Problem 108

Least n such that 1/x + 1/y = 1/n has more than 1000 solutions.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 108
# Least n such that 1/x + 1/y = 1/n has more than 1000 solutions.

function search(primes: array<i64, 12>, idx: i32, n: i64, divs: i64, maxe: i32, limit: i64, best0: i64) -> i64 {
    let mut best: i64 = best0
    if divs > limit {
        if n < best { best = n }
        return best
    }
    if idx >= 12 { return best }
    let p: i64 = primes[idx]
    let mut m: i64 = n
    let mut e: i32 = 1
    while e <= maxe {
        if m > best / p { break }
        m = m * p
        best = search(primes, idx + 1, m, divs * (2 * (e as i64) + 1), e, limit, best)
        e = e + 1
    }
    return best
}

function main() -> i32 {
    let primes: array<i64, 12>
    primes[0] = 2
    primes[1] = 3
    primes[2] = 5
    primes[3] = 7
    primes[4] = 11
    primes[5] = 13
    primes[6] = 17
    primes[7] = 19
    primes[8] = 23
    primes[9] = 29
    primes[10] = 31
    primes[11] = 37
    let best: i64 = search(primes, 0, 1, 1, 40, 2000, 9223372036854775807)
    printf("%lld\n", best)
    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; }

int64_t search_array_12_i64_i32_i64_i64_i32_i64_i64(int64_t* primes, int32_t idx, int64_t n, int64_t divs, int32_t maxe, int64_t limit, int64_t best0);
int32_t main(void);

int64_t search_array_12_i64_i32_i64_i64_i32_i64_i64(int64_t* primes, int32_t idx, int64_t n, int64_t divs, int32_t maxe, int64_t limit, int64_t best0) {
    int64_t best = best0;
    if (divs > limit) {
        if (n < best) {
            best = n;
        }
        return best;
    }
    if (idx >= 12) {
        return best;
    }
    int64_t p = (((unsigned)(idx) < 12) ? primes[idx] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(idx), 12), flow_fault_handler("array index out of bounds"), primes[0]));
    int64_t m = n;
    int32_t e = 1;
    while (e <= maxe) {
        if (m > FLOW_CHECKED_DIV((best), (p))) {
            break;
        }
        m = (m * p);
        best = search_array_12_i64_i32_i64_i64_i32_i64_i64(primes, (idx + 1), m, (divs * ((2 * ((int64_t)(e))) + 1)), e, limit, best);
        e = (e + 1);
    }
    return best;
}

