\n",
- " \n",
- " 0x06 0_11_0 = +0b1.0*2^1 = 2.0 \n",
- " | \n",
- " \n",
- " 0x0e 1_11_0 = -0b1.0*2^1 = -2.0 \n",
+ " table {\n",
+ " font-family: monospace;\n",
+ " text-align: left;\n",
+ " font-size: 1.3em;\n",
+ " }\n",
+ " .fourtables-td table {\n",
+ " width: 100%;\n",
+ " }\n",
+ " td.zmktbl {\n",
+ " border: 0px solid;\n",
+ " }\n",
+ " pre.zmktbl {\n",
+ " }\n",
+ " .fourtables-td tr:nth-child(odd) {\n",
+ " background-color: #eee;\n",
+ " }\n",
+ " .fourtables-td tr:nth-child(even) {\n",
+ " background-color: #ccc;\n",
+ " }\n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " | p3109_k4p3es | \n",
+ " p3109_k4p3fs | \n",
+ " p3109_k4p3eu | \n",
+ " p3109_k4p3fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0_01 = +0b0.01*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0_10 = +0b0.10*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0_11 = +0b0.11*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_1_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_1_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_1_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_1_11 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_0_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_0_01 = -0b0.01*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_0_10 = -0b0.10*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_0_11 = -0b0.11*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_1_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_1_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_1_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_1_11 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0_01 = +0b0.01*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0_10 = +0b0.10*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0_11 = +0b0.11*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_1_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_1_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_1_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_1_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_0_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_0_01 = -0b0.01*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_0_10 = -0b0.10*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_0_11 = -0b0.11*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_1_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_1_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_1_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_1_11 = -0b1.11*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00_01 = +0b0.01*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00_10 = +0b0.10*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00_11 = +0b0.11*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 01_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 01_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 01_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 01_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 10_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 10_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 10_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 10_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 11_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 11_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 11_10 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 11_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00_01 = +0b0.01*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00_10 = +0b0.10*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00_11 = +0b0.11*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 01_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 01_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 01_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 01_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 10_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 10_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 10_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 10_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 11_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 11_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 11_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 11_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k4p4es | \n",
+ " p3109_k4p4fs | \n",
+ " p3109_k4p4eu | \n",
+ " p3109_k4p4fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_001 = +0b0.001*2^1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_010 = +0b0.010*2^1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_011 = +0b0.011*2^1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_100 = +0b0.100*2^1 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_101 = +0b0.101*2^1 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_110 = +0b0.110*2^1 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_111 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_001 = -0b0.001*2^1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_010 = -0b0.010*2^1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_011 = -0b0.011*2^1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_100 = -0b0.100*2^1 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_101 = -0b0.101*2^1 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_110 = -0b0.110*2^1 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_111 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_001 = +0b0.001*2^1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_010 = +0b0.010*2^1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_011 = +0b0.011*2^1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_100 = +0b0.100*2^1 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_101 = +0b0.101*2^1 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_110 = +0b0.110*2^1 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_111 = +0b0.111*2^1 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_001 = -0b0.001*2^1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_010 = -0b0.010*2^1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_011 = -0b0.011*2^1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_100 = -0b0.100*2^1 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_101 = -0b0.101*2^1 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_110 = -0b0.110*2^1 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_111 = -0b0.111*2^1 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_001 = +0b0.001*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_010 = +0b0.010*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_011 = +0b0.011*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_100 = +0b0.100*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_101 = +0b0.101*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_110 = +0b0.110*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_111 = +0b0.111*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_110 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_001 = +0b0.001*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_010 = +0b0.010*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_011 = +0b0.011*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_100 = +0b0.100*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_101 = +0b0.101*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_110 = +0b0.110*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_111 = +0b0.111*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 1_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 1_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 1_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 1_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 1_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 1_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 1_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 1_111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "for p in (1, 2, 3, 4):\n",
+ " fis = [\n",
+ " format_info_p3109(4, p, domain, signedness == \"s\")\n",
+ " for signedness in (\"s\", \"u\")\n",
+ " for domain in (Domain.Extended, Domain.Finite)\n",
+ " ]\n",
+ " render(fis, short=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "27095cef",
+ "metadata": {},
+ "source": [
+ "## Check k=5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "c1bbf6b2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k5p1es | \n",
+ " p3109_k5p1fs | \n",
+ " p3109_k5p1eu | \n",
+ " p3109_k5p1fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000_ = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001_ = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010_ = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011_ = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100_ = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101_ = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110_ = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111_ = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000_ = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001_ = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010_ = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011_ = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100_ = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101_ = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110_ = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111_ = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000_ = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001_ = -0b1.0*2^-7 = ~-0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010_ = -0b1.0*2^-6 = ~-0.0156 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011_ = -0b1.0*2^-5 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100_ = -0b1.0*2^-4 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101_ = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110_ = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111_ = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000_ = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001_ = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010_ = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011_ = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100_ = -0b1.0*2^4 = -16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101_ = -0b1.0*2^5 = -32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110_ = -0b1.0*2^6 = -64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111_ = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000_ = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001_ = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010_ = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011_ = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100_ = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101_ = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110_ = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111_ = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000_ = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001_ = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010_ = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011_ = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100_ = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101_ = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110_ = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111_ = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000_ = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001_ = -0b1.0*2^-7 = ~-0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010_ = -0b1.0*2^-6 = ~-0.0156 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011_ = -0b1.0*2^-5 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100_ = -0b1.0*2^-4 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101_ = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110_ = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111_ = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000_ = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001_ = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010_ = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011_ = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100_ = -0b1.0*2^4 = -16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101_ = -0b1.0*2^5 = -32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110_ = -0b1.0*2^6 = -64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111_ = -0b1.0*2^7 = -128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00000_ = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00001_ = +0b1.0*2^-15 = ~3.052e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00010_ = +0b1.0*2^-14 = ~6.104e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00011_ = +0b1.0*2^-13 = ~0.0001 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00100_ = +0b1.0*2^-12 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00101_ = +0b1.0*2^-11 = ~0.0005 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00110_ = +0b1.0*2^-10 = ~0.0010 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00111_ = +0b1.0*2^-9 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 01000_ = +0b1.0*2^-8 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 01001_ = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 01010_ = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 01011_ = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 01100_ = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 01101_ = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 01110_ = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 01111_ = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 10000_ = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 10001_ = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 10010_ = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 10011_ = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 10100_ = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 10101_ = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 10110_ = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 10111_ = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 11000_ = +0b1.0*2^8 = 256.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 11001_ = +0b1.0*2^9 = 512.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 11010_ = +0b1.0*2^10 = 1024.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 11011_ = +0b1.0*2^11 = 2048.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 11100_ = +0b1.0*2^12 = 4096.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 11101_ = +0b1.0*2^13 = 8192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 11110_ = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 11111_ = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00000_ = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00001_ = +0b1.0*2^-15 = ~3.052e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00010_ = +0b1.0*2^-14 = ~6.104e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00011_ = +0b1.0*2^-13 = ~0.0001 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00100_ = +0b1.0*2^-12 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00101_ = +0b1.0*2^-11 = ~0.0005 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00110_ = +0b1.0*2^-10 = ~0.0010 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00111_ = +0b1.0*2^-9 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 01000_ = +0b1.0*2^-8 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 01001_ = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 01010_ = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 01011_ = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 01100_ = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 01101_ = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 01110_ = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 01111_ = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 10000_ = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 10001_ = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 10010_ = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 10011_ = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 10100_ = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 10101_ = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 10110_ = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 10111_ = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 11000_ = +0b1.0*2^8 = 256.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 11001_ = +0b1.0*2^9 = 512.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 11010_ = +0b1.0*2^10 = 1024.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 11011_ = +0b1.0*2^11 = 2048.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 11100_ = +0b1.0*2^12 = 4096.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 11101_ = +0b1.0*2^13 = 8192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 11110_ = +0b1.0*2^14 = 16384.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 11111_ = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k5p2es | \n",
+ " p3109_k5p2fs | \n",
+ " p3109_k5p2eu | \n",
+ " p3109_k5p2fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_000_1 = +0b0.1*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_001_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_001_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_010_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_010_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_011_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_011_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_100_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_100_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_101_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_101_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_110_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_110_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_111_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_111_1 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_000_0 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_000_1 = -0b0.1*2^-3 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_001_0 = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_001_1 = -0b1.1*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_010_0 = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_010_1 = -0b1.1*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_011_0 = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_011_1 = -0b1.1*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_100_0 = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_100_1 = -0b1.1*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_101_0 = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_101_1 = -0b1.1*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_110_0 = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_110_1 = -0b1.1*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_111_0 = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_111_1 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_000_1 = +0b0.1*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_001_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_001_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_010_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_010_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_011_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_011_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_100_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_100_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_101_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_101_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_110_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_110_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_111_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_111_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_000_0 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_000_1 = -0b0.1*2^-3 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_001_0 = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_001_1 = -0b1.1*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_010_0 = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_010_1 = -0b1.1*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_011_0 = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_011_1 = -0b1.1*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_100_0 = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_100_1 = -0b1.1*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_101_0 = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_101_1 = -0b1.1*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_110_0 = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_110_1 = -0b1.1*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_111_0 = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_111_1 = -0b1.1*2^3 = -12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0000_1 = +0b0.1*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1111_0 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1111_1 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0000_1 = +0b0.1*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1111_0 = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1111_1 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k5p3es | \n",
+ " p3109_k5p3fs | \n",
+ " p3109_k5p3eu | \n",
+ " p3109_k5p3fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_00_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_00_01 = +0b0.01*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_00_10 = +0b0.10*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_00_11 = +0b0.11*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_01_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_01_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_01_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_01_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_10_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_10_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_10_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_10_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_11_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_11_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_11_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_11_11 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_00_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_00_01 = -0b0.01*2^-1 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_00_10 = -0b0.10*2^-1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_00_11 = -0b0.11*2^-1 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_01_00 = -0b1.00*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_01_01 = -0b1.01*2^-1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_01_10 = -0b1.10*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_01_11 = -0b1.11*2^-1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_10_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_10_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_10_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_10_11 = -0b1.11*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_11_00 = -0b1.00*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_11_01 = -0b1.01*2^1 = -2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_11_10 = -0b1.10*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_11_11 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_00_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_00_01 = +0b0.01*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_00_10 = +0b0.10*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_00_11 = +0b0.11*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_01_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_01_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_01_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_01_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_10_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_10_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_10_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_10_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_11_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_11_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_11_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_11_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_00_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_00_01 = -0b0.01*2^-1 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_00_10 = -0b0.10*2^-1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_00_11 = -0b0.11*2^-1 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_01_00 = -0b1.00*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_01_01 = -0b1.01*2^-1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_01_10 = -0b1.10*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_01_11 = -0b1.11*2^-1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_10_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_10_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_10_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_10_11 = -0b1.11*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_11_00 = -0b1.00*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_11_01 = -0b1.01*2^1 = -2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_11_10 = -0b1.10*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_11_11 = -0b1.11*2^1 = -3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 000_01 = +0b0.01*2^-3 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 000_10 = +0b0.10*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 000_11 = +0b0.11*2^-3 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 001_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 001_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 001_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 001_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 010_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 010_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 010_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 010_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 011_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 011_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 011_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 011_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 100_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 100_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 100_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 100_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 101_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 101_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 101_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 101_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 110_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 110_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 110_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 110_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 111_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 111_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 111_10 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 111_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 000_01 = +0b0.01*2^-3 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 000_10 = +0b0.10*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 000_11 = +0b0.11*2^-3 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 001_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 001_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 001_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 001_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 010_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 010_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 010_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 010_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 011_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 011_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 011_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 011_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 100_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 100_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 100_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 100_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 101_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 101_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 101_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 101_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 110_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 110_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 110_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 110_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 111_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 111_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 111_10 = +0b1.10*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 111_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k5p4es | \n",
+ " p3109_k5p4fs | \n",
+ " p3109_k5p4eu | \n",
+ " p3109_k5p4fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0_001 = +0b0.001*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0_010 = +0b0.010*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0_011 = +0b0.011*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0_100 = +0b0.100*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0_101 = +0b0.101*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0_110 = +0b0.110*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0_111 = +0b0.111*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1_111 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0_000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0_001 = -0b0.001*2^0 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0_010 = -0b0.010*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0_011 = -0b0.011*2^0 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0_100 = -0b0.100*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0_101 = -0b0.101*2^0 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0_110 = -0b0.110*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0_111 = -0b0.111*2^0 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1_000 = -0b1.000*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1_001 = -0b1.001*2^0 = -1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1_010 = -0b1.010*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1_011 = -0b1.011*2^0 = -1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1_100 = -0b1.100*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1_101 = -0b1.101*2^0 = -1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1_110 = -0b1.110*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1_111 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0_001 = +0b0.001*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0_010 = +0b0.010*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0_011 = +0b0.011*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0_100 = +0b0.100*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0_101 = +0b0.101*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0_110 = +0b0.110*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0_111 = +0b0.111*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1_111 = +0b1.111*2^0 = 1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0_000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0_001 = -0b0.001*2^0 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0_010 = -0b0.010*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0_011 = -0b0.011*2^0 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0_100 = -0b0.100*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0_101 = -0b0.101*2^0 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0_110 = -0b0.110*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0_111 = -0b0.111*2^0 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1_000 = -0b1.000*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1_001 = -0b1.001*2^0 = -1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1_010 = -0b1.010*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1_011 = -0b1.011*2^0 = -1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1_100 = -0b1.100*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1_101 = -0b1.101*2^0 = -1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1_110 = -0b1.110*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1_111 = -0b1.111*2^0 = -1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00_001 = +0b0.001*2^-1 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00_010 = +0b0.010*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00_011 = +0b0.011*2^-1 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00_100 = +0b0.100*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00_101 = +0b0.101*2^-1 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00_110 = +0b0.110*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00_111 = +0b0.111*2^-1 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 01_000 = +0b1.000*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 01_001 = +0b1.001*2^-1 = 0.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 01_010 = +0b1.010*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 01_011 = +0b1.011*2^-1 = 0.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 01_100 = +0b1.100*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 01_101 = +0b1.101*2^-1 = 0.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 01_110 = +0b1.110*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 01_111 = +0b1.111*2^-1 = 0.9375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 10_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 10_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 10_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 10_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 10_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 10_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 10_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 10_111 = +0b1.111*2^0 = 1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 11_000 = +0b1.000*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 11_001 = +0b1.001*2^1 = 2.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 11_010 = +0b1.010*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 11_011 = +0b1.011*2^1 = 2.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 11_100 = +0b1.100*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 11_101 = +0b1.101*2^1 = 3.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 11_110 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 11_111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00_001 = +0b0.001*2^-1 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00_010 = +0b0.010*2^-1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00_011 = +0b0.011*2^-1 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00_100 = +0b0.100*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00_101 = +0b0.101*2^-1 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00_110 = +0b0.110*2^-1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00_111 = +0b0.111*2^-1 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 01_000 = +0b1.000*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 01_001 = +0b1.001*2^-1 = 0.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 01_010 = +0b1.010*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 01_011 = +0b1.011*2^-1 = 0.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 01_100 = +0b1.100*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 01_101 = +0b1.101*2^-1 = 0.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 01_110 = +0b1.110*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 01_111 = +0b1.111*2^-1 = 0.9375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 10_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 10_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 10_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 10_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 10_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 10_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 10_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 10_111 = +0b1.111*2^0 = 1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 11_000 = +0b1.000*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 11_001 = +0b1.001*2^1 = 2.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 11_010 = +0b1.010*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 11_011 = +0b1.011*2^1 = 2.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 11_100 = +0b1.100*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 11_101 = +0b1.101*2^1 = 3.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 11_110 = +0b1.110*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 11_111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k5p5es | \n",
