I'm trying to make printf 'do the right thing' with floating point numbers, i.e.:
Never lose information, always print as many decimals as are needed for the exact value
Don't print a bunch of redundant trailing zeros
Switch to scientific notation if the output would otherwise be unreasonably large
%.20g seems to do all that, but there's one more thing I would like to get:
If the value is an integer, do print a trailing '.0' to indicate it is a floating point number with an integer value, not a number of type integer
Is there any way to get the fourth criterion without losing any of the first three?
It looks like the flag "#" will at least put a period at the end. Try %#.20g.
The # flag is for example documented here:
"Used with a, A, e, E, f, F, g or G it forces the written output to contain a decimal point even if no more digits follow. By default, if no digits follow, no decimal point is written."
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So i have been trying to make my own printf and now i stuck at %f.
The problem i have is i don't know what printf does in the background when i give it a float number like: f = 1.4769996 it print 1.477000.
but when i give it f = 1.4759995 it print the value 1.475999
float f = 1.4769996;
printf("%f\n", f); // 1.477000
f = 1.4759995;
printf("%f\n", f); // 1.475999
what i thought of is that printf see the 5 at last and it adds one but not working in the second example.
What is the logic behind this floating point ?
Your C implementation likely uses the IEEE-754 binary32 and binary64 formats for float and double. Given this, float f = 1.4769996; results in setting f to 1.47699964046478271484375, and f = 1.4759995; results in setting f to 1.47599947452545166015625.
Then it is easy to see that rounding 1.47699964046478271484375 to six digits after the decimal point results in 1.477000 (because the next digit is 6, so we round up), and rounding 1.47599947452545166015625 to six digits after the decimal point results in 1.475999 (because the next digit is 4, so we round down).
When working with floating-point numbers, it is important to understand each floating-point value represents one number exactly (unless it is a Not a Number [NaN] encoding). When you write 1.4769996 in source code, it is converted to a value representable in double. When you assign it to a float, it is converted to a value representable in float. Operations on the floating-point object behave as if the object have exactly the value it represents, not as if its value is the numeral you wrote in source code.
To provide some further details, the C standard requires (in C 2018 7.21.6.1 13) that formatting with f be correctly rounded if the number of digits requested is at most DECIMAL_DIG. DECIMAL_DIG is the number of decimal digits in the widest floating-point format the implementation supports such that converting any number in that format to a numeral with DECIMAL_DIG significant decimal digits and back to the floating-point format yields the original value (5.2.4.2.2 12). DECIMAL_DIG must be at least 10. If more than DECIMAL_DIG digits are requested, the C standard allows some leeway in rounding. However, high-quality C implementations will round correctly as specified by IEEE-754 (to the nearest number with the requested number of digits, with ties favoring an even low digit).
If you are trying to write your own printf, and if you are stuck on %f, there are three or four things you need to know:
When a "varargs" function like printf is called, arguments of type float are always implicitly promoted to type double. So when you've seen %f in the format string, and you're using va_arg() to pluck the next argument from the list, you'll want to pluck an argument of type double, not float. (This also means that you have just one case to handle, not two. Inside printf, you don't have to worry about handling type float at all.)
Printing the whole-number part of a double is easy; it's more or less the same problem as printing an int, which I'm guessing you've already figured out, if you've got %d working. And to do a straightforward, simpleminded job of printing the fractional part, it usually works pretty well to just repeatedly multiply by 10. That is, if you're trying to print 123.456, and you've already got the 123 part taken care of, you can then proceed to print the rest by taking the fractional part 0.456, multiplying by 10 to get 4.56 then truncating to get 4, then taking the new fractional part 0.56 and repeating.
There is no such number as 1.4769996. (There's no such number as the 123.456 I was just using, either.) When we write numbers like 1.4769996 and 123.456 we're thinking about decimal fractions, but most computers (including the one you're using) use binary fractions internally, and you can't represent decimal fractions like 1.4769996 and 123.456 exactly in binary, so the actual numbers are always a little bit different than you expect, which is why you often get slight "roundoff error", or extra 999's at the end when you expected 000.
Doing a proper job on this stuff is really, really hard. If you're trying to write your own printf, and you've gotten to %f, and if you can get it working pretty well most of the time, consider yourself lucky, and call it a day. Don't get bogged down on the last digit -- or if you're bound and determined to get the last digit right in every case (which is certainly a noble goal), do some research and set aside some time, because you're going to be working at it for a while.
Is there a format specifier in C that will output a numeric value with the decimal point left on a number, but with trailing zeroes AFTER the decimal point truncated?
