Problem 669

Fibonacci seating: position 89194853094755498 in a sequence mod 99194853094755497. Uses modular arithmetic with i128 intermediates.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 669: The King's Banquet
# Fibonacci seating: position 89194853094755498 in a sequence mod 99194853094755497.
# Uses modular arithmetic with i128 intermediates.

function main() -> i32 {
    let y: i64 = 99194853094755497
    let z: i64 = 61305790721611591
    let pos: i64 = 89194853094755498

    let mult: i64 = pos / 2

    # temp = (y - z * mult) % y = (-(z * mult)) % y
    let zmod: i64 = z % y
    let multmod: i64 = mult % y
    let prod: i128 = (zmod as i128) * (multmod as i128) % (y as i128)
    let temp: i64 = (y - (prod as i64) % y + y) % y

    # pos is even: temp = (-temp) % y
    if pos % 2 == 0 {
        temp = (y - temp) % y
    }

    printf("%lld\n", temp)
    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 y = 99194853094755497;
    int64_t z = 61305790721611591;
    int64_t pos = 89194853094755498;
    int64_t mult = FLOW_CHECKED_DIV((pos), (2));
    int64_t zmod = FLOW_CHECKED_MOD((z), (y));
    int64_t multmod = FLOW_CHECKED_MOD((mult), (y));
    __int128 prod = FLOW_CHECKED_MOD(((((__int128)(zmod)) * ((__int128)(multmod)))), (((__int128)(y))));
    int64_t temp = FLOW_CHECKED_MOD((((y - FLOW_CHECKED_MOD((((int64_t)(prod))), (y))) + y)), (y));
    if (FLOW_CHECKED_MOD((pos), (2)) == 0) {
        temp = FLOW_CHECKED_MOD(((y - temp)), (y));
    }
    printf("%lld\n", temp);
    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 99194848799788201 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 61305786426644295 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = arith.constant 89194848799788202 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = arith.constant 2 : i32
    %8 = arith.extsi %6 : i32 to i64
    %7 = arith.divsi %5, %8 : i64
    %9 = arith.remsi %3, %1 : i64
    %10 = arith.remsi %7, %1 : i64
    %11 = arith.extsi %9 : i64 to i128
    %12 = arith.extsi %10 : i64 to i128
    %14 = arith.trunci %11 : i128 to i64
    %15 = arith.trunci %12 : i128 to i64
    %13 = arith.muli %14, %15 : i64
    %16 = arith.extsi %1 : i64 to i128
    %18 = arith.trunci %16 : i128 to i64
    %17 = arith.remsi %13, %18 : i64
    %19 = arith.extsi %17 : i64 to i128
    %20 = arith.trunci %19 : i128 to i64
    %21 = arith.remsi %20, %1 : i64
    %22 = arith.subi %1, %21 : i64
    %23 = arith.addi %22, %1 : i64
    %24 = arith.remsi %23, %1 : i64
    %25 = arith.constant 2 : i32
    %27 = arith.extsi %25 : i32 to i64
    %26 = arith.remsi %5, %27 : i64
    %28 = arith.constant 0 : i32
    %30 = arith.extsi %28 : i32 to i64
    %29 = arith.cmpi eq, %26, %30 : i64
    %31 = scf.if %29 -> (i64) {
      %32 = arith.subi %1, %24 : i64
      %33 = arith.remsi %32, %1 : i64
      scf.yield %33 : i64
    } else {
      scf.yield %24 : i64
    }
    %34 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %35 = llvm.call @printf(%34, %31) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %36 = arith.constant 0 : i32
    func.return %36 : i32
  }
}