/ BBS in a Box 10 / BBS In A Box Volume X (AMUG) (January 1994).bin / Files / Prog / U-Z / VideoToolBox.cpt / VideoToolboxSources / Normal.c

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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 08 4e 6f 72 6d 61 6c | 2e 63 00 00 00 00 00 00 |..Normal|.c......|
|00000010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 4b 41 48 | 4c 01 00 00 00 00 00 00 |.TEXTKAH|L.......|
|00000050| 00 00 00 00 00 12 c3 00 | 00 02 5e a7 bb 5a b5 a7 |........|..^..Z..|
|00000060| bb 5a b5 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.Z......|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 ab d7 00 00 |........|........|
|00000080| 2f 2a 0d 4e 6f 72 6d 61 | 6c 2e 63 0d 73 74 61 74 |/*.Norma|l.c.stat|
|00000090| 69 73 74 69 63 61 6c 20 | 66 75 6e 63 74 69 6f 6e |istical |function|
|000000a0| 73 20 72 65 6c 61 74 65 | 64 20 74 6f 20 74 68 65 |s relate|d to the|
|000000b0| 20 6e 6f 72 6d 61 6c 20 | 64 69 73 74 72 69 62 75 | normal |distribu|
|000000c0| 74 69 6f 6e 2e 0d 43 6f | 70 79 72 69 67 68 74 20 |tion..Co|pyright |
|000000d0| 28 63 29 20 31 39 38 39 | 2c 31 39 39 30 2c 31 39 |(c) 1989|,1990,19|
|000000e0| 39 31 2c 31 39 39 32 20 | 44 65 6e 69 73 20 47 2e |91,1992 |Denis G.|
|000000f0| 20 50 65 6c 6c 69 0d 48 | 49 53 54 4f 52 59 3a 0d | Pelli.H|ISTORY:.|
|00000100| 31 39 38 39 09 64 67 70 | 20 77 72 6f 74 65 20 69 |1989.dgp| wrote i|
|00000110| 74 2e 0d 34 2f 38 2f 39 | 30 09 64 67 70 09 63 68 |t..4/8/9|0.dgp.ch|
|00000120| 61 6e 67 65 64 20 74 68 | 65 20 6e 61 6d 65 73 20 |anged th|e names |
|00000130| 6f 66 20 74 68 65 20 72 | 6f 75 74 69 6e 65 73 2e |of the r|outines.|
|00000140| 20 0d 09 09 09 4d 61 64 | 65 20 73 75 72 65 20 74 | ....Mad|e sure t|
|00000150| 68 61 74 20 64 6f 6d 61 | 69 6e 20 65 72 72 6f 72 |hat doma|in error|
|00000160| 20 70 72 6f 64 75 63 65 | 73 20 4e 41 4e 2e 0d 36 | produce|s NAN..6|
|00000170| 2f 39 30 09 64 67 70 09 | 61 64 64 65 64 20 4e 6f |/90.dgp.|added No|
|00000180| 72 6d 61 6c 53 61 6d 70 | 6c 65 28 29 0d 37 2f 33 |rmalSamp|le().7/3|
|00000190| 30 2f 39 31 09 64 67 70 | 09 6e 6f 77 20 75 73 65 |0/91.dgp|.now use|
|000001a0| 20 4e 41 4e 20 64 65 66 | 69 6e 65 64 20 69 6e 20 | NAN def|ined in |
|000001b0| 56 69 64 65 6f 54 6f 6f | 6c 62 6f 78 2e 68 0d 31 |VideoToo|lbox.h.1|
|000001c0| 32 2f 32 38 2f 39 31 20 | 64 67 70 20 73 70 65 64 |2/28/91 |dgp sped|
|000001d0| 20 75 70 20 4e 6f 72 6d | 61 6c 50 64 66 28 29 20 | up Norm|alPdf() |
|000001e0| 62 79 20 63 61 6c 63 75 | 6c 61 74 69 6e 67 20 74 |by calcu|lating t|
|000001f0| 68 65 20 73 63 61 6c 65 | 20 66 61 63 74 6f 72 20 |he scale| factor |
|00000200| 6f 6e 6c 79 20 6f 6e 63 | 65 0d 31 32 2f 32 39 2f |only onc|e.12/29/|
|00000210| 39 31 20 64 67 70 20 65 | 78 74 72 61 63 74 65 64 |91 dgp e|xtracted|
|00000220| 20 63 6f 64 65 20 74 6f | 20 63 72 65 61 74 65 20 | code to| create |
|00000230| 6e 65 77 20 72 6f 75 74 | 69 6e 65 20 55 6e 69 66 |new rout|ine Unif|
|00000240| 6f 72 6d 53 61 6d 70 6c | 65 2e 63 0d 31 2f 31 31 |ormSampl|e.c.1/11|
|00000250| 2f 39 32 09 64 67 70 09 | 72 65 77 72 6f 74 65 20 |/92.dgp.|rewrote |
|00000260| 4e 6f 72 6d 61 6c 28 29 | 27 73 20 70 6f 6c 79 6e |Normal()|'s polyn|
|00000270| 6f 6d 69 61 6c 20 65 76 | 61 6c 75 61 74 69 6f 6e |omial ev|aluation|
|00000280| 20 74 6f 20 68 61 6c 76 | 65 20 74 68 65 20 6e 75 | to halv|e the nu|
|00000290| 6d 62 65 72 20 6f 66 20 | 6d 75 6c 74 69 70 6c 69 |mber of |multipli|
|000002a0| 65 73 0d 09 09 09 52 65 | 6e 61 6d 65 64 20 4e 6f |es....Re|named No|