int32_t main(void) {
    int64_t primes[12];
    primes[0] = 2;
    primes[1] = 3;
    primes[2] = 5;
    primes[3] = 7;
    primes[4] = 11;
    primes[5] = 13;
    primes[6] = 17;
    primes[7] = 19;
    primes[8] = 23;
    primes[9] = 29;
    primes[10] = 31;
    primes[11] = 37;
    int64_t best = search_array_12_i64_i32_i64_i64_i32_i64_i64(primes, 0, 1, 1, 40, 2000, 9223372036854775807);
    printf("%lld\n", best);
    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 @search(%arg0: !llvm.ptr, %arg1: i32, %arg2: i64, %arg3: i64, %arg4: i32, %arg5: i64, %arg6: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg6, %1 : i64, !llvm.ptr
    %2 = arith.cmpi sgt, %arg3, %arg5 : i64
    cf.cond_br %2, ^bb0, ^bb1
    ^bb0:
      %3 = llvm.load %1 : !llvm.ptr -> i64
      %4 = arith.cmpi slt, %arg2, %3 : i64
      cf.cond_br %4, ^bb3, ^bb4
      ^bb3:
        llvm.store %arg2, %1 : i64, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %5 = llvm.load %1 : !llvm.ptr -> i64
      func.return %5 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %6 = arith.constant 12 : i32
    %7 = arith.cmpi sge, %arg1, %6 : i32
    cf.cond_br %7, ^bb6, ^bb7
    ^bb6:
      %8 = llvm.load %1 : !llvm.ptr -> i64
      func.return %8 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %10 = arith.extsi %arg1 : i32 to i64
    %11 = llvm.getelementptr %arg0[0, %10] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<12 x i64>
    %9 = llvm.load %11 : !llvm.ptr -> i64
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg2, %13 : i64, !llvm.ptr
    %14 = arith.constant 1 : i32
    %15 = llvm.mlir.constant(1 : i64) : i64
    %16 = llvm.alloca %15 x i32 : (i64) -> !llvm.ptr
    llvm.store %14, %16 : i32, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %17 = llvm.load %16 : !llvm.ptr -> i32
    %18 = arith.cmpi sle, %17, %arg4 : i32
    cf.cond_br %18, ^bb10, ^bb11
    ^bb10:
      %19 = llvm.load %13 : !llvm.ptr -> i64
      %20 = llvm.load %1 : !llvm.ptr -> i64
      %21 = arith.divsi %20, %9 : i64
      %22 = arith.cmpi sgt, %19, %21 : i64
      cf.cond_br %22, ^bb12, ^bb13
      ^bb12:
        cf.br ^bb11
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %23 = llvm.load %13 : !llvm.ptr -> i64
      %24 = arith.muli %23, %9 : i64
      llvm.store %24, %13 : i64, !llvm.ptr
      %26 = arith.constant 1 : i32
      %27 = arith.addi %arg1, %26 : i32
      %28 = llvm.load %13 : !llvm.ptr -> i64
      %29 = arith.constant 2 : i32
      %30 = llvm.load %16 : !llvm.ptr -> i32
      %31 = arith.extsi %30 : i32 to i64
      %33 = arith.extsi %29 : i32 to i64
      %32 = arith.muli %33, %31 : i64
      %34 = arith.constant 1 : i32
      %36 = arith.extsi %34 : i32 to i64
      %35 = arith.addi %32, %36 : i64
      %37 = arith.muli %arg3, %35 : i64
      %38 = llvm.load %16 : !llvm.ptr -> i32
      %39 = llvm.load %1 : !llvm.ptr -> i64
      %25 = func.call @search(%arg0, %27, %28, %37, %38, %arg5, %39) : (!llvm.ptr, i32, i64, i64, i32, i64, i64) -> i64
      llvm.store %25, %1 : i64, !llvm.ptr
      %40 = llvm.load %16 : !llvm.ptr -> i32
      %41 = arith.constant 1 : i32
      %42 = arith.addi %40, %41 : i32
      llvm.store %42, %16 : i32, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %43 = llvm.load %1 : !llvm.ptr -> i64
    func.return %43 : i64
  }
  func.func @main() -> i32 {
    %44 = memref.alloca() {type = memref<12xi64>} : memref<12xi64>
    %45 = arith.constant 2 : i32
    %46 = arith.constant 0 : i32
    %47 = arith.index_cast %46 : i32 to index
    %48 = arith.extsi %45 : i32 to i64
    memref.store %48, %44[%47] : memref<12xi64>
    %49 = arith.constant 3 : i32
    %50 = arith.constant 1 : i32
    %51 = arith.index_cast %50 : i32 to index
    %52 = arith.extsi %49 : i32 to i64
    memref.store %52, %44[%51] : memref<12xi64>
    %53 = arith.constant 5 : i32
    %54 = arith.constant 2 : i32
    %55 = arith.index_cast %54 : i32 to index
    %56 = arith.extsi %53 : i32 to i64
    memref.store %56, %44[%55] : memref<12xi64>
    %57 = arith.constant 7 : i32
    %58 = arith.constant 3 : i32
    %59 = arith.index_cast %58 : i32 to index
    %60 = arith.extsi %57 : i32 to i64
    memref.store %60, %44[%59] : memref<12xi64>
    %61 = arith.constant 11 : i32
    %62 = arith.constant 4 : i32
    %63 = arith.index_cast %62 : i32 to index
    %64 = arith.extsi %61 : i32 to i64
    memref.store %64, %44[%63] : memref<12xi64>
    %65 = arith.constant 13 : i32
    %66 = arith.constant 5 : i32
    %67 = arith.index_cast %66 : i32 to index
    %68 = arith.extsi %65 : i32 to i64
    memref.store %68, %44[%67] : memref<12xi64>
    %69 = arith.constant 17 : i32
    %70 = arith.constant 6 : i32
    %71 = arith.index_cast %70 : i32 to index
    %72 = arith.extsi %69 : i32 to i64
    memref.store %72, %44[%71] : memref<12xi64>
    %73 = arith.constant 19 : i32
    %74 = arith.constant 7 : i32
    %75 = arith.index_cast %74 : i32 to index
    %76 = arith.extsi %73 : i32 to i64
    memref.store %76, %44[%75] : memref<12xi64>
    %77 = arith.constant 23 : i32
    %78 = arith.constant 8 : i32
    %79 = arith.index_cast %78 : i32 to index
    %80 = arith.extsi %77 : i32 to i64
    memref.store %80, %44[%79] : memref<12xi64>
    %81 = arith.constant 29 : i32
    %82 = arith.constant 9 : i32
    %83 = arith.index_cast %82 : i32 to index
    %84 = arith.extsi %81 : i32 to i64
    memref.store %84, %44[%83] : memref<12xi64>
    %85 = arith.constant 31 : i32
    %86 = arith.constant 10 : i32
    %87 = arith.index_cast %86 : i32 to index
    %88 = arith.extsi %85 : i32 to i64
    memref.store %88, %44[%87] : memref<12xi64>
    %89 = arith.constant 37 : i32
    %90 = arith.constant 11 : i32
    %91 = arith.index_cast %90 : i32 to index
    %92 = arith.extsi %89 : i32 to i64
    memref.store %92, %44[%91] : memref<12xi64>
    %94 = arith.constant 0 : i32
    %95 = arith.constant 1 : i32
    %96 = arith.constant 1 : i32
    %97 = arith.constant 40 : i32
    %98 = arith.constant 2000 : i32
    %99 = arith.constant 9223372032559808511 : i32
    %101 = memref.extract_aligned_pointer_as_index %44 : memref<12xi64> -> index
    %102 = arith.index_cast %101 : index to i64
    %103 = llvm.inttoptr %102 : i64 to !llvm.ptr
    %104 = arith.extsi %95 : i32 to i64
    %105 = arith.extsi %96 : i32 to i64
    %106 = arith.extsi %98 : i32 to i64
    %107 = arith.extsi %99 : i32 to i64
    %93 = func.call @search(%103, %94, %104, %105, %97, %106, %107) : (!llvm.ptr, i32, i64, i64, i32, i64, i64) -> i64
    %108 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %109 = llvm.call @printf(%108, %93) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %110 = arith.constant 0 : i32
    func.return %110 : i32
  }
}