+ " p3109_k5p5fs | \n",
+ " p3109_k5p5eu | \n",
+ " p3109_k5p5fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001 = +0b0.0001*2^1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010 = +0b0.0010*2^1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011 = +0b0.0011*2^1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100 = +0b0.0100*2^1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101 = +0b0.0101*2^1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110 = +0b0.0110*2^1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111 = +0b0.0111*2^1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000 = +0b0.1000*2^1 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001 = +0b0.1001*2^1 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010 = +0b0.1010*2^1 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011 = +0b0.1011*2^1 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100 = +0b0.1100*2^1 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101 = +0b0.1101*2^1 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110 = +0b0.1110*2^1 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001 = -0b0.0001*2^1 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010 = -0b0.0010*2^1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011 = -0b0.0011*2^1 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100 = -0b0.0100*2^1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101 = -0b0.0101*2^1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110 = -0b0.0110*2^1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111 = -0b0.0111*2^1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000 = -0b0.1000*2^1 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001 = -0b0.1001*2^1 = -1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010 = -0b0.1010*2^1 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011 = -0b0.1011*2^1 = -1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100 = -0b0.1100*2^1 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101 = -0b0.1101*2^1 = -1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110 = -0b0.1110*2^1 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001 = +0b0.0001*2^1 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010 = +0b0.0010*2^1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011 = +0b0.0011*2^1 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100 = +0b0.0100*2^1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101 = +0b0.0101*2^1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110 = +0b0.0110*2^1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111 = +0b0.0111*2^1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000 = +0b0.1000*2^1 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001 = +0b0.1001*2^1 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010 = +0b0.1010*2^1 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011 = +0b0.1011*2^1 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100 = +0b0.1100*2^1 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101 = +0b0.1101*2^1 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110 = +0b0.1110*2^1 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111 = +0b0.1111*2^1 = 1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001 = -0b0.0001*2^1 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010 = -0b0.0010*2^1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011 = -0b0.0011*2^1 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100 = -0b0.0100*2^1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101 = -0b0.0101*2^1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110 = -0b0.0110*2^1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111 = -0b0.0111*2^1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000 = -0b0.1000*2^1 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001 = -0b0.1001*2^1 = -1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010 = -0b0.1010*2^1 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011 = -0b0.1011*2^1 = -1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100 = -0b0.1100*2^1 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101 = -0b0.1101*2^1 = -1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110 = -0b0.1110*2^1 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111 = -0b0.1111*2^1 = -1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001 = +0b0.0001*2^0 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010 = +0b0.0010*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011 = +0b0.0011*2^0 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100 = +0b0.0100*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101 = +0b0.0101*2^0 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110 = +0b0.0110*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111 = +0b0.0111*2^0 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000 = +0b0.1000*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001 = +0b0.1001*2^0 = 0.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010 = +0b0.1010*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011 = +0b0.1011*2^0 = 0.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100 = +0b0.1100*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101 = +0b0.1101*2^0 = 0.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110 = +0b0.1110*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111 = +0b0.1111*2^0 = 0.9375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000 = +0b1.0000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001 = +0b1.0001*2^0 = 1.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010 = +0b1.0010*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011 = +0b1.0011*2^0 = 1.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100 = +0b1.0100*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101 = +0b1.0101*2^0 = 1.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110 = +0b1.0110*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111 = +0b1.0111*2^0 = 1.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000 = +0b1.1000*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001 = +0b1.1001*2^0 = 1.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010 = +0b1.1010*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011 = +0b1.1011*2^0 = 1.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100 = +0b1.1100*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101 = +0b1.1101*2^0 = 1.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0001 = +0b0.0001*2^0 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0010 = +0b0.0010*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0011 = +0b0.0011*2^0 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0100 = +0b0.0100*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0101 = +0b0.0101*2^0 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0110 = +0b0.0110*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0111 = +0b0.0111*2^0 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_1000 = +0b0.1000*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_1001 = +0b0.1001*2^0 = 0.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_1010 = +0b0.1010*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_1011 = +0b0.1011*2^0 = 0.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_1100 = +0b0.1100*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_1101 = +0b0.1101*2^0 = 0.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_1110 = +0b0.1110*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_1111 = +0b0.1111*2^0 = 0.9375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 1_0000 = +0b1.0000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 1_0001 = +0b1.0001*2^0 = 1.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 1_0010 = +0b1.0010*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 1_0011 = +0b1.0011*2^0 = 1.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 1_0100 = +0b1.0100*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 1_0101 = +0b1.0101*2^0 = 1.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 1_0110 = +0b1.0110*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 1_0111 = +0b1.0111*2^0 = 1.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 1_1000 = +0b1.1000*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 1_1001 = +0b1.1001*2^0 = 1.5625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 1_1010 = +0b1.1010*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 1_1011 = +0b1.1011*2^0 = 1.6875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 1_1100 = +0b1.1100*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 1_1101 = +0b1.1101*2^0 = 1.8125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 1_1110 = +0b1.1110*2^0 = 1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 1_1111 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "for p in (1, 2, 3, 4, 5):\n",
+ " fis = [\n",
+ " format_info_p3109(5, p, domain, signedness == \"s\")\n",
+ " for signedness in (\"s\", \"u\")\n",
+ " for domain in (Domain.Extended, Domain.Finite)\n",
+ " ]\n",
+ " render(fis, short=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "452ae200",
+ "metadata": {},
+ "source": [
+ "### Now check unsigned vs signed, k=6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "ddc40cfa",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k6p2es | \n",
+ " p3109_k6p2fs | \n",
+ " p3109_k6p2eu | \n",
