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erfc.f
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1 *DECK ERFC
2  FUNCTION erfc (X)
3 C***BEGIN PROLOGUE ERFC
4 C***PURPOSE Compute the complementary error function.
5 C***LIBRARY SLATEC (FNLIB)
6 C***CATEGORY C8A, L5A1E
7 C***TYPE SINGLE PRECISION (ERFC-S, DERFC-D)
8 C***KEYWORDS COMPLEMENTARY ERROR FUNCTION, ERFC, FNLIB,
9 C SPECIAL FUNCTIONS
10 C***AUTHOR Fullerton, W., (LANL)
11 C***DESCRIPTION
12 C
13 C ERFC(X) calculates the single precision complementary error
14 C function for single precision argument X.
15 C
16 C Series for ERF on the interval 0. to 1.00000D+00
17 C with weighted error 7.10E-18
18 C log weighted error 17.15
19 C significant figures required 16.31
20 C decimal places required 17.71
21 C
22 C Series for ERFC on the interval 0. to 2.50000D-01
23 C with weighted error 4.81E-17
24 C log weighted error 16.32
25 C approx significant figures required 15.0
26 C
27 C
28 C Series for ERC2 on the interval 2.50000D-01 to 1.00000D+00
29 C with weighted error 5.22E-17
30 C log weighted error 16.28
31 C approx significant figures required 15.0
32 C decimal places required 16.96
33 C
34 C***REFERENCES (NONE)
35 C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG
36 C***REVISION HISTORY (YYMMDD)
37 C 770701 DATE WRITTEN
38 C 890531 Changed all specific intrinsics to generic. (WRB)
39 C 890531 REVISION DATE from Version 3.2
40 C 891214 Prologue converted to Version 4.0 format. (BAB)
41 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
42 C 920618 Removed space from variable names. (RWC, WRB)
43 C***END PROLOGUE ERFC
44  dimension erfcs(13), erfccs(24), erc2cs(23)
45  LOGICAL FIRST
46  SAVE erfcs, erc2cs, erfccs, sqrtpi, nterf, nterfc,
47  1 nterc2, xsml, xmax, sqeps, first
48  DATA erfcs( 1) / -.0490461212 34691808e0 /
49  DATA erfcs( 2) / -.1422612051 0371364e0 /
50  DATA erfcs( 3) / .0100355821 87599796e0 /
51  DATA erfcs( 4) / -.0005768764 69976748e0 /
52  DATA erfcs( 5) / .0000274199 31252196e0 /
53  DATA erfcs( 6) / -.0000011043 17550734e0 /
54  DATA erfcs( 7) / .0000000384 88755420e0 /
55  DATA erfcs( 8) / -.0000000011 80858253e0 /
56  DATA erfcs( 9) / .0000000000 32334215e0 /
57  DATA erfcs(10) / -.0000000000 00799101e0 /
58  DATA erfcs(11) / .0000000000 00017990e0 /
59  DATA erfcs(12) / -.0000000000 00000371e0 /
60  DATA erfcs(13) / .0000000000 00000007e0 /
61  DATA erc2cs( 1) / -.0696013466 02309501e0 /
62  DATA erc2cs( 2) / -.0411013393 62620893e0 /
63  DATA erc2cs( 3) / .0039144958 66689626e0 /
64  DATA erc2cs( 4) / -.0004906395 65054897e0 /
65  DATA erc2cs( 5) / .0000715747 90013770e0 /
66  DATA erc2cs( 6) / -.0000115307 16341312e0 /
67  DATA erc2cs( 7) / .0000019946 70590201e0 /
68  DATA erc2cs( 8) / -.0000003642 66647159e0 /
69  DATA erc2cs( 9) / .0000000694 43726100e0 /
70  DATA erc2cs(10) / -.0000000137 12209021e0 /
71  DATA erc2cs(11) / .0000000027 88389661e0 /
72  DATA erc2cs(12) / -.0000000005 81416472e0 /
73  DATA erc2cs(13) / .0000000001 23892049e0 /
74  DATA erc2cs(14) / -.0000000000 26906391e0 /
75  DATA erc2cs(15) / .0000000000 05942614e0 /
76  DATA erc2cs(16) / -.0000000000 01332386e0 /
77  DATA erc2cs(17) / .0000000000 00302804e0 /
78  DATA erc2cs(18) / -.0000000000 00069666e0 /
79  DATA erc2cs(19) / .0000000000 00016208e0 /
80  DATA erc2cs(20) / -.0000000000 00003809e0 /
81  DATA erc2cs(21) / .0000000000 00000904e0 /
82  DATA erc2cs(22) / -.0000000000 00000216e0 /
83  DATA erc2cs(23) / .0000000000 00000052e0 /
