# Questions tagged [precision]

For questions related to numerical precision in programming. For classification precision use the tag [precision-recall].

precision

5,379
questions

3967
votes

36
answers

587k
views

### Is floating-point math broken?

Consider the following code:
0.1 + 0.2 == 0.3 -> false
0.1 + 0.2 -> 0.30000000000000004
Why do these inaccuracies happen?

2409
votes

36
answers

5.7m
views

### Limiting floats to two decimal points

I want a to be rounded to 13.95. I tried using round, but I get:
>>> a
13.949999999999999
>>> round(a, 2)
13.949999999999999
For the analogous issue with the standard library ...

1024
votes

7
answers

606k
views

### decimal vs double! - Which one should I use and when? [duplicate]

I keep seeing people using doubles in C#. I know I read somewhere that doubles sometimes lose precision.
My question is when should a use a double and when should I use a decimal type?
Which type is ...

539
votes

14
answers

1.2m
views

### What is the difference between float and double?

I've read about the difference between double precision and single precision. However, in most cases, float and double seem to be interchangeable, i.e. using one or the other does not seem to affect ...

505
votes

14
answers

619k
views

### JavaScript displaying a float to 2 decimal places

I wanted to display a number to 2 decimal places.
I thought I could use toPrecision(2) in JavaScript .
However, if the number is 0.05, I get 0.0500. I'd rather it stay the same.
See it on JSbin.
...

452
votes

16
answers

709k
views

### How do I print a double value with full precision using cout?

In my earlier question I was printing a double using cout that got rounded when I wasn't expecting it. How can I make cout print a double using full precision?

314
votes

4
answers

406k
views

### How do I interpret precision and scale of a number in a database?

I have the following column specified in a database: decimal(5,2)
How does one interpret this?
According to the properties on the column as viewed in SQL Server Management studio I can see that it ...

298
votes

29
answers

377k
views

### How do you round a double in Dart to a given degree of precision AFTER the decimal point?

Given a double, I want to round it to a given number of points of precision after the decimal point, similar to PHP's round() function.
The closest thing I can find in the Dart docs is double....

293
votes

12
answers

587k
views

### Get DateTime.Now with milliseconds precision

How can I exactly construct a time stamp of actual time with milliseconds precision?
I need something like 16.4.2013 9:48:00:123. Is this possible? I have an application, where I sample values 10 ...

261
votes

5
answers

87k
views

### Why are floating point numbers inaccurate?

Why do some numbers lose accuracy when stored as floating point numbers?
For example, the decimal number 9.2 can be expressed exactly as a ratio of two decimal integers (92/10), both of which can be ...

225
votes

14
answers

840k
views

### Printing the correct number of decimal places with cout

I have a list of float values and I want to print them with cout with 2 decimal places.
For example:
10.900 should be printed as 10.90
1.000 should be printed as 1.00
122.345 should be printed as ...

208
votes

11
answers

357k
views

### What's the difference between a single precision and double precision floating point operation?

What is the difference between a single precision floating point operation and double precision floating operation?
I'm especially interested in practical terms in relation to video game consoles. ...

196
votes

3
answers

11k
views

### Why is a round-trip conversion via a string not safe for a double?

Recently I have had to serialize a double into text, and then get it back. The value seems to not be equivalent:
double d1 = 0.84551240822557006;
string s = d1.ToString("R");
double d2 = double.Parse(...

194
votes

36
answers

29k
views

### Unexpected results when working with very big integers on interpreted languages

I am trying to get the sum of 1 + 2 + ... + 1000000000, but I'm getting funny results in PHP and Node.js.
PHP
$sum = 0;
for($i = 0; $i <= 1000000000 ; $i++) {
$sum += $i;
}
printf("%s", ...

187
votes

24
answers

266k
views

### Retain precision with double in Java

public class doublePrecision {
public static void main(String[] args) {
double total = 0;
total += 5.6;
total += 5.8;
System.out.println(total);
}
}
The above ...

169
votes

9
answers

80k
views

### Difference between toFixed() and toPrecision()?

I'm new to JavaScript and just discovered toFixed() and toPrecision() to round numbers. However, I can't figure out what the difference between the two is.
What is the difference between number....

