15 January 2010 10:25:51 PM SOBOL_PRB C++ version Test the routines in the SOBOL library. TEST01 The C++ function ^ computes the bitwise exclusive OR of two integers. I J I^J 22 96 118 83 56 107 41 6 47 26 11 17 4 64 68 6 45 43 40 76 100 80 0 80 90 35 121 9 1 8 TEST02 I4_BIT_HI1 returns the location of the high bit in an integer. I I4_BIT_HI1(I) 22 5 96 7 83 7 56 6 41 6 6 3 26 5 11 4 4 3 64 7 TEST03 I4_BIT_LO0 returns the location of the low 0 bit in an integer. I I4_BIT_LO0(I) 22 1 96 1 83 3 56 1 41 2 6 1 26 1 11 3 4 1 64 1 TEST04 I4_SOBOL computes the next element of a Sobol sequence. In this test, we call I4_SOBOL repeatedly. Using dimension DIM_NUM = 2 Seed Seed I4_SOBOL In Out *SEED = 0 L = 1 0 1 0 0 *SEED = 1 L = 2 1 2 0.5 0.5 *SEED = 2 L = 1 2 3 0.75 0.25 *SEED = 3 L = 3 3 4 0.25 0.75 *SEED = 4 L = 1 4 5 0.375 0.375 *SEED = 5 L = 2 5 6 0.875 0.875 *SEED = 6 L = 1 6 7 0.625 0.125 *SEED = 7 L = 4 7 8 0.125 0.625 *SEED = 8 L = 1 8 9 0.1875 0.3125 *SEED = 9 L = 2 9 10 0.6875 0.8125 *SEED = 10 L = 1 10 11 0.9375 0.0625 *SEED = 11 L = 3 11 12 0.4375 0.5625 *SEED = 12 L = 1 .................... *SEED = 13 L = 2 *SEED = 14 L = 1 *SEED = 15 L = 5 *SEED = 16 L = 1 *SEED = 17 L = 2 *SEED = 18 L = 1 *SEED = 19 L = 3 *SEED = 20 L = 1 *SEED = 21 L = 2 *SEED = 22 L = 1 *SEED = 23 L = 4 *SEED = 24 L = 1 *SEED = 25 L = 2 *SEED = 26 L = 1 *SEED = 27 L = 3 *SEED = 28 L = 1 *SEED = 29 L = 2 *SEED = 30 L = 1 *SEED = 31 L = 6 *SEED = 32 L = 1 *SEED = 33 L = 2 *SEED = 34 L = 1 *SEED = 35 L = 3 *SEED = 36 L = 1 *SEED = 37 L = 2 *SEED = 38 L = 1 *SEED = 39 L = 4 *SEED = 40 L = 1 *SEED = 41 L = 2 *SEED = 42 L = 1 *SEED = 43 L = 3 *SEED = 44 L = 1 *SEED = 45 L = 2 *SEED = 46 L = 1 *SEED = 47 L = 5 *SEED = 48 L = 1 *SEED = 49 L = 2 *SEED = 50 L = 1 *SEED = 51 L = 3 *SEED = 52 L = 1 *SEED = 53 L = 2 *SEED = 54 L = 1 *SEED = 55 L = 4 *SEED = 56 L = 1 *SEED = 57 L = 2 *SEED = 58 L = 1 *SEED = 59 L = 3 *SEED = 60 L = 1 *SEED = 61 L = 2 *SEED = 62 L = 1 *SEED = 63 L = 7 *SEED = 64 L = 1 *SEED = 65 L = 2 *SEED = 66 L = 1 *SEED = 67 L = 3 *SEED = 68 L = 1 *SEED = 69 L = 2 *SEED = 70 L = 1 *SEED = 71 L = 4 *SEED = 72 L = 1 *SEED = 73 L = 2 *SEED = 74 L = 1 *SEED = 75 L = 3 *SEED = 76 L = 1 *SEED = 77 L = 2 *SEED = 78 L = 1 *SEED = 79 L = 5 *SEED = 80 L = 1 *SEED = 81 L = 2 *SEED = 82 L = 1 *SEED = 83 L = 3 *SEED = 84 L = 1 *SEED = 85 L = 2 *SEED = 86 L = 1 *SEED = 87 L = 4 *SEED = 88 L = 1 *SEED = 89 L = 2 *SEED = 90 L = 1 *SEED = 91 L = 3 *SEED = 92 L = 1 *SEED = 93 