Hi I would like to dynamically adjust the displayed decimal places of a string representation of a floating point number, but i couldn't find any information on how to do it.
E.g:
precision = 8
n = 7.12345678911
str_n = '{0:.{precision}}'.format(n)
print(str_n) should display -> 7.12345678
But instead i'm getting a "KeyError". What am i missing?
You need to specify where precision in your format string comes from:
precision = 8
n = 7.12345678911
print('{0:.{precision}}'.format(n, precision=precision))
The first time, you specified which argument you'd like to be the number using an index ({0}), so the formatting function knows where to get the argument from, but when you specify a placeholder by some key, you have to explicitly specify that key.
It's a little unusual to mix these two systems, i'd recommend staying with one:
print('{number:.{precision}}'.format(number=n, precision=precision)) # most readable
print('{0:.{1}}'.format(n, precision))
print('{:.{}}'.format(n, precision)) # automatic indexing, least obvious
It is notable that these precision values will include the numbers before the point, so
>>> f"{123.45:.3}"
'1.23e+02'
will give drop drop the decimals and only give the first three digits of the number.
Instead, the f can be supplied to the type of the format (See the documentation) to get fixed-point formatting with precision decimal digits.
print('{number:.{precision}f}'.format(number=n, precision=precision)) # most readable
print('{0:.{1}f}'.format(n, precision))
print('{:.{}f}'.format(n, precision)) # automatic indexing, least obvious
In addition to #Talon, for those interested in f-strings, this also works.
precision = 8
n = 7.12345678911
print(f'{n:.{precision}f}')
Related
I'm dividing a very long into much smaller number. Both are of type decimal.Decimal().
The result is coming out in scientific notation. How do I stop this? I need to print the number in full.
>>> decimal.getcontext().prec
50
>>> val
Decimal('1000000000000000000000000')
>>> units
Decimal('1500000000')
>>> units / val
Decimal('1.5E-15')
The precision is kept internally - you just have to explicitly call for the number of decimal places you want at the point you are exporting your decimal value to a string.
So, if you are going a print, or inserting the value in an HTML template, the first step is to use the string format method (or f-strings), to ensure the number is encompassed:
In [29]: print(f"{units/val:.50f}")
0.00000000000000150000000000000000000000000000000000
Unfortunatelly, the string-format minilanguage has no way to eliminate by itself the redundant zeroes on the right hand side. (the left side can be padded with "0", " ", custom characters, whatever one want, but all the precision after the decimal separator is converted to trailing 0s).
Since finding the least significant non-zero digit is complicated - otherwiser we could use a parameter extracted from the number instead of the "50" for precision in the format expression, the simpler thing is to remove those zeros after formatting take place, with the string .rstrip method:
In [30]: print(f"{units/val:.50f}".rstrip("0"))
0.0000000000000015
In short: this seems to be the only way to go: in all interface points, where the number is leaving the core to an output where it is representd as a string, you format it with an excess of precision with the fixed point notation, and strip out the tailing zeros with f-string:
return template.render(number=f"{number:.50f}".rstrip("0"), ...)
Render the decimal into a formatted string with a float type-indicator {:,f}, and it will display just the right number of digits to express the whole number, regardless of whether it is a very large integer or a very large decimal.
>>> val
Decimal('1000000000000000000000000')
>>> units
Decimal('1500000000')
>>> "{:,f}".format(units / val)
'0.0000000000000015'
# very large decimal integer, formatted as float-type string, appears without any decimal places at all when it has none! Nice!
>>> "{:,f}".format(units * val)
'1,500,000,000,000,000,000,000,000,000,000,000'
You don't need to specify the decimal places. It will display only as many as required to express the number, omitting that trail of useless zeros that appear after the final decimal digit when the decimal is shorter than a fixed format width. And you don't get any decimal places if the number has no fraction part.
Very large numbers are therefore accommodated without having to second guess how large they will be. And you don't have to second guess whether they will be have decimal places either.
