1: \ High level floating point 14jan94py
2:
3: \ Copyright (C) 1995,1997 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 2
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, write to the Free Software
19: \ Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
20:
21: \ 1 cells 4 = [IF]
22: \ ' cells Alias sfloats
23: \ ' cell+ Alias sfloat+
24: \ ' align Alias sfalign
25: \ ' aligned Alias sfaligned
26: \ [ELSE]
27: \ : sfloats 2* 2* ;
28: \ : sfloat+ 4 + ;
29: \ : sfaligned ( addr -- addr' ) 3 + -4 and ;
30: \ : sfalign ( -- ) here dup sfaligned swap ?DO bl c, LOOP ;
31: \ [THEN]
32:
33: \ 1 floats 8 = [IF]
34: \ ' floats Alias dfloats
35: \ ' float+ Alias dfloat+
36: \ ' falign Alias dfalign
37: \ ' faligned Alias dfaligned
38: \ [ELSE]
39: \ : dfloats 2* 2* 2* ;
40: \ : dfloat+ 8 + ;
41: \ : dfaligned ( addr -- addr' ) 7 + -8 and ;
42: \ : dfalign ( -- ) here dup dfaligned swap ?DO bl c, LOOP ;
43: \ [THEN]
44:
45: : sfalign ( -- ) \ float-ext s-f-align
46: \G If the data-space pointer is not single-float-aligned, reserve
47: \G enough space to align it.
48: here dup sfaligned swap ?DO bl c, LOOP ;
49: : dfalign ( -- ) \ float-ext d-f-align
50: \G If the data-space pointer is not double-float-aligned, reserve
51: \G enough space to align it.
52: here dup dfaligned swap ?DO bl c, LOOP ;
53:
54: 1 sfloats constant sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
55: \G Increment @i{sf-addr1} by the number of address units corresponding to the size of
56: \G a single-precision IEEE floating-point number, to give @i{sf-addr2}.""
57: dofield: lastxt code-address! \ change the constant into a field
58:
59: 1 dfloats constant dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
60: \G Increment @i{df-addr1} by the number of address units corresponding to the size of
61: \G a double-precision IEEE floating-point number, to give @i{df-addr2}.""
62: dofield: lastxt code-address! \ change the constant into a field
63:
64: : f, ( f -- ) \ gforth
65: \G Reserve data space for one floating-point number and store
66: \G @i{f} in the space.
67: here 1 floats allot f! ;
68:
69: : fconstant ( r "name" -- ) \ float
70: Create f,
71: DOES> ( -- r )
72: f@ ;
73:
74: : fdepth ( -- +n ) \ floating f-depth
75: \G @i{+n} is the current number of (floating-point) values on the
76: \G floating-point stack.
77: fp0 @ fp@ - [ 1 floats ] Literal / ;
78:
79: : FLit ( -- r ) r> dup f@ float+ >r ;
80: : FLiteral ( compilation r -- ; run-time -- r ) \ float
81: \G Compile appropriate code such that, at run-time, @i{r} is placed
82: \G on the (floating-point) stack. Interpretation semantics are undefined.
83: BEGIN here cell+ dup faligned <> WHILE postpone noop REPEAT
84: postpone FLit f, ; immediate
85:
86: &15 Value precision ( -- u ) \ floating-ext
87: \G @i{u} is the number of significant digits currently used by
88: \G @code{F.} @code{FE.} and @code{FS.}
89: : set-precision ( u -- ) \ floating-ext
90: \G Set the number of significant digits currently used by
91: \G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
92: to precision ;
93:
94: : scratch ( r -- addr len )
95: pad precision - precision ;
96:
97: : zeros ( n -- ) 0 max 0 ?DO '0 emit LOOP ;
98:
99: : -zeros ( addr u -- addr' u' )
100: BEGIN dup WHILE 1- 2dup + c@ '0 <> UNTIL 1+ THEN ;
101:
102: : f$ ( f -- n ) scratch represent 0=
103: IF 2drop scratch 3 min type rdrop EXIT THEN
104: IF '- emit THEN ;
105:
106: : f. ( r -- ) \ floating-ext f-dot
107: \G Display (the floating-point number) @i{r} using fixed-point notation,
108: \G followed by a space.
