PEP: 2XX Title: Adding a Decimal type to Python Version: $Revision:$ Author: mclay@nist.gov <mclay@nist.gov> Status: Draft Type: ?? Created: 25-Jul-2001 Python-Version: 2.2 Introduction This PEP describes the addition of a decimal number type to Python. Rationale The original Python numerical model included int, float, and long. By popular request the imaginary type was added to improve support for engineering and scientific applications. The addition of a decimal number type to Python will improve support for business applications as well as improve the utility of Python a teaching language. The number types currently used in Python are encoded as base two binary numbers. The base 2 arithmetic used by binary numbers closely approximates the decimal number system and for many applications the differences in the calculations are unimportant. The decimal number type encodes numbers as decimal digits and use base 10 arithmetic. This is the number system taught to the general public and it is the system used by businesses when making financial calculations. For financial and accounting applications the difference between binary and decimal types is significant. Consequently the computer languages used for business application development, such as COBOL, use decimal types. The decimal number type meets the expectations of non-computer scientists when making calculations. For these users the rounding errors that occur when using binary numbers is a source of confusion and irritation. Implementation The tokenizer will be modified to recognized number literals with a 'd' suffix and a decimal() function will be added to __builtins__. A decimal number can be used to represent integers and floating point numbers and decimal numbers can also be displayed using scientific notation. Examples of decimal numbers include: 1234d -1234d 1234.56d -1234.56d 1234.56e2d -1234.56e-2d The type returned by either a decimal floating point or a decimal integer is the same: >>> type(12.2d) <type 'decimal'> >>> type(12d) <type 'decimal'> >>> type(-12d+12d) <type 'decimal'> >>> type(12d+12.0d) <type 'decimal'> This proposal will also add an optional 'b' suffix to the representation of binary float type literals and binary int type literals. >>> float(12b) 12.0 >>> type(12.2b) <type 'float'> >>> type(float(12b)) <type 'float'> >>> type(12b) <type 'int'> The decimal() conversion function added to __builtins__ will support conversions of strings, and binary types to decimal. >>> type(decimal("12d")) <type 'decimal'> >>> type(decimal("12")) <type 'decimal'> >>> type(decimal(12b)) <type 'decimal'> >>> type(decimal(12.0b)) <type 'decimal'> >>> type(decimal(123456789123L)) <type 'decimal'> The conversion functions int() and float() in the __builtin__ module will support conversion of decimal numbers to the binary number types. >>> type(int(12d)) <type 'int'> >>> type(float(12.0d)) <type 'float'> Expressions that mix integers with decimals will automatically convert the integer to decimal and the result will be a decimal number. >>> type(12d + 4b) <type 'decimal'> >>> type(12b + 4d) <type 'decimal'> >>> type(12d + len('abc')) <type 'decimal'> >>> 3d/4b 0.75 Expressions that mix binary floats with decimals introduce the possibility of unexpected results because the two number types use different internal representations for the same numerical value. The severity of this problem is dependent on the application domain. For applications that normally use binary numbers the error may not be important and the conversion should be done silently. For newbie programmers a warning should be issued so the newbie will be able to locate the source of a discrepancy between the expected results and the results that were achieved. For financial applications the mixing of floating point with binary numbers should raise an exception. To accommodate the three possible usage models the python interpreter command line options will be used to set the level for warning and error messages. The three levels are: promiscuous mode, -f or --promiscuous safe mode -s or --save pedantic mode -p or --pedantic The default setting will be set to the safe setting. In safe mode mixing decimal and binary floats in a calculation will trigger a warning message. >>> type(12.3d + 12.2b) Warning: the calculation mixes decimal numbers with binary floats <type 'decimal'> In promiscuous mode warnings will be turned off. >>> type(12.3d + 12.2b) <type 'decimal'> In pedantic mode warning from safe mode will be turned into exceptions. >>> type(12.3d + 12.2b) Traceback (innermost last): File "<stdin>", line 1, in ? TypeError: the calculation mixes decimal numbers with binary floats Semantics of Decimal Numbers ??