Mercurial > octave-nkf
annotate libcruft/slatec-fn/derfc.f @ 14392:d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
numerical underflow or NaN values.
* slatec-fn/atanh,f (ATANH): Returns infinity for +-1 and NaN for >1
* slatec-fn/datanh.f (DATANH): Likewise.
* slatec-fn/erfc.f (ERFC): Returns NaN for Nan input.
* slatec-fn/derfc.f (DERFC): Likewise.
| author | Michael Goffioul <michael.goffioul@gmail.com> |
|---|---|
| date | Thu, 23 Feb 2012 09:12:47 +0000 |
| parents | 30c606bec7a8 |
| children |
| rev | line source |
|---|---|
| 2329 | 1 *DECK DERFC |
| 2 DOUBLE PRECISION FUNCTION DERFC (X) | |
| 3 C***BEGIN PROLOGUE DERFC | |
| 4 C***PURPOSE Compute the complementary error function. | |
| 5 C***LIBRARY SLATEC (FNLIB) | |
| 6 C***CATEGORY C8A, L5A1E | |
| 7 C***TYPE DOUBLE 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 DERFC(X) calculates the double precision complementary error function | |
| 14 C for double precision argument X. | |
| 15 C | |
| 16 C Series for ERF on the interval 0. to 1.00000E+00 | |
| 17 C with weighted Error 1.28E-32 | |
| 18 C log weighted Error 31.89 | |
| 19 C significant figures required 31.05 | |
| 20 C decimal places required 32.55 | |
| 21 C | |
| 22 C Series for ERC2 on the interval 2.50000E-01 to 1.00000E+00 | |
| 23 C with weighted Error 2.67E-32 | |
| 24 C log weighted Error 31.57 | |
| 25 C significant figures required 30.31 | |
| 26 C decimal places required 32.42 | |
| 27 C | |
| 28 C Series for ERFC on the interval 0. to 2.50000E-01 | |
| 29 C with weighted error 1.53E-31 | |
| 30 C log weighted error 30.82 | |
| 31 C significant figures required 29.47 | |
| 32 C decimal places required 31.70 | |
| 33 C | |
| 34 C***REFERENCES (NONE) | |
| 35 C***ROUTINES CALLED D1MACH, DCSEVL, INITDS, 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 DERFC | |
| 44 DOUBLE PRECISION X, ERFCS(21), ERFCCS(59), ERC2CS(49), SQEPS, | |
| 45 1 SQRTPI, XMAX, TXMAX, XSML, Y, D1MACH, DCSEVL | |
| 46 LOGICAL FIRST | |
| 47 SAVE ERFCS, ERC2CS, ERFCCS, SQRTPI, NTERF, | |
| 48 1 NTERFC, NTERC2, XSML, XMAX, SQEPS, FIRST | |
| 49 DATA ERFCS( 1) / -.4904612123 4691808039 9845440333 76 D-1 / | |
| 50 DATA ERFCS( 2) / -.1422612051 0371364237 8247418996 31 D+0 / | |
| 51 DATA ERFCS( 3) / +.1003558218 7599795575 7546767129 33 D-1 / | |
| 52 DATA ERFCS( 4) / -.5768764699 7674847650 8270255091 67 D-3 / | |
| 53 DATA ERFCS( 5) / +.2741993125 2196061034 4221607914 71 D-4 / | |
| 54 DATA ERFCS( 6) / -.1104317550 7344507604 1353812959 05 D-5 / | |
| 55 DATA ERFCS( 7) / +.3848875542 0345036949 9613114981 74 D-7 / | |
| 56 DATA ERFCS( 8) / -.1180858253 3875466969 6317518015 81 D-8 / | |
| 57 DATA ERFCS( 9) / +.3233421582 6050909646 4029309533 54 D-10 / | |
