C C Version by w.g.bardsley, university of manchester, u.k., 26/10/98 C ================================================================= C DOUBLE PRECISION FUNCTION D1MACH(I) C===================================================== INTEGER I IF (I.EQ.1) THEN D1MACH = 2.2250739D-308 ELSEIF (I.EQ.2) THEN D1MACH = 1.7976931D+308 ELSEIF (I.EQ.3) THEN D1MACH = 1.1102230D-16 ELSEIF (I.EQ.4) THEN D1MACH = 2.220446D-16 ELSEIF (I.EQ.5) THEN D1MACH = 0.301029995663981195D+00 ELSE D1MACH = 0.0D+00 ENDIF RETURN C===================================================== C***BEGIN PROLOGUE D1MACH C***DATE WRITTEN 750101 (YYMMDD) C***REVISION DATE 890213 (YYMMDD) C***CATEGORY NO. R1 C***KEYWORDS LIBRARY=SLATEC,TYPE=DOUBLE PRECISION(R1MACH-S D1MACH-D), C MACHINE CONSTANTS C***AUTHOR FOX, P. A., (BELL LABS) C HALL, A. D., (BELL LABS) C SCHRYER, N. L., (BELL LABS) C***PURPOSE RETURNS DOUBLE PRECISION MACHINE DEPENDENT CONSTANTS C***DESCRIPTION C C D1MACH CAN BE USED TO OBTAIN MACHINE-DEPENDENT PARAMETERS C FOR THE LOCAL MACHINE ENVIRONMENT. IT IS A FUNCTION C SUBPROGRAM WITH ONE (INPUT) ARGUMENT, AND CAN BE CALLED C AS FOLLOWS, FOR EXAMPLE C C D = D1MACH(I) C C WHERE I=1,...,5. THE (OUTPUT) VALUE OF D ABOVE IS C DETERMINED BY THE (INPUT) VALUE OF I. THE RESULTS FOR C VARIOUS VALUES OF I ARE DISCUSSED BELOW. C C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. C D1MACH( 5) = LOG10(B) C C ASSUME DOUBLE PRECISION NUMBERS ARE REPRESENTED IN THE T-DIGIT, C BASE-B FORM C C SIGN (B**E)*( (X(1)/B) + ... + (X(T)/B**T) ) C C WHERE 0 .LE. X(I) .LT. B FOR I=1,...,T, 0 .LT. X(1), AND C EMIN .LE. E .LE. EMAX. C C THE VALUES OF B, T, EMIN AND EMAX ARE PROVIDED IN I1MACH AS C FOLLOWS: C I1MACH(10) = B, THE BASE. C I1MACH(14) = T, THE NUMBER OF BASE-B DIGITS. C I1MACH(15) = EMIN, THE SMALLEST EXPONENT E. C I1MACH(16) = EMAX, THE LARGEST EXPONENT E. C C TO ALTER THIS FUNCTION FOR A PARTICULAR ENVIRONMENT, C THE DESIRED SET OF DATA STATEMENTS SHOULD BE ACTIVATED BY C REMOVING THE C FROM COLUMN 1. ALSO, THE VALUES OF C D1MACH(1) - D1MACH(4) SHOULD BE CHECKED FOR CONSISTENCY C WITH THE LOCAL OPERATING SYSTEM. C C***REFERENCES FOX P.A., HALL A.D., SCHRYER N.L.,*FRAMEWORK FOR A C PORTABLE LIBRARY*, ACM TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOL. 4, NO. 2, JUNE 1978, PP. 177-188. C***ROUTINES CALLED XERROR C C THE CALL TO XERROR HAS BEEN COMMENTED TO GET A STAND ALONE ROUTINE C IT CAN BE ADAPTED TO FIT THE LOCAL ERROR HANDLING PROCEDURES C NOTE ADDED BY F. ROMANI 7/11/89 C C***END PROLOGUE D1MACH C C INTEGER SMALL(4) C INTEGER LARGE(4) C INTEGER RIGHT(4) C INTEGER DIVER(4) C INTEGER LOG10(4) C C DOUBLE PRECISION DMACH(5) C SAVE DMACH C C EQUIVALENCE (DMACH(1),SMALL(1)) C EQUIVALENCE (DMACH(2),LARGE(1)) C EQUIVALENCE (DMACH(3),RIGHT(1)) C EQUIVALENCE (DMACH(4),DIVER(1)) C EQUIVALENCE (DMACH(5),LOG10(1)) C C MACHINE CONSTANTS FOR THE AMIGA C ABSOFT FORTRAN COMPILER USING THE 68020/68881 COMPILER OPTION C C DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' / C DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' / C DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' / C DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' / C DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' / C C MACHINE CONSTANTS FOR THE AMIGA C ABSOFT FORTRAN COMPILER USING SOFTWARE FLOATING POINT C C DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' / C DATA LARGE(1), LARGE(2) / Z'7FDFFFFF', Z'FFFFFFFF' / C DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' / C DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' / C DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' / C C MACHINE CONSTANTS FOR THE APOLLO C C DATA SMALL(1), SMALL(2) / 16#00100000, 16#00000000 / C DATA LARGE(1), LARGE(2) / 16#7FFFFFFF, 16#FFFFFFFF / C DATA RIGHT(1), RIGHT(2) / 16#3CA00000, 16#00000000 / C DATA DIVER(1), DIVER(2) / 16#3CB00000, 16#00000000 / C DATA LOG10(1), LOG10(2) / 16#3FD34413, 16#509F79FF / C C MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM C C DATA SMALL(1) / ZC00800000 / C DATA SMALL(2) / Z000000000 / C DATA LARGE(1) / ZDFFFFFFFF / C DATA LARGE(2) / ZFFFFFFFFF / C DATA RIGHT(1) / ZCC5800000 / C DATA RIGHT(2) / Z000000000 / C DATA DIVER(1) / ZCC6800000 / C DATA DIVER(2) / Z000000000 / C DATA LOG10(1) / ZD00E730E7 / C DATA LOG10(2) / ZC77800DC0 / C C MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM C C DATA SMALL(1) / O1771000000000000 / C DATA SMALL(2) / O0000000000000000 / C DATA LARGE(1) / O0777777777777777 / C DATA LARGE(2) / O0007777777777777 / C DATA RIGHT(1) / O1461000000000000 / C DATA RIGHT(2) / O0000000000000000 / C DATA DIVER(1) / O1451000000000000 / C DATA DIVER(2) / O0000000000000000 / C DATA LOG10(1) / O1157163034761674 / C DATA LOG10(2) / O0006677466732724 / C C MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS C C DATA SMALL(1) / O1771000000000000 / C DATA SMALL(2) / O7770000000000000 / C DATA LARGE(1) / O0777777777777777 / C DATA LARGE(2) / O7777777777777777 / C DATA RIGHT(1) / O1461000000000000 / C DATA RIGHT(2) / O0000000000000000 / C DATA DIVER(1) / O1451000000000000 / C DATA DIVER(2) / O0000000000000000 / C DATA LOG10(1) / O1157163034761674 / C DATA LOG10(2) / O0006677466732724 / C C MACHINE CONSTANTS FOR THE CDC 170/180 SERIES USING NOS/VE C C DATA SMALL(1) / Z"3001800000000000" / C DATA SMALL(2) / Z"3001000000000000" / C DATA LARGE(1) / Z"4FFEFFFFFFFFFFFE" / C DATA LARGE(2) / Z"4FFE000000000000" / C DATA RIGHT(1) / Z"3FD2800000000000" / C DATA RIGHT(2) / Z"3FD2000000000000" / C DATA DIVER(1) / Z"3FD3800000000000" / C DATA DIVER(2) / Z"3FD3000000000000" / C DATA LOG10(1) / Z"3FFF9A209A84FBCF" / C DATA LOG10(2) / Z"3FFFF7988F8959AC" / C C MACHINE CONSTANTS FOR THE CDC 6000/7000 SERIES C C DATA SMALL(1) / 00564000000000000000B / C DATA SMALL(2) / 00000000000000000000B / C DATA LARGE(1) / 37757777777777777777B / C DATA LARGE(2) / 37157777777777777777B / C DATA RIGHT(1) / 15624000000000000000B / C DATA RIGHT(2) / 00000000000000000000B / C DATA DIVER(1) / 15634000000000000000B / C DATA DIVER(2) / 00000000000000000000B / C DATA LOG10(1) / 17164642023241175717B / C DATA