1 \ @(#) floats.fth 98/02/26 1.4 17:51:40
2 \ High Level Forth support for Floating Point
4 \ Author: Phil Burk and Darren Gibbs
5 \ Copyright 1994 3DO, Phil Burk, Larry Polansky, Devid Rosenboom
7 \ The pForth software code is dedicated to the public domain,
8 \ and any third party may reproduce, distribute and modify
9 \ the pForth software code or any derivative works thereof
10 \ without any compensation or license. The pForth software
11 \ code is provided on an "as is" basis without any warranty
12 \ of any kind, including, without limitation, the implied
13 \ warranties of merchantability and fitness for a particular
14 \ purpose and their equivalents under the laws of any jurisdiction.
16 \ 19970702 PLB Drop 0.0 in REPRESENT to fix 0.0 F.
17 \ 19980220 PLB Added FG. , fixed up large and small formatting
18 \ 19980812 PLB Now don't drop 0.0 in REPRESENT to fix 0.0 F. (!!!)
19 \ Fixed F~ by using (F.EXACTLY)
23 : FALIGNED ( addr -- a-addr )
29 : FALIGN ( -- , align DP )
33 \ account for size of create when aligning floats
36 fp-create-size swap - constant CREATE_SIZE
38 : FALIGN.CREATE ( -- , align DP for float after CREATE )
46 : FCREATE ( <name> -- , create with float aligned data )
51 : FVARIABLE ( <name> -- ) ( F: -- )
52 FCREATE 1 floats allot
56 FCREATE here 1 floats allot f!
60 : F0SP ( -- ) ( F: ? -- )
61 fdepth 0 max 0 ?DO fdrop LOOP
64 \ Convert between single precision and floating point
65 : S>F ( s -- ) ( F: -- r )
68 : F>S ( -- s ) ( F: r -- )
72 : (F.EXACTLY) ( r1 r2 -f- flag , return true if encoded equally ) { | caddr1 caddr2 fsize fcells }
74 fsize cell 1- + cell 1- invert and \ round up to nearest multiple of stack size
75 cell / -> fcells ( number of cells per float )
76 \ make room on data stack for floats data
81 \ compare bit representation
84 caddr1 fsize caddr2 fsize compare 0=
85 >r fcells 2* 0 ?DO drop LOOP r> \ drop float bits
88 : F~ ( -0- flag ) ( r1 r2 r3 -f- )
91 frot frot ( -- r3 r1 r2 )
92 fover fover ( -- r3 r1 r2 r1 r2 )
93 f- fabs ( -- r3 r1 r2 |r1-r2| )
94 frot frot ( -- r3 |r1-r2| r1 r2 )
95 fabs fswap fabs f+ ( -- r3 |r1-r2| |r1|+|r2| )
96 frot fabs f* ( -- |r1-r2| |r1|+|r2|*|r3| )
102 (f.exactly) \ f- f0= \ 19980812 Used to cheat. Now actually compares bit patterns.
104 frot frot ( -- r3 r1 r2 )
105 f- fabs ( -- r3 |r1-r2| )
111 \ FP Output --------------------------------------------------------
112 fvariable FVAR-REP \ scratch var for represent
113 : REPRESENT { c-addr u | n flag1 flag2 -- n flag1 flag2 , FLOATING } ( F: r -- )
114 TRUE -> flag2 \ FIXME - need to check range
120 fvar-rep f@ fabs fvar-rep f! \ absolute value
127 \ fdrop \ 19970702 \ 19980812 Remove FDROP to fix "0.0 F."
128 c-addr u [char] 0 fill
135 1 s>f f+ \ round up exponent
138 \ ." REP - n = " n . cr
139 \ normalize r to u digits
141 10 s>f u n - s>f f** f*
142 1 s>f 2 s>f f/ f+ \ round result
144 \ convert float to double_int then convert to text
146 \ ." REP - d = " over . dup . cr
147 <# u 1- 0 ?DO # loop #s #> \ ( -- addr cnt )
148 \ Adjust exponent if rounding caused number of digits to increase.
149 \ For example from 9999 to 10000.
157 variable FP-PRECISION
159 \ Set maximum digits that are meaningful for the precision that we use.
160 1 FLOATS 4 / 7 * constant FP_PRECISION_MAX
165 : SET-PRECISION ( u -- )
171 32 constant FP_REPRESENT_SIZE
172 64 constant FP_OUTPUT_SIZE
174 create FP-REPRESENT-PAD FP_REPRESENT_SIZE allot \ used with REPRESENT
175 create FP-OUTPUT-PAD FP_OUTPUT_SIZE allot \ used to assemble final output
176 variable FP-OUTPUT-PTR \ points into FP-OUTPUT-PAD
178 : FP.HOLD ( char -- , add char to output )
179 fp-output-ptr @ fp-output-pad 64 + <
181 fp-output-ptr @ tuck c!