| 58 DATA ERFCS( 10) / -.7991015947 0045487581 6073747085 95 D-12 / | |
| 59 DATA ERFCS( 11) / +.1799072511 3961455611 9672454866 34 D-13 / | |
| 60 DATA ERFCS( 12) / -.3718635487 8186926382 3168282094 93 D-15 / | |
| 61 DATA ERFCS( 13) / +.7103599003 7142529711 6899083946 66 D-17 / | |
| 62 DATA ERFCS( 14) / -.1261245511 9155225832 4954248533 33 D-18 / | |
| 63 DATA ERFCS( 15) / +.2091640694 1769294369 1705002666 66 D-20 / | |
| 64 DATA ERFCS( 16) / -.3253973102 9314072982 3641600000 00 D-22 / | |
| 65 DATA ERFCS( 17) / +.4766867209 7976748332 3733333333 33 D-24 / | |
| 66 DATA ERFCS( 18) / -.6598012078 2851343155 1999999999 99 D-26 / | |
| 67 DATA ERFCS( 19) / +.8655011469 9637626197 3333333333 33 D-28 / | |
| 68 DATA ERFCS( 20) / -.1078892517 7498064213 3333333333 33 D-29 / | |
| 69 DATA ERFCS( 21) / +.1281188399 3017002666 6666666666 66 D-31 / | |
| 70 DATA ERC2CS( 1) / -.6960134660 2309501127 3915082619 7 D-1 / | |
| 71 DATA ERC2CS( 2) / -.4110133936 2620893489 8221208466 6 D-1 / | |
| 72 DATA ERC2CS( 3) / +.3914495866 6896268815 6114370524 4 D-2 / | |
| 73 DATA ERC2CS( 4) / -.4906395650 5489791612 8093545077 4 D-3 / | |
| 74 DATA ERC2CS( 5) / +.7157479001 3770363807 6089414182 5 D-4 / | |
| 75 DATA ERC2CS( 6) / -.1153071634 1312328338 0823284791 2 D-4 / | |
| 76 DATA ERC2CS( 7) / +.1994670590 2019976350 5231486770 9 D-5 / | |
| 77 DATA ERC2CS( 8) / -.3642666471 5992228739 3611843071 1 D-6 / | |
| 78 DATA ERC2CS( 9) / +.6944372610 0050125899 3127721463 3 D-7 / | |
| 79 DATA ERC2CS( 10) / -.1371220902 1043660195 3460514121 0 D-7 / | |
| 80 DATA ERC2CS( 11) / +.2788389661 0071371319 6386034808 7 D-8 / | |
| 81 DATA ERC2CS( 12) / -.5814164724 3311615518 6479105031 6 D-9 / | |
| 82 DATA ERC2CS( 13) / +.1238920491 7527531811 8016881795 0 D-9 / | |
| 83 DATA ERC2CS( 14) / -.2690639145 3067434323 9042493788 9 D-10 / | |
| 84 DATA ERC2CS( 15) / +.5942614350 8479109824 4470968384 0 D-11 / | |
| 85 DATA ERC2CS( 16) / -.1332386735 7581195792 8775442057 0 D-11 / | |
| 86 DATA ERC2CS( 17) / +.3028046806 1771320171 7369724330 4 D-12 / | |
| 87 DATA ERC2CS( 18) / -.6966648814 9410325887 9586758895 4 D-13 / | |
| 88 DATA ERC2CS( 19) / +.1620854541 0539229698 1289322762 8 D-13 / | |
| 89 DATA ERC2CS( 20) / -.3809934465 2504919998 7691305772 9 D-14 / | |
| 90 DATA ERC2CS( 21) / +.9040487815 9788311493 6897101297 5 D-15 / | |
| 91 DATA ERC2CS( 22) / -.2164006195 0896073478 0981204700 3 D-15 / | |
| 92 DATA ERC2CS( 23) / +.5222102233 9958549846 0798024417 2 D-16 / | |
| 93 DATA ERC2CS( 24) / -.1269729602 3645553363 7241552778 0 D-16 / | |
| 94 DATA ERC2CS( 25) / +.3109145504 2761975838 3622741295 1 D-17 / | |
| 95 DATA ERC2CS( 26) / -.7663762920 3203855240 0956671481 1 D-18 / | |
