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

  • 941 calculation policies
  • 6,917 calculations in 1,248 source files
  • 143 exact
  • 6,286 in 64-bit
  • 335 with a 32-bit step
  • 437 open items
  • Last reviewed

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.

  • 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
    64-bit, stated limit
    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
    64-bit, stated limit
    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
  • Spline through fit points

    Works out the control points and knots of a cubic spline that a drawing stores only by its fit points and end tangents.

    • CadCraft
    • BimCraft
    • ModelCraft
    • TakeoffCraft
    • CivilCraft
    64-bit, direct
    5 calculations
    64-bit Open item
  • Spread between coarse and refined results

    States how far a coarse live result is from the refined one, as a fraction.

    • CadCraft
    • BimCraft
    • DetailCraft
    • PartCraft
    64-bit, direct
    1 calculation
    64-bit
  • Sprinkler layout and hydraulic calculation

    Places sprinkler heads on a grid in a room, builds the branch and main network, sizes the pipes and finds the pressure and flow the design area needs against the water supply.

    • BimCraft
    64-bit, stated limit
    16 calculations in 3 files
    64-bit Open item
  • Stack plume rise and air dispersion screening

    Works out the effective height of a stack plume, the worst-case and hour-by-hour ground concentrations at receptors, and the contours drawn on a plan.

    • CadCraft
    • BimCraft
    64-bit, stated limit
    10 calculations in 2 files
    64-bit Open item
  • Stair family from a sketch

    Writes a sketched stair as a family recipe with its width, tread, total rise, tread counts and riser height as parameters.

    • BimCraft
    64-bit, direct
    2 calculations
    64-bit
  • Stair risers, treads and stairwell

    Works out how many risers a stair needs and how high each is, lays out the treads, landings, winders or spiral wedges, checks them against the limits, and cuts the stairwell in the floor above.

    • BimCraft
    64-bit, direct
    12 calculations in 2 files
    64-bit
  • Starter door and window sizes

    The width, height and sill of the starter door and window types, written in inches and stored in millimeters.

    • BimCraft
    64-bit, direct
    2 calculations
    64-bit
  • Statistical comparison of rendered pictures

    Decides whether two renderers give the same picture, and whether a test scene returns the expected brightness, by comparing block means against the pictures' own noise.

    • BimCraft
    • ModelCraft
    64-bit, stated limit
    5 calculations
    64-bit
  • Steel member checks on a solved frame

    Runs the steel code checks along every member for every strength combination, finds the governing ratio, checks the deflection limit, and finds what gives way first.

    • CadCraft
    • BimCraft
    • DetailCraft
    64-bit, stated limit
    12 calculations in 2 files
    64-bit
  • Steel member resistance to EN 1993-1-1

    The design resistances of a rolled I or H section: classification, tension, bending, shear, buckling, lateral-torsional buckling and the combined checks.

    • CadCraft
    • BimCraft
    • DetailCraft
    64-bit, stated limit
    11 calculations
    64-bit Open item
  • Steel member strength to AISC 360-16

    The design strengths of a rolled I-shape in tension, compression, bending and shear, and the combined bending and axial check.

    • CadCraft
    • BimCraft
    • DetailCraft
    64-bit, stated limit
    12 calculations
    64-bit Open item
  • Steel section dimensions, areas and outlines

    Gives the dimensions, published area and mass of every steel section in millimeters, the exact area from the dimensions, and the outline used to draw and sweep it.

    • CadCraft
    • BimCraft
    • DetailCraft
    • PartCraft
    64-bit, direct
    6 calculations
    64-bit Open item
  • STEP curves and surfaces: parameters from points

    Finds where a 3D point of an edge lies on a free-form curve or surface, so the face it bounds can be laid out flat and triangulated.

    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    5 calculations
    64-bit
  • STEP curves and surfaces: points from parameters

    Works out the 3D point at a parameter on each kind of curve and surface a STEP file can hold, which is where the triangles of an imported solid get their corners.

    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    14 calculations
    64-bit
  • STEP import: triangles for curved faces

    Turns each face of an imported STEP solid into triangles that stay within a chord tolerance of the true surface and share their edge points with the neighboring faces.

