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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Reverberation time of a box room
Works out the reverberation time of a box-shaped room in each frequency band by four formulas: Sabine, Eyring, Fitzroy and Arau-Puchades.
- BimCraft
- 2 calculations
64-bit -
Revision overlay: what changed under a mark
Compares the pictures of an old sheet and its revision and flags the marks whose drawing changed.
- TakeoffCraft
- 4 calculations in 2 files
64-bit -
Rigid body simulation
Drops, stacks and collides boxes and spheres under gravity and records where each one is at every frame, to be baked into keys.
- ModelCraft
- 12 calculations
64-bit Open item -
Rigid-body dynamics of a mechanism
Joint torques for a given motion, the mass matrix, joint accelerations for given torques, energy, and a simulated motion over time.
Every app 64-bit, stated limit- 6 calculations
64-bit -
River water surface profiles by the standard step method
Works out the water surface, energy level, critical depth, velocities, Froude number and flow split at each river cross section for steady flow.
- CivilCraft
- 15 calculations in 2 files
64-bit Open item -
Road intersections, striping and signs
Works out curb returns, the pavement outline and area of an intersection, sight distance, stripe and dash layouts, crosswalk bars, sign positions and the quantities of each.
- CivilCraft
- 14 calculations
64-bit Open item -
Roof faces, gable ends, fascia and soffit
Matches each roof edge to the wall under it and builds the roof's sloped slabs, gable walls, fascia boards and soffit panels with their areas and lengths.
- BimCraft
- 7 calculations
64-bit -
Room outline by flood fill
Finds the room around a clicked point on a picture of the sheet and returns its outline as an area mark.
- TakeoffCraft
- 4 calculations in 2 files
64-bit -
Room outline, walls and openings
Builds the room a cabinet job sits in: its corners, the frame of each wall, inside tests, distances to walls, and the doors and windows along the walls.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations in 2 files
64-bit Open item -
Room reverberation time
Works out how long sound takes to die away in each room, per octave band, from the room's volume, its surfaces and the air.
- BimCraft
- 11 calculations in 2 files
64-bit Open item -
Room, floor and ceiling quantities
Writes the shape, areas, perimeter and volume of rooms, floor slabs and ceilings found from the drawn walls.
- BimCraft
- 6 calculations
64-bit Open item -
Running saved geotechnical, survey, pit and link items
Converts a saved item from project units to meters, runs the engine for it (soil profile, slope stability, settlement, traverse, pit, radio link, coverage) and converts the results back.
- CivilCraft
- 9 calculations
64-bit -
Sanitary drain sizing by fixture units
Adds up the fixture units each drain carries, finds which run flows into which, and picks the smallest pipe size the plumbing tables allow.
- BimCraft
- 4 calculations
64-bit -
Sanitary sewer design flows and pipe sizes
Works out the peak sanitary flow in each pipe of a gravity network from people and area, checks capacity and velocity, and picks pipe sizes.
- CivilCraft
- 6 calculations
64-bit Open item -
Scan clean-up and JPEG decoding
Reads a scanned image, turns it into black and white, finds how far the sheet is rotated and turns it straight.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 6 calculations in 2 files
64-bit Open item -
Scanned drawings: size, scale, align, crop and trace
Places a scanned picture, scales and turns it from picked points, crops it, and turns its traced ink into lines, arcs and circles in drawing coordinates.
- CadCraft
- 9 calculations in 2 files
64-bit Open item -
Scattered plants, rocks and people: how many and where
Works out how many items a scatter set asks for from the area it covers and its density, and picks the points they stand on.
- BimCraft
- ModelCraft
- 4 calculations
64-bit -
Schedule risk (Monte Carlo)
The finish at P10, P50, P80 and P90, how often each task is critical, and which durations drive the finish.
Every app 64-bit, stated limit- 3 calculations
64-bit -
Script result fields and meshes shown in the window
The scalar a script's field plot colors by, its range, and the outer surface of a result mesh.
- PartCraft
- 4 calculations
32-bit, display only -
Seam allowance: the cut line
Draws the cut line round a pattern piece at each edge's seam allowance, with the corner rules pattern makers use (Apparel add-on).
- CadCraft
- 7 calculations
64-bit Open item -
Seismic loads and story drift to ASCE 7-22
The seismic base shear and story forces by the equivalent lateral force procedure, the building's period, the weight of each floor and the drift check.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations in 2 files
64-bit -
Settlement, flexible mats, pile groups and retaining walls
Estimates elastic settlement, analyzes a footing as a plate on springs, shares a load over a pile group and checks a cantilever retaining wall.
- DetailCraft
- 11 calculations
64-bit -
Sheet metal bends and flat pattern
Works out the bent profile of a sheet metal base, the bend allowance of every bend, and the flat pattern with its bend lines, size and area.
- PartCraft
- 13 calculations in 2 files
64-bit Open item -
Sheet nesting
Lays parts out on sheets or a roll, reports the sheets used and the efficiency, checks the result, reads part outlines from DXF and writes the nest as DXF.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations
64-bit Open item -
Sheet scale read from the sheet's text
Finds scale notations in a PDF sheet's text and picks the listed scale to offer for the sheet.
