version 1.20, 1996/09/10 16:08:37
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version 1.67, 2012/05/28 14:20:04
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\ High level floating point 14jan94py |
\ High level floating point 14jan94py |
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\ Copyright (C) 1995 Free Software Foundation, Inc. |
\ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009,2010,2011 Free Software Foundation, Inc. |
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\ This file is part of Gforth. |
\ This file is part of Gforth. |
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\ Gforth is free software; you can redistribute it and/or |
\ Gforth is free software; you can redistribute it and/or |
\ modify it under the terms of the GNU General Public License |
\ modify it under the terms of the GNU General Public License |
\ as published by the Free Software Foundation; either version 2 |
\ as published by the Free Software Foundation, either version 3 |
\ of the License, or (at your option) any later version. |
\ of the License, or (at your option) any later version. |
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\ This program is distributed in the hope that it will be useful, |
\ This program is distributed in the hope that it will be useful, |
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\ GNU General Public License for more details. |
\ GNU General Public License for more details. |
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\ You should have received a copy of the GNU General Public License |
\ You should have received a copy of the GNU General Public License |
\ along with this program; if not, write to the Free Software |
\ along with this program. If not, see http://www.gnu.org/licenses/. |
\ Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. |
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\ 1 cells 4 = [IF] |
\ 1 cells 4 = [IF] |
\ ' cells Alias sfloats |
\ ' cells Alias sfloats |
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\ [THEN] |
\ [THEN] |
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: sfalign ( -- ) \ float-ext s-f-align |
: sfalign ( -- ) \ float-ext s-f-align |
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\G If the data-space pointer is not single-float-aligned, reserve |
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\G enough space to align it. |
here dup sfaligned swap ?DO bl c, LOOP ; |
here dup sfaligned swap ?DO bl c, LOOP ; |
: dfalign ( -- ) \ float-ext d-f-align |
: dfalign ( -- ) \ float-ext d-f-align |
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\G If the data-space pointer is not double-float-aligned, reserve |
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\G enough space to align it. |
here dup dfaligned swap ?DO bl c, LOOP ; |
here dup dfaligned swap ?DO bl c, LOOP ; |
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1 sfloats constant sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus |
(Field) sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus |
dofield: lastxt code-address! \ change the constant into a field |
\G @code{1 sfloats +}. |
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1 sfloats , |
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(Field) dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus |
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\G @code{1 dfloats +}. |
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1 dfloats , |
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: f, ( f -- ) \ gforth |
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\G Reserve data space for one floating-point number and store |
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\G @i{f} in the space. |
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here 1 floats allot f! ; |
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1 dfloats constant dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus |
: fconstant ( r "name" -- ) \ float f-constant |
dofield: lastxt code-address! \ change the constant into a field |
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: f, ( f -- ) here 1 floats allot f! ; |
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: fconstant ( r "name" -- ) \ float |
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Create f, |
Create f, |
DOES> ( -- r ) |
DOES> ( -- r ) |
f@ ; |
f@ ; |
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: fdepth ( -- n ) f0 @ fp@ - [ 1 floats ] Literal / ; |
: fdepth ( -- +n ) \ float f-depth |
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\G @i{+n} is the current number of (floating-point) values on the |
: FLit ( -- r ) r> dup f@ float+ >r ; |
\G floating-point stack. |
: FLiteral ( r -- ) |
fp0 @ fp@ - [ 1 floats ] Literal / ; |
BEGIN here cell+ dup faligned <> WHILE postpone noop REPEAT |
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postpone FLit f, ; immediate |
: FLiteral ( compilation r -- ; run-time -- r ) \ float f-literal |
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\G Compile appropriate code such that, at run-time, @i{r} is placed |
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\G on the (floating-point) stack. Interpretation semantics are undefined. |
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BEGIN here cell+ cell+ dup faligned <> WHILE postpone noop REPEAT |
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postpone ahead here >r f, postpone then |
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r> postpone literal postpone f@ ; immediate |
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&15 Value precision ( -- u ) \ float-ext |
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\G @i{u} is the number of significant digits currently used by |
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\G @code{F.} @code{FE.} and @code{FS.} |
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: set-precision ( u -- ) \ float-ext |
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\G Set the number of significant digits currently used by |
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\G @code{F.} @code{FE.} and @code{FS.} to @i{u}. |
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to precision ; |
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&15 Value precision |
