Why 5.0/3 is 1.666667 in C? - c

I'm new in C language, but I've tried integer, float and double division in C as I'm normally doing in Java, but when I execute 5.0/3 instead of 1.6666666666666667 I'm getting 1.666667 for double division and for float division.
I had tried to execute the program using Visual Studio as I always do but I got the message "First number is 1, second one is 1.666667 and the last one is 1.666667." after executing:
#include <stdio.h>
int main()
{
int firstNumber = 5 / 3;
float secondNumber = 5.0f / 3.0f;
double thirdNumber = 5.0 / 3.0;
printf("First number is %d, second one is %f and the last one is %lf.", firstNumber, secondNumber, thirdNumber);
return 0;
}
Why I'm getting the same result for 'secondNumber' and for 'thirdNumber'?

Typical float can represent about 232 different values.
Typical double can represent about 264 different values.
In both types, 5/3, the exact quotient of the division, is not in that set. Instead a nearby value (some binary fraction) is used.
float secondNumber = 5.0f / 3.0f; // 1.66666662693023681640625
double thirdNumber = 5.0 / 3.0; // 1.6666666666666667406815349750104360282421112060546875
When using "%f", 6 places past the decimal point are used. The printed text is a rounded one. In both cases, rounding to the same.
1.666667
To see more digits, use "%.10f", "%.20f", etc. #xing
printf("%.10f\n", secondNumber);
printf("%.10f\n", thirdNumber);
Output
1.6666666269
1.6666666667

Related

Round 37.1-28.75 float calculation correctly to 8.4 instead of 8.3

I have problem with floating point rounding. I want to calculate floating point numbers and round them to (given) N decimals. In this example I want to round to 1 decimal places.
Calculation 37.1-28.75 will result into floating point 8.349998 (instead of 8.35), which will result printf rounding to 8.3 instead of 8.4 for 1 decimal places.
The actual result in math is 37.10-28.75=8.35000000, but due to floating point imprecision it is converted into 8.349998, which is then converted into 8.3 instead of 8.4 when using 1 decimal place rounding.
Minimum reproducible example:
float a = 37.10;
float b = 28.75;
//a-b = 8.35 = 8.4
printf("%.1f\n", a - b); //outputs 8.3 instead of 8.4
Is it valid to add following to the result:
float result = a - b;
if (result > 0.0f)
{
result += powf(10, -nr_of_decimals - 1) / 2;
}
else
{
result -= powf(10, -nr_of_decimals - 1) / 2;
}
EDIT: corrected that I want 1 decimal place rounded output, not 2 decimal places
EDIT2: negative results are needed as well (28.75-37.1 = -8.4)
On my system I do actually get 8.35. It's possible that you have to set the rounding direction to "nearest" first, try this (compile with e.g. gcc ... -lm):
#include <fenv.h>
#include <stdio.h>
int main()
{
float a = 37.10;
float b = 28.75;
float res = a - b;
fesetround(FE_TONEAREST);
printf("%.2f\n", res);
}
Binary floating point is, after all, binary, and if you do care about the correct decimal rounding this much, then your choices would be:
decimal floating point, or
fixed point.
I'd say the solution is to use fixed point, especially if you're on embedded, and forget about everything else.
With
int32_t a = 3710;
int32_t b = 2875;
the result of
a - b
will exactly be
835
every time; and then you just need to have a simple fixed point printing routine for the desired precision, and check the following digit after the last digit to see if it needs to be rounded up.
If you want to round to 2 decimals, you can add 0.005 to the result and then offset it with floorf:
float f = 37.10f - 28.75f;
float r = floorf((f + 0.005f) * 100.f) / 100.f;
printf("%f\n", r);
The output is 8.350000
Why are you using floats instead of doubles?
Regarding your question:
Is it valid to add following to the result:
float result = a - b;
if (result > 0.0f)
{
result += powf(10, -nr_of_decimals - 1) / 2;
}
else
{
result -= powf(10, -nr_of_decimals - 1) / 2;
}
It doesn't seem so, on my computer I get 8.350498 instead of 8.350000.
After your edit:
Calculation 37.1-28.75 will result into floating point 8.349998, which will result printf rounding to 8.3 instead of 8.4.
Then
float r = roundf((f + (f < 0.f ? -0.05f : +0.05f)) * 10.f) / 10.f;
is what you are looking for.