LOG10(2) / 16367571421742254654B / C C MACHINE CONSTANTS FOR THE CELERITY C1260 C C DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' / C DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' / C DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' / C DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' / C DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' / C C MACHINE CONSTANTS FOR THE CONVEX C-1 C C DATA SMALL(1), SMALL(2) / '00100000'X,'00000000'X / C DATA LARGE(1), LARGE(2) / '7FFFFFFF'X,'FFFFFFFF'X / C DATA RIGHT(1), RIGHT(2) / '3CC00000'X,'00000000'X / C DATA DIVER(1), DIVER(2) / '3CD00000'X,'00000000'X / C DATA LOG10(1), LOG10(2) / '3FF34413'X,'509F79FF'X / C C MACHINE CONSTANTS FOR THE CRAY-1 C C DATA SMALL(1) / 201354000000000000000B / C DATA SMALL(2) / 000000000000000000000B / C DATA LARGE(1) / 577767777777777777777B / C DATA LARGE(2) / 000007777777777777774B / C DATA RIGHT(1) / 376434000000000000000B / C DATA RIGHT(2) / 000000000000000000000B / C DATA DIVER(1) / 376444000000000000000B / C DATA DIVER(2) / 000000000000000000000B / C DATA LOG10(1) / 377774642023241175717B / C DATA LOG10(2) / 000007571421742254654B / C C MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200 C C NOTE - IT MAY BE APPROPRIATE TO INCLUDE THE FOLLOWING CARD - C STATIC DMACH(5) C C DATA SMALL / 20K, 3*0 / C DATA LARGE / 77777K, 3*177777K / C DATA RIGHT / 31420K, 3*0 / C DATA DIVER / 32020K, 3*0 / C DATA LOG10 / 40423K, 42023K, 50237K, 74776K / C C MACHINE CONSTANTS FOR THE ELXSI 6400 C (ASSUMING REAL*8 IS THE DEFAULT DOUBLE PRECISION) C C DATA SMALL(1), SMALL(2) / '00100000'X,'00000000'X / C DATA LARGE(1), LARGE(2) / '7FEFFFFF'X,'FFFFFFFF'X / C DATA RIGHT(1), RIGHT(2) / '3CB00000'X,'00000000'X / C DATA DIVER(1), DIVER(2) / '3CC00000'X,'00000000'X / C DATA LOG10(1), LOG10(2) / '3FD34413'X,'509F79FF'X / C C MACHINE CONSTANTS FOR THE HARRIS 220 C C DATA SMALL(1), SMALL(2) / '20000000, '00000201 / C DATA LARGE(1), LARGE(2) / '37777777, '37777577 / C DATA RIGHT(1), RIGHT(2) / '20000000, '00000333 / C DATA DIVER(1), DIVER(2) / '20000000, '00000334 / C DATA LOG10(1), LOG10(2) / '23210115, '10237777 / C C MACHINE CONSTANTS FOR THE HONEYWELL 600/6000 SERIES C C DATA SMALL(1), SMALL(2) / O402400000000, O000000000000 / C DATA LARGE(1), LARGE(2) / O376777777777, O777777777777 / C DATA RIGHT(1), RIGHT(2) / O604400000000, O000000000000 / C DATA DIVER(1), DIVER(2) / O606400000000, O000000000000 / C DATA LOG10(1), LOG10(2) / O776464202324, O117571775714 / C C MACHINE CONSTANTS FOR THE HP 2100 C THREE WORD DOUBLE PRECISION OPTION WITH FTN4 C C DATA SMALL(1), SMALL(2), SMALL(3) / 40000B, 0, 1 / C DATA LARGE(1), LARGE(2), LARGE(3) / 77777B, 177777B, 177776B / C DATA RIGHT(1), RIGHT(2), RIGHT(3) / 40000B, 0, 265B / C DATA DIVER(1), DIVER(2), DIVER(3) / 40000B, 0, 276B / C DATA LOG10(1), LOG10(2), LOG10(3) / 46420B, 46502B, 77777B / C C MACHINE CONSTANTS FOR THE HP 2100 C FOUR WORD DOUBLE PRECISION OPTION WITH FTN4 C C DATA SMALL(1), SMALL(2) / 40000B, 0 / C DATA SMALL(3), SMALL(4) / 0, 1 / C DATA