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annotate libcruft/amos/cunik.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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children
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7789
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1 SUBROUTINE CUNIK(ZR, FNU, IKFLG, IPMTR, TOL, INIT, PHI, ZETA1,
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2 * ZETA2, SUM, CWRK)
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3 C***BEGIN PROLOGUE CUNIK
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4 C***REFER TO CBESI,CBESK
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5 C
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6 C CUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC
82be108cc558 First attempt at single precision tyeps
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7 C EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2
82be108cc558 First attempt at single precision tyeps
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8 C RESPECTIVELY BY
82be108cc558 First attempt at single precision tyeps
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9 C
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10 C W(FNU,ZR) = PHI*EXP(ZETA)*SUM
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11 C
82be108cc558 First attempt at single precision tyeps
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12 C WHERE ZETA=-ZETA1 + ZETA2 OR
82be108cc558 First attempt at single precision tyeps
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13 C ZETA1 - ZETA2
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14 C
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15 C THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE
82be108cc558 First attempt at single precision tyeps
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16 C SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG=
82be108cc558 First attempt at single precision tyeps
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17 C 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
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18 C ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
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19 C ZETA1,ZETA2.
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20 C
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21 C***ROUTINES CALLED (NONE)
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22 C***END PROLOGUE CUNIK
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23 COMPLEX CFN, CON, CONE, CRFN, CWRK, CZERO, PHI, S, SR, SUM, T,
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24 * T2, ZETA1, ZETA2, ZN, ZR
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25 REAL AC, C, FNU, RFN, TEST, TOL, TSTR, TSTI
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26 INTEGER I, IKFLG, INIT, IPMTR, J, K, L
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27 DIMENSION C(120), CWRK(16), CON(2)
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28 DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) /
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29 DATA CON(1), CON(2) /
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30 1(3.98942280401432678E-01,0.0E0),(1.25331413731550025E+00,0.0E0)/
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31 DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
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32 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
82be108cc558 First attempt at single precision tyeps
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33 2 C(19), C(20), C(21), C(22), C(23), C(24)/
82be108cc558 First attempt at single precision tyeps
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34 3 1.00000000000000000E+00, -2.08333333333333333E-01,
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35 4 1.25000000000000000E-01, 3.34201388888888889E-01,
82be108cc558 First attempt at single precision tyeps
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36 5 -4.01041666666666667E-01, 7.03125000000000000E-02,
82be108cc558 First attempt at single precision tyeps
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37 6 -1.02581259645061728E+00, 1.84646267361111111E+00,
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38 7 -8.91210937500000000E-01, 7.32421875000000000E-02,
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39 8 4.66958442342624743E+00, -1.12070026162229938E+01,
82be108cc558 First attempt at single precision tyeps
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40 9 8.78912353515625000E+00, -2.36408691406250000E+00,
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41 A 1.12152099609375000E-01, -2.82120725582002449E+01,
82be108cc558 First attempt at single precision tyeps
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42 B 8.46362176746007346E+01, -9.18182415432400174E+01,
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43 C 4.25349987453884549E+01, -7.36879435947963170E+00,
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44 D 2.27108001708984375E-01, 2.12570130039217123E+02,
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45 E -7.65252468141181642E+02, 1.05999045252799988E+03/
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46 DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
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47 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
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48 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
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49 3 -6.99579627376132541E+02, 2.18190511744211590E+02,
82be108cc558 First attempt at single precision tyeps
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50 4 -2.64914304869515555E+01, 5.72501420974731445E-01,
82be108cc558 First attempt at single precision tyeps
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51 5 -1.91945766231840700E+03, 8.06172218173730938E+03,
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52 6 -1.35865500064341374E+04, 1.16553933368645332E+04,
82be108cc558 First attempt at single precision tyeps
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53 7 -5.30564697861340311E+03, 1.20090291321635246E+03,
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54 8 -1.08090919788394656E+02, 1.72772750258445740E+00,
82be108cc558 First attempt at single precision tyeps
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55 9 2.02042913309661486E+04, -9.69805983886375135E+04,
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56 A 1.92547001232531532E+05, -2.03400177280415534E+05,
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57 B 1.22200464983017460E+05, -4.11926549688975513E+04,
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58 C 7.10951430248936372E+03, -4.93915304773088012E+02,
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59 D 6.07404200127348304E+00, -2.42919187900551333E+05,
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60 E 1.31176361466297720E+06, -2.99801591853810675E+06/
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61 DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
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62 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
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63 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
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64 3 3.76327129765640400E+06, -2.81356322658653411E+06,
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65 4 1.26836527332162478E+06, -3.31645172484563578E+05,
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66 5 4.52187689813627263E+04, -2.49983048181120962E+03,
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67 6 2.43805296995560639E+01, 3.28446985307203782E+06,
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68 7 -1.97068191184322269E+07, 5.09526024926646422E+07,
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69 8 -7.41051482115326577E+07, 6.63445122747290267E+07,
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70 9 -3.75671766607633513E+07, 1.32887671664218183E+07,
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71 A -2.78561812808645469E+06, 3.08186404612662398E+05,
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72 B -1.38860897537170405E+04, 1.10017140269246738E+02,
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73 C -4.93292536645099620E+07, 3.25573074185765749E+08,
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74 D -9.39462359681578403E+08, 1.55359689957058006E+09,
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75 E -1.62108055210833708E+09, 1.10684281682301447E+09/
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76 DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
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77 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
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78 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
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79 3 -4.95889784275030309E+08, 1.42062907797533095E+08,
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80 4 -2.44740627257387285E+07, 2.24376817792244943E+06,
