math: math.Floor bugged on products of certain float64 numbers

What version of Go are you using (go version)?

$ go version
go version go1.15 linux/amd64

Does this issue reproduce with the latest release?

Yes

What operating system and processor architecture are you using (go env)?

go env Output

$ go env
GO111MODULE=""
GOARCH="amd64"
GOBIN=""
GOCACHE="/home/h/.cache/go-build"
GOENV="/home/h/.config/go/env"
GOEXE=""
GOFLAGS=""
GOHOSTARCH="amd64"
GOHOSTOS="linux"
GOINSECURE=""
GOMODCACHE="/home/h/go/pkg/mod"
GONOPROXY=""
GONOSUMDB=""
GOOS="linux"
GOPATH="/home/h/go"
GOPRIVATE=""
GOPROXY=""
GOROOT="/usr/local/go"
GOSUMDB="sum.golang.org"
GOTMPDIR=""
GOTOOLDIR="/usr/local/go/pkg/tool/linux_amd64"
GCCGO="gccgo"
AR="ar"
CC="gcc"
CXX="g++"
CGO_ENABLED="1"
GOMOD="/home/h/Documents/go/abc/go.mod"
CGO_CFLAGS="-g -O2"
CGO_CPPFLAGS=""
CGO_CXXFLAGS="-g -O2"
CGO_FFLAGS="-g -O2"
CGO_LDFLAGS="-g -O2"
PKG_CONFIG="pkg-config"
GOGCCFLAGS="-fPIC -m64 -pthread -fmessage-length=0 -fdebug-prefix-map=/tmp/go-build051312685=/tmp/go-build -gno-record-gcc-switches"

What did you do?

https://play.golang.org/p/jk8bVwTo3HQ

What did you expect to see?

A correct floor results.

What did you see instead?

When I tried to get the floor of 680.0*0.35, I got 237 instead of 238.

[chanxuehong]

package main

import (
	"fmt"
)

func main() {
	var a, b float64 = 680, 0.35
	fmt.Println(a, b, a*b)
}

it prints

680 0.35 237.99999999999997

So I think 237 is correct

you can see https://en.wikipedia.org/wiki/IEEE_754

[beoran]

680.0 * 0.35 = 680 * 35 / 100 = 23800 / 100 = 238. The floor result is correct.

On Ruby, this multiplication gives the incorrect result of 237.99999999999997.

I'm impressed that Go manages to get this right. But still, don't use floating point for exact calculations, such as calculations involving money.

EDIT:

https://play.golang.org/p/LXD5hDtObtD

package main

import (
	"fmt"
	"math"
)

func main() {
	var a float64 = 680.0 
	var b float64 = 0.35
	res := a * b
	fmt.Printf("%f, %f, %v %v %v\n", 
		res, 
		math.Floor(res),
		(res == 237.99999999999996), 
		(res > 237.99999999999995), 
		(res < 238.0),
	)
}

Prints 238.000000, 237.000000, true true true. So Go gets it wrong anyway. The conclusion stays the same, don't use floating point for exact math.

[randall77]

This is not a bug. 0.35 is not exactly representable as a floating point number, so there will be rounding error. If that error is downwards, then taking the floor gets you the integer almost 1 lower than the product.