Video Signals And Timing

This page is a work in progress.

This page may thus be incomplete. Its content may be changed in the near future.

Warning: Setting incorrect video settings can damage a monitor

Display Signal

There are a large amount of pins in a standard VGA Cable. When your video card sends its video data to the monitor, it uses 5 data channels:

• Analog Red
• Analog Green
• Analog Blue
• Horizontal Sync
• Vertical Sync

The screen is built up scanline by scanline, by sending the appropriate RGB values over the connection. However, only having a stream of colours will not tell you which part of the stream belongs to the top-left-pixel on the screen. To solve this they added two more signals: the horizontal sync which pulses when a horizontal line is done, and the vertical sync, which pulses when all rows have been completed. Thus, each frame corresponds to a single vertical synchronisation pulse. Since each frame has the same amount of pixels, the time between consecutive pulses is a constant. The monitor times the frequency of the pulses, then based on that it knows at what time the color data should be sent to what position on the screen.

The system is however not that simple. The first monitors were CRTs, which used magnetic fields to project electron beams onto a phosphoric layer, making them visible for a short period of time. The magnetic fields of a CRT had some inertia - they couldn't be set from a random location to another random location in the time available for one pixel. Hence the video signal has to have some gaps to cope with the time a monitor needs to alter the magnetic fields and point the electron beam back to the other side of the screen. In the meantime there could be no color signal, or you might have gotten stripes on the screen.

CRTs have improved a lot since then, and are now being superseded by the highly intelligent LCD display. The standard for signaling hasn't changed since. Since the original standard was made for CRTs, the rest of the document will implicitly assume an (old) CRT. LCD displays basically decode a CRT signal and then restructure it to fit their own screen grid. Similarly, in many other references you will see that the display unit of a video card is referred to as the "CRTC" or "CRT Controller"

Display Composition

All frames of a video signal have a specific layout, and video cards have a semi-standard way of thinking about these signals. Basically, you will have to provide the video card with enough information to be able to derive all sizes present in the following diagram. VGA Hardware explains how you can give these sizes to a VGA compatible. For other hardware, you should check your card's documentation on how these values are stored within them.

Both horizontally and vertically, there are 6 states, and hence, 6 sizes. Each size is in pixels. Most of the emitted data is part of the active display, the area of x resolution * y resolution pixels. Each of the cuts are where:

• active display goes into overscan
• where overscan goes into blanking
• where blanking gets the synchronization line changed
• where the sync is restored to its original value
• where the blanking goes back into overscan
• where the overscan goes into active display, where the scanline or frame is completed and the next one is started.

Video cards usually gives you the following registers to program (both horizontally and vertially)

• Resolution (pixel size of active display)
• Total (total number of 'pixels' in a single run)
• Blanking start and end (or start and size) - marks the location of the blanking. The are that is neither blanking nor active display becomes the overscan area.
• Sync start and end (or start and size) - marks the location of the synchronization pulse

Frequencies

When you increase the resolution, you will need to send more pixels to the display. If you would keep sending pixels at the same rate, the time to transmit one frame will go up, and consequently the amount of frames in a certain timespan will go down. Since a CRT displayed pixel only gives light for a short time before running out of energy, it needs to be repeatedly refreshed. If this is done fast enough (at about 60Hz, 60 times a second) the screen appears almost constant to the human eye. This improves further when the refresh rate goes up to a point where it doesn't matter to the human eye. However when it drops too much, the screen starts appearing flashing, causing headaches to the user. Hence, we need to keep the frequency at at least 60Hz for user's sanity, and below some other rate dictated by the monitor's capabilities. To make a full frame of pixels fit within one sixtieth of a second, we will have to adjust the speed at which these pixels are transmitted. This speed is called the pixel clock, or dot clock. For example, a VGA's dot clock is either 25MHz or 28MHz, corresponding to 25 million pixels per second or 28 million pixels per second, the latter one being only just enough to display a resolution of 720x480 at 60Hz (recall that the active display is only a part of the frame). Most higher resolution video can therefore use a wide range of dot clocks, well above 25Hz, with the current range allowing enough bandwith to easily exceed 1600x1200 at a 100Hz.

While the resolution is limited by the video card, In most non-VGA scenario's, it is the monitor that can not handle the speed of the signal. The monitor has a allowed vertical frequency (the amount of frames per second, usually listed in Hz), and horizontal frequency (listed in KHz). Some CRTs are fixed frequency, only allowing certain frequencies to be used both horizontally and vertically. Old VGA displays are infamous for burning out when you feed them a signal that doesn't exactly match these rates. While modern CRTs are mostly protected from bad signaling, you must know that you can break hardware in this fashion, and that you need to be careful.

