This question already has answers here:
Is the Swift divide "/" operator not working or have I missed something?
(3 answers)
Division not working properly in Swift
(3 answers)
Closed 1 year ago.
I have created a for loop in which I calculate a few values.
for i in 1...100{
let xValue = i/100
print(xValue) // returns 0 every time except when i == 100
}
This is a recreation of a part of that for loop. Why is it that I do not get the right value for 'xValue'?
For info I have also tried the following:
let xValue: Float = Float(i/100)
And that doesn't work either, despite me being very specific. I must have forgotten something basic about these arithmetic
operators in swift.
When you divide an Int by an Int, the result will be rounded down. Use a floating point type, like Double or Float for more precision.
for i in 1...100 {
let xValue = Float(i)/100
print(xValue)
}
To address your attempted solution - when you do:
let xValue: Float = Float(i/100)
The Int result is first computed in i/100 (and rounded down to 0) then you are casting to a Float.
Therefore, we cast i to a Float before the division so the result is computed as a Float.
Since i and 100 are both integer values, / will do integer division and the result will be truncated to 0.
Even when you do let xValue: Float = Float(i/100), the result of division inside the parentheses is already truncated to 0 before the value can be converted to a Float.
Convert i to a floating-point value before dividing to prevent the result from being truncated.
for i in 1...100{
let xValue = Float(i)/100
print(xValue)
}
Related
This question already has answers here:
How do you round a double in Dart to a given degree of precision AFTER the decimal point?
(28 answers)
Closed 10 months ago.
I've coded this simple function to round doubles to a custom step size.
The normal .round() function retuns an int and can only rounds to the nearest 1.
My function returns a double and can round to the nearest 100.0, 5.0, 1.0, 0.1 or 0.23, you get it.
But when I put in certain doubles the result doesn't really work out and is a very tiny fraction off.
I think this has something to do with how computers do floating comma calcualations, but I need an efficient way to get around it.
Run on DartPad
void main() {
stepround(61.337551616741315, 0.1); // this should be 61.3 but is 61.300000000000004
}
/// rounds a double with given steps/precision
double stepround(double value, double steps) {
double rounded = (value / steps).round() * steps;
print(value.toString() + " rounded to the nearest " + steps.toString() + " is " + rounded.toString());
return rounded;
}
As mentioned in the comments, the cause of this issue the way that computers deal with floating numbers. Please refer to the links in the comments for further explanation.
However in a nutshell the problem is mostly caused when dividing or multiplying decimals with decimals. Therefore we can create a similar method to the one you created but with a different approach. We we will take the precision to be as an int.
I.e: 0.1 => 10; 0.001 => 1000
double stepround(double value, int place){
return (value * place).round() / place;
}
Example
// This will return 61.3
stepround(61.337551616741315, 10);
// This will return 61.34
stepround(61.337551616741315, 100);
// This will return 61.338
stepround(61.337551616741315, 1000);
This method works since the small fraction that is caused by the multiplication is removed by round(). And after that we are doing a division by an integer which doesn't create such a problem.
I observed something really strange. If you run this code in Swift:
Int(Float(Int.max))
It crashes with the error message:
fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
This is really counter-intuitive, so I expanded the expression into 3 lines and tried to see what happens in each step in a playground:
let a = Int.max
let b = Float(a)
let c = Int(b)
It crashes with the same message. This time, I see that a is 9223372036854775807 and b is 9.223372e+18. It is obvious that a is greater than b by 36854775807. I also understand that floating points are inaccurate, so I expected something less than Int.max, with the last few digits being 0.
I also tried this with Double, it crashes too.
Then I thought, maybe this is just how floating point numbers behave, so I tested the same thing in Java:
long a = Long.MAX_VALUE;
float b = (float)a;
long c = (long)b;
System.out.println(c);
It prints the expected 9223372036854775807!
What is wrong with swift?
There aren't enough bits in the mantissa of a Double or Float to accurately represent 19 significant digits, so you are getting a rounded result.
If you print the Float using String(format:) you can see a more accurate representation of the value of the Float:
let a = Int.max
print(a) // 9223372036854775807
let b = Float(a)
print(String(format: "%.1f", b)) // 9223372036854775808.0
So the value represented by the Float is 1 larger than Int.max.
Many values will be converted to the same Float value. The question becomes, how much would you have to reduce Int.max before it results in a different Double or Float value.
