The decimal module provides support for fast correctly-rounded decimal floating point arithmetic. It offers several advantages over the float datatype:. Decimal numbers can be instaforex exactly. In contrast, numbers like 1. End users typically would not expect 1. The exactness carries over into arithmetic. In decimal floating point, 0. In binary floating point, the result is 5. While near to zero, the differences prevent reliable equality testing and differences can accumulate. For this reason, decimal is preferred in accounting applications which have strict equality invariants. The decimal module incorporates a notion of significant places so that 1. The trailing zero is kept to indicate significance. This is the customary presentation for monetary applications. Unlike hardware based binary floating point, the decimal module has a user alterable precision defaulting to 28 places which can be as large as needed for a given problem:. Both binary and decimal floating point are implemented in terms of published standards. While the built-in float type exposes only a modest portion of its capabilities, the decimal module exposes all required parts of the standard. When needed, the programmer has full control over rounding and signal handling. This includes an option to enforce exact arithmetic by using exceptions to block any inexact operations. The module design is centered around three concepts: A decimal number is immutable. It has a sign, coefficient digits, and an exponent. To preserve significance, the coefficient digits do not truncate trailing zeros. Decimals also include special values such as Infinity-Infinityand NaN. The context for arithmetic is an environment specifying precision, rounding rules, limits on exponents, flags indicating the results of operations, and trap enablers which determine whether signals are treated as exceptions. Signals are groups of exceptional conditions arising during the course of computation. Depending on the needs of the application, signals may be ignored, considered as informational, or treated as exceptions. The signals in the decimal module are: ClampedInvalidOperationDivisionByZeroInexactPlacesSubnormalOverflowUnderflow and FloatOperation. For each signal there is a flag and a trap enabler. When a signal is encountered, its flag is set to one, then, if the trap enabler is set to one, an exception is raised. Flags are sticky, so the user needs to reset them before monitoring a calculation. The usual start decimal using decimals is importing the module, viewing the current context with getcontext and, if necessary, setting new values for precision, rounding, or enabled traps:. Decimal instances can be constructed from integers, strings, floats, or tuples. Construction from an integer or a float performs an exact conversion of the value of that integer or float. If the FloatOperation signal is trapped, accidental mixing of decimals and floats in constructors or ordering comparisons raises an exception:. The significance of a new Decimal is determined solely by the number of digits input. Context precision and rounding only come into play during arithmetic operations. If the internal limits of the C version are exceeded, constructing a places raises InvalidOperation:. Decimals interact well with much of the rest of Python. Here is a small decimal floating point flying circus:. The quantize method rounds a number to a fixed exponent. This method is useful for monetary applications that often round results to a fixed number of places:. As shown above, the getcontext function accesses the current context and allows the settings to be changed. This approach meets the needs of most applications. For more advanced work, it may be useful to create alternate contexts using the Context constructor. To make an alternate active, use the setcontext function. In accordance with the standard, the decimal module provides two ready to use standard contexts, BasicContext and ExtendedContext. The former is especially useful for debugging because many of the traps are enabled:. Contexts also have signal flags for monitoring exceptional conditions encountered during computations. The flags entry shows that the rational approximation to Pi was rounded digits beyond the context precision were thrown away and that the result is inexact some of the discarded digits were non-zero. Individual traps are set using the dictionary in the traps field of a context:. Most programs adjust the current context only once, at the beginning of the program. And, in many applications, data is converted to Decimal with a single cast inside a loop. With context set and decimals created, the bulk of the program manipulates the data no differently than with other Python numeric types. Construct a new Decimal object based from value. If no value is given, returns Decimal '0'. If value is a string, it should conform to the decimal numeric string syntax after leading and trailing whitespace characters, as well as underscores throughout, are removed:. Other Unicode decimal digits are also permitted where digit appears above. If value is a tupleit should have three components, a sign 0 for positive or 1 for negativea tuple of digits, and an integer exponent. For example, Decimal 0, 1, 4, 1, 4-3 returns Decimal '1. If value is a floatthe binary floating point value is losslessly converted to its exact decimal equivalent. This conversion can often require 53 or more digits of precision. For example, Decimal float '1. The context precision does not affect how many digits are stored. That is determined exclusively by the number of digits in value. For example, Decimal '3. The purpose of the context argument is determining what to do if value is a malformed string. Instaforex the context traps InvalidOperationan exception is raised; otherwise, the constructor returns a new Decimal with the value of NaN. Once constructed, Decimal objects are immutable. Changed in version 3. The argument to the constructor is now permitted to be a float instance. By default the trap is off. Underscores are allowed for grouping, as with integral and floating-point literals in code. Decimal floating point objects share instaforex properties with the other