Problem 243

Least n with resilience R(n) < 15499/94744.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 243
# Least n with resilience R(n) < 15499/94744.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

function phi_with_primes(x: i64, primes: ptr<i64>, pc: i32) -> i64 {
    let mut result: i64 = x
    let mut reduced: i64 = x
    let mut i: i32 = 0
    while i < pc {
        let p: i64 = primes[i]
        if p * p > reduced { break }
        if reduced % p == 0 {
            while reduced % p == 0 { reduced = reduced / p }
            result = result - result / p
        }
        i = i + 1
    }
    if reduced > 1 {
        result = result - result / reduced
    }
    return result
}

function is_less(a1: i64, b1: i64, a2: i64, b2: i64) -> bool {
    return a1 * b2 < a2 * b1
}

function main() -> i32 {
    let num: i64 = 15499
    let den: i64 = 94744
    let primes: ptr<i64> = calloc(100, 8)
    if primes == null { return 1 }
    let mut pc: i32 = 0
    let mut current: i64 = 1
    let mut i: i64 = 2
    while true {
        let mut is_p: bool = true
        let mut j: i32 = 0
        while j < pc {
            if primes[j] * primes[j] > i { break }
            if i % primes[j] == 0 { is_p = false; break }
            j = j + 1
        }
        if !is_p {
            i = i + 1
            continue
        }
        primes[pc] = i
        pc = pc + 1
        current = current * i
        if is_less(phi_with_primes(current, primes, pc), current - 1, num, den) {
            break
        }
        i = i + 1
    }
    current = current / primes[pc - 1]
    let mut k: i64 = 1
    while true {
        let nxt: i64 = current * k
        if is_less(phi_with_primes(nxt, primes, pc), nxt - 1, num, den) {
            printf("%lld\n", nxt)
            free(primes)
            return 0
        }
        k = k + 1
    }
    return 1
}

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 phi_with_primes_i64_ptr_i64_i32(int64_t x, int64_t* primes, int32_t pc);
bool is_less_i64_i64_i64_i64(int64_t a1, int64_t b1, int64_t a2, int64_t b2);
int32_t main(void);



int64_t phi_with_primes_i64_ptr_i64_i32(int64_t x, int64_t* primes, int32_t pc) {
    int64_t result = x;
    int64_t reduced = x;
    int32_t i = 0;
    while (i < pc) {
        int64_t p = primes[i];
        if ((p * p) > reduced) {
            break;
        }
        if (FLOW_CHECKED_MOD((reduced), (p)) == 0) {
            while (FLOW_CHECKED_MOD((reduced), (p)) == 0) {
                reduced = FLOW_CHECKED_DIV((reduced), (p));
            }
            result = (result - FLOW_CHECKED_DIV((result), (p)));
        }
        i = (i + 1);
    }
    if (reduced > 1) {
        result = (result - FLOW_CHECKED_DIV((result), (reduced)));
    }
    return result;
}

bool is_less_i64_i64_i64_i64(int64_t a1, int64_t b1, int64_t a2, int64_t b2) {
    return (a1 * b2) < (a2 * b1);
}

int32_t main(void) {
    int64_t num = 15499;
    int64_t den = 94744;
    int64_t* primes = (int64_t*)(calloc(100, 8));
    if (primes == NULL) {
        return 1;
    }
    int32_t pc = 0;
    int64_t current = 1;
    int64_t i = 2;
    while (1) {
        bool is_p = 1;
        int32_t j = 0;
        while (j < pc) {
            if ((primes[j] * primes[j]) > i) {
                break;
            }
            if (FLOW_CHECKED_MOD((i), (primes[j])) == 0) {
                is_p = 0;
                break;
            }
            j = (j + 1);
        }
        if ((!(is_p))) {
            i = (i + 1);
            continue;
        }
        primes[pc] = i;
        pc = (pc + 1);
        current = (current * i);
        if (is_less_i64_i64_i64_i64(phi_with_primes_i64_ptr_i64_i32(current, primes, pc), (current - 1), num, den)) {
            break;
        }
        i = (i + 1);
    }
    current = FLOW_CHECKED_DIV((current), (primes[(pc - 1)]));
    int64_t k = 1;
    while (1) {
        int64_t nxt = (current * k);
        if (is_less_i64_i64_i64_i64(phi_with_primes_i64_ptr_i64_i32(nxt, primes, pc), (nxt - 1), num, den)) {
            printf("%lld\n", nxt);
            free(primes);
            return 0;
        }
        k = (k + 1);
    }
    return 1;
}