L = 2 *SEED = 94 L = 1 *SEED = 95 L = 6 95 96 0.0546875 0.929688 *SEED = 96 L = 1 96 97 0.0390625 0.132812 *SEED = 97 L = 2 97 98 0.539062 0.632812 *SEED = 98 L = 1 98 99 0.789062 0.382812 *SEED = 99 L = 3 99 100 0.289062 0.882812 *SEED = 100 L = 1 100 101 0.414062 0.257812 *SEED = 101 L = 2 101 102 0.914062 0.757812 *SEED = 102 L = 1 102 103 0.664062 0.0078125 *SEED = 103 L = 4 103 104 0.164062 0.507812 *SEED = 104 L = 1 104 105 0.226562 0.445312 *SEED = 105 L = 2 105 106 0.726562 0.945312 *SEED = 106 L = 1 106 107 0.976562 0.195312 *SEED = 107 L = 3 107 108 0.476562 0.695312 *SEED = 108 L = 1 108 109 0.351562 0.0703125 *SEED = 109 L = 2 109 110 0.851562 0.570312 *SEED = 110 L = 1 110 111 0.601562 0.320312 Using dimension DIM_NUM = 3 Seed Seed I4_SOBOL In Out *SEED = 0 L = 1 0 1 0 0 0 *SEED = 1 L = 2 1 2 0.5 0.5 0.5 *SEED = 2 L = 1 2 3 0.75 0.25 0.75 *SEED = 3 L = 3 3 4 0.25 0.75 0.25 *SEED = 4 L = 1 4 5 0.375 0.375 0.625 *SEED = 5 L = 2 5 6 0.875 0.875 0.125 *SEED = 6 L = 1 6 7 0.625 0.125 0.375 *SEED = 7 L = 4 7 8 0.125 0.625 0.875 *SEED = 8 L = 1 8 9 0.1875 0.3125 0.3125 *SEED = 9 L = 2 9 10 0.6875 0.8125 0.8125 *SEED = 10 L = 1 10 11 0.9375 0.0625 0.5625 *SEED = 11 L = 3 11 12 0.4375 0.5625 0.0625 *SEED = 12 L = 1 .................... *SEED = 13 L = 2 *SEED = 14 L = 1 *SEED = 15 L = 5 *SEED = 16 L = 1 *SEED = 17 L = 2 *SEED = 18 L = 1 *SEED = 19 L = 3 *SEED = 20 L = 1 *SEED = 21 L = 2 *SEED = 22 L = 1 *SEED = 23 L = 4 *SEED = 24 L = 1 *SEED = 25 L = 2 *SEED = 26 L = 1 *SEED = 27 L = 3 *SEED = 28 L = 1 *SEED = 29 L = 2 *SEED = 30 L = 1 *SEED = 31 L = 6 *SEED = 32 L = 1 *SEED = 33 L = 2 *SEED = 34 L = 1 *SEED = 35 L = 3 *SEED = 36 L = 1 *SEED = 37 L = 2 *SEED = 38 L = 1 *SEED = 39 L = 4 *SEED = 40 L = 1 *SEED = 41 L = 2 *SEED = 42 L = 1 *SEED = 43 L = 3 *SEED = 44 L = 1 *SEED = 45 L = 2 *SEED = 46 L = 1 *SEED = 47 L = 5 *SEED = 48 L = 1 *SEED = 49 L = 2 *SEED = 50 L = 1 *SEED = 51 L = 3 *SEED = 52 L = 1 *SEED = 53 L = 2 *SEED = 54 L = 1 *SEED = 55 L = 4 *SEED = 56 L = 1 *SEED = 57 L = 2 *SEED = 58 L = 1 *SEED = 59 L = 3 *SEED = 60 L = 1 *SEED = 61 L = 2 *SEED = 62 L = 1 *SEED = 63 L = 7 *SEED = 64 L = 1 *SEED = 65 L = 2 *SEED = 66 L = 1 *SEED = 67 L = 3 *SEED = 68 L = 1 *SEED = 69 L = 2 *SEED = 70 L = 1 *SEED = 71 L = 4 *SEED = 72 L = 1 *SEED = 73 L = 2 *SEED = 74 L = 1 *SEED = 75 L = 3 *SEED = 76 L = 1 *SEED = 77 L = 2 *SEED = 78 L = 1 *SEED = 79 L = 5 *SEED = 80 L = 1 *SEED = 81 L = 2 *SEED = 82 L = 1 *SEED = 83 L = 3 *SEED = 84 L = 