--- gforth/float.fs 1994/07/21 10:52:40 1.6 +++ gforth/float.fs 2009/12/31 15:32:35 1.56 @@ -1,46 +1,92 @@ \ High level floating point 14jan94py -1 cells 4 = [IF] -' cells Alias sfloats -' cell+ Alias sfloat+ -' align Alias sfalign -' aligned Alias sfaligned -[ELSE] -: sfloats 4 * ; -: 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 8 * ; -: dfloat+ 8 + ; -: dfaligned ( addr -- addr' ) 7 + -8 and ; -: dfalign ( -- ) here dup dfaligned swap ?DO bl c, LOOP ; -[THEN] - -: f, ( f -- ) here 1 floats allot f! ; - -\ !! have create produce faligned pfas -: fconstant ( r -- ) - falign here f, Create A, - DOES> @ f@ ; - -: fvariable - falign here 0. d>f f, AConstant ; +\ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009 Free Software Foundation, Inc. -: fdepth ( -- n ) f0 @ fp@ - [ 1 floats ] Literal / ; +\ This file is part of Gforth. -: FLit ( -- r ) r> faligned dup f@ float+ >r ; -: FLiteral ( r -- ) postpone FLit falign f, ; immediate - -&16 Value precision -: set-precision to precision ; +\ 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 ( r -- addr len ) pad precision - precision ; @@ -54,7 +100,10 @@ IF 2drop scratch 3 min type rdrop EXIT THEN IF '- emit THEN ; -: f. ( r -- ) f$ dup >r 0< +: 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 @@ -62,35 +111,145 @@ \ I'm afraid this does not really implement ansi semantics wrt precision. \ Shouldn't precision indicate the number of places shown after the point? -: fe. ( r -- ) f$ 1- s>d 3 fm/mod 3 * >r 1+ >r - scratch r@ min type '. emit scratch r> /string type +\ 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 -- ) f$ 1- +: 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 . ; -: fnumber ( string -- r / ) - ?dup IF dup count >float 0= - IF defers notfound - ELSE drop state @ - IF postpone FLiteral THEN THEN THEN ; - -' fnumber IS notfound - -1e0 fasin 2e0 f* fconstant pi - -: f2* 2e0 f* ; -: f2/ 2e0 f/ ; -: 1/f 1e0 fswap f/ ; - -: falog ( f -- 10^f ) [ 10e0 fln ] FLiteral f* fexp ; - -: fsinh fexpm1 fdup fdup 1e0 f+ f/ f+ f2/ ; -: fcosh fexp fdup 1/f f+ f2/ ; -: ftanh f2* fexpm1 fdup 2e0 f+ f/ ; - -: fatanh fdup f0< >r fabs 1e0 fover f- f/ f2* flnp1 f2/ - r> IF fnegate THEN ; -: facosh fdup fdup f* 1e0 f- fsqrt f+ fln ; -: fasinh fdup fdup f* 1e0 f+ fsqrt f/ fatanh ; +: sfnumber ( c-addr u -- r true | false ) + 2dup [CHAR] e scan ( c-addr u c-addr2 u2 ) + dup 0= + IF + 2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 ) + THEN + nip + IF + >float + ELSE + 2drop false + THEN ; + +[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 + +: 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|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 fp@ c@ $80 = [if] 0 [else] 7 [endif] constant fsign-offset + +: 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 +\ 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- ; +