The values being calculated are floats, and using %.4g gets close to the desired output, except that leaving the decimal point off the number creates problems.
The following number formats are legitimate for the machine control to read in through the RS232 port : ( 10.0001 , 0.111 , .22 , 0. )
However, sending code including a numeral without a decimal point; for example "G00 X4" results in the machine saving the string "G00 X00.0004" . The machine interprets the input character or characters without a decimal point as being the least significant digits of a properly formed input.
I could simply use the %.4f conversion, but part of the goal is to remove the trailing zeroes. This machine has severely limited memory, and every character counts. The other option is to generate the intended output numbers, convert them to characters, and then test each number for trailing zeroes and truncate as needed. I was very much hoping for something more elegant, but I'm not finding anything in the conversion characters.
Thanks in advance.
Hey i need to know how %f works , that is how
printf("%f",number);
extract a floating point number from a series of bits in number.
Consider the code:
main()
{
int i=1;
printf("\nd %d\nf %f",i,i);
}
Output is :
d 1
f -0.000000
So ultimately it doesn't depend on variable 'i', but just depends on the usage of %d and %f(or whatever) i just need to know how %f extracts the float number corresponding to series of bits in 'i'
To all those who misunderstood my question i know that %f can't be used to an integer and would load garbage values if size of integer was smaller than float. As for my case the size of integer and float are 4 bytes.
Let me be clear if value of is 1 then the corresponding binary value of i will be this:
0000 0000 0000 0000 0000 0000 0000 0001 [32 bits]
How would %f extract -0.0000 as in this case from this series of bits.(How it knows where to put decimal point etc , i can't find it from IEEE 754)
[PLEASE DO CORRECT ME IF I AM WRONG IN MY EXPLANATION OR ASSUMPION]
It's undefined behavior to use "%f" to an int, so the answer to your question is: you don't need to know, and you shouldn't do it.
The output depends on the format specifier like "%f" instead of the type of the argument i is because variadic functions (like printf() or scanf()) have no way of knowing the type of variable argument part.
As others have said, giving mismatched "%" specifier and arguments is undefined behavior, and, according to the C standard, anything can happen.
What does happen, in this case, on most modern computers, is this:
printf looks at the place in memory where the data should have been, interprets whatever data it finds there as a floating-point number, and prints that number.
Since printf is a function that can take a variable number of arguments, all floats are converted to doubles before being sent to the function, so printf expects to find a double, which (on normal modern computers) is 64 bits. But you send an int, which is only 32 bits, so printf will look at the 32 bits from the int, and 32 more bits of garbage that just happened to be there. When you tried this, it seems that the combination was a bit pattern corresponding to the double floating-point value -0.0.
Well.
It's easy to see how an integer can be packed into bytes, but how do you represent decimals?
The simplest technique is fixed point: of the n bits, the first m are before the point and the rest after. This is not a very good representation, however. Bits are wasted on some numbers, and it has uniform precision, while in real life, most desired decimals are between 0 and 1.
Enter floating point. The IEEE 754 spec defines a way of interpreting bits that has, since then, been almost universally accepted. It has very high near-zero precision, is compact, expandable and allows for very large numbers as well.
The linked articles are a good read.
You can output a floating-point number (float x;) manually by treating the value as a "black box" and extracting the digits one-by-one.
First, check if x < 0. If so, output a minus-sign - and negate the number. Now we know that it is positive.
Next, output the integer portion. Assign the floating-point number to an integer variable, which will truncate it, ie. int integer = x;. Then determine how many digits there are using the base-10 logarithm log10(). Note, log10(0) is undefined, so you'll have to handle zero as a special case. Then iterate from 0 up to the number of digits, each time dividing by 10^digit_index to move the desired digit into the unit's position, and take the 10-residue (modulus).
for (i=digits; i>=0; i--)
dig = (integer / pow(10,i)) % 10;
Then, output the decimal point ..
For the fractional part, subtract the integer from the original (absolute-value, remember) floating-point number. And output each digit in a similar way, but this time multiplying by 10^frac_digits. You won't be able to predict the number of significant fractional digits this way, so just use a fixed precision (constant number of fractional digits).
I have C code to fill a string with the representation of a floating-point number here, although I make no claims as to its readability.
IEEE formats store the number as a normalized binary fraction. It's more similar to scientific notation, like 3.57×102 instead of 357.0. So it is stored as an exponent-mantissa pair. Being "normalized" means there's actually an implicit additional 1 bit at the front of the mantissa that is not stored. Hopefully that's enough to help you understand a more detailed description of the format from elsewhere.
