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|00000db0| 20 20 2a 0a 58 20 20 20 | 20 2a 2a 2a 2a 2a 2a 2a |  *.X   | *******|
|00000dc0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000dd0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 0a 58 0a |********|*****.X.|
|00000de0| 58 20 20 20 20 44 45 53 | 43 52 49 50 54 49 4f 4e |X    DES|CRIPTION|
|00000df0| 3a 20 20 4d 75 6c 74 69 | 70 6c 79 20 74 77 6f 20 |:  Multi|ply two |
|00000e00| 67 65 6e 65 72 61 6c 20 | 33 78 33 20 6d 61 74 72 |general |3x3 matr|
|00000e10| 69 63 69 65 73 2e 20 20 | 49 66 20 6f 6e 65 20 6f |icies.  |If one o|
|00000e20| 66 0a 58 20 20 20 20 20 | 20 74 68 65 20 69 6e 70 |f.X     | the inp|
|00000e30| 75 74 20 6d 61 74 72 69 | 63 65 73 20 69 73 20 74 |ut matri|ces is t|
|00000e40| 68 65 20 73 61 6d 65 20 | 61 73 20 74 68 65 20 6f |he same |as the o|
|00000e50| 75 74 70 75 74 2c 20 77 | 72 69 74 65 20 74 68 65 |utput, w|rite the|
|00000e60| 0a 58 20 20 20 20 20 20 | 72 65 73 75 6c 74 20 74 |.X      |result t|
|00000e70| 6f 20 61 20 74 65 6d 70 | 6f 72 61 72 79 20 6d 61 |o a temp|orary ma|
|00000e80| 74 72 69 78 20 64 75 72 | 69 6e 67 20 6d 75 6c 74 |trix dur|ing mult|
|00000e90| 69 70 6c 69 63 61 74 69 | 6f 6e 2c 20 74 68 65 6e |iplicati|on, then|
|00000ea0| 0a 58 20 20 20 20 20 20 | 63 6f 70 79 20 74 6f 20 |.X      |copy to |
|00000eb0| 74 68 65 20 6f 75 74 70 | 75 74 20 6d 61 74 72 69 |the outp|ut matri|
|00000ec0| 78 2e 0a 58 0a 58 20 20 | 20 20 45 4e 54 52 59 3a |x..X.X  |  ENTRY:|
|00000ed0| 0a 58 20 20 20 20 20 20 | 61 20 2d 2d 20 70 6f 69 |.X      |a -- poi|
|00000ee0| 6e 74 65 72 20 74 6f 20 | 6c 65 66 74 20 6d 61 74 |nter to |left mat|
|00000ef0| 72 69 78 0a 58 20 20 20 | 20 20 20 62 20 2d 2d 20 |rix.X   |   b -- |
|00000f00| 70 6f 69 6e 74 65 72 20 | 74 6f 20 72 69 67 68 74 |pointer |to right|
|00000f10| 20 6d 61 74 72 69 78 0a | 58 20 20 20 20 20 20 72 | matrix.|X      r|
|00000f20| 65 73 75 6c 74 20 2d 2d | 20 72 65 73 75 6c 74 20 |esult --| result |
|00000f30| 6d 61 74 72 69 78 0a 58 | 0a 58 20 20 20 20 45 58 |matrix.X|.X    EX|
|00000f40| 49 54 3a 20 20 72 65 74 | 75 72 6e 73 20 27 72 65 |IT:  ret|urns 're|
|00000f50| 73 75 6c 74 27 0a 58 2a | 2f 0a 58 0a 58 4d 61 74 |sult'.X*|/.X.XMat|
|00000f60| 72 69 78 33 20 2a 56 32 | 4d 61 74 4d 75 6c 20 28 |rix3 *V2|MatMul (|
|00000f70| 20 61 2c 20 62 2c 20 72 | 65 73 75 6c 74 20 29 0a | a, b, r|esult ).|
|00000f80| 58 72 65 67 69 73 74 65 | 72 20 4d 61 74 72 69 78 |Xregiste|r Matrix|
|00000f90| 33 20 2a 61 2c 2a 62 3b | 0a 58 4d 61 74 72 69 78 |3 *a,*b;|.XMatrix|
|00000fa0| 33 20 2a 72 65 73 75 6c | 74 3b 0a 58 7b 0a 58 72 |3 *resul|t;.X{.Xr|
|00000fb0| 65 67 69 73 74 65 72 20 | 4d 61 74 72 69 78 33 20 |egister |Matrix3 |
|00000fc0| 2a 6d 70 74 72 3b 0a 58 | 69 6e 74 20 75 73 65 74 |*mptr;.X|int uset|
|00000fd0| 65 6d 70 3b 20 20 2f 2a | 20 62 6f 6f 6c 65 61 6e |emp;  /*| boolean|
|00000fe0| 20 2a 2f 0a 58 4d 61 74 | 72 69 78 33 20 74 65 6d | */.XMat|rix3 tem|
|00000ff0| 70 78 3b 0a 58 0a 58 2f | 2a 20 64 65 63 69 64 65 |px;.X.X/|* decide|
|00001000| 20 77 68 65 72 65 20 69 | 6e 74 65 72 6d 65 64 69 | where i|ntermedi|
|00001010| 61 74 65 20 72 65 73 75 | 6c 74 20 67 6f 65 73 20 |ate resu|lt goes |
|00001020| 2a 2f 0a 58 75 73 65 74 | 65 6d 70 20 3d 20 28 20 |*/.Xuset|emp = ( |
|00001030| 61 20 3d 3d 20 72 65 73 | 75 6c 74 20 20 7c 7c 20 |a == res|ult  || |
|00001040| 20 62 20 3d 3d 20 72 65 | 73 75 6c 74 20 29 3b 0a | b == re|sult );.|
|00001050| 58 69 66 20 28 20 75 73 | 65 74 65 6d 70 20 29 0a |Xif ( us|etemp ).|
|00001060| 58 20 20 6d 70 74 72 20 | 3d 20 26 20 74 65 6d 70 |X  mptr |= & temp|
|00001070| 78 3b 0a 58 65 6c 73 65 | 0a 58 20 20 6d 70 74 72 |x;.Xelse|.X  mptr|
|00001080| 20 3d 20 72 65 73 75 6c | 74 3b 0a 58 0a 58 4d 56 | = resul|t;.X.XMV|
|00001090| 41 4c 28 6d 70 74 72 2c | 30 2c 30 29 20 3d 0a 58 |AL(mptr,|0,0) =.X|
|000010a0| 20 20 20 20 20 4d 56 41 | 4c 28 61 2c 30 2c 30 29 |     MVA|L(a,0,0)|
|000010b0| 20 2a 20 4d 56 41 4c 28 | 62 2c 30 2c 30 29 0a 58 | * MVAL(|b,0,0).X|
|000010c0| 20 20 2b 20 20 4d 56 41 | 4c 28 61 2c 30 2c 31 29 |  +  MVA|L(a,0,1)|
|000010d0| 20 2a 20 4d 56 41 4c 28 | 62 2c 31 2c 30 29 0a 58 | * MVAL(|b,1,0).X|
|000010e0| 20 20 2b 20 20 4d 56 41 | 4c 28 61 2c 30 2c 32 29 |  +  MVA|L(a,0,2)|
|000010f0| 20 2a 20 4d 56 41 4c 28 | 62 2c 32 2c 30 29 3b 0a | * MVAL(|b,2,0);.|
|00001100| 58 0a 58 4d 56 41 4c 28 | 6d 70 74 72 2c 30 2c 31 |X.XMVAL(|mptr,0,1|
|00001110| 29 20 3d 0a 58 20 20 20 | 20 20 4d 56 41 4c 28 61 |) =.X   |  MVAL(a|
|00001120| 2c 30 2c 30 29 20 2a 20 | 4d 56 41 4c 28 62 2c 30 |,0,0) * |MVAL(b,0|
|00001130| 2c 31 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,1).X  +|  MVAL(a|
|00001140| 2c 30 2c 31 29 20 2a 20 | 4d 56 41 4c 28 62 2c 31 |,0,1) * |MVAL(b,1|
|00001150| 2c 31 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,1).X  +|  MVAL(a|
|00001160| 2c 30 2c 32 29 20 2a 20 | 4d 56 41 4c 28 62 2c 32 |,0,2) * |MVAL(b,2|
|00001170| 2c 31 29 3b 0a 58 0a 58 | 4d 56 41 4c 28 6d 70 74 |,1);.X.X|MVAL(mpt|
|00001180| 72 2c 30 2c 32 29 20 3d | 0a 58 20 20 20 20 20 4d |r,0,2) =|.X     M|
|00001190| 56 41 4c 28 61 2c 30 2c | 30 29 20 2a 20 4d 56 41 |VAL(a,0,|0) * MVA|
|000011a0| 4c 28 62 2c 30 2c 32 29 | 0a 58 20 20 2b 20 20 4d |L(b,0,2)|.X  +  M|
|000011b0| 56 41 4c 28 61 2c 30 2c | 31 29 20 2a 20 4d 56 41 |VAL(a,0,|1) * MVA|
|000011c0| 4c 28 62 2c 31 2c 32 29 | 0a 58 20 20 2b 20 20 4d |L(b,1,2)|.X  +  M|
|000011d0| 56 41 4c 28 61 2c 30 2c | 32 29 20 2a 20 4d 56 41 |VAL(a,0,|2) * MVA|
|000011e0| 4c 28 62 2c 32 2c 32 29 | 3b 0a 58 0a 58 4d 56 41 |L(b,2,2)|;.X.XMVA|
|000011f0| 4c 28 6d 70 74 72 2c 31 | 2c 30 29 20 3d 0a 58 20 |L(mptr,1|,0) =.X |
|00001200| 20 20 20 20 4d 56 41 4c | 28 61 2c 31 2c 30 29 20 |    MVAL|(a,1,0) |
|00001210| 2a 20 4d 56 41 4c 28 62 | 2c 30 2c 30 29 0a 58 20 |* MVAL(b|,0,0).X |
|00001220| 20 2b 20 20 4d 56 41 4c | 28 61 2c 31 2c 31 29 20 | +  MVAL|(a,1,1) |
|00001230| 2a 20 4d 56 41 4c 28 62 | 2c 31 2c 30 29 0a 58 20 |* MVAL(b|,1,0).X |
|00001240| 20 2b 20 20 4d 56 41 4c | 28 61 2c 31 2c 32 29 20 | +  MVAL|(a,1,2) |
|00001250| 2a 20 4d 56 41 4c 28 62 | 2c 32 2c 30 29 3b 0a 58 |* MVAL(b|,2,0);.X|
|00001260| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 31 2c 31 29 |.XMVAL(m|ptr,1,1)|
|00001270| 20 3d 0a 58 20 20 20 20 | 20 4d 56 41 4c 28 61 2c | =.X    | MVAL(a,|
|00001280| 31 2c 30 29 20 2a 20 4d | 56 41 4c 28 62 2c 30 2c |1,0) * M|VAL(b,0,|
|00001290| 31 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |1).X  + | MVAL(a,|
|000012a0| 31 2c 31 29 20 2a 20 4d | 56 41 4c 28 62 2c 31 2c |1,1) * M|VAL(b,1,|
|000012b0| 31 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |1).X  + | MVAL(a,|
|000012c0| 31 2c 32 29 20 2a 20 4d | 56 41 4c 28 62 2c 32 2c |1,2) * M|VAL(b,2,|
|000012d0| 31 29 3b 0a 58 0a 58 4d | 56 41 4c 28 6d 70 74 72 |1);.X.XM|VAL(mptr|
|000012e0| 2c 31 2c 32 29 20 3d 0a | 58 20 20 20 20 20 4d 56 |,1,2) =.|X     MV|
|000012f0| 41 4c 28 61 2c 31 2c 30 | 29 20 2a 20 4d 56 41 4c |AL(a,1,0|) * MVAL|
|00001300| 28 62 2c 30 2c 32 29 0a | 58 20 20 2b 20 20 4d 56 |(b,0,2).|X  +  MV|
|00001310| 41 4c 28 61 2c 31 2c 31 | 29 20 2a 20 4d 56 41 4c |AL(a,1,1|) * MVAL|
|00001320| 28 62 2c 31 2c 32 29 0a | 58 20 20 2b 20 20 4d 56 |(b,1,2).|X  +  MV|
|00001330| 41 4c 28 61 2c 31 2c 32 | 29 20 2a 20 4d 56 41 4c |AL(a,1,2|) * MVAL|
|00001340| 28 62 2c 32 2c 32 29 3b | 0a 58 0a 58 4d 56 41 4c |(b,2,2);|.X.XMVAL|
|00001350| 28 6d 70 74 72 2c 32 2c | 30 29 20 3d 0a 58 20 20 |(mptr,2,|0) =.X  |
|00001360| 20 20 20 4d 56 41 4c 28 | 61 2c 32 2c 30 29 20 2a |   MVAL(|a,2,0) *|
|00001370| 20 4d 56 41 4c 28 62 2c | 30 2c 30 29 0a 58 20 20 | MVAL(b,|0,0).X  |
|00001380| 2b 20 20 4d 56 41 4c 28 | 61 2c 32 2c 31 29 20 2a |+  MVAL(|a,2,1) *|
|00001390| 20 4d 56 41 4c 28 62 2c | 31 2c 30 29 0a 58 20 20 | MVAL(b,|1,0).X  |
|000013a0| 2b 20 20 4d 56 41 4c 28 | 61 2c 32 2c 32 29 20 2a |+  MVAL(|a,2,2) *|
|000013b0| 20 4d 56 41 4c 28 62 2c | 32 2c 30 29 3b 0a 58 0a | MVAL(b,|2,0);.X.|
|000013c0| 58 4d 56 41 4c 28 6d 70 | 74 72 2c 32 2c 31 29 20 |XMVAL(mp|tr,2,1) |
|000013d0| 3d 0a 58 20 20 20 20 20 | 4d 56 41 4c 28 61 2c 32 |=.X     |MVAL(a,2|
|000013e0| 2c 30 29 20 2a 20 4d 56 | 41 4c 28 62 2c 30 2c 31 |,0) * MV|AL(b,0,1|
|000013f0| 29 0a 58 20 20 2b 20 20 | 4d 56 41 4c 28 61 2c 32 |).X  +  |MVAL(a,2|
|00001400| 2c 31 29 20 2a 20 4d 56 | 41 4c 28 62 2c 31 2c 31 |,1) * MV|AL(b,1,1|
|00001410| 29 0a 58 20 20 2b 20 20 | 4d 56 41 4c 28 61 2c 32 |).X  +  |MVAL(a,2|
|00001420| 2c 32 29 20 2a 20 4d 56 | 41 4c 28 62 2c 32 2c 31 |,2) * MV|AL(b,2,1|
|00001430| 29 3b 0a 58 0a 58 4d 56 | 41 4c 28 6d 70 74 72 2c |);.X.XMV|AL(mptr,|
|00001440| 32 2c 32 29 20 3d 0a 58 | 20 20 20 20 20 4d 56 41 |2,2) =.X|     MVA|
