math: Exp(x) function on amd64 can not return denormal numbers

[erifan]

Please answer these questions before submitting your issue. Thanks!

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

Go version devel +2de98eb Sat Dec 16 23:30:58 2017 +0000 linux/amd64

Does this issue reproduce with the latest release?

Yes

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

GOARCH="amd64"
GOBIN=""
GOCACHE="/home/username/.cache/go-build"
GOEXE=""
GOHOSTARCH="amd64"
GOHOSTOS="linux"
GOOS="linux"
GOPATH="/home/username/golangworkspace"
GORACE=""
GOROOT="/home/username/golang"
GOTMPDIR=""
GOTOOLDIR="/home/username/golang/pkg/tool/linux_amd64"
GCCGO="gccgo"
CC="gcc"
CXX="g++"
CGO_ENABLED="1"
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-build362762432=/tmp/go-build -gno-record-gcc-switches"

What did you do?

Add a test case: Exp(-740.0) for Exp(x) function, and verify the correctness of Exp(x) with commands:
cd golang/src/math/
../../bin/go test -c
./math.test -test.run TestExp$
Changes are as follow:

diff --git a/src/math/all_test.go b/src/math/all_test.go
index 0412c19..47cf947 100644
--- a/src/math/all_test.go
+++ b/src/math/all_test.go
@@ -1012,6 +1012,7 @@ var vfexpSC = []float64{
        1.48852223e+09,
        1.4885222e+09,
        1,
+       -7.40e+02,                           // The input parameters of Exp(x) function
 }
 var expSC = []float64{
        0,
@@ -1023,6 +1024,7 @@ var expSC = []float64{
        Inf(1),
        Inf(1),
        2.718281828459045,
+       4.2e-322,                             // The expected result of Exp(-740.0)
 }

 var vfexp2SC = []float64{

What did you expect to see?

PASS

What did you see instead?

--- FAIL: TestExp (0.00s)
all_test.go:2277: Exp(-740) = 0, want 4.2e-322
FAIL

[odeke-em]

@erifan thank you for the report. I have modified your issue just to display your diff in markdown.

/cc @griesemer

[ALTree]

This is a limitation of the algorithm used in the amd64 assembly implementation of Exp (the pure go version we use e.g. for 386 does not have this issue and correctly returns 4.2e-322). AFAIK it's not the only issue the amd64 implementation has. It's much faster than the pure go version, but accuracy-wise it's not as good. It has been like this since forever, anyway, it's not a recent regression.

[odeke-em]

Thank you @ALTree! I'll mark this for Go1.11 then.

[gopherbot]

Change https://golang.org/cl/87337 mentions this issue: math: handle denormals in AMD64 Exp

[griesemer]

@erifan This has not been submitted yet. Re-opening. Once it's submitted, the issue will be closed automatically.