Problem 100

First arrangement with total > 1e12 blue discs such that P(BB)=1/2.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 100
# First arrangement with total > 1e12 blue discs such that P(BB)=1/2.

function main() -> i32 {
    # b(b-1) / t(t-1) = 1/2 ⇒ 2b(b-1) = t(t-1)
    # Diophantine; solutions via pell-like recurrence:
    # b_{n+1} = 3b_n + 2t_n - 2
    # t_{n+1} = 4b_n + 3t_n - 3
    # with seed (b,t) = (15,21) or (3,4)
    let mut b: i64 = 15
    let mut t: i64 = 21
    let limit: i64 = 1000000000000
    while t <= limit {
        let nb: i64 = 3 * b + 2 * t - 2
        let nt: i64 = 4 * b + 3 * t - 3
        b = nb
        t = nt
    }
    printf("%lld\n", b)
    return 0
}

Generated C

#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
    while (flow_temp_head) {
        flow_temp_node* n = flow_temp_head;
        flow_temp_head = n->next;
        free(n);
    }
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
    flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
    if (!node) return NULL;
    node->next = flow_temp_head;
    flow_temp_head = node;
    if (!flow_temp_atexit_set) {
        flow_temp_atexit_set = 1;
        atexit(flow_temp_free_all);
    }
    return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
    size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
    char* r = (char*)flow_temp_alloc(la + lb + 1);
    if (!r) return NULL;
    if (la) memcpy(r, a, la);
    if (lb) memcpy(r + la, b, lb);
    r[la + lb] = '\0';
    return r;
}

#define __flow_in_arr(arr, val) __extension__ ({ \
    int _found = 0; \
    size_t _n = sizeof(arr)/sizeof((arr)[0]); \
    for (size_t _i = 0; _i < _n; _i++) { \
        if ((arr)[_i] == (val)) { _found = 1; break; } \
    } _found; })

/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
    fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
    abort();
#if defined(__GNUC__) || defined(__clang__)
    __builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")

#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif

#include <math.h>

void* _ui_state = NULL;

static inline float i32_to_f32(int32_t v) { return (float)v; }

/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }

int32_t main(void);

int32_t main(void) {
    int64_t b = 15;
    int64_t t = 21;
    int64_t limit = 1000000000000;
    while (t <= limit) {
        int64_t nb = (((3 * b) + (2 * t)) - 2);
        int64_t nt = (((4 * b) + (3 * t)) - 3);
        b = nb;
        t = nt;
    }
    printf("%lld\n", b);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func @main() -> i32 {
    %0 = arith.constant 15 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    %4 = arith.constant 21 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    %8 = arith.constant 995705032704 : i32
    %9 = arith.extsi %8 : i32 to i64
    cf.br ^bb0
    ^bb0:
    %10 = llvm.load %7 : !llvm.ptr -> i64
    %11 = arith.cmpi sle, %10, %9 : i64
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %12 = arith.constant 3 : i32
      %13 = llvm.load %3 : !llvm.ptr -> i64
      %15 = arith.extsi %12 : i32 to i64
      %14 = arith.muli %15, %13 : i64
      %16 = arith.constant 2 : i32
      %17 = llvm.load %7 : !llvm.ptr -> i64
      %19 = arith.extsi %16 : i32 to i64
      %18 = arith.muli %19, %17 : i64
      %20 = arith.addi %14, %18 : i64
      %21 = arith.constant 2 : i32
      %23 = arith.extsi %21 : i32 to i64
      %22 = arith.subi %20, %23 : i64
      %24 = arith.constant 4 : i32
      %25 = llvm.load %3 : !llvm.ptr -> i64
      %27 = arith.extsi %24 : i32 to i64
      %26 = arith.muli %27, %25 : i64
      %28 = arith.constant 3 : i32
      %29 = llvm.load %7 : !llvm.ptr -> i64
      %31 = arith.extsi %28 : i32 to i64
      %30 = arith.muli %31, %29 : i64
      %32 = arith.addi %26, %30 : i64
      %33 = arith.constant 3 : i32
      %35 = arith.extsi %33 : i32 to i64
      %34 = arith.subi %32, %35 : i64
      llvm.store %22, %3 : i64, !llvm.ptr
      llvm.store %34, %7 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %36 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %37 = llvm.load %3 : !llvm.ptr -> i64
    %38 = llvm.call @printf(%36, %37) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %39 = arith.constant 0 : i32
    func.return %39 : i32
  }
}