|00001450| 4c 28 61 2c 32 2c 30 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,0)| * MVAL(|
|00001460| 62 2c 30 2c 32 29 0a 58 | 20 20 2b 20 20 4d 56 41 |b,0,2).X|  +  MVA|
|00001470| 4c 28 61 2c 32 2c 31 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,1)| * MVAL(|
|00001480| 62 2c 31 2c 32 29 0a 58 | 20 20 2b 20 20 4d 56 41 |b,1,2).X|  +  MVA|
|00001490| 4c 28 61 2c 32 2c 32 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,2)| * MVAL(|
|000014a0| 62 2c 32 2c 32 29 3b 0a | 58 0a 58 2f 2a 20 63 6f |b,2,2);.|X.X/* co|
|000014b0| 70 79 20 74 65 6d 70 20 | 6d 61 74 72 69 78 20 74 |py temp |matrix t|
|000014c0| 6f 20 72 65 73 75 6c 74 | 20 69 66 20 6e 65 65 64 |o result| if need|
|000014d0| 65 64 20 2a 2f 0a 58 69 | 66 20 28 20 75 73 65 74 |ed */.Xi|f ( uset|
|000014e0| 65 6d 70 20 29 0a 58 20 | 20 2a 72 65 73 75 6c 74 |emp ).X | *result|
|000014f0| 20 3d 20 2a 6d 70 74 72 | 3b 0a 58 0a 58 72 65 74 | = *mptr|;.X.Xret|
|00001500| 75 72 6e 20 72 65 73 75 | 6c 74 3b 0a 58 7d 0a 58 |urn resu|lt;.X}.X|
|00001510| 0a 58 0a 58 0a 58 0a 58 | 2f 2a 20 20 2a 2a 2a 2a |.X.X.X.X|/*  ****|
|00001520| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001530| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001540| 0a 58 20 20 20 20 2a 20 | 20 20 20 20 20 20 20 20 |.X    * |        |
|00001550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001560| 20 20 20 20 20 20 20 20 | 20 2a 0a 58 20 20 20 20 |        | *.X    |
|00001570| 2a 20 20 20 20 20 20 20 | 20 20 20 20 56 33 4d 61 |*       |    V3Ma|
|00001580| 74 4d 75 6c 20 20 20 20 | 20 20 20 20 20 20 20 20 |tMul    |        |
|00001590| 20 20 20 2a 0a 58 20 20 | 20 20 2a 20 20 20 20 20 |   *.X  |  *     |
|000015a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2a 0a 58 |        |     *.X|
|000015c0| 20 20 20 20 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |    ****|********|
|000015d0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000015e0| 2a 2a 2a 2a 2a 2a 2a 2a | 0a 58 0a 58 20 20 20 20 |********|.X.X    |
|000015f0| 44 45 53 43 52 49 50 54 | 49 4f 4e 3a 20 20 4d 75 |DESCRIPT|ION:  Mu|
|00001600| 6c 74 69 70 6c 79 20 74 | 77 6f 20 67 65 6e 65 72 |ltiply t|wo gener|
|00001610| 61 6c 20 34 78 34 20 6d | 61 74 72 69 63 69 65 73 |al 4x4 m|atricies|
|00001620| 2e 20 20 49 66 20 6f 6e | 65 20 6f 66 0a 58 20 20 |.  If on|e of.X  |
|00001630| 20 20 20 20 74 68 65 20 | 69 6e 70 75 74 20 6d 61 |    the |input ma|
|00001640| 74 72 69 63 65 73 20 69 | 73 20 74 68 65 20 73 61 |trices i|s the sa|
|00001650| 6d 65 20 61 73 20 74 68 | 65 20 6f 75 74 70 75 74 |me as th|e output|
|00001660| 2c 20 77 72 69 74 65 20 | 74 68 65 0a 58 20 20 20 |, write |the.X   |
|00001670| 20 20 20 72 65 73 75 6c | 74 20 74 6f 20 61 20 74 |   resul|t to a t|
|00001680| 65 6d 70 6f 72 61 72 79 | 20 6d 61 74 72 69 78 20 |emporary| matrix |
|00001690| 64 75 72 69 6e 67 20 6d | 75 6c 74 69 70 6c 69 63 |during m|ultiplic|
|000016a0| 61 74 69 6f 6e 2c 20 74 | 68 65 6e 0a 58 20 20 20 |ation, t|hen.X   |
|000016b0| 20 20 20 63 6f 70 79 20 | 74 6f 20 74 68 65 20 6f |   copy |to the o|
|000016c0| 75 74 70 75 74 20 6d 61 | 74 72 69 78 2e 0a 58 0a |utput ma|trix..X.|
|000016d0| 58 20 20 20 20 45 4e 54 | 52 59 3a 0a 58 20 20 20 |X    ENT|RY:.X   |
|000016e0| 20 20 20 61 20 2d 2d 20 | 70 6f 69 6e 74 65 72 20 |   a -- |pointer |
|000016f0| 74 6f 20 6c 65 66 74 20 | 6d 61 74 72 69 78 0a 58 |to left |matrix.X|
|00001700| 20 20 20 20 20 20 62 20 | 2d 2d 20 70 6f 69 6e 74 |      b |-- point|
|00001710| 65 72 20 74 6f 20 72 69 | 67 68 74 20 6d 61 74 72 |er to ri|ght matr|
|00001720| 69 78 0a 58 20 20 20 20 | 20 20 72 65 73 75 6c 74 |ix.X    |  result|
|00001730| 20 2d 2d 20 72 65 73 75 | 6c 74 20 6d 61 74 72 69 | -- resu|lt matri|
|00001740| 78 0a 58 0a 58 20 20 20 | 20 45 58 49 54 3a 20 20 |x.X.X   | EXIT:  |
|00001750| 72 65 74 75 72 6e 73 20 | 27 72 65 73 75 6c 74 27 |returns |'result'|
|00001760| 0a 58 2a 2f 0a 58 0a 58 | 4d 61 74 72 69 78 34 20 |.X*/.X.X|Matrix4 |
|00001770| 2a 56 33 4d 61 74 4d 75 | 6c 20 28 20 61 2c 20 62 |*V3MatMu|l ( a, b|
|00001780| 2c 20 72 65 73 75 6c 74 | 20 29 0a 58 72 65 67 69 |, result| ).Xregi|
|00001790| 73 74 65 72 20 4d 61 74 | 72 69 78 34 20 2a 61 2c |ster Mat|rix4 *a,|
|000017a0| 2a 62 3b 0a 58 4d 61 74 | 72 69 78 34 20 2a 72 65 |*b;.XMat|rix4 *re|
|000017b0| 73 75 6c 74 3b 0a 58 7b | 0a 58 72 65 67 69 73 74 |sult;.X{|.Xregist|
|000017c0| 65 72 20 4d 61 74 72 69 | 78 34 20 2a 6d 70 74 72 |er Matri|x4 *mptr|
|000017d0| 3b 0a 58 69 6e 74 20 75 | 73 65 74 65 6d 70 3b 20 |;.Xint u|setemp; |
|000017e0| 20 2f 2a 20 62 6f 6f 6c | 65 61 6e 20 2a 2f 0a 58 | /* bool|ean */.X|
|000017f0| 4d 61 74 72 69 78 34 20 | 74 65 6d 70 78 3b 0a 58 |Matrix4 |tempx;.X|
|00001800| 0a 58 2f 2a 20 64 65 63 | 69 64 65 20 77 68 65 72 |.X/* dec|ide wher|
|00001810| 65 20 69 6e 74 65 72 6d | 65 64 69 61 74 65 20 72 |e interm|ediate r|
|00001820| 65 73 75 6c 74 20 67 6f | 65 73 20 2a 2f 0a 58 75 |esult go|es */.Xu|
|00001830| 73 65 74 65 6d 70 20 3d | 20 28 20 61 20 3d 3d 20 |setemp =| ( a == |
|00001840| 72 65 73 75 6c 74 20 20 | 7c 7c 20 20 62 20 3d 3d |result  |||  b ==|
|00001850| 20 72 65 73 75 6c 74 20 | 29 3b 0a 58 69 66 20 28 | result |);.Xif (|
|00001860| 20 75 73 65 74 65 6d 70 | 20 29 0a 58 20 20 6d 70 | usetemp| ).X  mp|
|00001870| 74 72 20 3d 20 26 20 74 | 65 6d 70 78 3b 0a 58 65 |tr = & t|empx;.Xe|
|00001880| 6c 73 65 0a 58 20 20 6d | 70 74 72 20 3d 20 72 65 |lse.X  m|ptr = re|
|00001890| 73 75 6c 74 3b 0a 58 0a | 58 4d 56 41 4c 28 6d 70 |sult;.X.|XMVAL(mp|
|000018a0| 74 72 2c 30 2c 30 29 20 | 3d 0a 58 20 20 20 20 20 |tr,0,0) |=.X     |
|000018b0| 4d 56 41 4c 28 61 2c 30 | 2c 30 29 20 2a 20 4d 56 |MVAL(a,0|,0) * MV|
|000018c0| 41 4c 28 62 2c 30 2c 30 | 29 0a 58 20 20 2b 20 20 |AL(b,0,0|).X  +  |
|000018d0| 4d 56 41 4c 28 61 2c 30 | 2c 31 29 20 2a 20 4d 56 |MVAL(a,0|,1) * MV|
|000018e0| 41 4c 28 62 2c 31 2c 30 | 29 0a 58 20 20 2b 20 20 |AL(b,1,0|).X  +  |
|000018f0| 4d 56 41 4c 28 61 2c 30 | 2c 32 29 20 2a 20 4d 56 |MVAL(a,0|,2) * MV|
|00001900| 41 4c 28 62 2c 32 2c 30 | 29 0a 58 20 20 2b 20 20 |AL(b,2,0|).X  +  |
|00001910| 4d 56 41 4c 28 61 2c 30 | 2c 33 29 20 2a 20 4d 56 |MVAL(a,0|,3) * MV|
|00001920| 41 4c 28 62 2c 33 2c 30 | 29 3b 0a 58 0a 58 4d 56 |AL(b,3,0|);.X.XMV|
|00001930| 41 4c 28 6d 70 74 72 2c | 30 2c 31 29 20 3d 0a 58 |AL(mptr,|0,1) =.X|
|00001940| 20 20 20 20 20 4d 56 41 | 4c 28 61 2c 30 2c 30 29 |     MVA|L(a,0,0)|
|00001950| 20 2a 20 4d 56 41 4c 28 | 62 2c 30 2c 31 29 0a 58 | * MVAL(|b,0,1).X|
|00001960| 20 20 2b 20 20 4d 56 41 | 4c 28 61 2c 30 2c 31 29 |  +  MVA|L(a,0,1)|
|00001970| 20 2a 20 4d 56 41 4c 28 | 62 2c 31 2c 31 29 0a 58 | * MVAL(|b,1,1).X|
|00001980| 20 20 2b 20 20 4d 56 41 | 4c 28 61 2c 30 2c 32 29 |  +  MVA|L(a,0,2)|
|00001990| 20 2a 20 4d 56 41 4c 28 | 62 2c 32 2c 31 29 0a 58 | * MVAL(|b,2,1).X|
|000019a0| 20 20 2b 20 20 4d 56 41 | 4c 28 61 2c 30 2c 33 29 |  +  MVA|L(a,0,3)|
|000019b0| 20 2a 20 4d 56 41 4c 28 | 62 2c 33 2c 31 29 3b 0a | * MVAL(|b,3,1);.|
|000019c0| 58 0a 58 4d 56 41 4c 28 | 6d 70 74 72 2c 30 2c 32 |X.XMVAL(|mptr,0,2|
|000019d0| 29 20 3d 0a 58 20 20 20 | 20 20 4d 56 41 4c 28 61 |) =.X   |  MVAL(a|
|000019e0| 2c 30 2c 30 29 20 2a 20 | 4d 56 41 4c 28 62 2c 30 |,0,0) * |MVAL(b,0|
|000019f0| 2c 32 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,2).X  +|  MVAL(a|
|00001a00| 2c 30 2c 31 29 20 2a 20 | 4d 56 41 4c 28 62 2c 31 |,0,1) * |MVAL(b,1|
|00001a10| 2c 32 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,2).X  +|  MVAL(a|
|00001a20| 2c 30 2c 32 29 20 2a 20 | 4d 56 41 4c 28 62 2c 32 |,0,2) * |MVAL(b,2|
|00001a30| 2c 32 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,2).X  +|  MVAL(a|
|00001a40| 2c 30 2c 33 29 20 2a 20 | 4d 56 41 4c 28 62 2c 33 |,0,3) * |MVAL(b,3|
|00001a50| 2c 32 29 3b 0a 58 0a 58 | 4d 56 41 4c 28 6d 70 74 |,2);.X.X|MVAL(mpt|
|00001a60| 72 2c 30 2c 33 29 20 3d | 0a 58 20 20 20 20 20 4d |r,0,3) =|.X     M|
|00001a70| 56 41 4c 28 61 2c 30 2c | 30 29 20 2a 20 4d 56 41 |VAL(a,0,|0) * MVA|
|00001a80| 4c 28 62 2c 30 2c 33 29 | 0a 58 20 20 2b 20 20 4d |L(b,0,3)|.X  +  M|
|00001a90| 56 41 4c 28 61 2c 30 2c | 31 29 20 2a 20 4d 56 41 |VAL(a,0,|1) * MVA|
|00001aa0| 4c 28 62 2c 31 2c 33 29 | 0a 58 20 20 2b 20 20 4d |L(b,1,3)|.X  +  M|
|00001ab0| 56 41 4c 28 61 2c 30 2c | 32 29 20 2a 20 4d 56 41 |VAL(a,0,|2) * MVA|
|00001ac0| 4c 28 62 2c 32 2c 33 29 | 0a 58 20 20 2b 20 20 4d |L(b,2,3)|.X  +  M|
|00001ad0| 56 41 4c 28 61 2c 30 2c | 33 29 20 2a 20 4d 56 41 |VAL(a,0,|3) * MVA|
|00001ae0| 4c 28 62 2c 33 2c 33 29 | 3b 0a 58 0a 58 4d 56 41 |L(b,3,3)|;.X.XMVA|
|00001af0| 4c 28 6d 70 74 72 2c 31 | 2c 30 29 20 3d 0a 58 20 |L(mptr,1|,0) =.X |
|00001b00| 20 20 20 20 4d 56 41 4c | 28 61 2c 31 2c 30 29 20 |    MVAL|(a,1,0) |
