File size: 3,470 Bytes
abecf61 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 | #include <stdio.h>
#include <stdint.h>
#include <math.h>
// Pingala's Chandas Shastra: Binary number system
// Generates all possible meters (binary strings) of length n
// This is identical to:
// 1. Activation pattern search in neural networks
// 2. Beam search initialization
// 3. Feature combination enumeration
// Pingala's recursive rule (Sutra):
// "Parvarya dvirardhe" - Double at each step, with half for the next
// Generate all binary patterns of length n (Pingala's method)
void pingala_meters(int n) {
int total = 1 << n; // 2^n total meters
printf("Pingala's Meters (Binary Patterns) for n=%d:\n", n);
printf("Total: %d patterns\n\n", total);
for (int i = 0; i < total; i++) {
printf(" Meter %2d: ", i);
// Pingala's right-to-left representation
for (int j = n-1; j >= 0; j--) {
printf("%c", (i >> j) & 1 ? 'G' : 'L'); // Guru/Laghu
}
printf(" (0x%0*X)\n", (n+3)/4, i);
}
}
// Pingala's Meru Prastara (Pascal's Triangle) - combinatorial count
// Used in modern AI for:
// - Network architecture search
// - Weight initialization patterns
// - Dropout mask generation
void pingala_meru_prastara(int rows) {
printf("\nPingala's Meru Prastara (Pascal's Triangle):\n");
printf("Used for combinatorial counting in architecture search\n\n");
int triangle[20][20] = {0};
for (int i = 0; i < rows; i++) {
triangle[i][0] = 1;
triangle[i][i] = 1;
for (int j = 1; j < i; j++) {
triangle[i][j] = triangle[i-1][j-1] + triangle[i-1][j];
}
// Print row
for (int s = 0; s < rows - i; s++) printf(" ");
for (int j = 0; j <= i; j++) {
printf("%4d", triangle[i][j]);
}
printf("\n");
}
}
// Pingala's algorithm for finding nCr (combinations)
// Directly used in: attention head selection, mixture-of-experts routing
uint64_t pingala_nCr(int n, int r) {
if (r > n) return 0;
if (r == 0 || r == n) return 1;
// Pingala's method: iterative multiplication-division
uint64_t result = 1;
for (int i = 1; i <= r; i++) {
result = result * (n - r + i) / i;
}
return result;
}
int main() {
printf("╔══════════════════════════════════════════════════╗\n");
printf("║ PINGALA'S ALGORITHMS (Chandas Shastra) ║\n");
printf("║ ~300 BCE - First Binary System ║\n");
printf("╚══════════════════════════════════════════════════╝\n\n");
// 1. Binary enumeration
pingala_meters(4);
// 2. Meru Prastara (Pascal's Triangle)
pingala_meru_prastara(8);
// 3. Combinatorial selection
printf("\nPingala's nCr (Attention Head Selection):\n");
int n = 14; // Like 14 attention heads
for (int r = 0; r <= n; r += 2) {
printf(" C(%2d, %2d) = %10lu\n", n, r, pingala_nCr(n, r));
}
printf("\n✅ These map directly to:\n");
printf(" • Neural architecture search (all patterns)\n");
printf(" • Attention head selection (nCr)\n");
printf(" • Beam search initialization (binary enumeration)\n");
printf(" • Dropout mask generation (random meter selection)\n");
return 0;
}
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