Starting with Double:
var y = Int.max
while Double(y) == Double(Int.max) {
y -= 1
}
print(Int.max - y) // 512
So with Double, the last 512 Ints all convert to the same Double.
Float has fewer bits to represent the value, so there are more values that all map to the same Float. Switching to - 1000 so that it runs in reasonable time:
var y = Int.max
while Float(y) == Float(Int.max) {
y -= 1000
}
print(Int.max - y) // 274877907000
So, your expectation that a Float could accurately represent a specific Int was misplaced.
Follow up question from the comments:
If float does not have enough bits to represent Int.max, how is it
able to represent a number one larger than that?
Floating point numbers are represented as two parts: mantissa and exponent. The mantissa represents the significant digits (in binary) and the exponent represents the power of 2. As a result, a floating point number can accurately express an even power of 2 by having a mantissa of 1 with an exponent that represents the power.
Numbers that are not even powers of 2 may have a binary pattern that contains more digits than can be represented in the mantissa. This is the case for Int.max (which is 2^63 - 1) because in binary that is 111111111111111111111111111111111111111111111111111111111111111 (63 1's). A Float which is 32 bits cannot store a mantissa which is 63 bits, so it has to be rounded or truncated. In the case of Int.max, rounding up by 1 results in the value
1000000000000000000000000000000000000000000000000000000000000000. Starting from the left, there is only 1 significant bit to be represented by the mantissa (the trailing 0's come for free), so this number is a mantissa of 1 and an exponent of 64.
See #MartinR's answer for an explanation of what Java is doing.
Swift and Java behave differently when converting a "too large" floating point
number to an integer. Java truncates any floating point value
larger than Long.MAX_VALUE = 2^63-1:
long c = (long)(1.0E+30f);
System.out.println(c);
// 9223372036854775807
Swift expects that the value is in the range of Int, and aborts
with a runtime exception otherwise:
/// Creates a new instance by rounding the given floating-point value toward
/// zero.
///
/// - Parameter other: A floating-point value. When `other` is rounded toward
/// zero, the result must be within the range `Int.min...Int.max`.
public init(_ value: Float)
Example:
let c = Int(Float(1.0E30))
print(c)
// fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
The same happens with your value Float(Int.max), which is the
floating point representable value closest to Int.max and happens
to be larger than Int.max.
I want to round a double down to 1 decimal place. For example if I have a double let val = 3.1915 I want to round this down to 3.1. Normal rounding functions will round it to 3.2 but I want to basically just drop the remaining decimal places. What is the best way to do this? Is there a native function for this? I know this is pretty straight forward to do but I want to know what the best way to do this would be where I am not using any kind of workaround or bad practices. This is not a duplicate of other rounding questions because I am not asking about about rounding, I am asking how to drop decimal places.
Similarly, if the value was 3.1215, it would also round to 3.1
Use the function trunc() (which stands for truncate) which will chop away the decimal portion without rounding. Specifically, multiply the Double value by 10, truncate it, then divide by 10 again. Then, to display using 1 decimal place, use String(format:):
let aDouble = 1.15
let truncated = trunc(aDouble * 10) / 10
let string = String(format: "%.1f", truncated
print(string)
(displays "1.1")
or, to process an entire array of sample values:
let floats = stride(from: 1.099, to: 2.0, by: 0.1)
let truncs = floats
.map { trunc($0 * 10) / 10 }
.map { String(format: "%.1f", $0) }
let beforeAndAfter = zip(floats, truncs)
.map { (float: $0.0, truncString: $0.1)}
beforeAndAfter.forEach { print(String(format: "%.3f truncated to 1 place is %#", $0.0, $0.1)) }
Outputs:
1.099 truncated to 1 place is 1.0
1.199 truncated to 1 place is 1.1
1.299 truncated to 1 place is 1.2
1.399 truncated to 1 place is 1.3
1.499 truncated to 1 place is 1.4
1.599 truncated to 1 place is 1.5
1.699 truncated to 1 place is 1.6
1.799 truncated to 1 place is 1.7
1.899 truncated to 1 place is 1.8
1.999 truncated to 1 place is 1.9
By your example I assume you meant you want to Truncate, if so using multiply and casting into Int then Dividing and casting back into Float/Double will do.
Example: 3.1915 -> 3.1
var val = 3.1915
let intVal:Int = Int(val*10)
val = Float(intVal)/10.0
print(val) //3.1
If you want more decimal places simply multiply and divide by 100 or 1000 instead.