    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    14 calculations
    64-bit
  • STEP import: units, points and assembly placement

    Turns the numbers of a STEP file into millimeters and radians and puts every solid where the file's assembly structure places it.

    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    10 calculations
    64-bit
  • Sun gain through windows

    Works out the heat the sun brings through each window over one clear day: the gain at each time step, the peak and the daily total.

    • BimCraft
    64-bit, stated limit
    4 calculations
    64-bit
  • Sun position and light on a tilted plane for solar

    Gives the sun's direction for each solar hour and the direct, sky and ground-reflected light falling on a module plane, from a clear-sky model or typed monthly totals.

    • BimCraft
    • CivilCraft
    64-bit, stated limit
    8 calculations
    64-bit
  • Sun position for shadows

    The sun's altitude and azimuth for a date, clock time, latitude, longitude and time zone, and the direction shadows are cast from.

    • CadCraft
    • BimCraft
    • ModelCraft
    • CivilCraft
    64-bit, stated limit
    5 calculations
    64-bit
  • Surface triangulation

    Builds a triangulated surface from survey points and breaklines, then its elevations, contours and slopes.

    • BimCraft
    • CivilCraft
    Exact predicates
    6 calculations
    64-bit
  • Survey levels from text and the survey check

    Reads spot levels written as text or block attributes into points with a height, and checks a surveyor's drawing for unit, origin, flat-contour, outlier and duplicate problems.

    • CadCraft
    • BimCraft
    • CivilCraft
    64-bit, stated limit
    6 calculations
    64-bit
  • Three-phase flash

    Splits a mixture into a vapor and two liquids at a temperature and pressure with an activity-coefficient model.

    • CadCraft
    • BimCraft
    64-bit, stated limit
    4 calculations
    64-bit
  • TIFF scan resolution

    Reads the resolution of a scanned drawing from a TIFF file as dots per inch.

    • CadCraft
    • BimCraft
    • ModelCraft
    • CivilCraft
    • PartCraft
    64-bit, direct
    2 calculations
    64-bit
  • Tracing a scan into lines and arcs

    Turns the black-and-white pixels of a scanned drawing into lines and arcs, cleans them up, and offers their ends, middles, centers and crossings as snap points.

    • CadCraft
    • BimCraft
    • ModelCraft
    • CivilCraft
    • PartCraft
    64-bit, stated limit
    10 calculations in 2 files
    64-bit Open item
  • Triangle mesh built from IFC geometry

    Holds every shape read from an IFC file as triangles, moves and joins them, and hands the result to the app.

    • BimCraft
    • TakeoffCraft
    • CivilCraft
    • DetailCraft
    32-bit step, flagged
    5 calculations
    32-bit in part Open item
  • Trim, extend and corner walls

    Finds where two wall center lines meet and the new ends of a wall trimmed or extended to another.

    • BimCraft
    64-bit, direct
    5 calculations
    64-bit
  • Truss geometry, cut list and shop outputs

    Builds the centerline frame of a truss from its type or from the roof's section, and produces the cut list, joint schedule, jig drawing, stock plan, 3D members and CAD drawings.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    26 calculations in 7 files
    64-bit Open item
  • Truss layout 3D picture

    Draws the truss layout as a wireframe picture seen from an angle.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    Display only
    3 calculations
    32-bit, display only
  • Truss layout over a roof

    Sets out the trusses along a roof: where each one stands, its span, and which trusses share a design, including hip-end girders and jacks and valley sets.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    9 calculations in 2 files
    64-bit Open item
  • Truss member forces and timber checks

    Works out the force in every member of a roof truss for each load case and combination, checks each member in tension or compression with bending, picks sizes, and estimates deflection and bearing reactions.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    20 calculations in 3 files
    64-bit Open item
  • Turning a face mesh back into an extrusion

    Recognizes a closed triangle mesh that is a straight prism and rewrites it in the IFC file as an outline pulled along a depth, so it stays editable.

    • BimCraft
    64-bit, stated limit
    6 calculations
    64-bit Open item
  • Typed lengths, angles and pitches

    Turns what a person types (feet and inches, fractions, metric, a point or a polar step, a roof pitch) into millimeters and degrees, and formats areas, angles and pitches for display.