187 : FP.APPEND { addr cnt -- , add string to output }
194 : FP.STRIP.TRAILING.ZEROS ( -- , remove trailing zeros from fp output )
196 fp-output-ptr @ fp-output-pad u>
197 fp-output-ptr @ 1- c@ [char] 0 =
204 : FP.APPEND.ZEROS ( numZeros -- )
210 : FP.MOVE.DECIMAL { n prec -- , append with decimal point shifted }
211 fp-represent-pad n prec min fp.append
212 n prec - fp.append.zeros
215 prec n - 0 max fp.append
218 : (EXP.) ( n -- addr cnt , convert exponent to two digit value )
228 : FP.REPRESENT ( -- n flag1 flag2 ) ( r -f- )
231 : (FS.) ( -- addr cnt ) ( F: r -- , scientific notation )
232 fp-output-pad fp-output-ptr ! \ setup pointer
233 fp-represent-pad precision represent
234 \ ." (FS.) - represent " fp-represent-pad precision type cr
239 1 precision fp.move.decimal
241 1- (exp.) fp.append \ n
244 s" <FP-OUT-OF-RANGE>" fp.append
246 fp-output-pad fp-output-ptr @ over -
249 : FS. ( F: r -- , scientific notation )
253 : (FE.) ( -- addr cnt ) ( F: r -- , engineering notation ) { | n n3 -- }
254 fp-output-pad fp-output-ptr ! \ setup pointer
255 fp-represent-pad precision represent
260 \ convert exponent to multiple of three
262 n 1- s>d 3 fm/mod \ use floored divide
264 1+ precision fp.move.decimal \ amount to move decimal point
266 n3 (exp.) fp.append \ n
269 s" <FP-OUT-OF-RANGE>" fp.append
271 fp-output-pad fp-output-ptr @ over -
274 : FE. ( F: r -- , engineering notation )
278 : (FG.) ( F: r -- , normal or scientific ) { | n n3 ndiff -- }
279 fp-output-pad fp-output-ptr ! \ setup pointer
280 fp-represent-pad precision represent
285 \ compare n with precision to see whether we do scientific display
288 IF \ use exponential notation
289 1 precision fp.move.decimal
290 fp.strip.trailing.zeros
292 1- (exp.) fp.append \ n
296 \ POSITIVE EXPONENT - place decimal point in middle
297 precision fp.move.decimal
299 \ NEGATIVE EXPONENT - use 0.000????
301 \ output leading zeros
302 negate fp.append.zeros
303 fp-represent-pad precision fp.append
305 fp.strip.trailing.zeros
309 s" <FP-OUT-OF-RANGE>" fp.append
311 fp-output-pad fp-output-ptr @ over -
318 : (F.) ( F: r -- , normal or scientific ) { | n n3 ndiff prec' -- }
319 fp-output-pad fp-output-ptr ! \ setup pointer
320 fp-represent-pad \ place to put number
321 fdup flog 1 s>f f+ f>s precision max
322 fp_precision_max min dup -> prec'
326 \ add '-' sign if negative
329 \ compare n with precision to see whether we must do scientific display
330 dup fp_precision_max >
331 IF \ use exponential notation
332 1 precision fp.move.decimal
333 fp.strip.trailing.zeros
335 1- (exp.) fp.append \ n
339 \ POSITIVE EXPONENT - place decimal point in middle
340 prec' fp.move.decimal
342 \ NEGATIVE EXPONENT - use 0.000????
344 \ output leading zeros
345 dup negate precision min
347 fp-represent-pad precision rot + fp.append
352 s" <FP-OUT-OF-RANGE>" fp.append
354 fp-output-pad fp-output-ptr @ over -
361 : F.S ( -- , print FP stack )
368 fdepth i - 1- \ index of next float
377 \ FP Input ----------------------------------------------------------
378 variable FP-REQUIRE-E \ must we put an E in FP numbers?
379 false fp-require-e ! \ violate ANSI !!
381 : >FLOAT { c-addr u | dlo dhi u' fsign flag nshift -- flag }
382 u 0= IF false exit THEN
386 \ check for minus sign
387 c-addr c@ [char] - = dup -> fsign
388 c-addr c@ [char] + = OR
389 IF 1 +-> c-addr -1 +-> u \ skip char
392 \ convert first set of digits
393 0 0 c-addr u >number -> u' -> c-addr -> dhi -> dlo
396 \ convert optional second set of digits
399 dlo dhi c-addr 1+ u' 1- dup -> nshift >number
400 dup nshift - -> nshift
401 -> u' -> c-addr -> dhi -> dlo
407 c-addr c@ [char] e = OR
409 1 +-> c-addr -1 +-> u' \ skip E char
412 c-addr c@ [char] + = \ ignore + on exponent
414 1 +-> c-addr -1 +-> u' \ skip char
416 c-addr u' ((number?))
423 true -> flag \ allow "1E"
427 \ only require E field if this variable is true
428 fp-require-e @ not -> flag
431 \ convert double precision int to float
435 10 s>f nshift s>f f** f* \ apply exponent
444 3 constant NUM_TYPE_FLOAT \ possible return type for NUMBER?
446 : (FP.NUMBER?) ( $addr -- 0 | n 1 | d 2 | r 3 , convert string to number )
447 \ check to see if it is a valid float, if not use old (NUMBER?)
459 : FP.TERM ( -- , deinstall fp conversion )
462 what's fp.old.number? is number?
467 : FP.INIT ( -- , install FP converion )
469 what's number? is fp.old.number?
470 ['] (fp.number?) is number?
472 ." Floating point numeric conversion installed." cr
481 23.8e-9 fconstant fsmall
482 1.0 fsmall f- fconstant falmost1
483 ." Should be 1.0 = " falmost1 f. cr
485 : TSEGF ( r -f- , print in all formats )
486 ." --------------------------------" cr
489 fdup fs. 4 spaces fdup fe. 4 spaces
490 fdup fg. 4 spaces fdup f. cr
499 0.927 fsin 1.234e+22 f* tsegf