| \ High level floating point 14jan94py |
\ High level floating point 14jan94py |
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| 1 cells 4 = [IF] |
\ Copyright (C) 1995,1997,2003 Free Software Foundation, Inc. |
| ' cells Alias sfloats |
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| ' cell+ Alias sfloat+ |
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| ' align Alias sfalign |
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| ' aligned Alias sfaligned |
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| [ELSE] |
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| : sfloats 2* 2* ; |
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| : sfloat+ 4 + ; |
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| : sfaligned ( addr -- addr' ) 3 + -4 and ; |
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| : sfalign ( -- ) here dup sfaligned swap ?DO bl c, LOOP ; |
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| [THEN] |
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| 1 floats 8 = [IF] |
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| ' floats Alias dfloats |
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| ' float+ Alias dfloat+ |
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| ' falign Alias dfalign |
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| ' faligned Alias dfaligned |
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| [ELSE] |
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| : dfloats 2* 2* 2* ; |
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| : dfloat+ 8 + ; |
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| : dfaligned ( addr -- addr' ) 7 + -8 and ; |
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| : dfalign ( -- ) here dup dfaligned swap ?DO bl c, LOOP ; |
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| [THEN] |
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| : f, ( f -- ) here 1 floats allot f! ; |
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| \ !! have create produce faligned pfas |
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| : fconstant ( r -- ) |
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| falign here f, Create A, |
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| DOES> @ f@ ; |
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| : fvariable |
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| falign here 0. d>f f, AConstant ; |
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| : fdepth ( -- n ) f0 @ fp@ - [ 1 floats ] Literal / ; |
\ This file is part of Gforth. |
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| : FLit ( -- r ) r> faligned dup f@ float+ >r ; |
\ Gforth is free software; you can redistribute it and/or |
| : FLiteral ( r -- ) postpone FLit falign f, ; immediate |
\ modify it under the terms of the GNU General Public License |
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\ as published by the Free Software Foundation; either version 2 |
| &16 Value precision |
\ of the License, or (at your option) any later version. |
| : set-precision to precision ; |
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\ This program is distributed in the hope that it will be useful, |
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\ but WITHOUT ANY WARRANTY; without even the implied warranty of |
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\ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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\ GNU General Public License for more details. |
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\ You should have received a copy of the GNU General Public License |
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\ along with this program; if not, write to the Free Software |
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\ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA. |
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\ 1 cells 4 = [IF] |
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\ ' cells Alias sfloats |
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\ ' cell+ Alias sfloat+ |
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\ ' align Alias sfalign |
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\ ' aligned Alias sfaligned |
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\ [ELSE] |
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\ : sfloats 2* 2* ; |
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\ : sfloat+ 4 + ; |
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\ : sfaligned ( addr -- addr' ) 3 + -4 and ; |
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\ : sfalign ( -- ) here dup sfaligned swap ?DO bl c, LOOP ; |
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\ [THEN] |
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\ 1 floats 8 = [IF] |
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\ ' floats Alias dfloats |
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\ ' float+ Alias dfloat+ |
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\ ' falign Alias dfalign |
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\ ' faligned Alias dfaligned |
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\ [ELSE] |
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\ : dfloats 2* 2* 2* ; |
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\ : dfloat+ 8 + ; |
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\ : dfaligned ( addr -- addr' ) 7 + -8 and ; |
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\ : dfalign ( -- ) here dup dfaligned swap ?DO bl c, LOOP ; |
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\ [THEN] |
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: 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. |
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here dup sfaligned swap ?DO bl c, LOOP ; |
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: 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. |
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here dup dfaligned swap ?DO bl c, LOOP ; |
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1 sfloats (Field) sfloat+ , ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus |
