##
6.3.7 Recipes

Here are a few recipes that serve as utility functions and that demonstrate ways to work with the `Decimal` class:

    def moneyfmt(value, places=2, curr='', sep=',', dp='.',
                 pos='', neg='-', trailneg=''):
        """Convert Decimal to a money formatted string.

        places:  required number of places after the decimal point
        curr:    optional currency symbol before the sign (may be blank)
        sep:     optional grouping separator (comma, period, space, or blank)
        dp:      decimal point indicator (comma or period)
                 only specify as blank when places is zero
        pos:     optional sign for positive numbers: '+', space or blank
        neg:     optional sign for negative numbers: '-', '(', space or blank
        trailneg:optional trailing minus indicator:  '-', ')', space or blank

        >>> d = Decimal('-1234567.8901')
        >>> moneyfmt(d, curr='$')
        '-$1,234,567.89'
        >>> moneyfmt(d, places=0, sep='.', dp='', neg='', trailneg='-')
        '1.234.568-'
        >>> moneyfmt(d, curr='$', neg='(', trailneg=')')
        '($1,234,567.89)'
        >>> moneyfmt(Decimal(123456789), sep=' ')
        '123 456 789.00'
        >>> moneyfmt(Decimal('-0.02'), neg='<', trailneg='>')
        '<.02>'

        """
        q = Decimal((0, (1,), -places))    # 2 places --> '0.01'
        sign, digits, exp = value.quantize(q).as_tuple()
        assert exp == -places
        result = []
        digits = map(str, digits)
        build, next = result.append, digits.pop
        if sign:
            build(trailneg)
        for i in range(places):
            if digits:
                build(next())
            else:
                build('0')
        build(dp)
        i = 0
        while digits:
            build(next())
            i += 1
            if i == 3 and digits:
                i = 0
                build(sep)
        build(curr)
        if sign:
            build(neg)
        else:
            build(pos)
        result.reverse()
        return ''.join(result)

    def pi():
        """Compute Pi to the current precision.

        >>> print pi()
        3.141592653589793238462643383

        """
        getcontext().prec += 2  # extra digits for intermediate steps
        three = Decimal(3)      # substitute "three=3.0" for regular floats
        lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
        while s != lasts:
            lasts = s
            n, na = n+na, na+8
            d, da = d+da, da+32
            t = (t * n) / d
            s += t
        getcontext().prec -= 2
        return +s               # unary plus applies the new precision

    def exp(x):
        """Return e raised to the power of x.  Result type matches input type.

        >>> print exp(Decimal(1))
        2.718281828459045235360287471
        >>> print exp(Decimal(2))
        7.389056098930650227230427461
        >>> print exp(2.0)
        7.38905609893
        >>> print exp(2+0j)
        (7.38905609893+0j)

        """
        getcontext().prec += 2
        i, lasts, s, fact, num = 0, 0, 1, 1, 1
        while s != lasts:
            lasts = s
            i += 1
            fact *= i
            num *= x
            s += num / fact
        getcontext().prec -= 2
        return +s

    def cos(x):
        """Return the cosine of x as measured in radians.

        >>> print cos(Decimal('0.5'))
        0.8775825618903727161162815826
        >>> print cos(0.5)
        0.87758256189
        >>> print cos(0.5+0j)
        (0.87758256189+0j)

        """
        getcontext().prec += 2
        i, lasts, s, fact, num, sign = 0, 0, 1, 1, 1, 1
        while s != lasts:
            lasts = s
            i += 2
            fact *= i * (i-1)
            num *= x * x
            sign *= -1
            s += num / fact * sign
        getcontext().prec -= 2
        return +s

    def sin(x):
        """Return the sine of x as measured in radians.

        >>> print sin(Decimal('0.5'))
        0.4794255386042030002732879352
        >>> print sin(0.5)
        0.479425538604
        >>> print sin(0.5+0j)
        (0.479425538604+0j)

        """
        getcontext().prec += 2
        i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1
        while s != lasts:
            lasts = s
            i += 2
            fact *= i * (i-1)
            num *= x * x
            sign *= -1
            s += num / fact * sign
        getcontext().prec -= 2
        return +s