fvn_fnlib.f90 21.1 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949
module fvn_fnlib

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! This module is a generic interface for fn library
! http://www.netlib.org/fn
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Elementary Functions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Argument
interface carg
      real(4) function carg(z)
            complex(4) :: z
      end function carg
      real(8) function zarg(z)
            complex(8) :: z
      end function zarg
end interface carg

! Cubic root
interface cbrt
      real(4) function cbrt(x)
            real(4) :: x
      end function cbrt
      real(8) function dcbrt(x)
            real(8) :: x
      end function dcbrt
      complex(4) function ccbrt(z)
            complex(4) :: z
      end function ccbrt
      complex(8) function zcbrt(z)
            complex(8) :: z
      end function zcbrt
end interface cbrt

! (exp(x) -1)/x
interface exprl
      real(4) function exprel(x)
            real(4) :: x
      end function exprel
      real(8) function dexprl(x)
            real(8) :: x
      end function dexprl
      complex(4) function cexprl(z)
            complex(4) :: z
      end function cexprl
      complex(8) function zexprl(z)
            complex(8) :: z
      end function zexprl
end interface exprl

! log10 extension to complex arguments
interface log10
      complex(4) function clog10(z)
            complex(4) :: z
      end function clog10
      complex(8) function zlog10(z)
            complex(8) :: z
      end function zlog10
end interface log10 

! ln(x+1)
interface alnrel
      real(4) function alnrel(x)
            real(4) :: x
      end function alnrel
      real(8) function dlnrel(x)
            real(8) :: x
      end function dlnrel
      complex(4) function clnrel(z)
            complex(4) :: z
      end function clnrel
      complex(8) function zlnrel(z)
            complex(8) :: z
      end function zlnrel
end interface alnrel

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Elementary Functions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Extension de la tangente aux arguments complexes
interface tan
      complex(4) function ctan(z)
            complex(4) :: z
      end function ctan
      complex(8) function ztan(z)
            complex(8) :: z
      end function ztan
end interface tan

! Cotangente
interface cot
      real(4) function cot(x)
            real(4) :: x
      end function cot
      real(8) function dcot(x)
            real(8) :: x
      end function dcot
      complex(4) function ccot(z)
            complex(4) :: z
      end function ccot
      complex(8) function zcot(z)
            complex(8) :: z
      end function zcot
end interface cot

! Sinus in degree
interface sindg
      real(4) function sindg(x)
            real(4) :: x
      end function sindg
      real(8) function dsindg(x)
            real(8) :: x
      end function dsindg
end interface sindg

! Cosinus in degree
interface cosdg
      real(4) function cosdg(x)
            real(4) :: x
      end function cosdg
      real(8) function dcosdg(x)
            real(8) :: x
      end function dcosdg
end interface cosdg


! Extension de l'arcsinus aux arguments complexes
interface asin
      complex(4) function casin(z)
            complex(4) :: z
      end function casin
      complex(8) function zasin(z)
            complex(8) :: z
      end function zasin
end interface asin

! Extension de l'arccosinus aux arguments complexes
interface acos
      complex(4) function cacos(z)
            complex(4) :: z
      end function cacos
      complex(8) function zacos(z)
            complex(8) :: z
      end function zacos
end interface acos

! Extension de l'arctangente aux arguments complexes
interface atan
      complex(4) function catan(z)
            complex(4) :: z
      end function catan
      complex(8) function zatan(z)
            complex(8) :: z
      end function zatan
end interface atan

! Extension de atan2 aux arguments complexes
interface atan2
      complex(4) function catan2(csn,ccs)
            complex(4) :: csn,ccs
      end function catan2
      complex(8) function zatan2(csn,ccs)
            complex(8) :: csn,ccs
      end function zatan2
end interface atan2


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Hyperbolic Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Extension du Sinus hyperbolique aux arguments complexes
interface sinh
      complex(4) function csinh(z)
            complex(4) :: z
      end function csinh
      complex(8) function zsinh(z)
            complex(8) :: z
      end function zsinh
end interface sinh

