Currently, math.Pow() and math.sqrt take float64 type arguments.
Do we have equivalent functions that take int type arguments?
If your return value is a float, you can use Ceil or Floor from the math package and then convert it to an int.
n := 5.5
o := math.Floor(n)
p := int(math.Pow(o, 2))
fmt.Println("Float:", n)
fmt.Println("Floor:", o)
fmt.Println("Square:", p)
5.5
5
25
Keep in mind that Floor still returns a float64, so you will still want to wrap it in int()
just create a float64 object using the int value. Example if int = 10.
var x float64 = 10
var b = math.Pow(2, x)
There are fast approximate algorithms described elsewhere on SO, such as this one. If performance is important, porting one of the C algorithms to Go might be worth the effort.
What you can do is type-cast a float to your value.
int a=10,b=2;
math.Pow(float(a),float(b));
Related
I need to find the square root of a big.Rat. Is there a way to do it without losing (already existing) accuracy?
For example, I could convert the numerator and denominator into floats, get the square root, and then convert it back...
func ratSquareRoot(num *big.Rat) *big.Rat {
f, exact := num.Float64() //Yuck! Floats!
squareRoot := math.Sqrt(f)
var accuracy int64 = 10 ^ 15 //Significant digits of precision for float64
return big.NewRat(int64(squareRoot*float64(accuracy)), accuracy)
// ^ This is now totally worthless. And also probably not simplified very well.
}
...but that would eliminate all of the accuracy of using a rational. Is there a better way of doing this?
The big.Float type has a .Sqrt(x) operation, and handles defining explicitly the precision you aim for. I'd try to use that and convert the result back to a Rat with the same operations in your question, only manipulating big.Int values.
r := big.NewRat(1, 3)
var x big.Float
x.SetPrec(30) // I didn't figure out the 'Prec' part correctly, read the docs more carefully than I did and experiement
x.SetRat(r)
var s big.Float
s.SetPrec(15)
s.Sqrt(&x)
r, _ = s.Rat(nil)
fmt.Println(x.String(), s.String())
fmt.Println(r.String(), float64(18919)/float64(32768))
playground
A specification reads as follows:
It still considers real numbers equal if they differ in their last
binary digit.
I would like to implement this way of comparing floats for the float64 data type in Go. Unfortunately, the bitwise operators aren't defined for floating point numbers. Is there a way to achieve this way of comparing floats in the Go language?
This looks like a perfect use case for the following function from the math package:
func equal(x, y float64) bool {
return math.Nextafter(x, y) == y
}
Nextafter returns the next representable float64 value after x towards y.
Special cases are:
Nextafter(x, x) = x
Nextafter(NaN, y) = NaN
Nextafter(x, NaN) = NaN
https://play.golang.org/p/unRkkoe6wb
If you want to know if two float64 values are adjacent (that is, there's no float64 value between them):
func almostEqual(a, b float64) bool {
ai, bi := int64(math.Float64bits(a)), int64(math.Float64bits(b))
return a == b || -1 <= ai-bi && ai-bi <= 1
}
Mostly that's the same as saying they differ in the lowest bit of their mantissa.
This code doesn't work if a or b are NaNs, zeros or infinities, but you could add special cases if you wished.
See https://randomascii.wordpress.com/2012/01/23/stupid-float-tricks-2/
What is the correct way to store and do arithmetic on currency in Go? There doesn't seem to be a corresponding decimal type and using floats is a big no.
I'd say a way to go is to store amounts of money using properly sized integer type, normalized to the lowest possible amount. Say, if you need to store amounts in US dollars down to one cent, multiply your values by 100 and hence store them in full cents.
Another way is to implement a custom type which would model what is "decimal" in some other languages, that is, it would use two integer numbers to represent amount of money.
This seems like a great opportunity to create a type, which stores the value in a safe and precise integer-based way, but gives you extra behavior you'd want from a decimal type. For instance, a quick implementation might look like this (https://play.golang.org/p/nYbLiadQOc):
// USD represents US dollar amount in terms of cents
type USD int64
// ToUSD converts a float64 to USD
// e.g. 1.23 to $1.23, 1.345 to $1.35
func ToUSD(f float64) USD {
return USD((f * 100) + 0.5)
}
// Float64 converts a USD to float64
func (m USD) Float64() float64 {
x := float64(m)
x = x / 100
return x
}
// Multiply safely multiplies a USD value by a float64, rounding
// to the nearest cent.
func (m USD) Multiply(f float64) USD {
x := (float64(m) * f) + 0.5
return USD(x)
}
// String returns a formatted USD value
func (m USD) String() string {
x := float64(m)
x = x / 100
return fmt.Sprintf("$%.2f", x)
}
The given type behaves the way one might expect, especially given tricky use-cases.
fmt.Println("Product costs $9.09. Tax is 9.75%.")
f := 9.09
t := 0.0975
ft := f * t
fmt.Printf("Floats: %.18f * %.18f = %.18f\n", f, t, ft)
u := ToUSD(9.09)
ut := u.Multiply(t)
fmt.Printf("USD: %v * %v = %v\n", u, t, ut)
Product costs $9.09. Tax is 9.75%.
Floats: 9.089999999999999858 * 0.097500000000000003 = 0.886275000000000035
USD: $9.09 * 0.0975 = $0.89
Rational numbers are quite a good solution for representing money values. That is, a type that has a numerator and a denominator.
Often monetary data structures are overly complex - Java's BigDecimal being an example. A more mathematically-consistent approach is to define a type that handles rational numbers. When 64bit integers are used, a huge range of numbers can be accurately and efficiently represented. Errors and rounding issues are less of a problem than for any solution that needs to convert binary fractions to/from decimal fractions.