| 96 DATA ERC2CS( 27) / +.1900819251 3627452025 3692973329 0 D-18 / | |
| 97 DATA ERC2CS( 28) / -.4742207279 0690395452 2565599996 5 D-19 / | |
| 98 DATA ERC2CS( 29) / +.1189649200 0765283828 8068307845 1 D-19 / | |
| 99 DATA ERC2CS( 30) / -.3000035590 3257802568 4527131306 6 D-20 / | |
| 100 DATA ERC2CS( 31) / +.7602993453 0432461730 1938527709 8 D-21 / | |
| 101 DATA ERC2CS( 32) / -.1935909447 6068728815 6981104913 0 D-21 / | |
| 102 DATA ERC2CS( 33) / +.4951399124 7733378810 0004238677 3 D-22 / | |
| 103 DATA ERC2CS( 34) / -.1271807481 3363718796 0862198988 8 D-22 / | |
| 104 DATA ERC2CS( 35) / +.3280049600 4695130433 1584165205 3 D-23 / | |
| 105 DATA ERC2CS( 36) / -.8492320176 8228965689 2479242239 9 D-24 / | |
| 106 DATA ERC2CS( 37) / +.2206917892 8075602235 1987998719 9 D-24 / | |
| 107 DATA ERC2CS( 38) / -.5755617245 6965284983 1281950719 9 D-25 / | |
| 108 DATA ERC2CS( 39) / +.1506191533 6392342503 5414405119 9 D-25 / | |
| 109 DATA ERC2CS( 40) / -.3954502959 0187969531 0428569599 9 D-26 / | |
| 110 DATA ERC2CS( 41) / +.1041529704 1515009799 8464505173 3 D-26 / | |
| 111 DATA ERC2CS( 42) / -.2751487795 2787650794 5017890133 3 D-27 / | |
| 112 DATA ERC2CS( 43) / +.7290058205 4975574089 9770368000 0 D-28 / | |
| 113 DATA ERC2CS( 44) / -.1936939645 9159478040 7750109866 6 D-28 / | |
| 114 DATA ERC2CS( 45) / +.5160357112 0514872983 7005482666 6 D-29 / | |
| 115 DATA ERC2CS( 46) / -.1378419322 1930940993 8964480000 0 D-29 / | |
| 116 DATA ERC2CS( 47) / +.3691326793 1070690422 5109333333 3 D-30 / | |
| 117 DATA ERC2CS( 48) / -.9909389590 6243654206 5322666666 6 D-31 / | |
| 118 DATA ERC2CS( 49) / +.2666491705 1953884133 2394666666 6 D-31 / | |
| 119 DATA ERFCCS( 1) / +.7151793102 0292477450 3697709496 D-1 / | |
| 120 DATA ERFCCS( 2) / -.2653243433 7606715755 8893386681 D-1 / | |
| 121 DATA ERFCCS( 3) / +.1711153977 9208558833 2699194606 D-2 / | |
| 122 DATA ERFCCS( 4) / -.1637516634 5851788416 3746404749 D-3 / | |
| 123 DATA ERFCCS( 5) / +.1987129350 0552036499 5974806758 D-4 / | |
| 124 DATA ERFCCS( 6) / -.2843712412 7665550875 0175183152 D-5 / | |
| 125 DATA ERFCCS( 7) / +.4606161308 9631303696 9379968464 D-6 / | |
| 126 DATA ERFCCS( 8) / -.8227753025 8792084205 7766536366 D-7 / | |
| 127 DATA ERFCCS( 9) / +.1592141872 7709011298 9358340826 D-7 / | |
| 128 DATA ERFCCS( 10) / -.3295071362 2528432148 6631665072 D-8 / | |
| 129 DATA ERFCCS( 11) / +.7223439760 4005554658 1261153890 D-9 / | |
| 130 DATA ERFCCS( 12) / -.1664855813 3987295934 4695966886 D-9 / | |
| 131 DATA ERFCCS( 13) / +.4010392588 2376648207 7671768814 D-10 / | |
| 132 DATA ERFCCS( 14) / -.1004816214 4257311327 2170176283 D-10 / | |