109: f$ dup >r 0<
110: IF '0 emit
111: ELSE scratch r@ min type r@ precision - zeros THEN
112: '. emit r@ negate zeros
113: scratch r> 0 max /string 0 max -zeros type space ;
114: \ I'm afraid this does not really implement ansi semantics wrt precision.
115: \ Shouldn't precision indicate the number of places shown after the point?
116:
117: : fe. ( r -- ) \ floating-ext f-e-dot
118: \G Display @i{r} using engineering notation, followed by a space.
119: f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
120: scratch r@ min type '. emit scratch r> /string type
121: 'E emit r> . ;
122:
123: : fs. ( r -- ) \ floating-ext f-s-dot
124: \G Display @i{r} using scientific notation, followed by a space.
125: f$ 1-
126: scratch over c@ emit '. emit 1 /string type
127: 'E emit . ;
128:
129: require debugs.fs
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: :noname ( c-addr u -- )
145: 2dup sfnumber
146: IF
147: 2drop POSTPONE FLiteral
148: ELSE
149: defers compiler-notfound
150: ENDIF ;
151: IS compiler-notfound
152:
153: :noname ( c-addr u -- r )
154: 2dup sfnumber
155: IF
156: 2drop
157: ELSE
158: defers interpreter-notfound
159: ENDIF ;
160: IS interpreter-notfound
161:
162: : fvariable ( "name" -- ) \ float
163: Create 0.0E0 f, ;
164: \ does> ( -- f-addr )
165:
166: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
167: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
168: \G to its diameter.
169:
170: : f2* ( r1 -- r2 ) \ gforth
171: \G Multiply @i{r1} by 2.0e0
172: 2.0e0 f* ;
173:
174: : f2/ ( r1 -- r2 ) \ gforth
175: \G Multiply @i{r1} by 0.5e0
176: 0.5e0 f* ;
177:
178: : 1/f ( r1 -- r2 ) \ gforth
179: \G Divide 1.0e0 by @i{r1}.
180: 1.0e0 fswap f/ ;
181:
182:
183: \ We now have primitives for these, so we need not define them
184:
185: \ : falog ( f -- 10^f ) [ 10.0e0 fln ] FLiteral f* fexp ;
186:
187: \ : fsinh fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
188: \ : fcosh fexp fdup 1/f f+ f2/ ;
189: \ : ftanh f2* fexpm1 fdup 2.0e0 f+ f/ ;
190:
191: \ : fatanh fdup f0< >r fabs 1.0e0 fover f- f/ f2* flnp1 f2/
192: \ r> IF fnegate THEN ;
193: \ : facosh fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
194: \ : fasinh fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
195:
196: : f~abs ( r1 r2 r3 -- flag ) \ gforth
197: \G Approximate equality with absolute error: |r1-r2|<r3.
198: frot frot f- fabs fswap f< ;
199:
200: : f~rel ( r1 r2 r3 -- flag ) \ gforth
201: \G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
202: frot frot fover fabs fover fabs f+ frot frot
203: f- fabs frot frot f* f< ;
204:
205: : f~ ( r1 r2 r3 -- flag ) \ float-ext
206: \G ANS Forth medley: r3>0: @code{f~abs}; r3=0: r1=r2; r3<0: @code{fnegate f~abs}.
207: fdup f0=
208: IF
209: fdrop f= \ !! this does not work, because 0=-0 with f= on Linux-Intel
210: \ the standard says they should compare unequal
211: \ the comparison should be done with COMPARE
212: EXIT
213: THEN
214: fdup f0>
215: IF
216: f~abs
217: ELSE
218: fnegate f~rel
219: THEN ;
220:
221: : f.s ( -- ) \ gforth f-dot-s
222: \G Display the number of items on the floating-point stack,
223: \G followed by a list of the items; TOS is the right-most item.
224: ." <" fdepth 0 .r ." > " fdepth 0 max maxdepth-.s @ min dup 0
225: ?DO dup i - 1- floats fp@ + f@ f. LOOP drop ;
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