#include <stddef.h>
#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <errno.h>
#include <ctype.h>
#include "lina.h"

/* Function: lina_dot
**
**   Evaluates the dot product C = A * B. The A,B
**   matrices are, respectively, mxn and nxl, which
**   means C is mxl. The resulting C matrix is stored
**   in a memory  region specified by the caller. 
**
** Notes:
**
**   - A,B must be provided as contiguous memory regions
**     represented in row-major order. Also, C is stored
**     that way too.
**
**   - The C pointer CAN'T refer to the same memory region 
**     of either A or B.
**
**   - m,n,l must be greater than 0.
**
**   - This function can never fail.
*/
void lina_dot(double *A, double *B, double *C, int m, int n, int l){

    assert(m > 0 && n > 0 && l > 0);
    assert(A != NULL && B != NULL && C != NULL);
    assert(A != C && B != C);

    // Iteration over A's rows
    for(int i = 0; i < m; i++)
        {
            // Iteration over B's columns
            for(int k = 0; k < l; k++)
                {
                    double pos = 0;

                    // Iteration over the single B column 
                    // for executing the product of sum
                    
                    for(int j=0; j < n; j++)

                        pos += A[i*n + j] * B[j*l + k];

                    C[i*l + k] = pos;
                }
        }
}

/* Function: lina_add
**
**   Evaluates the matrix addition C = A + B. The result
**   is stored in a memory region provided by the caller.
**   All matrices involved are mxn. 
**
** Notes:
**
**   - A,B must be provided as contiguous memory regions
**     represented in row-major order. Also, C is stored
**     that way too.
**
**   - The C pointer CAN refer to the same memory region 
**     of either A or B.
**
**   - m,n must be greater than 0.
**
**   - This function can never fail.
*/
void lina_add(double *A, double *B, double *C, int m, int n){

    assert(m > 0 && n > 0);
    assert(A != NULL && B != NULL && C != NULL);
    
    for(int i = 0; i < m; i++)
        for(int j = 0; j < n; j++)

            C[i*n + j] = A[i*n + j] + B[i*n + j];
}

/* Function: lina_scale
**
**   Evaluate B = k * A, where A,B are matrices mxn 
**   and  k is a scalar. The result is stored in a 
**   memory region provided by the caller. 
**
** Notes:
**   - The B pointer CAN refer to the same memory 
**     region of A.
**
**   - m,n must be greater than 0.
**
**   - This function can never fail.
*/
void lina_scale(double *A, double *B, double k, int m, int n){

    assert(m > 0 && n > 0);
    assert(A != NULL && B != NULL);

    for(int i = 0; i < m*n; i += 1)
        B[i] = k * A[i];   
}

/* Function: lina_transpose
**
**   Evaluate the transpose of A and store it in B. 
**   The matrix A is mxn, which means B will be nxm.
**
** Notes:
**   - The B pointer CAN refer to the same memory 
**     region of A.
**
**   - m,n must be greater than 0.
**
**   - This function can never fail.
*/
void lina_transpose(double *A, double *B, int m, int n)
{
    assert(m > 0 && n > 0);
    assert(A != NULL && B != NULL);

    if(m == 1 || n == 1)
        {
            memcpy(B, A, sizeof(A[0]) * m * n);
            return;
        }

    if(m == n)
        {
            for(int i = 0; i < n; i += 1)
                for(int j = 0; j < i+1; j += 1)
                    {
                        double temp = A[i*n + j];
                        B[i*n + j] = A[j*n + i];
                        B[j*n + i] = temp;
                    }
        }
    else
        {
            B[0] = A[0];
            B[m*n-1] = A[m*n-1];

            double item = A[1];
            int    next = m;

            while(next != 1)
                {
                    double temp = A[next];
                    B[next] = item;
                    item = temp;
                    next = (next % n) * m + (next / n);
                }

