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1 | \ @(#) floats.fth 98/02/26 1.4 17:51:40\r |
2 | \ High Level Forth support for Floating Point\r |
3 | \\r |
4 | \ Author: Phil Burk and Darren Gibbs\r |
5 | \ Copyright 1994 3DO, Phil Burk, Larry Polansky, Devid Rosenboom\r |
6 | \\r |
7 | \ The pForth software code is dedicated to the public domain,\r |
8 | \ and any third party may reproduce, distribute and modify\r |
9 | \ the pForth software code or any derivative works thereof\r |
10 | \ without any compensation or license. The pForth software\r |
11 | \ code is provided on an "as is" basis without any warranty\r |
12 | \ of any kind, including, without limitation, the implied\r |
13 | \ warranties of merchantability and fitness for a particular\r |
14 | \ purpose and their equivalents under the laws of any jurisdiction.\r |
15 | \\r |
16 | \ 19970702 PLB Drop 0.0 in REPRESENT to fix 0.0 F.\r |
17 | \ 19980220 PLB Added FG. , fixed up large and small formatting\r |
18 | \ 19980812 PLB Now don't drop 0.0 in REPRESENT to fix 0.0 F. (!!!)\r |
19 | \ Fixed F~ by using (F.EXACTLY)\r |
20 | \r |
21 | ANEW TASK-FLOATS.FTH\r |
22 | \r |
23 | : FALIGNED ( addr -- a-addr )\r |
24 | 1 floats 1- +\r |
25 | 1 floats /\r |
26 | 1 floats *\r |
27 | ;\r |
28 | \r |
29 | : FALIGN ( -- , align DP )\r |
30 | dp @ faligned dp !\r |
31 | ;\r |
32 | \r |
33 | \ account for size of create when aligning floats\r |
34 | here\r |
35 | create fp-create-size\r |
36 | fp-create-size swap - constant CREATE_SIZE\r |
37 | \r |
38 | : FALIGN.CREATE ( -- , align DP for float after CREATE )\r |
39 | dp @\r |
40 | CREATE_SIZE +\r |
41 | faligned\r |
42 | CREATE_SIZE -\r |
43 | dp !\r |
44 | ;\r |
45 | \r |
46 | : FCREATE ( <name> -- , create with float aligned data )\r |
47 | falign.create\r |
48 | CREATE\r |
49 | ;\r |
50 | \r |
51 | : FVARIABLE ( <name> -- ) ( F: -- )\r |
52 | FCREATE 1 floats allot\r |
53 | ;\r |
54 | \r |
55 | : FCONSTANT\r |
56 | FCREATE here 1 floats allot f! \r |
57 | DOES> f@ \r |
58 | ;\r |
59 | \r |
60 | : F0SP ( -- ) ( F: ? -- )\r |
61 | fdepth 0 max 0 ?DO fdrop LOOP \r |
62 | ;\r |
63 | \r |
64 | \ Convert between single precision and floating point\r |
65 | : S>F ( s -- ) ( F: -- r )\r |
66 | s>d d>f\r |
67 | ;\r |
68 | : F>S ( -- s ) ( F: r -- )\r |
69 | f>d d>s\r |
70 | ; \r |
71 | \r |
72 | : (F.EXACTLY) ( r1 r2 -f- flag , return true if encoded equally ) { | caddr1 caddr2 fsize fcells }\r |
73 | 1 floats -> fsize\r |
74 | fsize cell 1- + cell 1- invert and \ round up to nearest multiple of stack size\r |
75 | cell / -> fcells ( number of cells per float )\r |
76 | \ make room on data stack for floats data\r |
77 | fcells 0 ?DO 0 LOOP\r |
78 | sp@ -> caddr1\r |
79 | fcells 0 ?DO 0 LOOP\r |
80 | sp@ -> caddr2\r |
81 | \ compare bit representation\r |
82 | caddr1 f!\r |
83 | caddr2 f!\r |
84 | caddr1 fsize caddr2 fsize compare 0= \r |
85 | >r fcells 2* 0 ?DO drop LOOP r> \ drop float bits\r |
86 | ;\r |
87 | \r |
