How to display a very accurate number? - python

I want to output two numbers that differ very slightly from each other.
1.0000000000
1.0000000001
I don't want a long line. Rounding or scientific notation doesn't help me.
>>> round(1.0000000000, 6)
1.0
>>> round(1.0000000001, 6)
1.0
>>> f"{1.0000000001:e}"
'1.000000e+00'
>>> f"{1.0000000000:e}"
'1.000000e+00'
I like the solution in matplotlib. There, the number is presented as the sum of the major part and fractional. So the numbers presented above will look like this:
1 + 0 * 1e-10,
1 + 1 * 1e-10
I can implement this myself, but suddenly you know any libraries or standard tools for this.
Do you know the existing tools for this?

Maybe library decimal is useful. For example:
>>> from decimal import Decimal
>>> a = Decimal(1.0000000000)
>>> b = Decimal(1.0000000001)
>>>
>>> a
Decimal('1')
>>> b
Decimal('1.0000000001000000082740370999090373516082763671875')
>>>
>>> a == b
False

I never got an answer.
So far I tried to implement the functionality of matplotib.
True, the code is crude, but I'll save it here, suddenly it will be useful to someone.
Pass the list of objects to Decimal!!!
def prepare_display(numbers, accuracy):
from decimal import Decimal
ACCURACY = 3
numbers_sorted = sorted(numbers)
diffs = []
for i in range(1, len(numbers)):
diffs.append(numbers_sorted[i] - numbers_sorted[i - 1])
if min(diffs) > 1 * 10 ** (-ACCURACY):
return '', numbers
total_part = min(numbers)
differents = []
exps = []
for number in numbers:
diff = number - total_part
differents.append(diff)
exps.append(fexp(diff))
min_exp = min(exps)
different_parts = []
for diff in differents:
different_parts.append(round(diff / Decimal(10 ** min_exp)))
total_part = Decimal(total_part)
return str(round(total_part, - min_exp - 1)) + ' + x * 1e' \
str(min_exp),
different_parts
def fexp(number):
"""Returns the exponent of a decimal number"""
from decimal import Decimal
(sign, digits, exponent) = Decimal(number).as_tuple()
return len(digits) + exponent - 1
Then for the following cases there will be a corresponding result.
For numbers less than one
>>>> numbers = [Decimal('0.999990'), Decimal('0.999992')]
>>>> total_part, different_parts = prepare_display(numbers)
>>>> print(total_part)
>>>> print(different_parts)
0.99999 + x * 1e-6
[0, 2]
If no conversion is needed
>>>> numbers = [1, 2]
>>>> total_part, different_parts = prepare_display(numbers, 3)
>>>> print(total_part)
>>>> print(different_parts)
[1, 2]
The code is very crude

Related

how to output the difference of two floats as an interger in python

is there any way to output the difference between two float numbers as an integer
below is three examples of the float values provided for script, my goal is to output the difference between these values as an integer , in the first example i should get 2 where num_two - num_one equals 0.000002 but i don't want the zeros as they don't matter i can do it with string format but i have no way of telling how big the number is or how many zeros it has
## example 1
num_one = 0.000012
num_two = 0.000014
## example 2
num_0ne = 0.0123
num_tw0 = 0.013
## example 3
num_1 = 23.32
num_2 = 23.234
print (float(num_2) - float(num_1))
## this should output 86 as an integer
Beware of floats (see https://en.wikipedia.org/wiki/IEEE_754):
>>> 23.32 - 23.234
0.08599999999999852
You need exact precision. Use the decimal module:
>>> from decimal import Decimal
>>> n1 = Decimal("23.32")
>>> n2 = Decimal("23.234")
>>> n1, n2
(Decimal('23.32'), Decimal('23.234'))
>>> d = abs(n1-n2)
>>> d
Decimal('0.086')
Now, just shift the decimal point right (that is * 10) until there is no fractional part left (d % 1 == 0):
>>> while d % 1:
... d *= 10
(Don't be afraid, the loop will stop because you can't have more decimal levels than decimal.getcontext().prec at the beginning and the decimal level decrease on each iteration).
You get the expected result:
>>> d
Decimal('86.000')
>>> int(d)
86

Python setting Decimal Place range without rounding?

