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- *DECK ALNREL
- FUNCTION ALNREL (X)
- C***BEGIN PROLOGUE ALNREL
- C***PURPOSE Evaluate ln(1+X) accurate in the sense of relative error.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C4B
- C***TYPE SINGLE PRECISION (ALNREL-S, DLNREL-D, CLNREL-C)
- C***KEYWORDS ELEMENTARY FUNCTIONS, FNLIB, LOGARITHM
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C ALNREL(X) evaluates ln(1+X) accurately in the sense of relative
- C error when X is very small. This routine must be used to
- C maintain relative error accuracy whenever X is small and
- C accurately known.
- C
- C Series for ALNR on the interval -3.75000D-01 to 3.75000D-01
- C with weighted error 1.93E-17
- C log weighted error 16.72
- C significant figures required 16.44
- C decimal places required 17.40
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG
- C***REVISION HISTORY (YYMMDD)
- C 770401 DATE WRITTEN
- C 890531 Changed all specific intrinsics to generic. (WRB)
- C 890531 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
- C 900326 Removed duplicate information from DESCRIPTION section.
- C (WRB)
- C***END PROLOGUE ALNREL
- DIMENSION ALNRCS(23)
- LOGICAL FIRST
- SAVE ALNRCS, NLNREL, XMIN, FIRST
- DATA ALNRCS( 1) / 1.0378693562 743770E0 /
- DATA ALNRCS( 2) / -.1336430150 4908918E0 /
- DATA ALNRCS( 3) / .0194082491 35520563E0 /
- DATA ALNRCS( 4) / -.0030107551 12753577E0 /
- DATA ALNRCS( 5) / .0004869461 47971548E0 /
- DATA ALNRCS( 6) / -.0000810548 81893175E0 /
- DATA ALNRCS( 7) / .0000137788 47799559E0 /
- DATA ALNRCS( 8) / -.0000023802 21089435E0 /
- DATA ALNRCS( 9) / .0000004164 04162138E0 /
- DATA ALNRCS(10) / -.0000000735 95828378E0 /
- DATA ALNRCS(11) / .0000000131 17611876E0 /
- DATA ALNRCS(12) / -.0000000023 54670931E0 /
- DATA ALNRCS(13) / .0000000004 25227732E0 /
- DATA ALNRCS(14) / -.0000000000 77190894E0 /
- DATA ALNRCS(15) / .0000000000 14075746E0 /
- DATA ALNRCS(16) / -.0000000000 02576907E0 /
- DATA ALNRCS(17) / .0000000000 00473424E0 /
- DATA ALNRCS(18) / -.0000000000 00087249E0 /
- DATA ALNRCS(19) / .0000000000 00016124E0 /
- DATA ALNRCS(20) / -.0000000000 00002987E0 /
- DATA ALNRCS(21) / .0000000000 00000554E0 /
- DATA ALNRCS(22) / -.0000000000 00000103E0 /
- DATA ALNRCS(23) / .0000000000 00000019E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT ALNREL
- IF (FIRST) THEN
- NLNREL = INITS (ALNRCS, 23, 0.1*R1MACH(3))
- XMIN = -1.0 + SQRT(R1MACH(4))
- ENDIF
- FIRST = .FALSE.
- C
- IF (X .LE. (-1.0)) CALL XERMSG ('SLATEC', 'ALNREL', 'X IS LE -1',
- + 2, 2)
- IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'ALNREL',
- + 'ANSWER LT HALF PRECISION BECAUSE X TOO NEAR -1', 1, 1)
- C
- IF (ABS(X).LE.0.375) ALNREL = X*(1. -
- 1 X*CSEVL (X/.375, ALNRCS, NLNREL))
- IF (ABS(X).GT.0.375) ALNREL = LOG (1.0+X)
- C
- RETURN
- END
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