1 *SEED = 85 L = 2 *SEED = 86 L = 1 *SEED = 87 L = 4 *SEED = 88 L = 1 *SEED = 89 L = 2 *SEED = 90 L = 1 *SEED = 91 L = 3 *SEED = 92 L = 1 *SEED = 93 L = 2 *SEED = 94 L = 1 *SEED = 95 L = 6 95 96 0.0546875 0.929688 0.101562 *SEED = 96 L = 1 96 97 0.0390625 0.132812 0.929688 *SEED = 97 L = 2 97 98 0.539062 0.632812 0.429688 *SEED = 98 L = 1 98 99 0.789062 0.382812 0.179688 *SEED = 99 L = 3 99 100 0.289062 0.882812 0.679688 *SEED = 100 L = 1 100 101 0.414062 0.257812 0.304688 *SEED = 101 L = 2 101 102 0.914062 0.757812 0.804688 *SEED = 102 L = 1 102 103 0.664062 0.0078125 0.554688 *SEED = 103 L = 4 103 104 0.164062 0.507812 0.0546875 *SEED = 104 L = 1 104 105 0.226562 0.445312 0.742188 *SEED = 105 L = 2 105 106 0.726562 0.945312 0.242188 *SEED = 106 L = 1 106 107 0.976562 0.195312 0.492188 *SEED = 107 L = 3 107 108 0.476562 0.695312 0.992188 *SEED = 108 L = 1 108 109 0.351562 0.0703125 0.117188 *SEED = 109 L = 2 109 110 0.851562 0.570312 0.617188 *SEED = 110 L = 1 110 111 0.601562 0.320312 0.867188 Using dimension DIM_NUM = 4 Seed Seed I4_SOBOL In Out *SEED = 0 L = 1 0 1 0 0 0 0 *SEED = 1 L = 2 1 2 0.5 0.5 0.5 0.5 *SEED = 2 L = 1 2 3 0.75 0.25 0.75 0.25 *SEED = 3 L = 3 3 4 0.25 0.75 0.25 0.75 *SEED = 4 L = 1 4 5 0.375 0.375 0.625 0.125 *SEED = 5 L = 2 5 6 0.875 0.875 0.125 0.625 *SEED = 6 L = 1 6 7 0.625 0.125 0.375 0.375 *SEED = 7 L = 4 7 8 0.125 0.625 0.875 0.875 *SEED = 8 L = 1 8 9 0.1875 0.3125 0.3125 0.6875 *SEED = 9 L = 2 9 10 0.6875 0.8125 0.8125 0.1875 *SEED = 10 L = 1 10 11 0.9375 0.0625 0.5625 0.9375 *SEED = 11 L = 3 11 12 0.4375 0.5625 0.0625 0.4375 *SEED = 12 L = 1 .................... *SEED = 13 L = 2 *SEED = 14 L = 1 *SEED = 15 L = 5 *SEED = 16 L = 1 *SEED = 17 L = 2 *SEED = 18 L = 1 *SEED = 19 L = 3 *SEED = 20 L = 1 *SEED = 21 L = 2 *SEED = 22 L = 1 *SEED = 23 L = 4 *SEED = 24 L = 1 *SEED = 25 L = 2 *SEED = 26 L = 1 *SEED = 27 L = 3 *SEED = 28 L = 1 *SEED = 29 L = 2 *SEED = 30 L = 1 *SEED = 31 L = 6 *SEED = 32 L = 1 *SEED = 33 L = 2 *SEED = 34 L = 1 *SEED = 35 L = 3 *SEED = 36 L = 1 *SEED = 37 L = 2 *SEED = 38 L = 1 *SEED = 39 L = 4 *SEED = 40 L = 1 *SEED = 41 L = 2 *SEED = 42 L = 1 *SEED = 43 L = 3 *SEED = 44 L = 1 *SEED = 45 L = 2 *SEED = 46 L = 1 *SEED = 47 L = 5 *SEED = 48 L = 1 *SEED = 49 L = 2 *SEED = 50 L = 1 *SEED = 51 L = 3 *SEED = 52 L = 1 *SEED = 53 L = 2 *SEED = 54 L = 1 *SEED = 55 L = 4 *SEED = 56 L = 1 *SEED = 57 L = 2 *SEED = 58 L = 1 *SEED = 59 L = 3 *SEED = 60 L = 1 *SEED = 61 L = 2 *SEED = 62 L = 1 *SEED = 63 