84  DATA erfccs( 1) / 0.0715179310 202925e0 /
85  DATA erfccs( 2) / -.0265324343 37606719e0 /
86  DATA erfccs( 3) / .0017111539 77920853e0 /
87  DATA erfccs( 4) / -.0001637516 63458512e0 /
88  DATA erfccs( 5) / .0000198712 93500549e0 /
89  DATA erfccs( 6) / -.0000028437 12412769e0 /
90  DATA erfccs( 7) / .0000004606 16130901e0 /
91  DATA erfccs( 8) / -.0000000822 77530261e0 /
92  DATA erfccs( 9) / .0000000159 21418724e0 /
93  DATA erfccs(10) / -.0000000032 95071356e0 /
94  DATA erfccs(11) / .0000000007 22343973e0 /
95  DATA erfccs(12) / -.0000000001 66485584e0 /
96  DATA erfccs(13) / .0000000000 40103931e0 /
97  DATA erfccs(14) / -.0000000000 10048164e0 /
98  DATA erfccs(15) / .0000000000 02608272e0 /
99  DATA erfccs(16) / -.0000000000 00699105e0 /
100  DATA erfccs(17) / .0000000000 00192946e0 /
101  DATA erfccs(18) / -.0000000000 00054704e0 /
102  DATA erfccs(19) / .0000000000 00015901e0 /
103  DATA erfccs(20) / -.0000000000 00004729e0 /
104  DATA erfccs(21) / .0000000000 00001432e0 /
105  DATA erfccs(22) / -.0000000000 00000439e0 /
106  DATA erfccs(23) / .0000000000 00000138e0 /
107  DATA erfccs(24) / -.0000000000 00000048e0 /
108  DATA sqrtpi /1.772453850 9055160e0/
109  DATA first /.true./
110 C***FIRST EXECUTABLE STATEMENT ERFC
111  IF (first) THEN
112  eta = 0.1*r1mach(3)
113  nterf = inits(erfcs, 13, eta)
114  nterfc = inits(erfccs, 24, eta)
115  nterc2 = inits(erc2cs, 23, eta)
116 C
117  xsml = -sqrt(-log(sqrtpi*r1mach(3)))
118  txmax = sqrt(-log(sqrtpi*r1mach(1)))
119  xmax = txmax - 0.5*log(txmax)/txmax - 0.01
120  sqeps = sqrt(2.0*r1mach(3))
121  ENDIF
122  first = .false.
123 C
124  IF (isnan(x)) THEN
125  erfc = x
126  RETURN
127  ENDIF
128 C
129  IF (x.GT.xsml) go to 20
130 C
131 C ERFC(X) = 1.0 - ERF(X) FOR X .LT. XSML
132 C
133  erfc = 2.
134  RETURN
135 C
136  20 IF (x.GT.xmax) go to 40
137  y = abs(x)
138  IF (y.GT.1.0) go to 30
139 C
140 C ERFC(X) = 1.0 - ERF(X) FOR -1. .LE. X .LE. 1.
141 C
142  IF (y.LT.sqeps) erfc = 1.0 - 2.0*x/sqrtpi
143  IF (y.GE.sqeps) erfc = 1.0 -
144  1 x*(1.0 + csevl(2.*x*x-1., erfcs, nterf) )
145  RETURN
146 C
147 C ERFC(X) = 1.0 - ERF(X) FOR 1. .LT. ABS(X) .LE. XMAX
148 C
149  30 y = y*y
150  IF (y.LE.4.) erfc = exp(-y)/abs(x) * (0.5 + csevl((8./y-5.)/3.,
151  1 erc2cs, nterc2) )
152  IF (y.GT.4.) erfc = exp(-y)/abs(x) * (0.5 + csevl(8./y-1.,
153  1 erfccs, nterfc) )
154  IF (x.LT.0.) erfc = 2.0 - erfc
155  RETURN
156 C
157  40 erfc = 0.
158  RETURN
159 C
160  END
function inits(OS, NOS, ETA)
Definition: inits.f:2
function csevl(X, CS, N)
Definition: csevl.f:2
function erfc(X)
Definition: erfc.f:2
OCTAVE_EXPORT octave_value_list or N dimensional array whose elements are all equal to the base of natural logarithms The constant ex $e satisfies the equation log(e)
int exp(void) const
Definition: DET.h:66
is false
Definition: cellfun.cc:398
may be zero for pure relative error test tem the relative tolerance must be greater than or equal to
Definition: Quad-opts.cc:233
OCTAVE_EXPORT octave_value_list etc The functions then dimension(columns)
OCTAVE_EXPORT octave_value_list return the value of the option it must match the dimension of the state and the relative tolerance must also be a vector of the same length tem it must match the dimension of the state and the absolute tolerance must also be a vector of the same length The local error test applied at each integration step is xample roup abs(local error in x(i))<
octave_value sqrt(void) const
Definition: ov.h:1388