    • BimCraft
    64-bit, direct
    6 calculations
    64-bit Open item
  • Typed points and door or window positions

    Turns a typed length, step, polar entry or distance into the next wall point, and places a door or window along a wall from the pointer or a typed distance.

    • BimCraft
    64-bit, direct
    2 calculations
    64-bit
  • Unit conversion

    Converts lengths, areas, volumes, angles and slopes between 57 units.

    Every app Exact values
    4 calculations
    64-bit
  • Unit table: reading and writing values

    Holds every unit's size as an exact fraction, reads typed values such as 12'6 1/2", 45°30'15" or 3:1, and writes values as feet and inches, degrees-minutes-seconds or decimals.

    Every app Exact values
    8 calculations
    64-bit
  • USD export and render hand-off

    Writes the open IFC models as an OpenUSD file and works out the transform that places the cameras, sun and lamps of a render hand-off in that file's world.

    • BimCraft
    32-bit step, flagged
    6 calculations in 2 files
    32-bit in part Open item
  • USD mesh coordinates in saved and exported files

    Writes the points of every mesh into a USD file and reads them back when a USD file is opened.

    • CadCraft
    • BimCraft
    • ModelCraft
    • TakeoffCraft
    • CivilCraft
    • DetailCraft
    • PartCraft
    32-bit step, flagged
    7 calculations in 3 files
    32-bit in part Open item
  • USD transforms and placement

    Works out where every object of a USD scene sits: each object's own transform, its place in the world, the change to meters with Z up, and the placement of instanced copies.

    • CadCraft
    • BimCraft
    • ModelCraft
    • TakeoffCraft
    • CivilCraft
    • DetailCraft
    • PartCraft
    64-bit, direct
    11 calculations in 3 files
    64-bit Open item
  • Vector PDF output

    Writes drawings to a PDF file: the page size, the millimeter scale, lines, circles and text positions.

    • BimCraft
    • DetailCraft
    64-bit, stated limit
    6 calculations
    64-bit Open item
  • Vessel outline and inside volume

    Works out the revolved outline of a vessel with its two heads, its height and inside volume, and where a nozzle sits on it.

    • CadCraft
    • BimCraft
    64-bit, stated limit
    4 calculations
    64-bit Open item
  • Wall dimensions, heights and quantities

    Reads a drawn wall's ends, length, thickness and height from the file and writes its shape, side areas, footprint and volumes.

    • BimCraft
    64-bit, stated limit
    12 calculations
    64-bit Open item
  • Wall faces and plan frames from element meshes

    Finds the faces of walls in plan so a placed item can sit against one, and the turned box of copied elements that the paste ghost and wall snap use.

    • BimCraft
    32-bit step, flagged
    5 calculations
    32-bit in part Open item
  • Wall joins and plan outlines

    Works out the plan outline of every drawn wall with its corners, tees and crossings cleaned, which becomes the wall's solid and closes rooms.

    • BimCraft
    64-bit, direct
    9 calculations
    64-bit
  • Wall layers drawn in plans and sections

    Works out the outline of each wall layer where a plan or a section cuts a wall, and the wall edges an elevation shows, as the linework drawn on screen and on sheets.

    • BimCraft
    64-bit, direct
    11 calculations in 2 files
    64-bit
  • Wall, floor and roof framing layout

    Works out where every stud, plate, header, joist, rafter, truss and collar tie goes, which lumber size a span needs, and the lengths and board feet written on each piece.

    • BimCraft
    64-bit, stated limit
    21 calculations
    64-bit Open item
  • Walls and openings from PDF pages and scans

    Reads the lines and door-swing arcs of a plan page, scales them to millimeters from two picked points, and turns them into walls with door and window openings.

    • BimCraft
    64-bit, stated limit
    9 calculations
    64-bit
  • Walls and openings traced from a drawing

    Turns the lines and blocks of a DWG or DXF drawing into wall center lines, thicknesses, door and window positions, and a reference underlay.

    • BimCraft
    64-bit, stated limit
    10 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

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.

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.

A point C almost on the line from A to B. Magnified, C is a tiny distance to one side of the line. A B C C left or right?
C lies a rounding error away from the line through A and B. Which side it is on decides how the geometry is built.

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.