-
Notifications
You must be signed in to change notification settings - Fork 41
/
fn.html
939 lines (899 loc) · 29.5 KB
/
fn.html
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
<html>
<head>
<title>
FN - The Fullerton Function Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FN <br> The Fullerton Function Library.
</h1>
<hr>
<p>
<b>FN</b>
is a C++ library which
evaluates elementary and special functions using Chebyshev polynomials;
functions include Airy, Bessel I, J, K and Y, beta, confluent
hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals
include hyperbolic cosine, cosine, Dawson, exponential, logarithmic,
hyperbolic sine, sine; by Wayne Fullerton.
</p>
<p>
The original version of the library provided routines for
complex, single precision real, and double precision real arguments
and used the prefixes "C" and "D" to indicate the complex
and double precision versions.
</p>
<p>
This scheme has been modified for consistency, and also
to avoid conflict with the names of functions commonly
provided by various compilers. The prefixes "C4_", "R4_"
and "R8_" are used to indicate functions for complex,
single precision real, and double precision real arguments.
For example, the sine function can be calculated by the functions
<b>C4_SIN</b>, <b>R4_SIN</b> or <b>R8_SIN</b>.
</p>
<p>
The original, true, correct version of FN
is available through NETLIB:
<a href = "http://www.netlib.org/fn/index.html">
http://www.netlib.org/fn/index.html</a>.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FN</b> is available in
<a href = "../../c_src/fn/fn.html">a C version</a> and
<a href = "../../cpp_src/fn/fn.html">a C++ version</a> and
<a href = "../../f77_src/fn/fn.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fn/fn.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fn/fn.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/c4lib/c4lib.html">
C4LIB</a>,
a C++ library which
implements certain elementary functions for "C4"
or single precision complex variables
using the C++ "complex <float>" datatype.
</p>
<p>
<a href = "../../cpp_src/c8lib/c8lib.html">
C8LIB</a>,
a C++ library which
implements certain elementary functions for "C8"
or double precision complex variables
using the C++ "complex <double>" datatype.
</p>
<p>
<a href = "../../cpp_src/chebyshev_series/chebyshev_series.html">
CHEBYSHEV_SERIES</a>,
a C++ library which
can evaluate a Chebyshev series approximating a function f(x),
while efficiently computing one, two or three derivatives of the
series, which approximate f'(x), f''(x), and f'''(x).
</p>
<p>
<a href = "../../cpp_src/cordic/cordic.html">
CORDIC</a>,
a C++ library which
uses the CORDIC method to compute certain elementary functions.
</p>
<p>
<a href = "../../cpp_src/g++_intrinsics/g++_intrinsics.html">
G++_INTRINSICS</a>,
a C++ program which
tests or demonstrates some of the intrinsic functions provided
by the G++ compiler.
</p>
<p>
<a href = "../../cpp_src/legendre_polynomial/legendre_polynomial.html">
LEGENDRE_POLYNOMIAL</a>,
a C++ library which
evaluates the Legendre polynomial and associated functions.
</p>
<p>
<a href = "../../cpp_src/machar/machar.html">
MACHAR</a>,
a C++ library which
computes the appropriate values of machine constants for a given machine.
</p>
<p>
<a href = "../../cpp_src/machine/machine.html">
MACHINE</a>,
a C++ library which
stores the appropriate values of machine constants for a given machine.
</p>
<p>
<a href = "../../cpp_src/r4lib/r4lib.html">
R4LIB</a>,
a C++ library which
contains many utility routines, using "R4" or
"single precision real" arithmetic.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines, using "R8" or
"double precision real" arithmetic.
</p>
<p>
<a href = "../../cpp_src/test_values/test_values.html">
TEST_VALUES</a>,
a C++ library which
supplies test values of various mathematical functions.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Roger Broucke,<br>
Algorithm 446:
Ten Subroutines for the Manipulation of Chebyshev Series,<br>
Communications of the ACM,<br>
Volume 16, Number 4, April 1973, pages 254-256.
</li>
<li>
William Cody,<br>
ACM Algorithm 665, MACHAR, a subroutine to dynamically determine
machine parameters,<br>
ACM Transactions on Mathematical Software,<br>
Volume 14, Number 4, pages 303-311, 1988.
</li>
<li>
William Cody, William Waite,<br>
Software Manual for the Elementary Functions,<br>
Prentice Hall, 1980.
<li>
Phyllis Fox, Andrew Hall, Norman Schryer,<br>
Algorithm 528,
Framework for a Portable Library,<br>
ACM Transactions on Mathematical Software,<br>
Volume 4, Number 2, June 1978, page 176-188.
