* Cyclic Jacobi eigenvalue algorithm for a real symmetric matrix. * `A` is n x n symmetric; on success `eigvals` (length n) holds the eigenvalues *

Swaps columns `i` and `j` of an n-column matrix stored row-major. */

* @brief Creates a submatrix by excluding a specified row and column. * * This function generates a submatrix from the input matrix by removing the

* @brief Computes the inverse of a square matrix. * * This function calculates the inverse of a square matrix by first computing its determinant. *

* @brief Checks if two matrices are equal. * * Two matrices are considered equal if they have the same dimensions and their corresponding elements a

* @brief Checks if a matrix is symmetric. * * A matrix is symmetric if it is equal to its transpose, meaning the element at position * (i, j) is e

* @brief Computes the arithmetic mean of every element of a matrix. * * The C analogue of NumPy's `numpy.mean(M)`: returns the sum of all elements

* @brief Swaps two rows of a matrix. * * This function swaps the elements of two rows in the given matrix. * If the matrix pointer is NULL or the r

* @brief Parses a JSON array from the input string. * * This function assumes that the current token is the start of a JSON array (`[`). * It cont

* @brief Parses a JSON object from the input string. * * This function assumes that the current token is the start of a JSON object ('{'). * It p

* @brief Parses a JSON string from the input string. * * This function assumes that the current token is the start of a JSON string (`"`). * It re

* @brief Convenience setter for the axis (and frame) colour. * * The axis colour is reused as the colour of the x/y axis lines, the * plot title, b

* @brief Convenience setter for the background colour. * * Overrides the colour passed to ClearBackground() at the start of * every frame. Useful w

* @brief Convenience setter for the grid line colour. * * Changes the colour of the 11x11 grid drawn behind the plotted * series. Has no effect whe

* @brief Convenience setter for the legend background + text colours. * * Updates the legend's fill colour and the colour of its label text in * on

* @brief Destroy the priority queue and release all memory it owns. * * Frees both the underlying vector AND the PriorityQueue header. * NULL-safe.

* @brief Destroy the queue and release all memory it owns. * * Frees both the underlying vector AND the Queue header itself. NULL-safe. * * @param

* @brief Generates a random double number based on the Gamma distribution. * * @param shape The shape parameter of the distribution (must be greater

* @brief Generates a random double number based on the Gaussian (normal) distribution. * * @param mean The mean (mu) of the distribution. * @param

Walk the LIVE nodes (recursion depth = tree height = O(log n)) and run the * optional key/value deallocators. Node memory itself is NOT freed here —

Release every slab (used on clear / deallocate). O(number of slabs). */

Return a node's slot to the free-list for reuse (used on erase / dup). */

@brief Rightmost (maximum) node of a subtree, or NULL. */

Release every slab (used on clear / deallocate). O(number of slabs). */

* @brief Internal: shared engine for regex_replace and regex_replace_first. * * @param max_replacements -1 means "replace all". Any other non-negati

* @brief Searches for the given regex pattern in the provided string. * * @param regex The compiled regex object. * @param string The string to se

Draw the plot contents into the currently-bound render target. * Shared by plot_draw (live window) and plot_export_image (offscreen). */

* @brief Internal: draw an unbiased, uniformly-distributed size_t in [0, n). * * Uses rejection sampling against the largest exact multiple of @p n

* @brief Serializes a string value into a JSON-formatted string. * * This function takes a string and appends it to a String object in JSON format,

* Shift the byte to the left by the specified offset * This function calls shift_right with the negative of the offset, * effectively performing a l

* @brief Convert an arbitrary array into a max-heap in place (Floyd's method). * * Runs in O(n) by heapifying from the last non-leaf node downward.

* @brief In-place heap sort. * * Builds a max-heap then repeatedly extracts the root to the end of the * array. **Not stable.** Worst-case guarante

* @brief Introspective sort variant with cutoffs and depth-limited recursion. * * - Arrays of ≤16 elements: insertion sort. * - Otherwise: median-o

* @brief Lomuto partition around `array[right]` as pivot. * * Reorders `array[left..right]` so that elements `<=` pivot come first and * elements `

* @brief Quicksort with median-of-three pivot selection and small-array cutoff. * * For arrays of ≤10 elements, falls back to insertion sort (which

* @brief Shell sort with Knuth's halving gap sequence. * * Generalized insertion sort: starts with a large gap (`size/2`), halves it * each pass, a

Sift the element at index i down a max-heap of n elements. */

* @brief Destroy a stack and release all underlying memory. * Safe to call with NULL (no-op). */

* @brief Compares two elements based on their memory content using memcmp. * This function is useful for comparing elements of different types in ge

this helper function function has been corrected to handle ties by averaging the ranks of tied values. Returns true on success, false on allocation fa

Allocate an ascending-sorted copy of `data` (n doubles); caller frees. Distinct `statp_` prefix from the public `statistics_` API. NULL on OOM. */

* @brief Assigns a new string to the String object, replacing its current contents. * * This function replaces the current contents of the String ob

* @brief Returns a constant C-string representation of the string. * * This function returns a constant pointer to the character array managed by th

* @brief Initializes the network API (Windows only). * * This function initializes the Winsock library on Windows systems. On Unix-like systems,

* @brief Send EXACTLY `len` bytes, looping over partial writes. * * `tcp_send` (and the underlying `send()`) is allowed to return having * written