: scratch ( -- addr len ) |
: set-precision to precision ; |
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: scratch ( r -- addr len ) |
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pad precision - precision ; |
pad precision - precision ; |
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: zeros ( n -- ) 0 max 0 ?DO '0 emit LOOP ; |
: zeros ( n -- ) 0 max 0 ?DO '0 emit LOOP ; |
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Line 100 DOES> ( -- r )
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IF 2drop scratch 3 min type rdrop EXIT THEN |
IF 2drop scratch 3 min type rdrop EXIT THEN |
IF '- emit THEN ; |
IF '- emit THEN ; |
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: f. ( r -- ) f$ dup >r 0< |
: f. ( r -- ) \ float-ext f-dot |
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\G Display (the floating-point number) @i{r} without exponent, |
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\G followed by a space. |
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f$ dup >r 0<= |
IF '0 emit |
IF '0 emit |
ELSE scratch r@ min type r@ precision - zeros THEN |
ELSE scratch r@ min type r@ precision - zeros THEN |
'. emit r@ negate zeros |
'. emit r@ negate zeros |
Line 90 DOES> ( -- r )
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Line 111 DOES> ( -- r )
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\ I'm afraid this does not really implement ansi semantics wrt precision. |
\ I'm afraid this does not really implement ansi semantics wrt precision. |
\ Shouldn't precision indicate the number of places shown after the point? |
\ Shouldn't precision indicate the number of places shown after the point? |
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: fe. ( r -- ) f$ 1- s>d 3 fm/mod 3 * >r 1+ >r |
\ Why do you think so? ANS Forth appears ambiguous on this point. -anton. |
scratch r@ min type '. emit scratch r> /string type |
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: fe. ( r -- ) \ float-ext f-e-dot |
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\G Display @i{r} using engineering notation (with exponent dividable |
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\G by 3), followed by a space. |
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f$ 1- s>d 3 fm/mod 3 * >r 1+ >r |
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scratch r@ tuck min tuck - >r type r> zeros |
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'. emit scratch r> /string type |
'E emit r> . ; |
'E emit r> . ; |
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: fs. ( r -- ) f$ 1- |
: fs. ( r -- ) \ float-ext f-s-dot |
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\G Display @i{r} using scientific notation (with exponent), followed |
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\G by a space. |
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f$ 1- |
scratch over c@ emit '. emit 1 /string type |
scratch over c@ emit '. emit 1 /string type |
'E emit . ; |
'E emit . ; |
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require debugging.fs |
[IFDEF] fp-char |
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: sfnumber ( c-addr u -- r true | false ) |
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fp-char @ >float1 ; |
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Create si-prefixes ," PTGMk munpf" |
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si-prefixes count bl scan drop Constant zero-exp |
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: prefix-number ( c-addr u -- r true | false ) |
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si-prefixes count bounds DO |
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2dup I c@ scan nip dup 0<> IF |
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1 = IF 1- fp-char @ ELSE I c@ THEN |
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>float1 |
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dup IF 1000 s>f zero-exp I - s>f f** f* THEN |
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UNLOOP EXIT THEN drop |
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LOOP |
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sfnumber ; |
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[ELSE] |
: sfnumber ( c-addr u -- r true | false ) |
: sfnumber ( c-addr u -- r true | false ) |
2dup [CHAR] e scan ( c-addr u c-addr2 u2 ) |
>float ; |
dup 0= |
: prefix-number sfnumber ; |
IF |
[THEN] |
2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 ) |
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THEN |
[ifdef] recognizer: |
nip |
[IFDEF] 2lit, |
IF |
: flit, postpone Fliteral ; |
>float |
:noname ['] noop ; |
ELSE |
:noname ['] flit, ; |
2drop false |
[ELSE] |
THEN ; |
' noop |
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:noname postpone Fliteral ; |
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[THEN] |
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dup |
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recognizer: r:fnumber |
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: fnum-recognizer ( addr u -- float int-table | addr u r:fail ) |
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2dup prefix-number |
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IF |
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2drop r:fnumber EXIT |
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THEN |
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r:fail ; |
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' fnum-recognizer |
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forth-recognizer get-recognizers |
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1+ forth-recognizer set-recognizers |
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[else] |
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[ifundef] compiler-notfound1 |
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defer compiler-notfound1 |
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' no.extensions IS compiler-notfound1 |
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:noname compiler-notfound1 execute ; is compiler-notfound |
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defer interpreter-notfound1 |