</li>
<li>
Wayne Fullerton,<br>
Portable Special Function Routines,<br>
in Portability of Numerical Software,<br>
edited by Wayne Cowell,<br>
Lecture Notes in Computer Science, Volume 57, pages 452-483,<br>
Springer 1977,<br>
ISBN: 978-3-540-08446-4,<br>
LC: QA297.W65.
</li>
<li>
Malcolm Pike, David Hill,<br>
Algorithm 266:
Pseudo-Random Numbers,<br>
Communications of the ACM,<br>
Volume 8, Number 10, October 1965, page 605.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fn.cpp">fn.cpp</a>, the source code.
</li>
<li>
<a href = "fn.hpp">fn.hpp</a>, the include file.
</li>
<li>
<a href = "fn.sh">fn.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fn_prb.cpp">fn_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "fn_prb.sh">fn_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "fn_prb_output.txt">fn_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>FN_PRB2</b> looks at the system sine and cosine functions,
versus R8_SIN and R8_COS.
<ul>
<li>
<a href = "fn_prb2.c">fn_prb2.c</a>,
a sample calling program.
</li>
<li>
<a href = "fn_prb2.sh">fn_prb2.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "fn_prb2_output.txt">fn_prb2_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_COS</b> evaluates the cosine of a C4 argument.
</li>
<li>
<b>C4_SIN</b> evaluates the sine of a C4 argument.
</li>
<li>
<b>I4_ABS</b> returns the absolute value of an I4.
</li>
<li>
<b>I4_MACH</b> returns integer machine constants.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_POW</b> returns the value of I^J.
</li>
<li>
<b>R4_ABS</b> returns the absolute value of an R4.
</li>
<li>
<b>R4_ACOS</b> evaluates the arc-cosine of an R4 argument.
</li>
<li>
<b>R4_ACOSH</b> evaluates the arc-hyperbolic cosine of an R4 argument.
</li>
<li>
<b>R4_ADMP:</b> modulus and phase of the derivative of the Airy function.
</li>
<li>
<b>R4_AI</b> evaluates the Airy function Ai of an R4 argument.
</li>
<li>
<b>R4_AID</b> evaluates the derivative of the Airy function Ai of an R4 argument.
</li>
<li>
<b>R4_AIDE:</b> exponentially scaled derivative, Airy function Ai of an R4 argument.
</li>
<li>
<b>R4_AIE</b> evaluates the exponential scaled Airy function Ai of an R4 argument.
</li>
<li>
<b>R4_AIMP</b> evaluates the modulus and phase of the Airy function.
</li>
<li>
<b>R4_AINT</b> truncates an R4 argument to an integer.
</li>
<li>
<b>R4_ASIN</b> evaluates the arc-sine of an R4 argument.
</li>
<li>
<b>R4_ASINH</b> evaluates the arc-sine of an R4 argument.
</li>
<li>
<b>R4_ATAN</b> evaluates the arc-tangent of an R4 argument.
</li>
<li>
<b>R4_ATAN2</b> evaluates the arc-tangent of two R4 arguments.
</li>
<li>
<b>R4_ATANH</b> evaluates the arc-hyperbolic tangent of an R4 argument.
</li>
<li>
<b>R4_BESI0</b> evaluates the Bessel function I of order 0 of an R4 argument.
</li>
<li>
<b>R4_BESI0E</b> evaluates the exponentially scaled Bessel function I0(X).
</li>
<li>
<b>R4_BESI1</b> evaluates the Bessel function I of order 1 of an R4 argument.
</li>
<li>
<b>R4_BESJ0</b> evaluates the Bessel function J of order 0 of an R4 argument.
</li>
<li>
<b>R4_BESJ1</b> evaluates the Bessel function J of order 1 of an R4 argument.
</li>
<li>
<b>R4_BESK0</b> evaluates the Bessel function K of order 0 of an R4 argument.
</li>
<li>
<b>R4_BESK0E</b> evaluates the exponentially scaled Bessel function K0(X).
</li>
<li>
<b>R4_BESK1</b> evaluates the Bessel function K of order 1 of an R4 argument.
</li>
<li>
<b>R4_BESK1E</b> evaluates the exponentially scaled Bessel function K1(X).
</li>
<li>
<b>R4_BESKES</b> evaluates a sequence of exponentially scaled K Bessel functions at X.
</li>
<li>
<b>R4_BESKS</b> evaluates a sequence of K Bessel functions at X.