L = 7 *SEED = 64 L = 1 *SEED = 65 L = 2 *SEED = 66 L = 1 *SEED = 67 L = 3 *SEED = 68 L = 1 *SEED = 69 L = 2 *SEED = 70 L = 1 *SEED = 71 L = 4 *SEED = 72 L = 1 *SEED = 73 L = 2 *SEED = 74 L = 1 *SEED = 75 L = 3 *SEED = 76 L = 1 *SEED = 77 L = 2 *SEED = 78 L = 1 *SEED = 79 L = 5 *SEED = 80 L = 1 *SEED = 81 L = 2 *SEED = 82 L = 1 *SEED = 83 L = 3 *SEED = 84 L = 1 *SEED = 85 L = 2 *SEED = 86 L = 1 *SEED = 87 L = 4 *SEED = 88 L = 1 *SEED = 89 L = 2 *SEED = 90 L = 1 *SEED = 91 L = 3 *SEED = 92 L = 1 *SEED = 93 L = 2 *SEED = 94 L = 1 *SEED = 95 L = 6 95 96 0.0546875 0.929688 0.101562 0.960938 *SEED = 96 L = 1 96 97 0.0390625 0.132812 0.929688 0.351562 *SEED = 97 L = 2 97 98 0.539062 0.632812 0.429688 0.851562 *SEED = 98 L = 1 98 99 0.789062 0.382812 0.179688 0.101562 *SEED = 99 L = 3 99 100 0.289062 0.882812 0.679688 0.601562 *SEED = 100 L = 1 100 101 0.414062 0.257812 0.304688 0.476562 *SEED = 101 L = 2 101 102 0.914062 0.757812 0.804688 0.976562 *SEED = 102 L = 1 102 103 0.664062 0.0078125 0.554688 0.226562 *SEED = 103 L = 4 103 104 0.164062 0.507812 0.0546875 0.726562 *SEED = 104 L = 1 104 105 0.226562 0.445312 0.742188 0.914062 *SEED = 105 L = 2 105 106 0.726562 0.945312 0.242188 0.414062 *SEED = 106 L = 1 106 107 0.976562 0.195312 0.492188 0.664062 *SEED = 107 L = 3 107 108 0.476562 0.695312 0.992188 0.164062 *SEED = 108 L = 1 108 109 0.351562 0.0703125 0.117188 0.789062 *SEED = 109 L = 2 109 110 0.851562 0.570312 0.617188 0.289062 *SEED = 110 L = 1 110 111 0.601562 0.320312 0.867188 0.539062 TEST05 I4_SOBOL computes the next element of a Sobol sequence. In this test, we demonstrate how the SEED can be manipulated to skip ahead in the sequence, or to come back to any part of the sequence. Using dimension DIM_NUM = 3 Seed Seed I4_SOBOL In Out *SEED = 0 L = 1 0 1 0 0 0 *SEED = 1 L = 2 1 2 0.5 0.5 0.5 *SEED = 2 L = 1 2 3 0.75 0.25 0.75 *SEED = 3 L = 3 3 4 0.25 0.75 0.25 *SEED = 4 L = 1 4 5 0.375 0.375 0.625 *SEED = 5 L = 2 5 6 0.875 0.875 0.125 *SEED = 6 L = 1 6 7 0.625 0.125 0.375 *SEED = 7 L = 4 7 8 0.125 0.625 0.875 *SEED = 8 L = 1 8 9 0.1875 0.3125 0.3125 *SEED = 9 L = 2 9 10 0.6875 0.8125 0.8125 *SEED = 10 L = 1 10 11 0.9375 0.0625 0.5625 Jump ahead by increasing SEED: Seed Seed I4_SOBOL In Out *SEED = 100 L = 1 100 101 0.414062 0.257812 0.304688 *SEED = 101 L = 2 101 102 0.914062 0.757812 0.804688 *SEED = 102 L = 1 102 103 0.664062 0.0078125 0.554688 *SEED = 103 L = 4 103 104 0.164062 0.507812 0.0546875 *SEED = 104 L = 1 104 105 0.226562 