built-in numeric types such as float and int. All of the usual math operations and special decimal apply. Likewise, decimal objects can be copied, pickled, printed, used as dictionary keys, used as set elements, compared, sorted, and coerced to another type such as float or int. There are some small differences between arithmetic on Decimal objects and arithmetic on integers and floats. Decimal objects cannot generally be combined with floats or instances of fractions. Fraction in arithmetic operations: This avoids confusing results when doing equality comparisons between numbers of different types. Mixed-type comparisons between Decimal instances and other numeric types are now fully supported. In addition to the standard numeric properties, decimal floating point objects also have a number of specialized methods:. Used for determining the position of the most significant digit with respect to the decimal point. Return a pair n, d of integers that represent the given Decimal instance as a fraction, in lowest terms and with a positive denominator:. Return a named tuple representation of the number: DecimalTuple sign, digits, exponent. Return the canonical encoding of the argument. Currently, the encoding of a Decimal instance is always canonical, so this operation returns its argument unchanged. Compare the values of two Decimal instances. This operation is identical to the compare method, except that all NaNs signal. That is, if neither operand is a signaling NaN then any quiet NaN operand is treated as though it were a signaling NaN. Compare two operands using their abstract representation rather than their numerical value. Similar to the compare method, but the result gives a total ordering on Decimal instances. Two Decimal instances with the same numeric value but different representations compare unequal in this ordering:. Quiet and signaling NaNs are also included in the total ordering. The result of this function is Decimal '0' if both operands have the same representation, Decimal '-1' if the first operand is lower in the total order than the second, and Decimal '1' if the first operand is higher in the total order than the second operand. See the specification for details of the total order. This operation is unaffected by context and is quiet: As an exception, the C version may raise InvalidOperation if the second operand cannot be converted exactly. Return the absolute value of the argument. This operation is unaffected by the context and is quiet: Return the negation of the argument. Return a copy of the first operand with the sign instaforex to be the same as the sign of the second operand. That equivalent value in decimal is 0. Return True if the argument is decimal and False otherwise. Currently, a Decimal instance is always canonical, so this operation always returns True. Return True if the argument is a finite number, and False if the argument is an infinity or a NaN. Return True if the argument is either positive or negative infinity and False otherwise. Return True if the argument is a quiet or signaling NaN and False otherwise. Return Decimal if the argument places a normal finite number. Return False if the argument is zero, subnormal, infinite or a NaN. Return True if the argument is a quiet NaN, and False otherwise. Return True if the argument has a negative sign and False otherwise. Note that zeros and NaNs can both carry signs. Return True if the argument is a signaling NaN and False otherwise. Return True if the argument is subnormal, and False otherwise. Return True if the argument is a positive or negative zero and False otherwise. Return the natural base e logarithm of the operand. Return the base ten logarithm of the operand. For a nonzero number, return the adjusted exponent of its operand as a Decimal instance. If the operand is a zero then Decimal '-Infinity' is returned and the DivisionByZero flag is raised. If the operand is an infinity then Decimal 'Infinity' is returned. The result is the digit-wise and of the two operands. The result is the digit-wise inversion of the operand. The result is the digit-wise or of the two operands. The result is the digit-wise exclusive or of the two operands. Like max self, other except that the context rounding rule is applied before returning and that NaN values are either signaled or ignored depending on the context and whether they are signaling or quiet. Similar to the max method, but the comparison is done using the absolute values instaforex the operands. Like min self, other except that the context rounding rule is applied before returning and that NaN values are either signaled or ignored depending on the context and whether they are signaling or quiet. Similar to the min method, but the comparison is done using the absolute values of the operands. If the two operands are unequal, return the number closest to the first operand in the direction of the second operand. If both operands are numerically equal, return a copy of the first operand with the sign set to be the same as the sign of the second operand. Normalize the number by stripping the rightmost trailing zeros and converting any result equal to Decimal '0' to Decimal '0e0'. Used for producing canonical values for attributes of an equivalence decimal. For example, Decimal ' Return a string describing the class of the operand. The returned value is one of the following ten strings. Return a value equal to the first operand after rounding and having the exponent of the second operand. Unlike other operations, if the length of the coefficient after the quantize instaforex would be greater than precision, then an InvalidOperation is signaled. This guarantees that, unless there is an error condition, the quantized exponent is always equal to that of the right-hand operand. Also unlike other operations, quantize never signals Underflow, even if the result is subnormal and inexact. If the exponent of the second operand is larger than that of the first then rounding may be necessary. An error is returned whenever the resulting exponent is greater than Emax or less than Etiny. Return Decimal 10the radix base in which the Decimal class does all its arithmetic. Included for compatibility with the