Windows mouse pointer acceleration (Enhance pointer precision) is partially broken - Part zero

Until Windows 7, mouse handling in Windows has been subtly broken in some ways, and it has taken Microsoft 8 years to fix those problems.

You can fairly easily see these problems (in Vista and XP).
They appear when the Mouse Properties 'Enhance pointer precision' option is turned on (* Note).

In a previous blog I wrote about one of the problems: mouse pointer DPI scaling is wrong in Vista and XP. I'll summarise that problem and also describe another problem.

Rounding of Fractional Intermediate Results Causes Pointer Jitter and Drift

The various internal acceleration and scaling calculations result in a fractional mouse-pointer movement.
This fractional movement is turned into an integer actual number of pixels moved and a fractional remainder.
The fractional remainder is saved internally and applied to the next mouse input.

Such calculations have been done for some while for the 'Mouse Speed' slider, at least since Windows 98.
Typically the fractional result is truncated towards zero, leaving a remainder that has the same sign as the integer part.
(For example, +2.7 is truncated to +2 with remainder +0.7; -3.3 is truncated to -3 with remainder -0.3)

• Windows 7 adds in the previous remainder, then truncates the fractional result towards zero, and stores the new remainder.
  This is desirable and good.
  
  If you record how the Windows 7 pointer responds to mouse input, you can create a picture like this (* Note):
  (The small red dot is on-mouse-pad mouse movement, moving slowly in a circle of diameter 20 'dots' or Mickeys.
  The pointer is how the Windows 7 pointer moves on the screen in response.
  Note that the red dot moves in a larger circle than the pointer does: This is what the 'Enhance pointer precision' option does: If you move the mouse slowly, the pointer moves even slower to allow you fine control over objects selected.)
  
  
• Vista sometimes adds in the previous remainder and sometimes discards the previous remainder, then truncates towards -infinity, and stores the new remainder.
  
  Truncating towards -infinity means that the remainders are always +ve numbers. Sometimes discarding the +ve remainder can cause the mouse pointer to drift up and left over time relative to the actual on-mouse-pad mouse position.
  
  (You can see the drift if you move your on-mouse-pad mouse in a slow circle, making sure to keep the physical mouse near the same point on the mouse pad. Over time the mouse pointer drifts up and left.)
  
  
• XP sometimes adds in the previous remainder and sometimes discards the previous remainder, then truncates towards -infinity, and stores the new remainder.
  It discards the remainder more frequently than Vista.
  
  Truncating towards -infinity means that the remainders are always +ve numbers. Sometimes discarding the +ve remainder can cause the mouse pointer to drift up and left over time relative to the actual on-mouse-pad mouse position, and may cause gently curved near-horizontal or gently curved near-vertical mouse input to result in the mouse pointer 'snapping' to exactly-horizontal or exactly-vertical lines.
  These effects are far more pronounced in XP than they are in Vista.
  
  (You can see the drift the same as for Vista. Also, slow movement at 45 degrees down and right is grossly slowed down and slow movement 45 degrees up and left is sped up.)
  
  If you record how the Windows XP pointer responds to mouse input, you can create a picture like this (* Note):
  (The small red dot is on-mouse-pad mouse movement, moving slowly in a circle of diameter 20 'dots' or Mickeys.
  The pointer is how the Windows XP pointer moves on the screen in response.
  Note that the pointer slowly moves up and left even though the mouse is circling in place.)

Mouse Pointer DPI Scaling is Completely Wrong in Vista and XP

For a long while (Win9x+), Windows has scaled user interface (UI) elements according to the monitor DPI Setting.
Larger DPI settings cause UI elements to be drawn larger on-screen.

Starting in XP, Microsoft attempted to apply DPI scaling to mouse pointer movement.

• In Windows 7, mouse pointer movement is scaled according to DPI. For a given on-mouse-pad mouse movement, larger DPI settings cause larger on-screen pointer movement.
  An internal calculation includes a factor '* DPI'.
  
  
• In XP and Vista, Microsoft got the internal scaling calculation wrong. For a given on-mouse-pad mouse movement, larger DPI settings cause smaller on-screen pointer movement.
  An internal calculation includes a divisor '/ DPI'.

Mouse Pointer Monitor Refresh Rate Scaling Occurs in Vista and XP When It Should Not

• Windows 7 does not scale mouse pointer movement according to the monitor refresh rate.
  
  
• XP and Vista do scale mouse pointer movement according to monitor refresh rate.
  This is incorrect (see my previous post for details).
  An internal calculation includes a factor '* RefreshRate'.

* Note. To see these effects requires the Mouse Properties 'Enhance pointer precision' checkbox to be ON, and might be masked by mouse drivers specific to a particular mouse, for example: Logitech SetPoint mouse drivers with the 'Game Mode > Speed and Acceleration > SetPoint implemention' option selected do not exhibit the above behaviours. The animations were created with the Control Panel Mouse Speed slider set to the middle, 6th position.