|00001b10| 2a 20 4d 56 41 4c 28 62 | 2c 30 2c 30 29 0a 58 20 |* MVAL(b|,0,0).X |
|00001b20| 20 2b 20 20 4d 56 41 4c | 28 61 2c 31 2c 31 29 20 | +  MVAL|(a,1,1) |
|00001b30| 2a 20 4d 56 41 4c 28 62 | 2c 31 2c 30 29 0a 58 20 |* MVAL(b|,1,0).X |
|00001b40| 20 2b 20 20 4d 56 41 4c | 28 61 2c 31 2c 32 29 20 | +  MVAL|(a,1,2) |
|00001b50| 2a 20 4d 56 41 4c 28 62 | 2c 32 2c 30 29 0a 58 20 |* MVAL(b|,2,0).X |
|00001b60| 20 2b 20 20 4d 56 41 4c | 28 61 2c 31 2c 33 29 20 | +  MVAL|(a,1,3) |
|00001b70| 2a 20 4d 56 41 4c 28 62 | 2c 33 2c 30 29 3b 0a 58 |* MVAL(b|,3,0);.X|
|00001b80| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 31 2c 31 29 |.XMVAL(m|ptr,1,1)|
|00001b90| 20 3d 0a 58 20 20 20 20 | 20 4d 56 41 4c 28 61 2c | =.X    | MVAL(a,|
|00001ba0| 31 2c 30 29 20 2a 20 4d | 56 41 4c 28 62 2c 30 2c |1,0) * M|VAL(b,0,|
|00001bb0| 31 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |1).X  + | MVAL(a,|
|00001bc0| 31 2c 31 29 20 2a 20 4d | 56 41 4c 28 62 2c 31 2c |1,1) * M|VAL(b,1,|
|00001bd0| 31 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |1).X  + | MVAL(a,|
|00001be0| 31 2c 32 29 20 2a 20 4d | 56 41 4c 28 62 2c 32 2c |1,2) * M|VAL(b,2,|
|00001bf0| 31 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |1).X  + | MVAL(a,|
|00001c00| 31 2c 33 29 20 2a 20 4d | 56 41 4c 28 62 2c 33 2c |1,3) * M|VAL(b,3,|
|00001c10| 31 29 3b 0a 58 0a 58 4d | 56 41 4c 28 6d 70 74 72 |1);.X.XM|VAL(mptr|
|00001c20| 2c 31 2c 32 29 20 3d 0a | 58 20 20 20 20 20 4d 56 |,1,2) =.|X     MV|
|00001c30| 41 4c 28 61 2c 31 2c 30 | 29 20 2a 20 4d 56 41 4c |AL(a,1,0|) * MVAL|
|00001c40| 28 62 2c 30 2c 32 29 0a | 58 20 20 2b 20 20 4d 56 |(b,0,2).|X  +  MV|
|00001c50| 41 4c 28 61 2c 31 2c 31 | 29 20 2a 20 4d 56 41 4c |AL(a,1,1|) * MVAL|
|00001c60| 28 62 2c 31 2c 32 29 0a | 58 20 20 2b 20 20 4d 56 |(b,1,2).|X  +  MV|
|00001c70| 41 4c 28 61 2c 31 2c 32 | 29 20 2a 20 4d 56 41 4c |AL(a,1,2|) * MVAL|
|00001c80| 28 62 2c 32 2c 32 29 0a | 58 20 20 2b 20 20 4d 56 |(b,2,2).|X  +  MV|
|00001c90| 41 4c 28 61 2c 31 2c 33 | 29 20 2a 20 4d 56 41 4c |AL(a,1,3|) * MVAL|
|00001ca0| 28 62 2c 33 2c 32 29 3b | 0a 58 0a 58 4d 56 41 4c |(b,3,2);|.X.XMVAL|
|00001cb0| 28 6d 70 74 72 2c 31 2c | 33 29 20 3d 0a 58 20 20 |(mptr,1,|3) =.X  |
|00001cc0| 20 20 20 4d 56 41 4c 28 | 61 2c 31 2c 30 29 20 2a |   MVAL(|a,1,0) *|
|00001cd0| 20 4d 56 41 4c 28 62 2c | 30 2c 33 29 0a 58 20 20 | MVAL(b,|0,3).X  |
|00001ce0| 2b 20 20 4d 56 41 4c 28 | 61 2c 31 2c 31 29 20 2a |+  MVAL(|a,1,1) *|
|00001cf0| 20 4d 56 41 4c 28 62 2c | 31 2c 33 29 0a 58 20 20 | MVAL(b,|1,3).X  |
|00001d00| 2b 20 20 4d 56 41 4c 28 | 61 2c 31 2c 32 29 20 2a |+  MVAL(|a,1,2) *|
|00001d10| 20 4d 56 41 4c 28 62 2c | 32 2c 33 29 0a 58 20 20 | MVAL(b,|2,3).X  |
|00001d20| 2b 20 20 4d 56 41 4c 28 | 61 2c 31 2c 33 29 20 2a |+  MVAL(|a,1,3) *|
|00001d30| 20 4d 56 41 4c 28 62 2c | 33 2c 33 29 3b 0a 58 0a | MVAL(b,|3,3);.X.|
|00001d40| 58 4d 56 41 4c 28 6d 70 | 74 72 2c 32 2c 30 29 20 |XMVAL(mp|tr,2,0) |
|00001d50| 3d 0a 58 20 20 20 20 20 | 4d 56 41 4c 28 61 2c 32 |=.X     |MVAL(a,2|
|00001d60| 2c 30 29 20 2a 20 4d 56 | 41 4c 28 62 2c 30 2c 30 |,0) * MV|AL(b,0,0|
|00001d70| 29 0a 58 20 20 2b 20 20 | 4d 56 41 4c 28 61 2c 32 |).X  +  |MVAL(a,2|
|00001d80| 2c 31 29 20 2a 20 4d 56 | 41 4c 28 62 2c 31 2c 30 |,1) * MV|AL(b,1,0|
|00001d90| 29 0a 58 20 20 2b 20 20 | 4d 56 41 4c 28 61 2c 32 |).X  +  |MVAL(a,2|
|00001da0| 2c 32 29 20 2a 20 4d 56 | 41 4c 28 62 2c 32 2c 30 |,2) * MV|AL(b,2,0|
|00001db0| 29 0a 58 20 20 2b 20 20 | 4d 56 41 4c 28 61 2c 32 |).X  +  |MVAL(a,2|
|00001dc0| 2c 33 29 20 2a 20 4d 56 | 41 4c 28 62 2c 33 2c 30 |,3) * MV|AL(b,3,0|
|00001dd0| 29 3b 0a 58 0a 58 4d 56 | 41 4c 28 6d 70 74 72 2c |);.X.XMV|AL(mptr,|
|00001de0| 32 2c 31 29 20 3d 0a 58 | 20 20 20 20 20 4d 56 41 |2,1) =.X|     MVA|
|00001df0| 4c 28 61 2c 32 2c 30 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,0)| * MVAL(|
|00001e00| 62 2c 30 2c 31 29 0a 58 | 20 20 2b 20 20 4d 56 41 |b,0,1).X|  +  MVA|
|00001e10| 4c 28 61 2c 32 2c 31 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,1)| * MVAL(|
|00001e20| 62 2c 31 2c 31 29 0a 58 | 20 20 2b 20 20 4d 56 41 |b,1,1).X|  +  MVA|
|00001e30| 4c 28 61 2c 32 2c 32 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,2)| * MVAL(|
|00001e40| 62 2c 32 2c 31 29 0a 58 | 20 20 2b 20 20 4d 56 41 |b,2,1).X|  +  MVA|
|00001e50| 4c 28 61 2c 32 2c 33 29 | 20 2a 20 4d 56 41 4c 28 |L(a,2,3)| * MVAL(|
|00001e60| 62 2c 33 2c 31 29 3b 0a | 58 0a 58 4d 56 41 4c 28 |b,3,1);.|X.XMVAL(|
|00001e70| 6d 70 74 72 2c 32 2c 32 | 29 20 3d 0a 58 20 20 20 |mptr,2,2|) =.X   |
|00001e80| 20 20 4d 56 41 4c 28 61 | 2c 32 2c 30 29 20 2a 20 |  MVAL(a|,2,0) * |
|00001e90| 4d 56 41 4c 28 62 2c 30 | 2c 32 29 0a 58 20 20 2b |MVAL(b,0|,2).X  +|
|00001ea0| 20 20 4d 56 41 4c 28 61 | 2c 32 2c 31 29 20 2a 20 |  MVAL(a|,2,1) * |
|00001eb0| 4d 56 41 4c 28 62 2c 31 | 2c 32 29 0a 58 20 20 2b |MVAL(b,1|,2).X  +|
|00001ec0| 20 20 4d 56 41 4c 28 61 | 2c 32 2c 32 29 20 2a 20 |  MVAL(a|,2,2) * |
|00001ed0| 4d 56 41 4c 28 62 2c 32 | 2c 32 29 0a 58 20 20 2b |MVAL(b,2|,2).X  +|
|00001ee0| 20 20 4d 56 41 4c 28 61 | 2c 32 2c 33 29 20 2a 20 |  MVAL(a|,2,3) * |
|00001ef0| 4d 56 41 4c 28 62 2c 33 | 2c 32 29 3b 0a 58 0a 58 |MVAL(b,3|,2);.X.X|
|00001f00| 4d 56 41 4c 28 6d 70 74 | 72 2c 32 2c 33 29 20 3d |MVAL(mpt|r,2,3) =|
|00001f10| 0a 58 20 20 20 20 20 4d | 56 41 4c 28 61 2c 32 2c |.X     M|VAL(a,2,|
|00001f20| 30 29 20 2a 20 4d 56 41 | 4c 28 62 2c 30 2c 33 29 |0) * MVA|L(b,0,3)|
|00001f30| 0a 58 20 20 2b 20 20 4d | 56 41 4c 28 61 2c 32 2c |.X  +  M|VAL(a,2,|
|00001f40| 31 29 20 2a 20 4d 56 41 | 4c 28 62 2c 31 2c 33 29 |1) * MVA|L(b,1,3)|
|00001f50| 0a 58 20 20 2b 20 20 4d | 56 41 4c 28 61 2c 32 2c |.X  +  M|VAL(a,2,|
|00001f60| 32 29 20 2a 20 4d 56 41 | 4c 28 62 2c 32 2c 33 29 |2) * MVA|L(b,2,3)|
|00001f70| 0a 58 20 20 2b 20 20 4d | 56 41 4c 28 61 2c 32 2c |.X  +  M|VAL(a,2,|
|00001f80| 33 29 20 2a 20 4d 56 41 | 4c 28 62 2c 33 2c 33 29 |3) * MVA|L(b,3,3)|
|00001f90| 3b 0a 58 0a 58 4d 56 41 | 4c 28 6d 70 74 72 2c 33 |;.X.XMVA|L(mptr,3|
|00001fa0| 2c 30 29 20 3d 0a 58 20 | 20 20 20 20 4d 56 41 4c |,0) =.X |    MVAL|
|00001fb0| 28 61 2c 33 2c 30 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,3,0) |* MVAL(b|
|00001fc0| 2c 30 2c 30 29 0a 58 20 | 20 2b 20 20 4d 56 41 4c |,0,0).X | +  MVAL|
|00001fd0| 28 61 2c 33 2c 31 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,3,1) |* MVAL(b|
|00001fe0| 2c 31 2c 30 29 0a 58 20 | 20 2b 20 20 4d 56 41 4c |,1,0).X | +  MVAL|
|00001ff0| 28 61 2c 33 2c 32 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,3,2) |* MVAL(b|
|00002000| 2c 32 2c 30 29 0a 58 20 | 20 2b 20 20 4d 56 41 4c |,2,0).X | +  MVAL|
|00002010| 28 61 2c 33 2c 33 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,3,3) |* MVAL(b|
|00002020| 2c 33 2c 30 29 3b 0a 58 | 0a 58 4d 56 41 4c 28 6d |,3,0);.X|.XMVAL(m|
|00002030| 70 74 72 2c 33 2c 31 29 | 20 3d 0a 58 20 20 20 20 |ptr,3,1)| =.X    |
|00002040| 20 4d 56 41 4c 28 61 2c | 33 2c 30 29 20 2a 20 4d | MVAL(a,|3,0) * M|
|00002050| 56 41 4c 28 62 2c 30 2c | 31 29 0a 58 20 20 2b 20 |VAL(b,0,|1).X  + |
|00002060| 20 4d 56 41 4c 28 61 2c | 33 2c 31 29 20 2a 20 4d | MVAL(a,|3,1) * M|
|00002070| 56 41 4c 28 62 2c 31 2c | 31 29 0a 58 20 20 2b 20 |VAL(b,1,|1).X  + |
|00002080| 20 4d 56 41 4c 28 61 2c | 33 2c 32 29 20 2a 20 4d | MVAL(a,|3,2) * M|
|00002090| 56 41 4c 28 62 2c 32 2c | 31 29 0a 58 20 20 2b 20 |VAL(b,2,|1).X  + |
|000020a0| 20 4d 56 41 4c 28 61 2c | 33 2c 33 29 20 2a 20 4d | MVAL(a,|3,3) * M|
|000020b0| 56 41 4c 28 62 2c 33 2c | 31 29 3b 0a 58 0a 58 4d |VAL(b,3,|1);.X.XM|
|000020c0| 56 41 4c 28 6d 70 74 72 | 2c 33 2c 32 29 20 3d 0a |VAL(mptr|,3,2) =.|
|000020d0| 58 20 20 20 20 20 4d 56 | 41 4c 28 61 2c 33 2c 30 |X     MV|AL(a,3,0|
|000020e0| 29 20 2a 20 4d 56 41 4c | 28 62 2c 30 2c 32 29 0a |) * MVAL|(b,0,2).|
|000020f0| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 33 2c 31 |X  +  MV|AL(a,3,1|
|00002100| 29 20 2a 20 4d 56 41 4c | 28 62 2c 31 2c 32 29 0a |) * MVAL|(b,1,2).|
|00002110| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 33 2c 32 |X  +  MV|AL(a,3,2|
|00002120| 29 20 2a 20 4d 56 41 4c | 28 62 2c 32 2c 32 29 0a |) * MVAL|(b,2,2).|
|00002130| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 33 2c 33 |X  +  MV|AL(a,3,3|
|00002140| 29 20 2a 20 4d 56 41 4c | 28 62 2c 33 2c 32 29 3b |) * MVAL|(b,3,2);|
|00002150| 0a 58 0a 58 4d 56 41 4c | 28 6d 70 74 72 2c 33 2c |.X.XMVAL|(mptr,3,|
|00002160| 33 29 20 3d 0a 58 20 20 | 20 20 20 4d 56 41 4c 28 |3) =.X  |   MVAL(|
|00002170| 61 2c 33 2c 30 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,0) *| MVAL(b,|
|00002180| 30 2c 33 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |0,3).X  |+  MVAL(|