LARGE(1), LARGE(2) / 77777B, 177777B / C DATA LARGE(3), LARGE(4) / 177777B, 177776B / C DATA RIGHT(1), RIGHT(2) / 40000B, 0 / C DATA RIGHT(3), RIGHT(4) / 0, 225B / C DATA DIVER(1), DIVER(2) / 40000B, 0 / C DATA DIVER(3), DIVER(4) / 0, 227B / C DATA LOG10(1), LOG10(2) / 46420B, 46502B / C DATA LOG10(3), LOG10(4) / 76747B, 176377B / C C MACHINE CONSTANTS FOR THE HP 9000 C C DATA SMALL(1), SMALL(2) / 00040000000B, 00000000000B / C DATA LARGE(1), LARGE(2) / 17737777777B, 37777777777B / C DATA RIGHT(1), RIGHT(2) / 07454000000B, 00000000000B / C DATA DIVER(1), DIVER(2) / 07460000000B, 00000000000B / C DATA LOG10(1), LOG10(2) / 07764642023B, 12047674777B / C C MACHINE CONSTANTS FOR THE IBM 360/370 SERIES, C THE XEROX SIGMA 5/7/9, THE SEL SYSTEMS 85/86, AND C THE PERKIN ELMER (INTERDATA) 7/32. C C DATA SMALL(1), SMALL(2) / Z00100000, Z00000000 / C DATA LARGE(1), LARGE(2) / Z7FFFFFFF, ZFFFFFFFF / C DATA RIGHT(1), RIGHT(2) / Z33100000, Z00000000 / C DATA DIVER(1), DIVER(2) / Z34100000, Z00000000 / C DATA LOG10(1), LOG10(2) / Z41134413, Z509F79FF / C C MACHINE CONSTANTS FOR THE IBM PC C ASSUMES THAT ALL ARITHMETIC IS DONE IN DOUBLE PRECISION C ON 8088, I.E., NOT IN 80 BIT FORM FOR THE 8087. C C DATA SMALL(1) / 2.23D-308 / C DATA LARGE(1) / 1.79D+308 / C DATA RIGHT(1) / 1.11D-16 / C DATA DIVER(1) / 2.22D-16 / C DATA LOG10(1) / 0.301029995663981195D0 / C C MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR) C C DATA SMALL(1), SMALL(2) / "033400000000, "000000000000 / C DATA LARGE(1), LARGE(2) / "377777777777, "344777777777 / C DATA RIGHT(1), RIGHT(2) / "113400000000, "000000000000 / C DATA DIVER(1), DIVER(2) / "114400000000, "000000000000 / C DATA LOG10(1), LOG10(2) / "177464202324, "144117571776 / C C MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR) C C DATA SMALL(1), SMALL(2) / "000400000000, "000000000000 / C DATA LARGE(1), LARGE(2) / "377777777777, "377777777777 / C DATA RIGHT(1), RIGHT(2) / "103400000000, "000000000000 / C DATA DIVER(1), DIVER(2) / "104400000000, "000000000000 / C DATA LOG10(1), LOG10(2) / "177464202324, "476747767461 / C C MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING C 32-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). C C DATA SMALL(1), SMALL(2) / 8388608, 0 / C DATA LARGE(1), LARGE(2) / 2147483647, -1 / C DATA RIGHT(1), RIGHT(2) / 612368384, 0 / C DATA DIVER(1), DIVER(2) / 620756992, 0 / C DATA LOG10(1), LOG10(2) / 1067065498, -2063872008 / C C DATA SMALL(1), SMALL(2) / O00040000000, O00000000000 / C DATA LARGE(1), LARGE(2) / O17777777777, O37777777777 / C DATA RIGHT(1), RIGHT(2) / O04440000000, O00000000000 / C DATA DIVER(1), DIVER(2) / O04500000000, O00000000000 / C DATA LOG10(1), LOG10(2) / O07746420232, O20476747770 / C C MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING C 16-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). C C DATA SMALL(1), SMALL(2) / 128, 0 / C DATA SMALL(3), SMALL(4) / 0, 0 / C DATA LARGE(1), LARGE(2) / 32767, -1 / C DATA LARGE(3), LARGE(4) / -1, -1 / C DATA RIGHT(1), RIGHT(2) / 9344, 0 / C DATA RIGHT(3), RIGHT(4) / 