NumCore

Launch NumCore Simulator

Run the full firmware math engine in your browser
No download required · 429 KB · Works offline

Note: The simulator may not function correctly on mobile devices — for the best experience, use a PC.

Bare-metal scientific calculator firmware for the LM3S811 ARM Cortex-M3 (64 KB Flash, 8 KB SRAM), written in Rust with #![no_std] #![no_main].

Features a Q31.32 fixed-point math engine with CORDIC + Taylor-corrected trig, minimax polynomial exp/log, CLZ-based square root, rational minimax arctangent, Smith's robust complex division, Stirling's log-gamma, overflow-aware scientific notation, adaptive Simpson integration, matrix operations up to 4x4, and a bytecode VM evaluator with zero C stack growth. No heap, no allocator, no OS.

Project highlights

• Bytecode VM evaluation — recursive-descent compiler emits opcodes into a 256 B buffer; flat execute() loop with 16-entry value stack eliminates all C recursion. Expressions like 1+1+1+1+1+1+1+1+1+1 work correctly (the previous recursive evaluator overflowed at depth 4, silently corrupting .bss).
• Q31.32 fixed-point — i64 storage, i128 intermediates, saturating arithmetic, EvalResult error model (Value / Overflow / DomainError), precision of $2^{-32}\approx2.33\times10^{-10}$ (~9 decimal digits)
• CORDIC sin/cos — 22 iterations + first-order Taylor correction on residual angle ($|\delta|<2^{-21}$, corrected to $O(\delta^2)<2.3\times10^{-13}$)
• Rational minimax atan — $\operatorname{atan}(r)=r\cdot P(r^2)/Q(r^2)$, Ganssle-Homer form, Horner evaluation, error $<1.6\times10^{-10}$ rad
• Minimax exp — degree-7 polynomial, max error $\sim5.95\times10^{-11}$
• Minimax ln — degree-10 polynomial, max error $\sim1.62\times10^{-9}$
• CLZ reciprocal sqrt — 32-entry LUT + 3 Newton iterations on $1/\sqrt{x}$
  • 1 final Newton refinement on $\sqrt{x}$
• Smith's complex division — overflow-safe branch on $|c|\ge|d|$, handles values up to $\sim10^9$ in Q31.32
• Stirling's ln gamma — asymptotic series $z\ge5$ with recurrence and reflection formula, $\sim6$ ULP worst-case error
• Adaptive Simpson integration — iterative bisection, $\tau\approx10^{-8}$, max depth 20; integrates $\int_0^{10}\sinh x\,dx$ accurate to $<2\times10^{-6}$
• Overflow-aware scientific notation — results exceeding Q31.32 range display as 1.34406E+43; binary operations adjust the overflow estimate
• Bytecode compiler — same recursive-descent grammar, emits opcodes instead of AST nodes; 12 opcodes, 256 B fixed-size buffer
• Complex numbers — full arithmetic + analytic-continuation trig
• Matrix operations — 4x4 max, determinant, inverse, transpose, cofactor, adjugate, scalar broadcast, matrix multiplication
• Scientific notation mode — 1.5E+10 syntax, ±99 exponent hard limit, auto-conversion to Scalar when value fits Q31.32 exactly
• Log-space distributions — ln_gamma (Stirling), ln_factorial (hybrid table/Stirling), binomial/Poisson PMF, chi-squared CDF
• 300/300 host-side tests pass, 6 pre-existing ignored (overflow/underflow at Q31.32 boundaries)

Supported functions

Arithmetic: + - * / ^ %. Trigonometric: sin cos tan asin acos atan. Hyperbolic: sinh cosh tanh asinh acosh atanh. Other: sqrt abs exp ln log log2 floor ceil round deg rad nthroot lngamma. Distributions: binompp poissonp chicdf. Loops: sum int. Matrix: det transpose identity inv cofactor adjugate. Storage: sto. Constants: pi e. Variables: Ans A-Z (scalar), MatA MatB MatC (matrix).

See Math Engine for full reference.

Modes

Mode	Scope	Key features
Standard	Arithmetic + transcendentals	All functions, real numbers only
Advanced	Standard + complex	Imaginary unit i, complex arithmetic
Matrix	Standard + matrix ops	Matrix literals [(a,b)(c,d)], 4x4 limit
Scientific	Standard + E-notation	1.5E+10 literal syntax, exponent arithmetic

Cycle modes with Esc key.

Firmware metrics

Metric	Value	Budget	Usage
Flash (.text + .data)	63,029 B	64 KB	96.2%
SRAM (.data + .bss + .stack)	4,312 B	8 KB	52.6%

Quick start

# Build firmware (release, size-optimised)
cargo build -p numcore-lm3s811 --release --target thumbv7m-none-eabi

# Run host-side unit tests (300 tests)
cargo test -p numcore_math --tests

# Run in QEMU
qemu-system-arm -M lm3s811evb -serial mon:stdio -display none \
  -kernel target/thumbv7m-none-eabi/release/NumCore

# Pipe expression
echo "2+2" | timeout 5 qemu-system-arm -M lm3s811evb -serial stdio -display none \
  -kernel target/thumbv7m-none-eabi/release/NumCore

Source code: github.com/NumCore/NumCore