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1 aw0a 1 DOUBLE PRECISION FUNCTION D1MACH(I)
2     C
3     C DOUBLE-PRECISION MACHINE CONSTANTS
4     C
5     C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE.
6     C
7     C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE.
8     C
9     C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING.
10     C
11     C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING.
12     C
13     C D1MACH( 5) = LOG10(B)
14     C
15     C TO ALTER THIS FUNCTION FOR A PARTICULAR ENVIRONMENT,
16     C THE DESIRED SET OF DATA STATEMENTS SHOULD BE ACTIVATED BY
17     C REMOVING THE C FROM COLUMN 1.
18     C ON RARE MACHINES A STATIC STATEMENT MAY NEED TO BE ADDED.
19     C (BUT PROBABLY MORE SYSTEMS PROHIBIT IT THAN REQUIRE IT.)
20     C
21     C FOR IEEE-ARITHMETIC MACHINES (BINARY STANDARD), ONE OF THE FIRST
22     C TWO SETS OF CONSTANTS BELOW SHOULD BE APPROPRIATE. IF YOU DO NOT
23     C KNOW WHICH SET TO USE, TRY BOTH AND SEE WHICH GIVES PLAUSIBLE
24     C VALUES.
25     C
26     C WHERE POSSIBLE, DECIMAL, OCTAL OR HEXADECIMAL CONSTANTS ARE USED
27     C TO SPECIFY THE CONSTANTS EXACTLY. SOMETIMES THIS REQUIRES USING
28     C EQUIVALENT INTEGER ARRAYS. IF YOUR COMPILER USES HALF-WORD
29     C INTEGERS BY DEFAULT (SOMETIMES CALLED INTEGER*2), YOU MAY NEED TO
30     C CHANGE INTEGER TO INTEGER*4 OR OTHERWISE INSTRUCT YOUR COMPILER
31     C TO USE FULL-WORD INTEGERS IN THE NEXT 5 DECLARATIONS.
32     C
33     C COMMENTS JUST BEFORE THE END STATEMENT (LINES STARTING WITH *)
34     C GIVE C SOURCE FOR D1MACH.
35     C
36     INTEGER SMALL(2)
37     INTEGER LARGE(2)
38     INTEGER RIGHT(2)
39     INTEGER DIVER(2)
40     INTEGER LOG10(2)
41     INTEGER SC
42     C
43     DOUBLE PRECISION DMACH(5)
44     C
45     EQUIVALENCE (DMACH(1),SMALL(1))
46     EQUIVALENCE (DMACH(2),LARGE(1))
47     EQUIVALENCE (DMACH(3),RIGHT(1))
48     EQUIVALENCE (DMACH(4),DIVER(1))
49     EQUIVALENCE (DMACH(5),LOG10(1))
50     C
51     C MACHINE CONSTANTS FOR BIG-ENDIAN IEEE ARITHMETIC (BINARY FORMAT)
52     C MACHINES IN WHICH THE MOST SIGNIFICANT BYTE IS STORED FIRST,
53     C SUCH AS THE AT&T 3B SERIES, MOTOROLA 68000 BASED MACHINES (E.G.
54     C SUN 3), AND MACHINES THAT USE SPARC, HP, OR IBM RISC CHIPS.
55     C
56     c DATA SMALL(1),SMALL(2) / 1048576, 0 /
57     c DATA LARGE(1),LARGE(2) / 2146435071, -1 /
58     c DATA RIGHT(1),RIGHT(2) / 1017118720, 0 /
59     c DATA DIVER(1),DIVER(2) / 1018167296, 0 /
60     c DATA LOG10(1),LOG10(2) / 1070810131, 1352628735 /, SC/987/
61     C
62     C MACHINE CONSTANTS FOR LITTLE-ENDIAN (BINARY) IEEE ARITHMETIC
63     C MACHINES IN WHICH THE LEAST SIGNIFICANT BYTE IS STORED FIRST,
64     C E.G. IBM PCS AND OTHER MACHINES THAT USE INTEL 80X87 OR DEC
65     C ALPHA CHIPS.
66     C
67     DATA SMALL(1),SMALL(2) / 0, 1048576 /
68     DATA LARGE(1),LARGE(2) / -1, 2146435071 /
69     DATA RIGHT(1),RIGHT(2) / 0, 1017118720 /
70     DATA DIVER(1),DIVER(2) / 0, 1018167296 /
71     DATA LOG10(1),LOG10(2) / 1352628735, 1070810131 /, SC/987/
72     C
73     C MACHINE CONSTANTS FOR AMDAHL MACHINES.
74     C
