How can I round a float value (such as 37.777779) to two decimal places (37.78) in C?
If you just want to round the number for output purposes, then the "%.2f" format string is indeed the correct answer. However, if you actually want to round the floating point value for further computation, something like the following works:
#include <math.h>
float val = 37.777779;
float rounded_down = floorf(val * 100) / 100; /* Result: 37.77 */
float nearest = roundf(val * 100) / 100; /* Result: 37.78 */
float rounded_up = ceilf(val * 100) / 100; /* Result: 37.78 */
Notice that there are three different rounding rules you might want to choose: round down (ie, truncate after two decimal places), rounded to nearest, and round up. Usually, you want round to nearest.
As several others have pointed out, due to the quirks of floating point representation, these rounded values may not be exactly the "obvious" decimal values, but they will be very very close.
For much (much!) more information on rounding, and especially on tie-breaking rules for rounding to nearest, see the Wikipedia article on Rounding.
Using %.2f in printf. It only print 2 decimal points.
Example:
printf("%.2f", 37.777779);
Output:
37.77
Assuming you're talking about round the value for printing, then Andrew Coleson and AraK's answer are correct:
printf("%.2f", 37.777779);
But note that if you're aiming to round the number to exactly 37.78 for internal use (eg to compare against another value), then this isn't a good idea, due to the way floating point numbers work: you usually don't want to do equality comparisons for floating point, instead use a target value +/- a sigma value. Or encode the number as a string with a known precision, and compare that.
See the link in Greg Hewgill's answer to a related question, which also covers why you shouldn't use floating point for financial calculations.
How about this:
float value = 37.777779;
float rounded = ((int)(value * 100 + .5) / 100.0);
printf("%.2f", 37.777779);
If you want to write to C-string:
char number[24]; // dummy size, you should take care of the size!
sprintf(number, "%.2f", 37.777779);
Always use the printf family of functions for this. Even if you want to get the value as a float, you're best off using snprintf to get the rounded value as a string and then parsing it back with atof:
#include <math.h>
#include <stdio.h>
#include <stddef.h>
#include <stdlib.h>
double dround(double val, int dp) {
int charsNeeded = 1 + snprintf(NULL, 0, "%.*f", dp, val);
char *buffer = malloc(charsNeeded);
snprintf(buffer, charsNeeded, "%.*f", dp, val);
double result = atof(buffer);
free(buffer);
return result;
}
I say this because the approach shown by the currently top-voted answer and several others here -
multiplying by 100, rounding to the nearest integer, and then dividing by 100 again - is flawed in two ways:
For some values, it will round in the wrong direction because the multiplication by 100 changes the decimal digit determining the rounding direction from a 4 to a 5 or vice versa, due to the imprecision of floating point numbers
For some values, multiplying and then dividing by 100 doesn't round-trip, meaning that even if no rounding takes place the end result will be wrong
To illustrate the first kind of error - the rounding direction sometimes being wrong - try running this program:
int main(void) {
// This number is EXACTLY representable as a double
double x = 0.01499999999999999944488848768742172978818416595458984375;
printf("x: %.50f\n", x);
double res1 = dround(x, 2);
double res2 = round(100 * x) / 100;
printf("Rounded with snprintf: %.50f\n", res1);
printf("Rounded with round, then divided: %.50f\n", res2);
}
You'll see this output:
x: 0.01499999999999999944488848768742172978818416595459
Rounded with snprintf: 0.01000000000000000020816681711721685132943093776703
Rounded with round, then divided: 0.02000000000000000041633363423443370265886187553406
Note that the value we started with was less than 0.015, and so the mathematically correct answer when rounding it to 2 decimal places is 0.01. Of course, 0.01 is not exactly representable as a double, but we expect our result to be the double nearest to 0.01. Using snprintf gives us that result, but using round(100 * x) / 100 gives us 0.02, which is wrong. Why? Because 100 * x gives us exactly 1.5 as the result. Multiplying by 100 thus changes the correct direction to round in.
