\ High level floating point 14jan94py \ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009,2010 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 ( r -- 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 . ; : 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 ; [ifdef] recognizer: ' noop :noname postpone Fliteral ; dup recognizer: r:fnumber : fnum-recognizer ( addr u -- float int-table | addr u r:fail ) 2dup sfnumber 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|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 \ 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- ;