75     C DATA SMALL(1),SMALL(2) / 1048576, 0 /
76     C DATA LARGE(1),LARGE(2) / 2147483647, -1 /
77     C DATA RIGHT(1),RIGHT(2) / 856686592, 0 /
78     C DATA DIVER(1),DIVER(2) / 873463808, 0 /
79     C DATA LOG10(1),LOG10(2) / 1091781651, 1352628735 /, SC/987/
80     C
81     C MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM.
82     C
83     C DATA SMALL(1) / ZC00800000 /
84     C DATA SMALL(2) / Z000000000 /
85     C
86     C DATA LARGE(1) / ZDFFFFFFFF /
87     C DATA LARGE(2) / ZFFFFFFFFF /
88     C
89     C DATA RIGHT(1) / ZCC5800000 /
90     C DATA RIGHT(2) / Z000000000 /
91     C
92     C DATA DIVER(1) / ZCC6800000 /
93     C DATA DIVER(2) / Z000000000 /
94     C
95     C DATA LOG10(1) / ZD00E730E7 /
96     C DATA LOG10(2) / ZC77800DC0 /, SC/987/
97     C
98     C MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM.
99     C
100     C DATA SMALL(1) / O1771000000000000 /
101     C DATA SMALL(2) / O0000000000000000 /
102     C
103     C DATA LARGE(1) / O0777777777777777 /
104     C DATA LARGE(2) / O0007777777777777 /
105     C
106     C DATA RIGHT(1) / O1461000000000000 /
107     C DATA RIGHT(2) / O0000000000000000 /
108     C
109     C DATA DIVER(1) / O1451000000000000 /
110     C DATA DIVER(2) / O0000000000000000 /
111     C
112     C DATA LOG10(1) / O1157163034761674 /
113     C DATA LOG10(2) / O0006677466732724 /, SC/987/
114     C
115     C MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS.
116     C
117     C DATA SMALL(1) / O1771000000000000 /
118     C DATA SMALL(2) / O7770000000000000 /
119     C
120     C DATA LARGE(1) / O0777777777777777 /
121     C DATA LARGE(2) / O7777777777777777 /
122     C
123     C DATA RIGHT(1) / O1461000000000000 /
124     C DATA RIGHT(2) / O0000000000000000 /
125     C
126     C DATA DIVER(1) / O1451000000000000 /
127     C DATA DIVER(2) / O0000000000000000 /
128     C
129     C DATA LOG10(1) / O1157163034761674 /
130     C DATA LOG10(2) / O0006677466732724 /, SC/987/
131     C
132     C MACHINE CONSTANTS FOR FTN4 ON THE CDC 6000/7000 SERIES.
133     C
134     C DATA SMALL(1) / 00564000000000000000B /
135     C DATA SMALL(2) / 00000000000000000000B /
136     C
137     C DATA LARGE(1) / 37757777777777777777B /
138     C DATA LARGE(2) / 37157777777777777774B /
139     C
140     C DATA RIGHT(1) / 15624000000000000000B /
141     C DATA RIGHT(2) / 00000000000000000000B /
142     C
143     C DATA DIVER(1) / 15634000000000000000B /
144     C DATA DIVER(2) / 00000000000000000000B /
145     C
146     C DATA LOG10(1) / 17164642023241175717B /
147     C DATA LOG10(2) / 16367571421742254654B /, SC/987/
148     C
149     C MACHINE CONSTANTS FOR FTN5 ON THE CDC 6000/7000 SERIES.
150     C
151     C DATA SMALL(1) / O"00564000000000000000" /
152     C DATA SMALL(2) / O"00000000000000000000" /
153     C
154     C DATA LARGE(1) / O"37757777777777777777" /
155     C DATA LARGE(2) / O"37157777777777777774" /
156     C
157     C DATA RIGHT(1) / O"15624000000000000000" /
158     C DATA RIGHT(2) / O"00000000000000000000" /
159     C
160     C DATA DIVER(1) / O"15634000000000000000" /
161     C DATA DIVER(2) / O"00000000000000000000" /
