other:python:misc_by_jyp
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other:python:misc_by_jyp [2023/05/04 09:46] jypeter [Data representation] Added the Base notions section |
other:python:misc_by_jyp [2023/05/04 15:25] jypeter [Numerical values] Lots of changes |
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| ==== Base notions ==== | ==== Base notions ==== | ||
| - | * **Never forget** that all the bits and pieces of information we use are coded in [[https://en.wikipedia.org/wiki/Binary_number#Counting_in_binary|base 2]] (''0''s and ''1''s), grouped in bytes! | + | * **Never forget** that all the bits and pieces of information we use are coded in [[https://en.wikipedia.org/wiki/Binary_number#Counting_in_binary|base 2]] (''0''s and ''1''s ...), grouped in bytes! |
| * Some things can be stored exactly (integers, characters, ...) | * Some things can be stored exactly (integers, characters, ...) | ||
| * In other cases (**//real// numbers** that we work with all the time, compressed images/videos/music) we only store **//good enough approximation//** | * In other cases (**//real// numbers** that we work with all the time, compressed images/videos/music) we only store **//good enough approximation//** | ||
| Line 476: | Line 476: | ||
| * 1 byte <=> 8 bits | * 1 byte <=> 8 bits | ||
| * ''REAL*4'' <=> 4 bytes <=> 32 bits | * ''REAL*4'' <=> 4 bytes <=> 32 bits | ||
| - | * For easier written/displayed representation, 1 byte is usually split into 2 groups of 4 bits, using base 16 and [[https://en.wikipedia.org/wiki/Hexadecimal|hexadecimal representation]] | + | * For easier written/displayed representation, 1 byte is usually split into 2 groups of 4 bits, and displayed using base 16 and [[https://en.wikipedia.org/wiki/Hexadecimal|hexadecimal representation]] (characters ''0'', ''1'', ..., ''A'', ''B'', ..., ''F'') |
| - | * ''0000'' <=> ''0'', ''0010'' <=> ''1'', ..., ''1111'' <=> ''F'' | + | * ''0000'' <=> ''0'',\\ ''0010'' <=> ''1'', ...,\\ ''1111'' <=> ''F'' |
| * ''1101'' <=> ''D'' in hexadecimal <=> ''13'' in decimal (''**1** * 8 + **1** * 4 + **0** * 2 + **1** * 1'') | * ''1101'' <=> ''D'' in hexadecimal <=> ''13'' in decimal (''**1** * 8 + **1** * 4 + **0** * 2 + **1** * 1'') | ||
| - | * ''11111101'' <=> ''1111 1101'' <=> ''FC'' in hexadecimal <=> ''253'' in decimal (''15 * 16 + 13'') | + | * ''11111101'' in //base 2// <=> ''1111 1101'' <=> ''FD'' in //hexadecimal// <=> ''253'' (''15 * 16 + 13'') in //decimal// |
| - | * Conversion with Python | + | * Base conversion with Python |
| * <code>>>> hex(13) # Decimal to Hexadecimal conversion | * <code>>>> hex(13) # Decimal to Hexadecimal conversion | ||
| '0xd' | '0xd' | ||
| - | >>> hex(255) | + | >>> hex(253) |
| - | '0xff' | + | '0xfd' |
| >>> hex(256) | >>> hex(256) | ||
| '0x100' | '0x100' | ||
| >>> int('0x100', 16) # Hexadecimal to Decimal conversion | >>> int('0x100', 16) # Hexadecimal to Decimal conversion | ||
| 256 | 256 | ||
| - | >>> int('11', 2) | ||
| - | 3 | ||
| >>> int('1111', 2) # Binary to Decimal conversion | >>> int('1111', 2) # Binary to Decimal conversion | ||
| 15 | 15 | ||
| - | >>> int('11111101', 2) | + | >>> int('11111101', 2) # '11111101' <=> '1111 1101' <=> 'FD' <=> 15 * 16 + 13 = 253 |