Remember, we're in binary, so there's no "decimal point". And with the exponent-mantissa notation, there isn't even a binary point in the format. It's implicitly represented in the exponent.
On the tangentially-related issue of passing floats to printf, remember that this is a variadic function. So it does not declare types of arguments that it receives, and all arguments passed undergo automatic conversions. So, float will automatically promote to double. So what you're doing is (substituting hex for brevity), passing 2 64-bit values:
double f, double f
0xabcdefgh 0xijklmnop 0xabcdefgh 0xijklmnop
Then you tell printf to interpret this sequence of words as an int followed by a double. So the 32-bit int seen by printf is only the first half of the floating-point number, and then the floating-point number seem by printf has its words reversed. The fourth word is never used.
To get the integer representation, you'll need to use type-punning with a pointer.
printf("%d %f\n", *(int *)&f, f);
Which reads (from right-to-left): take the address of the float, treat it as a pointer-to-int, follow the pointer.
I want to print doubles so that the decimals line up. For example:
1.2345
12.3456
should result in
1.2345
12.3456
I have looked everywhere, and the top recommendation is to use the following method (the 5s can be anything):
printf(%5.5f\n");
I have tried this with the following (very) simple program:
#include <stdio.h>
int main() {
printf("%10.10f\n", 0.523431);
printf("%10.10f\n", 10.43454);
return 0;
}
My output is:
0.5234310000
10.4345400000
Why doesn't this work?
The number before the . is minimum characters total, not just before the radix point.
printf("%21.10f\n", 0.523431);
When you use "%10.10f" you are telling printf() "use 10 character positions to print the number (optional minus sign, integer part, decimal point and decimal part). From these 10 positions, reserve 10 for decimal part. If this is not possible, ignore the first number and use whatever positions needed to print the number so that the number of decimal positions is kept"
So that's what's printf() is doing.
So you need to indicate how many positions you are going to use, for example, 15, and how many positions from these are going to be decimals.... for example, 9. That will leave you with 5 positions for the minus sign and integer part and one position for the decimal point.
That is, try "%15.9f" in your printf's
I'm trying to read in a file in c with the following format:
6.43706064058,4.15417249035
3.43706064058,1.15417249035
...
I'm able to parse out the two doubles, but when I print out what I've parsed, I notice that I only get up to 6 decimal places. Here is my code:
long double d1;
long double d2;
fscanf(file, "%Lf,%Lf", &d1, &d2);
printf("x:%Lf, y:%Lf", d1, d2);
Output:
x:6.437061, y:4.154172
...
Where am I losing the precision? Is it possible that its being read in correctly, but my printf statement isn't showing all the precision?
Is it possible that its being read in correctly, but my printf statement isn't showing all the precision?
That's exactly what's happening. From the printf(3) man page:
... the number of digits after the
decimal-point character is equal to the precision specification.
If the precision is missing, it is taken as 6 ...
Tell printf to show more precision by changing your format string:
printf("x:%.11Lf, y:%.11Lf", d1, d2);
The default %f format only prints 6 places after the decimal point, which gives you much less precision than the actual floating point value (unless the exponent is large) and possibly no precision at all (if the exponent is more than slightly negative). Unless you know all your values are bounded away from zero (e.g. all greater than 1), you really need to use the %g format (which can switch to exponential notation as needed) or the %e format (which always uses exponential notation) to print floating point values in a way that preserves their precision.
You also need to use sufficiently many decimal places. For IEEE double precision, 17 decimal places is sufficient, so %.17g would be the preferred format. For long double, it depends on the type used on your particular implementation. Thankfully, C offers a macro, DECIMAL_DIG, that gives you exactly the number of places you need. So you would use:
printf("%.*Lg", DECIMAL_DIG, x);
or similar. Note that this will print more places than were originally present in your input file. If you know your input always has a particular number of places, you could perhaps just hard-code that instead of using DECIMAL_DIG to get a more uniform output.
The reason you are not as far with the precision as you'd like to be is because the level of the spacing in the number is not enough. In the first number, 6.43706064058, you have 13 numbers, including the decimal, so you'd put
printf("x:%13Lf, y:%Lf", d1, d2);
allowing 13 spaces for the x:
for the second number, 4.15417249035, you have 13 also, so for that, you'd put
printf("x:%13Lf, y:13%Lf", d1, d2);
and that will print:
x:6.43706064058, y:4.15417249035
you must allow room for all of the spaces within the number when doing the printf function.
Hope that helped!