|000002b0| 72 6d 61 6c 50 44 46 28 | 29 20 74 6f 20 4e 6f 72 |rmalPDF(|) to Nor|
|000002c0| 6d 61 6c 50 64 66 28 29 | 2e 0d 31 2f 31 39 2f 39 |malPdf()|..1/19/9|
|000002d0| 32 09 64 67 70 09 64 65 | 66 69 6e 65 64 20 74 68 |2.dgp.de|fined th|
|000002e0| 65 20 63 6f 6e 73 74 61 | 6e 74 73 20 4c 4f 47 32 |e consta|nts LOG2|
|000002f0| 20 61 6e 64 20 4c 4f 47 | 50 49 20 69 6e 20 56 69 | and LOG|PI in Vi|
|00000300| 64 65 6f 54 6f 6f 6c 62 | 6f 78 2e 68 0d 09 09 09 |deoToolb|ox.h....|
|00000310| 41 64 64 65 64 20 6d 6f | 72 65 20 64 6f 6d 61 69 |Added mo|re domai|
|00000320| 6e 20 74 65 73 74 73 2c | 20 72 65 74 75 72 6e 69 |n tests,| returni|
|00000330| 6e 67 20 4e 41 4e 20 69 | 66 20 6f 75 74 73 69 64 |ng NAN i|f outsid|
|00000340| 65 2e 20 0d 09 09 09 41 | 64 64 65 64 20 6d 6f 72 |e. ....A|dded mor|
|00000350| 65 20 63 68 65 63 6b 73 | 20 74 6f 20 6d 61 69 6e |e checks| to main|
|00000360| 28 29 2e 0d 09 09 09 57 | 72 6f 74 65 20 4e 6f 72 |().....W|rote Nor|
|00000370| 6d 61 6c 32 44 50 64 66 | 28 29 2c 4e 6f 72 6d 61 |mal2DPdf|(),Norma|
|00000380| 6c 32 44 28 29 2c 49 6e | 76 65 72 73 65 4e 6f 72 |l2D(),In|verseNor|
|00000390| 6d 61 6c 32 44 28 29 2c | 61 6e 64 20 4e 6f 72 6d |mal2D(),|and Norm|
|000003a0| 61 6c 32 44 53 61 6d 70 | 6c 65 28 29 2e 0d 32 2f |al2DSamp|le()..2/|
|000003b0| 31 2f 39 32 09 64 67 70 | 09 52 65 64 65 66 69 6e |1/92.dgp|.Redefin|
|000003c0| 65 64 20 4e 6f 72 6d 61 | 6c 32 44 50 64 66 28 72 |ed Norma|l2DPdf(r|
|000003d0| 29 20 74 6f 20 6e 6f 77 | 2c 20 6d 6f 72 65 20 73 |) to now|, more s|
|000003e0| 65 6e 73 69 62 6c 79 2c | 20 74 72 65 61 74 20 72 |ensibly,| treat r|
|000003f0| 20 61 73 20 74 68 65 20 | 72 61 6e 64 6f 6d 0d 09 | as the |random..|
|00000400| 09 09 76 61 72 69 61 62 | 6c 65 2c 20 72 61 74 68 |..variab|le, rath|
|00000410| 65 72 20 74 68 61 6e 20 | 74 68 65 20 69 6d 70 6c |er than |the impl|
|00000420| 69 63 69 74 20 78 20 61 | 6e 64 20 79 2c 20 77 68 |icit x a|nd y, wh|
|00000430| 65 72 65 20 72 3d 73 71 | 72 74 28 78 5e 32 2b 79 |ere r=sq|rt(x^2+y|
|00000440| 5e 32 29 2e 20 0d 09 09 | 09 50 72 65 76 69 6f 75 |^2). ...|.Previou|
|00000450| 73 6c 79 2c 20 4e 6f 72 | 6d 61 6c 32 44 28 52 29 |sly, Nor|mal2D(R)|
|00000460| 3d 49 6e 74 65 67 72 61 | 74 65 5b 32 20 50 69 20 |=Integra|te[2 Pi |
|00000470| 72 20 4e 6f 72 6d 61 6c | 32 44 50 64 66 28 72 29 |r Normal|2DPdf(r)|
|00000480| 2c 7b 72 2c 30 2c 52 7d | 5d 0d 09 09 09 6e 6f 77 |,{r,0,R}|]....now|
|00000490| 20 4e 6f 72 6d 61 6c 32 | 44 28 52 29 3d 49 6e 74 | Normal2|D(R)=Int|
|000004a0| 65 67 72 61 74 65 5b 4e | 6f 72 6d 61 6c 32 44 50 |egrate[N|ormal2DP|
|000004b0| 64 66 28 72 29 2c 7b 72 | 2c 30 2c 52 7d 5d 2e 20 |df(r),{r|,0,R}]. |
|000004c0| 54 68 65 72 65 20 69 73 | 20 6e 6f 20 63 68 61 6e |There is| no chan|
|000004d0| 67 65 0d 09 09 09 69 6e | 20 4e 6f 72 6d 61 6c 32 |ge....in| Normal2|
|000004e0| 44 28 29 2e 20 49 20 73 | 75 73 70 65 63 74 20 74 |D(). I s|uspect t|
|000004f0| 68 61 74 20 4e 6f 72 6d | 61 6c 32 44 20 69 73 20 |hat Norm|al2D is |
|00000500| 69 6e 20 66 61 63 74 20 | 74 68 65 20 52 61 6c 65 |in fact |the Rale|
|00000510| 69 67 68 20 64 69 73 74 | 72 69 62 75 74 69 6f 6e |igh dist|ribution|
|00000520| 2c 0d 09 09 09 61 6e 64 | 20 49 20 77 69 6c 6c 20 |,....and| I will |
|00000530| 72 65 6e 61 6d 65 20 69 | 74 20 69 66 20 74 68 69 |rename i|t if thi|
|00000540| 73 20 69 73 20 69 6e 20 | 66 61 63 74 20 74 68 65 |s is in |fact the|
|00000550| 20 63 61 73 65 2e 0d 31 | 31 2f 31 33 2f 39 32 20 | case..1|1/13/92 |
|00000560| 64 67 70 20 49 6e 76 65 | 72 73 65 4e 6f 72 6d 61 |dgp Inve|rseNorma|