+ " p3109_k6p2fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0000_1 = +0b0.1*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_0100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_0100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_0101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_0101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_0110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_0110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_0111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_0111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0_1000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0_1000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0_1001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0_1001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0_1010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0_1010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0_1011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0_1011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0_1100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0_1100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0_1101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0_1101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0_1110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0_1110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0_1111_0 = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0_1111_1 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1_0000_0 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1_0000_1 = -0b0.1*2^-7 = ~-0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1_0001_0 = -0b1.0*2^-7 = ~-0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1_0001_1 = -0b1.1*2^-7 = ~-0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1_0010_0 = -0b1.0*2^-6 = ~-0.0156 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1_0010_1 = -0b1.1*2^-6 = ~-0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1_0011_0 = -0b1.0*2^-5 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1_0011_1 = -0b1.1*2^-5 = ~-0.0469 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1_0100_0 = -0b1.0*2^-4 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1_0100_1 = -0b1.1*2^-4 = -0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1_0101_0 = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1_0101_1 = -0b1.1*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1_0110_0 = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1_0110_1 = -0b1.1*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1_0111_0 = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1_0111_1 = -0b1.1*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1_1000_0 = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1_1000_1 = -0b1.1*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1_1001_0 = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1_1001_1 = -0b1.1*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1_1010_0 = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1_1010_1 = -0b1.1*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1_1011_0 = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1_1011_1 = -0b1.1*2^3 = -12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1_1100_0 = -0b1.0*2^4 = -16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1_1100_1 = -0b1.1*2^4 = -24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1_1101_0 = -0b1.0*2^5 = -32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1_1101_1 = -0b1.1*2^5 = -48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1_1110_0 = -0b1.0*2^6 = -64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1_1110_1 = -0b1.1*2^6 = -96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1_1111_0 = -0b1.0*2^7 = -128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1_1111_1 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0000_1 = +0b0.1*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_0010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_0010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_0011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_0011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_0100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_0100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_0101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_0101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_0110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_0110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_0111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_0111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0_1000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0_1000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0_1001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0_1001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0_1010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0_1010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0_1011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0_1011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0_1100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0_1100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0_1101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0_1101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0_1110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0_1110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0_1111_0 = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0_1111_1 = +0b1.1*2^7 = 192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1_0000_0 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1_0000_1 = -0b0.1*2^-7 = ~-0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1_0001_0 = -0b1.0*2^-7 = ~-0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1_0001_1 = -0b1.1*2^-7 = ~-0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1_0010_0 = -0b1.0*2^-6 = ~-0.0156 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1_0010_1 = -0b1.1*2^-6 = ~-0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1_0011_0 = -0b1.0*2^-5 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1_0011_1 = -0b1.1*2^-5 = ~-0.0469 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1_0100_0 = -0b1.0*2^-4 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1_0100_1 = -0b1.1*2^-4 = -0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1_0101_0 = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1_0101_1 = -0b1.1*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1_0110_0 = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1_0110_1 = -0b1.1*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1_0111_0 = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1_0111_1 = -0b1.1*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1_1000_0 = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1_1000_1 = -0b1.1*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1_1001_0 = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1_1001_1 = -0b1.1*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1_1010_0 = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1_1010_1 = -0b1.1*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1_1011_0 = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1_1011_1 = -0b1.1*2^3 = -12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1_1100_0 = -0b1.0*2^4 = -16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1_1100_1 = -0b1.1*2^4 = -24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1_1101_0 = -0b1.0*2^5 = -32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1_1101_1 = -0b1.1*2^5 = -48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1_1110_0 = -0b1.0*2^6 = -64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1_1110_1 = -0b1.1*2^6 = -96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1_1111_0 = -0b1.0*2^7 = -128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1_1111_1 = -0b1.1*2^7 = -192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00000_1 = +0b0.1*2^-15 = ~1.526e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00001_0 = +0b1.0*2^-15 = ~3.052e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00001_1 = +0b1.1*2^-15 = ~4.578e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00010_0 = +0b1.0*2^-14 = ~6.104e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00010_1 = +0b1.1*2^-14 = ~9.155e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00011_0 = +0b1.0*2^-13 = ~0.0001 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00011_1 = +0b1.1*2^-13 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 00100_0 = +0b1.0*2^-12 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 00100_1 = +0b1.1*2^-12 = ~0.0004 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 00101_0 = +0b1.0*2^-11 = ~0.0005 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 00101_1 = +0b1.1*2^-11 = ~0.0007 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 00110_0 = +0b1.0*2^-10 = ~0.0010 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 00110_1 = +0b1.1*2^-10 = ~0.0015 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 00111_0 = +0b1.0*2^-9 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 00111_1 = +0b1.1*2^-9 = ~0.0029 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 01000_0 = +0b1.0*2^-8 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 01000_1 = +0b1.1*2^-8 = ~0.0059 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 01001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 01001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 01010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 01010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 01011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 01011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 01100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 01100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 01101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 01101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 01110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 01110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 01111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 01111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 10000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 10000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 10001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 10001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 10010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 10010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 10011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 10011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 10100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 10100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 10101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 10101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 10110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 10110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 10111_0 = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 10111_1 = +0b1.1*2^7 = 192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 11000_0 = +0b1.0*2^8 = 256.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 11000_1 = +0b1.1*2^8 = 384.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 11001_0 = +0b1.0*2^9 = 512.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 11001_1 = +0b1.1*2^9 = 768.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 11010_0 = +0b1.0*2^10 = 1024.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 11010_1 = +0b1.1*2^10 = 1536.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 11011_0 = +0b1.0*2^11 = 2048.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 11011_1 = +0b1.1*2^11 = 3072.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 11100_0 = +0b1.0*2^12 = 4096.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 11100_1 = +0b1.1*2^12 = 6144.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 11101_0 = +0b1.0*2^13 = 8192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 11101_1 = +0b1.1*2^13 = 12288.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 11110_0 = +0b1.0*2^14 = 16384.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 11110_1 = +0b1.1*2^14 = 24576.