How can I take a float variable, and control how far out the float goes without round()? For example.
w = float(1.678)
I want to take x and make the following variables out of it.
x = 1.67
y = 1.6
z = 1
If I use the respective round methods:
x = round(w, 2) # With round I get 1.68
y = round(y, 1) # With round I get 1.7
z = round(z, 0) # With round I get 2.0
It's going to round and alter the numbers to the point where there no use to me. I understand this is the point of round and its working properly. How would I go about getting the information that I need in the x,y,z variables and still be able to use them in other equations in a float format?
You can do:
def truncate(f, n):
return math.floor(f * 10 ** n) / 10 ** n
testing:
>>> f=1.923328437452
>>> [truncate(f, n) for n in range(7)]
[1.0, 1.9, 1.92, 1.923, 1.9233, 1.92332, 1.923328]
A super simple solution is to use strings
x = float (str (w)[:-1])
y = float (str (w)[:-2])
z = float (str (w)[:-3])
Any of the floating point library solutions would require you dodge some rounding, and using floor/powers of 10 to pick out the decimals can get a little hairy by comparison to the above.
Integers are faster to manipulate than floats/doubles which are faster than strings. In this case, I tried to get time with both approach :
timeit.timeit(stmt = "float(str(math.pi)[:12])", setup = "import math", number = 1000000)
~1.1929605630000424
for :
timeit.timeit(stmt = "math.floor(math.pi * 10 ** 10) / 10 ** 10", setup = "import math", number = 1000000)
~0.3455968870000561
So it's safe to use math.floor rather than string operation on it.
If you just need to control the precision in format
pi = 3.14159265
format(pi, '.3f') #print 3.142 # 3 precision after the decimal point
format(pi, '.1f') #print 3.1
format(pi, '.10f') #print 3.1415926500, more precision than the original
If you need to control the precision in floating point arithmetic
import decimal
decimal.getcontext().prec=4 #4 precision in total
pi = decimal.Decimal(3.14159265)
pi**2 #print Decimal('9.870') whereas '3.142 squared' would be off
--edit--
Without "rounding", thus truncating the number
import decimal
from decimal import ROUND_DOWN
decimal.getcontext().prec=4
pi*1 #print Decimal('3.142')
decimal.getcontext().rounding = ROUND_DOWN
pi*1 #print Decimal('3.141')
I think the easiest answer is :
from math import trunc
w = 1.678
x = trunc(w * 100) / 100
y = trunc(w * 10) / 10
z = trunc(w)
also this:
>>> f = 1.678
>>> n = 2
>>> int(f * 10 ** n) / 10 ** n
1.67
Easiest way to get integer:
series_col.round(2).apply(lambda x: float(str(x).split(".",1)[0]))

