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.
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Counting blocks, shapes and texts in a CAD drawing
Finds every block reference, shape and text of a DWG or DXF drawing with its place, and counts the ones that match.
- TakeoffCraft
- 5 calculations in 2 files
64-bit -
CraftScript array arithmetic
The elementwise operators, matrix product, backslash, ranges and sums that a script's own formulas run on.
- PartCraft
- 9 calculations
64-bit Open item -
CraftScript core math functions
The built-in math of the scripting language: elementary functions, rounding, the gamma function, sums and statistics, interpolation, polynomial fitting and number-to-text conversion.
- PartCraft
- 18 calculations
64-bit Open item -
CraftScript dense linear algebra
Solves dense systems and works out inverses, determinants, factorizations, eigenvalues, norms and condition numbers in a script.
- PartCraft
- 13 calculations
64-bit Open item -
CraftScript file readers and writers
Turns STL, OBJ, CSV, JSON, NPY and HDF5 files into script values and back, and writes a plot's data as CSV.
- PartCraft
- 14 calculations in 2 files
64-bit Open item -
CraftScript iterative solvers and sparse eigenvalues
Solves large sparse systems by iteration in a script and finds the smallest eigenvalues of a sparse problem.
- PartCraft
- 6 calculations
64-bit Open item -
CraftScript meshes and element kernels
Makes simple meshes in a script and gives scripts the app's own element matrices, voxel solver, stresses and lattice Boltzmann fields.
- PartCraft
- 10 calculations
64-bit -
CraftScript number type conversions
The script functions that convert values to single precision or to whole-number types.
- PartCraft
- 2 calculations
32-bit in part Open item -
CraftScript operators in the interpreter
Carries out the arithmetic a script writes: scalar operations, matrix division and powers, and the values of a counted loop.
- PartCraft
- 3 calculations
64-bit -
CraftScript sparse matrices and direct factorization
Builds sparse matrices in a script, adds and multiplies them, assembles element matrices, and factors a symmetric positive definite one.
- PartCraft
- 8 calculations
64-bit -
CraftScript values: storage, reading and number text
Holds the numbers a script works with, reads them back from a saved part, and writes the text shown when a statement echoes its result.
- PartCraft
- 5 calculations
64-bit -
Cross sections and end-area volumes along an alignment
Cuts the ground and the design along sample lines square to an alignment, works out cut and fill areas at each section and the volumes between sections.
- CivilCraft
- 10 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 -
Culverts, bridges and junctions in a river model
Works out the headwater above a culvert, the water surface above a bridge, and the flows and water levels where river reaches join, for the steady water surface profile.
- CivilCraft
- 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 -
Curve objects
Evaluates Bézier, NURBS and poly splines and makes the mesh a curve object shows: a tube, a ribbon, or a filled flat shape with thickness and a rounded edge.
- ModelCraft
- 14 calculations in 2 files
64-bit Open item -
Curved walls
Works out the circle, length and points of a wall whose center line is an arc, where doors and windows sit in it, and the curves it is saved with.
- BimCraft
- 11 calculations
64-bit -
Curves through points
Makes a curve that passes through every given point, with optional end directions.
- ModelCraft
- PartCraft
- 5 calculations in 2 files
64-bit -
Cut and fill map, spot levels, sloped pads and free sections
Works out the depth of cut or fill cell by cell with its volumes, spot levels on a grid, the elevations of a sloped pad or ramp, and a section cut along any line with its cut and fill areas.
- CivilCraft
- 8 calculations
64-bit -
Cut and fill volumes by the grid method
The cut, fill and net volume between two surfaces.
- CivilCraft
- 2 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 -
Cut-list nesting of bars
Nests the linear parts of a model on stock bars and reports the bars to buy, the length bought and used, the drop of each bar and the waste.
- BimCraft
- DetailCraft
- 3 calculations
64-bit -
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 -
Cutting speeds, feeds and tool profiles
Works out spindle speed and feed rates for a tool in a material, and the shape of each tool's tip used by the simulation and 3D finishing.
- PartCraft
- 3 calculations
64-bit -
Data collector files and polar reduction
Reads total-station field books (RW5, GSI, JobXML, CSV), reduces each shot to coordinates, and prepares directions and distances for the network adjustment.
- CivilCraft
- 6 calculations
64-bit Open item -
Decal placement and size
Works out where a clicked point lies on a face in the face's own coordinates, and the size a placed decal is stored with.
- ModelCraft
- 5 calculations
64-bit Open item -
Decimate modifier
Reduces the number of triangles of a mesh to a ratio of the original while keeping its shape as closely as the method allows.
- ModelCraft
- 4 calculations
64-bit -
Depth and angle set by dragging a handle
Works out the new extrude depth or revolve angle when the handle of a selected feature is dragged.
- PartCraft
- 3 calculations
64-bit -
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 -
Design-it sizing and hand checks
Sizes a shelf bracket or a round shaft from a load and a material, and reports the stresses, deflection, bolt loads, volume and mass.
- PartCraft
- 9 calculations
64-bit Open item -
Detention pond hydrology and routing
Builds a runoff hydrograph, a stage and storage table and an outlet rating, routes the storm through the pond, sizes an orifice, and checks the result.
- CivilCraft
- 12 calculations
64-bit -
Deterministic sine, cosine, exp, log and power
Works out sin, cos, exp, log, powers and inverse trigonometric functions from + − × ÷ and √ only, so every browser gives the same bits.
- PartCraft
- 21 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 -
Dimensions and views on drawing sheets
Lays out plans, elevations, assembly drawings and anchor plans, and works out the dimension figures, scales and hidden lines printed on them.
- DetailCraft
- 13 calculations
64-bit Open item -
Distance grid: baking, sampling and volume
Stores a shape as signed distances on a sparse voxel lattice, built from a formula or from a closed triangle mesh, and reads values, gradients and the enclosed volume back from it.
- PartCraft
- 14 calculations in 4 files
32-bit in part 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 -
Doors and windows in walls
Works out where a door or window sits along its wall, whether it fits, the box that cuts the wall, and the sizes and area written with it.
- BimCraft
- 9 calculations
64-bit -
Dormer geometry
Works out a gable or shed dormer on a roof face: its roof planes, front and cheek walls, where it meets the main roof, and the hole cut in the roof.
- BimCraft
- 5 calculations
64-bit -
Draft and curvature analysis
Works out the draft angle of each face corner against a pull direction, the areas that pass or need draft, and the curvature limit shown with the curvature colors.
- PartCraft
- 3 calculations
32-bit in part Open item -
Drafting lines and hatch regions
Keeps the drafting lines and hatch regions drawn in a view, checks them, moves them and works out the strokes of each hatch pattern inside its region.
- BimCraft
- 11 calculations in 2 files
64-bit -
Drainage structure types and their library items
Works out the inside and outside size of a manhole, inlet or junction type, and writes the type as a library item in millimeters and reads it back.
- CivilCraft
- 6 calculations
64-bit -
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 annotations: tolerance frames, datums and surface finish
Lays out feature control frames, datum symbols and surface texture symbols on a drawing sheet and writes their tolerance and roughness values.
- PartCraft
- 3 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
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
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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.
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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.
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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
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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.
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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.
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Stated tolerances
Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.
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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.
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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.
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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.