|00002190| 61 2c 33 2c 31 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,1) *| MVAL(b,|
|000021a0| 31 2c 33 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |1,3).X  |+  MVAL(|
|000021b0| 61 2c 33 2c 32 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,2) *| MVAL(b,|
|000021c0| 32 2c 33 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |2,3).X  |+  MVAL(|
|000021d0| 61 2c 33 2c 33 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,3) *| MVAL(b,|
|000021e0| 33 2c 33 29 3b 0a 58 0a | 58 2f 2a 20 63 6f 70 79 |3,3);.X.|X/* copy|
|000021f0| 20 74 65 6d 70 20 6d 61 | 74 72 69 78 20 74 6f 20 | temp ma|trix to |
|00002200| 72 65 73 75 6c 74 20 69 | 66 20 6e 65 65 64 65 64 |result i|f needed|
|00002210| 20 2a 2f 0a 58 69 66 20 | 28 20 75 73 65 74 65 6d | */.Xif |( usetem|
|00002220| 70 20 29 0a 58 20 20 2a | 72 65 73 75 6c 74 20 3d |p ).X  *|result =|
|00002230| 20 2a 6d 70 74 72 3b 0a | 58 0a 58 72 65 74 75 72 | *mptr;.|X.Xretur|
|00002240| 6e 20 72 65 73 75 6c 74 | 3b 0a 58 7d 0a 58 0a 58 |n result|;.X}.X.X|
|00002250| 0a 58 0a 58 0a 58 0a 58 | 2f 2a 20 20 2a 2a 2a 2a |.X.X.X.X|/*  ****|
|00002260| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002270| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002280| 0a 58 20 20 20 20 2a 20 | 20 20 20 20 20 20 20 20 |.X    * |        |
|00002290| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022a0| 20 20 20 20 20 20 20 20 | 20 2a 0a 58 20 20 20 20 |        | *.X    |
|000022b0| 2a 20 20 20 20 20 20 20 | 20 56 33 41 66 66 4d 61 |*       | V3AffMa|
|000022c0| 74 4d 75 6c 20 20 20 20 | 20 20 20 20 20 20 20 20 |tMul    |        |
|000022d0| 20 20 20 2a 0a 58 20 20 | 20 20 2a 20 20 20 20 20 |   *.X  |  *     |
|000022e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2a 0a 58 |        |     *.X|
|00002300| 20 20 20 20 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |    ****|********|
|00002310| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002320| 2a 2a 2a 2a 2a 2a 2a 2a | 0a 58 0a 58 20 20 20 20 |********|.X.X    |
|00002330| 44 45 53 43 52 49 50 54 | 49 4f 4e 3a 20 20 4d 75 |DESCRIPT|ION:  Mu|
|00002340| 6c 74 69 70 6c 79 20 74 | 77 6f 20 61 66 66 69 6e |ltiply t|wo affin|
|00002350| 65 20 34 78 34 20 6d 61 | 74 72 69 63 69 65 73 2e |e 4x4 ma|tricies.|
|00002360| 20 20 54 68 65 0a 58 20 | 20 20 20 20 20 72 6f 75 |  The.X |     rou|
|00002370| 74 69 6e 65 20 61 73 73 | 75 6d 65 73 20 74 68 65 |tine ass|umes the|
|00002380| 20 72 69 67 68 74 6d 6f | 73 74 20 63 6f 6c 75 6d | rightmo|st colum|
|00002390| 6e 20 6f 66 20 65 61 63 | 68 20 69 6e 70 75 74 0a |n of eac|h input.|
|000023a0| 58 20 20 20 20 20 20 6d | 61 74 72 69 78 20 69 73 |X      m|atrix is|
|000023b0| 20 5b 30 20 30 20 30 20 | 31 5d 2e 20 20 54 68 65 | [0 0 0 |1].  The|
|000023c0| 20 6f 75 74 70 75 74 20 | 6d 61 74 72 69 78 20 77 | output |matrix w|
|000023d0| 69 6c 6c 20 68 61 76 65 | 20 74 68 65 0a 58 20 20 |ill have| the.X  |
|000023e0| 20 20 20 20 73 61 6d 65 | 20 70 72 6f 70 65 72 74 |    same| propert|
|000023f0| 79 2e 0a 58 20 20 20 20 | 0a 58 20 20 20 20 20 20 |y..X    |.X      |
|00002400| 49 66 20 6f 6e 65 20 6f | 66 20 74 68 65 20 69 6e |If one o|f the in|
|00002410| 70 75 74 20 6d 61 74 72 | 69 63 65 73 20 69 73 20 |put matr|ices is |
|00002420| 74 68 65 20 73 61 6d 65 | 20 61 73 20 74 68 65 20 |the same| as the |
|00002430| 6f 75 74 70 75 74 2c 0a | 58 20 20 20 20 20 20 77 |output,.|X      w|
|00002440| 72 69 74 65 20 74 68 65 | 20 72 65 73 75 6c 74 20 |rite the| result |
|00002450| 74 6f 20 61 20 74 65 6d | 70 6f 72 61 72 79 20 6d |to a tem|porary m|
|00002460| 61 74 72 69 78 20 64 75 | 72 69 6e 67 20 6d 75 6c |atrix du|ring mul|
|00002470| 74 69 70 6c 69 63 61 74 | 69 6f 6e 2c 0a 58 20 20 |tiplicat|ion,.X  |
|00002480| 20 20 20 20 74 68 65 6e | 20 63 6f 70 79 20 74 6f |    then| copy to|
|00002490| 20 74 68 65 20 6f 75 74 | 70 75 74 20 6d 61 74 72 | the out|put matr|
|000024a0| 69 78 2e 0a 58 0a 58 20 | 20 20 20 45 4e 54 52 59 |ix..X.X |   ENTRY|
|000024b0| 3a 0a 58 20 20 20 20 20 | 20 61 20 2d 2d 20 70 6f |:.X     | a -- po|
|000024c0| 69 6e 74 65 72 20 74 6f | 20 6c 65 66 74 20 6d 61 |inter to| left ma|
|000024d0| 74 72 69 78 0a 58 20 20 | 20 20 20 20 62 20 2d 2d |trix.X  |    b --|
|000024e0| 20 70 6f 69 6e 74 65 72 | 20 74 6f 20 72 69 67 68 | pointer| to righ|
|000024f0| 74 20 6d 61 74 72 69 78 | 0a 58 20 20 20 20 20 20 |t matrix|.X      |
|00002500| 72 65 73 75 6c 74 20 2d | 2d 20 72 65 73 75 6c 74 |result -|- result|
|00002510| 20 6d 61 74 72 69 78 0a | 58 0a 58 20 20 20 20 45 | matrix.|X.X    E|
|00002520| 58 49 54 3a 20 20 72 65 | 74 75 72 6e 73 20 27 72 |XIT:  re|turns 'r|
|00002530| 65 73 75 6c 74 27 0a 58 | 2a 2f 0a 58 0a 58 4d 61 |esult'.X|*/.X.XMa|
|00002540| 74 72 69 78 34 20 2a 56 | 33 41 66 66 4d 61 74 4d |trix4 *V|3AffMatM|
|00002550| 75 6c 20 28 20 61 2c 20 | 62 2c 20 72 65 73 75 6c |ul ( a, |b, resul|
|00002560| 74 20 29 0a 58 72 65 67 | 69 73 74 65 72 20 4d 61 |t ).Xreg|ister Ma|
|00002570| 74 72 69 78 34 20 2a 61 | 2c 2a 62 3b 0a 58 4d 61 |trix4 *a|,*b;.XMa|
|00002580| 74 72 69 78 34 20 2a 72 | 65 73 75 6c 74 3b 0a 58 |trix4 *r|esult;.X|
|00002590| 7b 0a 58 72 65 67 69 73 | 74 65 72 20 4d 61 74 72 |{.Xregis|ter Matr|
|000025a0| 69 78 34 20 2a 6d 70 74 | 72 3b 0a 58 69 6e 74 20 |ix4 *mpt|r;.Xint |
|000025b0| 75 73 65 74 65 6d 70 3b | 20 20 2f 2a 20 62 6f 6f |usetemp;|  /* boo|
|000025c0| 6c 65 61 6e 20 2a 2f 0a | 58 4d 61 74 72 69 78 34 |lean */.|XMatrix4|
|000025d0| 20 74 65 6d 70 78 3b 0a | 58 0a 58 2f 2a 20 64 65 | tempx;.|X.X/* de|
|000025e0| 63 69 64 65 20 77 68 65 | 72 65 20 69 6e 74 65 72 |cide whe|re inter|
|000025f0| 6d 65 64 69 61 74 65 20 | 72 65 73 75 6c 74 20 67 |mediate |result g|
|00002600| 6f 65 73 20 2a 2f 0a 58 | 75 73 65 74 65 6d 70 20 |oes */.X|usetemp |
|00002610| 3d 20 28 20 61 20 3d 3d | 20 72 65 73 75 6c 74 20 |= ( a ==| result |
|00002620| 20 7c 7c 20 20 62 20 3d | 3d 20 72 65 73 75 6c 74 | ||  b =|= result|
|00002630| 20 29 3b 0a 58 69 66 20 | 28 20 75 73 65 74 65 6d | );.Xif |( usetem|
|00002640| 70 20 29 0a 58 20 20 6d | 70 74 72 20 3d 20 26 20 |p ).X  m|ptr = & |
|00002650| 74 65 6d 70 78 3b 0a 58 | 65 6c 73 65 0a 58 20 20 |tempx;.X|else.X  |
|00002660| 6d 70 74 72 20 3d 20 72 | 65 73 75 6c 74 3b 0a 58 |mptr = r|esult;.X|
|00002670| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 30 2c 30 29 |.XMVAL(m|ptr,0,0)|
|00002680| 20 3d 0a 58 20 20 20 20 | 20 4d 56 41 4c 28 61 2c | =.X    | MVAL(a,|
|00002690| 30 2c 30 29 20 2a 20 4d | 56 41 4c 28 62 2c 30 2c |0,0) * M|VAL(b,0,|
|000026a0| 30 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |0).X  + | MVAL(a,|
|000026b0| 30 2c 31 29 20 2a 20 4d | 56 41 4c 28 62 2c 31 2c |0,1) * M|VAL(b,1,|
|000026c0| 30 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |0).X  + | MVAL(a,|
|000026d0| 30 2c 32 29 20 2a 20 4d | 56 41 4c 28 62 2c 32 2c |0,2) * M|VAL(b,2,|
|000026e0| 30 29 3b 0a 58 0a 58 4d | 56 41 4c 28 6d 70 74 72 |0);.X.XM|VAL(mptr|
|000026f0| 2c 30 2c 31 29 20 3d 0a | 58 20 20 20 20 20 4d 56 |,0,1) =.|X     MV|
|00002700| 41 4c 28 61 2c 30 2c 30 | 29 20 2a 20 4d 56 41 4c |AL(a,0,0|) * MVAL|
|00002710| 28 62 2c 30 2c 31 29 0a | 58 20 20 2b 20 20 4d 56 |(b,0,1).|X  +  MV|
|00002720| 41 4c 28 61 2c 30 2c 31 | 29 20 2a 20 4d 56 41 4c |AL(a,0,1|) * MVAL|
|00002730| 28 62 2c 31 2c 31 29 0a | 58 20 20 2b 20 20 4d 56 |(b,1,1).|X  +  MV|
|00002740| 41 4c 28 61 2c 30 2c 32 | 29 20 2a 20 4d 56 41 4c |AL(a,0,2|) * MVAL|
|00002750| 28 62 2c 32 2c 31 29 3b | 0a 58 0a 58 4d 56 41 4c |(b,2,1);|.X.XMVAL|
|00002760| 28 6d 70 74 72 2c 30 2c | 32 29 20 3d 0a 58 20 20 |(mptr,0,|2) =.X  |
|00002770| 20 20 20 4d 56 41 4c 28 | 61 2c 30 2c 30 29 20 2a |   MVAL(|a,0,0) *|
|00002780| 20 4d 56 41 4c 28 62 2c | 30 2c 32 29 0a 58 20 20 | MVAL(b,|0,2).X  |
|00002790| 2b 20 20 4d 56 41 4c 28 | 61 2c 30 2c 31 29 20 2a |+  MVAL(|a,0,1) *|
|000027a0| 20 4d 56 41 4c 28 62 2c | 31 2c 32 29 0a 58 20 20 | MVAL(b,|1,2).X  |
|000027b0| 2b 20 20 4d 56 41 4c 28 | 61 2c 30 2c 32 29 20 2a |+  MVAL(|a,0,2) *|
|000027c0| 20 4d 56 41 4c 28 62 2c | 32 2c 32 29 3b 0a 58 0a | MVAL(b,|2,2);.X.|
|000027d0| 58 4d 56 41 4c 28 6d 70 | 74 72 2c 30 2c 33 29 20 |XMVAL(mp|tr,0,3) |
|000027e0| 3d 20 30 2e 30 3b 0a 58 | 0a 58 4d 56 41 4c 28 6d |= 0.0;.X|.XMVAL(m|
|000027f0| 70 74 72 2c 31 2c 30 29 | 20 3d 0a 58 20 20 20 20 |ptr,1,0)| =.X    |
|00002800| 20 4d 56 41 4c 28 61 2c | 31 2c 30 29 20 2a 20 4d | MVAL(a,|1,0) * M|
|00002810| 56 41 4c 28 62 2c 30 2c | 30 29 0a 58 20 20 2b 20 |VAL(b,0,|0).X  + |
|00002820| 20 4d 56 41 4c 28 61 2c | 31 2c 31 29 20 2a 20 4d | MVAL(a,|1,1) * M|
|00002830| 56 41 4c 28 62 2c 31 2c | 30 29 0a 58 20 20 2b 20 |VAL(b,1,|0).X  + |