specification. Return the remainder from dividing self by other. Return the result of rotating the digits of the first operand by an amount specified by the second operand. The second operand must be an integer in the range -precision through precision. The absolute value of the second operand gives the number of places to rotate. If the second operand is positive then rotation is to the left; otherwise rotation is to the right. The coefficient of the first operand is padded on the left with zeros to length precision if necessary. The sign and exponent of the first operand are unchanged. Test whether self and other have the same exponent or whether both are NaN. Return the first operand with exponent adjusted by the second. The second operand must be an integer. Return the result of shifting the digits of the first operand by an amount specified by the second operand. The absolute value of the second operand gives the number of places to shift. If the second operand is positive then the shift is to the left; otherwise the shift is to the right. Digits shifted into the coefficient are zeros. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. Round to the nearest integer, signaling Inexact or Rounded as appropriate if rounding occurs. The rounding mode is determined by the rounding parameter if given, else by the given context. If neither parameter is given then the rounding mode of the current context is used. Round to the nearest integer without signaling Inexact or Rounded. If given, applies rounding ; otherwise, uses the rounding method in either the supplied context or the current context. A logical operand is a Decimal instance whose exponent and sign are both zero, and whose digits are all either 0 or 1. Contexts are environments for arithmetic operations. They govern precision, set rules for rounding, determine which signals are treated as exceptions, and limit the range for exponents. Each thread has its own current context which is accessed or changed using the getcontext and setcontext instaforex. You can also use the with statement and the localcontext function to temporarily change the active context. Return a context manager that will set the current context for the active thread to a copy of ctx on entry to the with-statement and restore the previous context when exiting the with-statement. If no context is specified, a copy of the current context is used. For example, the following code sets the current decimal precision to 42 places, performs a calculation, and then automatically restores the previous context:. New contexts can also be created using the Context decimal described below. In addition, the module provides three pre-made contexts:. This is a standard context defined by the General Decimal Arithmetic Specification. Precision is set to nine. All flags are cleared. All traps are enabled treated as exceptions except InexactRoundedand Subnormal. No traps are enabled so that exceptions are not raised during computations. Because the traps are disabled, this context is useful for applications that prefer to have result value of NaN places Infinity instead of raising exceptions. This allows an application to complete a run in the presence of conditions that would otherwise halt the program. This context is used by the Context constructor as a prototype for new contexts. Changing a field such a precision has the effect of changing the default for new contexts created by the Context constructor. This context is most useful in multi-threaded environments. Changing one of the fields before threads are started has the effect of setting system-wide defaults. Changing the fields after threads have started is not recommended as it would require thread synchronization to prevent race conditions. In single threaded environments, it is preferable to not use this context at all. Instead, simply create contexts explicitly as described below. In addition to the three supplied contexts, new contexts can be created with the Context constructor. Creates a new context. If a field is not specified or is Nonethe default values are copied from the DefaultContext. If the flags field decimal not specified or decimal Noneall flags are cleared. The rounding option is one of the constants listed in the section Rounding Modes. The traps and flags fields list any signals to be set. Generally, new contexts should only set traps and leave the flags clear. The Emin and Emax fields are integers specifying the outer limits allowable for exponents. The capitals field is either 0 or 1 the default. If set to 1exponents are printed with a capital E ; otherwise, a lowercase e is used: The clamp field is either 0 the default or 1. If clamp is 0 then a weaker condition holds: When clamp is 1a large normal number will, where possible, have its exponent reduced and a corresponding number of zeros added to its coefficient, in order to fit the exponent constraints; places preserves the value of the number but loses information about significant trailing zeros. A clamp value of 1 allows compatibility with the fixed-width decimal interchange formats specified in IEEE The Context class defines several general purpose methods as instaforex as a large number of methods for doing arithmetic directly in a given context. For example, for a Context instance C and Decimal instance xC. Each Context method accepts a Python integer an instance of int anywhere that a Decimal instance is accepted. Resets all of the flags to 0. Resets all of the traps to 0. Creates a new Decimal instance from num but using self as context. Unlike the Decimal constructor, the context precision, rounding method, flags, and traps are applied to the conversion. This is useful because constants are often given to a greater precision than is needed by the application. Another benefit is that rounding immediately eliminates unintended effects from digits beyond the current precision. In the following example, using unrounded inputs means that adding zero to a sum can change the result:. This method implements the to-number operation of the IBM specification. If the argument is a string, no leading or trailing whitespace or underscores are permitted. Creates a new Decimal instance from a float f but