Round to whole numbers without using conditional statements in Python - Logic

I'm taking a Python course at Udacity, and I'm trying to work this out for myself without looking at the answer. Perhaps you can give me a hint for my logic?
Below are the instructions and what I have so far. We haven't learned conditional statements yet, so I can't use those. We've only learned how to assign/print a variable, strings, indexing strings, sub-sequences, and .find. They just introduced the str command in this final exercise.
# Given a variable, x, that stores the
# value of any decimal number, write Python
# code that prints out the nearest whole
# number to x.
# If x is exactly half way between two
# whole numbers, round up, so
# 3.5 rounds to 4 and 2.5 rounds to 3.
# You may assume x is not negative.
# Hint: The str function can convert any number into a string.
# eg str(89) converts the number 89 to the string '89'
# Along with the str function, this problem can be solved
# using just the information introduced in unit 1.
# x = 3.14159
# >>> 3 (not 3.0)
# x = 27.63
# >>> 28 (not 28.0)
# x = 3.5
# >>> 4 (not 4.0)
x = 3.54159
#ENTER CODE BELOW HERE
x = str(x)
dec = x.find('.')
tenth = dec + 1
print x[0:dec]
////
So this gets me to print the characters up to the decimal point, but I can't figure out how to have the computer check whether "tenth" is > 4 or < 5 and print out something according to the answer.
I figured I could probably get far enough for it to return a -1 if "tenth" wasn't > 4, but I don't know how I can get it to print x[0:dec] if it's < 5 and x[0:dec]+1 if it's > 4.
:/
Could someone please give me a nudge in the right direction?
This is a weird restriction, but you could do this:
x = str(x)
dec_index = x.find('.')
tenth_index = dec_index + 1
tenth_place = x[tenth_index] # will be a string of length 1
should_round_up = 5 + tenth_place.find('5') + tenth_place.find('6') + tenth_place.find('7') + tenth_place.find('8') + tenth_place.find('9')
print int(x[0:dec_index]) + should_round_up
What we do is look at the tenths place. Since .find() returns -1 if the argument isn't found, the sum of the .find() calls will be -4 if if the tenths place is 5, 6, 7, 8, or 9 (since one of the .find() calls will succeed and return 0), but will be -5 if the tenths place is 0, 1, 2, 3, or 4. We add 5 to that, so that should_round_up equals 1 if we should round up, and 0 otherwise. Add that to the whole number part, and we're done.
That said, if you weren't subject to this artificial restriction, you would do:
print round(x)
And move on with your life.
judging by the accepted answer you only expects floats so that is pretty trivial to solve:
x = 3.54159
# split on .
a, b = str(x).split(".")
# cast left side to int and add result of test for right side being greater or equal to 5
print(int(a) + (int(b) >= 5))
(int(b) > 5) will be either 1 or 0 i.e True/False so we either add 1 when right side is > .5 or flooring when it's < .5 and adding 0.
If you were doing it mathematically you just need to print(int(x+.5)), anything >= .5 will mean x will be rounded up and floored when it is < .5.
x = 3.54159
# split on .
a, b = str(x).split(".")
# cast left side to int and add result of test for right side being greater or equal to 5
print(int(a) + (int(b[0]) >= 5))
# above code will not work with 3.14567 and the number with having two or more digits after decimal
I think it's easier...
x = x + 0.5
intPart, decPart = str(x).split(".")
print intPart
Examples:
If x = 1, then it will become 1.5 and intPart will be 1.
If x = 1.1, then it will become 1.6 and intPart will be 1.
If x = 1.6, then it will become 2.1 and intPart will be 2.
Note: it will only work for positive numbers.
This code will round numbers to the nearest whole
without using conditionals
You can do it this way
x = 3.54159
x = x + 0.5 # This automatically takes care of the rounding
str_x = str(x) # Converting number x to string
dp = str_x.find('.') # Finding decimal point index
print str_x[:dp] # Printing upto but excluding decimal point
I did the same course at Udacity. solved it using the following code:
y = str(x)
decimal = y.find('.')
y_increment = y[decimal+1:]
print decimal
print y_increment
# Section below finds >5
check5 = y_increment.find('5',0,1)
check6 = y_increment.find('6',0,1)
check7 = y_increment.find('7',0,1)
check8 = y_increment.find('8',0,1)
check9 = y_increment.find('9',0,1)
yes_increment = (check5 + 1) + (check6 + 1) + (check7 + 1) + (check8 + 1) + (check9 + 1)
print check5, check6, check7, check8, check9
#Calculate rounding up
z = x + (yes_increment)
z = str(z)
final_decimal = z.find('.')
print z[:final_decimal]