162     C
163     C DATA LOG10(1) / O"17164642023241175717" /
164     C DATA LOG10(2) / O"16367571421742254654" /, SC/987/
165     C
166     C MACHINE CONSTANTS FOR CONVEX C-1
167     C
168     C DATA SMALL(1),SMALL(2) / '00100000'X, '00000000'X /
169     C DATA LARGE(1),LARGE(2) / '7FFFFFFF'X, 'FFFFFFFF'X /
170     C DATA RIGHT(1),RIGHT(2) / '3CC00000'X, '00000000'X /
171     C DATA DIVER(1),DIVER(2) / '3CD00000'X, '00000000'X /
172     C DATA LOG10(1),LOG10(2) / '3FF34413'X, '509F79FF'X /, SC/987/
173     C
174     C MACHINE CONSTANTS FOR THE CRAY 1, XMP, 2, AND 3.
175     C
176     C DATA SMALL(1) / 201354000000000000000B /
177     C DATA SMALL(2) / 000000000000000000000B /
178     C
179     C DATA LARGE(1) / 577767777777777777777B /
180     C DATA LARGE(2) / 000007777777777777776B /
181     C
182     C DATA RIGHT(1) / 376434000000000000000B /
183     C DATA RIGHT(2) / 000000000000000000000B /
184     C
185     C DATA DIVER(1) / 376444000000000000000B /
186     C DATA DIVER(2) / 000000000000000000000B /
187     C
188     C DATA LOG10(1) / 377774642023241175717B /
189     C DATA LOG10(2) / 000007571421742254654B /, SC/987/
190     C
191     C MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200
192     C
193     C SMALL, LARGE, RIGHT, DIVER, LOG10 SHOULD BE DECLARED
194     C INTEGER SMALL(4), LARGE(4), RIGHT(4), DIVER(4), LOG10(4)
195     C
196     C NOTE - IT MAY BE APPROPRIATE TO INCLUDE THE FOLLOWING LINE -
197     C STATIC DMACH(5)
198     C
199     C DATA SMALL/20K,3*0/,LARGE/77777K,3*177777K/
200     C DATA RIGHT/31420K,3*0/,DIVER/32020K,3*0/
201     C DATA LOG10/40423K,42023K,50237K,74776K/, SC/987/
202     C
203     C MACHINE CONSTANTS FOR THE HARRIS SLASH 6 AND SLASH 7
204     C
205     C DATA SMALL(1),SMALL(2) / '20000000, '00000201 /
206     C DATA LARGE(1),LARGE(2) / '37777777, '37777577 /
207     C DATA RIGHT(1),RIGHT(2) / '20000000, '00000333 /
208     C DATA DIVER(1),DIVER(2) / '20000000, '00000334 /
209     C DATA LOG10(1),LOG10(2) / '23210115, '10237777 /, SC/987/
210     C
211     C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES.
212     C
213     C DATA SMALL(1),SMALL(2) / O402400000000, O000000000000 /
214     C DATA LARGE(1),LARGE(2) / O376777777777, O777777777777 /
215     C DATA RIGHT(1),RIGHT(2) / O604400000000, O000000000000 /
216     C DATA DIVER(1),DIVER(2) / O606400000000, O000000000000 /
217     C DATA LOG10(1),LOG10(2) / O776464202324, O117571775714 /, SC/987/
218     C
219     C MACHINE CONSTANTS FOR THE IBM 360/370 SERIES,
220     C THE XEROX SIGMA 5/7/9 AND THE SEL SYSTEMS 85/86.
221     C
222     C DATA SMALL(1),SMALL(2) / Z00100000, Z00000000 /
223     C DATA LARGE(1),LARGE(2) / Z7FFFFFFF, ZFFFFFFFF /
224     C DATA RIGHT(1),RIGHT(2) / Z33100000, Z00000000 /
225     C DATA DIVER(1),DIVER(2) / Z34100000, Z00000000 /
226     C DATA LOG10(1),LOG10(2) / Z41134413, Z509F79FF /, SC/987/
227     C
228     C MACHINE CONSTANTS FOR THE INTERDATA 8/32
229     C WITH THE UNIX SYSTEM FORTRAN 77 COMPILER.
230     C
231     C FOR THE INTERDATA FORTRAN VII COMPILER REPLACE
232     C THE Z'S SPECIFYING HEX CONSTANTS WITH Y'S.