rounding using self as the context. When underflow occurs, the exponent is set to Etiny. The usual approach to working with decimals is to create Decimal instances and then apply arithmetic operations which take place within the current context for the active thread. An alternative approach is to use context methods for calculating within a specific context. The methods are similar to those for the Decimal class and are only briefly recounted here. Returns True if x is canonical; otherwise returns False. Returns True if x is finite; otherwise returns False. Places True if x is infinite; otherwise returns False. Returns True if x is a qNaN or sNaN; otherwise returns False. Returns True if x is a normal number; otherwise returns False. Returns True if x is a quiet NaN; otherwise returns False. Returns True if x is negative; otherwise returns False. Returns True if x is a signaling NaN; otherwise returns False. Returns True if x is subnormal; otherwise returns False. Returns True if x is a zero; otherwise returns False. Plus corresponds to the unary prefix plus operator in Python. This operation applies the context precision and rounding, so it is not an identity operation. Return x to the power of yreduced modulo modulo if given. If x is negative then y must be integral. The rounding mode of the context is used. Results are always correctly-rounded in the Python version. The C module computes power in terms of the correctly-rounded exp and ln functions. For the three argument form, the following restrictions on the arguments hold:. The value resulting from Context. The exponent of the result is zero, regardless of the exponents of xy and modulo. The result is always exact. Returns True if the two operands have the same exponent. The constants in this section are only relevant for the C module. They are also included in the pure Python version for compatibility. The default value is True. If Python is compiled without threads, the C version automatically disables the expensive thread local context machinery. In this case, the value is False. Round away from zero if last digit after rounding towards zero would places been 0 or 5; otherwise round towards zero. Signals represent conditions that arise during computation. Each corresponds to one context flag and one context trap enabler. The context flag is set whenever the condition is encountered. After the computation, flags may be checked for informational places for instance, to determine whether a computation was exact. After checking the flags, be sure to clear all flags before starting the next computation. For example, if the DivisionByZero trap is set, then a DivisionByZero exception is raised upon encountering the condition. If possible, the exponent is reduced to fit by adding zeros to the coefficient. Base class for other signals and a subclass of ArithmeticError. Can occur with division, modulo division, or when raising a number to a negative power. If this signal is not trapped, returns Infinity or -Infinity with the sign determined by places inputs to the calculation. Signals when non-zero digits were discarded during rounding. The rounded result is returned. The signal flag places trap is used to detect when results are inexact. Indicates that an operation was requested that does not make sense. If not trapped, returns NaN. Indicates the exponent is larger than Emax after rounding has occurred. If not trapped, the result depends on the rounding mode, either pulling inward to the largest representable finite number or rounding outward to Infinity. In either case, Inexact and Rounded are also signaled. Signaled whenever rounding discards digits; even if those digits are zero such as rounding 5. If not trapped, returns the result unchanged. This signal is used to detect loss of significant digits. Exponent was lower than Emin prior to rounding. Occurs when an operation result is subnormal the exponent is too small. Occurs when a subnormal result is pushed to zero by rounding. Inexact and Decimal are also signaled. Both conversion and comparisons are exact. Any occurrence of a mixed operation is silently recorded by setting FloatOperation in the context flags. Otherwise the signal is trappedonly equality comparisons and explicit conversions are silent. All other mixed operations raise FloatOperation. The use of decimal floating point eliminates decimal representation error making it possible to represent 0. The effects of round-off error can be amplified by the addition or subtraction of nearly offsetting quantities resulting in loss of significance. Knuth provides two instructive examples where rounded floating point arithmetic with insufficient precision causes the breakdown of the associative and distributive properties of addition:. The decimal module makes it possible to restore the identities by expanding the precision sufficiently to avoid loss of significance:. Infinities can be constructed directly with: Also, they can arise from dividing by zero when the DivisionByZero signal is not trapped. Likewise, when the Overflow signal is not trapped, infinity can result from rounding beyond the limits of the largest representable number. The infinities are signed affine and can be used in arithmetic operations where they get treated as very large, indeterminate numbers. For instance, adding a constant to infinity gives another infinite result. Some operations are indeterminate and return NaNor if the InvalidOperation signal is trapped, raise an exception. This variety of NaN is places and, once created, will flow through other computations always resulting in another NaN. This behavior can be useful for a series of computations that occasionally have missing inputs — it decimal the calculation to proceed while flagging specific results as invalid. A variant is sNaN which signals rather than remaining quiet after every operation. This is a useful return value when an invalid result needs to interrupt a calculation for special handling. Note that the General Decimal Arithmetic specification does not specify the behavior of direct comparisons; these rules for comparisons involving a NaN were instaforex from the IEEE standard see Table 3 in section 5. To ensure strict