General Timing Formula

In order to cope with all the CRT antiquities, VESA has produced a set of equations that allows you to compute the various display settings you need, given the desired resolution. There are three separate sets of formulae: One to compute all settings from resolution and desired refresh rate, one taking resolution and horizontal frequency, and one taking resolution and dot clock.

Normally before setting a mode you would do the following:

• Compute the horizontal refresh rate and pixel clock from resolution and frequency
• Check the video card for the nearest pixel clock it can give you
• Compute all settings given the resolution and pixel clock.
• Check if the horizontal and vertical frequencies are within the monitor's allowed range.

If the frequencies happen to be out of range, you will have to adjust the refresh rate and or resolution. Since the refresh rate can go down a bit without giving issues, that's usually the first choice to fix. Hence:

• Clamp the horizontal frequency to its limit
• Compute pixel clock and vertical frequency from resolution and the new horizontal frequency
• Select the appropriate pixel clock the video card has (making sure you are rounding away from the limit, so round down if you use the maximum horizontal frequency)
• Compute the horizontal and vertical frequency given the new dot clock
• Check if the frequencies are within range.

The horizontal frequency should now be correct, you can decide whether or not to allow the new mode because the vertical rate has dropped below an acceptable rate, and you can inform the user that the mode is not supported.

The formula's provided by VESA use various scales of constants. Brendan's working on changing the scales to units. Right now, the scale space is still unknown.

Common parts of the GTF formulas

H_PIXELS_RND = ( ROUND ( H_PIXELS / CELL_GRAN_RND ) ) * CELL_GRAN_RND

if ( INTERLACE_REQUIRED == true )
{

V_LINES_RND = ROUND ( V_LINES / 2 )

V_FIELD_RATE_REQUIRED = REFRESH_RATE_REQUIRED * 2

INTERLACE = 0.5

} else {

V_LINES_RND = ROUND ( V_LINES) )

V_FIELD_RATE_REQUIRED = REFRESH_RATE_REQUIRED

INTERLACE = 0

}

if ( #MARGINS_REQUIRED == true ) {

TOP_MARGIN_LINES = ROUND ( #MARGIN_PRECENT / 100 * #V_LINES_RND )

BOTTOM_MARGIN_LINES = ROUND ( #MARGIN_PRECENT / 100 * #V_LINES_RND )

LEFT_MARGIN_PIXELS = ( ROUND ( #H_PIXELS_RND * #MARGIN_PRECENT / 100 / #CELL_GRAN_RND ) ) * #CELL_GRAN_RND

RIGHT_MARGIN_PIXELS = ( ROUND ( #H_PIXELS_RND * #MARGIN_PRECENT / 100 / #CELL_GRAN_RND ) ) * #CELL_GRAN_RND

} else {

TOP_MARGIN_LINES = 0

BOTTOM_MARGIN_LINES = 0

LEFT_MARGIN_PIXELS = 0

RIGHT_MARGIN_PIXELS = 0

}

GTF Using resolution and refresh rate

#H_PERIOD_ESTIMATE = ( 1 / #V_FIELD_RATE_REQUIRED - #MIN_V_SYNC_AND_BACK_PORCH / 1000000 )

/ ( #V_LINES_RND + 2 * #TOP_MARGIN_LINES + #MIN_PORCH_RND + #INTERLACE ) * 1000000

#V_SYNC_AND_BACK_PORCH = ROUND ( #MIN_V_SYNC_AND_BACK_PORCH / #H_PERIOD_ESTIMATE )