|00000570| 6c 28 30 2e 30 29 20 6e | 6f 77 20 72 65 74 75 72 |l(0.0) n|ow retur|
|00000580| 6e 73 20 2d 49 4e 46 2c | 20 61 6e 64 20 49 6e 76 |ns -INF,| and Inv|
|00000590| 65 72 73 65 4e 6f 72 6d | 61 6c 28 31 29 20 72 65 |erseNorm|al(1) re|
|000005a0| 74 75 72 6e 73 20 49 4e | 46 2e 0d 2a 2f 0d 23 69 |turns IN|F..*/.#i|
|000005b0| 6e 63 6c 75 64 65 20 22 | 56 69 64 65 6f 54 6f 6f |nclude "|VideoToo|
|000005c0| 6c 62 6f 78 2e 68 22 0d | 23 69 6e 63 6c 75 64 65 |lbox.h".|#include|
|000005d0| 20 3c 61 73 73 65 72 74 | 2e 68 3e 0d 23 69 6e 63 | <assert|.h>.#inc|
|000005e0| 6c 75 64 65 20 3c 6d 61 | 74 68 2e 68 3e 0d 0d 23 |lude <ma|th.h>..#|
|000005f0| 69 66 20 30 0d 23 69 6e | 63 6c 75 64 65 20 3c 73 |if 0.#in|clude <s|
|00000600| 61 6e 65 2e 68 3e 0d 65 | 78 74 65 6e 64 65 64 20 |ane.h>.e|xtended |
|00000610| 44 6f 75 62 6c 65 54 6f | 45 78 74 65 6e 64 65 64 |DoubleTo|Extended|
|00000620| 28 64 6f 75 62 6c 65 20 | 78 29 3b 0d 64 6f 75 62 |(double |x);.doub|
|00000630| 6c 65 20 45 78 74 65 6e | 64 65 64 54 6f 44 6f 75 |le Exten|dedToDou|
|00000640| 62 6c 65 28 65 78 74 65 | 6e 64 65 64 20 78 38 30 |ble(exte|nded x80|
|00000650| 29 3b 0d 76 6f 69 64 20 | 6d 61 69 6e 28 29 0d 7b |);.void |main().{|
|00000660| 0d 09 64 6f 75 62 6c 65 | 20 78 2c 79 2c 73 75 6d |..double| x,y,sum|
|00000670| 2c 64 78 2c 61 2c 62 2c | 6d 65 61 6e 2c 73 64 3b |,dx,a,b,|mean,sd;|
|00000680| 0d 09 73 74 61 74 69 63 | 20 64 6f 75 62 6c 65 20 |..static| double |
|00000690| 7a 5b 31 30 30 30 5d 3b | 0d 09 69 6e 74 20 69 3b |z[1000];|..int i;|
|000006a0| 0d 09 65 78 74 65 6e 64 | 65 64 20 65 2c 65 65 3b |..extend|ed e,ee;|
|000006b0| 0d 09 0d 09 52 65 71 75 | 69 72 65 28 30 29 3b 0d |....Requ|ire(0);.|
|000006c0| 09 73 72 61 6e 64 28 63 | 6c 6f 63 6b 28 29 29 3b |.srand(c|lock());|
|000006d0| 0d 09 70 72 69 6e 74 66 | 28 22 25 34 73 25 31 35 |..printf|("%4s%15|
|000006e0| 73 25 31 35 73 25 32 30 | 73 25 31 35 73 5c 6e 22 |s%15s%20|s%15s\n"|
|000006f0| 2c 22 78 22 2c 22 4e 6f | 72 6d 61 6c 50 64 66 28 |,"x","No|rmalPdf(|
|00000700| 78 29 22 2c 22 4e 6f 72 | 6d 61 6c 28 78 29 22 2c |x)","Nor|mal(x)",|
|00000710| 22 49 6e 76 65 72 73 65 | 4e 6f 72 6d 61 6c 22 2c |"Inverse|Normal",|
|00000720| 22 45 72 72 6f 72 22 29 | 3b 0d 09 66 6f 72 28 78 |"Error")|;..for(x|
|00000730| 3d 2d 34 2e 30 3b 78 3c | 3d 34 2e 30 3b 78 2b 3d |=-4.0;x<|=4.0;x+=|
|00000740| 32 2e 30 29 7b 0d 09 09 | 70 72 69 6e 74 66 28 22 |2.0){...|printf("|
|00000750| 25 34 2e 31 66 25 31 35 | 2e 38 66 25 31 35 2e 38 |%4.1f%15|.8f%15.8|
|00000760| 66 25 32 30 2e 34 66 25 | 31 35 2e 34 66 5c 6e 22 |f%20.4f%|15.4f\n"|
|00000770| 2c 0d 09 09 78 2c 4e 6f | 72 6d 61 6c 50 64 66 28 |,...x,No|rmalPdf(|
|00000780| 78 29 2c 4e 6f 72 6d 61 | 6c 28 78 29 2c 49 6e 76 |x),Norma|l(x),Inv|
|00000790| 65 72 73 65 4e 6f 72 6d | 61 6c 28 4e 6f 72 6d 61 |erseNorm|al(Norma|
|000007a0| 6c 28 78 29 29 2c 49 6e | 76 65 72 73 65 4e 6f 72 |l(x)),In|verseNor|
|000007b0| 6d 61 6c 28 4e 6f 72 6d | 61 6c 28 78 29 29 2d 78 |mal(Norm|al(x))-x|
|000007c0| 29 3b 0d 09 7d 0d 09 73 | 75 6d 3d 30 2e 30 3b 0d |);..}..s|um=0.0;.|
|000007d0| 09 64 78 3d 30 2e 30 30 | 31 3b 0d 09 66 6f 72 28 |.dx=0.00|1;..for(|
|000007e0| 78 3d 2d 31 2e 3b 78 3c | 30 2e 3b 78 2b 3d 64 78 |x=-1.;x<|0.;x+=dx|
|000007f0| 29 73 75 6d 2b 3d 4e 6f | 72 6d 61 6c 50 64 66 28 |)sum+=No|rmalPdf(|
|00000800| 78 29 3b 0d 09 73 75 6d | 2a 3d 64 78 3b 0d 09 73 |x);..sum|*=dx;..s|
|00000810| 75 6d 2d 3d 4e 6f 72 6d | 61 6c 28 30 2e 30 29 2d |um-=Norm|al(0.0)-|
|00000820| 4e 6f 72 6d 61 6c 28 2d | 31 2e 30 29 3b 0d 09 70 |Normal(-|1.0);..p|