Any specified thousands separator {:,f} will likewise only have effect if it turns out that the number is a large integer instead of a long decimal.
Proviso
Decimal(), however, has this idea of significant places, by which it will add trailing zeros if it thinks you want them.
The idea is that it intelligently handles situations where you might be dealing with currency digits such as £ 10.15. To use the example from the documentation:
>>> decimal.Decimal('1.30') + decimal.Decimal('1.20')
Decimal('2.50')
It makes no difference if you format the Decimal() - you still get the trailing zero if the Decimal() deems it to be significant:
>>> "{:,f}".format( decimal.Decimal('1.30') + decimal.Decimal('1.20'))
'2.50'
The same thing happens (perhaps for some good reason?) when you treat thousands and fractions together:
>>> decimal.Decimal(2500) * decimal.Decimal('0.001')
Decimal('2.500')
Remove significant trailing zeros with the Decimal().normalize() method:
>>> (2500 * decimal.Decimal('0.001')).normalize()
Decimal('2.5')
I'm really curious about why the behaviour is so different when add this "f" to the end of the number which I want to display:
# CASE with f
float1 = 10.1444786
print(f"{float1:.4f}")
# print out: 10.1445
# CASE without f
print(f"{float1:.4}")
# print out: 10.14
Why only 2 characters are displayed in the second example?
The implied type specifier is g, as given in the documentation Thanks #Barmar for adding a comment with this info!
None: For float this is the same as 'g', except that when fixed-point notation is used to format the result, it always includes at least one digit past the decimal point. The precision used is as large as needed to represent the given value faithfully.
For Decimal, this is the same as either 'g' or 'G' depending on the value of context.capitals for the current decimal context.
The overall effect is to match the output of str() as altered by the other format modifiers.
An experiment:
for _ in range(10000):
r = random.random() * random.randint(1, 10)
assert f"{r:.6}" == f"{r:.6g}"
Works every time
From https://docs.python.org/3/library/string.html#formatstrings,
General format. For a given precision p >= 1, this rounds the number to p significant digits and then formats the result in either fixed-point format or in scientific notation, depending on its magnitude. A precision of 0 is treated as equivalent to a precision of 1.
So in your second example, you ask for 4 sigfigs, but in your first you ask for 4 digits of precision.
Unfortunately the printing instruction of a code was written without an end-of-the-line character and one every 26 numbers consists of two numbers joined together. The following is a code that shows an example of such behaviour; at the end there is a fragment of the original database.
import numpy as np
for _ in range(2):
A=np.random.rand()+np.random.randint(0,100)
B=np.random.rand()+np.random.randint(0,100)
C=np.random.rand()+np.random.randint(0,100)
D=np.random.rand()+np.random.randint(0,100)
with open('file.txt','a') as f:
f.write(f'{A},{B},{C},{D}')
And thus the output example file looks very similar to what follows:
40.63358599010553,53.86722741700399,21.800795158561158,13.95828176311762557.217562728494684,2.626308403991772,4.840593988487278,32.401778122213486
With the issue being that there are two numbers 'printed together', in the example they were as follows:
13.95828176311762557.217562728494684
So you cannot know if they should be
13.958281763117625, 57.217562728494684
or
13.9582817631176255, 7.217562728494684
Please understand that in this case they are only two options, but the problem that I want to address considers 'unbounded numbers' which are type Python's "float" (where 'unbounded' means in a range we don't know e.g. in the range +- 1E4)
Can the original numbers be reconstructed based on "some" python internal behavior I'm missing?