</li>
<li>
<b>R4_BESY0</b> evaluates the Bessel function Y of order 0 of an R4 argument.
</li>
<li>
<b>R4_BESY1</b> evaluates the Bessel function Y of order 1 of an R4 argument.
</li>
<li>
<b>R4_BETA</b> evaluates the beta function of R4 arguments.
</li>
<li>
<b>R4_BETAI</b> evaluates the incomplete beta ratio of R4 arguments.
</li>
<li>
<b>R4_BI</b> evaluates the Airy function Bi of an R4 argument.
</li>
<li>
<b>R4_BID</b> evaluates the derivative of the Airy function Bi of an R4 argument.
</li>
<li>
<b>R4_BIDE:</b> exponentially scaled derivative, Airy function Bi of an R4 argument.
</li>
<li>
<b>R4_BIE</b> evaluates the exponentially scaled Airy function Bi of an R4 argument.
</li>
<li>
<b>R4_BINOM</b> evaluates the binomial coefficient using R4 arithmetic.
</li>
<li>
<b>R4_CBRT</b> computes the cube root of an R4.
</li>
<li>
<b>R4_CHI</b> evaluates the hyperbolic cosine integral of an R4 argument.
</li>
<li>
<b>R4_CHU</b> evaluates the confluent hypergeometric function of R4 arguments.
</li>
<li>
<b>R4_CHU_SCALED:</b> scaled confluent hypergeometric function of R4 arguments.
</li>
<li>
<b>R4_CI</b> evaluates the cosine integral Ci of an R4 argument.
</li>
<li>
<b>R4_CIN</b> evaluates the alternate cosine integral Cin of an R4 argument.
</li>
<li>
<b>R4_CINH</b> evaluates the alternate hyperbolic cosine integral Cinh of an R4 argument.
</li>
<li>
<b>R4_COS</b> evaluates the cosine of an R4 argument.
</li>
<li>
<b>R4_COS_DEG</b> evaluates the cosine of an R4 argument in degrees.
</li>
<li>
<b>R4_COSH</b> evaluates the hyperbolic cosine of an R4 argument.
</li>
<li>
<b>R4_COT</b> evaluates the cotangent of an R4 argument.
</li>
<li>
<b>R4_CSEVL</b> evaluates a Chebyshev series.
</li>
<li>
<b>R4_DAWSON</b> evaluates Dawson's integral of an R4 argument.
</li>
<li>
<b>R4_E1</b> evaluates the exponential integral E1 for an R4 argument.
</li>
<li>
<b>R4_EI</b> evaluates the exponential integral Ei for an R4 argument.
</li>
<li>
<b>R4_ERF</b> evaluates the error function of an R4 argument.
</li>
<li>
<b>R4_ERFC</b> evaluates the co-error function of an R4 argument.
</li>
<li>
<b>R4_EXP</b> evaluates the exponential of an R4 argument.
</li>
<li>
<b>R4_EXPREL</b> evaluates the exponential relative error term of an R4 argument.
</li>
<li>
<b>R4_FAC</b> evaluates the factorial of an I4 argument.
</li>
<li>
<b>R4_GAMI</b> evaluates the incomplete gamma function for an R4 argument.
</li>
<li>
<b>R4_GAMIC</b> evaluates the complementary incomplete gamma function.
</li>
<li>
<b>R4_GAMIT</b> evaluates Tricomi's incomplete gamma function for an R4 argument.
</li>
<li>
<b>R4_GAML</b> evaluates bounds for an R4 argument of the gamma function.
</li>
<li>
<b>R4_GAMMA</b> evaluates the gamma function of an R4 argument.
</li>
<li>
<b>R4_GAMR</b> evaluates the reciprocal gamma function of an R4 argument.
</li>
<li>
<b>R4_GMIC:</b> complementary incomplete gamma, small X, A near negative integer.
</li>
<li>
<b>R4_GMIT:</b> Tricomi's incomplete gamma function for small X.
</li>
<li>
<b>R4_INITS</b> initializes a Chebyshev series.
</li>
<li>
<b>R4_INT</b> returns the integer part of an R4 argument.
</li>
<li>
<b>R4_KNUS</b> computes a sequence of K Bessel functions.
</li>
<li>
<b>R4_LBETA</b> evaluates the logarithm of the beta function of R4 arguments.
</li>
<li>
<b>R4_LGAMS</b> evaluates the log of |gamma(x)| and sign, for an R4 argument.
