Annotation of gforth/float.fs, revision 1.60
1.1 anton 1: \ High level floating point 14jan94py
2:
1.58 anton 3: \ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009,2010 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:
1.59 pazsan 144: [ifdef] recognizer:
145: ' noop
146: :noname postpone Fliteral ;
147: dup
148: recognizer: r:fnumber
149:
1.60 ! pazsan 150: : fnum-recognizer ( addr u -- nt int-table true | addr u false )
1.59 pazsan 151: 2dup sfnumber dup
152: IF
153: drop 2drop r:fnumber true
1.60 ! pazsan 154: THEN ;
1.59 pazsan 155:
1.60 ! pazsan 156: ' fnum-recognizer
1.59 pazsan 157: forth-recognizer get-recognizers
158: 1+ forth-recognizer set-recognizers
159: [else]
1.47 anton 160: [ifundef] compiler-notfound1
161: defer compiler-notfound1
162: ' no.extensions IS compiler-notfound1
163:
164: :noname compiler-notfound1 execute ; is compiler-notfound
165:
166: defer interpreter-notfound1
167: ' no.extensions IS interpreter-notfound1
168:
169: :noname interpreter-notfound1 execute ; is interpreter-notfound
170: [then]
171:
172: :noname ( c-addr u -- ... xt )
1.19 anton 173: 2dup sfnumber
174: IF
1.47 anton 175: 2drop [comp'] FLiteral
1.19 anton 176: ELSE
1.47 anton 177: defers compiler-notfound1
1.19 anton 178: ENDIF ;
1.47 anton 179: IS compiler-notfound1
1.1 anton 180:
1.47 anton 181: :noname ( c-addr u -- ... xt )
1.19 anton 182: 2dup sfnumber
183: IF
1.47 anton 184: 2drop ['] noop
1.19 anton 185: ELSE
1.47 anton 186: defers interpreter-notfound1
1.19 anton 187: ENDIF ;
1.47 anton 188: IS interpreter-notfound1
1.59 pazsan 189: [then]
1.13 anton 190:
1.29 crook 191: : fvariable ( "name" -- ) \ float f-variable
1.15 pazsan 192: Create 0.0E0 f, ;
1.13 anton 193: \ does> ( -- f-addr )
1.1 anton 194:
1.24 crook 195: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
1.28 crook 196: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
1.24 crook 197: \G to its diameter.
198:
199: : f2* ( r1 -- r2 ) \ gforth
1.28 crook 200: \G Multiply @i{r1} by 2.0e0
1.24 crook 201: 2.0e0 f* ;
202:
203: : f2/ ( r1 -- r2 ) \ gforth
1.28 crook 204: \G Multiply @i{r1} by 0.5e0
1.24 crook 205: 0.5e0 f* ;
206:
207: : 1/f ( r1 -- r2 ) \ gforth
1.28 crook 208: \G Divide 1.0e0 by @i{r1}.
1.24 crook 209: 1.0e0 fswap f/ ;
1.6 pazsan 210:
1.36 pazsan 211: get-current environment-wordlist set-current
212: 1.7976931348623157e308 FConstant max-float
213: set-current
1.6 pazsan 214:
1.10 anton 215: \ We now have primitives for these, so we need not define them
1.6 pazsan 216:
1.15 pazsan 217: \ : falog ( f -- 10^f ) [ 10.0e0 fln ] FLiteral f* fexp ;
1.10 anton 218:
1.15 pazsan 219: \ : fsinh fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
1.10 anton 220: \ : fcosh fexp fdup 1/f f+ f2/ ;
1.15 pazsan 221: \ : ftanh f2* fexpm1 fdup 2.0e0 f+ f/ ;
1.10 anton 222:
1.15 pazsan 223: \ : fatanh fdup f0< >r fabs 1.0e0 fover f- f/ f2* flnp1 f2/
1.10 anton 224: \ r> IF fnegate THEN ;
1.15 pazsan 225: \ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
226: \ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
1.9 pazsan 227:
1.27 anton 228: : f~abs ( r1 r2 r3 -- flag ) \ gforth
229: \G Approximate equality with absolute error: |r1-r2|<r3.
230: frot frot f- fabs fswap f< ;
231:
232: : f~rel ( r1 r2 r3 -- flag ) \ gforth
233: \G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
234: frot frot fover fabs fover fabs f+ frot frot
235: f- fabs frot frot f* f< ;
236:
1.29 crook 237: : f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
1.31 anton 238: \G ANS Forth medley for comparing r1 and r2 for equality: r3>0:
239: \G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}.
1.16 anton 240: fdup f0=
1.31 anton 241: IF \ bitwise comparison
1.41 anton 242: fp@ float+ 1 floats over float+ over str=
1.31 anton 243: fdrop fdrop fdrop
1.27 anton 244: EXIT
1.16 anton 245: THEN
246: fdup f0>
247: IF
1.27 anton 248: f~abs
1.16 anton 249: ELSE
1.27 anton 250: fnegate f~rel
251: THEN ;
1.44 anton 252:
1.57 anton 253: -0e 8 0 [do] fp@ [i] + c@ $80 = [if] [i] constant fsign-offset [then] [loop]
1.54 anton 254:
255: : fcopysign ( r1 r2 -- r3 ) \ gforth
256: \G r3 takes its absolute value from r1 and its sign from r2
257: \ !! implementation relies on IEEE DP format
1.55 anton 258: fp@ fsign-offset + dup c@ $80 and >r ( r1 r2 addr-r1sign )
259: float+ dup c@ $7f and r> or swap c!
1.54 anton 260: fdrop ;
261:
1.44 anton 262: \ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com>
263: \ not sure if they are a good idea
264:
1.54 anton 265: : ftrunc ( r1 -- r2 ) \ X:ftrunc
1.44 anton 266: \ round towards 0
1.54 anton 267: fdup fabs floor fswap fcopysign ;
1.44 anton 268:
269: : FMOD ( r1 r2 -- r )
270: \ remainder of r1/r2
271: FOVER FOVER F/ ftrunc F* F- ;
1.54 anton 272:
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