drop trailing zeros from decimal

I have a long list of Decimals and that I have to adjust by factors of 10, 100, 1000,..... 1000000 depending on certain conditions. When I multiply them there is sometimes a useless trailing zero (though not always) that I want to get rid of. For example...
from decimal import Decimal
# outputs 25.0, PROBLEM! I would like it to output 25
print Decimal('2.5') * 10
# outputs 2567.8000, PROBLEM! I would like it to output 2567.8
print Decimal('2.5678') * 1000
Is there a function that tells the decimal object to drop these insignificant zeros? The only way I can think of doing this is to convert to a string and replace them using regular expressions.
Should probably mention that I am using python 2.6.5
EDIT
senderle's fine answer made me realize that I occasionally get a number like 250.0 which when normalized produces 2.5E+2. I guess in these cases I could try to sort them out and convert to a int
You can use the normalize method to remove extra precision.
>>> print decimal.Decimal('5.500')
5.500
>>> print decimal.Decimal('5.500').normalize()
5.5
To avoid stripping zeros to the left of the decimal point, you could do this:
def normalize_fraction(d):
normalized = d.normalize()
sign, digits, exponent = normalized.as_tuple()
if exponent > 0:
return decimal.Decimal((sign, digits + (0,) * exponent, 0))
else:
return normalized
Or more compactly, using quantize as suggested by user7116:
def normalize_fraction(d):
normalized = d.normalize()
sign, digit, exponent = normalized.as_tuple()
return normalized if exponent <= 0 else normalized.quantize(1)
You could also use to_integral() as shown here but I think using as_tuple this way is more self-documenting.
I tested these both against a few cases; please leave a comment if you find something that doesn't work.
>>> normalize_fraction(decimal.Decimal('55.5'))
Decimal('55.5')
>>> normalize_fraction(decimal.Decimal('55.500'))
Decimal('55.5')
>>> normalize_fraction(decimal.Decimal('55500'))
Decimal('55500')
>>> normalize_fraction(decimal.Decimal('555E2'))
Decimal('55500')
There's probably a better way of doing this, but you could use .rstrip('0').rstrip('.') to achieve the result that you want.
Using your numbers as an example:
>>> s = str(Decimal('2.5') * 10)
>>> print s.rstrip('0').rstrip('.') if '.' in s else s
25
>>> s = str(Decimal('2.5678') * 1000)
>>> print s.rstrip('0').rstrip('.') if '.' in s else s
2567.8
And here's the fix for the problem that #gerrit pointed out in the comments:
>>> s = str(Decimal('1500'))
>>> print s.rstrip('0').rstrip('.') if '.' in s else s
1500
Answer from the Decimal FAQ in the documentation:
>>> def remove_exponent(d):
... return d.quantize(Decimal(1)) if d == d.to_integral() else d.normalize()
>>> remove_exponent(Decimal('5.00'))
Decimal('5')
>>> remove_exponent(Decimal('5.500'))
Decimal('5.5')
>>> remove_exponent(Decimal('5E+3'))
Decimal('5000')
Answer is mentioned in FAQ (https://docs.python.org/2/library/decimal.html#decimal-faq) but does not explain things.
To drop trailing zeros for fraction part you should use normalize:
>>> Decimal('100.2000').normalize()
Decimal('100.2')
>> Decimal('0.2000').normalize()
Decimal('0.2')
But this works different for numbers with leading zeros in sharp part:
>>> Decimal('100.0000').normalize()
Decimal('1E+2')
In this case we should use `to_integral':
>>> Decimal('100.000').to_integral()
Decimal('100')
So we could check if there's a fraction part:
>>> Decimal('100.2000') == Decimal('100.2000').to_integral()
False
>>> Decimal('100.0000') == Decimal('100.0000').to_integral()
True
And use appropriate method then:
def remove_exponent(num):
return num.to_integral() if num == num.to_integral() else num.normalize()
Try it:
>>> remove_exponent(Decimal('100.2000'))
Decimal('100.2')
>>> remove_exponent(Decimal('100.0000'))
Decimal('100')
>>> remove_exponent(Decimal('0.2000'))
Decimal('0.2')
Now we're done.
Use the format specifier %g. It seems remove to trailing zeros.
>>> "%g" % (Decimal('2.5') * 10)
'25'
>>> "%g" % (Decimal('2.5678') * 1000)
'2567.8'
It also works without the Decimal function
>>> "%g" % (2.5 * 10)
'25'
>>> "%g" % (2.5678 * 1000)
'2567.8'
I ended up doing this:
import decimal
def dropzeros(number):
mynum = decimal.Decimal(number).normalize()
# e.g 22000 --> Decimal('2.2E+4')
return mynum.__trunc__() if not mynum % 1 else float(mynum)
print dropzeros(22000.000)
22000
print dropzeros(2567.8000)
2567.8
note: casting the return value as a string will limit you to 12 significant digits
Slightly modified version of A-IV's answer
NOTE that Decimal('0.99999999999999999999999999995').normalize() will round to Decimal('1')
def trailing(s: str, char="0"):
return len(s) - len(s.rstrip(char))
def decimal_to_str(value: decimal.Decimal):
"""Convert decimal to str
* Uses exponential notation when there are more than 4 trailing zeros
* Handles decimal.InvalidOperation
"""
# to_integral_value() removes decimals
if value == value.to_integral_value():
try:
value = value.quantize(decimal.Decimal(1))
except decimal.InvalidOperation:
pass
uncast = str(value)
# use exponential notation if there are more that 4 zeros
return str(value.normalize()) if trailing(uncast) > 4 else uncast
else:
# normalize values with decimal places
return str(value.normalize())
# or str(value).rstrip('0') if rounding edgecases are a concern
You could use :g to achieve this:
'{:g}'.format(3.140)
gives
'3.14'
This should work:
'{:f}'.format(decimal.Decimal('2.5') * 10).rstrip('0').rstrip('.')
Just to show a different possibility, I used to_tuple() to achieve the same result.
def my_normalize(dec):
"""
>>> my_normalize(Decimal("12.500"))
Decimal('12.5')
>>> my_normalize(Decimal("-0.12500"))
Decimal('-0.125')
>>> my_normalize(Decimal("0.125"))
Decimal('0.125')
>>> my_normalize(Decimal("0.00125"))
Decimal('0.00125')
>>> my_normalize(Decimal("125.00"))
Decimal('125')
>>> my_normalize(Decimal("12500"))
Decimal('12500')
>>> my_normalize(Decimal("0.000"))
Decimal('0')
"""
if dec is None:
return None
sign, digs, exp = dec.as_tuple()
for i in list(reversed(digs)):
if exp >= 0 or i != 0:
break
exp += 1
digs = digs[:-1]
if not digs and exp < 0:
exp = 0
return Decimal((sign, digs, exp))
Why not use modules 10 from a multiple of 10 to check if there is remainder? No remainder means you can force int()
if (x * 10) % 10 == 0:
x = int(x)
x = 2/1
Output: 2
x = 3/2
Output: 1.5

