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- *DECK ERFC
- FUNCTION ERFC (X)
- C***BEGIN PROLOGUE ERFC
- C***PURPOSE Compute the complementary error function.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C8A, L5A1E
- C***TYPE SINGLE PRECISION (ERFC-S, DERFC-D)
- C***KEYWORDS COMPLEMENTARY ERROR FUNCTION, ERFC, FNLIB,
- C SPECIAL FUNCTIONS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C ERFC(X) calculates the single precision complementary error
- C function for single precision argument X.
- C
- C Series for ERF on the interval 0. to 1.00000D+00
- C with weighted error 7.10E-18
- C log weighted error 17.15
- C significant figures required 16.31
- C decimal places required 17.71
- C
- C Series for ERFC on the interval 0. to 2.50000D-01
- C with weighted error 4.81E-17
- C log weighted error 16.32
- C approx significant figures required 15.0
- C
- C
- C Series for ERC2 on the interval 2.50000D-01 to 1.00000D+00
- C with weighted error 5.22E-17
- C log weighted error 16.28
- C approx significant figures required 15.0
- C decimal places required 16.96
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG
- C***REVISION HISTORY (YYMMDD)
- C 770701 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 920618 Removed space from variable names. (RWC, WRB)
- C***END PROLOGUE ERFC
- DIMENSION ERFCS(13), ERFCCS(24), ERC2CS(23)
- LOGICAL FIRST
- SAVE ERFCS, ERC2CS, ERFCCS, SQRTPI, NTERF, NTERFC,
- 1 NTERC2, XSML, XMAX, SQEPS, FIRST
- DATA ERFCS( 1) / -.0490461212 34691808E0 /
- DATA ERFCS( 2) / -.1422612051 0371364E0 /
- DATA ERFCS( 3) / .0100355821 87599796E0 /
- DATA ERFCS( 4) / -.0005768764 69976748E0 /
- DATA ERFCS( 5) / .0000274199 31252196E0 /
- DATA ERFCS( 6) / -.0000011043 17550734E0 /
- DATA ERFCS( 7) / .0000000384 88755420E0 /
- DATA ERFCS( 8) / -.0000000011 80858253E0 /
- DATA ERFCS( 9) / .0000000000 32334215E0 /
- DATA ERFCS(10) / -.0000000000 00799101E0 /
- DATA ERFCS(11) / .0000000000 00017990E0 /
- DATA ERFCS(12) / -.0000000000 00000371E0 /
- DATA ERFCS(13) / .0000000000 00000007E0 /
- DATA ERC2CS( 1) / -.0696013466 02309501E0 /
- DATA ERC2CS( 2) / -.0411013393 62620893E0 /
- DATA ERC2CS( 3) / .0039144958 66689626E0 /
- DATA ERC2CS( 4) / -.0004906395 65054897E0 /
- DATA ERC2CS( 5) / .0000715747 90013770E0 /
- DATA ERC2CS( 6) / -.0000115307 16341312E0 /
- DATA ERC2CS( 7) / .0000019946 70590201E0 /
- DATA ERC2CS( 8) / -.0000003642 66647159E0 /
- DATA ERC2CS( 9) / .0000000694 43726100E0 /
- DATA ERC2CS(10) / -.0000000137 12209021E0 /
- DATA ERC2CS(11) / .0000000027 88389661E0 /
- DATA ERC2CS(12) / -.0000000005 81416472E0 /
- DATA ERC2CS(13) / .0000000001 23892049E0 /
- DATA ERC2CS(14) / -.0000000000 26906391E0 /
- DATA ERC2CS(15) / .0000000000 05942614E0 /
