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3111
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1 *DECK DLNREL |
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2 DOUBLE PRECISION FUNCTION DLNREL (X) |
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3 C***BEGIN PROLOGUE DLNREL |
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4 C***PURPOSE Evaluate ln(1+X) accurate in the sense of relative error. |
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5 C***LIBRARY SLATEC (FNLIB) |
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6 C***CATEGORY C4B |
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7 C***TYPE DOUBLE PRECISION (ALNREL-S, DLNREL-D, CLNREL-C) |
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8 C***KEYWORDS ELEMENTARY FUNCTIONS, FNLIB, LOGARITHM |
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9 C***AUTHOR Fullerton, W., (LANL) |
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10 C***DESCRIPTION |
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11 C |
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12 C DLNREL(X) calculates the double precision natural logarithm of |
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13 C (1.0+X) for double precision argument X. This routine should |
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14 C be used when X is small and accurate to calculate the logarithm |
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15 C accurately (in the relative error sense) in the neighborhood |
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16 C of 1.0. |
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17 C |
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18 C Series for ALNR on the interval -3.75000E-01 to 3.75000E-01 |
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19 C with weighted error 6.35E-32 |
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20 C log weighted error 31.20 |
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21 C significant figures required 30.93 |
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22 C decimal places required 32.01 |
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23 C |
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24 C***REFERENCES (NONE) |
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25 C***ROUTINES CALLED D1MACH, DCSEVL, INITDS, XERMSG |
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26 C***REVISION HISTORY (YYMMDD) |
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27 C 770601 DATE WRITTEN |
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28 C 890531 Changed all specific intrinsics to generic. (WRB) |
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29 C 890531 REVISION DATE from Version 3.2 |
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30 C 891214 Prologue converted to Version 4.0 format. (BAB) |
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31 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) |
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32 C***END PROLOGUE DLNREL |
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33 DOUBLE PRECISION ALNRCS(43), X, XMIN, DCSEVL, D1MACH |
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34 LOGICAL FIRST |
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35 SAVE ALNRCS, NLNREL, XMIN, FIRST |
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36 DATA ALNRCS( 1) / +.1037869356 2743769800 6862677190 98 D+1 / |
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37 DATA ALNRCS( 2) / -.1336430150 4908918098 7660415531 33 D+0 / |
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38 DATA ALNRCS( 3) / +.1940824913 5520563357 9261993747 50 D-1 / |
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39 DATA ALNRCS( 4) / -.3010755112 7535777690 3765377765 92 D-2 / |
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40 DATA ALNRCS( 5) / +.4869461479 7154850090 4563665091 37 D-3 / |
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41 DATA ALNRCS( 6) / -.8105488189 3175356066 8099430086 22 D-4 / |
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42 DATA ALNRCS( 7) / +.1377884779 9559524782 9382514960 59 D-4 / |
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43 DATA ALNRCS( 8) / -.2380221089 4358970251 3699929149 35 D-5 / |
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44 DATA ALNRCS( 9) / +.4164041621 3865183476 3918599019 89 D-6 / |
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45 DATA ALNRCS( 10) / -.7359582837 8075994984 2668370319 98 D-7 / |
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46 DATA ALNRCS( 11) / +.1311761187 6241674949 1522943450 11 D-7 / |
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47 DATA ALNRCS( 12) / -.2354670931 7742425136 6960923301 75 D-8 / |
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48 DATA ALNRCS( 13) / +.4252277327 6034997775 6380529625 67 D-9 / |
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49 DATA ALNRCS( 14) / -.7719089413 4840796826 1081074933 00 D-10 / |
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50 DATA ALNRCS( 15) / +.1407574648 1359069909 2153564721 91 D-10 / |