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 private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @phi_with_primes(%arg0: i64, %arg1: !llvm.ptr, %arg2: i32) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %1 : i64, !llvm.ptr
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %3 : i64, !llvm.ptr
    %4 = arith.constant 0 : i32
    %5 = llvm.mlir.constant(1 : i64) : i64
    %6 = llvm.alloca %5 x i32 : (i64) -> !llvm.ptr
    llvm.store %4, %6 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %7 = llvm.load %6 : !llvm.ptr -> i32
    %8 = arith.cmpi slt, %7, %arg2 : i32
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %10 = llvm.load %6 : !llvm.ptr -> i32
      %11 = arith.extsi %10 : i32 to i64
      %12 = llvm.getelementptr %arg1[%11] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %9 = llvm.load %12 : !llvm.ptr -> i64
      %13 = arith.muli %9, %9 : i64
      %14 = llvm.load %3 : !llvm.ptr -> i64
      %15 = arith.cmpi sgt, %13, %14 : i64
      cf.cond_br %15, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %16 = llvm.load %3 : !llvm.ptr -> i64
      %17 = arith.remsi %16, %9 : i64
      %18 = arith.constant 0 : i32
      %20 = arith.extsi %18 : i32 to i64
      %19 = arith.cmpi eq, %17, %20 : i64
      cf.cond_br %19, ^bb6, ^bb7
      ^bb6:
        cf.br ^bb9
        ^bb9:
        %21 = llvm.load %3 : !llvm.ptr -> i64
        %22 = arith.remsi %21, %9 : i64
        %23 = arith.constant 0 : i32
        %25 = arith.extsi %23 : i32 to i64
        %24 = arith.cmpi eq, %22, %25 : i64
        cf.cond_br %24, ^bb10, ^bb11
        ^bb10:
          %26 = llvm.load %3 : !llvm.ptr -> i64
          %27 = arith.divsi %26, %9 : i64
          llvm.store %27, %3 : i64, !llvm.ptr
          cf.br ^bb9
        ^bb11:
        %28 = llvm.load %1 : !llvm.ptr -> i64
        %29 = llvm.load %1 : !llvm.ptr -> i64
        %30 = arith.divsi %29, %9 : i64
        %31 = arith.subi %28, %30 : i64
        llvm.store %31, %1 : i64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %32 = llvm.load %6 : !llvm.ptr -> i32
      %33 = arith.constant 1 : i32
      %34 = arith.addi %32, %33 : i32
      llvm.store %34, %6 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %35 = llvm.load %3 : !llvm.ptr -> i64
    %36 = arith.constant 1 : i32
    %38 = arith.extsi %36 : i32 to i64
    %37 = arith.cmpi sgt, %35, %38 : i64
    cf.cond_br %37, ^bb12, ^bb13
    ^bb12:
      %39 = llvm.load %1 : !llvm.ptr -> i64
      %40 = llvm.load %1 : !llvm.ptr -> i64
      %41 = llvm.load %3 : !llvm.ptr -> i64
      %42 = arith.divsi %40, %41 : i64
      %43 = arith.subi %39, %42 : i64
      llvm.store %43, %1 : i64, !llvm.ptr
      cf.br ^bb14
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %44 = llvm.load %1 : !llvm.ptr -> i64
    func.return %44 : i64
  }
  func.func @is_less(%arg0: i64, %arg1: i64, %arg2: i64, %arg3: i64) -> i1 {
    %45 = arith.muli %arg0, %arg3 : i64
    %46 = arith.muli %arg2, %arg1 : i64
    %47 = arith.cmpi slt, %45, %46 : i64
    func.return %47 : i1
  }
  func.func @main() -> i32 {
    %48 = arith.constant 15499 : i32
    %49 = arith.extsi %48 : i32 to i64
    %50 = arith.constant 94744 : i32
    %51 = arith.extsi %50 : i32 to i64
    %53 = arith.constant 100 : i32
    %54 = arith.constant 8 : i32
    %55 = arith.extsi %53 : i32 to i64
    %56 = arith.extsi %54 : i32 to i64
    %52 = func.call @calloc(%55, %56) : (i64, i64) -> !llvm.ptr