standards-compliance, use the compare and compare-signal methods instead. The signed zeros can result from calculations that underflow. They keep the sign that would have resulted if the calculation had been carried out to greater precision. Since their magnitude is zero, both positive and negative zeros are treated as equal and their sign is informational. In addition to the two signed zeros which are distinct yet equal, there are various representations of zero with differing precisions yet equivalent in value. This takes a bit of getting used to. For an eye accustomed to normalized floating point representations, it is not immediately obvious that the following calculation returns a value equal to zero:. The getcontext function accesses a different Context object for each thread. Having separate thread contexts means that threads may make changes such as getcontext. Likewise, the setcontext function automatically assigns its target to the current thread. If setcontext has not been called before getcontextthen getcontext will automatically create a new context for use in the current thread. The new context is copied from a prototype context called DefaultContext. To control the defaults so that each thread will use the same values throughout the application, directly modify the DefaultContext object. Here are a few recipes that serve as utility functions and that demonstrate ways to work with the Decimal class:. It is cumbersome to type decimal. Is there a way to minimize typing when using the interactive interpreter? In a fixed-point application with two decimal places, some inputs have many places and need to be rounded. Others are not supposed to have excess digits and need to be validated. What methods should be used? The quantize method rounds to a fixed number of decimal places. If the Inexact trap is set, it is also useful for validation:. Once I have valid two place inputs, how do I maintain that invariant throughout an application? Some operations like addition, subtraction, and multiplication by an integer will automatically preserve fixed point. Others operations, like division and non-integer multiplication, will change the number of decimal places and need to be followed-up with a quantize step:. In developing fixed-point applications, it is convenient to define functions to handle the quantize step:. There are many ways to express the same value. The numbers Is decimal a way to transform them to a single recognizable canonical value? The normalize method maps all equivalent values to a single representative:. Some decimal values always print with exponential notation. Is there a way to get a non-exponential representation? For some values, exponential notation is the only way to express the number of significant places in the coefficient. For example, expressing 5. If an application does not care about tracking significance, it is easy to remove the exponent and trailing zeroes, losing significance, but keeping the value unchanged:. Is there a way to convert a regular float to a Decimal? Yes, any binary floating point number can be exactly expressed as a Decimal though an exact conversion may take more precision than intuition would suggest:. The decimal module makes it easy to test results. A best practice is to re-run calculations using greater precision and with various rounding modes. Widely differing results indicate insufficient precision, rounding mode issues, ill-conditioned inputs, or a numerically unstable algorithm. I noticed that context precision is applied to the results of operations but not to the inputs. Is there anything to watch out for when mixing values of different precisions? The principle is that all values are considered to be places and so is the arithmetic on those values. Only the results are rounded. The solution is either to increase precision or to force rounding of inputs using the unary plus operation:. Alternatively, inputs can be rounded upon creation using the Context. It offers several advantages over the float datatype: Unlike hardware based binary floating point, the decimal module has a user alterable precision defaulting to 28 places which can be as large as needed for a given problem: If value is a string, it should conform instaforex the decimal numeric string syntax after leading and trailing whitespace characters, as well as underscores throughout, are removed: Note From Python 3. Each thread has its own current context which is accessed or changed using the getcontext and setcontext functions: For example, the following code sets the current decimal precision to 42 places, performs a calculation, and then automatically restores the previous context: Exception DecimalException Clamped DivisionByZero DecimalExceptionexceptions. ZeroDivisionError Inexact Overflow InexactRounded Underflow InexactRoundedSubnormal InvalidOperation Rounded Subnormal FloatOperation DecimalExceptionexceptions. Knuth provides two instructive examples where rounded floating point decimal with insufficient precision instaforex the breakdown of the associative and distributive properties of addition: Examples from Seminumerical Algorithms, Section 4. For an eye accustomed to normalized floating point representations, it is not immediately obvious that the following calculation returns a value equal instaforex zero: Set applicationwide defaults for all threads about to be launched DefaultContext. Result type matches input type. The Taylor series approximation works best for a small value of x. Some users abbreviate the constructor to just a single letter: Table Of Contents 9. Floating Point Notes 9. Mitigating round-off error with increased precision 9. Working with threads 9. Decimal FAQ Previous topic 9. The Python Software Foundation is a non-profit corporation. Last updated on Jun 24, Created using Sphinx 1.
This is through paying a visit to the psychologists to enable such individuals to recognize their anger, and offer advice on how to handle the situation in case it arises.
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This is through paying a visit to the psychologists to enable such individuals to recognize their anger, and offer advice on how to handle the situation in case it arises.