| - | 253 | + | |
| - | >>> 15 * 16 + 13 | + | |
| 253 | 253 | ||
| >>> 013 # DANGER! Python considers an integer to be in OCTAL base if it starts with a 0 | >>> 013 # DANGER! Python considers an integer to be in OCTAL base if it starts with a 0 | ||
| Line 502: | Line 498: | ||
| >>> int('13', 8) # 1*8 + 3 | >>> int('13', 8) # 1*8 + 3 | ||
| 11</code> | 11</code> | ||
| + | |||
| + | * More technical topics | ||
| + | * [[https://en.wikipedia.org/wiki/Bit_numbering|Bit numbering]]: the art of ordering bits, everything about MSB (Most Significant Byte) and LSB (Least Significant Byte) | ||
| + | * [[https://en.wikipedia.org/wiki/Endianness|Endianness]]: the art of ordering bytes | ||
| ==== Numerical values ==== | ==== Numerical values ==== | ||
| - | * Binary data representation of some numbers (not everythin is listed here): | + | * Binary data representation of some numbers (only some common types are listed here): |
| + | * Languages and packages **references** used below: | ||
| + | * Python: [[https://numpy.org/doc/stable/reference/arrays.scalars.html#sized-aliases|NumPy Sized aliases]] | ||
| + | * NetCDF: [[https://docs.unidata.ucar.edu/nug/current/md_types.html|Data Types]], [[https://docs.unidata.ucar.edu/netcdf-fortran/current/f90-variables.html#f90-language-types-corresponding-to-netcdf-external-data-types|Fortran related Data Types]], [[https://docs.unidata.ucar.edu/nug/current/_c_d_l.html#cdl_data_types|CDL Data Types]] | ||
| + | * Fortran: Intel Fortran Compiler [[https://www.intel.com/content/www/us/en/docs/fortran-compiler/developer-guide-reference/2023-1/intrinsic-data-types.html|Intrinsic Data Types]] | ||
| * [[https://en.wikipedia.org/wiki/Integer_(computer_science)|Integers]] | * [[https://en.wikipedia.org/wiki/Integer_(computer_science)|Integers]] | ||
| * Range: | * Range: | ||
| - | * 4-byte integers: −2,147,483,648 to 2,147,483,647 | + | * 4-byte //signed// integers: ''−2,147,483,648'' to ''2,147,483,647'' |
| * Python: ''numpy.int32'' | * Python: ''numpy.int32'' | ||
| - | * [[https://docs.unidata.ucar.edu/nug/current/md_types.html|NetCDF]], [[https://docs.unidata.ucar.edu/netcdf-fortran/current/f90-variables.html#f90-language-types-corresponding-to-netcdf-external-data-types|NetCDF-Fortran]]: ''int'', ''NC_INT64'', ''NF90_INT'' | + | * NetCDF: ''int'', ''NC_INT'' or ''NC_LONG'', ''NF90_INT'' |
| - | * Fortran: | + | * Fortran: ''INTEGER*4'' |
| - | * 8-byte integers: −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 | + | * 8-byte //signed// integers: ''−9,223,372,036,854,775,808'' to ''9,223,372,036,854,775,807'' |
| * Python: ''numpy.int64'' | * Python: ''numpy.int64'' | ||
| - | * [[https://docs.unidata.ucar.edu/nug/current/md_types.html|NetCDF]]: ''int64'', ''NC_INT64'' | + | * NetCDF: ''int64'', ''NC_INT64'' |
| - | * Fortran: | + | * Fortran: ''INTEGER*8'' |
| * Tech note: signed integers use [[https://en.wikipedia.org/wiki/Two%27s_complement|two's complement]] for coding negative integers | * Tech note: signed integers use [[https://en.wikipedia.org/wiki/Two%27s_complement|two's complement]] for coding negative integers | ||