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51 DATA ALNRCS( 16) / -.2576907205 8024680627 5370786275 84 D-11 / |
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52 DATA ALNRCS( 17) / +.4734240666 6294421849 1543950059 38 D-12 / |
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53 DATA ALNRCS( 18) / -.8724901267 4742641745 3012632926 75 D-13 / |
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54 DATA ALNRCS( 19) / +.1612461490 2740551465 7398331191 15 D-13 / |
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55 DATA ALNRCS( 20) / -.2987565201 5665773006 7107924168 15 D-14 / |
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56 DATA ALNRCS( 21) / +.5548070120 9082887983 0413216972 79 D-15 / |
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57 DATA ALNRCS( 22) / -.1032461915 8271569595 1413339619 32 D-15 / |
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58 DATA ALNRCS( 23) / +.1925023920 3049851177 8785032448 68 D-16 / |
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59 DATA ALNRCS( 24) / -.3595507346 5265150011 1897078442 66 D-17 / |
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60 DATA ALNRCS( 25) / +.6726454253 7876857892 1945742267 73 D-18 / |
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61 DATA ALNRCS( 26) / -.1260262416 8735219252 0824256375 46 D-18 / |
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62 DATA ALNRCS( 27) / +.2364488440 8606210044 9161589555 19 D-19 / |
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63 DATA ALNRCS( 28) / -.4441937705 0807936898 8783891797 33 D-20 / |
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64 DATA ALNRCS( 29) / +.8354659446 4034259016 2412939946 66 D-21 / |
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65 DATA ALNRCS( 30) / -.1573155941 6479562574 8992535210 66 D-21 / |
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66 DATA ALNRCS( 31) / +.2965312874 0247422686 1543697066 66 D-22 / |
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67 DATA ALNRCS( 32) / -.5594958348 1815947292 1560132266 66 D-23 / |
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68 DATA ALNRCS( 33) / +.1056635426 8835681048 1872841386 66 D-23 / |
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69 DATA ALNRCS( 34) / -.1997248368 0670204548 3149994666 66 D-24 / |
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70 DATA ALNRCS( 35) / +.3778297781 8839361421 0498559999 99 D-25 / |
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71 DATA ALNRCS( 36) / -.7153158688 9081740345 0381653333 33 D-26 / |
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72 DATA ALNRCS( 37) / +.1355248846 3674213646 5020245333 33 D-26 / |
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73 DATA ALNRCS( 38) / -.2569467304 8487567430 0798293333 33 D-27 / |
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74 DATA ALNRCS( 39) / +.4874775606 6216949076 4595199999 99 D-28 / |
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75 DATA ALNRCS( 40) / -.9254211253 0849715321 1323733333 33 D-29 / |
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76 DATA ALNRCS( 41) / +.1757859784 1760239233 2697600000 00 D-29 / |
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77 DATA ALNRCS( 42) / -.3341002667 7731010351 3770666666 66 D-30 / |
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78 DATA ALNRCS( 43) / +.6353393618 0236187354 1802666666 66 D-31 / |
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79 DATA FIRST /.TRUE./ |
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80 C***FIRST EXECUTABLE STATEMENT DLNREL |
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81 IF (FIRST) THEN |
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82 NLNREL = INITDS (ALNRCS, 43, 0.1*REAL(D1MACH(3))) |
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83 XMIN = -1.0D0 + SQRT(D1MACH(4)) |
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84 ENDIF |
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85 FIRST = .FALSE. |
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86 C |
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87 IF (X .LE. (-1.D0)) CALL XERMSG ('SLATEC', 'DLNREL', 'X IS LE -1' |
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88 + , 2, 2) |
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89 IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'DLNREL', |
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90 + 'ANSWER LT HALF PRECISION BECAUSE X TOO NEAR -1', 1, 1) |
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91 C |
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92 IF (ABS(X).LE.0.375D0) DLNREL = X*(1.D0 - |
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93 1 X*DCSEVL (X/.375D0, ALNRCS, NLNREL)) |
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94 C |
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95 IF (ABS(X).GT.0.375D0) DLNREL = LOG (1.0D0+X) |
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96 C |
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97 RETURN |
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98 END |
