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.)
Related
I am trying to write a program that outputs the number of the digits in the decimal portion of a given number (0.128).
I made the following program:
#include <stdio.h>
#include <math.h>
int main(){
float result = 0;
int count = 0;
int exp = 0;
for(exp = 0; int(1+result) % 10 != 0; exp++)
{
result = 0.128 * pow(10, exp);
count++;
}
printf("%d \n", count);
printf("%f \n", result);
return 0;
}
What I had in mind was that exp keeps being incremented until int(1+result) % 10 outputs 0. So for example when result = 0.128 * pow(10,4) = 1280, result mod 10 (int(1+result) % 10) will output 0 and the loop will stop.
I know that on a bigger scale this method is still inefficient since if result was a given input like 1.1208 the program would basically stop at one digit short of the desired value; however, I am trying to first find out the reason why I'm facing the current issue.
My Issue: The loop won't just stop at 1280; it keeps looping until its value reaches 128000000.000000.
Here is the output when I run the program:
10
128000000.000000
Apologies if my description is vague, any given help is very much appreciated.
I am trying to write a program that outputs the number of the digits in the decimal portion of a given number (0.128).
This task is basically impossible, because on a conventional (binary) machine the goal is not meaningful.
If I write
float f = 0.128;
printf("%f\n", f);
I see
0.128000
and I might conclude that 0.128 has three digits. (Never mind about the three 0's.)
But if I then write
printf("%.15f\n", f);
I see
0.128000006079674
Wait a minute! What's going on? Now how many digits does it have?
It's customary to say that floating-point numbers are "not accurate" or that they suffer from "roundoff error". But in fact, floating-point numbers are, in their own way, perfectly accurate — it's just that they're accurate in base two, not the base 10 we're used to thinking about.
The surprising fact is that most decimal (base 10) fractions do not exist as finite binary fractions. This is similar to the way that the number 1/3 does not even exist as a finite decimal fraction. You can approximate 1/3 as 0.333 or 0.3333333333 or 0.33333333333333333333, but without an infinite number of 3's it's only an approximation. Similarly, you can approximate 1/10 in base 2 as 0b0.00011 or 0b0.000110011 or 0b0.000110011001100110011001100110011, but without an infinite number of 0011's it, too, is only an approximation. (That last rendition, with 33 bits past the binary point, works out to about 0.0999999999767.)
And it's the same with most decimal fractions you can think of, including 0.128. So when I wrote
float f = 0.128;
what I actually got in f was the binary number 0b0.00100000110001001001101111, which in decimal is exactly 0.12800000607967376708984375.
Once a number has been stored as a float (or a double, for that matter) it is what it is: there is no way to rediscover that it was initially initialized from a "nice, round" decimal fraction like 0.128. And if you try to "count the number of decimal digits", and if your code does a really precise job, you're liable to get an answer of 26 (that is, corresponding to the digits "12800000607967376708984375"), not 3.
P.S. If you were working with computer hardware that implemented decimal floating point, this problem's goal would be meaningful, possible, and tractable. And implementations of decimal floating point do exist. But the ordinary float and double values any of is likely to use on any of today's common, mass-market computers are invariably going to be binary (specifically, conforming to IEEE-754).
P.P.S. Above I wrote, "what I actually got in f was the binary number 0b0.00100000110001001001101111". And if you count the number of significant bits there — 100000110001001001101111 — you get 24, which is no coincidence at all. You can read at single precision floating-point format that the significand portion of a float has 24 bits (with 23 explicitly stored), and here, you're seeing that in action.
float vs. code
A binary float cannot encode 0.128 exactly as it is not a dyadic rational.
Instead, it takes on a nearby value: 0.12800000607967376708984375. 26 digits.
Rounding errors
OP's approach incurs rounding errors in result = 0.128 * pow(10, exp);.
Extended math needed
The goal is difficult. Example: FLT_TRUE_MIN takes about 149 digits.
We could use double or long double to get us somewhat there.
Simply multiply the fraction by 10.0 in each step.
d *= 10.0; still incurs rounding errors, but less so than OP's approach.
#include <stdio.h>
#include <math.h> int main(){
int count = 0;
float f = 0.128f;
double d = f - trunc(f);
printf("%.30f\n", d);
while (d) {
d *= 10.0;
double ipart = trunc(d);
printf("%.0f", ipart);
d -= ipart;
count++;
}
printf("\n");
printf("%d \n", count);
return 0;
}
Output
0.128000006079673767089843750000
12800000607967376708984375
26
Usefulness
Typically, past FLT_DECMAL_DIG (9) or so significant decimal places, OP’s goal is usually not that useful.