164
votes

9
answers

398k
views

### Printf width specifier to maintain precision of floating-point value

Is there a printf width specifier which can be applied to a floating point specifier that would automatically format the output to the necessary number of significant digits such that when scanning ...

162
votes

10
answers

18k
views

### Is floating-point math consistent in C#? Can it be?

No, this is not another "Why is (1/3.0)*3 != 1" question.
I've been reading about floating-points a lot lately; specifically, how the same calculation might give different results on different ...

154
votes

3
answers

19k
views

### Why does adding 0.1 multiple times remain lossless?

I know the 0.1 decimal number cannot be represented exactly with a finite binary number (explanation), so double n = 0.1 will lose some precision and will not be exactly 0.1. On the other hand 0.5 can ...

153
votes

4
answers

328k
views

### Controlling number of decimal digits in print output in R

There is an option in R to get control over digit display. For example:
options(digits=10)
is supposed to give the calculation results in 10 digits till the end of R session. In the help file of R, ...

149
votes

13
answers

55k
views

### PHP7.1 json_encode() Float Issue

This isn't a question as it is more of a be aware. I updated an application that uses json_encode() to PHP7.1.1 and I was seeing an issue with floats being changed to sometimes extend out 17 digits. ...

138
votes

5
answers

524k
views

### Double precision floating values in Python?

Are there data types with better precision than float?

134
votes

24
answers

129k
views

### How to properly round-up half float numbers?

I am facing a strange behavior of the round() function:
for i in range(1, 15, 2):
n = i / 2
print(n, "=>", round(n))
This code prints:
0.5 => 0
1.5 => 2
2.5 => 2
3.5 => 4
4.5 ...

117
votes

6
answers

161k
views

### BigDecimal, precision and scale

I'm using BigDecimal for my numbers in my application, for example, with JPA. I did a bit of researching about the terms 'precision' and 'scale' but I don't understand what are they exactly.
Can ...

113
votes

11
answers

21k
views

### In which order should floats be added to get the most precise result?

This was a question I was asked at my recent interview and I want to know (I don't actually remember the theory of the numerical analysis, so please help me :)
If we have some function, which ...

113
votes

10
answers

90k
views

### Is it safe to check floating point values for equality to 0?

I know you can't rely on equality between double or decimal type values normally, but I'm wondering if 0 is a special case.
While I can understand imprecisions between 0.00000000000001 and 0....

110
votes

7
answers

67k
views

### C# DateTime.Now precision

I just ran into some unexpected behavior with DateTime.UtcNow while doing some unit tests. It appears that when you call DateTime.Now/UtcNow in rapid succession, it seems to give you back the same ...

105
votes

11
answers

116k
views

### Should I use double or float?

What are the advantages and disadvantages of using one instead of the other in C++?

104
votes

6
answers

13k
views

### How many double numbers are there between 0.0 and 1.0?

This is something that's been on my mind for years, but I never took the time to ask before.
Many (pseudo) random number generators generate a random number between 0.0 and 1.0. Mathematically there ...

99
votes

1
answer

282k
views

### Dividing two integers to produce a float result [duplicate]

Possible Duplicate:
Why can't I return a double from two ints being divided
My C++ program is truncating the output of my integer devision even when I try and place the output into a float. ...

96
votes

8
answers

62k
views

### PHP - Floating Number Precision [duplicate]

$a = '35';
$b = '-34.99';
echo ($a + $b);
Results in 0.009999999999998
What is up with that? I wondered why my program kept reporting odd results.
Why doesn't PHP return the expected 0.01?

89
votes

12
answers

14k
views

### Endless sine generation in C

I am working on a project which incorporates computing a sine wave as input for a control loop.
The sine wave has a frequency of 280 Hz, and the control loop runs every 30 µs and everything is written ...

88
votes

4
answers

82k
views

### What's the C++ suffix for long double literals?

In C++ (and C), a floating point literal without suffix defaults to double, while the suffix f implies a float. But what is the suffix to get a long double?
Without knowing, I would define, say,
...