88 | : F~ ( -0- flag ) ( r1 r2 r3 -f- )\r |
89 | fdup F0<\r |
90 | IF\r |
91 | frot frot ( -- r3 r1 r2 )\r |
92 | fover fover ( -- r3 r1 r2 r1 r2 )\r |
93 | f- fabs ( -- r3 r1 r2 |r1-r2| )\r |
94 | frot frot ( -- r3 |r1-r2| r1 r2 )\r |
95 | fabs fswap fabs f+ ( -- r3 |r1-r2| |r1|+|r2| )\r |
96 | frot fabs f* ( -- |r1-r2| |r1|+|r2|*|r3| )\r |
97 | f<\r |
98 | ELSE\r |
99 | fdup f0=\r |
100 | IF\r |
101 | fdrop\r |
102 | (f.exactly) \ f- f0= \ 19980812 Used to cheat. Now actually compares bit patterns.\r |
103 | ELSE\r |
104 | frot frot ( -- r3 r1 r2 )\r |
105 | f- fabs ( -- r3 |r1-r2| )\r |
106 | fswap f<\r |
107 | THEN\r |
108 | THEN\r |
109 | ;\r |
110 | \r |
111 | \ FP Output --------------------------------------------------------\r |
112 | fvariable FVAR-REP \ scratch var for represent\r |
113 | : REPRESENT { c-addr u | n flag1 flag2 -- n flag1 flag2 , FLOATING } ( F: r -- )\r |
114 | TRUE -> flag2 \ FIXME - need to check range\r |
115 | fvar-rep f!\r |
116 | \\r |
117 | fvar-rep f@ f0<\r |
118 | IF\r |
119 | -1 -> flag1\r |
120 | fvar-rep f@ fabs fvar-rep f! \ absolute value\r |
121 | ELSE\r |
122 | 0 -> flag1\r |
123 | THEN\r |
124 | \\r |
125 | fvar-rep f@ f0=\r |
126 | IF\r |
127 | \ fdrop \ 19970702 \ 19980812 Remove FDROP to fix "0.0 F."\r |
128 | c-addr u [char] 0 fill\r |
129 | 0 -> n\r |
130 | ELSE\r |
131 | fvar-rep f@ \r |
132 | flog\r |
133 | fdup f0< not\r |
134 | IF\r |
135 | 1 s>f f+ \ round up exponent\r |
136 | THEN\r |
137 | f>s -> n \r |
138 | \ ." REP - n = " n . cr\r |
139 | \ normalize r to u digits\r |
140 | fvar-rep f@\r |
141 | 10 s>f u n - s>f f** f*\r |
142 | 1 s>f 2 s>f f/ f+ \ round result\r |
143 | \\r |
144 | \ convert float to double_int then convert to text\r |
145 | f>d\r |
146 | \ ." REP - d = " over . dup . cr\r |
147 | <# u 1- 0 ?DO # loop #s #> \ ( -- addr cnt )\r |
148 | \ Adjust exponent if rounding caused number of digits to increase.\r |
149 | \ For example from 9999 to 10000.\r |
150 | u - +-> n \r |
151 | c-addr u move\r |
152 | THEN\r |
153 | \\r |
154 | n flag1 flag2\r |
155 | ;\r |
156 | \r |
157 | variable FP-PRECISION\r |
158 | \r |
159 | \ Set maximum digits that are meaningful for the precision that we use.\r |
160 | 1 FLOATS 4 / 7 * constant FP_PRECISION_MAX\r |
161 | \r |
162 | : PRECISION ( -- u )\r |
163 | fp-precision @\r |
164 | ;\r |
165 | : SET-PRECISION ( u -- )\r |
166 | fp_precision_max min\r |
167 | fp-precision !\r |
168 | ;\r |
169 | 7 set-precision\r |
170 | \r |
171 | 32 constant FP_REPRESENT_SIZE\r |
172 | 64 constant FP_OUTPUT_SIZE\r |
173 | \r |
174 | create FP-REPRESENT-PAD FP_REPRESENT_SIZE allot \ used with REPRESENT\r |
175 | create FP-OUTPUT-PAD FP_OUTPUT_SIZE allot \ used to assemble final output\r |
176 | variable FP-OUTPUT-PTR \ points into FP-OUTPUT-PAD\r |
177 | \r |
178 | : FP.HOLD ( char -- , add char to output )\r |
179 | fp-output-ptr @ fp-output-pad 64 + <\r |
180 | IF\r |
181 | fp-output-ptr @ tuck c!\r |
182 | 1+ fp-output-ptr !\r |
183 | ELSE\r |