#V_BACK_PORCH = #V_SYNC_AND_BACK_PORCH - #V_SYNC_RND

#TOTAL_V_LINES = #V_LINES_RND +

#TOP_MARGIN_LINES + #BOTTOM_MARGIN_LINES +

#V_SYNC_AND_BACK_PORCH + #INTERLACE + #MIN_PORCH_RND

#V_FIELD_RATE_ESTIMATE = 1000000 / #H_PERIOD_ESTIMATE / #TOTAL_V_LINES

#H_PERIOD = #H_PERIOD_ESTIMATE * #V_FIELD_RATE_ESTIMATE / #V_FIELD_RATE_REQUIRED

#V_FIELD_RATE = 1000000 / #H_PERIOD / #TOTAL_V_LINES

if ( INTERLACE_REQUIRED == true ) {

#V_FRAME_RATE = #V_FIELD_RATE / 2

} else {

#V_FRAME_RATE = #V_FIELD_RATE

}

#TOTAL_ACTIVE_PIXELS = #H_PIXELS_RND + #LEFT_MARGIN_PIXELS + #RIGHT_MARGIN_PIXELS

#IDEAL_DUTY_CYCLE = #C_PRIME - #M_PRIME * #H_PERIOD / 1000

#H_BLANK_PIXELS = ( ROUND (

( #TOTAL_ACTIVE_PIXELS * #IDEAL_DUTY_CYCLE / ( 100 - #IDEAL_DUTY_CYCLE ) / ( 2 * #CELL_GRAN_RND ) )

) ) * 2 * #CELL_GRAN_RND

#H_TOTAL = #TOTAL_ACTIVE_PIXELS + #H_BLANK_PIXELS

#PIXEL_FREQ = #TOTAL_PIXELS / #H_PERIOD * 1000000

#H_FREQ = 1 / #H_PERIOD

Variable reference

These are the variables used in the equations above:

Hardware properties

C_PRIME

Todo Equals 40

M_PRIME

Todo Equals 600

CELL_GRAN_RND

Cell granularity - the amount of pixels the timings should be aligned to. For example, a VGA uses horizontal timings in multiples of the character clock, each character being 8 (graphics and some text modes) or 9 (most text modes) pixels wide. For a VGA graphics mode, you'll want to supply 8 here because of that. Depending on your specific hardware, you supply either 8 or 1.

MIN_PORCH_RND

Todo Equals 1. Used to force at least one unit of blanking around the sync period in order to not confuse graphics hardware?

MIN_V_SYNC_AND_BACK_PORCH

Todo Equals 550

Video mode inputs

MARGINS_REQUIRED

The margins are used to add a visible black surrounding to the displayed picture. I assume small margins are intended to make sure the entire picture is still visible when the picture isn't perfectly centered on the screen.

In theory it would be possible to use margins to simulate a small screen on a larger screen, or to simulate different aspect ratios perfectly. For example, if you were setting up a 640 * 480 video mode on a 16:10 display you could make the left and right margin 64 pixels each (with no top or bottom margins), so that it looks exactly the same as it would on a 4:3 display, rather than being stretched to fit. The opposite is also possible (e.g. displaying 16:10 video data on a 4:3 display with "letterboxing"). Unfortunately the GTF calculations don't actually support different sized left/right and top/bottom margins.

MARGIN_PERCENT

(Fixme: Percentage!) Amount of margins you want to have around your screen. VESA suggests a default of 1.8 to allow for screens that do not perfectly fit the image to the center.

INTERLACE_REQUIRED

There are two kinds of video modes, interlaced and progressive modes. Progressive modes display the full frame in one go, while interlaced modes display each other scanline in each run, taking two frames to render the complete picture. Normally, you don't want this, and several video cards don't support it, so you will normally want to supply false here.

V_LINES

Vertical resolution of the display you want. For a 640x480 resolution, supply 480.

H_PIXELS

Horizontal resolution of the display you want. For a 640x480 resolution, supply 640. Note that video cards will usually want this to be a multiple of eight because of cell granularity.

REFRESH_RATE_REQUIRED

Todo

Outputs

TOP_MARGIN_LINES

Amount of margin at the top.

BOTTOM_MARGIN_LINES

Amount of margin at the bottom

LEFT_MARGIN_PIXELS

Amount of margin at the left

RIGHT_MARGIN_PIXELS

Amount of margin at the right

H_TOTAL

Amount of pixels in a scanline

Intermediates

V_LINES_RND

Amount of active display scanlines per frame. Equals the Y resolution unless interlaced modes are used.

H_PIXELS_RND

Actual horizontal resolution used. Basically contains the X resolution rounded to the nearest allowed boundary.

V_FIELD_RATE_REQUIRED

Rate of complete images being sent to the monitor per second. Unless interlaced mode is used, equals the refresh rate.

H_FREQ

The horizontal frequency in Hz

H_PERIOD

The time in seconds spent on a scanline

H_PERIOD

The initial estimate of time in seconds spent on a scanline

INTERLACE

todo

V_SYNC_AND_BACK_PORCH

The number of scanlines spent on VSync and bottom blanking

Brendan's Original Posts

>Any problems if I wikify this? None at all - IMHO this information is required just to use VBE reliably; along with EDID (but you can find version 1.1 of the EDID data structures on Wikipedia) and details for the VBE DDC function (which VESA will let you have for free).