0.445312 0.742188 Jump back by decreasing SEED: Seed Seed I4_SOBOL In Out *SEED = 3 L = 3 3 4 0.25 0.75 0.25 *SEED = 4 L = 1 4 5 0.375 0.375 0.625 *SEED = 5 L = 2 5 6 0.875 0.875 0.125 *SEED = 6 L = 1 6 7 0.625 0.125 0.375 *SEED = 7 L = 4 7 8 0.125 0.625 0.875 *SEED = 8 L = 1 8 9 0.1875 0.3125 0.3125 *SEED = 9 L = 2 9 10 0.6875 0.8125 0.8125 *SEED = 10 L = 1 10 11 0.9375 0.0625 0.5625 *SEED = 11 L = 3 11 12 0.4375 0.5625 0.0625 *SEED = 12 L = 1 12 13 0.3125 0.1875 0.9375 *SEED = 13 L = 2 13 14 0.8125 0.6875 0.4375 Jump ahead by increasing SEED: Seed Seed I4_SOBOL In Out *SEED = 98 L = 1 98 99 0.789062 0.382812 0.179688 *SEED = 99 L = 3 99 100 0.289062 0.882812 0.679688 *SEED = 100 L = 1 100 101 0.414062 0.257812 0.304688 *SEED = 101 L = 2 101 102 0.914062 0.757812 0.804688 *SEED = 102 L = 1 102 103 0.664062 0.0078125 0.554688 TEST055 The C++ function ^ computes the bitwise exclusive OR of two LONG LONG INT's. I J I^J 22 96 118 83 56 107 41 6 47 26 11 17 4 64 68 6 45 43 40 76 100 80 0 80 90 35 121 9 1 8 TEST06 I8_BIT_HI1 returns the location of the high bit in an integer. I I8_BIT_HI1(I) 22 5 96 7 83 7 56 6 41 6 6 3 26 5 11 4 4 3 64 7 TEST07 I8_BIT_LO0 returns the location of the low zero bit in an integer. I I8_BIT_LO0(I) 22 1 96 1 83 3 56 1 41 2 6 1 26 1 11 3 4 1 64 1 TEST08 I8_SOBOL computes the next element of a Sobol sequence. In this test, we call I8_SOBOL repeatedly. Using dimension DIM_NUM = 2 Seed Seed I8_SOBOL In Out 0 1 0 0 1 2 0.5 0.5 2 3 0.75 0.25 3 4 0.25 0.75 4 5 0.375 0.375 5 6 0.875 0.875 6 7 0.625 0.125 7 8 0.125 0.625 8 9 0.1875 0.3125 9 10 0.6875 0.8125 10 11 0.9375 0.0625 11 12 0.4375 0.5625 .................... 95 96 0.0546875 0.929688 96 97 0.0390625 0.132812 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.0078125 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.0703125 109 110 0.851562 0.570312 110 111 0.601562 0.320312 Using dimension DIM_NUM = 3 Seed Seed I8_SOBOL In Out 0 1 0 0 0 1 2 0.5 0.5 0.5 2 3 0.75 0.25 0.75 3 4 0.25 0.75 0.25 4 5 0.375 0.375 0.625 5 6 0.875 0.875 0.125 6 7 0.625 0.125 0.375 7 8 0.125 0.625 0.875 8 9 0.1875 0.3125 0.3125 9 10 0.6875 0.8125 0.8125 10 11 0.9375 0.0625 0.5625 11 12 0.4375 0.5625 0.0625 .................... 