! Extension du Cosinus hyperbolique aux arguments complexes
interface cosh
      complex(4) function ccosh(z)
            complex(4) :: z
      end function ccosh
      complex(8) function zcosh(z)
            complex(8) :: z
      end function zcosh
end interface cosh

! Extension de la tangente hyperbolique aux arguments complexes
interface tanh
      complex(4) function ctanh(z)
            complex(4) :: z
      end function ctanh
      complex(8) function ztanh(z)
            complex(8) :: z
      end function ztanh
end interface tanh

! Arc sinus hyperbolique
interface asinh
      real(4) function asinh(x)
            real(4) :: x
      end function asinh
      real(8) function dasinh(x)
            real(8) :: x
      end function dasinh
      complex(4) function casinh(z)
            complex(4) :: z
      end function casinh
      complex(8) function zasinh(z)
            complex(8) :: z
      end function zasinh
end interface asinh

! Arc cosinus hyperbolique
interface acosh
      real(4) function acosh(x)
            real(4) :: x
      end function acosh
      real(8) function dacosh(x)
            real(8) :: x
      end function dacosh
      complex(4) function cacosh(z)
            complex(4) :: z
      end function cacosh
      complex(8) function zacosh(z)
            complex(8) :: z
      end function zacosh
end interface acosh

! Arc tangente hyperbolique
interface atanh
      real(4) function atanh(x)
            real(4) :: x
      end function atanh
      real(8) function datanh(x)
            real(8) :: x
      end function datanh
      complex(4) function catanh(z)
            complex(4) :: z
      end function catanh
      complex(8) function zatanh(z)
            complex(8) :: z
      end function zatanh
end interface atanh

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Trigonometry
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Exponential integral and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Exponential integral ei(x)
interface ei
      real(4) function ei(x)
            real(4) :: x
      end function ei
      real(8) function dei(x)
            real(8) :: x
      end function dei
end interface ei

! Exponential integral e1(x)
interface e1
      real(4) function e1(x)
            real(4) :: x
      end function e1
      real(8) function de1(x)
            real(8) :: x
      end function de1
end interface e1

!!!!!!!!!!!!!!!
! MISSING ENE
!!!!!!!!!!!!!!!

! Logarithm integral
interface ali
      real(4) function ali(x)
            real(4) :: x
      end function ali
      real(8) function dli(x)
            real(8) :: x
      end function dli
end interface ali

! Sine integral
interface si
      real(4) function si(x)
            real(4) :: x
      end function si
      real(8) function dsi(x)
            real(8) :: x
      end function dsi
end interface si

! Cosine integral
interface ci
      real(4) function ci(x)
            real(4) :: x
      end function ci
      real(8) function dci(x)
            real(8) :: x
      end function dci
end interface ci

! Cosine integral alternate definition
interface cin
      real(4) function cin(x)
            real(4) :: x
      end function cin
      real(8) function dcin(x)
            real(8) :: x
      end function dcin
end interface cin

! Hyperbolic sine integral
interface shi
      real(4) function shi(x)
            real(4) :: x
      end function shi
      real(8) function dshi(x)
            real(8) :: x
      end function dshi
end interface shi

! Hyperbolic cosine integral
interface chi
      real(4) function chi(x)
            real(4) :: x
      end function chi
      real(8) function dchi(x)
            real(8) :: x
      end function dchi
end interface chi

! Hyperbolic cosine integral alternate definition
interface cinh
      real(4) function cinh(x)
            real(4) :: x
      end function cinh
      real(8) function dcinh(x)
            real(8) :: x
      end function dcinh
end interface cinh