0, 0 / C DATA DIVER(1), DIVER(2) / 9472, 0 / C DATA DIVER(3), DIVER(4) / 0, 0 / C DATA LOG10(1), LOG10(2) / 16282, 8346 / C DATA LOG10(3), LOG10(4) / -31493, -12296 / C C DATA SMALL(1), SMALL(2) / O000200, O000000 / C DATA SMALL(3), SMALL(4) / O000000, O000000 / C DATA LARGE(1), LARGE(2) / O077777, O177777 / C DATA LARGE(3), LARGE(4) / O177777, O177777 / C DATA RIGHT(1), RIGHT(2) / O022200, O000000 / C DATA RIGHT(3), RIGHT(4) / O000000, O000000 / C DATA DIVER(1), DIVER(2) / O022400, O000000 / C DATA DIVER(3), DIVER(4) / O000000, O000000 / C DATA LOG10(1), LOG10(2) / O037632, O020232 / C DATA LOG10(3), LOG10(4) / O102373, O147770 / C C MACHINE CONSTANTS FOR THE SUN C C DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' / C DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' / C DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' / C DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' / C DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' / C C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES FTN COMPILER C C DATA SMALL(1), SMALL(2) / O000040000000, O000000000000 / C DATA LARGE(1), LARGE(2) / O377777777777, O777777777777 / C DATA RIGHT(1), RIGHT(2) / O170540000000, O000000000000 / C DATA DIVER(1), DIVER(2) / O170640000000, O000000000000 / C DATA LOG10(1), LOG10(2) / O177746420232, O411757177572 / C C MACHINE CONSTANTS FOR VAX 11/780 C (EXPRESSED IN INTEGER AND HEXADECIMAL) C THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSYEMS C THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS C C DATA SMALL(1), SMALL(2) / 128, 0 / C DATA LARGE(1), LARGE(2) / -32769, -1 / C DATA RIGHT(1), RIGHT(2) / 9344, 0 / C DATA DIVER(1), DIVER(2) / 9472, 0 / C DATA LOG10(1), LOG10(2) / 546979738, -805796613 / C C DATA SMALL(1), SMALL(2) / Z00000080, Z00000000 / C DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF / C DATA RIGHT(1), RIGHT(2) / Z00002480, Z00000000 / C DATA DIVER(1), DIVER(2) / Z00002500, Z00000000 / C DATA LOG10(1), LOG10(2) / Z209A3F9A, ZCFF884FB / C C MACHINE CONSTANTS FOR VAX 11/780 (G-FLOATING) C (EXPRESSED IN INTEGER AND HEXADECIMAL) C THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSYEMS C THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS C C DATA SMALL(1), SMALL(2) / 16, 0 / C DATA LARGE(1), LARGE(2) / -32769, -1 / C DATA RIGHT(1), RIGHT(2) / 15552, 0 / C DATA DIVER(1), DIVER(2) / 15568, 0 / C DATA LOG10(1), LOG10(2) / 1142112243, 2046775455 / C C DATA SMALL(1), SMALL(2) / Z00000010, Z00000000 / C DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF / C DATA RIGHT(1), RIGHT(2) / Z00003CC0, Z00000000 / C DATA DIVER(1), DIVER(2) / Z00003CD0, Z00000000 / C DATA LOG10(1), LOG10(2) / Z44133FF3, Z79FF509F / C C C***FIRST EXECUTABLE STATEMENT D1MACH C C THE CALL TO XERROR HAS BEEN COMMENTED TO GET A STAND ALONE ROUTINE C IT CAN BE ADAPTED TO FIT THE LOCAL ERROR HANDLING PROCEDURES C NOTE ADDED BY F. ROMANI 7/11/89 C C IF (I .LT. 1 .OR. I .GT. 5) C 1 CALL XERROR ('D1MACH -- I OUT OF BOUNDS', 25, 1, 2) C C D1MACH = DMACH(I) C RETURN C END C C