keep_1st_sign_dig_in error.py

from decimal import Decimal
import numpy as np


def format_5(f):
    """
    Round floats that end with a '5' correctly, bypassing Python's issue
    with the round() function.

    See: http://codereview.stackexchange.com/q/122243/35351
    """
    # If the last digit is 5 or larger, round up.
    if int(f[-1]) >= 5:
        r_up_down = 'ROUND_UP'
    else:
        r_up_down = 'ROUND_DOWN'

    return Decimal.quantize(Decimal(f), Decimal(f[:-1]), rounding=r_up_down)


def count_zeros(sf):
    """
    Count the number of leading zeros until the first non-zero digit.
    Only works on float < 1.
    """
    nd = 0
    for d in sf[2:]:  # Remove trailing '0.'
        if d == '0':
            nd += 1
        else:
            # Stop at the first non-zero digit found.
            break
    return nd


def round1(f):
    """
    Round *positive* float to 1 significant figure.
    """
    # Float as string.
    sf = str(f)

    if f == 0.:
        f_r = 0.
    elif 0. < f < 1.:
        # Number of leading zeros.
        nd = count_zeros(sf)
        # If the float already has a single non-zero digit.
        if len(sf) == (2 + nd + 1):
            f_r = f
        else:
            # Isolate first two non-zero digits.
            dn = sf[2+nd:nd+4]
            # Create new float using the first two digits to round
            # to a single digit.
            sf_r = '0.' + dn
            # Round digits.
            sf_r5 = format_5(sf_r)
            # Generate final properly rounded float.
            # Catch special case.
            if sf_r5 == Decimal('1.0'):
                if nd > 0:
                    f_r = '0.' + '0'*nd + '1'
                else:
                    f_r = 1.
            else:
                # General case.
                f_r = '0.' + '0'*nd + str(sf_r5)[2:]
    elif 1. <= f < 10.:
        # Create float with first two digits, without the floating point.
        sf_r = '0.' + sf[0] + sf[2]
        # Round to one digit.
        sf_r5 = format_5(sf_r)
        # Catch special case.
        if sf_r5 == Decimal('1.0'):
            f_r = 10.
        else:
            # General case.
            f_r = str(sf_r5)[-1]
    else:
        # Number of digits before the decimal point.
        nb = len(sf.split('.')[0])
        # Create float with first two digits.
        sf_r = '0.' + sf[:2]
        # Round to one digit.
        sf_r5 = format_5(sf_r)
        # Catch special case.
        if sf_r5 == Decimal('1.0'):
            f_r = '1' + str(sf_r5)[-1] + '0'*(nb-1) + '.'
        else:
            # General case.
            f_r = str(sf_r5)[-1] + '0'*(nb-1) + '.'

    return float(f_r)


f_lst = [0.01, 0.1, 0.99, 0.099, 0.95, 0.094, 0.00012, 0.055, 0.0075, 0.23]
f_lst = [1.0025, 5.57, 6.99, 9.49, 9.55, 9.99]
f_lst = [10., 10.05, 500.5, 556, 9956.2]
f_lst = np.random.uniform(10., 100000., 100)
for f in f_lst:
    print 'orig:', f
    f_r = round1(f)
    print 'round:', f_r, '\n'