95 96 0.0546875 0.929688 0.101562 96 97 0.0390625 0.132812 0.929688 97 98 0.539062 0.632812 0.429688 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.0078125 0.554688 103 104 0.164062 0.507812 0.0546875 104 105 0.226562 0.445312 0.742188 105 106 0.726562 0.945312 0.242188 106 107 0.976562 0.195312 0.492188 107 108 0.476562 0.695312 0.992188 108 109 0.351562 0.0703125 0.117188 109 110 0.851562 0.570312 0.617188 110 111 0.601562 0.320312 0.867188 Using dimension DIM_NUM = 4 Seed Seed I8_SOBOL In Out 0 1 0 0 0 0 1 2 0.5 0.5 0.5 0.5 2 3 0.75 0.25 0.75 0.25 3 4 0.25 0.75 0.25 0.75 4 5 0.375 0.375 0.625 0.125 5 6 0.875 0.875 0.125 0.625 6 7 0.625 0.125 0.375 0.375 7 8 0.125 0.625 0.875 0.875 8 9 0.1875 0.3125 0.3125 0.6875 9 10 0.6875 0.8125 0.8125 0.1875 10 11 0.9375 0.0625 0.5625 0.9375 11 12 0.4375 0.5625 0.0625 0.4375 .................... 95 96 0.0546875 0.929688 0.101562 0.960938 96 97 0.0390625 0.132812 0.929688 0.351562 97 98 0.539062 0.632812 0.429688 0.851562 98 99 0.789062 0.382812 0.179688 0.101562 99 100 0.289062 0.882812 0.679688 0.601562 100 101 0.414062 0.257812 0.304688 0.476562 101 102 0.914062 0.757812 0.804688 0.976562 102 103 0.664062 0.0078125 0.554688 0.226562 103 104 0.164062 0.507812 0.0546875 0.726562 104 105 0.226562 0.445312 0.742188 0.914062 105 106 0.726562 0.945312 0.242188 0.414062 106 107 0.976562 0.195312 0.492188 0.664062 107 108 0.476562 0.695312 0.992188 0.164062 108 109 0.351562 0.0703125 0.117188 0.789062 109 110 0.851562 0.570312 0.617188 0.289062 110 111 0.601562 0.320312 0.867188 0.539062 TEST09 I8_SOBOL computes the next element of a Sobol sequence. In this test, we demonstrate how the SEED can be manipulated to skip ahead in the sequence, or to come back to any part of the sequence. Using dimension DIM_NUM = 3 Seed Seed I8_SOBOL In Out 0 1 0 0 0 1 2 0.5 0.5 0.5 2 3 0.75 0.25 0.75 3 4 0.25 0.75 0.25 4 5 0.375 0.375 0.625 5 6 0.875 0.875 0.125 6 7 0.625 0.125 0.375 7 8 0.125 0.625 0.875 8 9 0.1875 0.3125 0.3125 9 10 0.6875 0.8125 0.8125 10 11 0.9375 0.0625 0.5625 Jump ahead by increasing SEED: Seed Seed I8_SOBOL In Out 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.0078125 0.554688 103 104 0.164062 0.507812 0.0546875 104 105 0.226562 0.445312 0.742188 Jump back by decreasing SEED: Seed Seed I8_SOBOL In Out 3 4 0.25 0.75 0.25 4 5 0.375 0.375 0.625 5 6 0.875 0.875 0.125 6 7 0.625 0.125 0.375 7 8 0.125 0.625 0.875 8 9 0.1875 0.3125 0.3125 9 10 0.6875 0.8125 0.8125 10 11 0.9375 0.0625 0.5625 11 12 0.4375 0.5625 0.0625 12 13 0.3125 0.1875 0.9375 13 14 0.8125 0.6875 0.4375 Jump ahead by increasing SEED: Seed Seed I8_SOBOL In Out 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.0078125 0.554688 SOBOL_PRB Normal end of execution. 15 January 2010 10:25:51 PM