1: Software Calculation of IEEE Floating-Point Values, Intel Format |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
0 | 00000000000014C0 | -5 | 5 | C014 | 1 (-) | 0401 | 1025 | 2 |
00000000000010C0 | -4 | 4 | C010 | 1 (-) | 0401 | 1025 | 2 | |
00000000000008C0 | -3 | 3 | C008 | 1 (-) | 0400 | 1024 | 1 | |
00000000000000C0 | -2 | 2 | C000 | 1 (-) | 0400 | 1024 | 1 | |
000000000000F0BF | -1 | 1 | BFF0 | 1 (-) | 03FF | 1023 | 0 | |
0000000000000000 | 0 | 0 | 0000 | 0 (+) | 0000 | 0 | -1023 | |
000000000000F03F | 1 | 1 | 3FF0 | 0 (+) | 03FF | 1023 | 0 | |
0000000000000040 | 2 | 2 | 4000 | 0 (+) | 0400 | 1024 | 1 | |
0000000000000840 | 3 | 3 | 4008 | 0 (+) | 0400 | 1024 | 1 | |
0000000000001040 | 4 | 4 | 4010 | 0 (+) | 0401 | 1025 | 2 | |
0000000000001440 | 5 | 5 | 4014 | 0 (+) | 0401 | 1025 | 2 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
8 | 0000000000001840 | 6 | 6 | 4018 | 0 (+) | 0401 | 1025 | 2 |
0000000000001C40 | 7 | 7 | 401C | 0 (+) | 0401 | 1025 | 2 | |
0000000000002040 | 8 | 8 | 4020 | 0 (+) | 0402 | 1026 | 3 | |
0000000000002240 | 9 | 9 | 4022 | 0 (+) | 0402 | 1026 | 3 | |
0000000000002440 | 10 | 10 | 4024 | 0 (+) | 0402 | 1026 | 3 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
16 | 0000000000002C40 | 14 | 14 | 402C | 0 (+) | 0402 | 1026 | 3 |
0000000000002E40 | 15 | 15 | 402E | 0 (+) | 0402 | 1026 | 3 | |
0000000000003040 | 16 | 16 | 4030 | 0 (+) | 0403 | 1027 | 4 | |
0000000000003140 | 17 | 17 | 4031 | 0 (+) | 0403 | 1027 | 4 | |
0000000000003240 | 18 | 18 | 4032 | 0 (+) | 0403 | 1027 | 4 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
32 | 0000000000003E40 | 30 | 30 | 403E | 0 (+) | 0403 | 1027 | 4 |
0000000000003F40 | 31 | 31 | 403F | 0 (+) | 0403 | 1027 | 4 | |
0000000000004040 | 32 | 32 | 4040 | 0 (+) | 0404 | 1028 | 5 | |
0000000000804040 | 33 | 33 | 4040 | 0 (+) | 0404 | 1028 | 5 | |
0000000000004140 | 34 | 34 | 4041 | 0 (+) | 0404 | 1028 | 5 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
64 | 0000000000004F40 | 62 | 62 | 404F | 0 (+) | 0404 | 1028 | 5 |
0000000000804F40 | 63 | 63 | 404F | 0 (+) | 0404 | 1028 | 5 | |
0000000000005040 | 64 | 64 | 4050 | 0 (+) | 0405 | 1029 | 6 | |
0000000000405040 | 65 | 65 | 4050 | 0 (+) | 0405 | 1029 | 6 | |
0000000000805040 | 66 | 66 | 4050 | 0 (+) | 0405 | 1029 | 6 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
128 | 0000000000805F40 | 126 | 126 | 405F | 0 (+) | 0405 | 1029 | 6 |
0000000000C05F40 | 127 | 127 | 405F | 0 (+) | 0405 | 1029 | 6 | |
0000000000006040 | 128 | 128 | 4060 | 0 (+) | 0406 | 1030 | 7 | |
0000000000206040 | 129 | 129 | 4060 | 0 (+) | 0406 | 1030 | 7 | |
0000000000406040 | 130 | 130 | 4060 | 0 (+) | 0406 | 1030 | 7 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
256 | 0000000000C06F40 | 254 | 254 | 406F | 0 (+) | 0406 | 1030 | 7 |
0000000000E06F40 | 255 | 255 | 406F | 0 (+) | 0406 | 1030 | 7 | |
0000000000007040 | 256 | 256 | 4070 | 0 (+) | 0407 | 1031 | 8 | |
0000000000107040 | 257 | 257 | 4070 | 0 (+) | 0407 | 1031 | 8 | |
0000000000207040 | 258 | 258 | 4070 | 0 (+) | 0407 | 1031 | 8 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
512 | 0000000000F07F40 | 511 | 511 | 407F | 0 (+) | 0407 | 1031 | 8 |
0000000000008040 | 512 | 512 | 4080 | 0 (+) | 0408 | 1032 | 9 | |