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 11111_0 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 11111_1 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 00000_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 00000_1 = +0b0.1*2^-15 = ~1.526e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 00001_0 = +0b1.0*2^-15 = ~3.052e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 00001_1 = +0b1.1*2^-15 = ~4.578e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 00010_0 = +0b1.0*2^-14 = ~6.104e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 00010_1 = +0b1.1*2^-14 = ~9.155e-05 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 00011_0 = +0b1.0*2^-13 = ~0.0001 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 00011_1 = +0b1.1*2^-13 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 00100_0 = +0b1.0*2^-12 = ~0.0002 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 00100_1 = +0b1.1*2^-12 = ~0.0004 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 00101_0 = +0b1.0*2^-11 = ~0.0005 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 00101_1 = +0b1.1*2^-11 = ~0.0007 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 00110_0 = +0b1.0*2^-10 = ~0.0010 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 00110_1 = +0b1.1*2^-10 = ~0.0015 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 00111_0 = +0b1.0*2^-9 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 00111_1 = +0b1.1*2^-9 = ~0.0029 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 01000_0 = +0b1.0*2^-8 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 01000_1 = +0b1.1*2^-8 = ~0.0059 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 01001_0 = +0b1.0*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 01001_1 = +0b1.1*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 01010_0 = +0b1.0*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 01010_1 = +0b1.1*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 01011_0 = +0b1.0*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 01011_1 = +0b1.1*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 01100_0 = +0b1.0*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 01100_1 = +0b1.1*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 01101_0 = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 01101_1 = +0b1.1*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 01110_0 = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 01110_1 = +0b1.1*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 01111_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 01111_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 10000_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 10000_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 10001_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 10001_1 = +0b1.1*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 10010_0 = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 10010_1 = +0b1.1*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 10011_0 = +0b1.0*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 10011_1 = +0b1.1*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 10100_0 = +0b1.0*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 10100_1 = +0b1.1*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 10101_0 = +0b1.0*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 10101_1 = +0b1.1*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 10110_0 = +0b1.0*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 10110_1 = +0b1.1*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 10111_0 = +0b1.0*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 10111_1 = +0b1.1*2^7 = 192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 11000_0 = +0b1.0*2^8 = 256.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 11000_1 = +0b1.1*2^8 = 384.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 11001_0 = +0b1.0*2^9 = 512.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 11001_1 = +0b1.1*2^9 = 768.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 11010_0 = +0b1.0*2^10 = 1024.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 11010_1 = +0b1.1*2^10 = 1536.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 11011_0 = +0b1.0*2^11 = 2048.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 11011_1 = +0b1.1*2^11 = 3072.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 11100_0 = +0b1.0*2^12 = 4096.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 11100_1 = +0b1.1*2^12 = 6144.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 11101_0 = +0b1.0*2^13 = 8192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 11101_1 = +0b1.1*2^13 = 12288.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 11110_0 = +0b1.0*2^14 = 16384.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 11110_1 = +0b1.1*2^14 = 24576.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 11111_0 = +0b1.0*2^15 = 32768.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 11111_1 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " | p3109_k6p3es | \n",
+ " p3109_k6p3fs | \n",
+ " p3109_k6p3eu | \n",
+ " p3109_k6p3fu | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_000_01 = +0b0.01*2^-3 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_000_10 = +0b0.10*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_000_11 = +0b0.11*2^-3 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_001_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_001_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_001_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_001_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_010_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_010_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_010_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_010_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_011_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_011_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_011_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_011_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0_100_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0_100_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0_100_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0_100_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0_101_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0_101_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0_101_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0_101_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0_110_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0_110_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0_110_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0_110_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0_111_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0_111_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0_111_10 = +0b1.10*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0_111_11 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1_000_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1_000_01 = -0b0.01*2^-3 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1_000_10 = -0b0.10*2^-3 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1_000_11 = -0b0.11*2^-3 = -0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1_001_00 = -0b1.00*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1_001_01 = -0b1.01*2^-3 = -0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1_001_10 = -0b1.10*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1_001_11 = -0b1.11*2^-3 = -0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1_010_00 = -0b1.00*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1_010_01 = -0b1.01*2^-2 = -0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1_010_10 = -0b1.10*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1_010_11 = -0b1.11*2^-2 = -0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1_011_00 = -0b1.00*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1_011_01 = -0b1.01*2^-1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1_011_10 = -0b1.10*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1_011_11 = -0b1.11*2^-1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1_100_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1_100_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1_100_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1_100_11 = -0b1.11*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1_101_00 = -0b1.00*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1_101_01 = -0b1.01*2^1 = -2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1_101_10 = -0b1.10*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1_101_11 = -0b1.11*2^1 = -3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1_110_00 = -0b1.00*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1_110_01 = -0b1.01*2^2 = -5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1_110_10 = -0b1.10*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1_110_11 = -0b1.11*2^2 = -7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1_111_00 = -0b1.00*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1_111_01 = -0b1.01*2^3 = -10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1_111_10 = -0b1.10*2^3 = -12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1_111_11 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_000_01 = +0b0.01*2^-3 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_000_10 = +0b0.10*2^-3 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_000_11 = +0b0.11*2^-3 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_001_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_001_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_001_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_001_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_010_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_010_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_010_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_010_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_011_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_011_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_011_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_011_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0_100_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0_100_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0_100_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0_100_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0_101_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0_101_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0_101_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0_101_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0_110_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0_110_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0_110_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0_110_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0_111_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0_111_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0_111_10 = +0b1.10*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0_111_11 = +0b1.11*2^3 = 14.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1_000_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1_000_01 = -0b0.01*2^-3 = -0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1_000_10 = -0b0.10*2^-3 = -0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1_000_11 = -0b0.11*2^-3 = -0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1_001_00 = -0b1.00*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1_001_01 = -0b1.01*2^-3 = -0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1_001_10 = -0b1.10*2^-3 = -0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1_001_11 = -0b1.11*2^-3 = -0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1_010_00 = -0b1.00*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1_010_01 = -0b1.01*2^-2 = -0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1_010_10 = -0b1.10*2^-2 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1_010_11 = -0b1.11*2^-2 = -0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1_011_00 = -0b1.00*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1_011_01 = -0b1.01*2^-1 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1_011_10 = -0b1.10*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1_011_11 = -0b1.11*2^-1 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1_100_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1_100_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1_100_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1_100_11 = -0b1.11*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1_101_00 = -0b1.00*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1_101_01 = -0b1.01*2^1 = -2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1_101_10 = -0b1.10*2^1 = -3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1_101_11 = -0b1.11*2^1 = -3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1_110_00 = -0b1.00*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1_110_01 = -0b1.01*2^2 = -5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1_110_10 = -0b1.10*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1_110_11 = -0b1.11*2^2 = -7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1_111_00 = -0b1.00*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1_111_01 = -0b1.01*2^3 = -10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1_111_10 = -0b1.10*2^3 = -12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1_111_11 = -0b1.11*2^3 = -14.