</li>
<li>
<b>R4_LGIC</b> evaluates the log complementary incomplete gamma function for large X.
</li>
<li>
<b>R4_LGIT</b> evaluates the log of Tricomi's incomplete gamma function.
</li>
<li>
<b>R4_LGMC</b> evaluates the log gamma correction factor for an R4 argument.
</li>
<li>
<b>R4_LI</b> evaluates the logarithmic integral for an R4 argument.
</li>
<li>
<b>R4_LNGAM</b> evaluates the log of the absolute value of gamma of an R4 argument.
</li>
<li>
<b>R4_LNREL</b> evaluates log ( 1 + X ) for an R4 argument.
</li>
<li>
<b>R4_LOG</b> evaluates the logarithm of an R4.
</li>
<li>
<b>R4_LOG10</b> evaluates the logarithm, base 10, of an R4.
</li>
<li>
<b>R4_MACH</b> returns single precision real machine constants.
</li>
<li>
<b>R4_MACHAR</b> computes machine constants for R4 arithmetic.
</li>
<li>
<b>R4_MAX</b> returns the maximum of two R4's.
</li>
<li>
<b>R4_MIN</b> returns the minimum of two R4's..
</li>
<li>
<b>R4_MOD</b> returns the remainder of R4 division.
</li>
<li>
<b>R4_MOP</b> returns the I-th power of -1 as an R4 value.
</li>
<li>
<b>R4_PAK</b> packs a base 2 exponent into an R4.
</li>
<li>
<b>R4_POCH</b> evaluates Pochhammer's function of R4 arguments.
</li>
<li>
<b>R4_POCH1</b> evaluates a quantity related to Pochhammer's symbol.
</li>
<li>
<b>R4_POW</b> evaluates A^B.
</li>
<li>
<b>R4_PSI</b> evaluates the psi function of an R4 argument.
</li>
<li>
<b>R4_RAND</b> is a portable pseudorandom number generator.
</li>
<li>
<b>R4_RANDGS</b> generates a normally distributed random number.
</li>
<li>
<b>R4_RANDOM</b> is a portable pseudorandom number generator.
</li>
<li>
<b>R4_RANF</b> is a driver for R4_RANDOM.
</li>
<li>
<b>R4_REN</b> is a simple random number generator.
</li>
<li>
<b>R4_SHI</b> evaluates the hyperbolic sine integral Shi of an R4 argument.
</li>
<li>
<b>R4_SI</b> evaluates the sine integral Si of an R4 argument.
</li>
<li>
<b>R4_SIFG</b> is a utility routine.
</li>
<li>
<b>R4_SIGN</b> returns the sign of an R4.
</li>
<li>
<b>R4_SIN</b> evaluates the sine of an R4 argument.
</li>
<li>
<b>R4_SIN_DEG</b> evaluates the sine of an R4 argument in degrees.
</li>
<li>
<b>R4_SINH</b> evaluates the hyperbolic sine of an R4 argument.
</li>
<li>
<b>R4_SPENCE</b> evaluates a form of Spence's function for an R4 argument.
</li>
<li>
<b>R4_SQRT</b> computes the square root of an R4.
</li>
<li>
<b>R4_TAN</b> evaluates the tangent of an R4 argument.
</li>
<li>
<b>R4_TANH</b> evaluates the hyperbolic tangent of an R4 argument.
</li>
<li>
<b>R4_UPAK</b> unpacks an R4 into a mantissa and exponent.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_ACOS</b> evaluates the arc-cosine of an R8 argument.
</li>
<li>
<b>R8_ACOSH</b> evaluates the arc-hyperbolic cosine of an R8 argument.
</li>
<li>
<b>R8_ADMP:</b> modulus and phase of the derivative of the Airy function.
</li>
<li>
<b>R8_AI</b> evaluates the Airy function Ai of an R8 argument.
</li>
<li>
<b>R8_AID</b> evaluates the derivative of the Airy function Ai of an R8 argument.
</li>
<li>
<b>R8_AIDE:</b> exponentially scaled derivative, Airy function Ai of an R8 argument.
</li>
<li>
<b>R8_AIE</b> evaluates the exponentially scaled Airy function Ai of an R8 argument.
</li>
<li>
<b>R8_AIMP</b> evaluates the modulus and phase of the Airy function.
</li>
<li>
<b>R8_AINT</b> truncates an R8 argument to an integer.
</li>
<li>
<b>R8_ASIN</b> evaluates the arc-sine of an R8 argument.