            B[1] = item;
        }
}

/* Function: scanValue
**
**   Scans a numeric value (such as 12, 4.5, 2.1442) 
**   from the stream [fp] and store it in [buffer].
**   If more than [max_length] bytes would be written
**   to the buffer, this function fails. The first
**   character of the sequence is assumed to have 
**   been already read and is provided through the
**   [first] argument.
**
**   If the function fails, 0 is returned and an error
**   description is returned through the [error] pointer.
**   If it succeded, then:
**
**     - The [buffer] contains the whole zero-terminated
**       character sequence of the numeric value.
**
**     - Through the [final] pointer is returned the first
**       character that wasn't part of the digit sequence
**       (which was consumed by the function, so if the
**       caller were to read a character from the stream,
**       it would get the second character after the digit
**       sequence).
**
**     - 1 is returned if the sequence represents an integer
**       and -1 if the sequence represents a float.
**   
** Notes:
**   - The buffer is always zero terminated if the
**     function succeded.
**
**   - The [error] and [final] pointers are optional
**     (they can be NULL).
*/
static int scanValue(FILE *fp, char *buffer, int max_length, char first, char *final, char **error)
{
    assert(fp != NULL && buffer != NULL && error != NULL);
    assert(max_length >= 0);
    assert(isdigit(first));

    int n = 0;

    char c = first;

    // Scan the integer portion of
    // the numeric value and copy it
    // into the buffer.
    do
        {
            if(n == max_length)
                {
                    // ERROR: Internal buffer is too small to hold
                    //        the representation of this item.
                    *error = "Internal buffer is too small to hold "
                             "the representation of a numeric value";
                    return 0;
                }

            buffer[n++] = c;
            
            c = getc(fp);
        }
    while(c != EOF && isdigit(c));

    // Did the integer part end with
    // a dot?
    _Bool dot = (c == '.');

    // Now scan and copy the decimal 
    // part of the numeric value if 
    // a dot was found.
    if(dot)
        {
            if(n == max_length)
                {
                    // ERROR: Internal buffer is too small to hold
                    //        the representation of this item.
                    //        (The dot doesn't fit.)
                    *error = "Internal buffer is too small to hold "
                             "the representation of a numeric value";
                    return 0;
                }

            buffer[n++] = '.';

            c = getc(fp);

            if(!isdigit(c))
                {
                    // ERROR: Got something other than a 
                    //        digit after the dot.
                    *error = "Got something other than a digit after the dot.";
                    return 0;
                }
            
            do
                {
                    if(n == max_length)
                        {
                            // ERROR: Internal buffer is too small 
                            //        to hold the representation of
                            //        this item.
                            *error = "Internal buffer is too small to hold "
                                     "the representation of a numeric value";
                            return 0;
                        }

                    buffer[n++] = c;

                    c = getc(fp);
                }
            while(c != EOF && isdigit(c));
        }

    buffer[n] = '\0';
    
    if(final != NULL)
        *final = c;
    
    return dot ? -1 : 1;
}

/* Function: lina_loadMatrixFromStream
**
**   Load from the stream [fp] a matrix encoded as an
**   ASCII sequence in the form:
**
**     [a b c .. , d e f .. , ..]
**
**   where a,b,c,.. are either integers or floats.
**   For instance, the 4x4 identity matrix is 
**   represented as:
**
**     [1 0 0 0,
**      0 1 0 0,
**      0 0 1 0,
**      0 0 0 1]
**
**   or, equivalently:
**
**     [1 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1]
**
**   since whitespace doesn't matter.
**   The decoded matrix is returned through the return
**   value and is dynamically allocated, therefore the
**   caller must call [free] on it when he doesn't need
**   it anymore. The dimensions of the matrix are returned
**   through the [width] and [height] output arguments*
**
**   If an error occurres (either because an allocation
**   failed or because the matrix syntax is invalid),
**   NULL is returned and a human-readable description of
**   what happened is returned through the [error] pointer.
**
** Notes:
**   - This function skips any whitespace that comes before
**     the matrix in the stream.
**
**   - It can be called multiple times on a stream to get
**     more than one matrix from it.
**
**   - The [error] pointer is optional (it can be NULL).
**
**   - If the stream [fp] is NULL, then [stdin] is used.
*/
double *lina_loadMatrixFromStream(FILE *fp, int *width, int *height, char **error)
{
    assert(width != NULL && height != NULL);
    
    if(fp == NULL)
        fp = stdin;

    char *dummy;
    if(error == NULL)
        error = &dummy;
    else
        *error = NULL;

    char c = getc(fp);

    while(c != EOF && isspace(c))
        c = getc(fp);

    if(c == EOF)
        {
            // ERROR: Stream ended before a matrix was
            //        found.
            *error = "Stream ended before a matrix was found";
            return NULL;
        }

    if(c != '[')
        {
            // ERROR: Was expected a '[' as the first 
            //        character of a matrix, but got 
            //        something else instead.
            *error = "Got something other than a matrix "
                     "where one was expected";
            return NULL;
        }

    c = getc(fp);