To illustrate the second kind of error - the result sometimes being wrong due to * 100 and / 100 not truly being inverses of each other - we can do a similar exercise with a very big number:
int main(void) {
double x = 8631192423766613.0;
printf("x: %.1f\n", x);
double res1 = dround(x, 2);
double res2 = round(100 * x) / 100;
printf("Rounded with snprintf: %.1f\n", res1);
printf("Rounded with round, then divided: %.1f\n", res2);
}
Our number now doesn't even have a fractional part; it's an integer value, just stored with type double. So the result after rounding it should be the same number we started with, right?
If you run the program above, you'll see:
x: 8631192423766613.0
Rounded with snprintf: 8631192423766613.0
Rounded with round, then divided: 8631192423766612.0
Oops. Our snprintf method returns the right result again, but the multiply-then-round-then-divide approach fails. That's because the mathematically correct value of 8631192423766613.0 * 100, 863119242376661300.0, is not exactly representable as a double; the closest value is 863119242376661248.0. When you divide that back by 100, you get 8631192423766612.0 - a different number to the one you started with.
Hopefully that's a sufficient demonstration that using roundf for rounding to a number of decimal places is broken, and that you should use snprintf instead. If that feels like a horrible hack to you, perhaps you'll be reassured by the knowledge that it's basically what CPython does.
Also, if you're using C++, you can just create a function like this:
string prd(const double x, const int decDigits) {
stringstream ss;
ss << fixed;
ss.precision(decDigits); // set # places after decimal
ss << x;
return ss.str();
}
You can then output any double myDouble with n places after the decimal point with code such as this:
std::cout << prd(myDouble,n);
There isn't a way to round a float to another float because the rounded float may not be representable (a limitation of floating-point numbers). For instance, say you round 37.777779 to 37.78, but the nearest representable number is 37.781.
However, you can "round" a float by using a format string function.
You can still use:
float ceilf(float x); // don't forget #include <math.h> and link with -lm.
example:
float valueToRound = 37.777779;
float roundedValue = ceilf(valueToRound * 100) / 100;
In C++ (or in C with C-style casts), you could create the function:
/* Function to control # of decimal places to be output for x */
double showDecimals(const double& x, const int& numDecimals) {
int y=x;
double z=x-y;
double m=pow(10,numDecimals);
double q=z*m;
double r=round(q);
return static_cast<double>(y)+(1.0/m)*r;
}
Then std::cout << showDecimals(37.777779,2); would produce: 37.78.
Obviously you don't really need to create all 5 variables in that function, but I leave them there so you can see the logic. There are probably simpler solutions, but this works well for me--especially since it allows me to adjust the number of digits after the decimal place as I need.
Use float roundf(float x).
"The round functions round their argument to the nearest integer value in floating-point format, rounding halfway cases away from zero, regardless of the current rounding direction." C11dr §7.12.9.5
#include <math.h>
float y = roundf(x * 100.0f) / 100.0f;
Depending on your float implementation, numbers that may appear to be half-way are not. as floating-point is typically base-2 oriented. Further, precisely rounding to the nearest 0.01 on all "half-way" cases is most challenging.
void r100(const char *s) {
float x, y;
sscanf(s, "%f", &x);
y = round(x*100.0)/100.0;
printf("%6s %.12e %.12e\n", s, x, y);
}
int main(void) {
r100("1.115");
r100("1.125");
r100("1.135");
return 0;
}
1.115 1.115000009537e+00 1.120000004768e+00
1.125 1.125000000000e+00 1.129999995232e+00
1.135 1.134999990463e+00 1.139999985695e+00
Although "1.115" is "half-way" between 1.11 and 1.12, when converted to float, the value is 1.115000009537... and is no longer "half-way", but closer to 1.12 and rounds to the closest float of 1.120000004768...
"1.125" is "half-way" between 1.12 and 1.13, when converted to float, the value is exactly 1.125 and is "half-way". It rounds toward 1.13 due to ties to even rule and rounds to the closest float of 1.129999995232...
