Compared results of different implementations of the 1982 Heim mass formulas
===========================================================================

Data input:
----------------------            GPROG 06 (Pascal)                             
 Pi                             = 3.14159265358979E+0000 
 base of natural logarithm: ebn = 2.71828182845905E+0000   
 plancks constant/2Pi:      hq  = 1.05457159600000E-0034 [Ws*s]
 speed of light : c             = 2.99792458000000E+0008 [m/s]
 gravitational constant: gam    = 6.67331980000000E-0011 [m**3/(kg*s*s)                       
 Vacuum wave resistance:   Rg   = 3.76730313461000E+0002 [Ohm]
 Fine structure constant: alfa  = 7.29735253328589E-0003   
 "strong" constant: beta        = 9.99985890199089E-0001   
 Conversion kg - MeV : fakMeV   = 5.60958920000000E+0029 [MeV/kg]
 Length unit:s0                 = 1.00000000000000E+0000 [m]

Derived constants:
-----------------
 Geometrical shortening: eta    = 9.89989640819342E-0001   
 Geometrical shortening: theta  = 7.93991266691442E+0000   
 Geometrical shortening: xi     = 1.61803398874989E+0000
 Elementary charge: eq          = 1.60216459374958E-0019 [As]
 Mass element amu               = 2.25898458329390E-0031 [kg]

              Geometrical shortening: alfp    Geometrical shortening: alfm 
Pascal 0.6    1.83221150779746E-0002          8.12834494443715E-0003  
Pascal 0.61   1.83221150781647E-0002          8.12834494462534E-0003
FORTRAN 1982  .183221150781649D-01            .812834494462544D-02    
Excel v.06    1,83221150781649E-02            8,12834494462544E-03    


Accuracy of numer types used:
---------+----------+-------------
FORTRAN  | double   |    15 digits
Excel    | ?        |    15 digits
Pascal   | extended | 19-20 digits