* @brief Sets the non-blocking mode for a TCP socket. * * This function sets or unsets the non-blocking mode on the given socket. In non-blocking mo

* @brief Closes an SSL-encrypted TCP connection. * * This function initiates the SSL/TLS shutdown sequence for the specified socket, frees the assoc

* @brief Initiates an SSL/TLS connection to a remote host. * * This function establishes a secure SSL/TLS connection to a remote host on the given s

* @brief Verification result of the peer certificate chain after a handshake. * @param socket A TCP socket with an active TLS session. * @return X50

* @brief Initialize a client-side SSL context (TLS_client_method). * * Unlike tcp_ssl_init (which builds a server context and requires a cert/key),

* @brief Wait until the socket has data ready to read, or time out. * * Blocks in `select()` until the socket is readable (data has arrived, or the

Wait until `socket` is ready for read (want_write=false) or write * (want_write=true), or until `timeout_ms` elapses. timeout_ms < 0 blocks * indefi

* @brief Stop all workers, join them, and free all pool resources. * * Any tasks still queued (not yet picked up by a worker) are discarded. * In-f

* @brief This function checks if the first Time object (`lhs`) represents an earlier time than the second Time object (`rhs`). * It compares the hou

Internal: append a text label to the turtle's recorded labels. */

* @brief Sets the turtle's heading to a specified angle. * * This function sets the direction in which the turtle is facing to the given angle in d

* @brief Deep-copy @p src into a brand-new Variant. * * For STRING and CUSTOM variants the underlying storage is duplicated * (using `info->copy` f

* @brief This function compares two vectors to determine if they are equal in size and content. * The comparison is performed element by element, an

True when a variant tag's payload lives entirely inside the inline union (no * owned heap storage), so a clone is simply a struct copy and a destroy

Remove `node` from its owning document's registry (if any) so that a * subsequent xml_deallocate_document does not free the wrapper a second * time.

* @brief Copies the provided text to a new dynamically allocated memory block. * * This function duplicates a given text string by allocating new m

Recursive helper: count every descendant (NOT including @p node * itself) whose tag matches @p tag_name. */

* @brief Free a list of attributes returned by xml_get_attributes. * * Releases every node in the singly-linked list along with the copied * name/v

* This function converts a UTF-16 encoded string to UTF-8. It handles surrogate pairs by converting * them to their corresponding UTF-32 representat

* This function converts a UTF-32 encoded string to UTF-8. It processes each UTF-32 character, * determining how many bytes are needed in UTF-8, and

* This function converts a UTF-8 encoded string to UTF-16. It iterates through the source UTF-8 string, * decodes each character, and checks for any

* This function converts a UTF-8 encoded string to UTF-32. It processes the UTF-8 input by decoding each character, * verifying its legality, and th

* @brief Append a record to the live-allocation tracking list. * * Used by `unittest_malloc`. If the tracking node itself fails to * allocate, `tot

* @brief Finds the first position in a sorted range where a value can be inserted without violating the order. * * This function performs a binary s

* @brief Sorts an array using a non-stable quicksort algorithm. * * @param base Pointer to the start of the array. * @param num Number of elements

* @brief Swaps the values of two elements. * * @param a Pointer to the first element. * @param b Pointer to the second element. * @param size Size

* @brief Finds the first position in a sorted range where a value is greater than a specified value. * * This function performs a binary search on a

* This function finds the index of a character within the BASE91_ALPHABET array, which is used for Base91 decoding. * If the character is not found,

* @brief Frees the memory of a BigFloat. * @param bf Pointer to the BigFloat to deallocate. */

* @brief Checks if a BigFloat is negative. * @param a Pointer to the BigFloat. * @return `true` if the BigFloat is negative, `false` otherwise. */

* @brief Checks if a BigInt is zero. * * Determines whether the BigInt is equal to zero. * * @param bi Pointer to the BigInt to check. * @return

* @brief Converts a BigInt to a decimal string. * * Converts the internal GMP value to a null-terminated decimal string. * The returned string is a

Function to calculate binomial coefficient

* @brief This function performs a binary search to find the index where a value x should be inserted in the * sorted array data while maintaining th

* @brief Similar to bisect_left, but it returns the index where x should * be inserted to the right of existing elements that are equal to x. This i

* @brief Checks if any bit in the Bitset is set. * * Returns true if at least one bit in the Bitset is set to 1. * * @param bs Pointer to the Bits

* @brief Compares two Bitsets for equality. * * This function checks if two Bitsets are identical in size and bit values. * It returns true if the

Linux specific virtualization detection remains the same

Serialize the request line + headers + body into `b`. Host and * Content-Length are generated; any user-supplied Host/Content-Length/ * Connection h

Read a complete response off the socket into a contiguous "headers\r\n\r\n + * de-framed body" buffer. Body framing: no body for HEAD / 1xx / 204 / 3

Build the absolute URL a Location header redirects to, relative to `base`. * Handles absolute (scheme://...), root-relative (/path) and relative path

Send the whole buffer, SSL-aware, bounded by a writable-timeout per chunk. */

Establish client TLS on an already-connected socket (SNI = host). When * !insecure, require the peer certificate chain to verify. */

* @brief Registers a new option with the CLI parser. * * This function adds a new option to the CLI parser, allowing it to be recognized and process