184 | drop\r |
185 | THEN\r |
186 | ;\r |
187 | : FP.APPEND { addr cnt -- , add string to output }\r |
188 | cnt 0 max 0\r |
189 | ?DO\r |
190 | addr i + c@ fp.hold\r |
191 | LOOP\r |
192 | ;\r |
193 | \r |
194 | : FP.STRIP.TRAILING.ZEROS ( -- , remove trailing zeros from fp output )\r |
195 | BEGIN\r |
196 | fp-output-ptr @ fp-output-pad u>\r |
197 | fp-output-ptr @ 1- c@ [char] 0 =\r |
198 | and\r |
199 | WHILE\r |
200 | -1 fp-output-ptr +!\r |
201 | REPEAT\r |
202 | ;\r |
203 | \r |
204 | : FP.APPEND.ZEROS ( numZeros -- )\r |
205 | 0 max 0\r |
206 | ?DO [char] 0 fp.hold\r |
207 | LOOP\r |
208 | ;\r |
209 | \r |
210 | : FP.MOVE.DECIMAL { n prec -- , append with decimal point shifted }\r |
211 | fp-represent-pad n prec min fp.append\r |
212 | n prec - fp.append.zeros\r |
213 | [char] . fp.hold\r |
214 | fp-represent-pad n +\r |
215 | prec n - 0 max fp.append\r |
216 | ;\r |
217 | \r |
218 | : (EXP.) ( n -- addr cnt , convert exponent to two digit value )\r |
219 | dup abs 0\r |
220 | <# # #s\r |
221 | rot 0<\r |
222 | IF [char] - HOLD\r |
223 | ELSE [char] + hold\r |
224 | THEN\r |
225 | #>\r |
226 | ;\r |
227 | \r |
228 | : FP.REPRESENT ( -- n flag1 flag2 ) ( r -f- )\r |
229 | ;\r |
230 | \r |
231 | : (FS.) ( -- addr cnt ) ( F: r -- , scientific notation )\r |
232 | fp-output-pad fp-output-ptr ! \ setup pointer\r |
233 | fp-represent-pad precision represent\r |
234 | \ ." (FS.) - represent " fp-represent-pad precision type cr\r |
235 | ( -- n flag1 flag2 )\r |
236 | IF\r |
237 | IF [char] - fp.hold\r |
238 | THEN\r |
239 | 1 precision fp.move.decimal\r |
240 | [char] e fp.hold\r |
241 | 1- (exp.) fp.append \ n\r |
242 | ELSE\r |
243 | 2drop\r |
244 | s" <FP-OUT-OF-RANGE>" fp.append\r |
245 | THEN\r |
246 | fp-output-pad fp-output-ptr @ over -\r |
247 | ;\r |
248 | \r |
249 | : FS. ( F: r -- , scientific notation )\r |
250 | (fs.) type space\r |
251 | ;\r |
252 | \r |
253 | : (FE.) ( -- addr cnt ) ( F: r -- , engineering notation ) { | n n3 -- }\r |
254 | fp-output-pad fp-output-ptr ! \ setup pointer\r |
255 | fp-represent-pad precision represent\r |
256 | ( -- n flag1 flag2 )\r |
257 | IF\r |
258 | IF [char] - fp.hold\r |
259 | THEN\r |
260 | \ convert exponent to multiple of three\r |
261 | -> n\r |
262 | n 1- s>d 3 fm/mod \ use floored divide\r |
263 | 3 * -> n3\r |
264 | 1+ precision fp.move.decimal \ amount to move decimal point\r |
265 | [char] e fp.hold\r |
266 | n3 (exp.) fp.append \ n\r |
267 | ELSE\r |
268 | 2drop\r |
269 | s" <FP-OUT-OF-RANGE>" fp.append\r |
270 | THEN\r |
271 | fp-output-pad fp-output-ptr @ over -\r |
272 | ;\r |
273 | \r |
274 | : FE. ( F: r -- , engineering notation )\r |
275 | (FE.) type space\r |
276 | ;\r |
277 | \r |
278 | : (FG.) ( F: r -- , normal or scientific ) { | n n3 ndiff -- }\r |
279 | fp-output-pad fp-output-ptr ! \ setup pointer\r |
280 | fp-represent-pad precision represent\r |
281 | ( -- n flag1 flag2 )\r |
282 | IF\r |
283 | IF [char] - fp.hold\r |
284 | THEN\r |
