Class Context

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__

(inherited documentation)

Show the current context.

Overrides: object.__repr__

A Context cannot be hashed.

Overrides: object.__hash__

Returns the absolute value of the operand.

If the operand is negative, the result is the same as using the minus operation on the operand. Otherwise, the result is the same as using the plus operation on the operand.

>>> ExtendedContext.abs(Decimal('2.1'))
Decimal("2.1")
>>> ExtendedContext.abs(Decimal('-100'))
Decimal("100")
>>> ExtendedContext.abs(Decimal('101.5'))
Decimal("101.5")
>>> ExtendedContext.abs(Decimal('-101.5'))
Decimal("101.5")

Return the sum of the two operands.

>>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
Decimal("19.00")
>>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
Decimal("1.02E+4")

Compares values numerically.

If the signs of the operands differ, a value representing each operand ('-1' if the operand is less than zero, '0' if the operand is zero or negative zero, or '1' if the operand is greater than zero) is used in place of that operand for the comparison instead of the actual operand.

The comparison is then effected by subtracting the second operand from the first and then returning a value according to the result of the subtraction: '-1' if the result is less than zero, '0' if the result is zero or negative zero, or '1' if the result is greater than zero.

>>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
Decimal("-1")
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
Decimal("0")
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
Decimal("0")
>>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
Decimal("1")
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
Decimal("1")
>>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
Decimal("-1")

Decimal division in a specified context.

>>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
Decimal("0.333333333")
>>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
Decimal("0.666666667")
>>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
Decimal("2.5")
>>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
Decimal("0.1")
>>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
Decimal("1")
>>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
Decimal("4.00")
>>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
Decimal("1.20")
>>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
Decimal("10")
>>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
Decimal("1000")
>>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
Decimal("1.20E+6")

Divides two numbers and returns the integer part of the result.

>>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
Decimal("0")
>>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
Decimal("3")
>>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
Decimal("3")

max compares two values numerically and returns the maximum.

If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the maximum (closer to positive infinity) of the two operands is chosen as the result.

>>> ExtendedContext.max(Decimal('3'), Decimal('2'))
Decimal("3")
>>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
Decimal("3")
>>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
Decimal("1")
>>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
Decimal("7")

min compares two values numerically and returns the minimum.

If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the minimum (closer to negative infinity) of the two operands is chosen as the result.

>>> ExtendedContext.min(Decimal('3'), Decimal('2'))
Decimal("2")
>>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
Decimal("-10")
>>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
Decimal("1.0")
>>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
Decimal("7")

Minus corresponds to unary prefix minus in Python.

The operation is evaluated using the same rules as subtract; the operation minus(a) is calculated as subtract('0', a) where the '0' has the same exponent as the operand.

>>> ExtendedContext.minus(Decimal('1.3'))
Decimal("-1.3")
>>> ExtendedContext.minus(Decimal('-1.3'))
Decimal("1.3")

multiply multiplies two operands.

If either operand is a special value then the general rules apply. Otherwise, the operands are multiplied together ('long multiplication'), resulting in a number which may be as long as the sum of the lengths of the two operands.

>>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
Decimal("3.60")
>>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
Decimal("21")
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
Decimal("0.72")
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
Decimal("-0.0")
>>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
Decimal("4.28135971E+11")

normalize reduces an operand to its simplest form.

Essentially a plus operation with all trailing zeros removed from the result.

>>> ExtendedContext.normalize(Decimal('2.1'))
Decimal("2.1")
>>> ExtendedContext.normalize(Decimal('-2.0'))
Decimal("-2")
>>> ExtendedContext.normalize(Decimal('1.200'))
Decimal("1.2")
>>> ExtendedContext.normalize(Decimal('-120'))
Decimal("-1.2E+2")
>>> ExtendedContext.normalize(Decimal('120.00'))
Decimal("1.2E+2")
>>> ExtendedContext.normalize(Decimal('0.00'))
Decimal("0")

Plus corresponds to unary prefix plus in Python.

The operation is evaluated using the same rules as add; the operation plus(a) is calculated as add('0', a) where the '0' has the same exponent as the operand.

>>> ExtendedContext.plus(Decimal('1.3'))
Decimal("1.3")
>>> ExtendedContext.plus(Decimal('-1.3'))
Decimal("-1.3")

Raises a to the power of b, to modulo if given.

The right-hand operand must be a whole number whose integer part (after any exponent has been applied) has no more than 9 digits and whose fractional part (if any) is all zeros before any rounding. The operand may be positive, negative, or zero; if negative, the absolute value of the power is used, and the left-hand operand is inverted (divided into 1) before use.

If the increased precision needed for the intermediate calculations exceeds the capabilities of the implementation then an Invalid operation condition is raised.

If, when raising to a negative power, an underflow occurs during the division into 1, the operation is not halted at that point but continues.