How to set the level of precision for the decimal expansion of a rational number

I'm trying to print out the decimal expansion of a rational number in C. The problem I have is that when I divide the numerator by the denominator I lose precision. C rounds up the repeating part when I don't want it to.
For example, 1562/4995 = 0.3127127127... but in my program I get 1562/4995 = 0.312713. As you can see a part of the number that I need has been lost.
Is there a way to specify C to preserve a higher level of decimal precision?
I have tried to declare the result as a double, long double and float. I also tried to split the expansion into 2 integers seperated by a '.'
However both methods haven't been successful.
int main() {
int numerator, denominator;
numerator = 1562;
denominator = 4995;
double result;
result = (double) numerator / (double) denominator;
printf("%f\n", result);
return 0;
}
I expected the output to be 1562/4995 = 0.3127127127... but the actual output is 1562/4995 = 0.312713
The %f format specifier to printf shows 6 digits after the decimal point by default. If you want to show more digits, use a precision specifier:
printf("%.10f\n", result);
Also, the double type can only accurately store roughly 16 decimal digits of precision.
You need to change your output format, like this:
printf("%.10lf\n", result);
Note two things:
The value after the . specifies the decimal precision required (10 decimal places, here).
Note that I have added an l before the f to explicitly state that the argument is a double rather than a (single-precision) float.
EDIT: Note that, for the printf function, it is not strictly necessary to include the l modifier. However, when you come to use the 'corresponding' scanf function for input, it's absence will generate a warning and (probably) undefined behaviour:
scanf("%f", &result); // Not correct
scanf("%lf", &result); // Correct
If printing is all you want to do, you can do this with the same long division you were taught in elementary school:
#include <stdio.h>
/* Print the decimal representation of N/D with up to
P digits after the decimal point.
*/
#define P 60
static void PrintDecimal(unsigned N, unsigned D)
{
// Print the integer portion.
printf("%u.", N/D);
// Take the remainder.
N %= D;
for (int i = 0; i < P && N; ++i)
{
// Move to next digit position and print next digit.
N *= 10;
printf("%u", N/D);
// Take the remainder.
N %= D;
}
}
int main(void)
{
PrintDecimal(1562, 4995);
putchar('\n');
}

How to make your result on divide number is not rounded?

Example (in C):
#include<stdio.h>
int main()
{
int a, b = 999;
float c = 0.0;
scanf("%d", &a);
c = (float)a/b;
printf("%.3lf...", c);
return 0;
}
If I put 998 it will come out 0.999, but I want the result be 0.998; how?
It looks like you want to truncate instead of round.
The mathematical result of 999/998 is 0.9989989989... Rounded to three decimal places, that is 0.999. So if you use %.3f to print it, that's what you're going to get.
When you convert a floating-point number to integer in C, the fractional part is truncated. So if you had the number 998.9989989 and you converted it to an int, you'd get 998. So you can get the result you want by multiplying by 1000, truncating to an int, and dividing by 1000 again:
c = c * 1000;
c = (int)c;
c = c / 1000;
Or you could shorten that to
c = (int)(c * 1000) / 1000.;
This will work fine for problems such as 998/999 ≈ 0.998, but you're close to the edge of where type float's limited precision will start introducing its own rounding issues. Using double would be a better choice. (Type float's limited precision almost always introduces issues.)

How to get the exact fractional part from a floating point number as an integer?

