Resources
Numerical accuracy
The calculations in our apps: the policy each one is under, the precision it runs at, and the code itself.
This device: processor, memory, graphics The standard Precision is not robustness
Calculation policies
A policy says how one family of calculations keeps its precision. Open one to see its calculations, by source file, and their code.
-
Check report values
The required and found values written in the Problems panel and in the check report exported as CSV.
Every app 64-bit, direct- 1 calculation
64-bit Open item -
Circles tangent to two or three objects
Finds the circle of a given radius tangent to two picked lines or circles, and the circle tangent to three.
- CadCraft
- 8 calculations
64-bit Open item -
Circuit solver
Operating point, DC sweep, AC response and transient of a circuit of resistors, capacitors, inductors, sources, diodes, transistors and switches.
Every app 64-bit, stated limit- 18 calculations in 2 files
64-bit Open item -
Clipping block references to a boundary
Cuts the lines, arcs and fills of a clipped block reference or linked drawing at the clip polygon, and converts the clip between drawing and block coordinates.
- CadCraft
- 10 calculations
64-bit Open item -
Concrete member and slab checks on a solved frame
Checks every concrete beam and column of a solved frame for every strength combination, magnifies the moments of slender columns, and sizes a slab's reinforcement from the plate moments.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations in 3 files
64-bit -
Concrete member strength to ACI 318-19
The design strengths of a rectangular reinforced concrete section in bending, shear and combined axial force and bending.
- CadCraft
- BimCraft
- DetailCraft
- 9 calculations
64-bit Open item -
Concrete section by strain compatibility
The axial force and moment a rectangular reinforced concrete section carries for a given neutral axis depth, and the depth that balances a given axial force.
- CadCraft
- BimCraft
- DetailCraft
- 5 calculations
64-bit -
Conduit and tray fill, cable schedule
Works out how full a conduit or cable tray is, picks the smallest conduit that holds a set of cables, routes cables through the carriers and lists their lengths.
- CadCraft
- BimCraft
- 8 calculations
64-bit Open item -
Constraint values and signs
Measures what a dimensional constraint holds (distance, radius, diameter, angle), records which side or direction a constraint applies to, and decides what an edit moved.
- CadCraft
- 13 calculations
64-bit Open item -
Constraints kept through mirror and trim
Works out again the sense of an angle constraint on mirrored geometry and decides which piece of a trimmed object keeps each constraint.
- CadCraft
- 2 calculations
64-bit -
Controller standard functions and integer types
Timers, counters, arithmetic functions and type conversions of the soft controller.
Every app 64-bit, direct- 6 calculations
64-bit Open item -
Coordinate reference systems
Converts project coordinates to and from a named map projection, longitude and latitude, and other systems, and reports grid scale factor, convergence and elevation factor at a point.
- CadCraft
- BimCraft
- CivilCraft
- 17 calculations in 2 files
64-bit -
Cores of a cable on a schematic
Finds which wires a cable marker's slash crosses, in order, for the cable list.
- CadCraft
- 2 calculations
64-bit Open item -
Corner cabinet drilling positions
Works out where the shelf-pin, hinge-plate, fixing, pivot and shaft holes go on the parts of a corner cabinet.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Corner cabinets: parts and solids
Builds the cut list, door sizes, hardware counts and 3D solids of L-shaped, diagonal and lazy-susan corner cabinets (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
64-bit Open item -
Cubic equations of state
Works out compressibility, fugacity coefficients, enthalpy and entropy departures and vapor pressure from the Peng–Robinson and Soave–Redlich–Kwong equations.
- CadCraft
- BimCraft
- 8 calculations
64-bit Open item -
Cursor point and status readouts
Works out the point a click stands for when ortho is on, and the coordinates, distance and angle shown in the status line and beside the cursor.