As others have said, the number of decimal digits is meaningless when using binary floating-point.
But you also have a flawed termination condition. The loop test is (int)(1+result) % 10 != 0 meaning that it will stop whenever we reach an integer whose last digit is 9.
That means that 0.9, 0.99 and 0.9999 all give a result of 2.
We also lose precision by truncating the double value we start with by storing into a float.
The most useful thing we could do is terminate when the remaining fractional part is less than the precision of the type used.
Suggested working code:
#include <math.h>
#include <float.h>
#include <stdio.h>
int main(void)
{
double val = 0.128;
double prec = DBL_EPSILON;
double result;
int count = 0;
while (fabs(modf(val, &result)) > prec) {
++count;
val *= 10;
prec *= 10;
}
printf("%d digit(s): %0*.0f\n", count, count, result);
}
Results:
3 digit(s): 128
I don't understand why doesn't the roundf() function from math.h round the donation variable, whilst it rounds livestockPM without a problem. I need to use the rounded values for other calculations, but I'm using printf to check if the values are correct, and it simply returns wrong values (doesn't round variable donation). Also, the variable final only returns values as if rounded to .00, doesn't matter what variables farmer1,2,3 hold.
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
int main(){
int farmer1 = 9940;
int farmer2 = 4241;
int farmer3 = 7779;
float livestockPM = (float)farmer1 / (float)farmer2;
printf("livestock: %f\n",livestockPM);
livestockPM = roundf(livestockPM * 100) / 100;
printf("livestock rounded: %f\n",livestockPM);
float donation = (float)livestockPM * (float)farmer3;
printf("donation: %f\n", donation);
donation = roundf(donation * 100.00) / 100.00;
printf("donation rounded: %f\n", donation);
float final = donation * (float)farmer2;
printf("final: %f\n", final);
return 0;
}
Output:
livestock: 2.343787
livestock rounded: 2.340000
donation: 18202.859375
donation rounded: 18202.859375
final: 77198328.000000
Anyone got any idea why? I was thinking because of multiplying float with int, but I can't seem to get it work like this. I've tried removing the (float) from integer variables, but the results were undesirable as well. Thanks.
OP's float is encoded using binary floating point and 18202.859375 lacks precision to take on a value that "%f" prints as 18202.860000.
A float cannot represent every possible number. As a binary floating point number it can represent numbers like below. See IEEE 754 Converter, but not in between.
18202.859375
18202.86138125
When the following executes, the best possible result is again 18202.859375.
float donation_rounded = roundf(18202.859375 * 100.00) / 100.00;
Recall that printf("%f\n", x) prints a number rounded textually to the closest 0.000001 value.
Code could use double, but the same problem will occur with very large numbers, but may meet OP''s immediate need. #user3386109
As OP appears to be trying to cope with money, there is no great solution in standard C. best money/currency representation goes into some of the issues.
Strange output when I use float instead of double
#include <stdio.h>
void main()
{
double p,p1,cost,cost1=30;
for (p = 0.1; p < 10;p=p+0.1)
{
cost = 30-6*p+p*p;
if (cost<cost1)
{
cost1=cost;
p1=p;
}
else
{
break;
}
printf("%lf\t%lf\n",p,cost);
}
printf("%lf\t%lf\n",p1,cost1);
}
Gives output as expected at p = 3;
But when I use float the output is a little weird.
#include <stdio.h>
void main()
{
float p,p1,cost,cost1=40;
for (p = 0.1; p < 10;p=p+0.1)
{
cost = 30-6*p+p*p;
if (cost<cost1)
{
cost1=cost;
p1=p;
}
else
{
break;
}
printf("%f\t%f\n",p,cost);
}
printf("%f\t%f\n",p1,cost1);
}
Why is the increment of p in the second case going weird after 2.7?
This is happening because the float and double data types store numbers in base 2. Most base-10 numbers can’t be stored exactly. Rounding errors add up much more quickly when using floats. Outside of embedded applications with limited memory, it’s generally better, or at least easier, to use doubles for this reason.
To see this happening for double types, consider the output of this code:
#include <stdio.h>
int main(void)
{
double d = 0.0;
for (int i = 0; i < 100000000; i++)
d += 0.1;
printf("%f\n", d);
return 0;
}
On my computer, it outputs 9999999.981129. So after 100 million iterations, rounding error made a difference of 0.018871 in the result.
For more information about how floating-point data types work, read What Every Computer Scientist Should Know About Floating-Point Arithmetic. Or, as akira mentioned in a comment, see the Floating-Point Guide.