</li>
<li>
<b>R8_ASINH</b> evaluates the arc-sine of an R8 argument.
</li>
<li>
<b>R8_ATAN</b> evaluates the arc-tangent of an R8 argument.
</li>
<li>
<b>R8_ATAN2</b> evaluates the arc-tangent of two R8 arguments.
</li>
<li>
<b>R8_B0MP</b> evaluates the modulus and phase for the Bessel J0 and Y0 functions.
</li>
<li>
<b>R8_B1MP</b> evaluates the modulus and phase for the Bessel J1 and Y1 functions.
</li>
<li>
<b>R8_BESI0</b> evaluates the Bessel function I of order 0 of an R8 argument.
</li>
<li>
<b>R8_BESI0E</b> evaluates the exponentially scaled Bessel function I0(X).
</li>
<li>
<b>R8_BESI1</b> evaluates the Bessel function I of order 1 of an R8 argument.
</li>
<li>
<b>R8_BESI1E</b> evaluates the exponentially scaled Bessel function I1(X).
</li>
<li>
<b>R8_BESJ0</b> evaluates the Bessel function J of order 0 of an R8 argument.
</li>
<li>
<b>R8_BESJ1</b> evaluates the Bessel function J of order 1 of an R8 argument.
</li>
<li>
<b>R8_BESK0</b> evaluates the Bessel function K of order 0 of an R8 argument.
</li>
<li>
<b>R8_BESK0E</b> evaluates the exponentially scaled Bessel function K0(X).
</li>
<li>
<b>R8_BESK1</b> evaluates the Bessel function K of order 1 of an R8 argument.
</li>
<li>
<b>R8_BESK1E</b> evaluates the exponentially scaled Bessel function K1(X).
</li>
<li>
<b>R8_BESKES:</b> a sequence of exponentially scaled K Bessel functions at X.
</li>
<li>
<b>R8_BESKS</b> evaluates a sequence of K Bessel functions at X.
</li>
<li>
<b>R8_BESY0</b> evaluates the Bessel function Y of order 0 of an R8 argument.
</li>
<li>
<b>R8_BESY1</b> evaluates the Bessel function Y of order 1 of an R8 argument.
</li>
<li>
<b>R8_BETA</b> evaluates the beta function of R8 arguments.
</li>
<li>
<b>R8_BETAI</b> evaluates the incomplete beta ratio of R8 arguments.
</li>
<li>
<b>R8_BI</b> evaluates the Airy function Bi of an R8 argument.
</li>
<li>
<b>R8_BID</b> evaluates the derivative of the Airy function Bi of an R8 argument.
</li>
<li>
<b>R8_BIDE:</b> exponentially scaled derivative, Airy function Bi of an R8 argument.
</li>
<li>
<b>R8_BIE</b> evaluates the exponentially scaled Airy function Bi of an R8 argument.
</li>
<li>
<b>R8_BINOM</b> evaluates the binomial coefficient using R8 arithmetic.
</li>
<li>
<b>R8_CBRT</b> computes the cube root of an R8.
</li>
<li>
<b>R8_CHI</b> evaluates the hyperbolic cosine integral of an R8 argument.
</li>
<li>
<b>R8_CHU</b> evaluates the confluent hypergeometric function of R8 arguments.
</li>
<li>
<b>R8_CHU_SCALED:</b> scaled confluent hypergeometric function of R8 arguments.
</li>
<li>
<b>R8_CI</b> evaluates the cosine integral Ci of an R8 argument.
</li>
<li>
<b>R8_CIN</b> evaluates the alternate cosine integral Cin of an R8 argument.
</li>
<li>
<b>R8_CINH:</b> alternate hyperbolic cosine integral Cinh of an R8 argument.
</li>
<li>
<b>R8_COS</b> evaluates the cosine of an R8 argument.
</li>
<li>
<b>R8_COS_DEG</b> evaluates the cosine of an R8 argument in degrees.
</li>
<li>
<b>R8_COSH</b> evaluates the hyperbolic cosine of an R8 argument.
</li>
<li>
<b>R8_COT</b> evaluates the cotangent of an R8 argument.
</li>
<li>
<b>R8_CSEVL</b> evaluates a Chebyshev series.
</li>
<li>
<b>R8_DAWSON</b> evaluates Dawson's integral of an R8 argument.
</li>
<li>
<b>R8_E1</b> evaluates the exponential integral E1 for an R8 argument.
</li>
<li>
<b>R8_EI</b> evaluates the exponential integral Ei for an R8 argument.
