Annotation of gforth/float.fs, revision 1.31

1.1       anton       1: \ High level floating point                            14jan94py
                      2: 
1.23      anton       3: \ Copyright (C) 1995,1997 Free Software Foundation, Inc.
1.18      anton       4: 
                      5: \ This file is part of Gforth.
                      6: 
                      7: \ Gforth is free software; you can redistribute it and/or
                      8: \ modify it under the terms of the GNU General Public License
                      9: \ as published by the Free Software Foundation; either version 2
                     10: \ of the License, or (at your option) any later version.
                     11: 
                     12: \ This program is distributed in the hope that it will be useful,
                     13: \ but WITHOUT ANY WARRANTY; without even the implied warranty of
                     14: \ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
                     15: \ GNU General Public License for more details.
                     16: 
                     17: \ You should have received a copy of the GNU General Public License
                     18: \ along with this program; if not, write to the Free Software
                     19: \ Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
                     20: 
1.17      anton      21: \ 1 cells 4 = [IF]
                     22: \ ' cells   Alias sfloats
                     23: \ ' cell+   Alias sfloat+
                     24: \ ' align   Alias sfalign
                     25: \ ' aligned Alias sfaligned
                     26: \ [ELSE]
                     27: \ : sfloats  2* 2* ;
                     28: \ : sfloat+  4 + ;
                     29: \ : sfaligned ( addr -- addr' )  3 + -4 and ;
                     30: \ : sfalign ( -- )  here dup sfaligned swap ?DO  bl c,  LOOP ;
                     31: \ [THEN]
1.6       pazsan     32: 
1.17      anton      33: \ 1 floats 8 = [IF]
                     34: \ ' floats   Alias dfloats
                     35: \ ' float+   Alias dfloat+
                     36: \ ' falign   Alias dfalign
                     37: \ ' faligned Alias dfaligned
                     38: \ [ELSE]
                     39: \ : dfloats  2* 2* 2* ;
                     40: \ : dfloat+  8 + ;
                     41: \ : dfaligned ( addr -- addr' )  7 + -8 and ;
                     42: \ : dfalign ( -- )  here dup dfaligned swap ?DO  bl c,  LOOP ;
                     43: \ [THEN]
                     44: 
                     45: : sfalign ( -- ) \ float-ext s-f-align
1.26      crook      46:     \G If the data-space pointer is not single-float-aligned, reserve
                     47:     \G enough space to align it.
1.17      anton      48:     here dup sfaligned swap ?DO  bl c,  LOOP ;
                     49: : dfalign ( -- ) \ float-ext d-f-align
1.26      crook      50:     \G If the data-space pointer is not double-float-aligned, reserve
                     51:     \G enough space to align it.
1.17      anton      52:     here dup dfaligned swap ?DO  bl c,  LOOP ;
                     53: 
1.30      pazsan     54: 1 sfloats (Field) sfloat+ , ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
1.31    ! anton      55: \G @code{1 sfloats +}.
1.17      anton      56: 
1.30      pazsan     57: 1 dfloats (Field) dfloat+ , ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
1.31    ! anton      58: \G @code{1 dfloats +}.
1.6       pazsan     59: 
1.26      crook      60: : f, ( f -- ) \ gforth
                     61:     \G Reserve data space for one floating-point number and store
                     62:     \G @i{f} in the space.
                     63:     here 1 floats allot f! ;
1.1       anton      64: 
1.29      crook      65: : fconstant  ( r "name" -- ) \ float f-constant
1.13      anton      66:     Create f,
1.16      anton      67: DOES> ( -- r )
                     68:     f@ ;
1.1       anton      69: 
1.29      crook      70: : fdepth ( -- +n ) \ float f-depth
1.28      crook      71:     \G @i{+n} is the current number of (floating-point) values on the
1.24      crook      72:     \G floating-point stack.
                     73:     fp0 @ fp@ - [ 1 floats ] Literal / ;
1.1       anton      74: 
1.14      pazsan     75: : FLit ( -- r )  r> dup f@ float+ >r ;
1.29      crook      76: : FLiteral ( compilation r -- ; run-time -- r ) \ float f-literal
1.28      crook      77:     \G Compile appropriate code such that, at run-time, @i{r} is placed
1.24      crook      78:     \G on the (floating-point) stack. Interpretation semantics are undefined.
                     79:     BEGIN  here cell+ dup faligned <>  WHILE  postpone noop  REPEAT
                     80:     postpone FLit  f, ;  immediate
                     81: 
1.29      crook      82: &15 Value precision ( -- u ) \ float-ext
1.28      crook      83: \G @i{u} is the number of significant digits currently used by
1.24      crook      84: \G @code{F.} @code{FE.} and @code{FS.} 
1.29      crook      85: : set-precision ( u -- ) \ float-ext
1.24      crook      86:     \G Set the number of significant digits currently used by
1.28      crook      87:     \G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
1.24      crook      88:     to precision ;
1.1       anton      89: 
                     90: : scratch ( r -- addr len )
                     91:   pad precision - precision ;
                     92: 
                     93: : zeros ( n -- )   0 max 0 ?DO  '0 emit  LOOP ;
                     94: 
                     95: : -zeros ( addr u -- addr' u' )
                     96:   BEGIN  dup  WHILE  1- 2dup + c@ '0 <>  UNTIL  1+  THEN ;
                     97: 
1.4       pazsan     98: : f$ ( f -- n )  scratch represent 0=
                     99:   IF  2drop  scratch 3 min type  rdrop  EXIT  THEN
                    100:   IF  '- emit  THEN ;
                    101: 
1.29      crook     102: : f.  ( r -- ) \ float-ext f-dot
1.28      crook     103: \G Display (the floating-point number) @i{r} using fixed-point notation,
1.24      crook     104: \G followed by a space.