However, I should point out that this information is incomplete - the value of certain constants are missing from my original post. The default values for these constants are: CELL_GRAN_RND = 8, MARGIN_PRECENT = 1.8, MIN_PORCH_RND = 1, MIN_V_SYNC_AND_BACK_PORCH = 550, C_PRIME = 40 and M_PRIME = 600. I'd also mention that for my version of the formulas REFRESH_RATE_REQUIRED, V_FIELD_RATE_REQUIRED, H_FREQ_REQUIRED, PIXEL_FREQ_REQUIRED, V_FIELD_RATE, H_FREQ, PIXEL_FREQ are all in Hz (and not a mixture of Hz, KHz and MHz), which helps to simplify the formulas.

There's also some strange things that can happen with these formulas. For example, if any of the calculations give a negative result then it indicates invalid input (e.g. if the PIXEL_FREQ_REQUIRED input parameter is too low, then you can end up with horizontal blanking that takes "negative N us"). In practice, some of these calculations probably have an allowed range (e.g. things like "horizontal blanking must be >= 20% of the horizontal total") but I've been unable to find anything indicating what the allowed ranges for anything is. :(

---

This is for my own reference, and in case anyone is wondering what they look like... The GTF formulas.

There's actually 3 separate calculations here - finding all timing parameters from X & Y resolution and desired refresh rate, finding all timing parameters from X & Y resolution and desired horizontal frequency, and finding all timing parameters from X & Y resolution and desired pixel clock frequency.

GTF Formulas For Using Desired Refresh Rate

H_PIXELS_RND = ( ROUND ( H_PIXELS / CELL_GRAN_RND ) ) * CELL_GRAN_RND

IF ( INTERLACE_REQUIRED == "y") {
    V_LINES_RND = ROUND ( V_LINES / 2 )
    V_FIELD_RATE_REQUIRED = REFRESH_RATE_REQUIRED * 2
    INTERLACE = 0.5
  } else {
    V_LINES_RND = ROUND ( V_LINES) )
    V_FIELD_RATE_REQUIRED = REFRESH_RATE_REQUIRED
    INTERLACE = 0
  }

IF ( MARGINS_REQUIRED == "y" ) {
    TOP_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    BOTTOM_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    LEFT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
    RIGHT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
  } else {
    TOP_MARGIN_LINES = 0
    BOTTOM_MARGIN_LINES = 0
    LEFT_MARGIN_PIXELS = 0
    RIGHT_MARGIN_PIXELS = 0
  }

H_PERIOD_ESTIMATE = ( 1 / V_FIELD_RATE_REQUIRED - MIN_V_SYNC_AND_BACK_PORCH / 1000000 ) / ( V_LINES_RND + 2 * TOP_MARGIN_LINES + MIN_PORCH_RND + INTERLACE ) * 1000000

V_SYNC_AND_BACK_PORCH = ROUND ( MIN_V_SYNC_AND_BACK_PORCH / H_PERIOD_ESTIMATE )

V_BACK_PORCH = V_SYNC_AND_BACK_PORCH - V_SYNC_RND

TOTAL_V_LINES = V_LINES_RND + TOP_MARGIN_LINES + BOTTOM_MARGIN_LINES + V_SYNC_AND_BACK_PORCH + INTERLACE + MIN_PORCH_RND

V_FIELD_RATE_ESTIMATE = 1000000 / H_PERIOD_ESTIMATE / TOTAL_V_LINES

H_PERIOD = H_PERIOD_ESTIMATE * V_FIELD_RATE_ESTIMATE / V_FIELD_RATE_REQUIRED

V_FIELD_RATE = 1000000 / H_PERIOD / TOTAL_V_LINES

IF ( INTERLACE_REQUIRED == "y") {
    V_FRAME_RATE = V_FIELD_RATE / 2
  } else {
    V_FRAME_RATE = V_FIELD_RATE
  }

TOTAL_ACTIVE_PIXELS = H_PIXELS_RND + LEFT_MARGIN_PIXELS + RIGHT_MARGIN_PIXELS

IDEAL_DUTY_CYCLE = C_PRIME - M_PRIME * H_PERIOD / 1000

H_BLANK_PIXELS = ( ROUND ( ( TOTAL_ACTIVE_PIXELS * IDEAL_DUTY_CYCLE / ( 100 - IDEAL_DUTY_CYCLE ) / ( 2 * CELL_GRAN_RND ) ) ) ) * 2 * CELL_GRAN_RND