|00000830| 72 69 6e 74 66 28 22 50 | 61 72 74 69 61 6c 20 69 |rintf("P|artial i|
|00000840| 6e 74 65 67 72 61 6c 20 | 6f 66 20 4e 6f 72 6d 61 |ntegral |of Norma|
|00000850| 6c 50 64 66 20 65 72 72 | 6f 72 20 25 2e 35 66 5c |lPdf err|or %.5f\|
|00000860| 6e 22 2c 73 75 6d 29 3b | 0d 09 66 6f 72 28 69 3d |n",sum);|..for(i=|
|00000870| 30 3b 69 3c 31 30 30 30 | 3b 69 2b 2b 29 7a 5b 69 |0;i<1000|;i++)z[i|
|00000880| 5d 3d 4e 6f 72 6d 61 6c | 53 61 6d 70 6c 65 28 29 |]=Normal|Sample()|
|00000890| 3b 0d 09 6d 65 61 6e 3d | 4d 65 61 6e 28 7a 2c 31 |;..mean=|Mean(z,1|
|000008a0| 30 30 30 2c 26 73 64 29 | 3b 0d 09 70 72 69 6e 74 |000,&sd)|;..print|
|000008b0| 66 28 22 31 30 30 30 20 | 73 61 6d 70 6c 65 73 20 |f("1000 |samples |
|000008c0| 6d 65 61 6e 20 25 2e 32 | 66 20 73 64 20 25 2e 32 |mean %.2|f sd %.2|
|000008d0| 66 5c 6e 22 2c 6d 65 61 | 6e 2c 73 64 29 3b 0d 09 |f\n",mea|n,sd);..|
|000008e0| 70 72 69 6e 74 66 28 22 | 5c 6e 22 29 3b 0d 0d 09 |printf("|\n");...|
|000008f0| 70 72 69 6e 74 66 28 22 | 25 34 73 25 31 35 73 25 |printf("|%4s%15s%|
|00000900| 31 35 73 25 32 30 73 25 | 31 35 73 5c 6e 22 2c 22 |15s%20s%|15s\n","|
|00000910| 78 22 2c 22 4e 6f 72 6d | 61 6c 32 44 50 64 66 28 |x","Norm|al2DPdf(|
|00000920| 78 29 22 2c 22 4e 6f 72 | 6d 61 6c 32 44 28 78 29 |x)","Nor|mal2D(x)|
|00000930| 22 2c 22 49 6e 76 65 72 | 73 65 4e 6f 72 6d 61 6c |","Inver|seNormal|
|00000940| 32 44 22 2c 22 45 72 72 | 6f 72 22 29 3b 0d 09 66 |2D","Err|or");..f|
|00000950| 6f 72 28 78 3d 2d 31 2e | 3b 78 3c 3d 35 2e 30 3b |or(x=-1.|;x<=5.0;|
|00000960| 78 2b 3d 31 2e 30 29 7b | 0d 09 09 70 72 69 6e 74 |x+=1.0){|...print|
|00000970| 66 28 22 25 34 2e 31 66 | 25 31 35 2e 38 66 25 31 |f("%4.1f|%15.8f%1|
|00000980| 35 2e 38 66 25 32 30 2e | 34 66 25 31 35 2e 34 66 |5.8f%20.|4f%15.4f|
|00000990| 5c 6e 22 2c 0d 09 09 78 | 2c 4e 6f 72 6d 61 6c 32 |\n",...x|,Normal2|
|000009a0| 44 50 64 66 28 78 29 2c | 4e 6f 72 6d 61 6c 32 44 |DPdf(x),|Normal2D|
|000009b0| 28 78 29 2c 49 6e 76 65 | 72 73 65 4e 6f 72 6d 61 |(x),Inve|rseNorma|
|000009c0| 6c 32 44 28 4e 6f 72 6d | 61 6c 32 44 28 78 29 29 |l2D(Norm|al2D(x))|
|000009d0| 2c 49 6e 76 65 72 73 65 | 4e 6f 72 6d 61 6c 32 44 |,Inverse|Normal2D|
|000009e0| 28 4e 6f 72 6d 61 6c 32 | 44 28 78 29 29 2d 78 29 |(Normal2|D(x))-x)|
|000009f0| 3b 0d 09 7d 0d 09 73 75 | 6d 3d 30 2e 30 3b 0d 09 |;..}..su|m=0.0;..|
|00000a00| 64 78 3d 30 2e 30 30 30 | 31 3b 0d 09 66 6f 72 28 |dx=0.000|1;..for(|
|00000a10| 78 3d 30 3b 78 3c 31 2e | 3b 78 2b 3d 64 78 29 73 |x=0;x<1.|;x+=dx)s|
|00000a20| 75 6d 2b 3d 4e 6f 72 6d | 61 6c 32 44 50 64 66 28 |um+=Norm|al2DPdf(|
|00000a30| 78 29 3b 0d 09 73 75 6d | 2a 3d 64 78 3b 0d 09 73 |x);..sum|*=dx;..s|
|00000a40| 75 6d 2d 3d 4e 6f 72 6d | 61 6c 32 44 28 31 2e 30 |um-=Norm|al2D(1.0|
|00000a50| 29 3b 0d 09 70 72 69 6e | 74 66 28 22 50 61 72 74 |);..prin|tf("Part|
|00000a60| 69 61 6c 20 69 6e 74 65 | 67 72 61 6c 20 6f 66 20 |ial inte|gral of |
|00000a70| 4e 6f 72 6d 61 6c 32 44 | 50 64 66 20 65 72 72 6f |Normal2D|Pdf erro|
|00000a80| 72 20 25 2e 35 66 5c 6e | 22 2c 73 75 6d 29 3b 0d |r %.5f\n|",sum);.|
|00000a90| 09 66 6f 72 28 69 3d 30 | 3b 69 3c 31 30 30 30 3b |.for(i=0|;i<1000;|
|00000aa0| 69 2b 2b 29 7a 5b 69 5d | 3d 4e 6f 72 6d 61 6c 32 |i++)z[i]|=Normal2|
|00000ab0| 44 53 61 6d 70 6c 65 28 | 29 3b 0d 09 6d 65 61 6e |DSample(|);..mean|
|00000ac0| 3d 4d 65 61 6e 28 7a 2c | 31 30 30 30 2c 26 73 64 |=Mean(z,|1000,&sd|
|00000ad0| 29 3b 0d 09 70 72 69 6e | 74 66 28 22 31 30 30 30 |);..prin|tf("1000|
|00000ae0| 20 73 61 6d 70 6c 65 73 | 20 72 6d 73 20 25 2e 32 | samples| rms %.2|