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Exponential integral and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Gamma family
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! No generic interface for fac and binom but we still
! define their prototypes
! Factorial
interface
      real(4) function fac(n)
            integer(4) :: n
      end function fac
      real(8) function dfac(n)
            integer(4) :: n
      end function dfac
! Binomial coefficient
      real(4) function binom(n,m)
            integer(4) :: n,m
      end function binom
      real(8) function dbinom(n,m)
            integer(4) :: n,m
      end function dbinom
end interface

! Gamma function
interface gamma
      real(4) function gamma(x)
            real(4) :: x
      end function gamma
      real(8) function dgamma(x)
            real(8) :: x
      end function dgamma
      complex(4) function cgamma(z)
            complex(4) :: z
      end function cgamma
      complex(8) function zgamma(z)
            complex(8) :: z
      end function zgamma
end interface gamma

! Reciprocal of gamma function
interface gamr
      real(4) function gamr(x)
            real(4) :: x
      end function gamr
      real(8) function dgamr(x)
            real(8) :: x
      end function dgamr
      complex(4) function cgamr(z)
            complex(4) :: z
      end function cgamr
      complex(8) function zgamr(z)
            complex(8) :: z
      end function zgamr
end interface gamr

! natural log of abs(gamma)
interface alngam
      real(4) function alngam(x)
            real(4) :: x
      end function alngam
      real(8) function dlngam(x)
            real(8) :: x
      end function dlngam
      complex(4) function clngam(z)
            complex(4) :: z
      end function clngam
      complex(8) function zlngam(z)
            complex(8) :: z
      end function zlngam
end interface alngam

! log abs gamma and sign
interface algams
      subroutine algams(x,algam,sgngam)
            real(4) :: x
      end subroutine algams
      subroutine dlgams(x,algam,sgngam)
            real(8) :: x
      end subroutine dlgams
end interface algams

! Incomplete gamma function
interface gami
      real(4) function gami(a,x)
            real(4) :: a,x
      end function gami
      real(8) function dgami(a,x)
            real(8) :: a,x
      end function dgami
end interface gami

! Complementary incomplete gamma function
interface gamic
      real(4) function gamic(a,x)
            real(4) :: a,x
      end function gamic
      real(8) function dgamic(a,x)
            real(8) :: a,x
      end function dgamic
end interface gamic

! Tricomi's incomplete gamma function
interface gamit
      real(4) function gamit(a,x)
            real(4) :: a,x
      end function gamit
      real(8) function dgamit(a,x)
            real(8) :: a,x
      end function dgamit
end interface gamit

! Psi function
interface psi
      real(4) function psi(x)
            real(4) :: x
      end function psi
      real(8) function dpsi(x)
            real(8) :: x
      end function dpsi
      complex(4) function cpsi(z)
            complex(4) :: z
      end function cpsi
      complex(8) function zpsi(z)
            complex(8) :: z
      end function zpsi
end interface psi

! Pochhammer
interface poch
      real(4) function poch(a,x)
            real(4) :: a,x
      end function poch
      real(8) function dpoch(a,x)
            real(8) :: a,x
      end function dpoch
end interface poch

! Pochhammer first order
interface poch1
      real(4) function poch1(a,x)
            real(4) :: a,x
      end function poch1
      real(8) function dpoch1(a,x)
            real(8) :: a,x
      end function dpoch1
end interface poch1

! Beta function
interface beta
      real(4) function beta(a,b)
            real(4) :: a,b
      end function beta
      real(8) function dbeta(a,b)
            real(8) :: a,b
      end function dbeta
      complex(4) function cbeta(a,b)
            complex(4) :: a,b
      end function cbeta
      complex(8) function zbeta(a,b)
            complex(8) :: a,b
      end function zbeta
end interface beta

! natural log of beta
interface albeta
      real(4) function albeta(a,b)
            real(4) :: a,b
      end function albeta
      real(8) function dlbeta(a,b)
            real(8) :: a,b
      end function dlbeta
      complex(4) function clbeta(a,b)
            complex(4) :: a,b
      end function clbeta
      complex(8) function zlbeta(a,b)
            complex(8) :: a,b
      end function zlbeta
end interface albeta