285 | \ compare n with precision to see whether we do scientific display\r |
286 | dup precision >\r |
287 | over -3 < OR\r |
288 | IF \ use exponential notation\r |
289 | 1 precision fp.move.decimal\r |
290 | fp.strip.trailing.zeros\r |
291 | [char] e fp.hold\r |
292 | 1- (exp.) fp.append \ n\r |
293 | ELSE\r |
294 | dup 0>\r |
295 | IF\r |
296 | \ POSITIVE EXPONENT - place decimal point in middle\r |
297 | precision fp.move.decimal\r |
298 | ELSE\r |
299 | \ NEGATIVE EXPONENT - use 0.000????\r |
300 | s" 0." fp.append\r |
301 | \ output leading zeros\r |
302 | negate fp.append.zeros\r |
303 | fp-represent-pad precision fp.append\r |
304 | THEN\r |
305 | fp.strip.trailing.zeros\r |
306 | THEN\r |
307 | ELSE\r |
308 | 2drop\r |
309 | s" <FP-OUT-OF-RANGE>" fp.append\r |
310 | THEN\r |
311 | fp-output-pad fp-output-ptr @ over -\r |
312 | ;\r |
313 | \r |
314 | : FG. ( F: r -- )\r |
315 | (fg.) type space\r |
316 | ;\r |
317 | \r |
318 | : (F.) ( F: r -- , normal or scientific ) { | n n3 ndiff prec' -- }\r |
319 | fp-output-pad fp-output-ptr ! \ setup pointer\r |
320 | fp-represent-pad \ place to put number\r |
321 | fdup flog 1 s>f f+ f>s precision max\r |
322 | fp_precision_max min dup -> prec'\r |
323 | represent\r |
324 | ( -- n flag1 flag2 )\r |
325 | IF\r |
326 | \ add '-' sign if negative\r |
327 | IF [char] - fp.hold\r |
328 | THEN\r |
329 | \ compare n with precision to see whether we must do scientific display\r |
330 | dup fp_precision_max >\r |
331 | IF \ use exponential notation\r |
332 | 1 precision fp.move.decimal\r |
333 | fp.strip.trailing.zeros\r |
334 | [char] e fp.hold\r |
335 | 1- (exp.) fp.append \ n\r |
336 | ELSE\r |
337 | dup 0>\r |
338 | IF\r |
339 | \ POSITIVE EXPONENT - place decimal point in middle\r |
340 | prec' fp.move.decimal\r |
341 | ELSE\r |
342 | \ NEGATIVE EXPONENT - use 0.000????\r |
343 | s" 0." fp.append\r |
344 | \ output leading zeros\r |
345 | dup negate precision min\r |
346 | fp.append.zeros\r |
347 | fp-represent-pad precision rot + fp.append\r |
348 | THEN\r |
349 | THEN\r |
350 | ELSE\r |
351 | 2drop\r |
352 | s" <FP-OUT-OF-RANGE>" fp.append\r |
353 | THEN\r |
354 | fp-output-pad fp-output-ptr @ over -\r |
355 | ;\r |
356 | \r |
357 | : F. ( F: r -- )\r |
358 | (f.) type space\r |
359 | ;\r |
360 | \r |
361 | : F.S ( -- , print FP stack )\r |
362 | ." FP> "\r |
363 | fdepth 0>\r |
364 | IF\r |
365 | fdepth 0\r |
366 | DO\r |
367 | cr?\r |
368 | fdepth i - 1- \ index of next float\r |
369 | fpick f. cr?\r |
370 | LOOP\r |
371 | ELSE\r |
372 | ." empty"\r |
373 | THEN\r |
374 | cr\r |
375 | ;\r |
376 | \r |
377 | \ FP Input ----------------------------------------------------------\r |
378 | variable FP-REQUIRE-E \ must we put an E in FP numbers?\r |
379 | false fp-require-e ! \ violate ANSI !!\r |
380 | \r |
381 | : >FLOAT { c-addr u | dlo dhi u' fsign flag nshift -- flag }\r |
382 | u 0= IF false exit THEN\r |
383 | false -> flag\r |
384 | 0 -> nshift\r |
385 | \\r |
386 | \ check for minus sign\r |