Then if for any reason you want to use the round() function there is a overloaded variant that accepts a FloatingPointRoundingRule it will work like:
var val = 3.1915
val*=10 //Determine decimal places
val.round(FloatingPoint.towardZero) // .down is also available which differs in rounding negative numbers.
val*=0.1 //This is a divide by 10
print(val) //3.1
In practical usage I'd suggest making an extension or global function instead of writing this chunk every time. It would look something like:
extension Float {
func trunc(_ decimal:Int) {
var temp = self
let multiplier = powf(10,decimal) //pow() for Double
temp = Float(Int(temp*multiplier))/multiplier //This is actually the first example put into one line
return temp
}
}
And used:
var val = 3.1915
print(val.trunc(1)) //3.1
I'm aware of some relatively similar questions on this site, but if they do apply to my problem (which I'm not certain they do) then I certainly don't understand them. Here's my problem;
var degrees = UInt32()
var radians = Double()
let degrees:UInt32 = arc4random_uniform(360)
let radians = angle * (M_PI / 180)
This returns an error, focused on the multiplication star, reading; "Binary operator "*" cannot be applied to operands of type 'UInt32' and 'Double'.
I'm fairly sure I need to have the degrees variable be of type UInt32 to randomise it, and also that the pi constant cannot be made to be of UInt32, or at least I don't know how, as I'm relatively new to Xcode and Swift in general.
I'd be very grateful if anyone had a solution to my problem.
Thanks in advance.
let degree = arc4random_uniform(360)
let radian = Double(degree) * .pi/180
you need to convert the degree to double before the multiplication .
from apple swift book:
Integer and Floating-Point Conversion
Conversions between integer and floating-point numeric types must be made explicit:
let three = 3
let pointOneFourOneFiveNine = 0.14159
let pi = Double(three) + pointOneFourOneFiveNine
// pi equals 3.14159, and is inferred to be of type Double
Here, the value of the constant three is used to create a new value of type Double, so that both sides of
the addition are of the same type. Without this conversion in place, the addition would not be allowed.
Floating-point to integer conversion must also be made explicit. An integer type can be initialized
with a Double or Float value:
1 let integerPi = Int(pi)
2 // integerPi equals 3, and is inferred to be of type Int
Floating-point values are always truncated when used to initialize a new integer value in this way.
This means that 4.75 becomes 4, and -3.9 becomes -3.
In a cocos2d game, I use arc4random to generate random numbers like this:
float x = (arc4random()%10 - 5)*delta;
(delta is the time between updates in the scheduled update method)
NSLog(#"x: %f", x);
I have been checking them like that.
Most of the numbers that I get are like this:
2012-12-29 15:37:18.206 Jumpy[1924:907] x: 0.033444
or
2012-12-29 15:37:18.247 Jumpy[1924:907] x: 0.033369
But for some reason I get numbers like this sometimes:
2012-12-29 15:37:18.244 Jumpy[1924:907] x: 71658664.000000
Edit: Delta is almost always:
2012-12-29 17:01:26.612 Jumpy[2059:907] delta: 0.016590
I thought it should return numbers in a range of -5 to 5 (multiplied by some small number). Why I am getting numbers like this?
arc4random returns a u_int32_t. The u_ part tells you that it's unsigned. So all of the operators inside the parentheses use unsigned arithmetic.
If you perform the subtraction 2 - 5 using unsigned 32-bit arithmetic, you get 232 + 2 - 5 = 232 - 3 = 4294967293 (a “huge number”).
Cast to a signed type before performing the subtraction. Also, prefer arc4random_uniform if your deployment target is iOS 4.3 or later:
float x = ((int)arc4random_uniform(10) - 5) * delta;
If you want the range to include -5 and 5, you need to use 11 instead of 10, because the range [-5,5] (inclusive) contains 11 elements:
float x = ((int)arc4random_uniform(11) - 5) * delta;
arc4random returns a u_int32_t, an unsigned type. The modulus is also performed using unsigned arithmetic, which yields a number between 0 and 9, as expected (by the way, don't ever do this; use arc4random_uniform instead). You then subtract 5, which is interpreted as an unsigned value, yielding a possibly huge positive value due to underflow.
The solution is to explicitly type the 5 by storing it in a variable of signed type or with a suffix (like 5L).
Looks like arc4random % 10 becomes less than 5, and you are working with negative integer later.
What is the value of delta?