- TakeoffCraft
- 3 calculations
64-bit -
SHX font text: strokes and width
Turns the shapes of a loaded .shx font into strokes, and gives a text's width and the position of each stroke in the drawing.
- CadCraft
- 7 calculations in 2 files
64-bit -
Simulation numbers shown as text
How the simulation window rounds the numbers it prints and puts into input boxes.
- PartCraft
- 2 calculations
64-bit -
Single-part shop drawing
Draws one part with its holes, copes and section, and prints its dimensions, cut angles and weight.
- DetailCraft
- 5 calculations
64-bit -
Site ground, building pads and cut and fill
Builds the site's ground from survey points, grades building pads into it, works out the cut and fill volumes, drapes paving on it and writes the ground to LandXML.
- BimCraft
- 17 calculations
64-bit Open item -
Site outline, building placement and levels
Stores the site boundary with its area and perimeter, places the building on the site, adds or splits levels, and turns a site-study mass into walls and floors.
- BimCraft
- 11 calculations in 2 files
64-bit Open item -
Site surroundings in local meters
Converts the buildings, parcels and zones found around an address from longitude and latitude to meters east and north of the address point, as suggestions a person can add to the model.
- BimCraft
- ModelCraft
- CivilCraft
- 4 calculations
64-bit -
Sketch exchange macro and import
Writes the drawing as a .swb sketch macro with its coordinates in meters, and reads an exported sketch back as geometry, constraints and dimensions.
- CadCraft
- 8 calculations
64-bit Open item -
Sketch intersections with splines
Finds where a sketch spline crosses a line, an arc, a circle or another spline.
- PartCraft
- 3 calculations
64-bit -
Sketch photo to drawing
Finds a sheet of paper in a photo, straightens it, and turns the pen lines on it into lines and arcs at a stated scale.
- CadCraft
- 6 calculations
64-bit Open item -
Sketch photo to drawing: sheet, perspective and scale
Finds the sheet of paper in a photo, straightens it, and places the traced lines and arcs in the drawing at a stated scale.
- ModelCraft
- CivilCraft
- 7 calculations in 2 files
64-bit Open item -
Sketch profiles as closed polygons
Turns the lines, arcs, circles and splines of a sketch into closed polygon loops, tests whether a point is inside them, and gives a loop's area.
- PartCraft
- 5 calculations
64-bit -
Sketch solver
Moves the points and radii of a sketch until every relation and dimension is met, and reports how many degrees of freedom are left and which relations conflict or repeat.
- PartCraft
- 11 calculations in 2 files
64-bit Open item -
Sketch splines: length, nearest point, polyline and offset
The length of a sketch spline, the point on it nearest a given point, its points within a chord tolerance, and its offset curve.
- PartCraft
- 4 calculations
64-bit -
Sky view and daylight factor
Works out how much of the sky each window sees and the daylight factor on a grid of points in a room.
- BimCraft
- 19 calculations
64-bit -
Slope stability
Finds the factor of safety of a circular slip surface by Bishop's simplified method or the ordinary method of slices, and searches for the critical circle.
- CivilCraft
- 6 calculations
64-bit Open item -
Snapping to and measuring the sheet's own linework
Reads the vector lines of a PDF page or a CAD sheet, snaps picked points to them, and measures a whole connected path or closed loop from one click.
- TakeoffCraft
- 11 calculations in 4 files
64-bit Open item -
Solar array layout on roofs and ground
Finds the roof planes that can carry modules, fits modules inside a plane with a setback, and lays out ground rows with a spacing that avoids shade at the winter solstice.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Solar array shading
Works out, for each hour of each month's representative day, the share of a solar array's sample points that the model shades from the direct sun, and the share of the beam light lost.
- BimCraft
- CivilCraft
- 4 calculations
64-bit -
Solar array site and saved summary
The latitude and longitude kept for a ground PV array and the numbers the file keeps for its plan.
- CivilCraft
- 2 calculations
64-bit -
Solar one-line currents, devices and wires
Works out the current on each run of a solar one-line diagram and picks the overcurrent device and wire size from the tables the person gives.
- BimCraft
- 6 calculations
64-bit Open item -
Solar yield estimate
Estimates the DC and AC energy a solar array gives in a year, month by month, with shading, temperature, losses and inverter clipping, and its performance ratio.
- BimCraft
- CivilCraft
- 8 calculations
64-bit Open item -
Solvers shared by the process engine
The linear solve, Newton iteration, ODE integrator and bracketed root finder that the flowsheet, reactors and design specifications call.
- CadCraft
- BimCraft
- 4 calculations
64-bit Open item -
Solving an expression for one parameter
Finds the value of one parameter that makes an expression give a wanted result, the other parameters held.
- CadCraft
- BimCraft
- PartCraft
- 2 calculations
64-bit Open item -
Sound insulation ratings and the mass law
Works out the single-number airborne and impact sound ratings from sixteen third-octave values, and estimates a plain wall's sound reduction from its mass.
- BimCraft
- 6 calculations
64-bit Open item -
Spending on a person's own AI model
Adds up what calls to a person's own AI model have cost today and this month, and stops a call that could pass the limits the person set.
Every app 64-bit, stated limit- 4 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.