| * [[https://en.wikipedia.org/wiki/IEEE_754|Floating point numbers]] (//IEEE 754// standard aka //IEEE Standard for Binary Floating-Point for Arithmetic//) | * [[https://en.wikipedia.org/wiki/IEEE_754|Floating point numbers]] (//IEEE 754// standard aka //IEEE Standard for Binary Floating-Point for Arithmetic//) | ||
| * Range: | * Range: | ||
| - | * 4-byte float: ~8 significant digits * 10E±38 | + | * 4-byte float: ''~8 significant digits * 10E±38'' |
| * Python: ''numpy.float32'' | * Python: ''numpy.float32'' | ||
| - | * [[https://docs.unidata.ucar.edu/nug/current/md_types.html|NetCDF]], [[https://docs.unidata.ucar.edu/netcdf-fortran/current/f90-variables.html#f90-language-types-corresponding-to-netcdf-external-data-types|NetCDF-Fortran]]: | + | * NetCDF: ''float'', ''NC-FLOAT'', ''NF90_FLOAT'' |
| - | * Fortran: | + | * Fortran:''REAL*4'' |
| * See also [[https://en.wikipedia.org/wiki/Single-precision_floating-point_format|Single-precision floating-point format]] | * See also [[https://en.wikipedia.org/wiki/Single-precision_floating-point_format|Single-precision floating-point format]] | ||
| - | * 8-byte float: ~15 significant digits * 10E±308 | + | * 8-byte float: ''~15 significant digits * 10E±308'' |
| * Python: ''numpy.float64'' | * Python: ''numpy.float64'' | ||
| - | * [[https://docs.unidata.ucar.edu/nug/current/md_types.html|NetCDF]], [[https://docs.unidata.ucar.edu/netcdf-fortran/current/f90-variables.html#f90-language-types-corresponding-to-netcdf-external-data-types|NetCDF-Fortran]]: | + | * NetCDF: ''double'', ''NC_DOUBLE'', ''NF90_DOUBLE'' |
| - | * Fortran: | + | * Fortran: ''REAL*8'' |
| - | * Special values: | + | * **Special values**: |
| - | * [[https://en.wikipedia.org/wiki/NaN|NaN]] (''numpy.nan''): //Not a Number// | + | * [[https://en.wikipedia.org/wiki/NaN|NaN]]: //Not a Number// |
| - | * Infinity (''-numpy.inf'' and ''numpy.inf'') | + | * Python: ''numpy.nan'' |
| + | * Infinity | ||
| + | * Python: ''-numpy.inf'' and ''numpy.inf'' | ||
| * Note: it is cleaner to use masks (and [[https://numpy.org/doc/stable/reference/maskedarray.generic.html|Numpy masked arrays]]) than NaNs, when you have to deal with missing values ! | * Note: it is cleaner to use masks (and [[https://numpy.org/doc/stable/reference/maskedarray.generic.html|Numpy masked arrays]]) than NaNs, when you have to deal with missing values ! | ||
| - | * [[https://en.wikipedia.org/wiki/Bit_numbering|Bit numbering]] | + | * <wrap hi>The RISKS of working with (the wrong) floats</wrap>: |
| - | * [[https://en.wikipedia.org/wiki/Endianness|Endianness]] | + | * [[https://en.wikipedia.org/wiki/Round-off_error|Round-off error]] |
| + | * [[https://en.wikipedia.org/wiki/Catastrophic_cancellation|Catastrophic cancellation]] | ||
| + | * [[https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html|What Every Computer Scientist Should Know About Floating-Point Arithmetic]] | ||
| * A rather technical example: we //play// with a numpy 4-byte integer scalar | * A rather technical example: we //play// with a numpy 4-byte integer scalar | ||
| * <code>>>> one_int32 = np.int32(1) | * <code>>>> one_int32 = np.int32(1) | ||
other/python/misc_by_jyp.txt · Last modified: 2024/04/19 12:02 by jypeter