|00000af0| 66 5c 6e 22 2c 73 71 72 | 74 28 6d 65 61 6e 2a 6d |f\n",sqr|t(mean*m|
|00000b00| 65 61 6e 2b 73 64 2a 73 | 64 29 29 3b 0d 09 70 72 |ean+sd*s|d));..pr|
|00000b10| 69 6e 74 66 28 22 5c 6e | 22 29 3b 0d 09 66 6f 72 |intf("\n|");..for|
|00000b20| 28 69 3d 30 3b 69 3c 31 | 30 30 30 3b 69 2b 2b 29 |(i=0;i<1|000;i++)|
|00000b30| 7b 0d 09 09 78 3d 4e 6f | 72 6d 61 6c 53 61 6d 70 |{...x=No|rmalSamp|
|00000b40| 6c 65 28 29 3b 0d 09 09 | 79 3d 4e 6f 72 6d 61 6c |le();...|y=Normal|
|00000b50| 53 61 6d 70 6c 65 28 29 | 3b 0d 09 09 7a 5b 69 5d |Sample()|;...z[i]|
|00000b60| 3d 73 71 72 74 28 28 78 | 2a 78 2b 79 2a 79 29 2f |=sqrt((x|*x+y*y)/|
|00000b70| 32 2e 29 3b 0d 09 7d 0d | 09 6d 65 61 6e 3d 4d 65 |2.);..}.|.mean=Me|
|00000b80| 61 6e 28 7a 2c 31 30 30 | 30 2c 26 73 64 29 3b 0d |an(z,100|0,&sd);.|
|00000b90| 09 70 72 69 6e 74 66 28 | 22 31 30 30 30 20 28 78 |.printf(|"1000 (x|
|00000ba0| 2c 79 29 20 6e 6f 72 6d | 61 6c 20 73 61 6d 70 6c |,y) norm|al sampl|
|00000bb0| 65 73 20 77 69 74 68 20 | 73 64 20 32 5e 2d 30 2e |es with |sd 2^-0.|
|00000bc0| 35 20 68 61 76 65 20 72 | 6d 73 20 68 79 70 6f 74 |5 have r|ms hypot|
|00000bd0| 65 6e 75 73 65 20 6f 66 | 20 25 2e 32 66 5c 6e 22 |enuse of| %.2f\n"|
|00000be0| 2c 73 71 72 74 28 6d 65 | 61 6e 2a 6d 65 61 6e 2b |,sqrt(me|an*mean+|
|00000bf0| 73 64 2a 73 64 29 29 3b | 0d 09 70 72 69 6e 74 66 |sd*sd));|..printf|
|00000c00| 28 22 5c 6e 22 29 3b 0d | 0d 09 61 3d 34 2e 30 2a |("\n");.|..a=4.0*|
|00000c10| 61 74 61 6e 28 31 2e 30 | 29 3b 0d 09 69 66 28 61 |atan(1.0|);..if(a|
|00000c20| 21 3d 50 49 29 70 72 69 | 6e 74 66 28 22 34 2a 61 |!=PI)pri|ntf("4*a|
|00000c30| 74 61 6e 28 31 29 2d 50 | 49 20 25 2e 31 39 66 5c |tan(1)-P|I %.19f\|
|00000c40| 6e 22 2c 61 2d 50 49 29 | 3b 0d 09 61 3d 45 78 74 |n",a-PI)|;..a=Ext|
|00000c50| 65 6e 64 65 64 54 6f 44 | 6f 75 62 6c 65 28 70 69 |endedToD|ouble(pi|
|00000c60| 28 29 29 3b 0d 09 69 66 | 28 61 21 3d 50 49 29 70 |());..if|(a!=PI)p|
|00000c70| 72 69 6e 74 66 28 22 45 | 72 72 6f 72 3a 20 70 69 |rintf("E|rror: pi|
|00000c80| 20 25 2e 31 39 66 2c 20 | 70 69 2d 50 49 20 25 2e | %.19f, |pi-PI %.|
|00000c90| 31 39 66 5c 6e 22 2c 61 | 2c 61 2d 50 49 29 3b 0d |19f\n",a|,a-PI);.|
|00000ca0| 09 61 3d 6c 6f 67 28 61 | 29 3b 0d 09 69 66 28 61 |.a=log(a|);..if(a|
|00000cb0| 21 3d 4c 4f 47 50 49 29 | 70 72 69 6e 74 66 28 22 |!=LOGPI)|printf("|
|00000cc0| 45 72 72 6f 72 3a 20 6c | 6f 67 28 50 49 29 20 25 |Error: l|og(PI) %|
|00000cd0| 2e 31 39 66 2c 20 65 72 | 72 6f 72 20 69 6e 20 4c |.19f, er|ror in L|
|00000ce0| 4f 47 50 49 20 25 2e 31 | 39 66 5c 6e 22 2c 61 2c |OGPI %.1|9f\n",a,|
|00000cf0| 4c 4f 47 50 49 2d 61 29 | 3b 0d 09 61 3d 6c 6f 67 |LOGPI-a)|;..a=log|
|00000d00| 28 32 2e 30 29 3b 0d 09 | 69 66 28 61 21 3d 4c 4f |(2.0);..|if(a!=LO|
|00000d10| 47 32 29 70 72 69 6e 74 | 66 28 22 45 72 72 6f 72 |G2)print|f("Error|
|00000d20| 3a 20 6c 6f 67 28 32 29 | 20 25 2e 31 39 66 2c 20 |: log(2)| %.19f, |
|00000d30| 65 72 72 6f 72 20 69 6e | 20 4c 4f 47 32 20 25 2e |error in| LOG2 %.|
|00000d40| 31 39 66 5c 6e 22 2c 61 | 2c 4c 4f 47 32 2d 61 29 |19f\n",a|,LOG2-a)|
|00000d50| 3b 0d 7d 0d 23 65 6e 64 | 69 66 0d 0d 64 6f 75 62 |;.}.#end|if..doub|
|00000d60| 6c 65 20 4e 6f 72 6d 61 | 6c 50 64 66 28 64 6f 75 |le Norma|lPdf(dou|
|00000d70| 62 6c 65 20 78 29 0d 2f | 2a 20 47 61 75 73 73 69 |ble x)./|* Gaussi|
|00000d80| 61 6e 20 70 64 66 2e 20 | 5a 65 72 6f 20 6d 65 61 |an pdf. |Zero mea|
|00000d90| 6e 20 61 6e 64 20 75 6e | 69 74 20 76 61 72 69 61 |n and un|it varia|
|00000da0| 6e 63 65 2e 20 2a 2f 0d | 7b 0d 09 69 66 28 49 73 |nce. */.|{..if(Is|