! Incomplete beta function
interface betai
      real(4) function betai(x,pin,qin)
            real(4) :: x,pin,qin
      end function betai
      real(8) function dbetai(x,pin,qin)
            real(8) :: x,pin,qin
      end function dbetai
end interface betai

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Gamma family
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Error function and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Error function
interface erf
      real(4) function erf(x)
            real(4) :: x
      end function erf
      real(8) function derf(x)
            real(8) :: x
      end function derf
end interface erf

! Complementary error function
interface erfc
      real(4) function erfc(x)
            real(4) :: x
      end function erfc
      real(8) function derfc(x)
            real(8) :: x
      end function derfc
end interface erfc

!!!!!!!!!!!
! MISSING ERFCE
! MISSING CERFI
! MISSING ERFI
! MISSING ERFCI
!!!!!!!!!!!!!!

! Dawson's function
interface daws
      real(4) function daws(x)
            real(4) :: x
      end function daws
      real(8) function ddaws(x)
            real(8) :: x
      end function ddaws
end interface daws

!!!!!!!!!!!!!!!!!
! MISSING FRESC
! MISSING FRESS
!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Error function and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Bessel functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!J0(x)
interface bsj0
      real(4) function besj0(x)
            real(4) :: x
      end function besj0
      real(8) function dbesj0(x)
            real(8) :: x
      end function dbesj0
end interface bsj0

!J1(x)
interface bsj1
      real(4) function besj1(x)
            real(4) :: x
      end function besj1
      real(8) function dbesj1(x)
            real(8) :: x
      end function dbesj1
end interface bsj1

!Y0(x)
interface bsy0
      real(4) function besy0(x)
            real(4) :: x
      end function besy0
      real(8) function dbesy0(x)
            real(8) x
      end function dbesy0
end interface bsy0

!Y1(x)
interface bsy1
      real(4) function besy1(x)
            real(4) :: x
      end function besy1
      real(8) function dbesy1(x)
            real(8) x
      end function dbesy1
end interface bsy1

!I0(x)
interface bsi0
      real(4) function besi0(x)
            real(4) :: x
      end function besi0
      real(8) function dbesi0(x)
            real(8) x
      end function dbesi0
end interface bsi0

!I1(x)
interface bsi1
      real(4) function besi1(x)
            real(4) :: x
      end function besi1
      real(8) function dbesi1(x)
            real(8) x
      end function dbesi1
end interface bsi1

!K0(x)
interface bsk0
      real(4) function besk0(x)
            real(4) :: x
      end function besk0
      real(8) function dbesk0(x)
            real(8) x
      end function dbesk0
end interface bsk0

!K1(x)
interface bsk1
      real(4) function besk1(x)
            real(4) :: x
      end function besk1
      real(8) function dbesk1(x)
            real(8) x
      end function dbesk1
end interface bsk1

! Exponentially scaled I0
interface bsi0e
      real(4) function besi0e(x)
            real(4) :: x
      end function besi0e
      real(8) function dbsi0e(x)
            real(8) :: x
      end function dbsi0e
end interface bsi0e

! Exponentially scaled I1
interface bsi1e
      real(4) function besi1e(x)
            real(4) :: x
      end function besi1e
      real(8) function dbsi1e(x)
            real(8) :: x
      end function dbsi1e
end interface bsi1e

! Exponentially scaled K0
interface bsk0e
      real(4) function besk0e(x)
            real(4) :: x
      end function besk0e
      real(8) function dbsk0e(x)
            real(8) :: x
      end function dbsk0e
end interface bsk0e

! Exponentially scaled K1
interface bsk1e
      real(4) function besk1e(x)
            real(4) :: x
      end function besk1e
      real(8) function dbsk1e(x)
            real(8) :: x
      end function dbsk1e
end interface bsk1e

!!!!!!!!!!!!!!!!!!!!!
! MISSING BSJNS
! MISSING BSINS
! MISSING BSJS
! MISSING BSYS
! MISSING BSIS
! MISSING BSIES
!!!!!!!!!!!!!!!!!!!!!

