Problem 313

Sliding game on prime squares: count primes p≤10^6 with search cost = p^2.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 313
# Sliding game on prime squares: count primes p≤10^6 with search cost = p^2.

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

function main() -> i32 {
    let limit: i64 = 1000000
    let half: i64 = (limit >> 1) + 1
    let sieve: ptr<i8> = calloc(half, 1)
    if sieve == null { return 1 }
    let mut i: i64 = 0
    while i < half {
        sieve[i] = 1
        i = i + 1
    }
    if half > 0 { sieve[0] = 0 }
    i = 1
    while 2 * i * i < half {
        if sieve[i] == 1 {
            let mut current: i64 = 3 * i + 1
            let step: i64 = 2 * i + 1
            while current < half {
                sieve[current] = 0
                current = current + step
            }
        }
        i = i + 1
    }

    let mut total: i64 = 0
    # p = 2
    # (4-1)/12 = 0 — skip; formula for odd primes
    let mut p: i64 = 3
    while p <= limit {
        let odd: i64 = p >> 1
        if sieve[odd] == 1 {
            if p == 3 {
                total = total + 2
            } else {
                total = total + (p * p - 1) / 12
            }
        }
        p = p + 2
    }
    printf("%lld\n", total)
    free(sieve)
    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 half = (FLOW_CHECKED_SHR((limit), (1)) + 1);
    int8_t* sieve = (int8_t*)(calloc(half, 1));
    if (sieve == NULL) {
        return 1;
    }
    int64_t i = 0;
    while (i < half) {
        sieve[i] = 1;
        i = (i + 1);
    }
    if (half > 0) {
        sieve[0] = 0;
    }
    i = 1;
    while (((2 * i) * i) < half) {
        if (sieve[i] == 1) {
            int64_t current = ((3 * i) + 1);
            int64_t step = ((2 * i) + 1);
            while (current < half) {
                sieve[current] = 0;
                current = (current + step);
            }
        }
        i = (i + 1);
    }
    int64_t total = 0;
    int64_t p = 3;
    while (p <= limit) {
        int64_t odd = FLOW_CHECKED_SHR((p), (1));
        if (sieve[odd] == 1) {
            if (p == 3) {
                total = (total + 2);
            } else {
                total = (total + FLOW_CHECKED_DIV((((p * p) - 1)), (12)));
            }
        }
        p = (p + 2);
    }
    printf("%lld\n", total);
    free(sieve);
    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 private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @main() -> i32 {
    %0 = arith.constant 1000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 1 : i32
    %4 = arith.extsi %2 : i32 to i64
    %3 = arith.shrsi %1, %4 : i64
    %5 = arith.constant 1 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.addi %3, %7 : i64
    %9 = arith.constant 1 : i32
    %10 = arith.extsi %9 : i32 to i64
    %8 = func.call @calloc(%6, %10) : (i64, i64) -> !llvm.ptr
    %11 = llvm.mlir.zero : !llvm.ptr
    %12 = llvm.icmp "eq" %8, %11 : !llvm.ptr
    cf.cond_br %12, ^bb0, ^bb1
    ^bb0:
      %13 = arith.constant 1 : i32
      func.return %13 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %14 = arith.constant 0 : i32
    %15 = arith.extsi %14 : i32 to i64
    %16 = llvm.mlir.constant(1 : i64) : i64
    %17 = llvm.alloca %16 x i64 : (i64) -> !llvm.ptr
    llvm.store %15, %17 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %18 = llvm.load %17 : !llvm.ptr -> i64
    %19 = arith.cmpi slt, %18, %6 : i64
    cf.cond_br %19, ^bb4, ^bb5
    ^bb4:
      %20 = arith.constant 1 : i32
      %21 = llvm.load %17 : !llvm.ptr -> i64
      %22 = arith.trunci %20 : i32 to i8
      %23 = llvm.getelementptr %8[%21] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      llvm.store %22, %23 : i8, !llvm.ptr
      %24 = llvm.load %17 : !llvm.ptr -> i64
      %25 = arith.constant 1 : i32
      %27 = arith.extsi %25 : i32 to i64
      %26 = arith.addi %24, %27 : i64
      llvm.store %26, %17 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %28 = arith.constant 0 : i32
    %30 = arith.extsi %28 : i32 to i64
    %29 = arith.cmpi sgt, %6, %30 : i64
    cf.cond_br %29, ^bb6, ^bb7
    ^bb6:
      %31 = arith.constant 0 : i32
      %32 = arith.constant 0 : i32
      %33 = arith.trunci %31 : i32 to i8
      %34 = arith.extsi %32 : i32 to i64
      %35 = llvm.getelementptr %8[%34] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      llvm.store %33, %35 : i8, !llvm.ptr
      cf.br ^bb8
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %36 = arith.constant 1 : i32
    %37 = arith.extsi %36 : i32 to i64
    llvm.store %37, %17 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %38 = arith.constant 2 : i32
    %39 = llvm.load %17 : !llvm.ptr -> i64
    %41 = arith.extsi %38 : i32 to i64
    %40 = arith.muli %41, %39 : i64
    %42 = llvm.load %17 : !llvm.ptr -> i64
