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https://github.com/zephyrproject-rtos/zscilibA C library for scientific computing, data analysis, and data manipulation on resource-constrained embedded hardware. It provides vector and matrix operations (including SVD and pseudoinverse), motion and orientation APIs (Quaternions, AHRS, and sensor fusion), and colorimetry conversions. Designed for use with Zephyr RTOS or as a standalone library, it includes ARM Thumb/Thumb-2 assembly optimizations for Cortex-M devices.
The Orientation API Test sample is a demonstration of the zscilib orientation capabilities. It shows how to process raw sensor data through the following pipeline:
The standalone example demonstrates two core mathematical capabilities of the library:
zsl_mtx_svd function to calculate the SVD of an input matrix. The results consist of $U$, $\Sigma$, and $V^T$ matrices, such that $\text{input} = U \cdot \Sigma \cdot V^T$.zsl_mtx_pinv function to calculate the pseudoinverse of a matrix (e.g., converting an $18 \times 3$ matrix into a $3 \times 18$ matrix).The following features are planned for future releases of zscilib:
An ARM mnemonic is composed of three potential parts:
add).s Modifier: Appending s (e.g., adds) tells the core to update the CPSR condition flags based on the result of the operation. By default, instructions do not modify flags.addeq). These can be combined with the s modifier (e.g., addseq).| Cond Code | Condition Flags | Meaning |
|---|---|---|
EQ | Z = 1 | Equal |
NE | Z = 0 | Not equal |
CS/HS | C = 1 | Carry condition flag set |
CC/LO | C = 0 | Carry condition flag clear |
MI | N = 1 | Negative |
PL | N = 0 | Positive or zero |
VS | V = 1 | Overflow set |
VC | V = 0 | Overflow not set |
HI | C = 1 and Z = 0 | Unsigned higher |
LS | C = 0 or Z = 1 | Unsigned lower or same |
GE | N = V | Signed greater than or equal |
LT | N != V | Signed less than |
GT | Z = 0 and N = V | Signed greater than |
LE | Z = 1 and N != V | Signed less than or equal |
AL | Default | Always (usually omitted) |
Most orientation fusion algorithms in zscilib follow a similar principle: they take an initial orientation and integrate angular velocity from a gyroscope over time to estimate new orientations.
To prevent gyroscope drift (common in MEMS sensors), accelerometer and/or magnetometer vectors are used to provide absolute references relative to gravity and/or magnetic north.
alpha). One estimate comes from the gyroscope (zsl_quat_from_ang_vel), and the second comes from the accelerometer and magnetometer (zsl_att_from_accelmag).alpha near 0.0: Gyroscope is prioritized.alpha near 1.0: Accel/Mag are prioritized.beta parameter based on your specific sensors to ensure stability and accuracy.ARM Cortex-M devices use different instruction sets depending on the specific architecture. When writing assembly for these devices, ensure you are targeting the correct set:
The library includes tooling to allow for optimized, architecture-specific implementations of key functions using assembly.
Initial optimization efforts target the Arm Cortex-M family of devices using the Thumb and Thumb-2 instruction sets. This design allows the library to achieve high performance on resource-constrained hardware by replacing generic C implementations with hand-optimized assembly where beneficial.
ARM processors use 32-bit registers to store values before operations. Registers are divided into general-purpose and special-purpose categories.
R0 through R10: General-purpose.R11 (fp): Frame pointer (used by compilers to track stack frames).R12 (ip): Inter-procedure scratch register (used by C libraries for DLL calls).R13 (sp): Stack Pointer. Holds the address where the stack currently ends. The stack grows downward (the value decreases as usage increases).R14 (lr): Link Register. Contains the return address for subroutines (usually the pc value from the caller).R15 (pc): Program Counter. Contains the address of the next instruction to be executed.You can apply unary or binary operations to matrices using the zsl_mtx_unary_op and zsl_mtx_binary_op functions. For operations not covered by the built-in list, you can provide user-defined functions via zsl_mtx_unary_func or zsl_mtx_binary_func.
// Example concept: applying a unary operation
// zsl_mtx_unary_op(matrix, operation_type)
// Example concept: applying a binary operation
// zsl_mtx_binary_op(matrix_a, matrix_b, operation_type)Immediate values are constants used as operands. They can be specified in decimal, octal (03), hexadecimal (0x2F), or binary (0b11010010).
There are two distinct syntaxes in GNU assembly depending on the instruction type:
=<immediate|symbol>. This specifies a 32-bit immediate value or the value of a symbol (label or .equ).#<immediate|symbol>.Important Restrictions:
= syntax is only for load/store instructions.# syntax is restricted: the assembler must be able to construct the value using only eight bits of data, a shift/rotate operation, and/or a complement. If a value cannot meet these constraints, you must use a ldr instruction with the = syntax to load it from a literal pool.; Example of using the = syntax for load/store
LDR R0, =0x12345678
; Example of using the # syntax for data processing
ADD R1, R2, #5ARM instructions are rigidly separated into two main types:
R5, R8). They typically use two source operands and one core register.The accuracy of the benchmark results depends on the hardware platform:
qemu_cortex_m3 or non-M3/M4 hardware, the sample uses the high-precision kernel clock. Data from these platforms is approximate and should not be compared directly against data from M3/M4 hardware.