math: math.Log does not handle subnormal floating point number on amd64

[liu-du]

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

$ go version
go version go1.18.3 darwin/amd64

Does this issue reproduce with the latest release?

Yes

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

macOS and amd64

go env Output

$ go env
GO111MODULE=""
GOARCH="amd64"
GOBIN=""
GOCACHE="/Users/$USER/Library/Caches/go-build"
GOENV="/Users/$USER/Library/Application Support/go/env"
GOEXE=""
GOEXPERIMENT=""
GOFLAGS=""
GOHOSTARCH="amd64"
GOHOSTOS="darwin"
GOINSECURE=""
GOMODCACHE="/Users/$USER/go/pkg/mod"
GONOPROXY=""
GONOSUMDB=""
GOOS="darwin"
GOPATH="/Users/$USER/go"
GOPRIVATE=""
GOPROXY="https://proxy.golang.org,direct"
GOROOT="/usr/local/Cellar/go/1.18.3/libexec"
GOSUMDB="sum.golang.org"
GOTMPDIR=""
GOTOOLDIR="/usr/local/Cellar/go/1.18.3/libexec/pkg/tool/darwin_amd64"
GOVCS=""
GOVERSION="go1.18.3"
GCCGO="gccgo"
GOAMD64="v1"
AR="ar"
CC="clang"
CXX="clang++"
CGO_ENABLED="1"
GOMOD="/Users/$USER/code/go/src/go.mod"
GOWORK=""
CGO_CFLAGS="-g -O2"
CGO_CPPFLAGS=""
CGO_CXXFLAGS="-g -O2"
CGO_FFLAGS="-g -O2"
CGO_LDFLAGS="-g -O2"
PKG_CONFIG="pkg-config"
GOGCCFLAGS="-fPIC -arch x86_64 -m64 -pthread -fno-caret-diagnostics -Qunused-arguments -fmessage-length=0 -fdebug-prefix-map=/var/folders/nn/pgfwsh7d0kn99mpmf7fd35_r0000gn/T/go-build681644206=/tmp/go-build -gno-record-gcc-switches -fno-common"

What did you do?

I tried math.Log on very small float64 (subnormal IEEE floating point number), it gives incorrect result. This only happens on amd64, when math/log_amd64.S is used.

Running the same go code on, for example, arm64 gives correct results. I found math/log_amd64.S doesn't normalize subnormal floating number, whereas the go implementation of math.log (which calls math.Frexp) does normalise the floating point number. Hence different arch gives different results.

What did you expect to see?

The natural log for subnormal floating number should be correct. The equivalent c code gives correct result (python/java also gives the same results as c, although they possibly just call the c implementation):

#include <stdio.h>
#include <math.h>

int main() {
    printf("%f\n", log(pow(2, -1074))); // -744.440072
    printf("%f\n", log(exp(1) * pow(2, -1074))); // -743.341460
    printf("%f\n", log(exp(2) * pow(2, -1074))); // -742.494162
    printf("%f\n", log(exp(3) * pow(2, -1074))); // -741.444340
}

What did you see instead?

// x should be around -744 but it's -709
x := math.Log(math.SmallestNonzeroFloat64) // -709.0895657128241

// should be around x + 1, but it's equal x
fmt.Println(math.Log(math.Exp(1) * math.SmallestNonzeroFloat64))// -709.0895657128241

// should be around x + 2, but it's equal x
fmt.Println(math.Log(math.Exp(2) * math.SmallestNonzeroFloat64)) // -709.0895657128241

// should be around x + 3, but it's equal x
fmt.Println(math.Log(math.Exp(3) * math.SmallestNonzeroFloat64)) // -709.0895657128241

go.dev/play link: https://go.dev/play/p/uksqrp1Zq0-

[gopherbot]

Change https://go.dev/cl/448216 mentions this issue: math: improve math.Log to handle subnormal floating number on amd64

[seankhliao]

cc @griesemer @rsc

[liu-du]

Hi @seankhliao, I'm revisiting this issue after while and hoping to make a (small) contribution and close the loop, do you have any feedback on the PR?