    %43 = arith.muli %40, %42 : i64
    %44 = arith.cmpi slt, %43, %6 : i64
    cf.cond_br %44, ^bb10, ^bb11
    ^bb10:
      %46 = llvm.load %17 : !llvm.ptr -> i64
      %47 = llvm.getelementptr %8[%46] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %45 = llvm.load %47 : !llvm.ptr -> i8
      %48 = arith.constant 1 : i32
      %50 = arith.extsi %45 : i8 to i32
      %49 = arith.cmpi eq, %50, %48 : i32
      cf.cond_br %49, ^bb12, ^bb13
      ^bb12:
        %51 = arith.constant 3 : i32
        %52 = llvm.load %17 : !llvm.ptr -> i64
        %54 = arith.extsi %51 : i32 to i64
        %53 = arith.muli %54, %52 : i64
        %55 = arith.constant 1 : i32
        %57 = arith.extsi %55 : i32 to i64
        %56 = arith.addi %53, %57 : i64
        %58 = llvm.mlir.constant(1 : i64) : i64
        %59 = llvm.alloca %58 x i64 : (i64) -> !llvm.ptr
        llvm.store %56, %59 : i64, !llvm.ptr
        %60 = arith.constant 2 : i32
        %61 = llvm.load %17 : !llvm.ptr -> i64
        %63 = arith.extsi %60 : i32 to i64
        %62 = arith.muli %63, %61 : i64
        %64 = arith.constant 1 : i32
        %66 = arith.extsi %64 : i32 to i64
        %65 = arith.addi %62, %66 : i64
        cf.br ^bb15
        ^bb15:
        %67 = llvm.load %59 : !llvm.ptr -> i64
        %68 = arith.cmpi slt, %67, %6 : i64
        cf.cond_br %68, ^bb16, ^bb17
        ^bb16:
          %69 = arith.constant 0 : i32
          %70 = llvm.load %59 : !llvm.ptr -> i64
          %71 = arith.trunci %69 : i32 to i8
          %72 = llvm.getelementptr %8[%70] : (!llvm.ptr, i64) -> !llvm.ptr, i8
          llvm.store %71, %72 : i8, !llvm.ptr
          %73 = llvm.load %59 : !llvm.ptr -> i64
          %74 = arith.addi %73, %65 : i64
          llvm.store %74, %59 : i64, !llvm.ptr
          cf.br ^bb15
        ^bb17:
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %75 = llvm.load %17 : !llvm.ptr -> i64
      %76 = arith.constant 1 : i32
      %78 = arith.extsi %76 : i32 to i64
      %77 = arith.addi %75, %78 : i64
      llvm.store %77, %17 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %79 = arith.constant 0 : i32
    %80 = arith.extsi %79 : i32 to i64
    %81 = llvm.mlir.constant(1 : i64) : i64
    %82 = llvm.alloca %81 x i64 : (i64) -> !llvm.ptr
    llvm.store %80, %82 : i64, !llvm.ptr
    %83 = arith.constant 3 : i32
    %84 = arith.extsi %83 : i32 to i64
    %85 = llvm.mlir.constant(1 : i64) : i64
    %86 = llvm.alloca %85 x i64 : (i64) -> !llvm.ptr
    llvm.store %84, %86 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %87 = llvm.load %86 : !llvm.ptr -> i64
    %88 = arith.cmpi sle, %87, %1 : i64
    cf.cond_br %88, ^bb19, ^bb20
    ^bb19:
      %89 = llvm.load %86 : !llvm.ptr -> i64
      %90 = arith.constant 1 : i32
      %92 = arith.extsi %90 : i32 to i64
      %91 = arith.shrsi %89, %92 : i64
      %94 = llvm.getelementptr %8[%91] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %93 = llvm.load %94 : !llvm.ptr -> i8
      %95 = arith.constant 1 : i32
      %97 = arith.extsi %93 : i8 to i32
      %96 = arith.cmpi eq, %97, %95 : i32
      cf.cond_br %96, ^bb21, ^bb22
      ^bb21:
        %98 = llvm.load %86 : !llvm.ptr -> i64
        %99 = arith.constant 3 : i32
        %101 = arith.extsi %99 : i32 to i64
        %100 = arith.cmpi eq, %98, %101 : i64
        cf.cond_br %100, ^bb24, ^bb25
        ^bb24:
          %102 = llvm.load %82 : !llvm.ptr -> i64
          %103 = arith.constant 2 : i32
          %105 = arith.extsi %103 : i32 to i64
          %104 = arith.addi %102, %105 : i64
          llvm.store %104, %82 : i64, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          %106 = llvm.load %82 : !llvm.ptr -> i64
          %107 = llvm.load %86 : !llvm.ptr -> i64
          %108 = llvm.load %86 : !llvm.ptr -> i64
          %109 = arith.muli %107, %108 : i64
          %110 = arith.constant 1 : i32
          %112 = arith.extsi %110 : i32 to i64
          %111 = arith.subi %109, %112 : i64
          %113 = arith.constant 12 : i32
          %115 = arith.extsi %113 : i32 to i64
          %114 = arith.divsi %111, %115 : i64
          %116 = arith.addi %106, %114 : i64
          llvm.store %116, %82 : i64, !llvm.ptr
          cf.br ^bb26
        ^bb26:
        cf.br ^bb23
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %117 = llvm.load %86 : !llvm.ptr -> i64
      %118 = arith.constant 2 : i32
      %120 = arith.extsi %118 : i32 to i64
      %119 = arith.addi %117, %120 : i64
      llvm.store %119, %86 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %121 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %122 = llvm.load %82 : !llvm.ptr -> i64
    %123 = llvm.call @printf(%121, %122) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%8) : (!llvm.ptr) -> ()
    %125 = arith.constant 0 : i32
    func.return %125 : i32
  }
}