- CadCraft
- 6 calculations
64-bit -
Cut list sizes, areas and banding lengths
Works out each part's cut size from its finished size and edge banding, and totals pieces, areas, banding lengths and a rough sheet count.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Cutting profile pieces from stock bars
Packs the pieces of each profile onto stock bars and reports the bars to buy, where each piece is cut, the offcuts and the waste.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Design study variants and ranking
Makes the list of variants a design study runs, checks each result against its limits, finds the trade-off front and ranks the variants.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
Device number check
The check on the accuracy page that reports how many bits this device's numbers carry, how many processor threads and how much memory the browser shows, and what it says about the graphics processor.
Every app 64-bit, direct- 2 calculations
64-bit -
DEXPI and PCF plant exchange files
Reads and writes plant models as DEXPI XML and piping component files (PCF), converting positions, sizes and angles between the file's units and the drawing.
- CadCraft
- BimCraft
- 15 calculations in 3 files
64-bit Open item -
Diagram layout into drawing objects
Places the blocks, connectors, arrowheads and labels of a diagram written as text, and turns them into lines, polylines, hatches and text in the drawing.
- CadCraft
- 7 calculations
64-bit -
Dimension measurement and geometry
Measures what a dimension spans from its defining points and works out its extension lines, dimension line, arrowheads and text position.
- CadCraft
- 8 calculations
64-bit -
Dimension text: units, rounding and tolerances
Writes the number a dimension shows: measurement scale, round-off, decimal places, degrees-minutes-seconds, alternate units and tolerance limits.
- CadCraft
- 11 calculations
64-bit Open item -
Dimensions and typed sizes in 3D
The length, radius, diameter or angle a 3D dimension shows, and how the model is resized when a new value is typed into a dimension, an edge length or a group size.
- CadCraft
- ModelCraft
- 13 calculations in 2 files
64-bit Open item -
Distance, area, angle and point inquiries
Works out what DIST, AREA, MEASUREGEOM, ID and LIST print: distances, Δx and Δy, angles, areas, perimeters, running area totals and coordinates; and the unit factor EXPORTPOINTS applies to the points it writes.
- CadCraft
- 8 calculations
64-bit -
Distillation and absorption columns
Sizes a column by shortcut methods and solves stage-by-stage columns, absorbers and strippers for flows, temperatures, compositions and duties.
- CadCraft
- BimCraft
- 18 calculations in 2 files
64-bit Open item -
Drawing an edge: welding, splitting and re-facing
What happens to the model when a line is drawn: which points become one vertex, where edges are split, and which closed loops become faces.
- CadCraft
- ModelCraft
- 11 calculations
64-bit -
Drawing audit: zero-size and duplicate objects
Finds lines of zero length, circles and arcs of zero radius, and objects that are exact copies of another, so they can be listed and erased.
- CadCraft
- 2 calculations
64-bit -
Drawing autocomplete
Finds a repeat, a stair or a nearly closed figure in the newest objects and offers the next copy, the next steps or the closing sides as geometry that is added to the drawing when accepted.
- CadCraft
- 7 calculations
64-bit Open item -
Drawing compare
Decides which objects are unchanged, moved, changed, added or removed between two versions of a drawing.
- CadCraft
- 4 calculations
64-bit -
Drawing location written to DWG and DXF
Writes where the drawing sits on its map grid (design point, reference point, north direction) into the file's GEODATA object, and reads another program's back.
- CadCraft
- 3 calculations
64-bit Open item -
Drawing placed on a map grid
Describes where the drawing's own coordinates sit on a projected map system: scale, rotation and one matching pair of points.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Drawing to laser paths
Turns the drawing's lines, arcs, polylines, curves and hatches into paths in millimeters for the laser panel.
- CadCraft
- 4 calculations
64-bit -
Drawing values handed to and from LISP routines
The numbers that pass between a LISP routine and the drawing: answers typed for a command, object data lists, object properties, system variables and coordinate transforms.