</li>
<li>
<b>R8_ERF</b> evaluates the error function of an R8 argument.
</li>
<li>
<b>R8_ERFC</b> evaluates the co-error function of an R8 argument.
</li>
<li>
<b>R8_EXP</b> evaluates the exponential of an R8 argument.
</li>
<li>
<b>R8_EXPREL</b> evaluates the exponential relative error term of an R8 argument.
</li>
<li>
<b>R8_FAC</b> evaluates the factorial of an I4 argument.
</li>
<li>
<b>R8_GAMI</b> evaluates the incomplete gamma function for an R8 argument.
</li>
<li>
<b>R8_GAMIC</b> evaluates the complementary incomplete gamma function.
</li>
<li>
<b>R8_GAMIT</b> evaluates Tricomi's incomplete gamma function for an R8 argument.
</li>
<li>
<b>R8_GAML</b> evaluates bounds for an R8 argument of the gamma function.
</li>
<li>
<b>R8_GAMMA</b> evaluates the gamma function of an R8 argument.
</li>
<li>
<b>R8_GAMR</b> evaluates the reciprocal gamma function of an R8 argument.
</li>
<li>
<b>R8_GMIC:</b> complementary incomplete gamma, small X, A near negative int.
</li>
<li>
<b>R8_GMIT:</b> Tricomi's incomplete gamma function for small X.
</li>
<li>
<b>R8_INITS</b> initializes a Chebyshev series.
</li>
<li>
<b>R8_INT</b> returns the integer part of an R8 argument.
</li>
<li>
<b>R8_KNUS</b> computes a sequence of K Bessel functions.
</li>
<li>
<b>R8_LBETA</b> evaluates the logarithm of the beta function of R8 arguments.
</li>
<li>
<b>R8_LGAMS</b> evaluates the log of |gamma(x)| and sign, for an R8 argument.
</li>
<li>
<b>R8_LGIC</b> evaluates the log complementary incomplete gamma function for large X.
</li>
<li>
<b>R8_LGIT</b> evaluates the log of Tricomi's incomplete gamma function.
</li>
<li>
<b>R8_LGMC</b> evaluates the log gamma correction factor for an R8 argument.
</li>
<li>
<b>R8_LI</b> evaluates the logarithmic integral for an R8 argument.
</li>
<li>
<b>R8_LNGAM:</b> log of the absolute value of gamma of an R8 argument.
</li>
<li>
<b>R8_LNREL</b> evaluates log ( 1 + X ) for an R8 argument.
</li>
<li>
<b>R8_LOG</b> evaluates the logarithm of an R8.
</li>
<li>
<b>R8_LOG10</b> evaluates the logarithm, base 10, of an R8.
</li>
<li>
<b>R8_MACH</b> returns double precision real machine constants.
</li>
<li>
<b>R8_MACHAR</b> computes machine constants for R8 arithmetic.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_MOD</b> returns the remainder of R8 division.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8 value.
</li>
<li>
<b>R8_PAK</b> packs a base 2 exponent into an R8.
</li>
<li>
<b>R8_POCH</b> evaluates Pochhammer's function of R8 arguments.
</li>
<li>
<b>R8_POCH1</b> evaluates a quantity related to Pochhammer's symbol.
</li>
<li>
<b>R8_POW</b> evaluates A^B.
</li>
<li>
<b>R8_PSI</b> evaluates the psi function of an R8 argument.
</li>
<li>
<b>R8_REN</b> is a simple random number generator.
</li>
<li>
<b>R8_SHI</b> evaluates the hyperbolic sine integral Shi of an R8 argument.
</li>
<li>
<b>R8_SI</b> evaluates the sine integral Si of an R8 argument.
</li>
<li>
<b>R8_SIFG</b> is a utility routine.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8_SIN</b> evaluates the sine of an R8 argument.
</li>
<li>
<b>R8_SIN_DEG</b> evaluates the sine of an R8 argument in degrees.
</li>
<li>
<b>R8_SINH</b> evaluates the hyperbolic sine of an R8 argument.
</li>
<li>
<b>R8_SPENCE</b> evaluates a form of Spence's function for an R8 argument.
</li>
<li>
<b>R8_SQRT</b> computes the square root of an R8.
</li>
<li>
<b>R8_TAN</b> evaluates the tangent of an R8 argument.
</li>
<li>
<b>R8_TANH</b> evaluates the hyperbolic tangent of an R8 argument.
</li>
<li>
<b>R8_UPAK</b> unpacks an R8 into a mantissa and exponent.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 16 September 2011.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>