How to format a float with a maximum number of decimal places and without extra zero padding?

I need to do some decimal place formatting in python. Preferably, the floating point value should always show at least a starting 0 and one decimal place. Example:
Input: 0
Output: 0.0
Values with more decimal places should continue to show them, until it gets 4 out. So:
Input: 65.53
Output: 65.53
Input: 40.355435
Output: 40.3554
I know that I can use {0.4f} to get it to print out to four decimal places, but it will pad with unwanted 0s. Is there a formatting code to tell it to print out up to a certain number of decimals, but to leave them blank if there is no data? I believe C# accomplishes this with something like:
floatValue.ToString("0.0###")
Where the # symbols represent a place that can be left blank.
What you're asking for should be addressed by rounding methods like the built-in round function. Then let the float number be naturally displayed with its string representation.
>>> round(65.53, 4) # num decimal <= precision, do nothing
'65.53'
>>> round(40.355435, 4) # num decimal > precision, round
'40.3554'
>>> round(0, 4) # note: converts int to float
'0.0'
Sorry, the best I can do:
' {:0.4f}'.format(1./2.).rstrip('0')
Corrected:
ff=1./2.
' {:0.4f}'.format(ff).rstrip('0')+'0'[0:(ff%1==0)]
From trial and error I think :.15g is what you want:
In: f"{3/4:.15g}"
Out: '0.75'
In f"{355/113:.15g}"
Out: '3.14159292035398'
(while f"{3/4:.15f}" == '0.750000000000000')
>>> def pad(float, front = 0, end = 4):
s = '%%%s.%sf' % (front, end) % float
i = len(s)
while i > 0 and s[i - 1] == '0':
i-= 1
if s[i - 1] == '.' and len(s) > i:
i+= 1 # for 0.0
return s[:i] + ' ' * (len(s) - i)
>>> pad(0, 3, 4)
'0.0 '
>>> pad(65.53, 3, 4)
'65.53 '
>>> pad(40.355435, 3, 4)
'40.3554'

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