|00000db0| 4e 61 6e 28 78 29 29 72 | 65 74 75 72 6e 20 78 3b |Nan(x))r|eturn x;|
|00000dc0| 0d 09 72 65 74 75 72 6e | 20 65 78 70 28 2d 30 2e |..return| exp(-0.|
|00000dd0| 35 2a 28 78 2a 78 2b 28 | 4c 4f 47 32 2b 4c 4f 47 |5*(x*x+(|LOG2+LOG|
|00000de0| 50 49 29 29 29 3b 0d 7d | 0d 0d 64 6f 75 62 6c 65 |PI)));.}|..double|
|00000df0| 20 4e 6f 72 6d 61 6c 28 | 78 29 0d 64 6f 75 62 6c | Normal(|x).doubl|
|00000e00| 65 20 78 3b 0d 2f 2a 0d | 43 75 6d 75 6c 61 74 69 |e x;./*.|Cumulati|
|00000e10| 76 65 20 6e 6f 72 6d 61 | 6c 20 64 69 73 74 72 69 |ve norma|l distri|
|00000e20| 62 75 74 69 6f 6e 2e 20 | 46 72 6f 6d 20 41 62 72 |bution. |From Abr|
|00000e30| 61 6d 6f 77 69 74 7a 20 | 61 6e 64 20 53 74 65 67 |amowitz |and Steg|
|00000e40| 75 6e 20 45 71 2e 20 28 | 32 36 2e 32 2e 31 37 29 |un Eq. (|26.2.17)|
|00000e50| 2e 0d 45 72 72 6f 72 20 | 7c 65 7c 3c 37 2e 35 20 |..Error ||e|<7.5 |
|00000e60| 31 30 5e 2d 38 0d 2a 2f | 0d 7b 0d 09 72 65 67 69 |10^-8.*/|.{..regi|
|00000e70| 73 74 65 72 20 64 6f 75 | 62 6c 65 20 50 2c 74 3b |ster dou|ble P,t;|
|00000e80| 0d 09 0d 09 69 66 28 78 | 3c 30 2e 30 29 20 72 65 |....if(x|<0.0) re|
|00000e90| 74 75 72 6e 20 31 2e 30 | 2d 4e 6f 72 6d 61 6c 28 |turn 1.0|-Normal(|
|00000ea0| 2d 78 29 3b 0d 09 74 3d | 31 2e 30 2f 28 31 2e 30 |-x);..t=|1.0/(1.0|
|00000eb0| 2b 30 2e 32 33 31 36 34 | 31 39 2a 78 29 3b 0d 09 |+0.23164|19*x);..|
|00000ec0| 50 3d 28 30 2e 33 31 39 | 33 38 31 35 33 30 2b 28 |P=(0.319|381530+(|
|00000ed0| 2d 30 2e 33 35 36 35 36 | 33 37 38 32 2b 28 31 2e |-0.35656|3782+(1.|
|00000ee0| 37 38 31 34 37 37 39 33 | 37 2b 28 2d 31 2e 38 32 |78147793|7+(-1.82|
|00000ef0| 31 32 35 35 39 37 38 2b | 31 2e 33 33 30 32 37 34 |1255978+|1.330274|
|00000f00| 34 32 39 2a 74 29 2a 74 | 29 2a 74 29 2a 74 29 2a |429*t)*t|)*t)*t)*|
|00000f10| 74 3b 0d 09 72 65 74 75 | 72 6e 20 31 2e 30 2d 4e |t;..retu|rn 1.0-N|
|00000f20| 6f 72 6d 61 6c 50 64 66 | 28 78 29 2a 50 3b 0d 7d |ormalPdf|(x)*P;.}|
|00000f30| 0d 0d 64 6f 75 62 6c 65 | 20 49 6e 76 65 72 73 65 |..double| Inverse|
|00000f40| 4e 6f 72 6d 61 6c 28 64 | 6f 75 62 6c 65 20 70 29 |Normal(d|ouble p)|
|00000f50| 0d 2f 2a 0d 49 6e 76 65 | 72 73 65 20 6f 66 20 4e |./*.Inve|rse of N|
|00000f60| 6f 72 6d 61 6c 28 29 2c | 20 62 61 73 65 64 20 6f |ormal(),| based o|
|00000f70| 6e 20 41 62 72 61 6d 6f | 77 69 74 7a 20 61 6e 64 |n Abramo|witz and|
|00000f80| 20 53 74 65 67 75 6e 20 | 45 71 2e 20 32 36 2e 32 | Stegun |Eq. 26.2|
|00000f90| 2e 32 33 2e 0d 45 72 72 | 6f 72 20 7c 65 7c 3c 34 |.23..Err|or |e|<4|
|00000fa0| 2e 35 20 31 30 5e 2d 34 | 2e 0d 2a 2f 0d 7b 0d 09 |.5 10^-4|..*/.{..|
|00000fb0| 72 65 67 69 73 74 65 72 | 20 64 6f 75 62 6c 65 20 |register| double |
|00000fc0| 74 2c 78 3b 0d 09 0d 09 | 69 66 28 49 73 4e 61 6e |t,x;....|if(IsNan|
|00000fd0| 28 70 29 29 72 65 74 75 | 72 6e 20 70 3b 0d 09 69 |(p))retu|rn p;..i|
|00000fe0| 66 28 70 3c 30 2e 30 29 | 72 65 74 75 72 6e 20 4e |f(p<0.0)|return N|
|00000ff0| 41 4e 3b 0d 09 69 66 28 | 70 3d 3d 30 2e 30 29 72 |AN;..if(|p==0.0)r|
|00001000| 65 74 75 72 6e 20 2d 49 | 4e 46 3b 0d 09 69 66 28 |eturn -I|NF;..if(|
|00001010| 70 3e 30 2e 35 29 20 72 | 65 74 75 72 6e 20 2d 49 |p>0.5) r|eturn -I|
|00001020| 6e 76 65 72 73 65 4e 6f | 72 6d 61 6c 28 31 2e 30 |nverseNo|rmal(1.0|
|00001030| 2d 70 29 3b 0d 09 74 3d | 73 71 72 74 28 2d 32 2e |-p);..t=|sqrt(-2.|
|00001040| 30 2a 6c 6f 67 28 70 29 | 29 3b 0d 09 78 3d 74 2d |0*log(p)|);..x=t-|
|00001050| 28 32 2e 35 31 35 35 31 | 37 2b 28 30 2e 38 30 32 |(2.51551|7+(0.802|
|00001060| 38 35 33 2b 30 2e 30 31 | 30 33 32 38 2a 74 29 2a |853+0.01|0328*t)*|
