Critics have remarked that those four worthies were truly peerless throughout the ages; yet the present falls short of the pastβthe ancients favored unadorned simplicity, whereas the moderns prefer refined elegance. Styles of substance and ornament rise and fall in succession, shifting with the changing mores of the times; such evolution is simply the natural order of things. The ideal lies in honoring antiquity without clashing with the present, and embracing modernity without succumbing to its flawsβembodying that perfect balance of substance and refinement that defines the true gentleman. There is surely no need to abandon a carved palace in favor of a cave dwelling, or to trade a jade carriage for a primitive cart with solid wooden wheels.
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"""General floating point formatting functions.
Functions:
fix(x, digits_behind)
sci(x, digits_behind)
Each takes a number or a string and a number of digits as arguments.
Parameters:
x: number to be formatted; or a string resembling a number
digits_behind: number of digits behind the decimal point
"""
from warnings import warnpy3k
warnpy3k("the fpformat module has been removed in Python 3.0", stacklevel=2)
del warnpy3k
import re
__all__ = ["fix","sci","NotANumber"]
# Compiled regular expression to "decode" a number
decoder = re.compile(r'^([-+]?)(\d*)((?:\.\d*)?)(([eE][-+]?\d+)?)$')
# \0 the whole thing
# \1 leading sign or empty
# \2 digits left of decimal point
# \3 fraction (empty or begins with point)
# \4 exponent part (empty or begins with 'e' or 'E')
try:
class NotANumber(ValueError):
pass
except TypeError:
NotANumber = 'fpformat.NotANumber'
def extract(s):
"""Return (sign, intpart, fraction, expo) or raise an exception:
sign is '+' or '-'
intpart is 0 or more digits beginning with a nonzero
fraction is 0 or more digits
expo is an integer"""
res = decoder.match(s)
if res is None: raise NotANumber, s
sign, intpart, fraction, exppart = res.group(1,2,3,4)
intpart = intpart.lstrip('0');
if sign == '+': sign = ''
if fraction: fraction = fraction[1:]
if exppart: expo = int(exppart[1:])
else: expo = 0
return sign, intpart, fraction, expo
def unexpo(intpart, fraction, expo):
"""Remove the exponent by changing intpart and fraction."""
if expo > 0: # Move the point left
f = len(fraction)
intpart, fraction = intpart + fraction[:expo], fraction[expo:]
if expo > f:
intpart = intpart + '0'*(expo-f)
elif expo < 0: # Move the point right
i = len(intpart)
intpart, fraction = intpart[:expo], intpart[expo:] + fraction
if expo < -i:
fraction = '0'*(-expo-i) + fraction
return intpart, fraction
def roundfrac(intpart, fraction, digs):
"""Round or extend the fraction to size digs."""
f = len(fraction)
if f <= digs:
return intpart, fraction + '0'*(digs-f)
i = len(intpart)
if i+digs < 0:
return '0'*-digs, ''
total = intpart + fraction
nextdigit = total[i+digs]
if nextdigit >= '5': # Hard case: increment last digit, may have carry!
n = i + digs - 1
while n >= 0:
if total[n] != '9': break
n = n-1
else:
total = '0' + total
i = i+1
n = 0
total = total[:n] + chr(ord(total[n]) + 1) + '0'*(len(total)-n-1)
intpart, fraction = total[:i], total[i:]
if digs >= 0:
return intpart, fraction[:digs]
else:
return intpart[:digs] + '0'*-digs, ''
def fix(x, digs):
"""Format x as [-]ddd.ddd with 'digs' digits after the point
and at least one digit before.
If digs <= 0, the point is suppressed."""
if type(x) != type(''): x = repr(x)
try:
sign, intpart, fraction, expo = extract(x)
except NotANumber:
return x
intpart, fraction = unexpo(intpart, fraction, expo)
intpart, fraction = roundfrac(intpart, fraction, digs)
while intpart and intpart[0] == '0': intpart = intpart[1:]
if intpart == '': intpart = '0'
if digs > 0: return sign + intpart + '.' + fraction
else: return sign + intpart
def sci(x, digs):
"""Format x as [-]d.dddE[+-]ddd with 'digs' digits after the point
and exactly one digit before.
If digs is <= 0, one digit is kept and the point is suppressed."""
if type(x) != type(''): x = repr(x)
sign, intpart, fraction, expo = extract(x)
if not intpart:
while fraction and fraction[0] == '0':
fraction = fraction[1:]
expo = expo - 1
if fraction:
intpart, fraction = fraction[0], fraction[1:]
expo = expo - 1
else:
intpart = '0'
else:
expo = expo + len(intpart) - 1
intpart, fraction = intpart[0], intpart[1:] + fraction
digs = max(0, digs)
intpart, fraction = roundfrac(intpart, fraction, digs)
if len(intpart) > 1:
intpart, fraction, expo = \
intpart[0], intpart[1:] + fraction[:-1], \
expo + len(intpart) - 1
s = sign + intpart
if digs > 0: s = s + '.' + fraction
e = repr(abs(expo))
e = '0'*(3-len(e)) + e
if expo < 0: e = '-' + e
else: e = '+' + e
return s + 'e' + e
def test():
"""Interactive test run."""
try:
while 1:
x, digs = input('Enter (x, digs): ')
print x, fix(x, digs), sci(x, digs)
except (EOFError, KeyboardInterrupt):
pass