|00002840| 20 4d 56 41 4c 28 61 2c | 31 2c 32 29 20 2a 20 4d | MVAL(a,|1,2) * M|
|00002850| 56 41 4c 28 62 2c 32 2c | 30 29 3b 0a 58 0a 58 4d |VAL(b,2,|0);.X.XM|
|00002860| 56 41 4c 28 6d 70 74 72 | 2c 31 2c 31 29 20 3d 0a |VAL(mptr|,1,1) =.|
|00002870| 58 20 20 20 20 20 4d 56 | 41 4c 28 61 2c 31 2c 30 |X     MV|AL(a,1,0|
|00002880| 29 20 2a 20 4d 56 41 4c | 28 62 2c 30 2c 31 29 0a |) * MVAL|(b,0,1).|
|00002890| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 31 2c 31 |X  +  MV|AL(a,1,1|
|000028a0| 29 20 2a 20 4d 56 41 4c | 28 62 2c 31 2c 31 29 0a |) * MVAL|(b,1,1).|
|000028b0| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 31 2c 32 |X  +  MV|AL(a,1,2|
|000028c0| 29 20 2a 20 4d 56 41 4c | 28 62 2c 32 2c 31 29 3b |) * MVAL|(b,2,1);|
|000028d0| 0a 58 0a 58 4d 56 41 4c | 28 6d 70 74 72 2c 31 2c |.X.XMVAL|(mptr,1,|
|000028e0| 32 29 20 3d 0a 58 20 20 | 20 20 20 4d 56 41 4c 28 |2) =.X  |   MVAL(|
|000028f0| 61 2c 31 2c 30 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,1,0) *| MVAL(b,|
|00002900| 30 2c 32 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |0,2).X  |+  MVAL(|
|00002910| 61 2c 31 2c 31 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,1,1) *| MVAL(b,|
|00002920| 31 2c 32 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |1,2).X  |+  MVAL(|
|00002930| 61 2c 31 2c 32 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,1,2) *| MVAL(b,|
|00002940| 32 2c 32 29 3b 0a 58 0a | 58 4d 56 41 4c 28 6d 70 |2,2);.X.|XMVAL(mp|
|00002950| 74 72 2c 31 2c 33 29 20 | 3d 20 30 2e 30 3b 0a 58 |tr,1,3) |= 0.0;.X|
|00002960| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 32 2c 30 29 |.XMVAL(m|ptr,2,0)|
|00002970| 20 3d 0a 58 20 20 20 20 | 20 4d 56 41 4c 28 61 2c | =.X    | MVAL(a,|
|00002980| 32 2c 30 29 20 2a 20 4d | 56 41 4c 28 62 2c 30 2c |2,0) * M|VAL(b,0,|
|00002990| 30 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |0).X  + | MVAL(a,|
|000029a0| 32 2c 31 29 20 2a 20 4d | 56 41 4c 28 62 2c 31 2c |2,1) * M|VAL(b,1,|
|000029b0| 30 29 0a 58 20 20 2b 20 | 20 4d 56 41 4c 28 61 2c |0).X  + | MVAL(a,|
|000029c0| 32 2c 32 29 20 2a 20 4d | 56 41 4c 28 62 2c 32 2c |2,2) * M|VAL(b,2,|
|000029d0| 30 29 3b 0a 58 0a 58 4d | 56 41 4c 28 6d 70 74 72 |0);.X.XM|VAL(mptr|
|000029e0| 2c 32 2c 31 29 20 3d 0a | 58 20 20 20 20 20 4d 56 |,2,1) =.|X     MV|
|000029f0| 41 4c 28 61 2c 32 2c 30 | 29 20 2a 20 4d 56 41 4c |AL(a,2,0|) * MVAL|
|00002a00| 28 62 2c 30 2c 31 29 0a | 58 20 20 2b 20 20 4d 56 |(b,0,1).|X  +  MV|
|00002a10| 41 4c 28 61 2c 32 2c 31 | 29 20 2a 20 4d 56 41 4c |AL(a,2,1|) * MVAL|
|00002a20| 28 62 2c 31 2c 31 29 0a | 58 20 20 2b 20 20 4d 56 |(b,1,1).|X  +  MV|
|00002a30| 41 4c 28 61 2c 32 2c 32 | 29 20 2a 20 4d 56 41 4c |AL(a,2,2|) * MVAL|
|00002a40| 28 62 2c 32 2c 31 29 3b | 0a 58 0a 58 4d 56 41 4c |(b,2,1);|.X.XMVAL|
|00002a50| 28 6d 70 74 72 2c 32 2c | 32 29 20 3d 0a 58 20 20 |(mptr,2,|2) =.X  |
|00002a60| 20 20 20 4d 56 41 4c 28 | 61 2c 32 2c 30 29 20 2a |   MVAL(|a,2,0) *|
|00002a70| 20 4d 56 41 4c 28 62 2c | 30 2c 32 29 0a 58 20 20 | MVAL(b,|0,2).X  |
|00002a80| 2b 20 20 4d 56 41 4c 28 | 61 2c 32 2c 31 29 20 2a |+  MVAL(|a,2,1) *|
|00002a90| 20 4d 56 41 4c 28 62 2c | 31 2c 32 29 0a 58 20 20 | MVAL(b,|1,2).X  |
|00002aa0| 2b 20 20 4d 56 41 4c 28 | 61 2c 32 2c 32 29 20 2a |+  MVAL(|a,2,2) *|
|00002ab0| 20 4d 56 41 4c 28 62 2c | 32 2c 32 29 3b 0a 58 0a | MVAL(b,|2,2);.X.|
|00002ac0| 58 4d 56 41 4c 28 6d 70 | 74 72 2c 32 2c 33 29 20 |XMVAL(mp|tr,2,3) |
|00002ad0| 3d 20 30 2e 30 3b 0a 58 | 0a 58 4d 56 41 4c 28 6d |= 0.0;.X|.XMVAL(m|
|00002ae0| 70 74 72 2c 33 2c 30 29 | 20 3d 0a 58 20 20 20 20 |ptr,3,0)| =.X    |
|00002af0| 20 4d 56 41 4c 28 61 2c | 33 2c 30 29 20 2a 20 4d | MVAL(a,|3,0) * M|
|00002b00| 56 41 4c 28 62 2c 30 2c | 30 29 0a 58 20 20 2b 20 |VAL(b,0,|0).X  + |
|00002b10| 20 4d 56 41 4c 28 61 2c | 33 2c 31 29 20 2a 20 4d | MVAL(a,|3,1) * M|
|00002b20| 56 41 4c 28 62 2c 31 2c | 30 29 0a 58 20 20 2b 20 |VAL(b,1,|0).X  + |
|00002b30| 20 4d 56 41 4c 28 61 2c | 33 2c 32 29 20 2a 20 4d | MVAL(a,|3,2) * M|
|00002b40| 56 41 4c 28 62 2c 32 2c | 30 29 0a 58 20 20 2b 20 |VAL(b,2,|0).X  + |
|00002b50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 4d |        |       M|
|00002b60| 56 41 4c 28 62 2c 33 2c | 30 29 3b 0a 58 0a 58 4d |VAL(b,3,|0);.X.XM|
|00002b70| 56 41 4c 28 6d 70 74 72 | 2c 33 2c 31 29 20 3d 0a |VAL(mptr|,3,1) =.|
|00002b80| 58 20 20 20 20 20 4d 56 | 41 4c 28 61 2c 33 2c 30 |X     MV|AL(a,3,0|
|00002b90| 29 20 2a 20 4d 56 41 4c | 28 62 2c 30 2c 31 29 0a |) * MVAL|(b,0,1).|
|00002ba0| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 33 2c 31 |X  +  MV|AL(a,3,1|
|00002bb0| 29 20 2a 20 4d 56 41 4c | 28 62 2c 31 2c 31 29 0a |) * MVAL|(b,1,1).|
|00002bc0| 58 20 20 2b 20 20 4d 56 | 41 4c 28 61 2c 33 2c 32 |X  +  MV|AL(a,3,2|
|00002bd0| 29 20 2a 20 4d 56 41 4c | 28 62 2c 32 2c 31 29 0a |) * MVAL|(b,2,1).|
|00002be0| 58 20 20 2b 20 20 20 20 | 20 20 20 20 20 20 20 20 |X  +    |        |
|00002bf0| 20 20 20 20 4d 56 41 4c | 28 62 2c 33 2c 31 29 3b |    MVAL|(b,3,1);|
|00002c00| 0a 58 0a 58 4d 56 41 4c | 28 6d 70 74 72 2c 33 2c |.X.XMVAL|(mptr,3,|
|00002c10| 32 29 20 3d 0a 58 20 20 | 20 20 20 4d 56 41 4c 28 |2) =.X  |   MVAL(|
|00002c20| 61 2c 33 2c 30 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,0) *| MVAL(b,|
|00002c30| 30 2c 32 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |0,2).X  |+  MVAL(|
|00002c40| 61 2c 33 2c 31 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,1) *| MVAL(b,|
|00002c50| 31 2c 32 29 0a 58 20 20 | 2b 20 20 4d 56 41 4c 28 |1,2).X  |+  MVAL(|
|00002c60| 61 2c 33 2c 32 29 20 2a | 20 4d 56 41 4c 28 62 2c |a,3,2) *| MVAL(b,|
|00002c70| 32 2c 32 29 0a 58 20 20 | 2b 20 20 20 20 20 20 20 |2,2).X  |+       |
|00002c80| 20 20 20 20 20 20 20 20 | 20 4d 56 41 4c 28 62 2c |        | MVAL(b,|
|00002c90| 33 2c 32 29 3b 0a 58 0a | 58 4d 56 41 4c 28 6d 70 |3,2);.X.|XMVAL(mp|
|00002ca0| 74 72 2c 33 2c 33 29 20 | 3d 20 31 2e 30 3b 0a 58 |tr,3,3) |= 1.0;.X|
|00002cb0| 0a 58 2f 2a 20 63 6f 70 | 79 20 74 65 6d 70 20 6d |.X/* cop|y temp m|
|00002cc0| 61 74 72 69 78 20 74 6f | 20 72 65 73 75 6c 74 20 |atrix to| result |
|00002cd0| 69 66 20 6e 65 65 64 65 | 64 20 2a 2f 0a 58 69 66 |if neede|d */.Xif|
|00002ce0| 20 28 20 75 73 65 74 65 | 6d 70 20 29 0a 58 20 20 | ( usete|mp ).X  |
|00002cf0| 2a 72 65 73 75 6c 74 20 | 3d 20 2a 6d 70 74 72 3b |*result |= *mptr;|
|00002d00| 0a 58 0a 58 72 65 74 75 | 72 6e 20 72 65 73 75 6c |.X.Xretu|rn resul|
|00002d10| 74 3b 0a 58 7d 0a 58 0a | 58 0a 58 0a 58 0a 58 0a |t;.X}.X.|X.X.X.X.|
|00002d20| 58 2f 2a 20 20 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |X/*  ***|********|
|00002d30| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002d40| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 0a 58 20 20 20 20 2a |********|*.X    *|
|00002d50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002d60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002d70| 20 20 2a 0a 58 20 20 20 | 20 2a 20 20 20 20 20 20 |  *.X   | *      |
|00002d80| 20 20 56 33 4c 69 6e 4d | 61 74 4d 75 6c 20 20 20 |  V3LinM|atMul   |
|00002d90| 20 20 20 20 20 20 20 20 | 20 20 20 20 2a 0a 58 20 |        |    *.X |
|00002da0| 20 20 20 2a 20 20 20 20 | 20 20 20 20 20 20 20 20 |   *    |        |
|00002db0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002dc0| 20 20 20 20 20 20 2a 0a | 58 20 20 20 20 2a 2a 2a |      *.|X    ***|
|00002dd0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002de0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00002df0| 2a 0a 58 0a 58 20 20 20 | 20 44 45 53 43 52 49 50 |*.X.X   | DESCRIP|
|00002e00| 54 49 4f 4e 3a 20 20 4d | 75 6c 74 69 70 6c 79 20 |TION:  M|ultiply |
|00002e10| 74 77 6f 20 61 66 66 69 | 6e 65 20 34 78 34 20 6d |two affi|ne 4x4 m|
|00002e20| 61 74 72 69 63 69 65 73 | 2e 20 20 54 68 65 0a 58 |atricies|.  The.X|
|00002e30| 20 20 20 20 20 20 72 6f | 75 74 69 6e 65 20 61 73 |      ro|utine as|
|00002e40| 73 75 6d 65 73 20 74 68 | 65 20 72 69 67 68 74 20 |sumes th|e right |
|00002e50| 63 6f 6c 75 6d 6e 20 61 | 6e 64 20 62 6f 74 74 6f |column a|nd botto|
|00002e60| 6d 20 6c 69 6e 65 0a 58 | 20 20 20 20 20 20 6f 66 |m line.X|      of|
|00002e70| 20 65 61 63 68 20 69 6e | 70 75 74 20 6d 61 74 72 | each in|put matr|
|00002e80| 69 78 20 69 73 20 5b 30 | 20 30 20 30 20 31 5d 2e |ix is [0| 0 0 1].|
|00002e90| 20 20 54 68 65 20 6f 75 | 74 70 75 74 20 6d 61 74 |  The ou|tput mat|
|00002ea0| 72 69 78 0a 58 20 20 20 | 20 20 20 77 69 6c 6c 20 |rix.X   |   will |
|00002eb0| 68 61 76 65 20 74 68 65 | 20 73 61 6d 65 20 70 72 |have the| same pr|
|00002ec0| 6f 70 65 72 74 79 2e 20 | 20 54 68 69 73 20 69 73 |operty. | This is|
|00002ed0| 20 70 72 65 74 74 79 20 | 6d 75 63 68 20 74 68 65 | pretty |much the|