TOTAL_PIXELS = TOTAL_ACTIVE_PIXELS + H_BLANK_PIXELS

PIXEL_FREQ = TOTAL_PIXELS / H_PERIOD * 1000000

H_FREQ = 1 / H_PERIOD

GTF Formulas For Using Horizontal Frequency

H_PIXELS_RND = ( ROUND ( H_PIXELS / CELL_GRAN_RND ) ) * CELL_GRAN_RND

IF ( INTERLACE_REQUIRED == "y") {
    V_LINES_RND = ROUND ( V_LINES / 2 )
    INTERLACE = 0.5
  } else {
    V_LINES_RND = ROUND ( V_LINES) )
    INTERLACE = 0
  }

IF ( MARGINS_REQUIRED == "y" ) {
    TOP_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    BOTTOM_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    LEFT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
    RIGHT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
  } else {
    TOP_MARGIN_LINES = 0
    BOTTOM_MARGIN_LINES = 0
    LEFT_MARGIN_PIXELS = 0
    RIGHT_MARGIN_PIXELS = 0
  }

H_FREQ = H_FREQ_REQUIRED

V_SYNC_AND_BACK_PORCH = ROUND ( MIN_V_SYNC_AND_BACK_PORCH * H_FREQ / 1000000 )

V_BACK_PORCH = V_SYNC_AND_BACK_PORCH - V_SYNC_RND

TOTAL_V_LINES = V_LINES_RND + TOP_MARGIN_LINES + BOTTOM_MARGIN_LINES + INTERLACE + V_SYNC_AND_BACK_PORCH + MIN_PORCH_RND

V_FIELD_RATE = H_FREQ / TOTAL_V_LINES

IF ( INTERLACE_REQUIRED == "y") {
    V_FRAME_RATE = V_FIELD_RATE / 2
  } else {
    V_FRAME_RATE = V_FIELD_RATE
  }

TOTAL_ACTIVE_PIXELS = H_PIXELS_RND + RIGHT_MARGIN_PIXELS + LEFT_MARGIN_PIXELS

IDEAL_DUTY_CYCLE = C_PRIME - ( M_PRIME / H_FREQ )

H_BLANK_PIXELS = ( ROUND ( TOTAL_ACTIVE_PIXELS * IDEAL_DUTY_CYCLE / ( 100 - IDEAL_DUTY_CYCLE ) / ( 2 * CELL_GRAN_RND ) ) ) * 2 * CELL_GRAN_RND

TOTAL_PIXELS = TOTAL_ACTIVE_PIXELS + H_BLANK_PIXELS

H_PERIOD = 1 / H_FREQ

PIXEL_FREQ = TOTAL_PIXELS * H_FREQ

GTF Formulas For Using Pixel Clock Frequency

H_PIXELS_RND = ( ROUND ( H_PIXELS / CELL_GRAN_RND ) ) * CELL_GRAN_RND

IF ( INTERLACE_REQUIRED == "y") {
    V_LINES_RND = ROUND ( V_LINES / 2 )
    INTERLACE = 0.5
  } else {
    V_LINES_RND = ROUND ( V_LINES) )
    INTERLACE = 0
  }

PIXEL_FREQ = PIXEL_FREQ_REQUIRED

IF ( MARGINS_REQUIRED == "y" ) {
    TOP_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    BOTTOM_MARGIN_LINES = ROUND ( MARGIN_PRECENT / 100 * V_LINES_RND )
    LEFT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
    RIGHT_MARGIN_PIXELS = ( ROUND ( ( H_PIXELS_RND * MARGIN_PRECENT / 100 / CELL_GRAN_RND ) , 0 ) ) * CELL_GRAN_RND
  } else {
    TOP_MARGIN_LINES = 0
    BOTTOM_MARGIN_LINES = 0
    LEFT_MARGIN_PIXELS = 0
    RIGHT_MARGIN_PIXELS = 0
  }

TOTAL_ACTIVE_PIXELS = H_PIXELS_RND + RIGHT_MARGIN_PIXELS + LEFT_MARGIN_PIXELS

IDEAL_H_PERIOD = ( ( C_PRIME - 100 ) + ( SQRT ( ( ( 100 - C_PRIME ) ^ 2 ) + ( 0.4 * M_PRIME * ( TOTAL_ACTIVE_PIXELS + RIGHT_MARGIN_PIXELS + LEFT_MARGIN_PIXELS ) / PIXEL_FREQ / 1000000 ) ) ) ) / 2 / M_PRIME * 1000