| 133 DATA ERFCCS( 15) / +.2608275913 3003338085 9341009439 D-11 / | |
| 134 DATA ERFCCS( 16) / -.6991110560 4040248655 7697812476 D-12 / | |
| 135 DATA ERFCCS( 17) / +.1929492333 2617070862 4205749803 D-12 / | |
| 136 DATA ERFCCS( 18) / -.5470131188 7543310649 0125085271 D-13 / | |
| 137 DATA ERFCCS( 19) / +.1589663309 7626974483 9084032762 D-13 / | |
| 138 DATA ERFCCS( 20) / -.4726893980 1975548392 0369584290 D-14 / | |
| 139 DATA ERFCCS( 21) / +.1435873376 7849847867 2873997840 D-14 / | |
| 140 DATA ERFCCS( 22) / -.4449510561 8173583941 7250062829 D-15 / | |
| 141 DATA ERFCCS( 23) / +.1404810884 7682334373 7305537466 D-15 / | |
| 142 DATA ERFCCS( 24) / -.4513818387 7642108962 5963281623 D-16 / | |
| 143 DATA ERFCCS( 25) / +.1474521541 0451330778 7018713262 D-16 / | |
| 144 DATA ERFCCS( 26) / -.4892621406 9457761543 6841552532 D-17 / | |
| 145 DATA ERFCCS( 27) / +.1647612141 4106467389 5301522827 D-17 / | |
| 146 DATA ERFCCS( 28) / -.5626817176 3294080929 9928521323 D-18 / | |
| 147 DATA ERFCCS( 29) / +.1947443382 2320785142 9197867821 D-18 / | |
| 148 DATA ERFCCS( 30) / -.6826305642 9484207295 6664144723 D-19 / | |
| 149 DATA ERFCCS( 31) / +.2421988887 2986492401 8301125438 D-19 / | |
| 150 DATA ERFCCS( 32) / -.8693414133 5030704256 3800861857 D-20 / | |
| 151 DATA ERFCCS( 33) / +.3155180346 2280855712 2363401262 D-20 / | |
| 152 DATA ERFCCS( 34) / -.1157372324 0496087426 1239486742 D-20 / | |
| 153 DATA ERFCCS( 35) / +.4288947161 6056539462 3737097442 D-21 / | |
| 154 DATA ERFCCS( 36) / -.1605030742 0576168500 5737770964 D-21 / | |
| 155 DATA ERFCCS( 37) / +.6063298757 4538026449 5069923027 D-22 / | |
| 156 DATA ERFCCS( 38) / -.2311404251 6979584909 8840801367 D-22 / | |
| 157 DATA ERFCCS( 39) / +.8888778540 6618855255 4702955697 D-23 / | |
| 158 DATA ERFCCS( 40) / -.3447260576 6513765223 0718495566 D-23 / | |
| 159 DATA ERFCCS( 41) / +.1347865460 2069650682 7582774181 D-23 / | |
| 160 DATA ERFCCS( 42) / -.5311794071 1250217364 5873201807 D-24 / | |
| 161 DATA ERFCCS( 43) / +.2109341058 6197831682 8954734537 D-24 / | |
| 162 DATA ERFCCS( 44) / -.8438365587 9237891159 8133256738 D-25 / | |
| 163 DATA ERFCCS( 45) / +.3399982524 9452089062 7359576337 D-25 / | |
| 164 DATA ERFCCS( 46) / -.1379452388 0732420900 2238377110 D-25 / | |
| 165 DATA ERFCCS( 47) / +.5634490311 8332526151 3392634811 D-26 / | |
| 166 DATA ERFCCS( 48) / -.2316490434 4770654482 3427752700 D-26 / | |
| 167 DATA ERFCCS( 49) / +.9584462844 6018101526 3158381226 D-27 / | |
| 168 DATA ERFCCS( 50) / -.3990722880 3301097262 4224850193 D-27 / | |
| 169 DATA ERFCCS( 51) / +.1672129225 9444773601 7228709669 D-27 / | |
| 170 DATA ERFCCS( 52) / -.7045991522 7660138563 8803782587 D-28 / | |
