Annotation of gforth/float.fs, revision 1.56

1.1       anton       1: \ High level floating point                            14jan94py
                      2: 
1.56    ! anton       3: \ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009 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
1.53      anton       9: \ as published by the Free Software Foundation, either version 3
1.18      anton      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
1.53      anton      18: \ along with this program. If not, see http://www.gnu.org/licenses/.
1.18      anton      19: 
1.17      anton      20: \ 1 cells 4 = [IF]
                     21: \ ' cells   Alias sfloats
                     22: \ ' cell+   Alias sfloat+
                     23: \ ' align   Alias sfalign
                     24: \ ' aligned Alias sfaligned
                     25: \ [ELSE]
                     26: \ : sfloats  2* 2* ;
                     27: \ : sfloat+  4 + ;
                     28: \ : sfaligned ( addr -- addr' )  3 + -4 and ;
                     29: \ : sfalign ( -- )  here dup sfaligned swap ?DO  bl c,  LOOP ;
                     30: \ [THEN]
1.6       pazsan     31: 
1.17      anton      32: \ 1 floats 8 = [IF]
                     33: \ ' floats   Alias dfloats
                     34: \ ' float+   Alias dfloat+
                     35: \ ' falign   Alias dfalign
                     36: \ ' faligned Alias dfaligned
                     37: \ [ELSE]
                     38: \ : dfloats  2* 2* 2* ;
                     39: \ : dfloat+  8 + ;
                     40: \ : dfaligned ( addr -- addr' )  7 + -8 and ;
                     41: \ : dfalign ( -- )  here dup dfaligned swap ?DO  bl c,  LOOP ;
                     42: \ [THEN]
                     43: 
                     44: : sfalign ( -- ) \ float-ext s-f-align
1.26      crook      45:     \G If the data-space pointer is not single-float-aligned, reserve
                     46:     \G enough space to align it.
1.17      anton      47:     here dup sfaligned swap ?DO  bl c,  LOOP ;
                     48: : dfalign ( -- ) \ float-ext d-f-align
1.26      crook      49:     \G If the data-space pointer is not double-float-aligned, reserve
                     50:     \G enough space to align it.
1.17      anton      51:     here dup dfaligned swap ?DO  bl c,  LOOP ;
                     52: 
1.51      anton      53: (Field) sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
1.31      anton      54: \G @code{1 sfloats +}.
1.51      anton      55:     1 sfloats ,
1.17      anton      56: 
1.51      anton      57: (Field) dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
1.31      anton      58: \G @code{1 dfloats +}.
1.51      anton      59:     1 dfloats ,
                     60:     
1.26      crook      61: : f, ( f -- ) \ gforth
                     62:     \G Reserve data space for one floating-point number and store
                     63:     \G @i{f} in the space.
                     64:     here 1 floats allot f! ;
1.1       anton      65: 
1.29      crook      66: : fconstant  ( r "name" -- ) \ float f-constant
1.13      anton      67:     Create f,
1.16      anton      68: DOES> ( -- r )
                     69:     f@ ;
1.1       anton      70: 
1.29      crook      71: : fdepth ( -- +n ) \ float f-depth
1.28      crook      72:     \G @i{+n} is the current number of (floating-point) values on the
1.24      crook      73:     \G floating-point stack.
                     74:     fp0 @ fp@ - [ 1 floats ] Literal / ;
1.1       anton      75: 
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.