- DATA ERC2CS(16) / -.0000000000 01332386E0 /
- DATA ERC2CS(17) / .0000000000 00302804E0 /
- DATA ERC2CS(18) / -.0000000000 00069666E0 /
- DATA ERC2CS(19) / .0000000000 00016208E0 /
- DATA ERC2CS(20) / -.0000000000 00003809E0 /
- DATA ERC2CS(21) / .0000000000 00000904E0 /
- DATA ERC2CS(22) / -.0000000000 00000216E0 /
- DATA ERC2CS(23) / .0000000000 00000052E0 /
- DATA ERFCCS( 1) / 0.0715179310 202925E0 /
- DATA ERFCCS( 2) / -.0265324343 37606719E0 /
- DATA ERFCCS( 3) / .0017111539 77920853E0 /
- DATA ERFCCS( 4) / -.0001637516 63458512E0 /
- DATA ERFCCS( 5) / .0000198712 93500549E0 /
- DATA ERFCCS( 6) / -.0000028437 12412769E0 /
- DATA ERFCCS( 7) / .0000004606 16130901E0 /
- DATA ERFCCS( 8) / -.0000000822 77530261E0 /
- DATA ERFCCS( 9) / .0000000159 21418724E0 /
- DATA ERFCCS(10) / -.0000000032 95071356E0 /
- DATA ERFCCS(11) / .0000000007 22343973E0 /
- DATA ERFCCS(12) / -.0000000001 66485584E0 /
- DATA ERFCCS(13) / .0000000000 40103931E0 /
- DATA ERFCCS(14) / -.0000000000 10048164E0 /
- DATA ERFCCS(15) / .0000000000 02608272E0 /
- DATA ERFCCS(16) / -.0000000000 00699105E0 /
- DATA ERFCCS(17) / .0000000000 00192946E0 /
- DATA ERFCCS(18) / -.0000000000 00054704E0 /
- DATA ERFCCS(19) / .0000000000 00015901E0 /
- DATA ERFCCS(20) / -.0000000000 00004729E0 /
- DATA ERFCCS(21) / .0000000000 00001432E0 /
- DATA ERFCCS(22) / -.0000000000 00000439E0 /
- DATA ERFCCS(23) / .0000000000 00000138E0 /
- DATA ERFCCS(24) / -.0000000000 00000048E0 /
- DATA SQRTPI /1.772453850 9055160E0/
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT ERFC
- IF (FIRST) THEN
- ETA = 0.1*R1MACH(3)
- NTERF = INITS (ERFCS, 13, ETA)
- NTERFC = INITS (ERFCCS, 24, ETA)
- NTERC2 = INITS (ERC2CS, 23, ETA)
- C
- XSML = -SQRT (-LOG(SQRTPI*R1MACH(3)))
- TXMAX = SQRT (-LOG(SQRTPI*R1MACH(1)))
- XMAX = TXMAX - 0.5*LOG(TXMAX)/TXMAX - 0.01
- SQEPS = SQRT (2.0*R1MACH(3))
- ENDIF
- FIRST = .FALSE.
- C
- IF (X.GT.XSML) GO TO 20
- C
- C ERFC(X) = 1.0 - ERF(X) FOR X .LT. XSML
- C
- ERFC = 2.
- RETURN
- C
- 20 IF (X.GT.XMAX) GO TO 40
- Y = ABS(X)
- IF (Y.GT.1.0) GO TO 30
- C
- C ERFC(X) = 1.0 - ERF(X) FOR -1. .LE. X .LE. 1.
- C
- IF (Y.LT.SQEPS) ERFC = 1.0 - 2.0*X/SQRTPI
- IF (Y.GE.SQEPS) ERFC = 1.0 -
- 1 X*(1.0 + CSEVL (2.*X*X-1., ERFCS, NTERF) )
- RETURN
- C
- C ERFC(X) = 1.0 - ERF(X) FOR 1. .LT. ABS(X) .LE. XMAX
- C
- 30 Y = Y*Y
- IF (Y.LE.4.) ERFC = EXP(-Y)/ABS(X) * (0.5 + CSEVL ((8./Y-5.)/3.,
- 1 ERC2CS, NTERC2) )
- IF (Y.GT.4.) ERFC = EXP(-Y)/ABS(X) * (0.5 + CSEVL (8./Y-1.,
- 1 ERFCCS, NTERFC) )
- IF (X.LT.0.) ERFC = 2.0 - ERFC
- RETURN
- C
- 40 CALL XERMSG ('SLATEC', 'ERFC', 'X SO BIG ERFC UNDERFLOWS', 1, 1)
- ERFC = 0.
- RETURN
- C
- END
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