runtime: avoid fma in mkfastlog2table
This lets us generate identical copies of fastlog2table.go on all hosts.
Tested by regenerating fastlog2table.go on linux-amd64 and darwin-arm64.
Fixes #49891
Change-Id: I279d6b5abb5a5290c049d9658050fd9c8d0c0190
Reviewed-on: https://go-review.googlesource.com/c/go/+/413976
Run-TryBot: Ian Lance Taylor <iant@google.com>
Run-TryBot: Ian Lance Taylor <iant@golang.org>
Reviewed-by: Ian Lance Taylor <iant@google.com>
Reviewed-by: Michael Knyszek <mknyszek@google.com>
TryBot-Result: Gopher Robot <gobot@golang.org>
Auto-Submit: Ian Lance Taylor <iant@google.com>
diff --git a/src/runtime/mkfastlog2table.go b/src/runtime/mkfastlog2table.go
index a55f547..614d1f7 100644
--- a/src/runtime/mkfastlog2table.go
+++ b/src/runtime/mkfastlog2table.go
@@ -46,7 +46,64 @@
func computeTable() []float64 {
fastlog2Table := make([]float64, 1<<fastlogNumBits+1)
for i := 0; i <= (1 << fastlogNumBits); i++ {
- fastlog2Table[i] = math.Log2(1.0 + float64(i)/(1<<fastlogNumBits))
+ fastlog2Table[i] = log2(1.0 + float64(i)/(1<<fastlogNumBits))
}
return fastlog2Table
}
+
+// log2 is a local copy of math.Log2 with an explicit float64 conversion
+// to disable FMA. This lets us generate the same output on all platforms.
+func log2(x float64) float64 {
+ frac, exp := math.Frexp(x)
+ // Make sure exact powers of two give an exact answer.
+ // Don't depend on Log(0.5)*(1/Ln2)+exp being exactly exp-1.
+ if frac == 0.5 {
+ return float64(exp - 1)
+ }
+ return float64(nlog(frac)*(1/math.Ln2)) + float64(exp)
+}
+
+// nlog is a local copy of math.Log with explicit float64 conversions
+// to disable FMA. This lets us generate the same output on all platforms.
+func nlog(x float64) float64 {
+ const (
+ Ln2Hi = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
+ Ln2Lo = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
+ L1 = 6.666666666666735130e-01 /* 3FE55555 55555593 */
+ L2 = 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
+ L3 = 2.857142874366239149e-01 /* 3FD24924 94229359 */
+ L4 = 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
+ L5 = 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
+ L6 = 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
+ L7 = 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
+ )
+
+ // special cases
+ switch {
+ case math.IsNaN(x) || math.IsInf(x, 1):
+ return x
+ case x < 0:
+ return math.NaN()
+ case x == 0:
+ return math.Inf(-1)
+ }
+
+ // reduce
+ f1, ki := math.Frexp(x)
+ if f1 < math.Sqrt2/2 {
+ f1 *= 2
+ ki--
+ }
+ f := f1 - 1
+ k := float64(ki)
+
+ // compute
+ s := float64(f / (2 + f))
+ s2 := float64(s * s)
+ s4 := float64(s2 * s2)
+ t1 := s2 * float64(L1+float64(s4*float64(L3+float64(s4*float64(L5+float64(s4*L7))))))
+ t2 := s4 * float64(L2+float64(s4*float64(L4+float64(s4*L6))))
+ R := float64(t1 + t2)
+ hfsq := float64(0.5 * f * f)
+ return float64(k*Ln2Hi) - ((hfsq - (float64(s*float64(hfsq+R)) + float64(k*Ln2Lo))) - f)
+}