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\G @code{1 sfloats +}. |
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1 dfloats (Field) dfloat+ , ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus |
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\G @code{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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: fconstant ( r "name" -- ) \ float f-constant |
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Create f, |
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DOES> ( -- r ) |
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f@ ; |
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: fdepth ( -- +n ) \ float f-depth |
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\G @i{+n} is the current number of (floating-point) values on the |
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\G floating-point stack. |
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fp0 @ fp@ - [ 1 floats ] Literal / ; |
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: 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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| : scratch ( r -- addr len ) |
: scratch ( r -- addr len ) |
| pad precision - precision ; |
pad precision - precision ; |
| 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 |
| \ 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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| : sfnumber ( c-addr u -- r / ) |
require debugs.fs |
| 2dup >float |
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| IF |
: sfnumber ( c-addr u -- r true | false ) |
| 2drop state @ |
2dup [CHAR] e scan ( c-addr u c-addr2 u2 ) |
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dup 0= |
| IF |
IF |
| postpone FLiteral |
2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 ) |
| THEN |
THEN |
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nip |
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IF |
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>float |
| ELSE |
ELSE |
| defers notfound |
2drop false |
| THEN ; |
THEN ; |
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| ' sfnumber IS notfound |
:noname ( c-addr u -- ) |
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2dup sfnumber |
| 1e0 fasin 2e0 f* fconstant pi |
IF |
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2drop POSTPONE FLiteral |
| : f2* 2e0 f* ; |
ELSE |
| : f2/ .5e0 f* ; |
defers compiler-notfound |
| : 1/f 1e0 fswap f/ ; |
ENDIF ; |
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IS compiler-notfound |
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:noname ( c-addr u -- r ) |
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2dup sfnumber |
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IF |
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2drop |
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ELSE |
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defers interpreter-notfound |
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ENDIF ; |
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IS interpreter-notfound |
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: fvariable ( "name" -- ) \ float f-variable |
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Create 0.0E0 f, ; |
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\ does> ( -- f-addr ) |
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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 |
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\G to its diameter. |
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: 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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| \ : falog ( f -- 10^f ) [ 10e0 fln ] FLiteral f* fexp ; |
\ : falog ( f -- 10^f ) [ 10.0e0 fln ] FLiteral f* fexp ; |
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| \ : fsinh fexpm1 fdup fdup 1e0 f+ f/ f+ f2/ ; |
\ : fsinh fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ; |
| \ : fcosh fexp fdup 1/f f+ f2/ ; |
\ : fcosh fexp fdup 1/f f+ f2/ ; |
| \ : ftanh f2* fexpm1 fdup 2e0 f+ f/ ; |
\ : ftanh f2* fexpm1 fdup 2.0e0 f+ f/ ; |
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| \ : fatanh fdup f0< >r fabs 1e0 fover f- f/ f2* flnp1 f2/ |
\ : fatanh fdup f0< >r fabs 1.0e0 fover f- f/ f2* flnp1 f2/ |
| \ r> IF fnegate THEN ; |
\ r> IF fnegate THEN ; |
| \ : facosh fdup fdup f* 1e0 f- fsqrt f+ fln ; |
\ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ; |
| \ : fasinh fdup fdup f* 1e0 f+ fsqrt f/ fatanh ; |
\ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ; |
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| : f~ ( f1 f2 f3 -- flag ) fdup f0= IF fdrop f= EXIT THEN |
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| fdup f0> IF frot frot f- fabs fswap |
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| ELSE fnegate frot frot fover fabs fover fabs f+ frot frot |
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| f- fabs frot frot f* THEN f< ; |
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| : f.s ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0 |
: f~abs ( r1 r2 r3 -- flag ) \ gforth |
| ?DO dup i - 1- floats fp@ + f@ f. LOOP drop ; |
\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}. |
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fdup f0= |
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IF \ bitwise comparison |
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fp@ float+ 1 floats over float+ over str= |
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fdrop fdrop fdrop |
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EXIT |
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THEN |
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fdup f0> |
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IF |
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f~abs |
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ELSE |
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fnegate f~rel |
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THEN ; |