- CadCraft
- 18 calculations in 3 files
64-bit Open item -
Duct network pressure: drawing adapter
Turns drawn duct runs into the network the pressure engine analyzes: runs in millimeters, the fan point, the terminals and their airflows, and the result rows.
- CadCraft
- 8 calculations
64-bit Open item -
Duct runs, fittings and schedule
Works out the elbows, transitions and branch fittings of drawn duct runs, the straight lengths between them, and the schedule of lengths and sheet-metal areas.
- CadCraft
- 15 calculations in 2 files
64-bit Open item -
DWG import: objects from the file's model
Turns the entities read from a DWG file into drawing objects: dimensions, hatch boundaries, block arrays, pictures, viewports, text angles and lineweights.
- CadCraft
- 13 calculations
64-bit Open item -
DWG object values written and read
Carries the coordinates, angles, widths and scales of drawing objects between the drawing and the DWG file's object records.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 15 calculations in 3 files
64-bit Open item -
DWG save: objects to the file's model
Turns drawing objects into the entities a DWG file holds: dimensions with their defining points, hatches with pattern lines, text, viewports, sheets, lineweights and extents.
- CadCraft
- 13 calculations
64-bit Open item -
DXF reading into the shared drawing model
Reads an ASCII DXF file into the same model the DWG reader gives, for the apps that list, convert or draw DXF content.
- CadCraft
- BimCraft
- TakeoffCraft
- CivilCraft
- 4 calculations
64-bit -
DXF reading: objects from the file's text
Reads the numbers of an ASCII DXF file into drawing objects: coordinates, angles, hatch boundaries and pattern lines, block arrays, dimensions, viewports, lineweights and sheet sizes.
- CadCraft
- 15 calculations
64-bit Open item -
DXF writing: numbers as text
Writes a drawing's coordinates, sizes and angles as decimal text in a DXF file, in the R12 and 2000 formats.
- CadCraft
- 21 calculations in 2 files
64-bit Open item -
DXF-AAMA and ASTM pattern files
Writes pattern pieces and their grade rules to DXF-AAMA or ASTM D6673 files with a RUL rule file, and reads such files back (Apparel add-on).
- CadCraft
- 14 calculations
64-bit Open item -
Dynamic input: points from typed distance, angle, X and Y
Works out the point a command receives when a distance, an angle, or X and Y are typed into the fields by the crosshair.
- CadCraft
- 4 calculations
64-bit Open item -
Dynamic simulation and controller tuning
Simulates tanks, reactors, gas vessels, valves and PID controllers over time and suggests controller settings from a step test.
- CadCraft
- BimCraft
- 12 calculations
64-bit -
E57 point cloud reading
Reads the points of an E57 scan file into absolute coordinates in meters, with each scan's pose applied, and the bounds of every point read.
- CadCraft
- BimCraft
- 8 calculations
64-bit -
Elevation grids into survey points and a grid surface
Places the cells of an elevation raster in the project's coordinates, converts heights between meters and feet, and makes survey points or a triangulated surface from the grid.
- CadCraft
- BimCraft
- CivilCraft
- 7 calculations
64-bit -
Ellipses and curves as short segments
Turns ellipses, sheared arcs, splines and outlines into runs of short straight segments, and measures ellipses.
- CadCraft
- 7 calculations
64-bit Open item
A policy is added only after its source was read. Each statement can be checked in the code shown on its page; the app repositories are public. When a release changes a calculation, its page says so until it has been read again.
The standard
-
64-bit everywhere
Every calculation runs in 64-bit floating point (IEEE 754 double precision), from the number you type to the number you read.
-
15 digits, always
A 64-bit number keeps any 15-digit value intact and takes 17 digits to write out in full. Our rule for every calculation: carry all 17 between steps, and order the arithmetic so that avoidable rounding never costs one of the first 15.
-
32-bit gets a warning
A 32-bit number keeps about 7 digits. Where a 32-bit step can reach a number you read, the calculation is flagged in the lists below, and the app will warn that the result can have less mathematical precision.