0000000000088040 | 513 | 513 | 4080 | 0 (+) | 0408 | 1032 | 9 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
1024 | 0000000000F88F40 | 1,023 | 1,023 | 408F | 0 (+) | 0408 | 1032 | 9 |
0000000000009040 | 1,024 | 1,024 | 4090 | 0 (+) | 0409 | 1033 | 10 | |
0000000000049040 | 1,025 | 1,025 | 4090 | 0 (+) | 0409 | 1033 | 10 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
2048 | 0000000000FC9F40 | 2,047 | 2,047 | 409F | 0 (+) | 0409 | 1033 | 10 |
000000000000A040 | 2,048 | 2,048 | 40A0 | 0 (+) | 040A | 1034 | 11 | |
000000000002A040 | 2,049 | 2,049 | 40A0 | 0 (+) | 040A | 1034 | 11 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
4096 | 0000000000FEAF40 | 4,095 | 4,095 | 40AF | 0 (+) | 040A | 1034 | 11 |
000000000000B040 | 4,096 | 4,096 | 40B0 | 0 (+) | 040B | 1035 | 12 | |
000000000001B040 | 4,097 | 4,097 | 40B0 | 0 (+) | 040B | 1035 | 12 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
8192 | 0000000000FFBF40 | 8,191 | 8,191 | 40BF | 0 (+) | 040B | 1035 | 12 |
000000000000C040 | 8,192 | 8,192 | 40C0 | 0 (+) | 040C | 1036 | 13 | |
000000008000C040 | 8,193 | 8,193 | 40C0 | 0 (+) | 040C | 1036 | 13 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
16384 | 0000000080FFCF40 | 16,383 | 16,383 | 40CF | 0 (+) | 040C | 1036 | 13 |
000000000000D040 | 16,384 | 16,384 | 40D0 | 0 (+) | 040D | 1037 | 14 | |
000000004000D040 | 16,385 | 16,385 | 40D0 | 0 (+) | 040D | 1037 | 14 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
32768 | 00000000C0FFDF40 | 32,767 | 32,767 | 40DF | 0 (+) | 040D | 1037 | 14 |
000000000000E040 | 32,768 | 32,768 | 40E0 | 0 (+) | 040E | 1038 | 15 | |
000000002000E040 | 32,769 | 32,769 | 40E0 | 0 (+) | 040E | 1038 | 15 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
65536 | 00000000E0FFEF40 | 65,535 | 65,535 | 40EF | 0 (+) | 040E | 1038 | 15 |
000000000000F040 | 65,536 | 65,536 | 40F0 | 0 (+) | 040F | 1039 | 16 | |
000000001000F040 | 65,537 | 65,537 | 40F0 | 0 (+) | 040F | 1039 | 16 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
131072 | 00000000F0FFFF40 | 131,071 | 131,071 | 40FF | 0 (+) | 040F | 1039 | 16 |
0000000000000041 | 131,072 | 131,072 | 4100 | 0 (+) | 0410 | 1040 | 17 | |
0000000008000041 | 131,073 | 131,073 | 4100 | 0 (+) | 0410 | 1040 | 17 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
262144 | 00000000F8FF0F41 | 262,143 | 262,143 | 410F | 0 (+) | 0410 | 1040 | 17 |
0000000000001041 | 262,144 | 262,144 | 4110 | 0 (+) | 0411 | 1041 | 18 | |
0000000004001041 | 262,145 | 262,145 | 4110 | 0 (+) | 0411 | 1041 | 18 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
524288 | 00000000FCFF1F41 | 524,287 | 524,287 | 411F | 0 (+) | 0411 | 1041 | 18 |
0000000000002041 | 524,288 | 524,288 | 4120 | 0 (+) | 0412 | 1042 | 19 | |
0000000002002041 | 524,289 | 524,289 | 4120 | 0 (+) | 0412 | 1042 | 19 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
1048576 | 00000000FEFF2F41 | 1,048,575 | 1,048,575 | 412F | 0 (+) | 0412 | 1042 | 19 |
0000000000003041 | 1,048,576 | 1,048,576 | 4130 | 0 (+) | 0413 | 1043 | 20 | |
0000000001003041 | 1,048,577 | 1,048,577 | 4130 | 0 (+) | 0413 | 1043 | 20 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
2097152 | 00000000FFFF3F41 | 2,097,151 | 2,097,151 | 413F | 0 (+) | 0413 | 1043 | 20 |
