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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Redline items placed in the drawing
Maps the marks of a redline package from sheet fractions to drawing coordinates and sizes the revision clouds drawn round accepted items.
- CadCraft
- 4 calculations
64-bit -
Redline package coordinates
The positions written into a redline package that lists each markup on its sheet.
- MarkupCraft
- 2 calculations
64-bit -
Reference geometry, sweep paths and extrude extents
Finds points on edges for reference planes, axes and points, chains curves into a sweep path, and works out how far an extrude runs when it stops at a face, a vertex or the next face.
- PartCraft
- 9 calculations
64-bit -
Reference picture size and position
Places a copied area of a sheet in the model at its true size.
- DetailCraft
- 4 calculations
64-bit -
Reference planes, axes and points
Works out a reference plane, axis or point from the faces, edges, planes and points it is defined by.
- PartCraft
- 9 calculations
64-bit -
Refrigeration copper tube sizes
Gives the outside diameter, wall and inside diameter of a refrigerant line from its trade size.
- BimCraft
- 1 calculation
64-bit -
Registered scans written as LAS and E57
Moves every point of the registered scans by its scan's matrix and writes the result as a LAS 1.2 or an E57 file.
- CadCraft
- BimCraft
- 6 calculations
32-bit in part Open item -
Regulation checks of rooms, doors, windows and outlets
Works out what the model has for each rule of the active regulation pack: room area and least dimension, window area and openable area as a share of the floor, escape openings, egress door width, outlet spacing along the walls.
- BimCraft
- 11 calculations in 2 files
64-bit -
Regulation limits in force and how values are written
Gives an app's tools the tightest limit of a rule across the ticked regulation packs, and writes required and found values in problems and on the code summary sheet.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 4 calculations in 2 files
64-bit Open item -
Regulation limits read from the pack's tables
Looks up the footing size, stud spacing and height, header span, joist and rafter span and wall insulation a regulation pack asks for, and compares the model with them.
- BimCraft
- 10 calculations
64-bit Open item -
Reinforcing bars and the bending schedule
Places the bars in a pad footing and works out their bends, cut lengths, counts and weights for the bending schedule.
- DetailCraft
- 13 calculations
64-bit Open item -
Release, fire, explosion and toxic screening
Works out how much escapes through a hole, how far fire radiation, blast overpressure and a toxic or flammable cloud reach, and the chance of harm from a dose.
- CadCraft
- BimCraft
- 19 calculations in 3 files
64-bit Open item -
Relief valve sizing, depressuring and flare loads
Works out the orifice area a relief valve needs for gas, liquid, steam or two-phase flow, the heat input from a fire, the back pressure in the outlet line and flare header, flare radiation distance and the pressure of a vessel as it is vented.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit Open item -
Render hand-off manifest
The camera, sun, lamps, materials, exposure and frame numbers written into the package that an outside render engine reads.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Rendered picture size
Works out the width and height in pixels of a picture an assistant asks the Render dialog for.
- BimCraft
- 1 calculation
64-bit -
Rendered picture: mixing, post and color
The pixel values of a high-quality render as shown and as saved to an 8-bit or 16-bit picture, after light mixing, denoising, exposure, bloom, the view transform and the sRGB curve.
- BimCraft
- ModelCraft
- 14 calculations in 5 files
32-bit in part Open item -
Rendered picture: sample sums and color tables
Adds up the light samples of a CPU render into the picture and applies .cube color tables to it.
- BimCraft
- ModelCraft
- 5 calculations in 2 files
32-bit, display only -
Rendered pictures
Draws still pictures and video frames of the model: the fast render, the path-traced render and the textures of the material library.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Rendering: sun direction, lamps and painted faces
Prepares the 3D model for a rendered picture: the sun's direction, the light fixtures as lamps, and which library material each painted face shows.
- BimCraft
- 3 calculations in 2 files
32-bit, display only -
Replacement schedule and cost over the building's life
Lists when each part of the building is replaced over a study period, what that costs with inflation and discounting, and how much embodied carbon the replacements add.
- BimCraft
- 6 calculations in 2 files
64-bit Open item -
Result fields sent to the plot, legend and probe
Copies the solved temperature, heat flux, stress, strain and displacement values onto the plot mesh that the result view colors, labels and probes.
- PartCraft
- 8 calculations in 2 files
32-bit in part Open item -
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: lining up two sheets and moving the takeoff
Fits the move, turn and scale that lays an old sheet over its revision from two pairs of picked points, and carries the marks and the scale across.
- TakeoffCraft
- 7 calculations in 3 files
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 -
Rib feature
Builds the region a rib fills from an open sketch line: the line extended past the body, swept to one side, and trimmed by the body.
- PartCraft
- 2 calculations
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 model: stations, cut sections and reach lengths
Builds the river model a water surface profile is computed from: river stations, cross-sections cut from the ground, bank positions, reach lengths, flows along the reach and the unit constants.
- CivilCraft
- 7 calculations in 2 files
64-bit Open item -
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 -
Roof faces, ridges and areas from an outline
Works out the roof over a building outline: the plan of every roof face, the ridge, hip and valley lines with their heights, the eave and fascia lines, and the roof's area and line lengths.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 23 calculations in 2 files
64-bit -
Roof pitch and slope factors
Reads a roof pitch and turns plan lengths and areas into lengths and areas along the slope.
- TakeoffCraft
- 4 calculations
64-bit -
Roof planes over an outline
Works out the sloping faces, ridges, eave and area of a roof from the building's outline, a pitch and an overhang, and the roof's height over any plan point.
- BimCraft
- 8 calculations
64-bit -
Room acoustic measures from an impulse response
Reads a recorded or computed impulse response and works out reverberation times, early decay time, clarity, definition and center time.
- BimCraft
- 4 calculations
32-bit in part Open item -
Room impulse response and listening
Builds a room's impulse response from its reverberation times, and the sound of a clap, speech or music heard through it, to play or save.
- BimCraft
- 9 calculations
32-bit in part Open item -
Room modes and low-frequency wave solver
Lists the standing-wave frequencies of a box-shaped room, the frequency below which the room behaves as separate modes, and runs a small wave simulation to find the resonances at a listener.
- BimCraft
- 5 calculations
32-bit in part Open item -
Room outline and furniture placement
Reads a floor face as a room (outline, holes, area), finds nearby doors and windows, and builds the matrix that sets each planned piece on its footprint.
- ModelCraft
- 4 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 -
Rooms and building outline from walls
Finds the closed rooms and the outer outline that a set of wall outlines encloses, with each room's area, perimeter and centroid.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
64-bit -
Rooms handed to add-ons with their doors, windows and walls
Gives an add-on each room of a level with its outline, area and elevation, and decides which doors, windows and walls belong to the room's edge.
- BimCraft
- 1 calculation
64-bit -
Rotations, transforms and small linear algebra (motion)
Rotation matrices, roll-pitch-yaw angles, rotation vectors, rigid transforms and the dense solve used by the robot and linkage calculations.
Every app 64-bit, direct- 7 calculations
64-bit Open item -
Rounding for display and for money
Rounds a number to a fixed count of decimals, and writes a length in feet and inches to the nearest fraction of an inch.
- TakeoffCraft
- 4 calculations
64-bit -
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 -
Samples per pixel reported after a render
Works out the average and the largest number of samples a pixel received in an adaptive path-traced render, shown on the finish line.
- BimCraft
- ModelCraft
- 1 calculation
32-bit in part Open item -
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
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.