From e2faf17bcc523557e44ef443b48a53f286886a53 Mon Sep 17 00:00:00 2001 From: "reed@google.com" Date: Mon, 6 Aug 2012 19:01:34 +0000 Subject: Even when the pts are restricted to 32K values, we can still overflow computing a fixed-point coefficient for quadratics. To avoid this, we bias these coefficients, storing 1/2 of their actual value, and then apply the 2x unbias in updateQuadratic(). Fixes http://code.google.com/p/chromium/issues/detail?id=140803 Review URL: https://codereview.appspot.com/6450099 git-svn-id: http://skia.googlecode.com/svn/trunk@4960 2bbb7eff-a529-9590-31e7-b0007b416f81 --- src/core/SkEdge.cpp | 35 ++++++++++++++++++++++++++++++----- 1 file changed, 30 insertions(+), 5 deletions(-) (limited to 'src/core') diff --git a/src/core/SkEdge.cpp b/src/core/SkEdge.cpp index aab1c76120..d328ca315b 100644 --- a/src/core/SkEdge.cpp +++ b/src/core/SkEdge.cpp @@ -23,6 +23,12 @@ or pt >> 8 for antialiasing. This is implemented as pt >> (10 - shift). */ +static inline SkFixed SkFDot6ToFixedDiv2(SkFDot6 value) { + // we want to return SkFDot6ToFixed(value >> 1), but we don't want to throw + // away data in value, so just perform a modify up-shift + return value << (16 - 6 - 1); +} + ///////////////////////////////////////////////////////////////////////// int SkEdge::setLine(const SkPoint& p0, const SkPoint& p1, const SkIRect* clip, @@ -221,19 +227,38 @@ int SkQuadraticEdge::setQuadratic(const SkPoint pts[3], int shift) } fWinding = SkToS8(winding); - fCurveShift = SkToU8(shift); //fCubicDShift only set for cubics fCurveCount = SkToS8(1 << shift); - SkFixed A = SkFDot6ToFixed(x0 - x1 - x1 + x2); - SkFixed B = SkFDot6ToFixed(x1 - x0 + x1 - x0); + /* + * We want to reformulate into polynomial form, to make it clear how we + * should forward-difference. + * + * p0 (1 - t)^2 + p1 t(1 - t) + p2 t^2 ==> At^2 + Bt + C + * + * A = p0 - 2p1 + p2 + * B = 2(p1 - p0) + * C = p0 + * + * Our caller must have constrained our inputs (p0..p2) to all fit into + * 16.16. However, as seen above, we sometimes compute values that can be + * larger (e.g. B = 2*(p1 - p0)). To guard against overflow, we will store + * A and B at 1/2 of their actual value, and just apply a 2x scale during + * application in updateQuadratic(). Hence we store (shift - 1) in + * fCurveShift. + */ + + fCurveShift = SkToU8(shift - 1); + + SkFixed A = SkFDot6ToFixedDiv2(x0 - x1 - x1 + x2); // 1/2 the real value + SkFixed B = SkFDot6ToFixed(x1 - x0); // 1/2 the real value fQx = SkFDot6ToFixed(x0); fQDx = B + (A >> shift); // biased by shift fQDDx = A >> (shift - 1); // biased by shift - A = SkFDot6ToFixed(y0 - y1 - y1 + y2); - B = SkFDot6ToFixed(y1 - y0 + y1 - y0); + A = SkFDot6ToFixedDiv2(y0 - y1 - y1 + y2); // 1/2 the real value + B = SkFDot6ToFixed(y1 - y0); // 1/2 the real value fQy = SkFDot6ToFixed(y0); fQDy = B + (A >> shift); // biased by shift -- cgit v1.2.3