Although "1.135" is "half-way" between 1.13 and 1.14, when converted to float, the value is 1.134999990463... and is no longer "half-way", but closer to 1.13 and rounds to the closest float of 1.129999995232...
If code used
y = roundf(x*100.0f)/100.0f;
Although "1.135" is "half-way" between 1.13 and 1.14, when converted to float, the value is 1.134999990463... and is no longer "half-way", but closer to 1.13 but incorrectly rounds to float of 1.139999985695... due to the more limited precision of float vs. double. This incorrect value may be viewed as correct, depending on coding goals.
Code definition :
#define roundz(x,d) ((floor(((x)*pow(10,d))+.5))/pow(10,d))
Results :
a = 8.000000
sqrt(a) = r = 2.828427
roundz(r,2) = 2.830000
roundz(r,3) = 2.828000
roundz(r,5) = 2.828430
double f_round(double dval, int n)
{
char l_fmtp[32], l_buf[64];
char *p_str;
sprintf (l_fmtp, "%%.%df", n);
if (dval>=0)
sprintf (l_buf, l_fmtp, dval);
else
sprintf (l_buf, l_fmtp, dval);
return ((double)strtod(l_buf, &p_str));
}
Here n is the number of decimals
example:
double d = 100.23456;
printf("%f", f_round(d, 4));// result: 100.2346
printf("%f", f_round(d, 2));// result: 100.23
I made this macro for rounding float numbers.
Add it in your header / being of file
#define ROUNDF(f, c) (((float)((int)((f) * (c))) / (c)))
Here is an example:
float x = ROUNDF(3.141592, 100)
x equals 3.14 :)
Let me first attempt to justify my reason for adding yet another answer to this question. In an ideal world, rounding is not really a big deal. However, in real systems, you may need to contend with several issues that can result in rounding that may not be what you expect. For example, you may be performing financial calculations where final results are rounded and displayed to users as 2 decimal places; these same values are stored with fixed precision in a database that may include more than 2 decimal places (for various reasons; there is no optimal number of places to keep...depends on specific situations each system must support, e.g. tiny items whose prices are fractions of a penny per unit); and, floating point computations performed on values where the results are plus/minus epsilon. I have been confronting these issues and evolving my own strategy over the years. I won't claim that I have faced every scenario or have the best answer, but below is an example of my approach so far that overcomes these issues:
Suppose 6 decimal places is regarded as sufficient precision for calculations on floats/doubles (an arbitrary decision for the specific application), using the following rounding function/method:
double Round(double x, int p)
{
if (x != 0.0) {
return ((floor((fabs(x)*pow(double(10.0),p))+0.5))/pow(double(10.0),p))*(x/fabs(x));
} else {
return 0.0;
}
}
Rounding to 2 decimal places for presentation of a result can be performed as:
double val;
// ...perform calculations on val
String(Round(Round(Round(val,8),6),2));
For val = 6.825, result is 6.83 as expected.
For val = 6.824999, result is 6.82. Here the assumption is that the calculation resulted in exactly 6.824999 and the 7th decimal place is zero.
For val = 6.8249999, result is 6.83. The 7th decimal place being 9 in this case causes the Round(val,6) function to give the expected result. For this case, there could be any number of trailing 9s.
For val = 6.824999499999, result is 6.83. Rounding to the 8th decimal place as a first step, i.e. Round(val,8), takes care of the one nasty case whereby a calculated floating point result calculates to 6.8249995, but is internally represented as 6.824999499999....
Finally, the example from the question...val = 37.777779 results in 37.78.
This approach could be further generalized as:
double val;
// ...perform calculations on val
String(Round(Round(Round(val,N+2),N),2));
where N is precision to be maintained for all intermediate calculations on floats/doubles. This works on negative values as well. I do not know if this approach is mathematically correct for all possibilities.