    %57 = llvm.mlir.zero : !llvm.ptr
    %58 = llvm.icmp "eq" %52, %57 : !llvm.ptr
    cf.cond_br %58, ^bb15, ^bb16
    ^bb15:
      %59 = arith.constant 1 : i32
      func.return %59 : i32
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %60 = arith.constant 0 : i32
    %61 = llvm.mlir.constant(1 : i64) : i64
    %62 = llvm.alloca %61 x i32 : (i64) -> !llvm.ptr
    llvm.store %60, %62 : i32, !llvm.ptr
    %63 = arith.constant 1 : i32
    %64 = arith.extsi %63 : i32 to i64
    %65 = llvm.mlir.constant(1 : i64) : i64
    %66 = llvm.alloca %65 x i64 : (i64) -> !llvm.ptr
    llvm.store %64, %66 : i64, !llvm.ptr
    %67 = arith.constant 2 : i32
    %68 = arith.extsi %67 : i32 to i64
    %69 = llvm.mlir.constant(1 : i64) : i64
    %70 = llvm.alloca %69 x i64 : (i64) -> !llvm.ptr
    llvm.store %68, %70 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %71 = arith.constant 1 : i1
    cf.cond_br %71, ^bb19, ^bb20
    ^bb19:
      %72 = arith.constant 1 : i1
      %73 = llvm.mlir.constant(1 : i64) : i64
      %74 = llvm.alloca %73 x i1 : (i64) -> !llvm.ptr
      llvm.store %72, %74 : i1, !llvm.ptr
      %75 = arith.constant 0 : i32
      %76 = llvm.mlir.constant(1 : i64) : i64
      %77 = llvm.alloca %76 x i32 : (i64) -> !llvm.ptr
      llvm.store %75, %77 : i32, !llvm.ptr
      cf.br ^bb21
      ^bb21:
      %78 = llvm.load %77 : !llvm.ptr -> i32
      %79 = llvm.load %62 : !llvm.ptr -> i32
      %80 = arith.cmpi slt, %78, %79 : i32
      cf.cond_br %80, ^bb22, ^bb23
      ^bb22:
        %82 = llvm.load %77 : !llvm.ptr -> i32
        %83 = arith.extsi %82 : i32 to i64
        %84 = llvm.getelementptr %52[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %81 = llvm.load %84 : !llvm.ptr -> i64
        %86 = llvm.load %77 : !llvm.ptr -> i32
        %87 = arith.extsi %86 : i32 to i64
        %88 = llvm.getelementptr %52[%87] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %85 = llvm.load %88 : !llvm.ptr -> i64
        %89 = arith.muli %81, %85 : i64
        %90 = llvm.load %70 : !llvm.ptr -> i64
        %91 = arith.cmpi sgt, %89, %90 : i64
        cf.cond_br %91, ^bb24, ^bb25
        ^bb24:
          cf.br ^bb23
        ^bb25:
          cf.br ^bb26
        ^bb26:
        %92 = llvm.load %70 : !llvm.ptr -> i64
        %94 = llvm.load %77 : !llvm.ptr -> i32
        %95 = arith.extsi %94 : i32 to i64
        %96 = llvm.getelementptr %52[%95] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %93 = llvm.load %96 : !llvm.ptr -> i64
        %97 = arith.remsi %92, %93 : i64
        %98 = arith.constant 0 : i32
        %100 = arith.extsi %98 : i32 to i64
        %99 = arith.cmpi eq, %97, %100 : i64
        cf.cond_br %99, ^bb27, ^bb28
        ^bb27:
          %101 = arith.constant 0 : i1
          llvm.store %101, %74 : i1, !llvm.ptr
          cf.br ^bb23
        ^bb28:
          cf.br ^bb29
        ^bb29:
        %102 = llvm.load %77 : !llvm.ptr -> i32
        %103 = arith.constant 1 : i32
        %104 = arith.addi %102, %103 : i32
        llvm.store %104, %77 : i32, !llvm.ptr
        cf.br ^bb21
      ^bb23:
      %105 = llvm.load %74 : !llvm.ptr -> i1
      %107 = arith.constant 1 : i1
      %106 = arith.xori %105, %107 : i1
      cf.cond_br %106, ^bb30, ^bb31
      ^bb30:
        %109 = llvm.load %70 : !llvm.ptr -> i64
        %110 = arith.constant 1 : i32
        %112 = arith.extsi %110 : i32 to i64
        %111 = arith.addi %109, %112 : i64