results
-----------------------------+------------+------------------------------------------------------------------------------------+-------------------------------------+----------------------+
                             |            | Absolute values                                                                    | Errors related to empirical values  |Errors between FORTRAN and
                             | Empirical  | GPROG FORTRAN | GPROG 0.6 Pascal     | GPROG 0.61 Pascal    | Excel v0.6           | Fortran   |Pascal 06   | Excel      | Pascal0.6 |Pascal 0.61
                             | CERN 2002  |               |                      | changed reamining    |                      | [%]       |[%]         | [%]        | [%]       | [%]      |
 #  Name    (kPQkap)x qx Cs  | Mean value |               |                      | reals to extended    |                      |           |            |            |           |          |
-----------------------------+------------+---------------+----------------------+----------------------+----------------------+-----------+------------+------------+-----------+----------|
01  eta     (1000)  1  0  0  | 547,3      | 5,4880235E+02 | 5,48802349198685E+02 | 5,48802349204379E+02 | 5,48802349204388E+02 |-0,2745021 | -0,2745020 | -0,2745020 |  0,000000 |  0,000000|
02  e0      (1110)  1  0  0  |            | 5,0687877E-01 | 5,06878771052940E-01 | 5,06878771058145E-01 | 4,97591675307314E-01 |           |            |            |           |          |
03  e-      (1110)  2 -1  0  | 0,51099907 | 5,1099885E-01 | 5,10998846697922E-01 | 5,01711750952360E-01 | 5,10965496282392E-01 | 0,0000431 |  0,0000437 |  0,0065702 | -0,000001 | -1,851083|
04  my      (1111)  1 -1  0  | 105,658389 | 1,0565854E+02 | 1,05658535754895E+02 | 1,05658535756002E+02 | 1,05658465699639E+02 |-0,0001429 | -0,0001389 | -0,0000726 | -0,000004 | -0,000004|
05  K+-     (1101)  1  1  1  | 493,677    | 4,9367795E+02 | 4,93677949365270E+02 | 4,93677949370403E+02 | 4,93678410571596E+02 |-0,0001924 | -0,0001923 | -0,0002857 |  0,000000 |  0,000000|
06  K0      (1101)  2  0  1  | 497,672    | 4,9766955E+02 | 4,97669554452197E+02 | 4,97669554457361E+02 | 4,97669554457370E+02 | 0,0004923 |  0,0004914 |  0,0004914 |  0,000001 |  0,000001|
07  pi0     (1200)  2  0  0  | 134,9766   | 1,3496154E+02 | 1,34961535383459E+02 | 1,34961535384859E+02 | 1,34961535384861E+02 | 0,0111575 |  0,0111609 |  0,0111609 | -0,000003 | -0,000003|
08  pi+-    (1200)  1  1  0  | 139,57018  | 1,3956581E+02 | 1,39565808464920E+02 | 1,39565808466381E+02 | 1,39565784170503E+02 | 0,0031310 |  0,0031321 |  0,0031495 | -0,000001 | -0,000001|
09  Lambda  (2010)  1  0 -1  | 1115,683   | 1,1155909E+03 | 1,11558164043715E+03 | 1,11558164044872E+03 | 1,11559092754449E+03 | 0,0082550 |  0,0090850 |  0,0082526 | -0,000830 | -0,000830|
10  om      (2030)  1 -1 -3  |            | 1,6722020E+03 | 1,67220204591898E+03 | 1,67220204593635E+03 | 1,67220204593638E+03 |           |            |            |           |          |
11  p       (2110)  1  1  0  | 938,27231  | 9,3827207E+02 | 9,38272070116816E+02 | 9,38272070126560E+02 | 9,38271921776457E+02 | 0,0000256 |  0,0000256 |  0,0000414 |  0,000000 |  0,000000|
12  n       (2110)  2  0  0  | 939,56563  | 9,3956549E+02 | 9,39565492307344E+02 | 9,39565492317092E+02 | 9,39565492317108E+02 | 0,0000149 |  0,0000147 |  0,0000147 |  0,000000 |  0,000000|
13  xi0     (2111)  1  0 -2  | 1314,9     | 1,3147744E+03 | 1,31477442763082E+03 | 1,31477442764446E+03 | 1,31477442764448E+03 | 0,0095521 |  0,0095500 |  0,0095500 |  0,000002 |  0,000002|
14  xi-     (2111)  2 -1 -2  | 1321,32    | 1,3213061E+03 | 1,32130610341039E+03 | 1,32130610342411E+03 | 1,32127776723429E+03 | 0,0010520 |  0,0010517 |  0,0031963 |  0,000000 |  0,000000|
15  sig+    (2210)  1  1 -1  | 1189,37    | 1,1893545E+03 | 1,18936382537436E+03 | 1,18936382538672E+03 | 1,18935477594549E+03 | 0,0013032 |  0,0005192 |  0,0012800 |  0,000784 |  0,000784|
16  sig0    (2210)  2  0 -1  | 1192,642   | 1,1924268E+03 | 1,19243607312886E+03 | 1,19243607314124E+03 | 1,19242678604550E+03 | 0,0180440 |  0,0172664 |  0,0180451 |  0,000778 |  0,000778|
17  sig-    (2210)  3 -1 -1  | 1197,449   | 1,1972755E+03 | 1,19728481036347E+03 | 1,19728481037591E+03 | 1,19727576093468E+03 | 0,0144891 |  0,0137116 |  0,0144673 |  0,000778 |  0,000778|
18  o--     (2310)  4 -2  0  | 1672,45    | 1,5340925E+03 | 1,50171945227284E+03 | 1,50171945228843E+03 | 1,53408849518099E+03 | 8,2727436 | 10,2084097 |  8,2729830 | -2,155732 | -2,155732|
19  o-      (2310)  3 -1  0  |            | 1,5309707E+03 | 1,64836678371277E+03 | 1,64836678372988E+03 | 1,53097046329979E+03 |           |            |            |  7,121964 |  7,121964|
20  o0      (2310)  2  0  0  |            | 1,5491707E+03 | 1,53485268022499E+03 | 1,53485268024091E+03 | 1,54912425125759E+03 |           |            |            | -0,932860 | -0,932860|
21  o+      (2310)  1  1  0  |            | 1,5399516E+03 | 1,52720846719356E+03 | 1,52720846720944E+03 | 1,53995131215791E+03 |           |            |            | -0,834407 | -0,834407|
22  delt++  (2330)  1  2  0  |            | 1,2302550E+03 | 1,23029214432023E+03 | 1,23029214433299E+03 | 1,23024902906903E+03 |           |            |            |  0,003019 |  0,003019|
23  delt+   (2330)  2  1  0  |            | 1,2299804E+03 | 1,22979459514165E+03 | 1,22979459515443E+03 | 1,22976641967070E+03 |           |            |            | -0,015109 | -0,015109|
24  delt    (2330)  3  0  0  |            | 1,2311277E+03 | 1,23126696760208E+03 | 1,23126696761485E+03 | 1,23112766117861E+03 |           |            |            |  0,011311 |  0,011311|
25  delt-   (2330)  4 -1  0  |            | 1,2356698E+03 | 1,23568837876626E+03 | 1,23568837877910E+03 | 1,23566943556094E+03 |           |            |            |  0,001504 |  0,001504|

