiler-notfound
defer interpreter-notfound1
' no.extensions IS interpreter-notfound1
:noname interpreter-notfound1 execute ; is interpreter-notfound
[then]
:noname ( c-addr u -- ... xt )
2dup sfnumber
IF
2drop [comp'] FLiteral
ELSE
defers compiler-notfound1
ENDIF ;
IS compiler-notfound1
:noname ( c-addr u -- ... xt )
2dup sfnumber
IF
2drop ['] noop
ELSE
defers interpreter-notfound1
ENDIF ;
IS interpreter-notfound1
[then]
: fvariable ( "name" -- ) \ float f-variable
Create 0.0E0 f, ;
\ does> ( -- f-addr )
1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
\G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
\G to its diameter.
: f2* ( r1 -- r2 ) \ gforth
\G Multiply @i{r1} by 2.0e0
2.0e0 f* ;
: f2/ ( r1 -- r2 ) \ gforth
\G Multiply @i{r1} by 0.5e0
0.5e0 f* ;
: 1/f ( r1 -- r2 ) \ gforth
\G Divide 1.0e0 by @i{r1}.
1.0e0 fswap f/ ;
get-current environment-wordlist set-current
1.7976931348623157e308 FConstant max-float
set-current
\ We now have primitives for these, so we need not define them
\ : falog ( f -- 10^f ) [ 10.0e0 fln ] FLiteral f* fexp ;
\ : fsinh fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
\ : fcosh fexp fdup 1/f f+ f2/ ;
\ : ftanh f2* fexpm1 fdup 2.0e0 f+ f/ ;
\ : fatanh fdup f0< >r fabs 1.0e0 fover f- f/ f2* flnp1 f2/
\ r> IF fnegate THEN ;
\ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
\ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
: f~abs ( r1 r2 r3 -- flag ) \ gforth
\G Approximate equality with absolute error: |r1-r2|<r3.
frot frot f- fabs fswap f< ;
: f~rel ( r1 r2 r3 -- flag ) \ gforth
\G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
frot frot fover fabs fover fabs f+ frot frot
f- fabs frot frot f* f< ;
: f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
\G ANS Forth medley for comparing r1 and r2 for equality: r3>0:
\G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}.
fdup f0=
IF \ bitwise comparison
fp@ float+ 1 floats over float+ over str=
fdrop fdrop fdrop
EXIT
THEN
fdup f0>
IF
f~abs
ELSE
fnegate f~rel
THEN ;
-0e 8 0 [do] fp@ [i] + c@ $80 = [if] [i] constant fsign-offset [then] [loop]
: fcopysign ( r1 r2 -- r3 ) \ gforth
\G r3 takes its absolute value from r1 and its sign from r2
\ !! implementation relies on IEEE DP format
fp@ fsign-offset + dup c@ $80 and >r ( r1 r2 addr-r1sign )
float+ dup c@ $7f and r> or swap c!
fdrop ;
\ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com>
\ not sure if they are a good idea
: ftrunc ( r1 -- r2 ) \ X:ftrunc
\ round towards 0
fdup fabs floor fswap fcopysign ;
: FMOD ( r1 r2 -- r )
\ remainder of r1/r2
FOVER FOVER F/ ftrunc F* F- ;
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>