1.39      anton      79:     BEGIN  here cell+ cell+ dup faligned <>  WHILE  postpone noop  REPEAT
                     80:     postpone ahead here >r f, postpone then
                     81:     r> postpone literal postpone f@ ;  immediate
1.24      crook      82: 
1.29      crook      83: &15 Value precision ( -- u ) \ float-ext
1.28      crook      84: \G @i{u} is the number of significant digits currently used by
1.24      crook      85: \G @code{F.} @code{FE.} and @code{FS.} 
1.29      crook      86: : set-precision ( u -- ) \ float-ext
1.24      crook      87:     \G Set the number of significant digits currently used by
1.28      crook      88:     \G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
1.24      crook      89:     to precision ;
1.1       anton      90: 
                     91: : scratch ( r -- addr len )
                     92:   pad precision - precision ;
                     93: 
                     94: : zeros ( n -- )   0 max 0 ?DO  '0 emit  LOOP ;
                     95: 
                     96: : -zeros ( addr u -- addr' u' )
                     97:   BEGIN  dup  WHILE  1- 2dup + c@ '0 <>  UNTIL  1+  THEN ;
                     98: 
1.4       pazsan     99: : f$ ( f -- n )  scratch represent 0=
                    100:   IF  2drop  scratch 3 min type  rdrop  EXIT  THEN
                    101:   IF  '- emit  THEN ;
                    102: 
1.29      crook     103: : f.  ( r -- ) \ float-ext f-dot
1.32      anton     104: \G Display (the floating-point number) @i{r} without exponent,
1.24      crook     105: \G followed by a space.
1.35      anton     106:   f$ dup >r 0<=
1.4       pazsan    107:   IF    '0 emit
1.1       anton     108:   ELSE  scratch r@ min type  r@ precision - zeros  THEN
                    109:   '. emit r@ negate zeros
                    110:   scratch r> 0 max /string 0 max -zeros type space ;
1.3       benschop  111: \ I'm afraid this does not really implement ansi semantics wrt precision.
                    112: \ Shouldn't precision indicate the number of places shown after the point?
1.1       anton     113: 
1.33      anton     114: \ Why do you think so? ANS Forth appears ambiguous on this point. -anton.
                    115: 
1.29      crook     116: : fe. ( r -- ) \ float-ext f-e-dot
1.32      anton     117: \G Display @i{r} using engineering notation (with exponent dividable
                    118: \G by 3), followed by a space.
1.24      crook     119:   f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
1.33      anton     120:   scratch r@ tuck min tuck - >r type r> zeros
                    121:   '. emit scratch r> /string type
1.1       anton     122:   'E emit r> . ;
                    123: 
1.29      crook     124: : fs. ( r -- ) \ float-ext f-s-dot
1.32      anton     125: \G Display @i{r} using scientific notation (with exponent), followed
                    126: \G by a space.
1.24      crook     127:   f$ 1-
1.4       pazsan    128:   scratch over c@ emit '. emit 1 /string type
                    129:   'E emit . ;
                    130: 
1.19      anton     131: : sfnumber ( c-addr u -- r true | false )
                    132:     2dup [CHAR] e scan ( c-addr u c-addr2 u2 )
1.16      anton     133:     dup 0=
                    134:     IF
1.19      anton     135:        2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 )
1.16      anton     136:     THEN
                    137:     nip
1.7       anton     138:     IF
1.19      anton     139:        >float
                    140:     ELSE
                    141:        2drop false
                    142:     THEN ;
                    143: 
1.47      anton     144: [ifundef] compiler-notfound1
                    145: defer compiler-notfound1
                    146: ' no.extensions IS compiler-notfound1
                    147: 
                    148: :noname compiler-notfound1 execute ; is compiler-notfound
                    149: 
                    150: defer interpreter-notfound1
                    151: ' no.extensions IS interpreter-notfound1
                    152: 
                    153: :noname interpreter-notfound1 execute ; is interpreter-notfound
                    154: [then]
                    155: 
                    156: :noname ( c-addr u -- ... xt )
1.19      anton     157:     2dup sfnumber
                    158:     IF
1.47      anton     159:        2drop [comp'] FLiteral
1.19      anton     160:     ELSE
1.47      anton     161:        defers compiler-notfound1
1.19      anton     162:     ENDIF ;
1.47      anton     163: IS compiler-notfound1
1.1       anton     164: 
1.47      anton     165: :noname ( c-addr u -- ... xt )
1.19      anton     166:     2dup sfnumber
                    167:     IF
1.47      anton     168:        2drop ['] noop
1.19      anton     169:     ELSE
1.47      anton     170:        defers interpreter-notfound1
1.19      anton     171:     ENDIF ;
1.47      anton     172: IS interpreter-notfound1
1.13      anton     173: 
1.29      crook     174: : fvariable ( "name" -- ) \ float f-variable
1.15      pazsan    175:     Create 0.0E0 f, ;
1.13      anton     176:     \ does> ( -- f-addr )
1.1       anton     177: 
1.24      crook     178: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
1.28      crook     179: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
1.24      crook     180: \G to its diameter.