I was trying to extract the exact fractional part from a floating point number. I tried with this:
float f=254.73;
int integer = (int)f;
float fractional = f-integer;
printf ("The fractional part is: %f", fractional);
But the output is: 0.729996. For this reason when I was doing this:
float f=254.73;
int integer = (int)f;
float fractional = f-integer;
int fractional_part_in_integer = ((int)(f*100)%100);
printf ("The value is: %d", fractional_part_in_integer);
It gives me 72 as output. But, I want to extract exactly 73 from the given number 254.73. I already know how to use %.2f during printf() function to print upto two decimal numbers. But in my code I don't want to print the number right now. I have some calculations with that fractional part as integer form i.e. 73.
So, my problem is how could I extract the fractional part from 254.73 so that I can get exact 73 as integer to do more calculations?
How to get the exact fractional part from a floating point number as an integer?
trying to extract the exact fractional part from a floating point number.
Use modf() or modff()
double modf(double value, double *iptr);
float modff(float value, float *iptr);
The modf functions break the argument value into integral and fractional parts, ...
C11 §7.12.6.12 2
#include <math.h>
double value = 1.234;
double ipart;
double frac = modf(value, &ipart);
A better approach for OP's need may be to first round a scaled value and then back into whole and fractional parts.
double value = 254.73;
value = round(value*100.0);
double frac = fmod(value, 100); // fmod computes the floating-point remainder of x/y.
double ipart = (value - frac)/100.0;
printf("%f %f\n", ipart, frac);
254.000000 73.000000
Ref detail: When OP uses 254.73, this is converted to the nearest float value which may be 254.729995727539....
float f = 254.73;
printf("%.30f\n", f);
// 254.729995727539062500000000000000
You can use sprintf and sscanf to print the value to a string and then extract the fraction. The %*d scans and discards the first integer of the formatted string. A dot is scanned and then the fraction.
#include <stdio.h>
int main( void)
{
char fp[30];
int fraction;
float f = 254.73f;
sprintf ( fp, "%.2f", f);
sscanf ( fp, "%*d.%d", &fraction);
printf ( "%d\n", fraction);
return 0;
}
The easiest way is to use standard library function ceil from <math.h>.
The float number 254.73 may be converted to 254.7299957275390625000000.
f-integer will give 0.7299957275390625000000.
Now multiply it by 100 and use ceil function to get the smallest integer value not less than 72.99957275390625000000.
int fractional_part_in_integer = ((int)ceil(fractional*100)) % 100;
UPDATE: As pointed in a comment by #Sneftel, the above suggested method in this answer will not work consistently.
A simple hack is to use round function from math.h to round the f and then extract the fractional part
float f=254.73;
int int_part = (int)f;
float fractional = round(f*100)/100 - int_part;
int fractional_part_in_integer = (int)(fractional*100);
printf("%d, %d\n ", int_part, fractional_part_in_integer);
Output:
254, 73
Take the number in string use the built-in function find() to find the position of ".".
#include <iostream>
using namespace std;
int main()
{
string f = "254.7356656";
int position = f.find(".");
cout << f.substr(position + 1);
return 0;
}
Output: 7356656

Moving decimal place to right in c

I'm new to C and when I run the code below, the value that is put out is 12098 instead of 12099.
I'm aware that working with decimals always involves a degree of inaccuracy, but is there a way to accurately move the decimal point to the right two places every time?
#include <stdio.h>
int main(void)
{
int i;
float f = 120.99;
i = f * 100;
printf("%d", i);
}
Use the round function
float f = 120.99;
int i = round( f * 100.0 );
Be aware however, that a float typically only has 6 or 7 digits of precision, so there's a maximum value where this will work. The smallest float value that won't convert properly is the number 131072.01. If you multiply by 100 and round, the result will be 13107202.
You can extend the range of your numbers by using double values, but even a double has limited range. (A double has 16 or 17 digits of precision.) For example, the following code will print 10000000000000098
double d = 100000000000000.99;
uint64_t j = round( d * 100.0 );
printf( "%llu\n", j );
That's just an example, finding the smallest number is that exceeds the precision of a double is left as an exercise for the reader.
Use fixed-point arithmetic on integers:
#include <stdio.h>
#define abs(x) ((x)<0 ? -(x) : (x))
int main(void)
{
int d = 12099;
int i = d * 100;
printf("%d.%02d\n", d/100, abs(d)%100);
printf("%d.%02d\n", i/100, abs(i)%100);
}
Your problem is that float are represented internaly using IEEE-754. That is in base 2 and not in base 10. 0.25 will have an exact representation, but 0.1 has not, nor has 120.99.
What really happens is that due to floating point inacuracy, the ieee-754 float closest to the decimal value 120.99 multiplied by 100 is slightly below 12099, so it is truncated to 12098. You compiler should have warned you that you had a truncation from float to in (mine did).
The only foolproof way to get what you expect is to add 0.5 to the float before the truncation to int :
i = (f * 100) + 0.5
But beware floating point are inherently inaccurate when processing decimal values.
Edit :
Of course for negative numbers, it should be i = (f * 100) - 0.5 ...
If you'd like to continue operating on the number as a floating point number, then the answer is more or less no. There's various things you can do for small numbers, but as your numbers get larger, you'll have issues.
If you'd like to only print the number, then my recommendation would be to convert the number to a string, and then move the decimal point there. This can be slightly complicated depending on how you represent the number in the string (exponential and what not).
If you'd like this to work and you don't mind not using floating point, then I'd recommend researching any number of fixed decimal libraries.
You can use
float f = 120.99f
or
double f = 120.99
by default c store floating-point values as double so if you store them in float variable implicit casting is happened and it is bad ...
i think this works.

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