vector: prevent fused multiply-add being used in floatingLineTo
The test code now produces bit-identical results across platforms.
Fixes golang/go#21460.
Change-Id: I58b72dacf3c7930e2804b4e37bd3ccd9ef3dc2f0
Reviewed-on: https://go-review.googlesource.com/61024
Run-TryBot: Michael Munday <mike.munday@ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Nigel Tao <nigeltao@golang.org>
diff --git a/vector/raster_floating.go b/vector/raster_floating.go
index 143b376..fd11db1 100644
--- a/vector/raster_floating.go
+++ b/vector/raster_floating.go
@@ -54,13 +54,25 @@
for ; y < yMax; y++ {
dy := floatingMin(float32(y+1), by) - floatingMax(float32(y), ay)
- xNext := x + dy*dxdy
+
+ // The "float32" in expressions like "float32(foo*bar)" here and below
+ // look redundant, since foo and bar already have type float32, but are
+ // explicit in order to disable the compiler's Fused Multiply Add (FMA)
+ // instruction selection, which can improve performance but can result
+ // in different rounding errors in floating point computations.
+ //
+ // This package aims to have bit-exact identical results across all
+ // GOARCHes, and across pure Go code and assembly, so it disables FMA.
+ //
+ // See the discussion at
+ // https://groups.google.com/d/topic/golang-dev/Sti0bl2xUXQ/discussion
+ xNext := x + float32(dy*dxdy)
if y < 0 {
x = xNext
continue
}
buf := z.bufF32[y*width:]
- d := dy * dir
+ d := float32(dy * dir)
x0, x1 := x, xNext
if x > xNext {
x0, x1 = x1, x0
@@ -71,48 +83,48 @@
x1Ceil := float32(x1i)
if x1i <= x0i+1 {
- xmf := 0.5*(x+xNext) - x0Floor
+ xmf := float32(0.5*(x+xNext)) - x0Floor
if i := clamp(x0i+0, width); i < uint(len(buf)) {
- buf[i] += d - d*xmf
+ buf[i] += d - float32(d*xmf)
}
if i := clamp(x0i+1, width); i < uint(len(buf)) {
- buf[i] += d * xmf
+ buf[i] += float32(d * xmf)
}
} else {
s := 1 / (x1 - x0)
x0f := x0 - x0Floor
oneMinusX0f := 1 - x0f
- a0 := 0.5 * s * oneMinusX0f * oneMinusX0f
+ a0 := float32(0.5 * s * oneMinusX0f * oneMinusX0f)
x1f := x1 - x1Ceil + 1
- am := 0.5 * s * x1f * x1f
+ am := float32(0.5 * s * x1f * x1f)
if i := clamp(x0i, width); i < uint(len(buf)) {
- buf[i] += d * a0
+ buf[i] += float32(d * a0)
}
if x1i == x0i+2 {
if i := clamp(x0i+1, width); i < uint(len(buf)) {
- buf[i] += d * (1 - a0 - am)
+ buf[i] += float32(d * (1 - a0 - am))
}
} else {
- a1 := s * (1.5 - x0f)
+ a1 := float32(s * (1.5 - x0f))
if i := clamp(x0i+1, width); i < uint(len(buf)) {
- buf[i] += d * (a1 - a0)
+ buf[i] += float32(d * (a1 - a0))
}
- dTimesS := d * s
+ dTimesS := float32(d * s)
for xi := x0i + 2; xi < x1i-1; xi++ {
if i := clamp(xi, width); i < uint(len(buf)) {
buf[i] += dTimesS
}
}
- a2 := a1 + s*float32(x1i-x0i-3)
+ a2 := a1 + float32(s*float32(x1i-x0i-3))
if i := clamp(x1i-1, width); i < uint(len(buf)) {
- buf[i] += d * (1 - a2 - am)
+ buf[i] += float32(d * (1 - a2 - am))
}
}
if i := clamp(x1i, width); i < uint(len(buf)) {
- buf[i] += d * am
+ buf[i] += float32(d * am)
}
}