|00002ee0| 0a 58 20 20 20 20 20 20 | 73 61 6d 65 20 74 68 69 |.X      |same thi|
|00002ef0| 6e 67 20 61 73 20 6d 75 | 6c 74 69 70 6c 79 69 6e |ng as mu|ltiplyin|
|00002f00| 67 20 74 77 6f 20 33 78 | 33 20 6d 61 74 72 69 63 |g two 3x|3 matric|
|00002f10| 65 73 2e 0a 58 20 20 20 | 20 0a 58 20 20 20 20 20 |es..X   | .X     |
|00002f20| 20 49 66 20 6f 6e 65 20 | 6f 66 20 74 68 65 20 69 | If one |of the i|
|00002f30| 6e 70 75 74 20 6d 61 74 | 72 69 63 65 73 20 69 73 |nput mat|rices is|
|00002f40| 20 74 68 65 20 73 61 6d | 65 20 61 73 20 74 68 65 | the sam|e as the|
|00002f50| 20 6f 75 74 70 75 74 2c | 0a 58 20 20 20 20 20 20 | output,|.X      |
|00002f60| 77 72 69 74 65 20 74 68 | 65 20 72 65 73 75 6c 74 |write th|e result|
|00002f70| 20 74 6f 20 61 20 74 65 | 6d 70 6f 72 61 72 79 20 | to a te|mporary |
|00002f80| 6d 61 74 72 69 78 20 64 | 75 72 69 6e 67 20 6d 75 |matrix d|uring mu|
|00002f90| 6c 74 69 70 6c 69 63 61 | 74 69 6f 6e 2c 0a 58 20 |ltiplica|tion,.X |
|00002fa0| 20 20 20 20 20 74 68 65 | 6e 20 63 6f 70 79 20 74 |     the|n copy t|
|00002fb0| 6f 20 74 68 65 20 6f 75 | 74 70 75 74 20 6d 61 74 |o the ou|tput mat|
|00002fc0| 72 69 78 2e 0a 58 0a 58 | 20 20 20 20 45 4e 54 52 |rix..X.X|    ENTR|
|00002fd0| 59 3a 0a 58 20 20 20 20 | 20 20 61 20 2d 2d 20 70 |Y:.X    |  a -- p|
|00002fe0| 6f 69 6e 74 65 72 20 74 | 6f 20 6c 65 66 74 20 6d |ointer t|o left m|
|00002ff0| 61 74 72 69 78 0a 58 20 | 20 20 20 20 20 62 20 2d |atrix.X |     b -|
|00003000| 2d 20 70 6f 69 6e 74 65 | 72 20 74 6f 20 72 69 67 |- pointe|r to rig|
|00003010| 68 74 20 6d 61 74 72 69 | 78 0a 58 20 20 20 20 20 |ht matri|x.X     |
|00003020| 20 72 65 73 75 6c 74 20 | 2d 2d 20 72 65 73 75 6c | result |-- resul|
|00003030| 74 20 6d 61 74 72 69 78 | 0a 58 0a 58 20 20 20 20 |t matrix|.X.X    |
|00003040| 45 58 49 54 3a 20 20 72 | 65 74 75 72 6e 73 20 27 |EXIT:  r|eturns '|
|00003050| 72 65 73 75 6c 74 27 0a | 58 2a 2f 0a 58 0a 58 4d |result'.|X*/.X.XM|
|00003060| 61 74 72 69 78 34 20 2a | 56 33 4c 69 6e 4d 61 74 |atrix4 *|V3LinMat|
|00003070| 4d 75 6c 20 28 20 61 2c | 20 62 2c 20 72 65 73 75 |Mul ( a,| b, resu|
|00003080| 6c 74 20 29 0a 58 72 65 | 67 69 73 74 65 72 20 4d |lt ).Xre|gister M|
|00003090| 61 74 72 69 78 34 20 2a | 61 2c 2a 62 3b 0a 58 4d |atrix4 *|a,*b;.XM|
|000030a0| 61 74 72 69 78 34 20 2a | 72 65 73 75 6c 74 3b 0a |atrix4 *|result;.|
|000030b0| 58 7b 0a 58 72 65 67 69 | 73 74 65 72 20 4d 61 74 |X{.Xregi|ster Mat|
|000030c0| 72 69 78 34 20 2a 6d 70 | 74 72 3b 0a 58 69 6e 74 |rix4 *mp|tr;.Xint|
|000030d0| 20 75 73 65 74 65 6d 70 | 3b 20 20 2f 2a 20 62 6f | usetemp|;  /* bo|
|000030e0| 6f 6c 65 61 6e 20 2a 2f | 0a 58 4d 61 74 72 69 78 |olean */|.XMatrix|
|000030f0| 34 20 74 65 6d 70 78 3b | 0a 58 0a 58 2f 2a 20 64 |4 tempx;|.X.X/* d|
|00003100| 65 63 69 64 65 20 77 68 | 65 72 65 20 69 6e 74 65 |ecide wh|ere inte|
|00003110| 72 6d 65 64 69 61 74 65 | 20 72 65 73 75 6c 74 20 |rmediate| result |
|00003120| 67 6f 65 73 20 2a 2f 0a | 58 75 73 65 74 65 6d 70 |goes */.|Xusetemp|
|00003130| 20 3d 20 28 20 61 20 3d | 3d 20 72 65 73 75 6c 74 | = ( a =|= result|
|00003140| 20 20 7c 7c 20 20 62 20 | 3d 3d 20 72 65 73 75 6c |  ||  b |== resul|
|00003150| 74 20 29 3b 0a 58 69 66 | 20 28 20 75 73 65 74 65 |t );.Xif| ( usete|
|00003160| 6d 70 20 29 0a 58 20 20 | 6d 70 74 72 20 3d 20 26 |mp ).X  |mptr = &|
|00003170| 20 74 65 6d 70 78 3b 0a | 58 65 6c 73 65 0a 58 20 | tempx;.|Xelse.X |
|00003180| 20 6d 70 74 72 20 3d 20 | 72 65 73 75 6c 74 3b 0a | mptr = |result;.|
|00003190| 58 0a 58 4d 56 41 4c 28 | 6d 70 74 72 2c 30 2c 30 |X.XMVAL(|mptr,0,0|
|000031a0| 29 20 3d 0a 58 20 20 20 | 20 20 4d 56 41 4c 28 61 |) =.X   |  MVAL(a|
|000031b0| 2c 30 2c 30 29 20 2a 20 | 4d 56 41 4c 28 62 2c 30 |,0,0) * |MVAL(b,0|
|000031c0| 2c 30 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,0).X  +|  MVAL(a|
|000031d0| 2c 30 2c 31 29 20 2a 20 | 4d 56 41 4c 28 62 2c 31 |,0,1) * |MVAL(b,1|
|000031e0| 2c 30 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,0).X  +|  MVAL(a|
|000031f0| 2c 30 2c 32 29 20 2a 20 | 4d 56 41 4c 28 62 2c 32 |,0,2) * |MVAL(b,2|
|00003200| 2c 30 29 3b 0a 58 0a 58 | 4d 56 41 4c 28 6d 70 74 |,0);.X.X|MVAL(mpt|
|00003210| 72 2c 30 2c 31 29 20 3d | 0a 58 20 20 20 20 20 4d |r,0,1) =|.X     M|
|00003220| 56 41 4c 28 61 2c 30 2c | 30 29 20 2a 20 4d 56 41 |VAL(a,0,|0) * MVA|
|00003230| 4c 28 62 2c 30 2c 31 29 | 0a 58 20 20 2b 20 20 4d |L(b,0,1)|.X  +  M|
|00003240| 56 41 4c 28 61 2c 30 2c | 31 29 20 2a 20 4d 56 41 |VAL(a,0,|1) * MVA|
|00003250| 4c 28 62 2c 31 2c 31 29 | 0a 58 20 20 2b 20 20 4d |L(b,1,1)|.X  +  M|
|00003260| 56 41 4c 28 61 2c 30 2c | 32 29 20 2a 20 4d 56 41 |VAL(a,0,|2) * MVA|
|00003270| 4c 28 62 2c 32 2c 31 29 | 3b 0a 58 0a 58 4d 56 41 |L(b,2,1)|;.X.XMVA|
|00003280| 4c 28 6d 70 74 72 2c 30 | 2c 32 29 20 3d 0a 58 20 |L(mptr,0|,2) =.X |
|00003290| 20 20 20 20 4d 56 41 4c | 28 61 2c 30 2c 30 29 20 |    MVAL|(a,0,0) |
|000032a0| 2a 20 4d 56 41 4c 28 62 | 2c 30 2c 32 29 0a 58 20 |* MVAL(b|,0,2).X |
|000032b0| 20 2b 20 20 4d 56 41 4c | 28 61 2c 30 2c 31 29 20 | +  MVAL|(a,0,1) |
|000032c0| 2a 20 4d 56 41 4c 28 62 | 2c 31 2c 32 29 0a 58 20 |* MVAL(b|,1,2).X |
|000032d0| 20 2b 20 20 4d 56 41 4c | 28 61 2c 30 2c 32 29 20 | +  MVAL|(a,0,2) |
|000032e0| 2a 20 4d 56 41 4c 28 62 | 2c 32 2c 32 29 3b 0a 58 |* MVAL(b|,2,2);.X|
|000032f0| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 30 2c 33 29 |.XMVAL(m|ptr,0,3)|
|00003300| 20 3d 20 30 2e 30 3b 0a | 58 0a 58 4d 56 41 4c 28 | = 0.0;.|X.XMVAL(|
|00003310| 6d 70 74 72 2c 31 2c 30 | 29 20 3d 0a 58 20 20 20 |mptr,1,0|) =.X   |
|00003320| 20 20 4d 56 41 4c 28 61 | 2c 31 2c 30 29 20 2a 20 |  MVAL(a|,1,0) * |
|00003330| 4d 56 41 4c 28 62 2c 30 | 2c 30 29 0a 58 20 20 2b |MVAL(b,0|,0).X  +|
|00003340| 20 20 4d 56 41 4c 28 61 | 2c 31 2c 31 29 20 2a 20 |  MVAL(a|,1,1) * |
|00003350| 4d 56 41 4c 28 62 2c 31 | 2c 30 29 0a 58 20 20 2b |MVAL(b,1|,0).X  +|
|00003360| 20 20 4d 56 41 4c 28 61 | 2c 31 2c 32 29 20 2a 20 |  MVAL(a|,1,2) * |
|00003370| 4d 56 41 4c 28 62 2c 32 | 2c 30 29 3b 0a 58 0a 58 |MVAL(b,2|,0);.X.X|
|00003380| 4d 56 41 4c 28 6d 70 74 | 72 2c 31 2c 31 29 20 3d |MVAL(mpt|r,1,1) =|
|00003390| 0a 58 20 20 20 20 20 4d | 56 41 4c 28 61 2c 31 2c |.X     M|VAL(a,1,|
|000033a0| 30 29 20 2a 20 4d 56 41 | 4c 28 62 2c 30 2c 31 29 |0) * MVA|L(b,0,1)|
|000033b0| 0a 58 20 20 2b 20 20 4d | 56 41 4c 28 61 2c 31 2c |.X  +  M|VAL(a,1,|
|000033c0| 31 29 20 2a 20 4d 56 41 | 4c 28 62 2c 31 2c 31 29 |1) * MVA|L(b,1,1)|
|000033d0| 0a 58 20 20 2b 20 20 4d | 56 41 4c 28 61 2c 31 2c |.X  +  M|VAL(a,1,|
|000033e0| 32 29 20 2a 20 4d 56 41 | 4c 28 62 2c 32 2c 31 29 |2) * MVA|L(b,2,1)|
|000033f0| 3b 0a 58 0a 58 4d 56 41 | 4c 28 6d 70 74 72 2c 31 |;.X.XMVA|L(mptr,1|
|00003400| 2c 32 29 20 3d 0a 58 20 | 20 20 20 20 4d 56 41 4c |,2) =.X |    MVAL|
|00003410| 28 61 2c 31 2c 30 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,1,0) |* MVAL(b|
|00003420| 2c 30 2c 32 29 0a 58 20 | 20 2b 20 20 4d 56 41 4c |,0,2).X | +  MVAL|
|00003430| 28 61 2c 31 2c 31 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,1,1) |* MVAL(b|
|00003440| 2c 31 2c 32 29 0a 58 20 | 20 2b 20 20 4d 56 41 4c |,1,2).X | +  MVAL|
|00003450| 28 61 2c 31 2c 32 29 20 | 2a 20 4d 56 41 4c 28 62 |(a,1,2) |* MVAL(b|
|00003460| 2c 32 2c 32 29 3b 0a 58 | 0a 58 4d 56 41 4c 28 6d |,2,2);.X|.XMVAL(m|
|00003470| 70 74 72 2c 31 2c 33 29 | 20 3d 20 30 2e 30 3b 0a |ptr,1,3)| = 0.0;.|
|00003480| 58 0a 58 4d 56 41 4c 28 | 6d 70 74 72 2c 32 2c 30 |X.XMVAL(|mptr,2,0|
|00003490| 29 20 3d 0a 58 20 20 20 | 20 20 4d 56 41 4c 28 61 |) =.X   |  MVAL(a|
|000034a0| 2c 32 2c 30 29 20 2a 20 | 4d 56 41 4c 28 62 2c 30 |,2,0) * |MVAL(b,0|
|000034b0| 2c 30 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,0).X  +|  MVAL(a|
|000034c0| 2c 32 2c 31 29 20 2a 20 | 4d 56 41 4c 28 62 2c 31 |,2,1) * |MVAL(b,1|
|000034d0| 2c 30 29 0a 58 20 20 2b | 20 20 4d 56 41 4c 28 61 |,0).X  +|  MVAL(a|
|000034e0| 2c 32 2c 32 29 20 2a 20 | 4d 56 41 4c 28 62 2c 32 |,2,2) * |MVAL(b,2|
|000034f0| 2c 30 29 3b 0a 58 0a 58 | 4d 56 41 4c 28 6d 70 74 |,0);.X.X|MVAL(mpt|
|00003500| 72 2c 32 2c 31 29 20 3d | 0a 58 20 20 20 20 20 4d |r,2,1) =|.X     M|
|00003510| 56 41 4c 28 61 2c 32 2c | 30 29 20 2a 20 4d 56 41 |VAL(a,2,|0) * MVA|
|00003520| 4c 28 62 2c 30 2c 31 29 | 0a 58 20 20 2b 20 20 4d |L(b,0,1)|.X  +  M|
|00003530| 56 41 4c 28 61 2c 32 2c | 31 29 20 2a 20 4d 56 41 |VAL(a,2,|1) * MVA|
|00003540| 4c 28 62 2c 31 2c 31 29 | 0a 58 20 20 2b 20 20 4d |L(b,1,1)|.X  +  M|
|00003550| 56 41 4c 28 61 2c 32 2c | 32 29 20 2a 20 4d 56 41 |VAL(a,2,|2) * MVA|
|00003560| 4c 28 62 2c 32 2c 31 29 | 3b 0a 58 0a 58 4d 56 41 |L(b,2,1)|;.X.XMVA|
|00003570| 4c 28 6d 70 74 72 2c 32 | 2c 32 29 20 3d 0a 58 20 |L(mptr,2|,2) =.X |