Edit: The Go standard library includes arbitrary-precision integers and rational numbers. The Rat type will work well for currency, especially for those cases that require arbitrary precision, e.g. foreign exchange. Here's an example.
Edit 2: I have used the decimal.Decimal Shopspring package extensively. Under the hood, this combines big.Int with an exponent to provide a fixed-point decimal with a nearly-unlimited range of values. The Decimal type is a rational number where the denominator is always a power of ten, which works very well in practice.
There are actually a few packages implementing a decimal type, though there's no clear leader among them.
Can someone explain the following. I have a function in go that accepts a couple of float64 and then uses this value to calculate a lot of other values. The function looks like
func (g *Geometry) CalcStresses(x, zmax, zmin float64)(Vertical)
the result is put into a struct like
type Vertical struct {
X float64
Stresses []Stress
}
Now the funny thing is this. If I call the function like this;
for i:=14.0; i<15.0; i+=0.1{
result := geo.CalcStresses(i, 10, -10)
}
then I get a lot of results where the Stress array is empty, antoher interesting detail is that x sometimes shows like a number with a LOT of decimals (like 14.3999999999999999998)
However, if I call the function like this;
for i:=0; i<10; i++{
x := 14.0 + float64(i) * 0.1
result := geo.CalcStresses(x,10,-10)
}
then everything is fine.
Does anyone know why this happens?
Thanks in advance,
Rob
Not all real numbers can be represented precisely in binary floating point format, therefore looping over floating point number is asking for trouble.
From Wikipedia on Floating point
The fact that floating-point numbers cannot precisely represent all real numbers, and that floating-point operations cannot precisely represent true arithmetic operations, leads to many surprising situations. This is related to the finite precision with which computers generally represent numbers.
For example, the non-representability of 0.1 and 0.01 (in binary) means that the result of attempting to square 0.1 is neither 0.01 nor the representable number closest to it.
This code
for i := 14.0; i < 15.0; i += 0.1 {
fmt.Println(i)
}
produces this
14
14.1
14.2
14.299999999999999
14.399999999999999
14.499999999999998
14.599999999999998
14.699999999999998
14.799999999999997
14.899999999999997
14.999999999999996
You may use math.big.Rat type to represent rational numbers accurately.
Example
x := big.NewRat(14, 1)
y := big.NewRat(15, 1)
z := big.NewRat(1, 10)
for i := x; i.Cmp(y) < 0; i = i.Add(i, z) {
v, _ := i.Float64()
fmt.Println(v)
}
Iv'e been working on a perlin script but have been having problems with creating simple pseudo random values.
I need to be able to create a seed value from an xy coordinate but x+y has obvious problems with recurring values. Also they go into negative space so x^y doesn't work.
Sorry if this has been already answered somewhere else but either I didn't understand or couldn't find it.
Do you want to assing a repetible random number to each x,y pair ?
Using a linear or in general function combination of the x,y as a seed will give artifacts in the distribution (at least if you don't use a very complex function).
Try with this, I've the same problem ant it worked for me
//seeded random for JS - integer
function irnd2()
{
a=1664525;
c=1013904223;
m=4294967296;
rnd2.r=(rnd2.r*a+c)%m;
return rnd2.r;
}
//seeded random for JS - double [0,1]
function rnd2()
{
a=1664525;
c=1013904223;
m=4294967296;
rnd2.r=(rnd2.r*a+c)%m;
return rnd2.r/m;
}
rnd2.r=192837463;
//seed function
function seed2(s)
{
s=s>0?s:-s;
rnd2.r=192837463^s;
}
//my smart seed from 2 integer
function myseed(x,y)
{
seed2(x);//x is integer
var sx=irnd2();//sx is integer
seed2(y);//y is integer
var sy=irnd2();//sy is integer
seed2(sx^sy);//using binary xor you won't lose information
}
In order to use it :
myseed(x,y);
irnd2();
In this manner you can obtain a good uncorrelated random sequence.
I use it in JS but it should work also in other languages supposing the argument of seed and the returned value of rnd is an integer.
You need to better define the problem to get an optimal answer.
If your x and y values are relatively small, you could place them into the high and low portions of an integer (is the seed in your language an integer), e.g. for a 32-bit platform:
int seed = x << 16 + y;
If the seed value is not allowed to be negative (I didn't fully understand what you meant by "negative space" in your question, whether you were referring to geography or the seed value), you can take the absolute value of the seed.
If you meant that the coordinates can have negative values, your best course of action depends on whether you want the same seed for a coordinate and for it's inverse.
Take the absolute value of both x and y first; then x^y will work fine. One of the easiest ways to create a pseudo-random source is with time. You might try multiplying x^y by the current system time; this method has an extremely low chance of generating recurring seed values.
If you know the range of values you have, you could simply cast x and y as strings padded with zeroes, append the two strings, then run the resulting string through a hash function.
In C#, adapted and improved from alexroat's answer. Just set Random.seed = MyUtils.GetSeedXY(x, y) and you're good to go.
public static class MyUtils
{
static int seed2(int _s)
{
var s = 192837463 ^ System.Math.Abs(_s);
var a = 1664525;
var c = 1013904223;
var m = 4294967296;
return (int) ((s * a + c) % m);
}
public static int GetSeedXY(int x, int y)
{
int sx = seed2(x * 1947);
int sy = seed2(y * 2904);
return seed2(sx ^ sy);
}
}