        llvm.store %111, %70 : i64, !llvm.ptr
        cf.br ^bb18
      ^bb31:
        cf.br ^bb32
      ^bb32:
      %113 = llvm.load %70 : !llvm.ptr -> i64
      %114 = llvm.load %62 : !llvm.ptr -> i32
      %115 = arith.extsi %114 : i32 to i64
      %116 = llvm.getelementptr %52[%115] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %113, %116 : i64, !llvm.ptr
      %117 = llvm.load %62 : !llvm.ptr -> i32
      %118 = arith.constant 1 : i32
      %119 = arith.addi %117, %118 : i32
      llvm.store %119, %62 : i32, !llvm.ptr
      %120 = llvm.load %66 : !llvm.ptr -> i64
      %121 = llvm.load %70 : !llvm.ptr -> i64
      %122 = arith.muli %120, %121 : i64
      llvm.store %122, %66 : i64, !llvm.ptr
      %125 = llvm.load %66 : !llvm.ptr -> i64
      %126 = llvm.load %62 : !llvm.ptr -> i32
      %124 = func.call @phi_with_primes(%125, %52, %126) : (i64, !llvm.ptr, i32) -> i64
      %127 = llvm.load %66 : !llvm.ptr -> i64
      %128 = arith.constant 1 : i32
      %130 = arith.extsi %128 : i32 to i64
      %129 = arith.subi %127, %130 : i64
      %123 = func.call @is_less(%124, %129, %49, %51) : (i64, i64, i64, i64) -> i1
      cf.cond_br %123, ^bb33, ^bb34
      ^bb33:
        cf.br ^bb20
      ^bb34:
        cf.br ^bb35
      ^bb35:
      %131 = llvm.load %70 : !llvm.ptr -> i64
      %132 = arith.constant 1 : i32
      %134 = arith.extsi %132 : i32 to i64
      %133 = arith.addi %131, %134 : i64
      llvm.store %133, %70 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %135 = llvm.load %66 : !llvm.ptr -> i64
    %137 = llvm.load %62 : !llvm.ptr -> i32
    %138 = arith.constant 1 : i32
    %139 = arith.subi %137, %138 : i32
    %140 = arith.extsi %139 : i32 to i64
    %141 = llvm.getelementptr %52[%140] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %136 = llvm.load %141 : !llvm.ptr -> i64
    %142 = arith.divsi %135, %136 : i64
    llvm.store %142, %66 : i64, !llvm.ptr
    %143 = arith.constant 1 : i32
    %144 = arith.extsi %143 : i32 to i64
    %145 = llvm.mlir.constant(1 : i64) : i64
    %146 = llvm.alloca %145 x i64 : (i64) -> !llvm.ptr
    llvm.store %144, %146 : i64, !llvm.ptr
    cf.br ^bb36
    ^bb36:
    %147 = arith.constant 1 : i1
    cf.cond_br %147, ^bb37, ^bb38
    ^bb37:
      %148 = llvm.load %66 : !llvm.ptr -> i64
      %149 = llvm.load %146 : !llvm.ptr -> i64
      %150 = arith.muli %148, %149 : i64
      %153 = llvm.load %62 : !llvm.ptr -> i32
      %152 = func.call @phi_with_primes(%150, %52, %153) : (i64, !llvm.ptr, i32) -> i64
      %154 = arith.constant 1 : i32
      %156 = arith.extsi %154 : i32 to i64
      %155 = arith.subi %150, %156 : i64
      %151 = func.call @is_less(%152, %155, %49, %51) : (i64, i64, i64, i64) -> i1
      cf.cond_br %151, ^bb39, ^bb40
      ^bb39:
        %157 = llvm.mlir.addressof @str_0 : !llvm.ptr
        %158 = llvm.call @printf(%157, %150) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
        func.call @free(%52) : (!llvm.ptr) -> ()
        %160 = arith.constant 0 : i32
        func.return %160 : i32
      ^bb40:
        cf.br ^bb41
      ^bb41:
      %161 = llvm.load %146 : !llvm.ptr -> i64
      %162 = arith.constant 1 : i32
      %164 = arith.extsi %162 : i32 to i64
      %163 = arith.addi %161, %164 : i64
      llvm.store %163, %146 : i64, !llvm.ptr
      cf.br ^bb36
    ^bb38:
    %165 = arith.constant 1 : i32
    func.return %165 : i32
  }
}