! K nu + k
interface bsks
      subroutine besks(xnu,x,nin,bk)
            real(4) :: xnu,x
            integer :: nin
            real(4), dimension(nin) :: bk
      end subroutine besks
      subroutine dbesks(xnu,x,nin,bk)
            real(8) :: xnu,x
            integer :: nin
            real(8), dimension(nin) :: bk
      end subroutine dbesks
end interface bsks

! Exponentially scaled K nu + k
interface bskes
      subroutine beskes(xnu,x,nin,bke)
            real(4) :: xnu,x
            integer :: nin
            real(4),dimension(nin) :: bke
      end subroutine beskes
      subroutine dbskes(xnu,x,nin,bke)
            real(8) :: xnu,x
            integer :: nin
            real(8),dimension(nin) :: bke
      end subroutine dbskes
end interface bskes

!!!!!!!!!!!!!!!!!!
! MISSING CBJS
! MISSING CBYS
! MISSING CBIS
!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Bessel functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Airy functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!ai(x)
interface ai
      real(4) function ai(x)
            real(4) :: x
      end function ai
      real(8) function dai(x)
            real(8) :: x
      end function dai
end interface ai

!bi(x)
interface bi
      real(4) function bi(x)
            real(4) :: x
      end function bi
      real(8) function dbi(x)
            real(8) :: x
      end function dbi
end interface bi

!ai'(x)
interface aid
      real(4) function aid(x)
            real(4) :: x
      end function aid
      real(8) function daid(x)
            real(8) :: x
      end function daid
end interface aid

!bi'(x)
interface bid
      real(4) function bid(x)
            real(4) :: x
      end function bid
      real(8) function dbid(x)
            real(8) :: x
      end function dbid
end interface bid

! Exponentially scaled Ai
interface aie
      real(4) function aie(x)
            real(4) :: x
      end function aie
      real(8) function daie(x)
            real(8) :: x
      end function daie
end interface aie

! Exponentially scaled Bi
interface bie
      real(4) function bie(x)
            real(4) :: x
      end function bie
      real(8) function dbie(x)
            real(8) :: x
      end function dbie
end interface bie

! Exponentially scaled Ai'(x)
interface aide
      real(4) function aide(x)
            real(4) :: x
      end function aide
      real(8) function daide(x)
            real(8) :: x
      end function daide
end interface aide

! Exponentially scaled Bi'(x)
interface bide
      real(4) function bide(x)
            real(4) :: x
      end function bide
      real(8) function dbide(x)
            real(8) :: x
      end function dbide
end interface bide

!!!!!!!!!!!!!!!!!!!!!!!
! MISSING CAI
! MISSING CBI
! MISSING CAID
! MISSING CBID
!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Airy functions and related
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Miscellanous functions 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Spence dilogarithm
interface spenc
      real(4) function spenc(x)
            real(4) :: x
      end function spenc
      real(8) function dspenc(x)
            real(8) :: x
      end function dspenc
end interface spenc

! Initialize a Chebyshev series
interface inits
      integer(4) function inits(os,nos,eta)
            real(4),dimension(nos) :: os
            integer(4) :: nos
            real(4) :: eta
      end function inits
      integer(4) function initds(dos,nos,eta)
            real(8),dimension(nos) :: dos
            integer(4) :: nos
            real(4) :: eta
      end function initds
end interface inits

! Evaluate a Chebyshev series
interface csevl
      real(4) function csevl(x,cs,n)
            real(4) :: x
            real(4),dimension(n) :: cs
            integer(4) :: n
      end function csevl
      real(8) function dcsevl(x,a,n)
            real(8) :: x
            real(8), dimension(n) :: a
            integer(4) :: n
      end function dcsevl
end interface csevl


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! END Miscellanous functions 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!





end module fvn_fnlib