233     C
234     C DATA SMALL(1),SMALL(2) / Z'00100000', Z'00000000' /
235     C DATA LARGE(1),LARGE(2) / Z'7EFFFFFF', Z'FFFFFFFF' /
236     C DATA RIGHT(1),RIGHT(2) / Z'33100000', Z'00000000' /
237     C DATA DIVER(1),DIVER(2) / Z'34100000', Z'00000000' /
238     C DATA LOG10(1),LOG10(2) / Z'41134413', Z'509F79FF' /, SC/987/
239     C
240     C MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR).
241     C
242     C DATA SMALL(1),SMALL(2) / "033400000000, "000000000000 /
243     C DATA LARGE(1),LARGE(2) / "377777777777, "344777777777 /
244     C DATA RIGHT(1),RIGHT(2) / "113400000000, "000000000000 /
245     C DATA DIVER(1),DIVER(2) / "114400000000, "000000000000 /
246     C DATA LOG10(1),LOG10(2) / "177464202324, "144117571776 /, SC/987/
247     C
248     C MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR).
249     C
250     C DATA SMALL(1),SMALL(2) / "000400000000, "000000000000 /
251     C DATA LARGE(1),LARGE(2) / "377777777777, "377777777777 /
252     C DATA RIGHT(1),RIGHT(2) / "103400000000, "000000000000 /
253     C DATA DIVER(1),DIVER(2) / "104400000000, "000000000000 /
254     C DATA LOG10(1),LOG10(2) / "177464202324, "047674776746 /, SC/987/
255     C
256     C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING
257     C 32-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL).
258     C
259     C DATA SMALL(1),SMALL(2) / 8388608, 0 /
260     C DATA LARGE(1),LARGE(2) / 2147483647, -1 /
261     C DATA RIGHT(1),RIGHT(2) / 612368384, 0 /
262     C DATA DIVER(1),DIVER(2) / 620756992, 0 /
263     C DATA LOG10(1),LOG10(2) / 1067065498, -2063872008 /, SC/987/
264     C
265     C DATA SMALL(1),SMALL(2) / O00040000000, O00000000000 /
266     C DATA LARGE(1),LARGE(2) / O17777777777, O37777777777 /
267     C DATA RIGHT(1),RIGHT(2) / O04440000000, O00000000000 /
268     C DATA DIVER(1),DIVER(2) / O04500000000, O00000000000 /
269     C DATA LOG10(1),LOG10(2) / O07746420232, O20476747770 /, SC/987/
270     C
271     C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING
272     C 16-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL).
273     C
274     C SMALL, LARGE, RIGHT, DIVER, LOG10 SHOULD BE DECLARED
275     C INTEGER SMALL(4), LARGE(4), RIGHT(4), DIVER(4), LOG10(4)
276     C
277     C DATA SMALL(1),SMALL(2) / 128, 0 /
278     C DATA SMALL(3),SMALL(4) / 0, 0 /
279     C
280     C DATA LARGE(1),LARGE(2) / 32767, -1 /
281     C DATA LARGE(3),LARGE(4) / -1, -1 /
282     C
283     C DATA RIGHT(1),RIGHT(2) / 9344, 0 /
284     C DATA RIGHT(3),RIGHT(4) / 0, 0 /
285     C
286     C DATA DIVER(1),DIVER(2) / 9472, 0 /
287     C DATA DIVER(3),DIVER(4) / 0, 0 /
288     C
289     C DATA LOG10(1),LOG10(2) / 16282, 8346 /
290     C DATA LOG10(3),LOG10(4) / -31493, -12296 /, SC/987/
291     C
292     C DATA SMALL(1),SMALL(2) / O000200, O000000 /
293     C DATA SMALL(3),SMALL(4) / O000000, O000000 /
294     C
295     C DATA LARGE(1),LARGE(2) / O077777, O177777 /
296     C DATA LARGE(3),LARGE(4) / O177777, O177777 /
297     C
298     C DATA RIGHT(1),RIGHT(2) / O022200, O000000 /
299     C DATA RIGHT(3),RIGHT(4) / O000000, O000000 /
300     C