...or you can do it the old-fashioned way without any libraries:
float a = 37.777779;
int b = a; // b = 37
float c = a - b; // c = 0.777779
c *= 100; // c = 77.777863
int d = c; // d = 77;
a = b + d / (float)100; // a = 37.770000;
That of course if you want to remove the extra information from the number.
this function takes the number and precision and returns the rounded off number
float roundoff(float num,int precision)
{
int temp=(int )(num*pow(10,precision));
int num1=num*pow(10,precision+1);
temp*=10;
temp+=5;
if(num1>=temp)
num1+=10;
num1/=10;
num1*=10;
num=num1/pow(10,precision+1);
return num;
}
it converts the floating point number into int by left shifting the point and checking for the greater than five condition.
Below is the code I've tested in a 64-bit environment and 32-bit. The result is off by one precisely each time. The expected result is: 1180000000 with the actual result being 1179999999. I'm not sure exactly why and I was hoping someone could educate me:
#include <stdint.h>
#include <iostream>
using namespace std;
int main() {
double odds = 1.18;
int64_t st = 1000000000;
int64_t res = st * odds;
cout << "result: " << res << endl;
return 1;
}
I appreciate any feedback.
1.18, or 118 / 100 can't be exactly represented in binary, it will have repeating decimals. The same happens if you write 1 / 3 in decimal.
So let's go over a similar case in decimal, let's calculate (1 / 3) × 30000, which of course should be 10000:
odds = 1 / 3 and st = 30000
Since computers have only a limited precision we have to truncate this number to a limited number of decimals, let's say 6, so:
odds = 0.333333
0.333333 × 10000 = 9999.99. The cast (which in your program is implicit) will truncate this number to 9999.
There is no 100% reliable way to work around this. float and double just have only limited precision. Dealing with this is a hard problem.
Your program contains an implicit cast from double to an integer on the line int64_t res = st * odds;. Many compilers will warn you about this. It can be the source of bugs of the type you are describing. This cast, which can be explicitly written as (int64_t) some_double, rounds the number towards zero.
An alternative is rounding to the nearest integer with round(some_double);. That will—in this case—give the expected result.
First of all - 1.18 is not exactly representable in double. Mathematically the result of:
double odds = 1.18;
is 1.17999999999999993782751062099 (according to an online calculator).
So, mathematically, odds * st is 1179999999.99999993782751062099.
But in C++, odds * st is an expression with type double. So your compiler has two options for implementing this:
Do the computation in double precision
Do the computation in higher precision and then round the result to double
Apparently, doing the computation in double precision in IEEE754 results in exactly 1180000000.
However, doing it in long double precision produces something more like 1179999999.99999993782751062099
Converting this to double is now implementation-defined as to whether it selects the next-highest or next-lowest value, but I believe it is typical for the next-lowest to be selected.
Then converting this next-lowest result to integer will truncate the fractional part.
There is an interesting blog post here where the author describes the behaviour of GCC:
It uses long double intermediate precision for x86 code (due to the x87 FPUs long double registers)
It uses actual types for x64 code (because the SSE/SSE2 FPU supports this more naturally)
According to the C++11 standard you should be able to inspect which intermediate precision is being used by outputting FLT_EVAL_METHOD from <cfloat>. 0 would mean actual values, 2 would mean long double is being used.
This code is calculating the Nth term of a series which is defined as
Tn+2=(Tn+1)^2+Tn, where 1st and 2nd terms are given as a and b in the code.
#include<iostream>
#include<string>
using namespace std;
int main()
{
int a,b,n;
char ch[100];
cin>>a>>b>>n;
long double res[3];
res[0]=a,res[1]=b;
for(int i=n-2;i>0;i--)
{
res[2]=res[1]*res[1]+res[0];
res[0]=res[1];
res[1]=res[2];
}
sprintf(ch,"%.0Lf",res[2]);
cout<<ch;
return 0;
}
Input: 0 1 10
Output:
84266613096281242861568 // in case of double res[3];
84266613096281243385856 // in case of long double res[3];
correct output : 84266613096281243382112
Since it is going out of the range of integer, therefore I am using double/long double.
But the problem is I am getting different output for double and long double, while none of the intermediate values are having non zero digit after decimal point, so there should not be any rounding off, I guess.
while none of the intermediate values are having non zero digit after decimal point, so there should not be any rounding off, I guess.