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0000_01 = +0b0.01*2^-7 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0000_10 = +0b0.10*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0000_11 = +0b0.11*2^-7 = ~0.0059 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0001_00 = +0b1.00*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0001_01 = +0b1.01*2^-7 = ~0.0098 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0001_10 = +0b1.10*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0001_11 = +0b1.11*2^-7 = ~0.0137 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0010_00 = +0b1.00*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0010_01 = +0b1.01*2^-6 = ~0.0195 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0010_10 = +0b1.10*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0010_11 = +0b1.11*2^-6 = ~0.0273 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0011_00 = +0b1.00*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0011_01 = +0b1.01*2^-5 = ~0.0391 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0011_10 = +0b1.10*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0011_11 = +0b1.11*2^-5 = ~0.0547 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0100_00 = +0b1.00*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0100_01 = +0b1.01*2^-4 = 0.078125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0100_10 = +0b1.10*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0100_11 = +0b1.11*2^-4 = 0.109375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0101_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0101_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0101_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0101_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0110_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0110_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0110_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0110_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0111_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0111_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0111_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0111_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1000_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1000_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1000_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1000_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1001_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1001_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1001_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1001_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1010_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1010_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1010_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1010_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1011_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1011_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1011_10 = +0b1.10*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1011_11 = +0b1.11*2^3 = 14.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1100_00 = +0b1.00*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1100_01 = +0b1.01*2^4 = 20.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1100_10 = +0b1.10*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1100_11 = +0b1.11*2^4 = 28.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1101_00 = +0b1.00*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1101_01 = +0b1.01*2^5 = 40.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1101_10 = +0b1.10*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1101_11 = +0b1.11*2^5 = 56.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1110_00 = +0b1.00*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1110_01 = +0b1.01*2^6 = 80.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1110_10 = +0b1.10*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1110_11 = +0b1.11*2^6 = 112.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1111_00 = +0b1.00*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1111_01 = +0b1.01*2^7 = 160.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1111_10 = inf = inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1111_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0000_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0000_01 = +0b0.01*2^-7 = ~0.0020 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0000_10 = +0b0.10*2^-7 = ~0.0039 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0000_11 = +0b0.11*2^-7 = ~0.0059 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0001_00 = +0b1.00*2^-7 = ~0.0078 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0001_01 = +0b1.01*2^-7 = ~0.0098 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0001_10 = +0b1.10*2^-7 = ~0.0117 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0001_11 = +0b1.11*2^-7 = ~0.0137 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0010_00 = +0b1.00*2^-6 = 0.015625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0010_01 = +0b1.01*2^-6 = ~0.0195 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0010_10 = +0b1.10*2^-6 = ~0.0234 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0010_11 = +0b1.11*2^-6 = ~0.0273 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0011_00 = +0b1.00*2^-5 = 0.03125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0011_01 = +0b1.01*2^-5 = ~0.0391 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0011_10 = +0b1.10*2^-5 = 0.046875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0011_11 = +0b1.11*2^-5 = ~0.0547 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0100_00 = +0b1.00*2^-4 = 0.0625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0100_01 = +0b1.01*2^-4 = 0.078125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0100_10 = +0b1.10*2^-4 = 0.09375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x13 = 0100_11 = +0b1.11*2^-4 = 0.109375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x14 = 0101_00 = +0b1.00*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x15 = 0101_01 = +0b1.01*2^-3 = 0.15625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x16 = 0101_10 = +0b1.10*2^-3 = 0.1875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0101_11 = +0b1.11*2^-3 = 0.21875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x18 = 0110_00 = +0b1.00*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x19 = 0110_01 = +0b1.01*2^-2 = 0.3125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0110_10 = +0b1.10*2^-2 = 0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0110_11 = +0b1.11*2^-2 = 0.4375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0111_00 = +0b1.00*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0111_01 = +0b1.01*2^-1 = 0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0111_10 = +0b1.10*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0111_11 = +0b1.11*2^-1 = 0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x20 = 1000_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x21 = 1000_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x22 = 1000_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x23 = 1000_11 = +0b1.11*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x24 = 1001_00 = +0b1.00*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x25 = 1001_01 = +0b1.01*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x26 = 1001_10 = +0b1.10*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x27 = 1001_11 = +0b1.11*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x28 = 1010_00 = +0b1.00*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x29 = 1010_01 = +0b1.01*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2a = 1010_10 = +0b1.10*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2b = 1010_11 = +0b1.11*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2c = 1011_00 = +0b1.00*2^3 = 8.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2d = 1011_01 = +0b1.01*2^3 = 10.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2e = 1011_10 = +0b1.10*2^3 = 12.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x2f = 1011_11 = +0b1.11*2^3 = 14.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x30 = 1100_00 = +0b1.00*2^4 = 16.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x31 = 1100_01 = +0b1.01*2^4 = 20.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x32 = 1100_10 = +0b1.10*2^4 = 24.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x33 = 1100_11 = +0b1.11*2^4 = 28.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x34 = 1101_00 = +0b1.00*2^5 = 32.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x35 = 1101_01 = +0b1.01*2^5 = 40.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x36 = 1101_10 = +0b1.10*2^5 = 48.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x37 = 1101_11 = +0b1.11*2^5 = 56.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x38 = 1110_00 = +0b1.00*2^6 = 64.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x39 = 1110_01 = +0b1.01*2^6 = 80.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3a = 1110_10 = +0b1.10*2^6 = 96.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3b = 1110_11 = +0b1.11*2^6 = 112.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3c = 1111_00 = +0b1.00*2^7 = 128.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3d = 1111_01 = +0b1.01*2^7 = 160.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3e = 1111_10 = +0b1.10*2^7 = 192.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x3f = 1111_11 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "for p in (2, 3):\n",
+ " fis = [\n",
+ " format_info_p3109(6, p, domain, signedness == \"s\")\n",
+ " for signedness in (\"s\", \"u\")\n",
+ " for domain in (Domain.Extended, Domain.Finite)\n",
+ " ]\n",
+ " render(fis, short=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d4707056",
+ "metadata": {},
+ "source": [
+ "### IEEE P3109 4-bit formats\n",
+ "\n",
+ "The IEEE P3109 interim report describes a family of formats parameterized by K and P, in which three 4-bit formats are defined.\n",
+ "\n",
+ "The p=2 format is similar to OCP E2M1, with inf and nan:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "01891136",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p2es\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p2es\n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_00_0 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " 0x08 = 1_00_0 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_00_1 = +0b0.1*2^-1 = 0.25 \n",
+ " | \n",
+ " \n",
+ " 0x09 = 1_00_1 = -0b0.1*2^-1 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_01_0 = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " 0x0a = 1_01_0 = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_01_1 = +0b1.1*2^-1 = 0.75 \n",
+ " | \n",
+ " \n",
+ " 0x0b = 1_01_1 = -0b1.1*2^-1 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_10_0 = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " 0x0c = 1_10_0 = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_10_1 = +0b1.1*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " 0x0d = 1_10_1 = -0b1.1*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_11_0 = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " 0x0e = 1_11_0 = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_11_1 = inf = inf \n",