301     C DATA DIVER(1),DIVER(2) / O022400, O000000 /
302     C DATA DIVER(3),DIVER(4) / O000000, O000000 /
303     C
304     C DATA LOG10(1),LOG10(2) / O037632, O020232 /
305     C DATA LOG10(3),LOG10(4) / O102373, O147770 /, SC/987/
306     C
307     C MACHINE CONSTANTS FOR THE PRIME 50 SERIES SYSTEMS
308     C WITH 32-BIT INTEGERS AND 64V MODE INSTRUCTIONS,
309     C SUPPLIED BY IGOR BRAY.
310     C
311     C DATA SMALL(1),SMALL(2) / :10000000000, :00000100001 /
312     C DATA LARGE(1),LARGE(2) / :17777777777, :37777677775 /
313     C DATA RIGHT(1),RIGHT(2) / :10000000000, :00000000122 /
314     C DATA DIVER(1),DIVER(2) / :10000000000, :00000000123 /
315     C DATA LOG10(1),LOG10(2) / :11504046501, :07674600177 /, SC/987/
316     C
317     C MACHINE CONSTANTS FOR THE SEQUENT BALANCE 8000
318     C
319     C DATA SMALL(1),SMALL(2) / $00000000, $00100000 /
320     C DATA LARGE(1),LARGE(2) / $FFFFFFFF, $7FEFFFFF /
321     C DATA RIGHT(1),RIGHT(2) / $00000000, $3CA00000 /
322     C DATA DIVER(1),DIVER(2) / $00000000, $3CB00000 /
323     C DATA LOG10(1),LOG10(2) / $509F79FF, $3FD34413 /, SC/987/
324     C
325     C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES.
326     C
327     C DATA SMALL(1),SMALL(2) / O000040000000, O000000000000 /
328     C DATA LARGE(1),LARGE(2) / O377777777777, O777777777777 /
329     C DATA RIGHT(1),RIGHT(2) / O170540000000, O000000000000 /
330     C DATA DIVER(1),DIVER(2) / O170640000000, O000000000000 /
331     C DATA LOG10(1),LOG10(2) / O177746420232, O411757177572 /, SC/987/
332     C
333     C MACHINE CONSTANTS FOR THE VAX UNIX F77 COMPILER
334     C
335     C DATA SMALL(1),SMALL(2) / 128, 0 /
336     C DATA LARGE(1),LARGE(2) / -32769, -1 /
337     C DATA RIGHT(1),RIGHT(2) / 9344, 0 /
338     C DATA DIVER(1),DIVER(2) / 9472, 0 /
339     C DATA LOG10(1),LOG10(2) / 546979738, -805796613 /, SC/987/
340     C
341     C MACHINE CONSTANTS FOR THE VAX-11 WITH
342     C FORTRAN IV-PLUS COMPILER
343     C
344     C DATA SMALL(1),SMALL(2) / Z00000080, Z00000000 /
345     C DATA LARGE(1),LARGE(2) / ZFFFF7FFF, ZFFFFFFFF /
346     C DATA RIGHT(1),RIGHT(2) / Z00002480, Z00000000 /
347     C DATA DIVER(1),DIVER(2) / Z00002500, Z00000000 /
348     C DATA LOG10(1),LOG10(2) / Z209A3F9A, ZCFF884FB /, SC/987/
349     C
350     C MACHINE CONSTANTS FOR VAX/VMS VERSION 2.2
351     C
352     C DATA SMALL(1),SMALL(2) / '80'X, '0'X /
353     C DATA LARGE(1),LARGE(2) / 'FFFF7FFF'X, 'FFFFFFFF'X /
354     C DATA RIGHT(1),RIGHT(2) / '2480'X, '0'X /
355     C DATA DIVER(1),DIVER(2) / '2500'X, '0'X /
356     C DATA LOG10(1),LOG10(2) / '209A3F9A'X, 'CFF884FB'X /, SC/987/
357     C
358     C *** ISSUE STOP 779 IF ALL DATA STATEMENTS ARE COMMENTED...
359     IF (SC .NE. 987) STOP 779
360     C *** ISSUE STOP 778 IF ALL DATA STATEMENTS ARE OBVIOUSLY WRONG...
361     IF (DMACH(4) .GE. 1.0D0) STOP 778
362     IF (I .LT. 1 .OR. I .GT. 5) GOTO 999
363     D1MACH = DMACH(I)
364     RETURN
365     999 WRITE(*,1999) I
366     1999 FORMAT(' D1MACH - I OUT OF BOUNDS',I10)
367     STOP
368     END

john.pye@anu.edu.au
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