IDEAL_DUTY_CYCLE = C_PRIME - ( M_PRIME * IDEAL_H_PERIOD / 1000 )

H_BLANK_PIXELS = ( ROUND ( TOTAL_ACTIVE_PIXELS * IDEAL_DUTY_CYCLE / ( 100 - IDEAL_DUTY_CYCLE ) / ( 2 * CELL_GRAN_RND ) ) ) * 2 * CELL_GRAN_RND

TOTAL_PIXELS = TOTAL_ACTIVE_PIXELS + H_BLANK_PIXELS

H_FREQ = PIXEL_FREQ / TOTAL_PIXELS

H_PERIOD = 1 / H_FREQ

V_SYNC_AND_BACK_PORCH = ROUND ( MIN_V_SYNC_AND_BACK_PORCH * H_FREQ / 1000000 )

V_BACK_PORCH = V_SYNC_AND_BACK_PORCH - V_SYNC_RND

TOTAL_V_LINES = V_LINES_RND + TOP_MARGIN_LINES + BOTTOM_MARGIN_LINES + INTERLACE + V_SYNC_AND_BACK_PORCH + MIN_PORCH_RND

V_FIELD_RATE = H_FREQ / TOTAL_V_LINES

IF ( INTERLACE_REQUIRED == "y") {
    V_FRAME_RATE = V_FIELD_RATE / 2
  } else {
    V_FRAME_RATE = V_FIELD_RATE
  }

Note: The "round()" function here rounds to the nearest integer (it doesn't round down or round up).

Cheers,

Brendan

More VESA Rants

I think part of the problem is that the original GTF formulas from VESA are copied from their spreadsheet, so that (for a silly example) instead of doing something like:

frequency = 10000000
period = 1 / frequency seconds

They'll do:

frequency_in_MHz = 10
period_in_ms = 1 / (frequency_in_MHz * 1000000) * 1000

And then simplify it to:

frequency_in_MHz = 10
period_in_ms = 1 / frequency_in_MHz / 1000

And then they'll remove any indication of what they've done:

frequency = 10
period = 1 / frequency / 1000

So that in the end, the formulas from VESA end up being a confusing mess where you're never too sure if there's a hidden scaling factor or not. Another simple example (that isn't made up) is "MARGINS_PERCENT", which is a value that would range from 0 to 50 that's typically divided by 100; and isn't a value that ranges from 0 to 0.5 that doesn't need scaling.

I plan on going through the formulas again, and making sure that all variables are either in pixels, lines, seconds or hertz (with no implied/hidden milliseconds, microseconds, kilohertz, megahertz or "percent" scaling factors).

I've also noticed that some of the calculations are the same in each formula. Rather than having 3 independent/larger pieces of code, it can be split into 3 smaller pieces of code that all use the same subroutines for common things. For example, you'd be able to replace about 10 lines from each formula with "call do_precalculations" to avoid code duplication (triplication?).

Also, I only posted "primary formulas". There's also a "secondary formula" where the results from the first set of calculations are used to find additional parameters; and there's another calculation (called the "blanking formula") for finding the values for "C_PRIME" and "M_PRIME" from some variables called C, M, J and K that's used for "secondary timings". I want to do the same for these formulas as I'm doing for the primary calculations. Then I need to go through all of these parameters and figure out which ones are actually useful (both for setting a video mode using VBE, and for setting a video mode in a "bare metal" video driver), and then work backwards removing redundant calculations (i.e. calculations that are only used to create information that you don't need anyway). After I've done this, I can combine it with the "common subroutines" idea, so that the entire "secondary formula" ends up being part of the "do_postcalculations()" routine, and so that the entire blanking formula becomes part of the "do_precalculations()" routine.

Then I want to find the valid ranges for all variables used in all calculations. This is mostly because of how I'm planning to implement it. For example, if I knew that "H_FREQ" ranges from 50000 to 1000000 then I'd be able to use "20:12" fixed point for this variable to improve the accuracy I get from a 32-bit integer.

Finally, all of these calculations can be simplified a lot if you assume that the "default GTF values" are being used. I want to provide simplified versions of the formulas, because most of the time you can use the default GTF values and can skip a lot of work.