Your program can work fine with float. You don't need double to compute a table of 100 values to a few significant digits. You can use double, and if you do, it will have chances to work even if you use binary floating-point binary at cross-purposes. The IEEE 754 double-precision format used for double by most C compilers is so precise that it makes many misuses of floating-point unnoticeable (but not all of them).
Values that are simple in decimal may not be simple in binary
A consequence is that a value that is simple in decimal may not be represented exactly in binary.
This is the case for 0.1: it is not simple in binary, and it is not represented exactly as either double or float, but the double representation has more digits and as a result, is closer to the intended value 1/10.
Floating-point operations are not exact in general
Binary floating-point operations in a format such as float or double have to produce a result in the intended format. This leads to some digits having to be dropped from the result each time an operation is computed. When using binary floating-point in an advanced manner, the programmer sometimes knows that the result will have few enough digits for all the digits to be represented in the format (in other words, sometimes a floating-point operation can be exact and advanced programmers can predict and take advantage of conditions in which this happens). But here, you are adding 0.1, which is not simple and (in binary) uses all the available digits, so most of the times, this addition is not be exact.
How to print a small table of values using only float
In for (p = 0.1; p < 10;p=p+0.1), the value of p, being a float, will be rounded at each iteration. Each iteration will be computed from a previous iteration that was already rounded, so the rounding errors will accumulate and make the end result drift away from the intended, mathematical value.
Here is a list of improvements over what you wrote, in reverse order of exactness:
for (i = 1, p = 0.1f; i < 100; i++, p = i * 0.1f)
In the above version, 0.1f is not exactly 1/10, but the computation of p involves only one multiplication and one rounding, instead of up to 100. That version gives a more precise approximation of i/10.
for (i = 1, p = 0.1f; i < 100; i++, p = i * 0.1)
In the very slightly different version above, i is multiplied by the double value 0.1, which more closely approximates 1/10. The result is always the closest float to i/10, but this solution is cheating a bit, since it uses a double multiplication. I said a solution existed with only float!
for (i = 1, p = 0.1f; i < 100; i++, p = i / 10.0f)
In this last solution, p is computed as the division of i, represented exactly as a float because it is a small integer, by 10.0f, which is also exact for the same reason. The only computation approximation is that of a single operation, and the arguments are exactly what we wanted them to, so this is the best solution. It produces the closest float to i/10 for all values of i between 1 and 99.
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.
I'm trying to convert the decimal portion of a double 247.32
into an int 32. I only need two decimal places.
I can cast the double as int and subtract from the double to get .32000
I can then multiply by 100 to get 32.000
But then when I try to cast that 32.000 as an int, it turns into 31.
Can I fix this?
Should I use a different datatype than a double to store that number?
Thanks
The problem (which skjaidev's answer doesn't solve) is that 247.32 cannot be represented exactly in binary floating-point. The actual stored value is likely to be:
247.31999999999999317878973670303821563720703125
So you can't just discard the integer part, multiply by 100, and convert to int, because the conversion truncates.
The round() function, declared in <math.h>, rounds a double value to the nearest integer -- though the result is still of type double.
double a = 247.32;
a -= trunc(a); /* a == 0.32 -- approximately */
a *= 100.0; /* a == 32.0 -- approximately */
a = round(a); /* a == 32.0 -- exactly */
printf ("%d\n", (int)a);
Or, putting the computation into a single line:
double a = 247.32;
printf("%d\n", (int)round(100.0 * (a - trunc(a))));
Actually, this is probably a cleaner way to do it:
double a = 247.32;
printf("%d\n", (int)round(100.0 * fmod(a, 1.0)));
Given input value x and output y:
char buf[5];
snprintf(buf, sizeof buf, "%.2f", fmod(x, 1.0));
y = strtol(buf+2, 0, 10);
Or just y = 10*(buf[2]-'0')+buf[3]-'0'; to avoid the strtol cost.
This is about the only way to do what you want without writing a ton of code yourself, since the printf family of functions are the only standard functions capable of performing decimal rounding.
If you have some additional constraints like that x is very close to a multiple of 1/100, you could perhaps cheat and just do something like:
int y = ((x+0.001)*100;
By the way, if your problem involves money, do not use floating point for money! Use integers in units of cents or whatever the natural smallest unit for your currency is.
Since you're only looking for 2 decimal places, this works for me:
double a = 247.32;
int b = (int) (a * 100)%100;
printf ("%d\n", b);
Update: See my comment below.