Mercurial > octave-nkf
view libcruft/amos/cunik.f @ 7789:82be108cc558
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 |
| parents | |
| children |
line wrap: on
line source
SUBROUTINE CUNIK(ZR, FNU, IKFLG, IPMTR, TOL, INIT, PHI, ZETA1, * ZETA2, SUM, CWRK) C***BEGIN PROLOGUE CUNIK C***REFER TO CBESI,CBESK C C CUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC C EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 C RESPECTIVELY BY C C W(FNU,ZR) = PHI*EXP(ZETA)*SUM C C WHERE ZETA=-ZETA1 + ZETA2 OR C ZETA1 - ZETA2 C C THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE C SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= C 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK C ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, C ZETA1,ZETA2. C C***ROUTINES CALLED (NONE) C***END PROLOGUE CUNIK COMPLEX CFN, CON, CONE, CRFN, CWRK, CZERO, PHI, S, SR, SUM, T, * T2, ZETA1, ZETA2, ZN, ZR REAL AC, C, FNU, RFN, TEST, TOL, TSTR, TSTI INTEGER I, IKFLG, INIT, IPMTR, J, K, L DIMENSION C(120), CWRK(16), CON(2) DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) / DATA CON(1), CON(2) / 1(3.98942280401432678E-01,0.0E0),(1.25331413731550025E+00,0.0E0)/ DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), 2 C(19), C(20), C(21), C(22), C(23), C(24)/ 3 1.00000000000000000E+00, -2.08333333333333333E-01, 4 1.25000000000000000E-01, 3.34201388888888889E-01, 5 -4.01041666666666667E-01, 7.03125000000000000E-02, 6 -1.02581259645061728E+00, 1.84646267361111111E+00, 7 -8.91210937500000000E-01, 7.32421875000000000E-02, 8 4.66958442342624743E+00, -1.12070026162229938E+01, 9 8.78912353515625000E+00, -2.36408691406250000E+00, A 1.12152099609375000E-01, -2.82120725582002449E+01, B 8.46362176746007346E+01, -9.18182415432400174E+01, C 4.25349987453884549E+01, -7.36879435947963170E+00, D 2.27108001708984375E-01, 2.12570130039217123E+02, E -7.65252468141181642E+02, 1.05999045252799988E+03/ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ 3 -6.99579627376132541E+02, 2.18190511744211590E+02, 4 -2.64914304869515555E+01, 5.72501420974731445E-01, 5 -1.91945766231840700E+03, 8.06172218173730938E+03, 6 -1.35865500064341374E+04, 1.16553933368645332E+04, 7 -5.30564697861340311E+03, 1.20090291321635246E+03, 8 -1.08090919788394656E+02, 1.72772750258445740E+00, 9 2.02042913309661486E+04, -9.69805983886375135E+04, A 1.92547001232531532E+05, -2.03400177280415534E+05, B 1.22200464983017460E+05, -4.11926549688975513E+04, C 7.10951430248936372E+03, -4.93915304773088012E+02, D 6.07404200127348304E+00, -2.42919187900551333E+05, E 1.31176361466297720E+06, -2.99801591853810675E+06/ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ 3 3.76327129765640400E+06, -2.81356322658653411E+06, 4 1.26836527332162478E+06, -3.31645172484563578E+05, 5 4.52187689813627263E+04, -2.49983048181120962E+03, 6 2.43805296995560639E+01, 3.28446985307203782E+06, 7 -1.97068191184322269E+07, 5.09526024926646422E+07, 8 -7.41051482115326577E+07, 6.63445122747290267E+07, 9 -3.75671766607633513E+07, 1.32887671664218183E+07, A -2.78561812808645469E+06, 3.08186404612662398E+05, B -1.38860897537170405E+04, 1.10017140269246738E+02, C -4.93292536645099620E+07, 3.25573074185765749E+08, D -9.39462359681578403E+08, 1.55359689957058006E+09, E -1.62108055210833708E+09, 1.10684281682301447E+09/ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ 3 -4.95889784275030309E+08, 1.42062907797533095E+08, 4 -2.44740627257387285E+07, 2.24376817792244943E+06, 5 -8.40054336030240853E+04, 5.51335896122020586E+02, 6 8.14789096118312115E+08, -5.86648149205184723E+09, 7 1.86882075092958249E+10, -3.46320433881587779E+10, 8 4.12801855797539740E+10, -3.30265997498007231E+10, 9 1.79542137311556001E+10, -6.56329379261928433E+09, A 1.55927986487925751E+09, -2.25105661889415278E+08, B 1.73951075539781645E+07, -5.49842327572288687E+05, C 3.03809051092238427E+03, -1.46792612476956167E+10, D 1.14498237732025810E+11, -3.99096175224466498E+11, E 8.19218669548577329E+11, -1.09837515608122331E+12/ DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), 1 C(105), C(106), C(107), C(108), C(109), C(110), C(111), 2 C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ 3 1.00815810686538209E+12, -6.45364869245376503E+11, 4 2.87900649906150589E+11, -8.78670721780232657E+10, 5 1.76347306068349694E+10, -2.16716498322379509E+09, 6 1.43157876718888981E+08, -3.87183344257261262E+06, 7 1.82577554742931747E+04, 2.86464035717679043E+11, 8 -2.40629790002850396E+12, 9.10934118523989896E+12, 9 -2.05168994109344374E+13, 3.05651255199353206E+13, A -3.16670885847851584E+13, 2.33483640445818409E+13, B -1.23204913055982872E+13, 4.61272578084913197E+12, C -1.19655288019618160E+12, 2.05914503232410016E+11, D -2.18229277575292237E+10, 1.24700929351271032E+09/ DATA C(119), C(120)/ 1 -2.91883881222208134E+07, 1.18838426256783253E+05/ C IF (INIT.NE.0) GO TO 40 C----------------------------------------------------------------------- C INITIALIZE ALL VARIABLES C----------------------------------------------------------------------- RFN = 1.0E0/FNU CRFN = CMPLX(RFN,0.0E0) C T = ZR*CRFN C----------------------------------------------------------------------- C OVERFLOW TEST (ZR/FNU TOO SMALL) C----------------------------------------------------------------------- TSTR = REAL(ZR) TSTI = AIMAG(ZR) TEST = R1MACH(1)*1.0E+3 AC = FNU*TEST IF (ABS(TSTR).GT.AC .OR. ABS(TSTI).GT.AC) GO TO 15 AC = 2.0E0*ABS(ALOG(TEST))+FNU ZETA1 = CMPLX(AC,0.0E0) ZETA2 = CMPLX(FNU,0.0E0) PHI=CONE RETURN 15 CONTINUE T=ZR*CRFN S = CONE + T*T SR = CSQRT(S) CFN = CMPLX(FNU,0.0E0) ZN = (CONE+SR)/T ZETA1 = CFN*CLOG(ZN) ZETA2 = CFN*SR T = CONE/SR SR = T*CRFN CWRK(16) = CSQRT(SR) PHI = CWRK(16)*CON(IKFLG) IF (IPMTR.NE.0) RETURN T2 = CONE/S CWRK(1) = CONE CRFN = CONE AC = 1.0E0 L = 1 DO 20 K=2,15 S = CZERO DO 10 J=1,K L = L + 1 S = S*T2 + CMPLX(C(L),0.0E0) 10 CONTINUE CRFN = CRFN*SR CWRK(K) = CRFN*S AC = AC*RFN TSTR = REAL(CWRK(K)) TSTI = AIMAG(CWRK(K)) TEST = ABS(TSTR) + ABS(TSTI) IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 20 CONTINUE K = 15 30 CONTINUE INIT = K 40 CONTINUE IF (IKFLG.EQ.2) GO TO 60 C----------------------------------------------------------------------- C COMPUTE SUM FOR THE I FUNCTION C----------------------------------------------------------------------- S = CZERO DO 50 I=1,INIT S = S + CWRK(I) 50 CONTINUE SUM = S PHI = CWRK(16)*CON(1) RETURN 60 CONTINUE C----------------------------------------------------------------------- C COMPUTE SUM FOR THE K FUNCTION C----------------------------------------------------------------------- S = CZERO T = CONE DO 70 I=1,INIT S = S + T*CWRK(I) T = -T 70 CONTINUE SUM = S PHI = CWRK(16)*CON(2) RETURN END