--- gforth/float.fs 1995/10/16 18:33:08 1.17 +++ gforth/float.fs 2002/11/02 15:26:03 1.38 @@ -1,5 +1,23 @@ \ High level floating point 14jan94py +\ Copyright (C) 1995,1997 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 2 +\ 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, write to the Free Software +\ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA. + \ 1 cells 4 = [IF] \ ' cells Alias sfloats \ ' cell+ Alias sfloat+ @@ -25,32 +43,49 @@ \ [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 ; -1 sfloats constant sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus -dofield: lastxt code-address! \ change the constant into a field +1 sfloats (Field) sfloat+ , ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus +\G @code{1 sfloats +}. -1 dfloats constant dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus -dofield: lastxt code-address! \ change the constant into a field +1 dfloats (Field) dfloat+ , ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus +\G @code{1 dfloats +}. -: f, ( f -- ) here 1 floats allot f! ; +: 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 -- ) \ float +: fconstant ( r "name" -- ) \ float f-constant Create f, DOES> ( -- r ) f@ ; -: fdepth ( -- n ) f0 @ fp@ - [ 1 floats ] Literal / ; +: 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 / ; : FLit ( -- r ) r> dup f@ float+ >r ; -: FLiteral ( r -- ) - BEGIN here cell+ dup faligned <> WHILE postpone noop REPEAT - postpone FLit f, ; immediate - -&15 Value precision -: set-precision to precision ; +: 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+ dup faligned <> WHILE postpone noop REPEAT + postpone FLit 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 ; @@ -64,7 +99,10 @@ DOES> ( -- r ) 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 @@ -72,47 +110,79 @@ DOES> ( -- r ) \ 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 . ; -require debugging.fs +require debugs.fs -: sfnumber ( c-addr u -- r / ) - 2dup [CHAR] e scan +: 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 + 2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 ) THEN nip IF - 2dup >float - IF - 2drop state @ - IF - POSTPONE FLiteral - THEN - EXIT - THEN - THEN - defers notfound ; + >float + ELSE + 2drop false + THEN ; -' sfnumber IS notfound +:noname ( c-addr u -- ) + 2dup sfnumber + IF + 2drop POSTPONE FLiteral + ELSE + defers compiler-notfound + ENDIF ; +IS compiler-notfound -: fvariable ( -- ) +:noname ( c-addr u -- r ) + 2dup sfnumber + IF + 2drop + ELSE + defers interpreter-notfound + ENDIF ; +IS interpreter-notfound + +: fvariable ( "name" -- ) \ float f-variable Create 0.0E0 f, ; \ does> ( -- f-addr ) -1.0e0 fasin 2.0e0 f* fconstant pi - -: f2* 2.0e0 f* ; -: f2/ 0.5e0 f* ; -: 1/f 1.0e0 fswap f/ ; - +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 @@ -127,20 +197,46 @@ require debugging.fs \ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ; \ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ; -\ !! factor out parts -: f~ ( f1 f2 f3 -- flag ) \ float-ext +: 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 - fdrop f= EXIT + IF \ bitwise comparison + fp@ float+ 1 floats over float+ -text 0= + fdrop fdrop fdrop + EXIT THEN fdup f0> IF - frot frot f- fabs fswap + f~abs ELSE - fnegate frot frot fover fabs fover fabs f+ frot frot - f- fabs frot frot f* - THEN - f< ; + fnegate f~rel + THEN ; + +1e 53 0 [do] f2* [loop] fconstant fround-offset \ 2^53 -: f.s ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0 - ?DO dup i - 1- floats fp@ + f@ f. LOOP drop ; +: fround ( r1 -- r2 ) \ float f-round +\G Round to nearest integral value. Break ties with round-to-even. + \ assumes IEEE DP FP in round-to-even mode. + \ for an explanation of this code read + \ <2002Oct26.113823@a0.complang.tuwien.ac.at> ff. + fdup f0> if + fround-offset f- fround-offset f+ + else fdup f0< if \ leave 0e and -0e as is + fround-offset f+ fround-offset f- + then then ; + +: f.s ( -- ) \ gforth f-dot-s + \G Display the number of items on the floating-point stack, + \G followed by a list of the items; TOS is the right-most item. + ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0 + ?DO dup i - 1- floats fp@ + f@ f. LOOP drop ;