|00001070| 74 29 2f 28 31 2e 30 2b | 28 31 2e 34 33 32 37 38 |t)/(1.0+|(1.43278|
|00001080| 38 2b 28 30 2e 31 38 39 | 32 36 39 2b 30 2e 30 30 |8+(0.189|269+0.00|
|00001090| 31 33 30 38 2a 74 29 2a | 74 29 2a 74 29 3b 0d 09 |1308*t)*|t)*t);..|
|000010a0| 72 65 74 75 72 6e 20 2d | 78 3b 0d 7d 0d 0d 64 6f |return -|x;.}..do|
|000010b0| 75 62 6c 65 20 4e 6f 72 | 6d 61 6c 53 61 6d 70 6c |uble Nor|malSampl|
|000010c0| 65 28 76 6f 69 64 29 0d | 7b 0d 09 72 65 74 75 72 |e(void).|{..retur|
|000010d0| 6e 20 49 6e 76 65 72 73 | 65 4e 6f 72 6d 61 6c 28 |n Invers|eNormal(|
|000010e0| 55 6e 69 66 6f 72 6d 53 | 61 6d 70 6c 65 28 29 29 |UniformS|ample())|
|000010f0| 3b 0d 7d 0d 0d 64 6f 75 | 62 6c 65 20 4e 6f 72 6d |;.}..dou|ble Norm|
|00001100| 61 6c 32 44 50 64 66 28 | 64 6f 75 62 6c 65 20 72 |al2DPdf(|double r|
|00001110| 29 0d 2f 2a 20 47 61 75 | 73 73 69 61 6e 20 70 64 |)./* Gau|ssian pd|
|00001120| 66 20 6f 76 65 72 20 74 | 77 6f 20 64 69 6d 65 6e |f over t|wo dimen|
|00001130| 73 69 6f 6e 73 2e 20 2a | 2f 0d 2f 2a 20 54 68 65 |sions. *|/./* The|
|00001140| 20 61 72 67 75 6d 65 6e | 74 20 69 73 20 74 61 6b | argumen|t is tak|
|00001150| 65 6e 20 74 6f 20 62 65 | 20 74 68 65 20 64 69 73 |en to be| the dis|
|00001160| 74 61 6e 63 65 20 66 72 | 6f 6d 20 74 68 65 20 6f |tance fr|om the o|
|00001170| 72 69 67 69 6e 2c 20 5b | 30 2c 49 6e 66 5d 2e 20 |rigin, [|0,Inf]. |
|00001180| 2a 2f 0d 2f 2a 20 54 68 | 65 20 72 6d 73 20 69 73 |*/./* Th|e rms is|
|00001190| 20 31 20 2a 2f 0d 7b 0d | 09 69 66 28 49 73 4e 61 | 1 */.{.|.if(IsNa|
|000011a0| 6e 28 72 29 29 72 65 74 | 75 72 6e 20 72 3b 0d 09 |n(r))ret|urn r;..|
|000011b0| 69 66 28 72 3c 3d 30 2e | 30 29 72 65 74 75 72 6e |if(r<=0.|0)return|
|000011c0| 20 30 2e 30 3b 0d 09 72 | 65 74 75 72 6e 20 32 2a | 0.0;..r|eturn 2*|
|000011d0| 72 2a 65 78 70 28 2d 72 | 2a 72 29 3b 0d 7d 0d 0d |r*exp(-r|*r);.}..|
|000011e0| 64 6f 75 62 6c 65 20 4e | 6f 72 6d 61 6c 32 44 28 |double N|ormal2D(|
|000011f0| 64 6f 75 62 6c 65 20 72 | 29 0d 2f 2a 20 49 6e 74 |double r|)./* Int|
|00001200| 65 67 72 61 6c 20 6f 66 | 20 4e 6f 72 6d 61 6c 32 |egral of| Normal2|
|00001210| 44 50 64 66 28 29 20 66 | 72 6f 6d 20 7a 65 72 6f |DPdf() f|rom zero|
|00001220| 20 74 6f 20 72 2e 20 2a | 2f 0d 7b 0d 09 69 66 28 | to r. *|/.{..if(|
|00001230| 49 73 4e 61 6e 28 72 29 | 29 72 65 74 75 72 6e 20 |IsNan(r)|)return |
|00001240| 72 3b 0d 09 69 66 28 72 | 3c 3d 30 2e 30 29 72 65 |r;..if(r|<=0.0)re|
|00001250| 74 75 72 6e 20 30 2e 30 | 3b 0d 09 72 65 74 75 72 |turn 0.0|;..retur|
|00001260| 6e 20 31 2e 30 2d 65 78 | 70 28 2d 72 2a 72 29 3b |n 1.0-ex|p(-r*r);|
|00001270| 0d 7d 0d 0d 64 6f 75 62 | 6c 65 20 49 6e 76 65 72 |.}..doub|le Inver|
|00001280| 73 65 4e 6f 72 6d 61 6c | 32 44 28 64 6f 75 62 6c |seNormal|2D(doubl|
|00001290| 65 20 70 29 0d 7b 0d 09 | 69 66 28 49 73 4e 61 6e |e p).{..|if(IsNan|
|000012a0| 28 70 29 29 72 65 74 75 | 72 6e 20 70 3b 0d 09 69 |(p))retu|rn p;..i|
|000012b0| 66 28 70 3c 30 2e 30 20 | 7c 7c 20 70 3e 31 2e 30 |f(p<0.0 ||| p>1.0|
|000012c0| 29 72 65 74 75 72 6e 20 | 4e 41 4e 3b 0d 09 72 65 |)return |NAN;..re|
|000012d0| 74 75 72 6e 20 73 71 72 | 74 28 2d 6c 6f 67 28 31 |turn sqr|t(-log(1|
|000012e0| 2e 30 2d 70 29 29 3b 0d | 7d 0d 0d 64 6f 75 62 6c |.0-p));.|}..doubl|
|000012f0| 65 20 4e 6f 72 6d 61 6c | 32 44 53 61 6d 70 6c 65 |e Normal|2DSample|
|00001300| 28 76 6f 69 64 29 0d 2f | 2a 20 72 6d 73 20 69 73 |(void)./|* rms is|
|00001310| 20 31 20 2a 2f 0d 7b 0d | 09 72 65 74 75 72 6e 20 | 1 */.{.|.return |
|00001320| 49 6e 76 65 72 73 65 4e | 6f 72 6d 61 6c 32 44 28 |InverseN|ormal2D(|