This device
What this browser can see of your machine. It is shown here only and sent nowhere; the desktop app reads the full hardware, a web page cannot.
The apps calculate in 64-bit on every device. Work handed to the graphics processor is the exception: browsers expose graphics processors as 32-bit calculators, which can provide less mathematical precision.
- Processor
- Memory
- Numbers in the apps
- Graphics processor (WebGL)
- WebGPU
A browser reports a rounded or capped view of the machine, never a full inventory: it gives the number of processor threads (not the model), memory rounded down and capped at 8 GB (Chromium only), and one graphics adapter even when a machine has several. What the browser reports about graphics is a capability, not a measurement of the card. The size of a graphics card's memory bus (a 192-bit bus, for example) says how fast data moves, not how precisely it calculates. Most graphics cards can calculate in 64-bit natively, slowly, but WebGL and WebGPU do not offer it to web pages.
Approaches
Every policy takes one of five approaches to keeping its precision.
- Exact values 8 policies
- Constants and factors are held as exact fractions from their definitions. The arithmetic is ordered so that no rounded factor is ever used.
- Exact predicates 1 policy
- Coordinates are 64-bit. The yes-or-no decisions that shape the geometry (which side of a line, inside or outside a circle) are computed exactly, so rounding cannot flip one.
- 64-bit, direct 337 policies
- Every value is a 64-bit number from input to result. Formulas are closed form or a direct solve, and every comparison uses a stated tolerance.
- 64-bit, stated limit 428 policies
- The arithmetic is 64-bit, but the method or the data sets the accuracy: a solver tolerance, a mesh, a step size, a datum shift, a table. The limit is stated where the result is shown.
- Display only 49 policies
- Computed to draw the screen, often in 32-bit on the graphics processor. No number a person reads, saves or exports comes from it.
- 32-bit step, flagged 118 policies
- One step stores or exchanges 32-bit values that reach a number a person reads. It is listed here with its open item, and the step is either moved to 64-bit or the app will warn where the number is read.
Precision is not robustness
Mathematical precision is how many digits a number keeps. Geometric robustness is whether a shape stays valid: every intersection found, every solid closed, every face joined to its neighbors. They are different properties, and a CAD system can have the first without the second.
Every geometric algorithm rests on yes-or-no questions. Is this point left or right of that line? Do these two edges cross? Is this point inside that circle? Each answer is the sign of a small expression. When three points are almost in line, the true value of that expression can be smaller than the rounding error of the arithmetic that computes it, and the sign comes out wrong. That happens at 15 digits as readily as at 7.
One wrong sign is not a small error in the last digit. It is a different decision: an intersection that is missed, two triangles that overlap, a face that points the wrong way, a solid with a gap in it. Every coordinate can be correct to 15 digits while the shape they describe is invalid.
What makes geometry robust
-
Exact predicates
The yes-or-no questions are answered exactly. The fast 64-bit answer is used when it is safely away from zero. When it is not, the sign is computed again with as many digits as it takes.
-
Decide once
A decision about a shape is recorded as topology, and every later step agrees with it. The same question is never asked twice with a chance of two answers.
-
Stated tolerances
Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.
-
Local origins
Coordinates far from zero are moved to a local origin before the work, so the digits are spent on the geometry and not on the distance to the origin.
-
Valid by construction
Algorithms whose result is guaranteed to be a closed solid, whatever the input, in place of ones that repair the result afterwards.
-
More than the language
These choices matter more than the programming language. JavaScript, C++ and Rust all compute with the same 64-bit numbers: the same algorithm is as robust, or as fragile, in each.
Where our apps stand
The list on this page records both properties. Surface triangulation in CivilCraft and BimCraft uses exact predicates. Solid modeling in PartCraft runs on a kernel whose result is a closed solid by construction. The intersections in the CadCraft app use stated tolerances today, and exact tests for the near-parallel and near-tangent cases are an open item. Each policy says which approach it takes.