This assumption is just plain wrong. All floating point numbers like double etc. are stored like
mantissa * 2^exponent
with a finite number of bits for both the mantissa and the exponent. So floating point numbers can store a fixed number of significant digits (for a double converted to decimal representation, around 16 usually). If a number has more digits before the decimal point, rounding will happen and the total rounding error gets bigger the more digits you need to "forget".
If you want more details on this, the most common floating point implementations follow the IEEE floating point standard.
This question already has answers here:
Precision loss with double C++
(4 answers)
Closed 9 years ago.
So I have the following code
int main(){
double d;
cin>>d;
while(d!=0.00)
{
cout<<d<<endl;
double m = 100*d;
int n = m;
cout<<n<<endl;
cin>>d;
}
return 0;}
When I enter the input 20.40 for d the value of n comes out to be 2039 instead of 2040.
I tried replacing int n = m with int n = (int) m but the result was the same.
Is there any way to fix this. Thanks in advance.
Your code truncates m but you need rounding. Include cmath and use int n = round(m).
Decimal values can, in general, not be represented exactly using binary floating points like double. Thus, the value 20.40 is represented as an approximation which can be used to restore the original value (20.4; the precision cannot be retained), e.g., when formatting the value. Doing computations with these approximated values will typically amplify the error.
As already mentioned in one of the comments, the relevant reference is the paper "What Every Computer Scientist Should Know About Floating-Point Arithmetic". One potential way out of your trouble is to use decimal floating points which are, however, not yet part of the C++ standard.
Single and double presicion floating point numbers are not stored the same way as integers, so whole numbers (e.g. 5, 10) may actually look like long decimals (e.g. 4.9999001, 10.000000001). When you cast to an int, all it does is truncate the whole number. So, if the number is currently represented as 4.999999999, casting it to an int will give you 4. std::round will provide you with a better result most of the time (if the number is 4.6 and you just want the whole number portion, round will not work well). The bigger question is then: what are you hoping to accomplish by casting a double to an int?
In general, when dealing with floating point numbers, you will want to use some epsilon value that is your minimum significant digits. So if you wanted to compare 4.9999999 to 5, you would do (pseudo-code): if abs(5 - 4.9999999) < epsilon, return 5.
Example
int main()
{
double d;
std::cin >> d;
while (std::fabs(d - 0.0) > DBL_EPSILON)
{
std::cout << d << std::endl;
double m = 100 * d;
int n = static_cast<int>(m);
if (std::fabs(static_cast<double>(n) - m) > DBL_EPSILON)
{
n++;
}
std::cout << n << std::endl;
std::cin >> d;
}
return 0;
}
Casting double to int truncates value so 20.40 is probably 20.399999 * 100 is 2039.99 because double is not base 10. You can use round() function that will not truncate but will get you nearest int.
int n = round(m);
Floating point numbers can't exactly represent all decimal numbers, sometimes an approximation is used. In your example the closest possible exact number is 20.39999999999999857891452847979962825775146484375. See IEEE-754 Analysis for a quick way to see exact values.
You can use rounding, but presumably you're really looking for the first two digits truncated. Just add a really small value, e.g. 0.0000000001 before or after you multiply.
This question already has answers here:
Write your own implementation of math's floor function, C
(5 answers)
Closed 1 year ago.
I would like to know how to write my own floor function to round a float down.
Is it possible to do this by setting the bits of a float that represent the numbers after the comma to 0?
If yes, then how can I access and modify those bits?
Thanks.