    // Skip spaces before the first element.
    while(c != EOF && isspace(c))
        c = getc(fp);

    if(c == EOF)
        {
            // ERROR: Stream ended where a numeric value
            //        was expected. 
            *error = "Stream ended where a numeric value "
                     "was expected";
            return NULL;
        }

    double *matrix = malloc(sizeof(matrix[0]) * 64);

    if(matrix == NULL)
        {
            // ERROR: Insufficient memory.
            *error = "Insufficient memory";
            return NULL;
        }
    
    int capacity = 64, size = 0, 
        w = -1, i = 0, j = 0;

    if(c != ']')
        while(1)
            {
                if(!isdigit(c))
                    {
                        // ERROR: Got something other than a digit 
                        //        where a numeric value was expected.
                        *error = "Got something other than a numeric "
                                 "value where one was expected";
                        return NULL;
                    }

                // Numeric values can't be represented
                // in strings bigger than this buffer
                // since they need to be copied in it
                // to be converted to actual numeric
                // variables.
                char buffer[128];
                
                int res = scanValue(fp, buffer, sizeof(buffer), c, &c, error);

                if(res == 0)
                    // Failed to scan the value, abort.
                    // NOTE: The error was already reported.
                    return NULL;

                assert(res == 1 || res == -1);

                // Make sure the matrix has enough space.
                if(size == capacity)
                    {
                        int new_capacity = capacity * 2;

                        double *temp = realloc(matrix, sizeof(double) * new_capacity);

                        if(temp == NULL)
                            {
                                // ERROR: Insufficient memory.
                                *error = "Insufficient memory";
                                free(matrix);
                                return NULL;
                            }

                        matrix = temp;
                        capacity = new_capacity;
                    }

                errno = 0;

                double casted;

                if(res == 1)
                    casted = (double) strtoll(buffer, NULL, 10);
                else
                    casted = strtod(buffer, NULL);

                if(errno)
                    {
                        // ERROR: Failed to convert a numeric value
                        //        from it's string form to a numeric 
                        //        variable.
                        *error = "Failed to convert string to number";
                        free(matrix);
                        return NULL;
                    }

                matrix[size++] = casted;

                i += 1;
                
                while(c != EOF && isspace(c))
                    c = getc(fp);

                if(c == ']' || c == ',')
                    {
                        // The matrix's row just ended.

                        if(w == -1)
                            // This was the first row.
                            w = i;
                        else
                            {
                                // This wasn't the first row,
                                // so it's possible that it's
                                // length is different from the
                                // previous ones.
                                assert(w > -1);

                                if(i != w)
                                    {
                                        // ERROR: The j-th row has the wrong
                                        //        number of elements.
                                        if(i < w)
                                            *error = "Matrix row is too short";
                                        else
                                            *error = "Matrix row is too long";
                                        return NULL;
                                    }
                            }

                        i = 0;
                        j += 1;

                        if(c == ']')
                            // The whole matrix ended!
                            break;
                    
                        c = getc(fp);

                        while(c != EOF && isspace(c))
                            c = getc(fp);
                    }

                if(c == EOF)
                    {
                        // ERROR: Stream ended inside a matrix, where 
                        //        either ',', ']' or a numeric value was
                        //        expected.
                        *error = "Stream ended inside a matrix, where either "
                                 "',', ']' or a numeric value was expected";
                        return NULL;
                    }
            }

    if(size == 0)
        {
            free(matrix);
            *error = "Empty matrix";
            return NULL;
        }

    // If the internal fragmentation is too much,
    // return a dynamic memory region with the
    // exact size instead of the buffer used to
    // build the matrix.
    int fragm_threshold = 30; // (It's a percentage)
    
    if(100.0 * size/capacity < fragm_threshold)
        {
            int new_capacity = (size == 0) ? 1 : size;

            double *temp = realloc(matrix, new_capacity * sizeof(double));

            if(temp != NULL)
                matrix = temp;
        }

    *width = w;
    *height = j;

    return matrix;
}