                    105:   f$ dup >r 0<
1.4       pazsan    106:   IF    '0 emit
1.1       anton     107:   ELSE  scratch r@ min type  r@ precision - zeros  THEN
                    108:   '. emit r@ negate zeros
                    109:   scratch r> 0 max /string 0 max -zeros type space ;
1.3       benschop  110: \ I'm afraid this does not really implement ansi semantics wrt precision.
                    111: \ Shouldn't precision indicate the number of places shown after the point?
1.1       anton     112: 
1.29      crook     113: : fe. ( r -- ) \ float-ext f-e-dot
1.28      crook     114: \G Display @i{r} using engineering notation, followed by a space.
1.24      crook     115:   f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
1.1       anton     116:   scratch r@ min type '. emit  scratch r> /string type
                    117:   'E emit r> . ;
                    118: 
1.29      crook     119: : fs. ( r -- ) \ float-ext f-s-dot
1.28      crook     120: \G Display @i{r} using scientific notation, followed by a space.
1.24      crook     121:   f$ 1-
1.4       pazsan    122:   scratch over c@ emit '. emit 1 /string type
                    123:   'E emit . ;
                    124: 
1.21      anton     125: require debugs.fs
1.16      anton     126: 
1.19      anton     127: : sfnumber ( c-addr u -- r true | false )
                    128:     2dup [CHAR] e scan ( c-addr u c-addr2 u2 )
1.16      anton     129:     dup 0=
                    130:     IF
1.19      anton     131:        2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 )
1.16      anton     132:     THEN
                    133:     nip
1.7       anton     134:     IF
1.19      anton     135:        >float
                    136:     ELSE
                    137:        2drop false
                    138:     THEN ;
                    139: 
                    140: :noname ( c-addr u -- )
                    141:     2dup sfnumber
                    142:     IF
                    143:        2drop POSTPONE FLiteral
                    144:     ELSE
                    145:        defers compiler-notfound
                    146:     ENDIF ;
                    147: IS compiler-notfound
1.1       anton     148: 
1.19      anton     149: :noname ( c-addr u -- r )
                    150:     2dup sfnumber
                    151:     IF
                    152:        2drop
                    153:     ELSE
                    154:        defers interpreter-notfound
                    155:     ENDIF ;
                    156: IS interpreter-notfound
1.13      anton     157: 
1.29      crook     158: : fvariable ( "name" -- ) \ float f-variable
1.15      pazsan    159:     Create 0.0E0 f, ;
1.13      anton     160:     \ does> ( -- f-addr )
1.1       anton     161: 
1.24      crook     162: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
1.28      crook     163: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
1.24      crook     164: \G to its diameter.
                    165: 
                    166: : f2* ( r1 -- r2 ) \ gforth
1.28      crook     167:     \G Multiply @i{r1} by 2.0e0
1.24      crook     168:     2.0e0 f* ;
                    169: 
                    170: : f2/ ( r1 -- r2 ) \ gforth
1.28      crook     171:     \G Multiply @i{r1} by 0.5e0
1.24      crook     172:     0.5e0 f* ;
                    173: 
                    174: : 1/f ( r1 -- r2 ) \ gforth
1.28      crook     175:     \G Divide 1.0e0 by @i{r1}.
1.24      crook     176:     1.0e0 fswap f/ ;
1.6       pazsan    177: 
                    178: 
1.10      anton     179: \ We now have primitives for these, so we need not define them
1.6       pazsan    180: 
1.15      pazsan    181: \ : falog ( f -- 10^f )  [ 10.0e0 fln ] FLiteral f* fexp ;
1.10      anton     182: 
1.15      pazsan    183: \ : fsinh    fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
1.10      anton     184: \ : fcosh    fexp fdup 1/f f+ f2/ ;
1.15      pazsan    185: \ : ftanh    f2* fexpm1 fdup 2.0e0 f+ f/ ;
1.10      anton     186: 
1.15      pazsan    187: \ : fatanh   fdup f0< >r fabs 1.0e0 fover f- f/  f2* flnp1 f2/
1.10      anton     188: \            r> IF  fnegate  THEN ;
1.15      pazsan    189: \ : facosh   fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
                    190: \ : fasinh   fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
1.9       pazsan    191: 
1.27      anton     192: : f~abs ( r1 r2 r3 -- flag ) \ gforth
                    193:     \G Approximate equality with absolute error: |r1-r2|<r3.
                    194:     frot frot f- fabs fswap f< ;
                    195: 
                    196: : f~rel ( r1 r2 r3 -- flag ) \ gforth
                    197:     \G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
                    198:        frot frot fover fabs fover fabs f+ frot frot
                    199:        f- fabs frot frot f* f< ;
                    200: 
1.29      crook     201: : f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
1.31    ! anton     202:     \G ANS Forth medley for comparing r1 and r2 for equality: r3>0:
        !           203:     \G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}.
1.16      anton     204:     fdup f0=
1.31    ! anton     205:     IF \ bitwise comparison
        !           206:        fp@ float+ 1 floats over float+ -text 0=
        !           207:        fdrop fdrop fdrop
1.27      anton     208:        EXIT
1.16      anton     209:     THEN
                    210:     fdup f0>
                    211:     IF
1.27      anton     212:        f~abs
1.16      anton     213:     ELSE
1.27      anton     214:        fnegate f~rel
                    215:     THEN ;
1.11      pazsan    216: 
1.24      crook     217: : f.s ( -- ) \ gforth f-dot-s
                    218:     \G Display the number of items on the floating-point stack,
                    219:     \G followed by a list of the items; TOS is the right-most item.
                    220:     ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0 
                    221:     ?DO  dup i - 1- floats fp@ + f@ f.  LOOP  drop ; 

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