*DECK R9LN2R FUNCTION R9LN2R (X) C***BEGIN PROLOGUE R9LN2R C***SUBSIDIARY C***PURPOSE Evaluate LOG(1+X) from second order relative accuracy so C that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X). C***LIBRARY SLATEC (FNLIB) C***CATEGORY C4B C***TYPE SINGLE PRECISION (R9LN2R-S, D9LN2R-D, C9LN2R-C) C***KEYWORDS ELEMENTARY FUNCTIONS, FNLIB, LOGARITHM, SECOND ORDER C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C Evaluate LOG(1+X) from 2-nd order with relative error accuracy so C that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X) C C Series for LN21 on the interval -6.25000D-01 to 0. C with weighted error 2.49E-17 C log weighted error 16.60 C significant figures required 15.87 C decimal places required 17.31 C C Series for LN22 on the interval 0. to 8.12500D-01 C with weighted error 1.42E-17 C log weighted error 16.85 C significant figures required 15.95 C decimal places required 17.50 C C***REFERENCES (NONE) C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG C***REVISION HISTORY (YYMMDD) C 780401 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 900720 Routine changed from user-callable to subsidiary. (WRB) C***END PROLOGUE R9LN2R REAL LN21CS(26), LN22CS(20) LOGICAL FIRST SAVE LN21CS, LN22CS, NTLN21, NTLN22, XMIN, XBIG, XMAX, FIRST DATA LN21CS( 1) / .1811196251 3478810E0 / DATA LN21CS( 2) / -.1562712319 2872463E0 / DATA LN21CS( 3) / .0286763053 61557275E0 / DATA LN21CS( 4) / -.0055586996 55948139E0 / DATA LN21CS( 5) / .0011178976 65229983E0 / DATA LN21CS( 6) / -.0002308050 89823279E0 / DATA LN21CS( 7) / .0000485988 53341100E0 / DATA LN21CS( 8) / -.0000103901 27388903E0 / DATA LN21CS( 9) / .0000022484 56370739E0 / DATA LN21CS(10) / -.0000004914 05927392E0 / DATA LN21CS(11) / .0000001082 82565070E0 / DATA LN21CS(12) / -.0000000240 25872763E0 / DATA LN21CS(13) / .0000000053 62460047E0 / DATA LN21CS(14) / -.0000000012 02995136E0 / DATA LN21CS(15) / .0000000002 71078892E0 / DATA LN21CS(16) / -.0000000000 61323562E0 / DATA LN21CS(17) / .0000000000 13920858E0 / DATA LN21CS(18) / -.0000000000 03169930E0 / DATA LN21CS(19) / .0000000000 00723837E0 / DATA LN21CS(20) / -.0000000000 00165700E0 / DATA LN21CS(21) / .0000000000 00038018E0 / DATA LN21CS(22) / -.0000000000 00008741E0 / DATA LN21CS(23) / .0000000000 00002013E0 / DATA LN21CS(24) / -.0000000000 00000464E0 / DATA LN21CS(25) / .0000000000 00000107E0 / DATA LN21CS(26) / -.0000000000 00000024E0 / DATA LN22CS( 1) / -.2224253253 5020461E0 / DATA LN22CS( 2) / -.0610471001 08078624E0 / DATA LN22CS( 3) / .0074272350 09750394E0 / DATA LN22CS( 4) / -.0009335018 26163697E0 / DATA LN22CS( 5) / .0001200499 07687260E0 / DATA LN22CS( 6) / -.0000157047 22952820E0 / DATA LN22CS( 7) / .0000020818 74781051E0 / DATA LN22CS( 8) / -.0000002789 19557764E0 / DATA LN22CS( 9) / .0000000376 93558237E0 / DATA LN22CS(10) / -.0000000051 30902896E0 / DATA LN22CS(11) / .0000000007 02714117E0 / DATA LN22CS(12) / -.0000000000 96748595E0 / DATA LN22CS(13) / .0000000000 13381046E0 / DATA LN22CS(14) / -.0000000000 01858102E0 / DATA LN22CS(15) / .0000000000 00258929E0 / DATA LN22CS(16) / -.0000000000 00036195E0 / DATA LN22CS(17) / .0000000000 00005074E0 / DATA LN22CS(18) / -.0000000000 00000713E0 / DATA LN22CS(19) / .0000000000 00000100E0 / DATA LN22CS(20) / -.0000000000 00000014E0 / DATA FIRST /.TRUE./ C***FIRST EXECUTABLE STATEMENT R9LN2R IF (FIRST) THEN EPS = R1MACH(3) NTLN21 = INITS (LN21CS, 26, 0.1*EPS) NTLN22 = INITS (LN22CS, 20, 0.1*EPS) C XMIN = -1.0 + SQRT(R1MACH(4)) SQEPS = SQRT(EPS) TXMAX = 6.0/SQEPS XMAX = TXMAX - (EPS*TXMAX**2 - 2.0*LOG(TXMAX)) / 1 (2.0*EPS*TXMAX) TXBIG = 4.0/SQRT(SQEPS) XBIG = TXBIG - (SQEPS*TXBIG**2 - 2.0*LOG(TXBIG)) / 1 (2.*SQEPS*TXBIG) ENDIF FIRST = .FALSE. C IF (X.LT.(-0.625) .OR. X.GT.0.8125) GO TO 20 C IF (X.LT.0.0) R9LN2R = 0.375 + CSEVL (16.*X/5.+1.0, LN21CS, 1 NTLN21) IF (X.GE.0.0) R9LN2R = 0.375 + CSEVL (32.*X/13.-1.0, LN22CS, 1 NTLN22) RETURN C 20 IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'R9LN2R', + 'ANSWER LT HALF PRECISION BECAUSE X IS TOO NEAR -1', 1, 1) IF (X .GT. XMAX) CALL XERMSG ('SLATEC', 'R9LN2R', + 'NO PRECISION IN ANSWER BECAUSE X IS TOO BIG', 3, 2) IF (X .GT. XBIG) CALL XERMSG ('SLATEC', 'R9LN2R', + 'ANSWER LT HALF PRECISION BECAUSE X IS TOO BIG', 2, 1) C R9LN2R = (LOG(1.0+X) - X*(1.0-0.5*X) ) / X**3 RETURN C END