You can do bit twiddling on floating point numbers, but getting it right depends on knowing exactly what the floating point binary representation is. For most machines these days its IEEE-754, which is reasonably straight-forward. For example IEEE-754 32-bit floats have 1 sign bit, 8 exponent bits, and 23 mantissa bits, so you can use shifts and masks to extract those fields and do things with them. So doing trunc (round to integer towards 0) is pretty easy:
float trunc(float x) {
union {
float f;
uint32_t i;
} val;
val.f = x;
int exponent = (val.i >> 23) & 0xff; // extract the exponent field;
int fractional_bits = 127 + 23 - exponent;
if (fractional_bits > 23) // abs(x) < 1.0
return 0.0;
if (fractional_bits > 0)
val.i &= ~((1U << fractional_bits) - 1);
return val.f;
}
First, we extract the exponent field, and use that to calculate how many bits after the
decimal point are present in the number. If there are more than the size of the mantissa, then we just return 0. Otherwise, if there's at least 1, we mask off (clear) that many low bits. Pretty simple. We're ignoring denormal, NaN, and infinity her, but that works out ok, as they have exponents of all 0s or all 1s, which means we end up converting denorms to 0 (they get caught in the first if, along with small normal numbers), and leaving NaN/Inf unchanged.
To do a floor, you'd also need to look at the sign, and rounds negative numbers 'up' towards negative infinity.
Note that this is almost certainly slower than using dedicated floating point intructions, so this sort of thing is really only useful if you need to use floating point numbers on hardware that has no native floating point support. Or if you just want to play around and learn how these things work at a low level.
Define from scratch. And no, setting the bits of your floating point number representing the numbers after the comma to 0 will not work. If you look at IEEE-754, you will see that you basically have all your floating-point numbers in the form:
0.xyzxyzxyz 2^(abc)
So to implement flooring, you can get the xyzxyzxyz and shift left by abc+1 times. Drop the rest. I suggest you read up on the binary representation of a floating point number (link above), this should shed light on the solution I suggested.
NOTE: You also need to take care of the sign bit. And the mantissa of your number is off by 127.
Here is an example, Let's say you have the number pi: 3.14..., you want to get 3.
Pi is represented in binary as
0 10000000 10010010000111111011011
This translate to
sign = 0 ; e = 1 ; s = 110010010000111111011011
The above I get directly from Wikipedia. Since e is 1. You will want to shift left s by 1 + 1 = 2, so you get 11 => 3.
#include <iostream>
#include <iomanip>
double round(double input, double roundto) {
return int(input / roundto) * roundto;
}
int main() {
double pi = 3.1415926353898;
double almostpi = round(pi, 0.0001);
std::cout << std::setprecision(14) << pi << '\n' << std::setprecision(14) << almostpi;
}
http://ideone.com/mdqFA
output:
3.1415926353898
3.1415
This will pretty much be faster than any bit twiddling you can come up with. And it works on all computers (with floats) instead of just one type.
Casting to unsigned while returning as a double does what you are seeking, but under the hood. This simple piece of code works for any POSITIVE number.
#include <iostream>
double floor(const double& num) {
return (unsigned long long) num;
}
This has been tested on tio.run (Try It Online) and onlinegdb.com. The function itself doesn't require any #include files, but to print out the answers, I have included stdio.h (in the tio.run and onlinegdb.com, not here). Here it is:
long double myFloor(long double x) /* Change this to your liking: long double might
be float in your situation. */
{
long double xcopy=x<0?x*-1:x;
unsigned int zeros=0;
long double n=1;
for(n=1;xcopy>n*10;n*=10,++zeros);
for(xcopy-=n;zeros!=-1;xcopy-=n)
if(xcopy<0)
{
xcopy+=n;
n/=10;
--zeros;
}
xcopy+=n;
return x<0?(xcopy==0?x:x-(1-xcopy)):(x-xcopy);
}
This function works everywhere (pretty sure) because it just removes all of the non-decimal parts instead of trying to work with the parts of floats.
The floor of a floating point number is the biggest integer less than or equal to it. Here are a some examples:
floor(5.7) = 5
floor(3) = 3
floor(9.9) = 9
floor(7.0) = 7
floor(-7.9) = -8
floor(-5.0) = -5
floor(-3.3) = -3
floor(0) = 0
floor(-0.0) = -0
floor(-0) = -0
Note: this is almost an exact copy from my other answer which answered a question that was basically the same as this one.