Actual data with periodicity 27 (i.e. the 26th number consists of 2 joined together):
0.9221878978925224, 0.9331311610066017,0.8600582424784715,0.8754578588852764,0.8738648974725404, 0.8897837559800233,0.6773502027673041,0.736325377603136,0.7956454122424133, 0.8083168444596229,0.7089031184165164, 0.7475306242508357,0.9702361286847581, 0.9900689384633811,0.7453878225174624, 0.7749000030576826,0.7743879170108678, 0.8032590543649807,0.002434,0.003673,0.004194,0.327903,11.357262,13.782266,20.14374,31.828905,33.9260060.9215201173775437, 0.9349343132442707,0.8605282244327555,0.8741626682026793,0.8742163597524663, 0.8874673376386358,0.7109322043854609,0.7376362393985332,0.796158275345
To expand my comment into an actual answer:
We do have some information - An IEEE-754 standard float only has 32 bits of precision, some of which is taken up by the mantissa (not all numbers can be represented by a float). For datasets like yours, they're brushing up against the edge of that precision.
We can make that work for us - we just need to test whether the number can, in fact, be represented by a float, at each possible split point. We can abuse strings for this, by testing num_str == str(float(num_str)) (i.e. a string remains the same after being converted to a float and back to a string)
If your number is able to be represented exactly by the IEEE float standard, then the before and after will be equal
If the number cannot be represented exactly by the IEEE float standard, it will be coerced into the nearest number that the float can represent. Obviously, if we then convert this back to a string, will not be identical to the original.
Here's a snippet, for example, that you can play around with
def parse_number(s: str) -> List[float]:
if s.count('.') == 2:
first_decimal = s.index('.')
second_decimal = s[first_decimal + 1:].index('.') + first_decimal + 1
split_idx = second_decimal - 1
for i in range(second_decimal - 1, first_decimal + 1, -1):
a, b = s[:split_idx], s[split_idx:]
if str(float(a)) == a and str(float(b)) == b:
return [float(a), float(b)]
# default to returning as large an a as possible
return [float(s[:second_decimal - 1]), float(s[second_decimal - 1:])]
else:
return [float(s)]
parse_number('33.9260060.9215201173775437')
# [33.926006, 0.9215201173775437]
# this is the only possible combination that actually works for this particular input
Obviously this isn't foolproof, and for some numbers there may not be enough information to differentiate the first number from the second. Additionally, for this to work, the tool that generated your data needs to have worked with IEEE standards-compliant floats (which does appear to be the case in this example, but may not be if the results were generated using a class like Decimal (python) or BigDecimal (java) or something else).
Some inputs might also have multiple possibilities. In the above snippet I've biased it to take the longest possible [first number], but you could modify it to go in the opposite order and instead take the shortest possible [first number].
Yes, you have one available weapon: you're using the default precision to display the numbers. In the example you cite, there are 15 digits after the decimal point, making it easy to reconstruct the original numbers.
Let's take a simple case, where you have only 3 digits after the decimal point. It's trivial to separate
13.95857.217
The formatting requires a maximum of 2 digits before the decimal point, and three after.
Any case that has five digits between the points, is trivial to split.
13.958 57.217
However, you run into the "trailing zero" problem in some cases. If you see, instead
13.9557.217
This could be either
13.950 57.217
or
13.955 07.217
Your data do not contain enough information to differentiate the two cases.
I have some number 0.0000002345E^-60. I want to print the floating point value as it is.
What is the way to do it?
print %f truncates it to 6 digits. Also %n.nf gives fixed numbers. What is the way to print without truncation.
Like this?
>>> print('{:.100f}'.format(0.0000002345E-60))
0.0000000000000000000000000000000000000000000000000000000000000000002344999999999999860343602938602754
As you might notice from the output, it’s not really that clear how you want to do it. Due to the float representation you lose precision and can’t really represent the number precisely. As such it’s not really clear where you want the number to stop displaying.
Also note that the exponential representation is often used to more explicitly show the number of significant digits the number has.