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81 5 -8.40054336030240853E+04, 5.51335896122020586E+02,
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82 6 8.14789096118312115E+08, -5.86648149205184723E+09,
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83 7 1.86882075092958249E+10, -3.46320433881587779E+10,
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84 8 4.12801855797539740E+10, -3.30265997498007231E+10,
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85 9 1.79542137311556001E+10, -6.56329379261928433E+09,
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86 A 1.55927986487925751E+09, -2.25105661889415278E+08,
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87 B 1.73951075539781645E+07, -5.49842327572288687E+05,
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88 C 3.03809051092238427E+03, -1.46792612476956167E+10,
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89 D 1.14498237732025810E+11, -3.99096175224466498E+11,
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90 E 8.19218669548577329E+11, -1.09837515608122331E+12/
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91 DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
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92 1 C(105), C(106), C(107), C(108), C(109), C(110), C(111),
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93 2 C(112), C(113), C(114), C(115), C(116), C(117), C(118)/
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94 3 1.00815810686538209E+12, -6.45364869245376503E+11,
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95 4 2.87900649906150589E+11, -8.78670721780232657E+10,
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96 5 1.76347306068349694E+10, -2.16716498322379509E+09,
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97 6 1.43157876718888981E+08, -3.87183344257261262E+06,
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98 7 1.82577554742931747E+04, 2.86464035717679043E+11,
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99 8 -2.40629790002850396E+12, 9.10934118523989896E+12,
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100 9 -2.05168994109344374E+13, 3.05651255199353206E+13,
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101 A -3.16670885847851584E+13, 2.33483640445818409E+13,
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102 B -1.23204913055982872E+13, 4.61272578084913197E+12,
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103 C -1.19655288019618160E+12, 2.05914503232410016E+11,
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104 D -2.18229277575292237E+10, 1.24700929351271032E+09/
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105 DATA C(119), C(120)/
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106 1 -2.91883881222208134E+07, 1.18838426256783253E+05/
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107 C
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108 IF (INIT.NE.0) GO TO 40
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109 C-----------------------------------------------------------------------
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110 C INITIALIZE ALL VARIABLES
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111 C-----------------------------------------------------------------------
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112 RFN = 1.0E0/FNU
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113 CRFN = CMPLX(RFN,0.0E0)
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114 C T = ZR*CRFN
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115 C-----------------------------------------------------------------------
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116 C OVERFLOW TEST (ZR/FNU TOO SMALL)
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117 C-----------------------------------------------------------------------
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118 TSTR = REAL(ZR)
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119 TSTI = AIMAG(ZR)
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120 TEST = R1MACH(1)*1.0E+3
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121 AC = FNU*TEST
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122 IF (ABS(TSTR).GT.AC .OR. ABS(TSTI).GT.AC) GO TO 15
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123 AC = 2.0E0*ABS(ALOG(TEST))+FNU
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124 ZETA1 = CMPLX(AC,0.0E0)
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125 ZETA2 = CMPLX(FNU,0.0E0)
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126 PHI=CONE
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127 RETURN
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128 15 CONTINUE
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129 T=ZR*CRFN
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130 S = CONE + T*T
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131 SR = CSQRT(S)
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132 CFN = CMPLX(FNU,0.0E0)
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133 ZN = (CONE+SR)/T
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134 ZETA1 = CFN*CLOG(ZN)
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135 ZETA2 = CFN*SR
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136 T = CONE/SR
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137 SR = T*CRFN
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138 CWRK(16) = CSQRT(SR)
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139 PHI = CWRK(16)*CON(IKFLG)
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140 IF (IPMTR.NE.0) RETURN
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141 T2 = CONE/S
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142 CWRK(1) = CONE
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143 CRFN = CONE
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144 AC = 1.0E0
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145 L = 1
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146 DO 20 K=2,15
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147 S = CZERO
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148 DO 10 J=1,K
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149 L = L + 1
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150 S = S*T2 + CMPLX(C(L),0.0E0)
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151 10 CONTINUE
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152 CRFN = CRFN*SR
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153 CWRK(K) = CRFN*S
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154 AC = AC*RFN
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155 TSTR = REAL(CWRK(K))
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156 TSTI = AIMAG(CWRK(K))
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157 TEST = ABS(TSTR) + ABS(TSTI)
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158 IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30
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159 20 CONTINUE
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160 K = 15
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161 30 CONTINUE
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162 INIT = K
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163 40 CONTINUE
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164 IF (IKFLG.EQ.2) GO TO 60
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165 C-----------------------------------------------------------------------
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166 C COMPUTE SUM FOR THE I FUNCTION
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167 C-----------------------------------------------------------------------
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168 S = CZERO
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169 DO 50 I=1,INIT
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170 S = S + CWRK(I)
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171 50 CONTINUE
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172 SUM = S
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173 PHI = CWRK(16)*CON(1)
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174 RETURN
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175 60 CONTINUE
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176 C-----------------------------------------------------------------------
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177 C COMPUTE SUM FOR THE K FUNCTION
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178 C-----------------------------------------------------------------------
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179 S = CZERO
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180 T = CONE
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181 DO 70 I=1,INIT
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182 S = S + T*CWRK(I)
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183 T = -T
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184 70 CONTINUE
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185 SUM = S
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186 PHI = CWRK(16)*CON(2)
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parents:
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187 RETURN
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188 END