ucalc is an interactive calculator and compute oracle for exploring,
comparing, and analyzing arithmetic across 42+ number types from the
Universal library. Instead of writing, compiling, and running C++ for
each experiment, you can compare representations, measure precision,
trace errors, and visualize arithmetic behavior interactively.
ucalc serves two audiences:
Humans use the interactive REPL to explore numerical behavior,
debug precision issues, and teach how different number systems work.AI agents use the MCP server to call ucalc tools
programmatically via JSON-RPC, making ucalc a compute oracle for
mixed-precision analysis.
cmake -DUNIVERSAL_BUILD_TOOLS_UCALC=ON ..
ucalc " type posit32; show 1/3 "
echo " compare sqrt(2) " | ucalc
Flag Description --jsonJSON output for all commands --csvCSV output for tabular commands --quietValue only, no decoration --mcpRun as MCP server (JSON-RPC over stdio) -t <type>Set active type from command line -f <file>Execute a script file (batch mode)
Expressions support standard arithmetic (+, -, *, /, ^), parentheses,
variables (x = expr), constants (pi, e, phi, ln2, ln10, sqrt2,
sqrt3, sqrt5), and functions (sqrt, abs, log, exp, sin, cos,
tan, asin, acos, atan, pow).
Constants are sourced at quad-double precision (~64 decimal digits) and
converted to the active type at its native precision.
Command Description type <name>Set the active arithmetic type typesList all 42+ available types show <expr>Value + decimal + binary + components compare <expr>Evaluate across all types in a table bits <expr>Raw bit pattern rangeSymmetry range: [maxneg … minneg] 0 [minpos … maxpos] precisionBinary/decimal digits, epsilon, minpos, maxpos ulp <value>Unit in the last place at a given value sweep <expr> for <var> in [a, b, n]Error analysis across a range faithful <expr>Check faithful rounding vs qd reference oracle <type> <expr>Canonical result with rounding verification increment <expr>Show value and next representable value decrement <expr>Show value and previous representable value color on/offToggle ANSI color-coded bit fields varsList defined variables
Command Description steps <expr>Step-by-step arithmetic (align, add, normalize, round)trace <expr>Show each operation with ULP error and rounding direction cancel <expr>Detect catastrophic cancellation in subtractions audit <expr>Rounding audit trail with signed ULP drift and ties-to-even detection diverge <expr> <t1> <t2> <tol> for <var> in [a, b]Find where two types first disagree suggest <expr>Find unstable patterns and suggest rewrites rewritesList available numerical rewrite patterns ast <expr>Show expression tree structure with provenance tags numberline [lo, hi]ASCII visualization of representable value density heatmapPrecision (significant bits) vs magnitude bar chart
Command Description quantize <fmt> [data] | -f <file>Quantize data, report RMSE/QSNR/errors block <fmt> [data] | -f <file>MX/NV block decomposition (scale + elements) dot [v1] [v2] [accum=<type>]Mixed-precision dot product with configurable accumulation clip <type> [data] | -f <file>Overflow/underflow map for a distribution
Command Description testvec <type> <func> [a, b, n]Generate golden test vectors (C++/JSON/CSV) errordist <expr> for <var> in [a, b, n]ULP error distribution histogram stochastic <expr> NSimulate stochastic rounding N times histogram [lo, hi, bins]Representable value distribution cond [[a,b],[c,d]]Condition number estimation (2x2 or 3x3)
ucalc registers 42 types spanning the major number system families:
Family Types Integer int8, int16, int32, int64 Fixed-point fixpnt16, fixpnt32 Decimal fixed-point dfixpnt8_4, dfixpnt16_8 Native IEEE float, double Classic float fp16, fp32, fp64, fp128 Google Brain Float bfloat16 FP8 (Deep Learning) fp8e2m5, fp8e3m4, fp8e4m3, fp8e5m2 Logarithmic lns8, lns16, lns32 Double-base dbns8, dbns16 Posit posit8, posit16, posit32, posit64 Takum takum8, takum16, takum32, takum64 Decimal float decimal32, decimal64 Hexadecimal float hfloat32, hfloat64 Rational rational8, rational16, rational32 Multi-component dd, dd_cascade, td_cascade, qd, qd_cascade