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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Costs on the schedule
Prices each element from its quantities, adds the cost up per scheduled task, spreads it over the task's days and totals the cash flow.
- BimCraft
- 13 calculations
64-bit Open item -
Countertop outline and quantities
Finds the run of cabinets a countertop covers, pushes the front edges out by the overhang, and writes the countertop's shape, area, perimeter and front edge length.
- BimCraft
- 4 calculations
64-bit -
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 -
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 -
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 -
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 -
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 -
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 -
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 sheets to scale and the PDF
Picks the scale of each plan, elevation and section, places it on its sheet, and writes the sheet's lines, fills and text into the PDF.
- BimCraft
- 14 calculations in 2 files
64-bit Open item -
Drawn floors: outline, openings and quantities
Checks a floor outline drawn by hand, cuts openings in it, and works out its perimeter, area and volume.
- BimCraft
- 7 calculations
64-bit Open item -
Drawn points: angle, length and wall-face paths
Decides the plan point a click becomes when it follows an angle step, a length step or a wall, and offsets a path drawn on a wall face to the wall's center line.
- BimCraft
- 4 calculations
64-bit -
DWG and DXF drawings compiled for the plan view
Turns the entities of a DWG or DXF drawing into the lines, fills and text of each space, in the drawing's own coordinates.
- BimCraft
- TakeoffCraft
- 20 calculations in 2 files
64-bit -
DWG and DXF drawings in 3D
Turns a drawing's model space into 3D lines, faces and text, with every block insert, elevation, thickness and extrusion direction applied.
- BimCraft
- 12 calculations in 2 files
64-bit -
DWG and DXF views on screen
Draws a compiled drawing in the 2D view and in the 3D view.
- BimCraft
- 3 calculations in 2 files
32-bit, display only -
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 -
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 -
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 -
Earthquake time-history of a building
Shakes a building of one mass per floor through a ground acceleration record and reports periods, mode shapes, story drifts, floor accelerations and base shear; the floor stiffness can come from the frame model.
- BimCraft
- 12 calculations in 2 files
64-bit Open item -
Electrical devices: positions, loads and circuit amps
Places sockets, switches and lights on wall faces or ceilings, keeps them on their wall when it moves, and totals the load and current of each circuit.
- BimCraft
- 7 calculations
64-bit Open item -
Element outlines in the IFC view
Finds the edge lines drawn on each element in the IFC view.
- BimCraft
- 2 calculations
32-bit, display only -
Element quantities for carbon and cost
Reads each element's volume, area and length and splits the volume between its materials, as the embodied carbon and cost calculations use them.
- BimCraft
- 5 calculations
64-bit Open item -
Element triangles for analysis
Hands the placed triangles of an IFC element, in the file's coordinates and length unit, to the daylight, solar, embodied-carbon, library and placement code.
- BimCraft
- 1 calculation
32-bit in part Open item -
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 -
Elevation grids read from GeoTIFF and ASCII files
Reads a terrain grid's position, cell size and elevations from a GeoTIFF or an ESRI ASCII grid, with its scale, offset and no-data value.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Energy model input file (IDF) and its results
Writes the rooms of a model as an IDF input file for an outside energy simulation engine, and reads back the design loads and yearly energy that engine reports.
- BimCraft
- 14 calculations
64-bit -
Equipment list from drawing tags
Reads the equipment schedule hidden in a foodservice drawing's item tags: one row per item, its quantity and the sheets that show it.
- BimCraft
- 3 calculations
64-bit -
Factory layout checks
Checks equipment placed on a floor for overlaps, blocked access strips, narrow aisles, items outside the room and floor load, and measures the path between items.
- BimCraft
- 8 calculations
64-bit -
Family editor: sketch points, handles and solved sizes
Changes a family's recipe when a point is moved or a handle is dragged, solving for the parameter that puts a face or a hotspot where it was dragged.
- BimCraft
- 13 calculations in 2 files
64-bit Open item -
Family geometry from parameters
Works out a family's solids, plan symbol and connectors from its parameters and formulas, and writes them to the IFC file.
- BimCraft
- 21 calculations in 3 files
64-bit -
Fast render lights and texture placement
Sets lamp strength, soft sun shadows and where a material's texture falls on a surface for the fast render and the 3D views.
- BimCraft
- ModelCraft
- 3 calculations in 2 files
32-bit, display only -
Fault trees and reliability block diagrams
The probability of a top event, minimal cut sets, importance measures, system reliability and mean time to failure.
Every app 64-bit, stated limit- 10 calculations
64-bit Open item -
Fermentation (Monod kinetics)
Biomass, substrate, product and volume over time in a batch or fed-batch vessel.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Field layout points from the model
Works out the points a crew sets out from the model (column feet, wall axis ends, anchor bolts, sleeves, chosen elements) in model or survey coordinates, in meters, millimeters or feet.
- BimCraft
- 3 calculations
64-bit -
Figures shown in the residential panels and schedules
Works out the numbers the residential tools show in Properties and on schedules: a roof plane's area, the cut list, board feet, cut and fill, a new stair's direction and a building's width on an elevation.
- BimCraft
- 7 calculations
64-bit -
Fitting losses summed from a pack
Adds up the loss coefficients K of the fittings on a pipe link and turns K into a head loss.
- CadCraft
- BimCraft
- 2 calculations
64-bit -
Floats read from USD files
Reads numbers from .usda and .usdc files, in the type each value is stored as.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 5 calculations in 2 files
32-bit in part Open item -
Flood depth and wind load playback
Works out how deep each room floods over time from a water-level record, the water's push on a wall, and the wind force, shear and overturning moment on each story.
- BimCraft
- 4 calculations
64-bit Open item -
Flow simulation (discrete events)
Queues, servers, conveyors, vehicles and resources simulated event by event: utilization, waiting times, throughput and their confidence ranges.
Every app 64-bit, stated limit- 15 calculations in 2 files
64-bit Open item -
Flowsheet solver and unit operations
Runs the units of a flowsheet in order, converges recycle loops and design specifications, and works out each unit's outlet streams, heat and work.
- CadCraft
- BimCraft
- 15 calculations in 2 files
64-bit -
Flowsheet variant metrics
Works out the heating, cooling and shaft power, the hourly operating cost and the hourly CO2 of one solved flowsheet variant, the numbers an optimization study ranks by.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Focus distance picked in the view
The focus distance set by clicking a point in the live rendered view.
- BimCraft
- ModelCraft
- 1 calculation
32-bit in part 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
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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.