1: \ High level floating point 14jan94py
2:
3: \ Copyright (C) 1995,1997,2003,2004,2005,2006,2007,2009 Free Software Foundation, Inc.
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 3
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, see http://www.gnu.org/licenses/.
19:
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]
31:
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
45: \G If the data-space pointer is not single-float-aligned, reserve
46: \G enough space to align it.
47: here dup sfaligned swap ?DO bl c, LOOP ;
48: : dfalign ( -- ) \ float-ext d-f-align
49: \G If the data-space pointer is not double-float-aligned, reserve
50: \G enough space to align it.
51: here dup dfaligned swap ?DO bl c, LOOP ;
52:
53: (Field) sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
54: \G @code{1 sfloats +}.
55: 1 sfloats ,
56:
57: (Field) dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
58: \G @code{1 dfloats +}.
59: 1 dfloats ,
60:
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! ;
65:
66: : fconstant ( r "name" -- ) \ float f-constant
67: Create f,
68: DOES> ( -- r )
69: f@ ;
70:
71: : fdepth ( -- +n ) \ float f-depth
72: \G @i{+n} is the current number of (floating-point) values on the
73: \G floating-point stack.
74: fp0 @ fp@ - [ 1 floats ] Literal / ;
75:
76: : FLiteral ( compilation r -- ; run-time -- r ) \ float f-literal
77: \G Compile appropriate code such that, at run-time, @i{r} is placed
78: \G on the (floating-point) stack. Interpretation semantics are undefined.
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
82:
83: &15 Value precision ( -- u ) \ float-ext
84: \G @i{u} is the number of significant digits currently used by
85: \G @code{F.} @code{FE.} and @code{FS.}
86: : set-precision ( u -- ) \ float-ext
87: \G Set the number of significant digits currently used by
88: \G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
89: to precision ;
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:
99: : f$ ( f -- n ) scratch represent 0=
100: IF 2drop scratch 3 min type rdrop EXIT THEN
101: IF '- emit THEN ;
102:
103: : f. ( r -- ) \ float-ext f-dot
104: \G Display (the floating-point number) @i{r} without exponent,
105: \G followed by a space.
106: f$ dup >r 0<=
107: IF '0 emit
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 ;
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?
113:
114: \ Why do you think so? ANS Forth appears ambiguous on this point. -anton.
115:
116: : fe. ( r -- ) \ float-ext f-e-dot
117: \G Display @i{r} using engineering notation (with exponent dividable
118: \G by 3), followed by a space.
119: f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
120: scratch r@ tuck min tuck - >r type r> zeros
121: '. emit scratch r> /string type
122: 'E emit r> . ;
123:
124: : fs. ( r -- ) \ float-ext f-s-dot
125: \G Display @i{r} using scientific notation (with exponent), followed
126: \G by a space.
127: f$ 1-
128: scratch over c@ emit '. emit 1 /string type
129: 'E emit . ;
130:
131: : sfnumber ( c-addr u -- r true | false )
132: 2dup [CHAR] e scan ( c-addr u c-addr2 u2 )
133: dup 0=
134: IF
135: 2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 )
136: THEN
137: nip
138: IF
139: >float
140: ELSE
141: 2drop false
142: THEN ;
143:
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 )
157: 2dup sfnumber
158: IF
159: 2drop [comp'] FLiteral
160: ELSE
161: defers compiler-notfound1
162: ENDIF ;
163: IS compiler-notfound1
164:
165: :noname ( c-addr u -- ... xt )
166: 2dup sfnumber
167: IF
168: 2drop ['] noop
169: ELSE
170: defers interpreter-notfound1
171: ENDIF ;
172: IS interpreter-notfound1
173:
174: : fvariable ( "name" -- ) \ float f-variable
175: Create 0.0E0 f, ;
176: \ does> ( -- f-addr )
177:
178: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
179: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
180: \G to its diameter.
181:
182: : f2* ( r1 -- r2 ) \ gforth
183: \G Multiply @i{r1} by 2.0e0
184: 2.0e0 f* ;
185:
186: : f2/ ( r1 -- r2 ) \ gforth
187: \G Multiply @i{r1} by 0.5e0
188: 0.5e0 f* ;
189:
190: : 1/f ( r1 -- r2 ) \ gforth
191: \G Divide 1.0e0 by @i{r1}.
192: 1.0e0 fswap f/ ;
193:
194: get-current environment-wordlist set-current
195: 1.7976931348623157e308 FConstant max-float
196: set-current
197:
198: \ We now have primitives for these, so we need not define them
199:
200: \ : falog ( f -- 10^f ) [ 10.0e0 fln ] FLiteral f* fexp ;
201:
202: \ : fsinh fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
203: \ : fcosh fexp fdup 1/f f+ f2/ ;
204: \ : ftanh f2* fexpm1 fdup 2.0e0 f+ f/ ;
205:
206: \ : fatanh fdup f0< >r fabs 1.0e0 fover f- f/ f2* flnp1 f2/
207: \ r> IF fnegate THEN ;
208: \ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
209: \ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
210:
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:
220: : f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
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}.
223: fdup f0=
224: IF \ bitwise comparison
225: fp@ float+ 1 floats over float+ over str=
226: fdrop fdrop fdrop
227: EXIT
228: THEN
229: fdup f0>
230: IF
231: f~abs
232: ELSE
233: fnegate f~rel
234: THEN ;
235:
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
241: fp@ fsign-offset + dup c@ $80 and >r ( r1 r2 addr-r1sign )
242: float+ dup c@ $7f and r> or swap c!
243: fdrop ;
244:
245: \ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com>
246: \ not sure if they are a good idea
247:
248: : ftrunc ( r1 -- r2 ) \ X:ftrunc
249: \ round towards 0
250: fdup fabs floor fswap fcopysign ;
251:
252: : FMOD ( r1 r2 -- r )
253: \ remainder of r1/r2
254: FOVER FOVER F/ ftrunc F* F- ;
255:
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