0000000000004041 | 2,097,152 | 2,097,152 | 4140 | 0 (+) | 0414 | 1044 | 21 | |
0000008000004041 | 2,097,153 | 2,097,153 | 4140 | 0 (+) | 0414 | 1044 | 21 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
4194304 | 00000080FFFF4F41 | 4,194,303 | 4,194,303 | 414F | 0 (+) | 0414 | 1044 | 21 |
0000000000005041 | 4,194,304 | 4,194,304 | 4150 | 0 (+) | 0415 | 1045 | 22 | |
0000004000005041 | 4,194,305 | 4,194,305 | 4150 | 0 (+) | 0415 | 1045 | 22 |
series | crbx | x | value | signexp | sign | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|
8388608 | 000000C0FFFF5F41 | 8,388,607 | 8,388,607 | 415F | 0 (+) | 0415 | 1045 | 22 |
0000000000006041 | 8,388,608 | 8,388,608 | 4160 | 0 (+) | 0416 | 1046 | 23 | |
0000002000006041 | 8,388,609 | 8,388,609 | 4160 | 0 (+) | 0416 | 1046 | 23 |
2: The Two Original Values and Their Difference |
Obs | x | crbx | y | crby | d | crbd | signexp | exponent | exp_biased | exp_use |
---|---|---|---|---|---|---|---|---|---|---|
1 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 0.01562500 | 000000000000903F | 3F90 | 03F9 | 1017 | -6 |
3: Values Immediately Adjacent to the Customer's Integer |
Obs | x | crbx | y | crby | lsb | d | lagd |
---|---|---|---|---|---|---|---|
1 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B165E7E555BDDB42 | 10110001 | -0.23437500 | . |
2 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B265E7E555BDDB42 | 10110010 | -0.21875000 | 0.015625 |
3 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B365E7E555BDDB42 | 10110011 | -0.20312500 | 0.015625 |
4 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B465E7E555BDDB42 | 10110100 | -0.18750000 | 0.015625 |
5 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B565E7E555BDDB42 | 10110101 | -0.17187500 | 0.015625 |
6 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B665E7E555BDDB42 | 10110110 | -0.15625000 | 0.015625 |
7 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B765E7E555BDDB42 | 10110111 | -0.14062500 | 0.015625 |
8 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B865E7E555BDDB42 | 10111000 | -0.12500000 | 0.015625 |
9 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | B965E7E555BDDB42 | 10111001 | -0.10937500 | 0.015625 |
10 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | BA65E7E555BDDB42 | 10111010 | -0.09375000 | 0.015625 |
11 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | BB65E7E555BDDB42 | 10111011 | -0.07812500 | 0.015625 |
12 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | BC65E7E555BDDB42 | 10111100 | -0.06250000 | 0.015625 |
13 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596950.000000 | BD65E7E555BDDB42 | 10111101 | -0.04687500 | 0.015625 |
14 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | BE65E7E555BDDB42 | 10111110 | -0.03125000 | 0.015625 |
15 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | BF65E7E555BDDB42 | 10111111 | -0.01562500 | 0.015625 |
16 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C065E7E555BDDB42 | 11000000 | 0.00000000 | 0.015625 |
17 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 11000001 | 0.01562500 | 0.015625 |
18 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C265E7E555BDDB42 | 11000010 | 0.03125000 | 0.015625 |
