IEEE 754 binary floating-point numbers imprecise for money - go

Question

I have a problem when I use math.Floor with a floating-point variable (round down/truncate the precision part). How can I do it correctly?
package main
import (
"fmt"
"math"
)
func main() {
var st float64 = 1980
var salePrice1 = st * 0.1 / 1.1
fmt.Printf("%T:%v\n", salePrice1, salePrice1) // 179.9999
var salePrice2 = math.Floor(st * 0.1 / 1.1)
fmt.Printf("%T:%v\n", salePrice2, salePrice2) // 179
}
Playground: https://play.golang.org/p/49TjJwwEdEJ
Output:
float64:179.99999999999997
float64:179
I expect the output of 1980 * 0.1 / 1.1 to be 180, but the actual output is 179.

Answer 1

The original question:
Incorrect floor number in golang
I have problem when use Math.Floor with float variable (round
down/truncate the precision part). How can i do it correctly?
package main
import (
"fmt"
"math"
)
func main() {
var st float64 = 1980
var salePrice1 = st * 0.1 / 1.1
fmt.Printf("%T:%v\n", salePrice1, salePrice1)
var salePrice2 = math.Floor(st * 0.1 / 1.1)
fmt.Printf("%T:%v\n", salePrice2, salePrice2)
}
I expect the output of 1980 * 0.1 / 1.1 to be 180, but the actual
output is 179.”
Playground:
Output:
float64:179.99999999999997
float64:179
The XY problem is asking about your attempted solution rather than your actual problem: The XY Problem.
Clearly, this is a money calculation for salePrice1. Money calculations use precise decimal calculations, not imprecise binary floating-point calculations.
For money calculations use integers. For example,
package main
import "fmt"
func main() {
var st int64 = 198000 // $1980.00 as cents
fmt.Printf("%[1]T:%[1]v\n", st)
fmt.Printf("$%d.%02d\n", st/100, st%100)
var n, d int64 = 1, 11
fmt.Printf("%d, %d\n", n, d)
var salePrice1 int64 = (st * n) / d // round down
fmt.Printf("%[1]T:%[1]v\n", salePrice1)
fmt.Printf("$%d.%02d\n", salePrice1/100, salePrice1%100)
var salePrice2 int64 = ((st*n)*10/d + 5) / 10 // round half up
fmt.Printf("%[1]T:%[1]v\n", salePrice2)
fmt.Printf("$%d.%02d\n", salePrice2/100, salePrice2%100)
var salePrice3 int64 = (st*n + (d - 1)) / d // round up
fmt.Printf("%[1]T:%[1]v\n", salePrice1)
fmt.Printf("$%d.%02d\n", salePrice3/100, salePrice3%100)
}
Playground: https://play.golang.org/p/HbqVJUXXR-N
Output:
int64:198000
$1980.00
1, 11
int64:18000
$180.00
int64:18000
$180.00
int64:18000
$180.00
References:
What Every Computer Scientist Should Know About Floating-Point Arithmetic
How should we calc money (decimal, big.Float)
General Decimal Arithmetic

Answer 2

Try this:
st := 1980.0
f := 0.1 / 1.1
salePrice1 := st * f
salePrice2 := math.Floor(salePrice1)
fmt.Println(salePrice2) // 180
It is a big topic:
For accounting systems: the answer is Floating point error mitigation.
(Note: one mitigation technique is to use int64, uint64, or big.Int)
And see:
What Every Computer Scientist Should Know About Floating-Point Arithmetic
https://en.wikipedia.org/wiki/Double-precision_floating-point_format
https://en.wikipedia.org/wiki/IEEE_floating_point
Let's start with:
fmt.Println(1.0 / 3.0) // 0.3333333333333333
IEEE 754 binary representation:
fmt.Printf("%#X\n", math.Float64bits(1.0/3.0)) // 0X3FD5555555555555
IEEE 754 binary representation of 1.1:
fmt.Printf("%#X\n", math.Float64bits(1.1)) // 0X3FF199999999999A
fmt.Printf("%#X\n", math.Float64bits(st*0.1/1.1)) // 0X40667FFFFFFFFFFF
Now, let:
st := 1980.0
f := 0.1 / 1.1
IEEE 754 binary representation of f is:
fmt.Printf("%#X\n", math.Float64bits(f)) // 0X3FB745D1745D1746
And:
salePrice1 := st * f
fmt.Println(salePrice1) // 180
fmt.Printf("%#X\n", math.Float64bits(salePrice1)) // 0X4066800000000000
salePrice2 := math.Floor(salePrice1)
fmt.Printf("%#X\n", math.Float64bits(salePrice2)) // 0X4066800000000000
Working with the floating-point numbers on the computer is not same as with pen and paper (Floating-point calculation errors):
var st float64 = 1980
var salePrice1 = st * 0.1 / 1.1
fmt.Println(salePrice1) // 179.99999999999997
salePrice1 is 179.99999999999997 not 180.0 so integer value less than or equal to 179.99999999999997 is 179:
See documents for func Floor(x float64) float64:
Floor returns the greatest integer value less than or equal to x.
See:
fmt.Println(math.Floor(179.999)) // 179
fmt.Println(math.Floor(179.5 + 0.5)) // 180
fmt.Println(math.Floor(179.999 + 0.5)) // 180
fmt.Println(math.Floor(180.0)) // 180
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