+ " | \n",
+ " \n",
+ " 0x0f = 1_11_1 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "HTML(airdoc(*mktbl(Airium(), format_info_p3109(4, 2), cols=2, width=8, d=3)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aaa20ff4",
+ "metadata": {},
+ "source": [
+ "While the p=1 format is a \"pure exponential\" format with values 2^-2 to 2^3:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "e7453dbd",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p1es\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p1es\n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_000_ = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " 0x08 = 1_000_ = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_001_ = +0b1.0*2^-3 = 0.125 \n",
+ " | \n",
+ " \n",
+ " 0x09 = 1_001_ = -0b1.0*2^-3 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_010_ = +0b1.0*2^-2 = 0.25 \n",
+ " | \n",
+ " \n",
+ " 0x0a = 1_010_ = -0b1.0*2^-2 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_011_ = +0b1.0*2^-1 = 0.5 \n",
+ " | \n",
+ " \n",
+ " 0x0b = 1_011_ = -0b1.0*2^-1 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_100_ = +0b1.0*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " 0x0c = 1_100_ = -0b1.0*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_101_ = +0b1.0*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " 0x0d = 1_101_ = -0b1.0*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_110_ = +0b1.0*2^2 = 4.0 \n",
+ " | \n",
+ " \n",
+ " 0x0e = 1_110_ = -0b1.0*2^2 = -4.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_111_ = inf = inf \n",
+ " | \n",
+ " \n",
+ " 0x0f = 1_111_ = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "HTML(airdoc(*mktbl(Airium(), format_info_p3109(4, 1), cols=2, width=8, d=3)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b701cd05",
+ "metadata": {},
+ "source": [
+ "And p=3, a linear format with values 0.25 * range(7)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "1d14d7ac",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p3es\n",
+ " \n",
+ " \n",
+ " FP4 Value Table, p3109_k4p3es\n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_0_00 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " 0x08 = 1_0_00 = nan = nan \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_0_01 = +0b0.01*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " 0x09 = 1_0_01 = -0b0.01*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_0_10 = +0b0.10*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " 0x0a = 1_0_10 = -0b0.10*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_0_11 = +0b0.11*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " 0x0b = 1_0_11 = -0b0.11*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_1_00 = +0b1.00*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " 0x0c = 1_1_00 = -0b1.00*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_1_01 = +0b1.01*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " 0x0d = 1_1_01 = -0b1.01*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_1_10 = +0b1.10*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " 0x0e = 1_1_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_1_11 = inf = inf \n",
+ " | \n",
+ " \n",
+ " 0x0f = 1_1_11 = -inf = -inf \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "HTML(airdoc(*mktbl(Airium(), format_info_p3109(4, 3), cols=2, width=8, d=3)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8a598f1b",
+ "metadata": {},
+ "source": [
+ "### OCP E2M3\n",
+ "\n",
+ "This 6-bit format has 32 values, with no `NaN` or `Inf`, but does have `-0`.\n",
+ "The positive subnormals are the linear ramp of eighths: [n/8 for n in 1:7].\n",
+ "\n",
+ "One might describe the format in text as:\n",
+ "\n",
+ "> zero to one by eighths, two to four by quarters, four to eight by halves\n",
+ "\n",
+ "where \"to\" is open-ended, or \"to\" is not \"thru\"."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "0e7a9398",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ " \n",
+ " FP6 Value Table, ocp_e2m3\n",
+ " \n",
+ " \n",
+ " FP6 Value Table, ocp_e2m3\n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x00 = 0_00_000 = 0.0 = 0.0 \n",
+ " | \n",
+ " \n",
+ " 0x20 = 1_00_000 = -0.0 = -0.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x01 = 0_00_001 = +0b0.001*2^0 = 0.125 \n",
+ " | \n",
+ " \n",
+ " 0x21 = 1_00_001 = -0b0.001*2^0 = -0.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x02 = 0_00_010 = +0b0.010*2^0 = 0.25 \n",
+ " | \n",
+ " \n",
+ " 0x22 = 1_00_010 = -0b0.010*2^0 = -0.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x03 = 0_00_011 = +0b0.011*2^0 = 0.375 \n",
+ " | \n",
+ " \n",
+ " 0x23 = 1_00_011 = -0b0.011*2^0 = -0.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x04 = 0_00_100 = +0b0.100*2^0 = 0.5 \n",
+ " | \n",
+ " \n",
+ " 0x24 = 1_00_100 = -0b0.100*2^0 = -0.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x05 = 0_00_101 = +0b0.101*2^0 = 0.625 \n",
+ " | \n",
+ " \n",
+ " 0x25 = 1_00_101 = -0b0.101*2^0 = -0.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x06 = 0_00_110 = +0b0.110*2^0 = 0.75 \n",
+ " | \n",
+ " \n",
+ " 0x26 = 1_00_110 = -0b0.110*2^0 = -0.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x07 = 0_00_111 = +0b0.111*2^0 = 0.875 \n",
+ " | \n",
+ " \n",
+ " 0x27 = 1_00_111 = -0b0.111*2^0 = -0.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x08 = 0_01_000 = +0b1.000*2^0 = 1.0 \n",
+ " | \n",
+ " \n",
+ " 0x28 = 1_01_000 = -0b1.000*2^0 = -1.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x09 = 0_01_001 = +0b1.001*2^0 = 1.125 \n",
+ " | \n",
+ " \n",
+ " 0x29 = 1_01_001 = -0b1.001*2^0 = -1.125 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0a = 0_01_010 = +0b1.010*2^0 = 1.25 \n",
+ " | \n",
+ " \n",
+ " 0x2a = 1_01_010 = -0b1.010*2^0 = -1.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0b = 0_01_011 = +0b1.011*2^0 = 1.375 \n",
+ " | \n",
+ " \n",
+ " 0x2b = 1_01_011 = -0b1.011*2^0 = -1.375 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0c = 0_01_100 = +0b1.100*2^0 = 1.5 \n",
+ " | \n",
+ " \n",
+ " 0x2c = 1_01_100 = -0b1.100*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0d = 0_01_101 = +0b1.101*2^0 = 1.625 \n",
+ " | \n",
+ " \n",
+ " 0x2d = 1_01_101 = -0b1.101*2^0 = -1.625 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0e = 0_01_110 = +0b1.110*2^0 = 1.75 \n",
+ " | \n",
+ " \n",
+ " 0x2e = 1_01_110 = -0b1.110*2^0 = -1.75 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x0f = 0_01_111 = +0b1.111*2^0 = 1.875 \n",
+ " | \n",
+ " \n",
+ " 0x2f = 1_01_111 = -0b1.111*2^0 = -1.875 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x10 = 0_10_000 = +0b1.000*2^1 = 2.0 \n",
+ " | \n",
+ " \n",
+ " 0x30 = 1_10_000 = -0b1.000*2^1 = -2.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x11 = 0_10_001 = +0b1.001*2^1 = 2.25 \n",
+ " | \n",
+ " \n",
+ " 0x31 = 1_10_001 = -0b1.001*2^1 = -2.25 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x12 = 0_10_010 = +0b1.010*2^1 = 2.5 \n",
+ " | \n",
+ " \n",
+ " 0x32 = 1_10_010 = -0b1.010*2^1 = -2.5 \n",
" | \n",
" \n",
- " \n",
- " \n",
- " 0x07 0_11_1 = inf \n",
+ " | \n",
+ " \n",
+ " 0x13 = 0_10_011 = +0b1.011*2^1 = 2.75 \n",
" | \n",
- " \n",
- " 0x0f 1_11_1 = -inf \n",
+ " | \n",
+ " 0x33 = 1_10_011 = -0b1.011*2^1 = -2.75 \n",
" | \n",
" \n",
- " "
- ],
- "text/plain": [
- " "
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "HTML(mktbl(format_info_p3109(4, 2), cols=2, vs_width=8, vs_d=3))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "While the p=1 format is a \"pure exponential\" format with values 2^-2 to 2^3:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n",
- "FP8 Value Table, p3109_4p1\n",
- "\n",
- " \n",
- " \n",
- " 0x00 0_000_ = 0.0 \n",
- " | \n",
- " \n",
- " 0x08 1_000_ = nan \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x01 0_001_ = +0b1.0*2^-2 = 0.25 \n",
- " | \n",
- " \n",
- " 0x09 1_001_ = -0b1.0*2^-2 = -0.25 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x02 0_010_ = +0b1.0*2^-1 = 0.5 \n",
- " | \n",
- " \n",
- " 0x0a 1_010_ = -0b1.0*2^-1 = -0.5 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x03 0_011_ = +0b1.0*2^0 = 1.0 \n",
- " | \n",
- " \n",
- " 0x0b 1_011_ = -0b1.0*2^0 = -1.0 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x04 0_100_ = +0b1.0*2^1 = 2.0 \n",
- " | \n",
- " \n",
- " 0x0c 1_100_ = -0b1.0*2^1 = -2.0 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x05 0_101_ = +0b1.0*2^2 = 4.0 \n",
- " | \n",
- " \n",
- " 0x0d 1_101_ = -0b1.0*2^2 = -4.0 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x06 0_110_ = +0b1.0*2^3 = 8.0 \n",
- " | \n",
- " \n",
- " 0x0e 1_110_ = -0b1.0*2^3 = -8.0 \n",
+ " | \n",
+ " \n",
+ " 0x14 = 0_10_100 = +0b1.100*2^1 = 3.0 \n",
+ " | \n",
+ " \n",
+ " 0x34 = 1_10_100 = -0b1.100*2^1 = -3.0 \n",
" | \n",
" \n",
- " \n",
- " \n",
- " 0x07 0_111_ = inf \n",
+ " | \n",
+ " \n",
+ " 0x15 = 0_10_101 = +0b1.101*2^1 = 3.25 \n",
" | \n",
- " \n",
- " 0x0f 1_111_ = -inf \n",
+ " | \n",
+ " 0x35 = 1_10_101 = -0b1.101*2^1 = -3.25 \n",
" | \n",
" \n",
- " "
- ],
- "text/plain": [
- ""
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "HTML(mktbl(format_info_p3109(4, 1), cols=2, vs_width=8, vs_d=3))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "And p=3, a linear format with values 0.25 * range(7)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n",
- "FP8 Value Table, p3109_4p3\n",
- "\n",
- " \n",
- " \n",
- " 0x00 0_0_00 = 0.0 \n",
- " | \n",
- " \n",
- " 0x08 1_0_00 = nan \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x01 0_0_01 = +0b0.01*2^0 = 0.25 \n",
- " | \n",
- " \n",
- " 0x09 1_0_01 = -0b0.01*2^0 = -0.25 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x02 0_0_10 = +0b0.10*2^0 = 0.5 \n",
- " | \n",
- " \n",
- " 0x0a 1_0_10 = -0b0.10*2^0 = -0.5 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x03 0_0_11 = +0b0.11*2^0 = 0.75 \n",
- " | \n",
- " \n",
- " 0x0b 1_0_11 = -0b0.11*2^0 = -0.75 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x04 0_1_00 = +0b1.00*2^0 = 1.0 \n",
- " | \n",
- " \n",
- " 0x0c 1_1_00 = -0b1.00*2^0 = -1.0 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x05 0_1_01 = +0b1.01*2^0 = 1.25 \n",
- " | \n",
- " \n",
- " 0x0d 1_1_01 = -0b1.01*2^0 = -1.25 \n",
- " | \n",
- " \n",
- " \n",
- " \n",
- " 0x06 0_1_10 = +0b1.10*2^0 = 1.5 \n",
- " | \n",
- " \n",
- " 0x0e 1_1_10 = -0b1.10*2^0 = -1.5 \n",
+ " | \n",
+ " \n",
+ " 0x16 = 0_10_110 = +0b1.110*2^1 = 3.5 \n",
+ " | \n",
+ " \n",
+ " 0x36 = 1_10_110 = -0b1.110*2^1 = -3.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x17 = 0_10_111 = +0b1.111*2^1 = 3.75 \n",
+ " | \n",
+ " \n",
+ " 0x37 = 1_10_111 = -0b1.111*2^1 = -3.75 \n",
" | \n",
" \n",
- " \n",
- " \n",
- " 0x07 0_1_11 = inf \n",
+ " | \n",
+ " \n",
+ " 0x18 = 0_11_000 = +0b1.000*2^2 = 4.0 \n",
" | \n",
- " \n",
- " 0x0f 1_1_11 = -inf \n",
+ " | \n",
+ " 0x38 = 1_11_000 = -0b1.000*2^2 = -4.0 \n",
" | \n",
" \n",
- " "
+ " \n",
+ " \n",
+ " 0x19 = 0_11_001 = +0b1.001*2^2 = 4.5 \n",
+ " | \n",
+ " \n",
+ " 0x39 = 1_11_001 = -0b1.001*2^2 = -4.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1a = 0_11_010 = +0b1.010*2^2 = 5.0 \n",
+ " | \n",
+ " \n",
+ " 0x3a = 1_11_010 = -0b1.010*2^2 = -5.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1b = 0_11_011 = +0b1.011*2^2 = 5.5 \n",
+ " | \n",
+ " \n",
+ " 0x3b = 1_11_011 = -0b1.011*2^2 = -5.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1c = 0_11_100 = +0b1.100*2^2 = 6.0 \n",
+ " | \n",
+ " \n",
+ " 0x3c = 1_11_100 = -0b1.100*2^2 = -6.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1d = 0_11_101 = +0b1.101*2^2 = 6.5 \n",
+ " | \n",
+ " \n",
+ " 0x3d = 1_11_101 = -0b1.101*2^2 = -6.5 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1e = 0_11_110 = +0b1.110*2^2 = 7.0 \n",
+ " | \n",
+ " \n",
+ " 0x3e = 1_11_110 = -0b1.110*2^2 = -7.0 \n",
+ " | \n",
+ " \n",
+ " \n",
+ " \n",
+ " 0x1f = 0_11_111 = +0b1.111*2^2 = 7.5 \n",
+ " | \n",
+ " \n",
+ " 0x3f = 1_11_111 = -0b1.111*2^2 = -7.5 \n",
+ " | \n",
+ " \n",
+ " |