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' no.extensions IS interpreter-notfound1 |
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:noname interpreter-notfound1 execute ; is interpreter-notfound |
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[then] |
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:noname ( c-addr u -- ) |
:noname ( c-addr u -- ... xt ) |
2dup sfnumber |
2dup sfnumber |
IF |
IF |
2drop POSTPONE FLiteral |
2drop [comp'] FLiteral |
ELSE |
ELSE |
defers compiler-notfound |
defers compiler-notfound1 |
ENDIF ; |
ENDIF ; |
IS compiler-notfound |
IS compiler-notfound1 |
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:noname ( c-addr u -- r ) |
:noname ( c-addr u -- ... xt ) |
2dup sfnumber |
2dup sfnumber |
IF |
IF |
2drop |
2drop ['] noop |
ELSE |
ELSE |
defers interpreter-notfound |
defers interpreter-notfound1 |
ENDIF ; |
ENDIF ; |
IS interpreter-notfound |
IS interpreter-notfound1 |
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[then] |
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: fvariable ( "name" -- ) \ float |
: fvariable ( "name" -- ) \ float f-variable |
Create 0.0E0 f, ; |
Create 0.0E0 f, ; |
\ does> ( -- f-addr ) |
\ does> ( -- f-addr ) |
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1.0e0 fasin 2.0e0 f* fconstant pi |
1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth |
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\G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area |
: f2* 2.0e0 f* ; |
\G to its diameter. |
: f2/ 0.5e0 f* ; |
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: 1/f 1.0e0 fswap f/ ; |
: f2* ( r1 -- r2 ) \ gforth |
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\G Multiply @i{r1} by 2.0e0 |
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2.0e0 f* ; |
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: f2/ ( r1 -- r2 ) \ gforth |
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\G Multiply @i{r1} by 0.5e0 |
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0.5e0 f* ; |
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: 1/f ( r1 -- r2 ) \ gforth |
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\G Divide 1.0e0 by @i{r1}. |
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1.0e0 fswap f/ ; |
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get-current environment-wordlist set-current |
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1.7976931348623157e308 FConstant max-float |
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set-current |
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\ We now have primitives for these, so we need not define them |
\ We now have primitives for these, so we need not define them |
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Line 155 IS interpreter-notfound
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Line 241 IS interpreter-notfound
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\ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ; |
\ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ; |
\ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ; |
\ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ; |
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\ !! factor out parts |
: f~abs ( r1 r2 r3 -- flag ) \ gforth |
: f~ ( f1 f2 f3 -- flag ) \ float-ext |
\G Approximate equality with absolute error: |r1-r2|<r3. |
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frot frot f- fabs fswap f< ; |
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: f~rel ( r1 r2 r3 -- flag ) \ gforth |
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\G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|. |
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frot frot fover fabs fover fabs f+ frot frot |
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f- fabs frot frot f* f< ; |
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: f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate |
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\G ANS Forth medley for comparing r1 and r2 for equality: r3>0: |
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\G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}. |
fdup f0= |
fdup f0= |
IF |
IF \ bitwise comparison |
fdrop f= EXIT |
fp@ float+ 1 floats over float+ over str= |
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fdrop fdrop fdrop |
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EXIT |
THEN |
THEN |
fdup f0> |
fdup f0> |
IF |
IF |
frot frot f- fabs fswap |
f~abs |
ELSE |
ELSE |
fnegate frot frot fover fabs fover fabs f+ frot frot |
fnegate f~rel |
f- fabs frot frot f* |
THEN ; |
THEN |
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f< ; |
-0e 8 0 [do] fp@ [i] + c@ $80 = [if] [i] constant fsign-offset [then] [loop] |
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: fcopysign ( r1 r2 -- r3 ) \ gforth |
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\G r3 takes its absolute value from r1 and its sign from r2 |
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\ !! implementation relies on IEEE DP format |
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fp@ fsign-offset + dup c@ $80 and >r ( r1 r2 addr-r1sign ) |
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float+ dup c@ $7f and r> or swap c! |
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fdrop ; |
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\ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com> |
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\ not sure if they are a good idea |
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: ftrunc ( r1 -- r2 ) \ X:ftrunc |
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\ round towards 0 |
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fdup fabs floor fswap fcopysign ; |
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: FMOD ( r1 r2 -- r ) |
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\ remainder of r1/r2 |
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FOVER FOVER F/ ftrunc F* F- ; |
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: f.s ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0 |
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?DO dup i - 1- floats fp@ + f@ f. LOOP drop ; |
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