```c 

#include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h>”>

#define HIDDEN_SIZE 100 #define VOCAB_SIZE 128 #define SEQ_LENGTH 25 #define LEARNING_RATE 1e-2 #define NUM_EPOCHS 1000 #define CLIP_VALUE 5

double Wxh[HIDDEN_SIZE][VOCAB_SIZE]; double Whh[HIDDEN_SIZE][HIDDEN_SIZE]; double Why[VOCAB_SIZE][HIDDEN_SIZE]; double bh[HIDDEN_SIZE]; double by[VOCAB_SIZE];

void initialize_parameters() { int i, j;


for (i = 0; i < HIDDEN_SIZE; ++i)
    for (j = 0; j < VOCAB_SIZE; ++j)
        Wxh[i][j] = ((double)rand() / (double)RAND_MAX) * 0.01;

for (i = 0; i < HIDDEN_SIZE; ++i)
    for (j = 0; j < HIDDEN_SIZE; ++j)
        Whh[i][j] = ((double)rand() / (double)RAND_MAX) * 0.01;

for (i = 0; i < VOCAB_SIZE; ++i)
    for (j = 0; j < HIDDEN_SIZE; ++j)
        Why[i][j] = ((double)rand() / (double)RAND_MAX) * 0.01;

for (i = 0; i < HIDDEN_SIZE; ++i)
    bh[i] = 0.0;

for (i = 0; i < VOCAB_SIZE; ++i)
    by[i] = 0.0;
}

void clip(double *array, int len) { for (int i = 0; i < len; ++i) array[i] = array[i] > CLIP_VALUE ? CLIP_VALUE : array[i] < -CLIP_VALUE ? -CLIP_VALUE : array[i]; }

double softmax(double *x, int size, int i) { int j; double sum_exp = 0.0; for (j = 0; j < size; ++j) { sum_exp += exp(x[j]); } return exp(x[i]) / sum_exp; }


void one_hot_encode(char character, double *encoded) {
    int index = character;
    for (int i = 0; i < VOCAB_SIZE; ++i) {
        encoded[i] = (i == index) ? 1.0 : 0.0;
    }
}

char one_hot_decode(double *encoded) {
    int index = 0;
    double max_val = encoded[0];
    for (int i = 1; i < VOCAB_SIZE; ++i) {
        if (encoded[i] > max_val) {
            index = i;
            max_val = encoded[i];
        }
    }
    return (char)index;
}


double forward(char *input, char *output, double *hprev) {
    // Initialize variables
    int i;
    double loss = 0.0;
    
    // Forward pass
    double xs[SEQ_LENGTH][VOCAB_SIZE]; // Input one-hot encoded
    double hs[SEQ_LENGTH + 1][HIDDEN_SIZE]; // Hidden states
    double ys[SEQ_LENGTH][VOCAB_SIZE]; // Output probabilities
    double ps[SEQ_LENGTH][VOCAB_SIZE]; // Output softmax probabilities
    
    // Initialize hidden state
    for (i = 0; i < HIDDEN_SIZE; ++i) {
        hs[0][i] = hprev[i];
    }
    
    // Perform forward pass for each character in sequence
    for (i = 0; i < SEQ_LENGTH; ++i) {
        // Convert input character to one-hot encoding
        double x[VOCAB_SIZE];
        one_hot_encode(input[i], x);
        
        // Update hidden state
        for (int j = 0; j < HIDDEN_SIZE; ++j) {
            double weighted_sum = bh[j];
            for (int k = 0; k < VOCAB_SIZE; ++k) {
                weighted_sum += Wxh[j][k] * x[k];
            }
            for (int k = 0; k < HIDDEN_SIZE; ++k) {
                weighted_sum += Whh[j][k] * hs[i][k];
            }
            hs[i+1][j] = tanh(weighted_sum);
        }
        
        // Calculate output
        for (int j = 0; j < VOCAB_SIZE; ++j) {
            double weighted_sum = by[j];
            for (int k = 0; k < HIDDEN_SIZE; ++k) {
                weighted_sum += Why[j][k] * hs[i+1][k];
            }
            ys[i][j] = weighted_sum;
        }
        
        // Apply softmax activation
        double sum_exp = 0.0;
        for (int j = 0; j < VOCAB_SIZE; ++j) {
            sum_exp += exp(ys[i][j]);
        }
        for (int j = 0; j < VOCAB_SIZE; ++j) {
            ps[i][j] = exp(ys[i][j]) / sum_exp;
        }
        
        // Calculate cross-entropy loss
        loss += -log(ps[i][output[i]]);
    }
    
    // Return mean squared error loss
    return loss / SEQ_LENGTH;
}

```

Given the above C code, continue the implementation of a CharRNN. Implement the backward pass function. Initialize dWxh, dWhh, dWhy… directly in the backward pass function