19 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C365E7E555BDDB42 | 11000011 | 0.04687500 | 0.015625 |
20 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C465E7E555BDDB42 | 11000100 | 0.06250000 | 0.015625 |
21 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C565E7E555BDDB42 | 11000101 | 0.07812500 | 0.015625 |
22 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C665E7E555BDDB42 | 11000110 | 0.09375000 | 0.015625 |
23 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C765E7E555BDDB42 | 11000111 | 0.10937500 | 0.015625 |
24 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C865E7E555BDDB42 | 11001000 | 0.12500000 | 0.015625 |
25 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C965E7E555BDDB42 | 11001001 | 0.14062500 | 0.015625 |
26 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CA65E7E555BDDB42 | 11001010 | 0.15625000 | 0.015625 |
27 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CB65E7E555BDDB42 | 11001011 | 0.17187500 | 0.015625 |
28 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CC65E7E555BDDB42 | 11001100 | 0.18750000 | 0.015625 |
29 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CD65E7E555BDDB42 | 11001101 | 0.20312500 | 0.015625 |
30 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CE65E7E555BDDB42 | 11001110 | 0.21875000 | 0.015625 |
31 | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | CF65E7E555BDDB42 | 11001111 | 0.23437500 | 0.015625 |
4: Incrementing the Least-Significant of 15 Significant Decimal Digits |
Obs | y | crby | ls_12bits_hex | ls_12bits_bin | d_10 | exp_use | Lowest 12 Bits Decoded |
---|---|---|---|---|---|---|---|
1 | 122000015596946.000000 | 8064E7E555BDDB42 | 480 | 010010000000 | . | 46 | 18.000 |
2 | 122000015596947.000000 | C064E7E555BDDB42 | 4C0 | 010011000000 | 64 | 46 | 19.000 |
3 | 122000015596948.000000 | 0065E7E555BDDB42 | 500 | 010100000000 | 64 | 46 | 20.000 |
4 | 122000015596949.000000 | 4065E7E555BDDB42 | 540 | 010101000000 | 64 | 46 | 21.000 |
5 | 122000015596950.000000 | 8065E7E555BDDB42 | 580 | 010110000000 | 64 | 46 | 22.000 |
6 | 122000015596951.000000 | C065E7E555BDDB42 | 5C0 | 010111000000 | 64 | 46 | 23.000 |
7 | 122000015596952.000000 | 0066E7E555BDDB42 | 600 | 011000000000 | 64 | 46 | 24.000 |
8 | 122000015596953.000000 | 4066E7E555BDDB42 | 640 | 011001000000 | 64 | 46 | 25.000 |
9 | 122000015596954.000000 | 8066E7E555BDDB42 | 680 | 011010000000 | 64 | 46 | 26.000 |
10 | 122000015596955.000000 | C066E7E555BDDB42 | 6C0 | 011011000000 | 64 | 46 | 27.000 |
11 | 122000015596956.000000 | 0067E7E555BDDB42 | 700 | 011100000000 | 64 | 46 | 28.000 |
5: Results of Miscellaneous Math Operations |
operation | x | crbx | y | crby | w | crbw | d |
---|---|---|---|---|---|---|---|
Divide | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 1.0000000 | 010000000000F03F | 2.22045E-16 |
Multiply | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 1.4884003805656E28 | E8CC8833E10BC845 | 2.19902E+12 |
Add | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 244000031193902.000000 | C065E7E555BDEB42 | 0.00000E+00 |
Fuzz | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 1.56250E-02 |
Round | 122000015596951.000000 | C065E7E555BDDB42 | 122000015596951.000000 | C165E7E555BDDB42 | 122000015596951.000000 | C065E7E555BDDB42 | 0.00000E+00 |