| 171 DATA ERFCCS( 53) / +.2979768402 8642063541 2357989444 D-28 / | |
| 172 DATA ERFCCS( 54) / -.1262522466 4606192972 2422632994 D-28 / | |
| 173 DATA ERFCCS( 55) / +.5395438704 5424879398 5299653154 D-29 / | |
| 174 DATA ERFCCS( 56) / -.2380992882 5314591867 5346190062 D-29 / | |
| 175 DATA ERFCCS( 57) / +.1099052830 1027615735 9726683750 D-29 / | |
| 176 DATA ERFCCS( 58) / -.4867713741 6449657273 2518677435 D-30 / | |
| 177 DATA ERFCCS( 59) / +.1525877264 1103575676 3200828211 D-30 / | |
| 178 DATA SQRTPI / 1.772453850 9055160272 9816748334 115D0 / | |
| 179 DATA FIRST /.TRUE./ | |
| 180 C***FIRST EXECUTABLE STATEMENT DERFC | |
| 181 IF (FIRST) THEN | |
| 182 ETA = 0.1*REAL(D1MACH(3)) | |
| 183 NTERF = INITDS (ERFCS, 21, ETA) | |
| 184 NTERFC = INITDS (ERFCCS, 59, ETA) | |
| 185 NTERC2 = INITDS (ERC2CS, 49, ETA) | |
| 186 C | |
| 187 XSML = -SQRT(-LOG(SQRTPI*D1MACH(3))) | |
| 188 TXMAX = SQRT(-LOG(SQRTPI*D1MACH(1))) | |
| 189 XMAX = TXMAX - 0.5D0*LOG(TXMAX)/TXMAX - 0.01D0 | |
| 190 SQEPS = SQRT(2.0D0*D1MACH(3)) | |
| 191 ENDIF | |
| 192 FIRST = .FALSE. | |
| 193 C | |
|
14392
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
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194 IF (ISNAN(X)) THEN |
|
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
|
195 DERFC = X |
|
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
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196 RETURN |
|
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
|
197 ENDIF |
|
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
|
198 C |
| 2329 | 199 IF (X.GT.XSML) GO TO 20 |
| 200 C | |
| 201 C ERFC(X) = 1.0 - ERF(X) FOR X .LT. XSML | |
| 202 C | |
| 203 DERFC = 2.0D0 | |
| 204 RETURN | |
| 205 C | |
| 206 20 IF (X.GT.XMAX) GO TO 40 | |
| 207 Y = ABS(X) | |
| 208 IF (Y.GT.1.0D0) GO TO 30 | |
| 209 C | |
| 210 C ERFC(X) = 1.0 - ERF(X) FOR ABS(X) .LE. 1.0 | |
| 211 C | |
| 212 IF (Y.LT.SQEPS) DERFC = 1.0D0 - 2.0D0*X/SQRTPI | |
| 213 IF (Y.GE.SQEPS) DERFC = 1.0D0 - X*(1.0D0 + DCSEVL (2.D0*X*X-1.D0, | |
| 214 1 ERFCS, NTERF)) | |
| 215 RETURN | |
| 216 C | |
| 217 C ERFC(X) = 1.0 - ERF(X) FOR 1.0 .LT. ABS(X) .LE. XMAX | |
| 218 C | |
| 219 30 Y = Y*Y | |
| 220 IF (Y.LE.4.D0) DERFC = EXP(-Y)/ABS(X) * (0.5D0 + DCSEVL ( | |
| 221 1 (8.D0/Y-5.D0)/3.D0, ERC2CS, NTERC2) ) | |
| 222 IF (Y.GT.4.D0) DERFC = EXP(-Y)/ABS(X) * (0.5D0 + DCSEVL ( | |
| 223 1 8.D0/Y-1.D0, ERFCCS, NTERFC) ) | |
| 224 IF (X.LT.0.D0) DERFC = 2.0D0 - DERFC | |
| 225 RETURN | |
| 226 C | |
|
14392
d17237256856
Make SLATEC-FN atanh/erfc functions more tolerant about edge cases like
Michael Goffioul <michael.goffioul@gmail.com>
parents:
2329
diff
changeset
|
227 40 DERFC = 0.D0 |
| 2329 | 228 RETURN |
| 229 C | |
| 230 END |