Fix buggy formula for critically-damped springs (#120488)

Fixes #109675.

This formula would produce an initial velocity quite different
from the one specified as an argument.

To update the test, I computed the expected results separately
by using the physical formula.

Happily, the framework by default never ends up actually exercising
this code.  Of the four SpringDescription call sites within the
framework, two are explicitly overdamped; the other two are by
design critically damped, but due to rounding they end up being
treated as (very slightly) overdamped too.  Details here:
  flutter/flutter#109675 (comment)

So the only way an app could be affected by this bug is if it called
a SpringDescription constructor itself, and managed to create a spring
description where the distinguishing formula in _SpringSolution comes
out exactly equal to zero.  It's likely nobody has ever shipped such
an app, because the behavior this produces would be so wildly wrong
that it'd be hard to miss when exercised.

Co-authored-by: Kate Lovett <katelovett@google.com>

Author: gnprice

packages/flutter/lib/src/physics/spring_simulation.dart

@@ -176,7 +176,7 @@ class _CriticalSolution implements _SpringSolution {
   ) {
     final double r = -spring.damping / (2.0 * spring.mass);
     final double c1 = distance;
-    final double c2 = velocity / (r * distance);
+    final double c2 = velocity - (r * distance);
     return _CriticalSolution.withArgs(r, c1, c2);
   }
 

packages/flutter/test/physics/newton_test.dart

@@ -167,19 +167,19 @@ void main() {
 
     expect(crit.isDone(0.0), false);
     expect(crit.x(0.0), 0.0);
-    expect(crit.dx(0.0), 5000.0);
+    expect(crit.dx(0.0), 0.0);
 
-    expect(crit.x(0.25).floor(), 458.0);
-    expect(crit.x(0.50).floor(), 496.0);
-    expect(crit.x(0.75).floor(), 499.0);
+    expect(crit.x(0.25).floor(), 356);
+    expect(crit.x(0.50).floor(), 479);
+    expect(crit.x(0.75).floor(), 497);
 
-    expect(crit.dx(0.25).floor(), 410);
-    expect(crit.dx(0.50).floor(), 33);
-    expect(crit.dx(0.75).floor(), 2);
+    expect(crit.dx(0.25).floor(), 1026);
+    expect(crit.dx(0.50).floor(), 168);
+    expect(crit.dx(0.75).floor(), 20);
 
-    expect(crit.isDone(1.50), true);
     expect(crit.x(1.5) > 499.0 && crit.x(1.5) < 501.0, true);
     expect(crit.dx(1.5) < 0.1, true /* basically within tolerance */);
+    expect(crit.isDone(1.60), true);
   });
 
   test('overdamped_spring', () {
@@ -195,6 +195,7 @@ void main() {
 
     expect(over.isDone(0.0), false);
     expect(over.x(0.0), 0.0);
+    expect(over.dx(0.0), moreOrLessEquals(0.0));
 
     expect(over.x(0.5).floor(), 445.0);
     expect(over.x(1.0).floor(), 495.0);
@@ -216,6 +217,8 @@ void main() {
     expect(under.type, SpringType.underDamped);
 
     expect(under.isDone(0.0), false);
+    expect(under.x(0.0), moreOrLessEquals(0.0));
+    expect(under.dx(0.0), moreOrLessEquals(0.0));
 
     // Overshot with negative velocity
     expect(under.x(1.0).floor(), 325);