|00003580| 20 20 20 20 4d 56 41 4c | 28 61 2c 32 2c 30 29 20 |    MVAL|(a,2,0) |
|00003590| 2a 20 4d 56 41 4c 28 62 | 2c 30 2c 32 29 0a 58 20 |* MVAL(b|,0,2).X |
|000035a0| 20 2b 20 20 4d 56 41 4c | 28 61 2c 32 2c 31 29 20 | +  MVAL|(a,2,1) |
|000035b0| 2a 20 4d 56 41 4c 28 62 | 2c 31 2c 32 29 0a 58 20 |* MVAL(b|,1,2).X |
|000035c0| 20 2b 20 20 4d 56 41 4c | 28 61 2c 32 2c 32 29 20 | +  MVAL|(a,2,2) |
|000035d0| 2a 20 4d 56 41 4c 28 62 | 2c 32 2c 32 29 3b 0a 58 |* MVAL(b|,2,2);.X|
|000035e0| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 32 2c 33 29 |.XMVAL(m|ptr,2,3)|
|000035f0| 20 3d 20 30 2e 30 3b 0a | 58 0a 58 4d 56 41 4c 28 | = 0.0;.|X.XMVAL(|
|00003600| 6d 70 74 72 2c 33 2c 30 | 29 20 3d 20 30 2e 30 3b |mptr,3,0|) = 0.0;|
|00003610| 0a 58 4d 56 41 4c 28 6d | 70 74 72 2c 33 2c 31 29 |.XMVAL(m|ptr,3,1)|
|00003620| 20 3d 20 30 2e 30 3b 0a | 58 4d 56 41 4c 28 6d 70 | = 0.0;.|XMVAL(mp|
|00003630| 74 72 2c 33 2c 32 29 20 | 3d 20 30 2e 30 3b 0a 58 |tr,3,2) |= 0.0;.X|
|00003640| 4d 56 41 4c 28 6d 70 74 | 72 2c 33 2c 33 29 20 3d |MVAL(mpt|r,3,3) =|
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|00004c40| 20 2a 20 20 47 65 6e 65 | 72 61 74 65 42 65 7a 69 | *  Gene|rateBezi|
|00004c50| 65 72 20 3a 0a 58 20 2a | 20 20 55 73 65 20 6c 65 |er :.X *|  Use le|
|00004c60| 61 73 74 2d 73 71 75 61 | 72 65 73 20 6d 65 74 68 |ast-squa|res meth|
|00004c70| 6f 64 20 74 6f 20 66 69 | 6e 64 20 42 65 7a 69 65 |od to fi|nd Bezie|
|00004c80| 72 20 63 6f 6e 74 72 6f | 6c 20 70 6f 69 6e 74 73 |r contro|l points|
|00004c90| 20 66 6f 72 20 72 65 67 | 69 6f 6e 2e 0a 58 20 2a | for reg|ion..X *|
|00004ca0| 0a 58 20 2a 2f 0a 58 73 | 74 61 74 69 63 20 42 65 |.X */.Xs|tatic Be|
|00004cb0| 7a 69 65 72 43 75 72 76 | 65 20 20 47 65 6e 65 72 |zierCurv|e  Gener|
|00004cc0| 61 74 65 42 65 7a 69 65 | 72 28 64 2c 20 66 69 72 |ateBezie|r(d, fir|
|00004cd0| 73 74 2c 20 6c 61 73 74 | 2c 20 75 50 72 69 6d 65 |st, last|, uPrime|
|00004ce0| 2c 20 74 48 61 74 31 2c | 20 74 48 61 74 32 29 0a |, tHat1,| tHat2).|
|00004cf0| 58 20 20 20 20 50 6f 69 | 6e 74 32 09 2a 64 3b 09 |X    Poi|nt2.*d;.|
|00004d00| 09 09 2f 2a 20 20 41 72 | 72 61 79 20 6f 66 20 64 |../*  Ar|ray of d|
|00004d10| 69 67 69 74 69 7a 65 64 | 20 70 6f 69 6e 74 73 09 |igitized| points.|
|00004d20| 2a 2f 0a 58 20 20 20 20 | 69 6e 74 09 09 66 69 72 |*/.X    |int..fir|
|00004d30| 73 74 2c 20 6c 61 73 74 | 3b 09 09 2f 2a 20 20 49 |st, last|;../*  I|
|00004d40| 6e 64 69 63 65 73 20 64 | 65 66 69 6e 69 6e 67 20 |ndices d|efining |
|00004d50| 72 65 67 69 6f 6e 09 2a | 2f 0a 58 20 20 20 20 64 |region.*|/.X    d|
|00004d60| 6f 75 62 6c 65 09 2a 75 | 50 72 69 6d 65 3b 09 09 |ouble.*u|Prime;..|
|00004d70| 2f 2a 20 20 50 61 72 61 | 6d 65 74 65 72 20 76 61 |/*  Para|meter va|
|00004d80| 6c 75 65 73 20 66 6f 72 | 20 72 65 67 69 6f 6e 20 |lues for| region |
|00004d90| 2a 2f 0a 58 20 20 20 20 | 56 65 63 74 6f 72 32 09 |*/.X    |Vector2.|
|00004da0| 74 48 61 74 31 2c 20 74 | 48 61 74 32 3b 09 2f 2a |tHat1, t|Hat2;./*|
|00004db0| 20 20 55 6e 69 74 20 74 | 61 6e 67 65 6e 74 73 20 |  Unit t|angents |
|00004dc0| 61 74 20 65 6e 64 70 6f | 69 6e 74 73 09 2a 2f 0a |at endpo|ints.*/.|
|00004dd0| 58 7b 0a 58 20 20 20 20 | 69 6e 74 20 09 69 3b 0a |X{.X    |int .i;.|
|00004de0| 58 20 20 20 20 56 65 63 | 74 6f 72 32 20 09 41 5b |X    Vec|tor2 .A[|
|00004df0| 4d 41 58 50 4f 49 4e 54 | 53 5d 5b 32 5d 3b 09 2f |MAXPOINT|S][2];./|
|00004e00| 2a 20 50 72 65 63 6f 6d | 70 75 74 65 64 20 72 68 |* Precom|puted rh|
|00004e10| 73 20 66 6f 72 20 65 71 | 6e 09 2a 2f 0a 58 20 20 |s for eq|n.*/.X  |
|00004e20| 20 20 69 6e 74 20 09 6e | 50 74 73 3b 09 09 09 2f |  int .n|Pts;.../|
|00004e30| 2a 20 4e 75 6d 62 65 72 | 20 6f 66 20 70 74 73 20 |* Number| of pts |
|00004e40| 69 6e 20 73 75 62 2d 63 | 75 72 76 65 20 2a 2f 0a |in sub-c|urve */.|
|00004e50| 58 20 20 20 20 64 6f 75 | 62 6c 65 20 09 43 5b 32 |X    dou|ble .C[2|
|00004e60| 5d 5b 32 5d 3b 09 09 09 | 2f 2a 20 4d 61 74 72 69 |][2];...|/* Matri|
|00004e70| 78 20 43 09 09 2a 2f 0a | 58 20 20 20 20 64 6f 75 |x C..*/.|X    dou|
|00004e80| 62 6c 65 20 09 58 5b 32 | 5d 3b 09 09 09 2f 2a 20 |ble .X[2|];.../* |
|00004e90| 4d 61 74 72 69 78 20 58 | 09 09 09 2a 2f 0a 58 20 |Matrix X|...*/.X |
|00004ea0| 20 20 20 64 6f 75 62 6c | 65 20 09 64 65 74 5f 43 |   doubl|e .det_C|
|00004eb0| 30 5f 43 31 2c 09 09 2f | 2a 20 44 65 74 65 72 6d |0_C1,../|* Determ|
|00004ec0| 69 6e 61 6e 74 73 20 6f | 66 20 6d 61 74 72 69 63 |inants o|f matric|
|00004ed0| 65 73 09 2a 2f 0a 58 20 | 20 20 20 09 20 20 20 09 |es.*/.X |   .   .|
|00004ee0| 64 65 74 5f 43 30 5f 58 | 2c 0a 58 09 20 20 20 09 |det_C0_X|,.X.   .|
|00004ef0| 09 64 65 74 5f 58 5f 43 | 31 3b 0a 58 20 20 20 20 |.det_X_C|1;.X    |
|00004f00| 64 6f 75 62 6c 65 20 09 | 61 6c 70 68 61 5f 6c 2c |double .|alpha_l,|
|00004f10| 09 09 2f 2a 20 41 6c 70 | 68 61 20 76 61 6c 75 65 |../* Alp|ha value|
|00004f20| 73 2c 20 6c 65 66 74 20 | 61 6e 64 20 72 69 67 68 |s, left |and righ|
|00004f30| 74 09 2a 2f 0a 58 20 20 | 20 20 09 20 20 20 09 61 |t.*/.X  |  .   .a|
|00004f40| 6c 70 68 61 5f 72 3b 0a | 58 20 20 20 20 56 65 63 |lpha_r;.|X    Vec|
|00004f50| 74 6f 72 32 20 09 74 6d | 70 3b 09 09 09 2f 2a 20 |tor2 .tm|p;.../* |
|00004f60| 55 74 69 6c 69 74 79 20 | 76 61 72 69 61 62 6c 65 |Utility |variable|
|00004f70| 09 09 2a 2f 0a 58 20 20 | 20 20 42 65 7a 69 65 72 |..*/.X  |  Bezier|
|00004f80| 43 75 72 76 65 09 62 65 | 7a 43 75 72 76 65 3b 09 |Curve.be|zCurve;.|
|00004f90| 2f 2a 20 52 45 54 55 52 | 4e 20 62 65 7a 69 65 72 |/* RETUR|N bezier|
|00004fa0| 20 63 75 72 76 65 20 63 | 74 6c 20 70 74 73 09 2a | curve c|tl pts.*|
|00004fb0| 2f 0a 58 0a 58 20 20 20 | 20 62 65 7a 43 75 72 76 |/.X.X   | bezCurv|
|00004fc0| 65 20 3d 20 28 50 6f 69 | 6e 74 32 20 2a 29 6d 61 |e = (Poi|nt2 *)ma|
|00004fd0| 6c 6c 6f 63 28 34 20 2a | 20 73 69 7a 65 6f 66 28 |lloc(4 *| sizeof(|
|00004fe0| 50 6f 69 6e 74 32 29 29 | 3b 0a 58 20 20 20 20 6e |Point2))|;.X    n|
|00004ff0| 50 74 73 20 3d 20 6c 61 | 73 74 20 2d 20 66 69 72 |Pts = la|st - fir|
|00005000| 73 74 20 2b 20 31 3b 0a | 58 0a 58 20 0a 58 20 20 |st + 1;.|X.X .X  |
|00005010| 20 20 2f 2a 20 43 6f 6d | 70 75 74 65 20 74 68 65 |  /* Com|pute the|
|00005020| 20 41 27 73 09 2a 2f 0a | 58 20 20 20 20 66 6f 72 | A's.*/.|X    for|
|00005030| 20 28 69 20 3d 20 30 3b | 20 69 20 3c 20 6e 50 74 | (i = 0;| i < nPt|
|00005040| 73 3b 20 69 2b 2b 29 20 | 7b 0a 58 09 09 56 65 63 |s; i++) |{.X..Vec|
|00005050| 74 6f 72 32 09 09 76 31 | 2c 20 76 32 3b 0a 58 09 |tor2..v1|, v2;.X.|
|00005060| 09 76 31 20 3d 20 74 48 | 61 74 31 3b 0a 58 09 09 |.v1 = tH|at1;.X..|
|00005070| 76 32 20 3d 20 74 48 61 | 74 32 3b 0a 58 09 09 56 |v2 = tHa|t2;.X..V|
|00005080| 32 53 63 61 6c 65 28 26 | 76 31 2c 20 42 31 28 75 |2Scale(&|v1, B1(u|
|00005090| 50 72 69 6d 65 5b 69 5d | 29 29 3b 0a 58 09 09 56 |Prime[i]|));.X..V|
|000050a0| 32 53 63 61 6c 65 28 26 | 76 32 2c 20 42 32 28 75 |2Scale(&|v2, B2(u|
|000050b0| 50 72 69 6d 65 5b 69 5d | 29 29 3b 0a 58 09 09 41 |Prime[i]|));.X..A|
|000050c0| 5b 69 5d 5b 30 5d 20 3d | 20 76 31 3b 0a 58 09 09 |[i][0] =| v1;.X..|
|000050d0| 41 5b 69 5d 5b 31 5d 20 | 3d 20 76 32 3b 0a 58 20 |A[i][1] |= v2;.X |
|000050e0| 20 20 20 7d 0a 58 0a 58 | 20 20 20 20 2f 2a 20 43 |   }.X.X|    /* C|
|000050f0| 72 65 61 74 65 20 74 68 | 65 20 43 20 61 6e 64 20 |reate th|e C and |
|00005100| 58 20 6d 61 74 72 69 63 | 65 73 09 2a 2f 0a 58 20 |X matric|es.*/.X |
|00005110| 20 20 20 43 5b 30 5d 5b | 30 5d 20 3d 20 30 2e 30 |   C[0][|0] = 0.0|
|00005120| 3b 0a 58 20 20 20 20 43 | 5b 30 5d 5b 31 5d 20 3d |;.X    C|[0][1] =|
|00005130| 20 30 2e 30 3b 0a 58 20 | 20 20 20 43 5b 31 5d 5b | 0.0;.X |   C[1][|
|00005140| 30 5d 20 3d 20 30 2e 30 | 3b 0a 58 20 20 20 20 43 |0] = 0.0|;.X    C|
|00005150| 5b 31 5d 5b 31 5d 20 3d | 20 30 2e 30 3b 0a 58 20 |[1][1] =| 0.0;.X |
|00005160| 20 20 20 58 5b 30 5d 20 | 20 20 20 3d 20 30 2e 30 |   X[0] |   = 0.0|
|00005170| 3b 0a 58 20 20 20 20 58 | 5b 31 5d 20 20 20 20 3d |;.X    X|[1]    =|
|00005180| 20 30 2e 30 3b 0a 58 0a | 58 20 20 20 20 66 6f 72 | 0.0;.X.|X    for|
|00005190| 20 28 69 20 3d 20 30 3b | 20 69 20 3c 20 6e 50 74 | (i = 0;| i < nPt|
|000051a0| 73 3b 20 69 2b 2b 29 20 | 7b 0a 58 20 20 20 20 20 |s; i++) |{.X     |
|000051b0| 20 20 20 43 5b 30 5d 5b | 30 5d 20 2b 3d 20 56 32 |   C[0][|0] += V2|
|000051c0| 44 6f 74 28 26 41 5b 69 | 5d 5b 30 5d 2c 20 26 41 |Dot(&A[i|][0], &A|
|000051d0| 5b 69 5d 5b 30 5d 29 3b | 0a 58 09 09 43 5b 30 5d |[i][0]);|.X..C[0]|
|000051e0| 5b 31 5d 20 2b 3d 20 56 | 32 44 6f 74 28 26 41 5b |[1] += V|2Dot(&A[|
|000051f0| 69 5d 5b 30 5d 2c 20 26 | 41 5b 69 5d 5b 31 5d 29 |i][0], &|A[i][1])|
|00005200| 3b 0a 58 2f 2a 09 09 09 | 09 09 43 5b 31 5d 5b 30 |;.X/*...|..C[1][0|
