Problem 071

Numerator of the fraction immediately to the left of 3/7 among fractions with denominator ≤ 1,000,000 in lowest terms. Maximize a/b < 3/7 => a/b = floor((3b-1)/7)/b; take best.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 071
# Numerator of the fraction immediately to the left of 3/7
# among fractions with denominator ≤ 1,000,000 in lowest terms.
# Maximize a/b < 3/7 => a/b = floor((3b-1)/7)/b; take best.

function main() -> i32 {
    let limit: i64 = 1000000
    let mut best_a: i64 = 0
    let mut best_b: i64 = 1
    let mut d: i64 = 1
    while d <= limit {
        # a = floor((3*d - 1) / 7)
        let a: i64 = (3 * d - 1) / 7
        # compare a/d > best_a/best_b => a*best_b > best_a*d
        if a * best_b > best_a * d {
            best_a = a
            best_b = d
        }
        d = d + 1
    }
    printf("%lld\n", best_a)
    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 limit = 1000000;
    int64_t best_a = 0;
    int64_t best_b = 1;
    int64_t d = 1;
    while (d <= limit) {
        int64_t a = FLOW_CHECKED_DIV((((3 * d) - 1)), (7));
        if ((a * best_b) > (best_a * d)) {
            best_a = a;
            best_b = d;
        }
        d = (d + 1);
    }
    printf("%lld\n", best_a);
    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 1000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 0 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %3, %5 : i64, !llvm.ptr
    %6 = arith.constant 1 : i32
    %7 = arith.extsi %6 : i32 to i64
    %8 = llvm.mlir.constant(1 : i64) : i64
    %9 = llvm.alloca %8 x i64 : (i64) -> !llvm.ptr
    llvm.store %7, %9 : i64, !llvm.ptr
    %10 = arith.constant 1 : i32
    %11 = arith.extsi %10 : i32 to i64
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %11, %13 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %14 = llvm.load %13 : !llvm.ptr -> i64
    %15 = arith.cmpi sle, %14, %1 : i64
    cf.cond_br %15, ^bb1, ^bb2
    ^bb1:
      %16 = arith.constant 3 : i32
      %17 = llvm.load %13 : !llvm.ptr -> i64
      %19 = arith.extsi %16 : i32 to i64
      %18 = arith.muli %19, %17 : i64
      %20 = arith.constant 1 : i32
      %22 = arith.extsi %20 : i32 to i64
      %21 = arith.subi %18, %22 : i64
      %23 = arith.constant 7 : i32
      %25 = arith.extsi %23 : i32 to i64
      %24 = arith.divsi %21, %25 : i64
      %26 = llvm.load %9 : !llvm.ptr -> i64
      %27 = arith.muli %24, %26 : i64
      %28 = llvm.load %5 : !llvm.ptr -> i64
      %29 = llvm.load %13 : !llvm.ptr -> i64
      %30 = arith.muli %28, %29 : i64
      %31 = arith.cmpi sgt, %27, %30 : i64
      cf.cond_br %31, ^bb3, ^bb4
      ^bb3:
        llvm.store %24, %5 : i64, !llvm.ptr
        %32 = llvm.load %13 : !llvm.ptr -> i64
        llvm.store %32, %9 : i64, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %33 = llvm.load %13 : !llvm.ptr -> i64
      %34 = arith.constant 1 : i32
      %36 = arith.extsi %34 : i32 to i64
      %35 = arith.addi %33, %36 : i64
      llvm.store %35, %13 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %37 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %38 = llvm.load %5 : !llvm.ptr -> i64
    %39 = llvm.call @printf(%37, %38) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %40 = arith.constant 0 : i32
    func.return %40 : i32
  }
}