                    181: 
                    182: : f2* ( r1 -- r2 ) \ gforth
1.28      crook     183:     \G Multiply @i{r1} by 2.0e0
1.24      crook     184:     2.0e0 f* ;
                    185: 
                    186: : f2/ ( r1 -- r2 ) \ gforth
1.28      crook     187:     \G Multiply @i{r1} by 0.5e0
1.24      crook     188:     0.5e0 f* ;
                    189: 
                    190: : 1/f ( r1 -- r2 ) \ gforth
1.28      crook     191:     \G Divide 1.0e0 by @i{r1}.
1.24      crook     192:     1.0e0 fswap f/ ;
1.6       pazsan    193: 
1.36      pazsan    194: get-current environment-wordlist set-current
                    195: 1.7976931348623157e308 FConstant max-float
                    196: set-current
1.6       pazsan    197: 
1.10      anton     198: \ We now have primitives for these, so we need not define them
1.6       pazsan    199: 
1.15      pazsan    200: \ : falog ( f -- 10^f )  [ 10.0e0 fln ] FLiteral f* fexp ;
1.10      anton     201: 
1.15      pazsan    202: \ : fsinh    fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
1.10      anton     203: \ : fcosh    fexp fdup 1/f f+ f2/ ;
1.15      pazsan    204: \ : ftanh    f2* fexpm1 fdup 2.0e0 f+ f/ ;
1.10      anton     205: 
1.15      pazsan    206: \ : fatanh   fdup f0< >r fabs 1.0e0 fover f- f/  f2* flnp1 f2/
1.10      anton     207: \            r> IF  fnegate  THEN ;
1.15      pazsan    208: \ : facosh   fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
                    209: \ : fasinh   fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
1.9       pazsan    210: 
1.27      anton     211: : f~abs ( r1 r2 r3 -- flag ) \ gforth
                    212:     \G Approximate equality with absolute error: |r1-r2|<r3.
                    213:     frot frot f- fabs fswap f< ;
                    214: 
                    215: : f~rel ( r1 r2 r3 -- flag ) \ gforth
                    216:     \G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
                    217:        frot frot fover fabs fover fabs f+ frot frot
                    218:        f- fabs frot frot f* f< ;
                    219: 
1.29      crook     220: : f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
1.31      anton     221:     \G ANS Forth medley for comparing r1 and r2 for equality: r3>0:
                    222:     \G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}.
1.16      anton     223:     fdup f0=
1.31      anton     224:     IF \ bitwise comparison
1.41      anton     225:        fp@ float+ 1 floats over float+ over str=
1.31      anton     226:        fdrop fdrop fdrop
1.27      anton     227:        EXIT
1.16      anton     228:     THEN
                    229:     fdup f0>
                    230:     IF
1.27      anton     231:        f~abs
1.16      anton     232:     ELSE
1.27      anton     233:        fnegate f~rel
                    234:     THEN ;
1.44      anton     235: 
1.54      anton     236: -0e fp@ c@ $80 = [if] 0 [else] 7 [endif] constant fsign-offset
                    237: 
                    238: : fcopysign ( r1 r2 -- r3 ) \ gforth
                    239: \G r3 takes its absolute value from r1 and its sign from r2
                    240:     \ !! implementation relies on IEEE DP format
1.55      anton     241:     fp@ fsign-offset + dup c@ $80 and >r ( r1 r2 addr-r1sign )
                    242:     float+ dup c@ $7f and r> or swap c!
1.54      anton     243:     fdrop ;
                    244: 
1.44      anton     245: \ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com>
                    246: \ not sure if they are a good idea
                    247: 
1.54      anton     248: : ftrunc ( r1 -- r2 ) \ X:ftrunc
1.44      anton     249:     \ round towards 0
1.54      anton     250:     fdup fabs floor fswap fcopysign ;
1.44      anton     251: 
                    252: : FMOD ( r1 r2 -- r )
                    253:     \ remainder of r1/r2
                    254:     FOVER FOVER F/ ftrunc F* F- ;
1.54      anton     255: 

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