You could also use decimal to not lose the precision due to binary float truncation:
>>> from decimal import Decimal
>>> d = Decimal('0.0000002345E-60')
>>> p = abs(d.as_tuple().exponent)
>>> print(('{:.%df}' % p).format(d))
0.0000000000000000000000000000000000000000000000000000000000000000002345
You can use decimal.Decimal:
>>> from decimal import Decimal
>>> str(Decimal(0.0000002345e-60))
'2.344999999999999860343602938602754401109865640550232148836753621775217856801120686600683401464097113374472942165409862789978024748827516129306833728589548440037314681709534891496105046826414763927459716796875E-67'
This is the actual value of float created by literal 0.0000002345e-60. Its value is a number representable as python float which is closest to actual 0.0000002345 * 10**-60.
float should be generally used for approximate calculations. If you want accurate results you should use something else, like mentioned Decimal.
If I understand, you want to print a float?
The problem is, you cannot print a float.
You can only print a string representation of a float. So, in short, you cannot print a float, that is your answer.
If you accept that you need to print a string representation of a float, and your question is how specify your preferred format for the string representations of your floats, then judging by the comments you have been very unclear in your question.
If you would like to print the string representations of your floats in exponent notation, then the format specification language allows this:
{:g} or {:G}, depending whether or not you want the E in the output to be capitalized). This gets around the default precision for e and E types, which leads to unwanted trailing 0s in the part before the exponent symbol.
Assuming your value is my_float, "{:G}".format(my_float) would print the output the way that the Python interpreter prints it. You could probably just print the number without any formatting and get the same exact result.
If your goal is to print the string representation of the float with its current precision, in non-exponentiated form, User poke describes a good way to do this by casting the float to a Decimal object.
If, for some reason, you do not want to do this, you can do something like is mentioned in this answer. However, you should set 'max_digits' to sys.float_info.max_10_exp, instead of 14 used in the answer. This requires you to import sys at some point prior in the code.
A full example of this would be:
import math
import sys
def precision_and_scale(x):
max_digits = sys.float_info.max_10_exp
int_part = int(abs(x))
magnitude = 1 if int_part == 0 else int(math.log10(int_part)) + 1
if magnitude >= max_digits:
return (magnitude, 0)
frac_part = abs(x) - int_part
multiplier = 10 ** (max_digits - magnitude)
frac_digits = multiplier + int(multiplier * frac_part + 0.5)
while frac_digits % 10 == 0:
frac_digits /= 10
scale = int(math.log10(frac_digits))
return (magnitude + scale, scale)
f = 0.0000002345E^-60
p, s = precision_and_scale(f)
print "{:.{p}f}".format(f, p=p)
But I think the method involving casting to Decimal is probably better, overall.
So, this may be a simple question but I'm having some trouble finding the answer anywhere.
Take for example I have a simple program where I want to divide a by b like so:
def main():
a = 12345678900000000
b = 1.25
answer = (a / b)
print(answer)
main()
This particular example would result in 9.87654312e+15. How do I get Python to ignore simplifying my number and just give me the whole number?
Thanks in advance, sorry if it's really basic, I wouldn't have asked if I could have found it through Google.
You are seeing the default str() conversion for floating point numbers at work. You can pick a different conversion by formatting the number explicitly.
The format() function can do this for you:
>>> n = 9.87654312e+15
>>> format(n, 'f')
'9876543120000000.000000'
See the Format Specification Mini-Language documentation for more options. The 'f' format is but one of several:
Fixed point. Displays the number as a fixed-point number. The default precision is 6.
The default precision resulting in the .000000 six digits after the decimal point; you can alter this by using .<precision>f instead:
>>> format(n, '.1f')
'9876543120000000.0'
but take into account that decimals are rounded to fit the requested precision.
The g format switches between using exponents (e) and f notation, depending on the size of the number, but won't include decimals if the number is whole; you could use a very large precision with 'g' to avoid printing decimals altogether:
>>> format(n, '.53g')
'9876543120000000'
To be explicit, str(n) is the same as format(n, '.12g'), repr(n) is format(n, '.17g'); both can use the exponent format when the exponent is larger than the precision.
just be more specific about the floating point format
>>> print answer
9.87654312e+15
>>> print "%.20f" % answer
9876543120000000.00000000000000000000