>>> ExtendedContext.power(Decimal('2'), Decimal('3'))
Decimal("8")
>>> ExtendedContext.power(Decimal('2'), Decimal('-3'))
Decimal("0.125")
>>> ExtendedContext.power(Decimal('1.7'), Decimal('8'))
Decimal("69.7575744")
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2'))
Decimal("0")
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1'))
Decimal("0")
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('0'))
Decimal("1")
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('1'))
Decimal("Infinity")
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('2'))
Decimal("Infinity")
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2'))
Decimal("0")
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1'))
Decimal("-0")
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0'))
Decimal("1")
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1'))
Decimal("-Infinity")
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2'))
Decimal("Infinity")
>>> ExtendedContext.power(Decimal('0'), Decimal('0'))
Decimal("NaN")

Returns a value equal to 'a' (rounded) and having the exponent of 'b'.

The coefficient of the result is derived from that of the left-hand operand. It may be rounded using the current rounding setting (if the exponent is being increased), multiplied by a positive power of ten (if the exponent is being decreased), or is unchanged (if the exponent is already equal to that of the right-hand operand).

Unlike other operations, if the length of the coefficient after the quantize operation would be greater than precision then an Invalid operation condition is raised. This guarantees that, unless there is an error condition, the exponent of the result of a quantize is always equal to that of the right-hand operand.

Also unlike other operations, quantize will never raise Underflow, even if the result is subnormal and inexact.

>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
Decimal("2.170")
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
Decimal("2.17")
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
Decimal("2.2")
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
Decimal("2")
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
Decimal("0E+1")
>>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
Decimal("-Infinity")
>>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
Decimal("NaN")
>>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
Decimal("-0")
>>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
Decimal("-0E+5")
>>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
Decimal("NaN")
>>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
Decimal("NaN")
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
Decimal("217.0")
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
Decimal("217")
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
Decimal("2.2E+2")
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
Decimal("2E+2")

Returns the remainder from integer division.

The result is the residue of the dividend after the operation of calculating integer division as described for divide-integer, rounded to precision digits if necessary. The sign of the result, if non-zero, is the same as that of the original dividend.

This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated).

>>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
Decimal("2.1")
>>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
Decimal("1")
>>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
Decimal("-1")
>>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
Decimal("0.2")
>>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
Decimal("0.1")
>>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
Decimal("1.0")

Returns to be "a - b * n", where n is the integer nearest the exact value of "x / b" (if two integers are equally near then the even one is chosen). If the result is equal to 0 then its sign will be the sign of a.

This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated).

>>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
Decimal("-0.9")
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
Decimal("-2")
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
Decimal("1")
>>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
Decimal("-1")
>>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
Decimal("0.2")
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
Decimal("0.1")
>>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
Decimal("-0.3")

Returns True if the two operands have the same exponent.

The result is never affected by either the sign or the coefficient of either operand.

>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
False
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
True
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
False
>>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
True

Returns the square root of a non-negative number to context precision.

If the result must be inexact, it is rounded using the round-half-even algorithm.

>>> ExtendedContext.sqrt(Decimal('0'))
Decimal("0")
>>> ExtendedContext.sqrt(Decimal('-0'))
Decimal("-0")
>>> ExtendedContext.sqrt(Decimal('0.39'))
Decimal("0.624499800")
>>> ExtendedContext.sqrt(Decimal('100'))
Decimal("10")
>>> ExtendedContext.sqrt(Decimal('1'))
Decimal("1")
>>> ExtendedContext.sqrt(Decimal('1.0'))
Decimal("1.0")
>>> ExtendedContext.sqrt(Decimal('1.00'))
Decimal("1.0")
>>> ExtendedContext.sqrt(Decimal('7'))
Decimal("2.64575131")
>>> ExtendedContext.sqrt(Decimal('10'))
Decimal("3.16227766")
>>> ExtendedContext.prec
9

Return the difference between the two operands.

>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
Decimal("0.23")
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
Decimal("0.00")
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
Decimal("-0.77")

Converts a number to a string, using scientific notation.

The operation is not affected by the context.

Converts a number to a string, using scientific notation.

The operation is not affected by the context.

Rounds to an integer.

When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting, except that no flags will be set. The rounding mode is taken from the context.

>>> ExtendedContext.to_integral(Decimal('2.1'))
Decimal("2")
>>> ExtendedContext.to_integral(Decimal('100'))
Decimal("100")
>>> ExtendedContext.to_integral(Decimal('100.0'))
Decimal("100")
>>> ExtendedContext.to_integral(Decimal('101.5'))
Decimal("102")
>>> ExtendedContext.to_integral(Decimal('-101.5'))
Decimal("-102")
>>> ExtendedContext.to_integral(Decimal('10E+5'))
Decimal("1.0E+6")
>>> ExtendedContext.to_integral(Decimal('7.89E+77'))
Decimal("7.89E+77")
>>> ExtendedContext.to_integral(Decimal('-Inf'))
Decimal("-Infinity")