|00005210| 5d 20 2b 3d 20 56 32 44 | 6f 74 28 26 41 5b 69 5d |] += V2D|ot(&A[i]|
|00005220| 5b 30 5d 2c 20 26 41 5b | 69 5d 5b 31 5d 29 3b 2a |[0], &A[|i][1]);*|
|00005230| 2f 09 0a 58 09 09 43 5b | 31 5d 5b 30 5d 20 3d 20 |/..X..C[|1][0] = |
|00005240| 43 5b 30 5d 5b 31 5d 3b | 0a 58 09 09 43 5b 31 5d |C[0][1];|.X..C[1]|
|00005250| 5b 31 5d 20 2b 3d 20 56 | 32 44 6f 74 28 26 41 5b |[1] += V|2Dot(&A[|
|00005260| 69 5d 5b 31 5d 2c 20 26 | 41 5b 69 5d 5b 31 5d 29 |i][1], &|A[i][1])|
|00005270| 3b 0a 58 0a 58 09 09 74 | 6d 70 20 3d 20 56 32 53 |;.X.X..t|mp = V2S|
|00005280| 75 62 49 49 28 64 5b 66 | 69 72 73 74 20 2b 20 69 |ubII(d[f|irst + i|
|00005290| 5d 2c 0a 58 09 20 20 20 | 20 20 20 20 20 56 32 41 |],.X.   |     V2A|
|000052a0| 64 64 49 49 28 0a 58 09 | 20 20 20 20 20 20 20 20 |ddII(.X.|        |
|000052b0| 20 20 56 32 53 63 61 6c | 65 49 49 28 64 5b 66 69 |  V2Scal|eII(d[fi|
|000052c0| 72 73 74 5d 2c 20 42 30 | 28 75 50 72 69 6d 65 5b |rst], B0|(uPrime[|
|000052d0| 69 5d 29 29 2c 0a 58 09 | 09 20 20 20 20 09 56 32 |i])),.X.|.    .V2|
|000052e0| 41 64 64 49 49 28 0a 58 | 09 09 20 20 20 20 20 20 |AddII(.X|..      |
|000052f0| 09 09 56 32 53 63 61 6c | 65 49 49 28 64 5b 66 69 |..V2Scal|eII(d[fi|
|00005300| 72 73 74 5d 2c 20 42 31 | 28 75 50 72 69 6d 65 5b |rst], B1|(uPrime[|
|00005310| 69 5d 29 29 2c 0a 58 09 | 09 20 20 20 20 20 20 20 |i])),.X.|.       |
|00005320| 20 09 09 09 56 32 41 64 | 64 49 49 28 0a 58 09 20 | ...V2Ad|dII(.X. |
|00005330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005340| 20 09 09 56 32 53 63 61 | 6c 65 49 49 28 64 5b 6c | ..V2Sca|leII(d[l|
|00005350| 61 73 74 5d 2c 20 42 32 | 28 75 50 72 69 6d 65 5b |ast], B2|(uPrime[|
|00005360| 69 5d 29 29 2c 0a 58 09 | 20 20 20 20 20 20 20 20 |i])),.X.|        |
|00005370| 20 20 20 20 20 20 20 20 | 20 20 20 20 09 09 56 32 |        |    ..V2|
|00005380| 53 63 61 6c 65 49 49 28 | 64 5b 6c 61 73 74 5d 2c |ScaleII(|d[last],|
|00005390| 20 42 33 28 75 50 72 69 | 6d 65 5b 69 5d 29 29 29 | B3(uPri|me[i])))|
|000053a0| 29 29 29 3b 0a 58 09 0a | 58 0a 58 09 58 5b 30 5d |)));.X..|X.X.X[0]|
|000053b0| 20 2b 3d 20 56 32 44 6f | 74 28 26 41 5b 69 5d 5b | += V2Do|t(&A[i][|
|000053c0| 30 5d 2c 20 26 74 6d 70 | 29 3b 0a 58 09 58 5b 31 |0], &tmp|);.X.X[1|
|000053d0| 5d 20 2b 3d 20 56 32 44 | 6f 74 28 26 41 5b 69 5d |] += V2D|ot(&A[i]|
|000053e0| 5b 31 5d 2c 20 26 74 6d | 70 29 3b 0a 58 20 20 20 |[1], &tm|p);.X   |
|000053f0| 20 7d 0a 58 0a 58 20 20 | 20 20 2f 2a 20 43 6f 6d | }.X.X  |  /* Com|
|00005400| 70 75 74 65 20 74 68 65 | 20 64 65 74 65 72 6d 69 |pute the| determi|
|00005410| 6e 61 6e 74 73 20 6f 66 | 20 43 20 61 6e 64 20 58 |nants of| C and X|
|00005420| 09 2a 2f 0a 58 20 20 20 | 20 64 65 74 5f 43 30 5f |.*/.X   | det_C0_|
|00005430| 43 31 20 3d 20 43 5b 30 | 5d 5b 30 5d 20 2a 20 43 |C1 = C[0|][0] * C|
|00005440| 5b 31 5d 5b 31 5d 20 2d | 20 43 5b 31 5d 5b 30 5d |[1][1] -| C[1][0]|
|00005450| 20 2a 20 43 5b 30 5d 5b | 31 5d 3b 0a 58 20 20 20 | * C[0][|1];.X   |
|00005460| 20 64 65 74 5f 43 30 5f | 58 20 20 3d 20 43 5b 30 | det_C0_|X  = C[0|
|00005470| 5d 5b 30 5d 20 2a 20 58 | 5b 31 5d 20 20 20 20 2d |][0] * X|[1]    -|
|00005480| 20 43 5b 30 5d 5b 31 5d | 20 2a 20 58 5b 30 5d 3b | C[0][1]| * X[0];|
|00005490| 0a 58 20 20 20 20 64 65 | 74 5f 58 5f 43 31 20 20 |.X    de|t_X_C1  |
|000054a0| 3d 20 58 5b 30 5d 20 20 | 20 20 2a 20 43 5b 31 5d |= X[0]  |  * C[1]|
|000054b0| 5b 31 5d 20 2d 20 58 5b | 31 5d 20 20 20 20 2a 20 |[1] - X[|1]    * |
|000054c0| 43 5b 30 5d 5b 31 5d 3b | 0a 58 0a 58 20 20 20 20 |C[0][1];|.X.X    |
|000054d0| 2f 2a 20 46 69 6e 61 6c | 6c 79 2c 20 64 65 72 69 |/* Final|ly, deri|
|000054e0| 76 65 20 61 6c 70 68 61 | 20 76 61 6c 75 65 73 09 |ve alpha| values.|
|000054f0| 2a 2f 0a 58 20 20 20 20 | 69 66 20 28 64 65 74 5f |*/.X    |if (det_|
|00005500| 43 30 5f 43 31 20 3d 3d | 20 30 2e 30 29 20 7b 0a |C0_C1 ==| 0.0) {.|
|00005510| 58 09 09 64 65 74 5f 43 | 30 5f 43 31 20 3d 20 28 |X..det_C|0_C1 = (|
|00005520| 43 5b 30 5d 5b 30 5d 20 | 2a 20 43 5b 31 5d 5b 31 |C[0][0] |* C[1][1|
|00005530| 5d 29 20 2a 20 31 30 65 | 2d 31 32 3b 0a 58 20 20 |]) * 10e|-12;.X  |
|00005540| 20 20 7d 0a 58 20 20 20 | 20 61 6c 70 68 61 5f 6c |  }.X   | alpha_l|
|00005550| 20 3d 20 64 65 74 5f 58 | 5f 43 31 20 2f 20 64 65 | = det_X|_C1 / de|
|00005560| 74 5f 43 30 5f 43 31 3b | 0a 58 20 20 20 20 61 6c |t_C0_C1;|.X    al|
|00005570| 70 68 61 5f 72 20 3d 20 | 64 65 74 5f 43 30 5f 58 |pha_r = |det_C0_X|
|00005580| 20 2f 20 64 65 74 5f 43 | 30 5f 43 31 3b 0a 58 0a | / det_C|0_C1;.X.|
|00005590| 58 0a 58 20 20 20 20 2f | 2a 20 20 49 66 20 61 6c |X.X    /|*  If al|
|000055a0| 70 68 61 20 6e 65 67 61 | 74 69 76 65 2c 20 75 73 |pha nega|tive, us|
|000055b0| 65 20 74 68 65 20 57 75 | 2f 42 61 72 73 6b 79 20 |e the Wu|/Barsky |
|000055c0| 68 65 75 72 69 73 74 69 | 63 20 28 73 65 65 20 74 |heuristi|c (see t|
|000055d0| 65 78 74 29 20 2a 2f 0a | 58 20 20 20 20 69 66 20 |ext) */.|X    if |
|000055e0| 28 61 6c 70 68 61 5f 6c | 20 3c 20 30 2e 30 20 7c |(alpha_l| < 0.0 ||
|000055f0| 7c 20 61 6c 70 68 61 5f | 72 20 3c 20 30 2e 30 29 || alpha_|r < 0.0)|
|00005600| 20 7b 0a 58 09 09 64 6f | 75 62 6c 65 09 64 69 73 | {.X..do|uble.dis|
|00005610| 74 20 3d 20 56 32 44 69 | 73 74 61 6e 63 65 42 65 |t = V2Di|stanceBe|
|00005620| 74 77 65 65 6e 32 50 6f | 69 6e 74 73 28 26 64 5b |tween2Po|ints(&d[|
|00005630| 6c 61 73 74 5d 2c 20 26 | 64 5b 66 69 72 73 74 5d |last], &|d[first]|
|00005640| 29 20 2f 0a 58 09 09 09 | 09 09 33 2e 30 3b 0a 58 |) /.X...|..3.0;.X|
|00005650| 0a 58 09 09 62 65 7a 43 | 75 72 76 65 5b 30 5d 20 |.X..bezC|urve[0] |
|00005660| 3d 20 64 5b 66 69 72 73 | 74 5d 3b 0a 58 09 09 62 |= d[firs|t];.X..b|
|00005670| 65 7a 43 75 72 76 65 5b | 33 5d 20 3d 20 64 5b 6c |ezCurve[|3] = d[l|
|00005680| 61 73 74 5d 3b 0a 58 09 | 09 56 32 41 64 64 28 26 |ast];.X.|.V2Add(&|
|00005690| 62 65 7a 43 75 72 76 65 | 5b 30 5d 2c 20 56 32 53 |bezCurve|[0], V2S|
|000056a0| 63 61 6c 65 28 26 74 48 | 61 74 31 2c 20 64 69 73 |cale(&tH|at1, dis|
|000056b0| 74 29 2c 20 26 62 65 7a | 43 75 72 76 65 5b 31 5d |t), &bez|Curve[1]|
|000056c0| 29 3b 0a 58 09 09 56 32 | 41 64 64 28 26 62 65 7a |);.X..V2|Add(&bez|
|000056d0| 43 75 72 76 65 5b 33 5d | 2c 20 56 32 53 63 61 6c |Curve[3]|, V2Scal|
|000056e0| 65 28 26 74 48 61 74 32 | 2c 20 64 69 73 74 29 2c |e(&tHat2|, dist),|
|000056f0| 20 26 62 65 7a 43 75 72 | 76 65 5b 32 5d 29 3b 0a | &bezCur|ve[2]);.|
|00005700| 58 09 09 72 65 74 75 72 | 6e 20 28 62 65 7a 43 75 |X..retur|n (bezCu|
|00005710| 72 76 65 29 3b 0a 58 20 | 20 20 20 7d 0a 58 0a 58 |rve);.X |   }.X.X|
|00005720| 20 20 20 20 2f 2a 20 20 | 46 69 72 73 74 20 61 6e |    /*  |First an|
|00005730| 64 20 6c 61 73 74 20 63 | 6f 6e 74 72 6f 6c 20 70 |d last c|ontrol p|
|00005740| 6f 69 6e 74 73 20 6f 66 | 20 74 68 65 20 42 65 7a |oints of| the Bez|
|00005750| 69 65 72 20 63 75 72 76 | 65 20 61 72 65 20 2a 2f |ier curv|e are */|
|00005760| 0a 58 20 20 20 20 2f 2a | 20 20 70 6f 73 69 74 69 |.X    /*|  positi|
|00005770| 6f 6e 65 64 20 65 78 61 | 63 74 6c 79 20 61 74 20 |oned exa|ctly at |
|00005780| 74 68 65 20 66 69 72 73 | 74 20 61 6e 64 20 6c 61 |the firs|t and la|
|00005790| 73 74 20 64 61 74 61 20 | 70 6f 69 6e 74 73 20 2a |st data |points *|
|000057a0| 2f 0a 58 20 20 20 20 2f | 2a 20 20 43 6f 6e 74 72 |/.X    /|*  Contr|
|000057b0| 6f 6c 20 70 6f 69 6e 74 | 73 20 31 20 61 6e 64 20 |ol point|s 1 and |
|000057c0| 32 20 61 72 65 20 70 6f | 73 69 74 69 6f 6e 65 64 |2 are po|sitioned|
|000057d0| 20 61 6e 20 61 6c 70 68 | 61 20 64 69 73 74 61 6e | an alph|a distan|
|000057e0| 63 65 20 6f 75 74 20 2a | 2f 0a 58 20 20 20 20 2f |ce out *|/.X    /|
|000057f0| 2a 20 20 6f 6e 20 74 68 | 65 20 74 61 6e 67 65 6e |*  on th|e tangen|
|00005800| 74 20 76 65 63 74 6f 72 | 73 2c 20 6c 65 66 74 20 |t vector|s, left |
|00005810| 61 6e 64 20 72 69 67 68 | 74 2c 20 72 65 73 70 65 |and righ|t, respe|
|00005820| 63 74 69 76 65 6c 79 20 | 2a 2f 0a 58 20 20 20 20 |ctively |*/.X    |
|00005830| 62 65 7a 43 75 72 76 65 | 5b 30 5d 20 3d 20 64 5b |bezCurve|[0] = d[|
|00005840| 66 69 72 73 74 5d 3b 0a | 58 20 20 20 20 62 65 7a |first];.|X    bez|
|00005850| 43 75 72 76 65 5b 33 5d | 20 3d 20 64 5b 6c 61 73 |Curve[3]| = d[las|
|00005860| 74 5d 3b 0a 58 20 20 20 | 20 56 32 41 64 64 28 26 |t];.X   | V2Add(&|
|00005870| 62 65 7a 43 75 72 76 65 | 5b 30 5d 2c 20 56 32 53 |bezCurve|[0], V2S|
|00005880| 63 61 6c 65 28 26 74 48 | 61 74 31 2c 20 61 6c 70 |cale(&tH|at1, alp|
|00005890| 68 61 5f 6c 29 2c 20 26 | 62 65 7a 43 75 72 76 65 |ha_l), &|bezCurve|
|000058a0| 5b 31 5d 29 3b 0a 58 20 | 20 20 20 56 32 41 64 64 |[1]);.X |   V2Add|
|000058b0| 28 26 62 65 7a 43 75 72 | 76 65 5b 33 5d 2c 20 56 |(&bezCur|ve[3], V|
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