------------------------------------------------------------------------------------------------

Different allocations of protosimplexes in omicrons (2310) because of different intermediate result w2
Ground level -- x=1 qx=1 --------------------------
            Q1   Q2   Q3   Q4     K1   K2   K3   K4   w2   
Pascal 06   24   31   34   15     28    8    3    1   4.83286841258744E-0001   Corrected K3, n3, K4, n4. This resonance is not allowed!
FORTRAN     24   31   34   15     28   16    9   11   
Excel 06    24   31   34   15     28   16    9   11   0,496854522  

Ground level --  x=2 qx=  -------------------------
            Q1   Q2   Q3   Q4     K1   K2   K3   K4  
Pascal 06   24   31   34   15     28   10    5   24  
FORTRAN     24   31   34   15     28   17   15   23  ### undefined ik4 via 3 in Gstruc :  
Excel 06    24   31   34   15     28   17   15   18  Corrected value of K3, n3, K4, n4. This resonance is not allowed!

Ground level ---x=3 qx=-1 ----------------------------
            Q1   Q2   Q3   Q4     K1   K2   K3   K4  
Pascal 06   24   31   34   15     27   46   40   51  Corrected value of K3, n3, K4, n4. This resonance is not allowed!
FORTRAN     24   31   34   15     28   11   12    6  
Excel 06    24   31   34   15     28   11   12    6

Ground level ---x=4 qx=-2 ----------------------------
            Q1   Q2   Q3   Q4     K1   K2   K3   K4    
Pascal 06   24   31   34   15     28   20   20    6    
FORTRAN     24   31   34   15     28   25   32   21  
Excel 06    24   31   34   15     28   25   32   21        

----------------------------------------------------------------------------------------
1. 
The error in the computation of strangeness of xi is absent here that happend in the 1982 DESY code. I used the equations given in the 1982 paper.

2.
There is an interesting variance in omicrons, when using Pascal. I don't know whether Pascal has more accuracy because of 20 digits used. At this point we need further investigation with a mathematical orientated programming language.

3.
Resonance limits calculated in excel and pascal are 100% identical (besides - of course - the omicrons mentioned).
Interesting enough these limits are in many cases significantly smaller than the limits Burkhard Heim has published in "Elementary structures", vol 2.
This may be a result of number types used.
You find the limits in the excel worksheet and in the file gprogout.dat. The Pascal version calculates resonances up to N=180.

4. 
As noted before I skipped the special truncation rule for values >x.99
This rule was mentioned in the 1982 paper and in "Elementary structures", vol 2.