387 | c-addr c@ [char] - = dup -> fsign\r |
388 | c-addr c@ [char] + = OR\r |
389 | IF 1 +-> c-addr -1 +-> u \ skip char\r |
390 | THEN\r |
391 | \\r |
392 | \ convert first set of digits\r |
393 | 0 0 c-addr u >number -> u' -> c-addr -> dhi -> dlo\r |
394 | u' 0>\r |
395 | IF\r |
396 | \ convert optional second set of digits\r |
397 | c-addr c@ [char] . =\r |
398 | IF\r |
399 | dlo dhi c-addr 1+ u' 1- dup -> nshift >number\r |
400 | dup nshift - -> nshift\r |
401 | -> u' -> c-addr -> dhi -> dlo\r |
402 | THEN\r |
403 | \ convert exponent\r |
404 | u' 0>\r |
405 | IF\r |
406 | c-addr c@ [char] E =\r |
407 | c-addr c@ [char] e = OR\r |
408 | IF\r |
409 | 1 +-> c-addr -1 +-> u' \ skip char\r |
410 | c-addr c@ [char] + = \ ignore + on exponent\r |
411 | IF\r |
412 | 1 +-> c-addr -1 +-> u' \ skip char\r |
413 | THEN\r |
414 | c-addr u' ((number?))\r |
415 | num_type_single =\r |
416 | IF\r |
417 | nshift + -> nshift\r |
418 | true -> flag\r |
419 | THEN\r |
420 | THEN\r |
421 | ELSE\r |
422 | \ only require E field if this variable is true\r |
423 | fp-require-e @ not -> flag\r |
424 | THEN\r |
425 | THEN\r |
426 | \ convert double precision int to float\r |
427 | flag\r |
428 | IF\r |
429 | dlo dhi d>f\r |
430 | 10 s>f nshift s>f f** f* \ apply exponent\r |
431 | fsign\r |
432 | IF\r |
433 | fnegate\r |
434 | THEN\r |
435 | THEN\r |
436 | flag\r |
437 | ;\r |
438 | \r |
439 | 3 constant NUM_TYPE_FLOAT \ possible return type for NUMBER?\r |
440 | \r |
441 | : (FP.NUMBER?) ( $addr -- 0 | n 1 | d 2 | r 3 , convert string to number )\r |
442 | \ check to see if it is a valid float, if not use old (NUMBER?)\r |
443 | dup count >float\r |
444 | IF\r |
445 | drop NUM_TYPE_FLOAT\r |
446 | ELSE\r |
447 | (number?)\r |
448 | THEN\r |
449 | ;\r |
450 | \r |
451 | defer fp.old.number?\r |
452 | variable FP-IF-INIT\r |
453 | \r |
454 | : FP.TERM ( -- , deinstall fp conversion )\r |
455 | fp-if-init @\r |
456 | IF\r |
457 | what's fp.old.number? is number?\r |
458 | fp-if-init off\r |
459 | THEN\r |
460 | ;\r |
461 | \r |
462 | : FP.INIT ( -- , install FP converion )\r |
463 | fp.term\r |
464 | what's number? is fp.old.number?\r |
465 | ['] (fp.number?) is number?\r |
466 | fp-if-init on\r |
467 | ." Floating point numeric conversion installed." cr\r |
468 | ;\r |
469 | \r |
470 | FP.INIT\r |
471 | if.forgotten fp.term\r |
472 | \r |
473 | \r |
474 | 0 [IF]\r |
475 | \r |
476 | 23.8e-9 fconstant fsmall\r |
477 | 1.0 fsmall f- fconstant falmost1\r |
478 | ." Should be 1.0 = " falmost1 f. cr\r |
479 | \r |
480 | : TSEGF ( r -f- , print in all formats )\r |
481 | ." --------------------------------" cr\r |
482 | 34 0\r |
483 | DO\r |
484 | fdup fs. 4 spaces fdup fe. 4 spaces\r |
485 | fdup fg. 4 spaces fdup f. cr\r |
486 | 10.0 f/\r |
487 | LOOP\r |
488 | fdrop\r |
489 | ;\r |
490 | \r |
491 | : TFP\r |
492 | 1.234e+22 tsegf\r |
493 | 1.23456789e+22 tsegf\r |
494 | 0.927 fsin 1.234e+22 f* tsegf\r |
495 | ;\r |
496 | \r |
497 | [THEN]\r |