|00001330| 55 6e 69 66 6f 72 6d 53 | 61 6d 70 6c 65 28 29 29 |UniformS|ample())|
|00001340| 3b 0d 7d 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |;.}.....|........|
|00001350| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001360| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001370| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001380| 00 00 01 00 00 00 02 20 | 00 00 01 20 00 00 00 3e |....... |... ...>|
|00001390| 28 78 29 0d 2f 2a 20 47 | 61 75 73 73 69 61 6e 20 |(x)./* G|aussian |
|000013a0| 70 64 66 20 2a 2f 0d 64 | 6f 75 62 6c 65 20 78 3b |pdf */.d|ouble x;|
|000013b0| 08 4e 6f 72 6d 61 6c 2e | 63 72 02 00 00 00 54 45 |.Normal.|cr....TE|
|000013c0| 58 54 4b 41 48 4c 00 00 | 00 00 00 00 00 00 00 00 |XTKAHL..|........|
|000013d0| 00 00 54 45 58 54 4b 41 | 48 4c 00 00 00 00 00 00 |..TEXTKA|HL......|
|000013e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000013f0| 00 00 a7 e5 d5 c1 00 00 | 00 00 00 00 02 5e 61 74 |........|.....^at|
|00001400| 69 76 65 20 6e 6f 72 6d | 61 6c 20 64 69 73 74 72 |ive norm|al distr|
|00001410| 69 62 75 74 69 6f 6e 2e | 20 46 72 6f 6d 20 41 62 |ibution.| From Ab|
|00001420| 72 61 6d 6f 77 69 74 7a | 20 61 6e 64 20 53 74 65 |ramowitz| and Ste|
|00001430| 67 75 6e 20 45 71 2e 20 | 28 32 36 2e 32 2e 31 37 |gun Eq. |(26.2.17|
|00001440| 29 2e 0d 45 72 72 6f 72 | 20 7c 65 7c 3c 37 2e 35 |)..Error| |e|<7.5|
|00001450| 20 31 30 5e 2d 38 0d 2a | 2f 0d 7b 0d 09 64 6f 75 | 10^-8.*|/.{..dou|
|00001460| 62 6c 65 20 50 2c 74 2c | 74 74 3b 0d 09 0d 09 69 |ble P,t,|tt;....i|
|00001470| 66 28 78 3c 30 2e 30 29 | 20 72 65 74 75 72 6e 20 |f(x<0.0)| return |
|00001480| 00 00 00 48 00 09 4d 6f | 6e 61 63 6f 00 69 6f 6e |...H..Mo|naco.ion|
|00001490| 73 20 72 65 6c 61 74 65 | 64 20 74 6f 20 74 68 65 |s relate|d to the|
|000014a0| 20 6e 6f 72 6d 61 00 06 | 00 04 00 dc 00 04 01 dd | norma..|........|
|000014b0| 02 3d 00 dc 00 04 01 dd | 02 3d a2 d5 5f 30 00 00 |.=......|.=.._0..|
|000014c0| 01 02 00 00 01 02 00 00 | 00 00 01 00 00 00 00 d0 |........|........|
|000014d0| 00 0a 00 00 0e b9 00 00 | 0e c6 0d 49 6e 76 65 72 |........|...Inver|
|000014e0| 73 65 4e 6f 72 6d 61 6c | 00 00 11 fb 00 00 12 0a |seNormal|........|
|000014f0| 0f 49 6e 76 65 72 73 65 | 4e 6f 72 6d 61 6c 32 44 |.Inverse|Normal2D|
|00001500| 00 00 11 60 00 00 11 60 | 13 49 6e 76 65 72 73 65 |...`...`|.Inverse|
|00001510| 4e 6f 72 6d 61 6c 32 44 | 50 64 66 00 00 00 05 d8 |Normal2D|Pdf.....|
|00001520| 00 00 05 dc 05 6d 61 69 | 6e 00 00 00 0d 71 00 00 |.....mai|n....q..|
|00001530| 0d 77 07 4e 6f 72 6d 61 | 6c 00 00 00 11 67 00 00 |.w.Norma|l....g..|
|00001540| 11 6f 09 4e 6f 72 6d 61 | 6c 32 44 00 00 00 10 7c |.o.Norma|l2D....||
|00001550| 00 00 10 87 0b 4e 6f 72 | 6d 61 6c 32 44 50 64 66 |.....Nor|mal2DPdf|
|00001560| 00 00 12 72 00 00 12 80 | 0f 4e 6f 72 6d 61 6c 32 |...r....|.Normal2|
|00001570| 44 53 61 6d 70 6c 65 00 | 00 00 0c e3 00 00 0c ec |DSample.|........|
|00001580| 09 4e 6f 72 6d 61 6c 50 | 64 66 00 00 10 35 00 00 |.NormalP|df...5..|
|00001590| 10 41 0d 4e 6f 72 6d 61 | 6c 53 61 6d 70 6c 65 00 |.A.Norma|lSample.|
|000015a0| 00 00 01 00 00 00 02 20 | 00 00 01 20 00 00 00 3e |....... |... ...>|
|000015b0| 00 55 f5 18 15 ac 00 00 | 00 1c 00 3e 00 00 4d 50 |.U......|...>..MP|
|000015c0| 53 52 00 01 00 0a 03 ed | ff ff 00 00 00 00 00 00 |SR......|........|
|000015d0| 00 00 03 ef ff ff 00 00 | 00 4c 00 00 00 00 00 00 |........|.L......|
|000015e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000015f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+