87
votes

7
answers

109k
views

### What range of numbers can be represented in a 16-, 32- and 64-bit IEEE-754 systems?

I know a little bit about how floating-point numbers are represented, but not enough, I'm afraid.
The general question is:
For a given precision (for my purposes, the number of accurate decimal ...

86
votes

8
answers

92k
views

### Is there any way to get current time in nanoseconds using JavaScript?

So, I know I can get current time in milliseconds using JavaScript. But, is it possible to get the current time in nanoseconds instead?

83
votes

2
answers

6k
views

### Why is 199.96 - 0 = 200 in SQL?

I have some clients getting weird bills. I was able to isolate the core problem:
SELECT 199.96 - (0.0 * FLOOR(CAST(1.0 AS DECIMAL(19, 4)) * CAST(199.96 AS DECIMAL(19, 4)))) -- 200 what the?
SELECT ...

73
votes

2
answers

28k
views

### In MATLAB, are variables REALLY double-precision by default?

This question arose out of something strange that I noticed after investigating this question further...
I always understood MATLAB variables to be double-precision by default. So, if I were to do ...

72
votes

5
answers

26k
views

### Why is 24.0000 not equal to 24.0000 in MATLAB?

I am writing a program where I need to delete duplicate points stored in a matrix. The problem is that when it comes to check whether those points are in the matrix, MATLAB can't recognize them in the ...

72
votes

5
answers

24k
views

### Are all integer values perfectly represented as doubles? [duplicate]

My question is whether all integer values are guaranteed to have a perfect double representation.
Consider the following code sample that prints "Same":
// Example program
#include <iostream>
...

71
votes

8
answers

70k
views

### Adjusting decimal precision, .net

These lines in C#
decimal a = 2m;
decimal b = 2.0m;
decimal c = 2.00000000m;
decimal d = 2.000000000000000000000000000m;
Console.WriteLine(a);
Console.WriteLine(b);
Console.WriteLine(c);
Console....

70
votes

8
answers

17k
views

### Emulate "double" using 2 "float"s

I am writing a program for an embedded hardware that only supports 32-bit single-precision floating-point arithmetic. The algorithm I am implementing, however, requires a 64-bit double-precision ...

67
votes

4
answers

128k
views

### Python: Find index of minimum item in list of floats [duplicate]

How can I find the index of the minimum item in a Python list of floats? If they were integers, I would simply do:
minIndex = myList.index(min(myList))
However, with a list of floats I get the ...

67
votes

4
answers

118k
views

### Convert Java Number to BigDecimal : best way

I am looking for the best way to convert a Number to a BigDecimal.
Is this good enough?
Number number;
BigDecimal big = new BigDecimal(number.toString());
Can we lose precision with the toString() ...

63
votes

5
answers

88k
views

### Set the display precision of a float in Ruby

Is it possible to set the display precision of a float in Ruby?
Something like:
z = 1/3
z.to_s #=> 0.33333333333333
z.to_s(3) #=> 0.333
z.to_s(5) #=> 0.33333
Or do I have to override ...

63
votes

2
answers

6k
views

### Why does double in C print fewer decimal digits than C++?

I have this code in C where I've declared 0.1 as double.
#include <stdio.h>
int main() {
double a = 0.1;
printf("a is %0.56f\n", a);
return 0;
}
This is what it prints, a is 0....

59
votes

6
answers

140k
views

### Set specific precision of a BigDecimal

I have an XSD that requires me to use a BigDecimal for a lat/lon. I currently have the lat/lon as doubles, and convert them to BigDecimal, but I am only required to use about 12 places of precision. ...

59
votes

7
answers

148k
views

### Double precision - decimal places

From what I have read, a value of data type double has an approximate precision of 15 decimal places. However, when I use a number whose decimal representation repeats, such as 1.0/7.0, I find that ...

56
votes

10
answers

18k
views

### Are doubles faster than floats in C#?

I'm writing an application which reads large arrays of floats and performs some simple operations with them. I'm using floats, because I thought it'd be faster than doubles, but after doing some ...

54
votes

5
answers

75k
views

### How to calculate precision and recall in Keras

I am building a multi-class classifier with Keras 2.02 (with Tensorflow backend)，and I do not know how to calculate precision and recall in Keras. Please help me.