Problem 077

First value which can be written as a sum of primes in over 5000 ways.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 077
# First value which can be written as a sum of primes in over 5000 ways.

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

function main() -> i32 {
    let limit: i32 = 200
    let sieve: ptr<i8> = calloc(limit as i64, 1)
    let primes: ptr<i32> = calloc(limit as i64, 4)
    let ways: ptr<i64> = calloc(limit as i64, 8)
    if sieve == null || primes == null || ways == null { return 1 }

    sieve[0] = 1
    sieve[1] = 1
    let mut p: i32 = 2
    while p * p < limit {
        if sieve[p] == 0 {
            let mut m: i32 = p * p
            while m < limit {
                sieve[m] = 1
                m = m + p
            }
        }
        p = p + 1
    }
    let mut pc: i32 = 0
    let mut i: i32 = 2
    while i < limit {
        if sieve[i] == 0 {
            primes[pc] = i
            pc = pc + 1
        }
        i = i + 1
    }

    ways[0] = 1
    let mut pi: i32 = 0
    while pi < pc {
        let c: i32 = primes[pi]
        let mut x: i32 = c
        while x < limit {
            ways[x] = ways[x] + ways[x - c]
            x = x + 1
        }
        pi = pi + 1
    }

    let mut ans: i64 = 0
    i = 2
    while i < limit {
        if ways[i] > 5000 {
            ans = i as i64
            break
        }
        i = i + 1
    }
    printf("%lld\n", ans)
    free(sieve)
    free(primes)
    free(ways)
    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) {
    int32_t limit = 200;
    int8_t* sieve = (int8_t*)(calloc(((int64_t)(limit)), 1));
    int32_t* primes = (int32_t*)(calloc(((int64_t)(limit)), 4));
    int64_t* ways = (int64_t*)(calloc(((int64_t)(limit)), 8));
    if (((sieve == NULL || primes == NULL) || ways == NULL)) {
        return 1;
    }
    sieve[0] = 1;
    sieve[1] = 1;
    int32_t p = 2;
    while ((p * p) < limit) {
        if (sieve[p] == 0) {
            int32_t m = (p * p);
            while (m < limit) {
                sieve[m] = 1;
                m = (m + p);
            }
        }
        p = (p + 1);
    }
    int32_t pc = 0;
    int32_t i = 2;
    while (i < limit) {
        if (sieve[i] == 0) {
            primes[pc] = i;
            pc = (pc + 1);
        }
        i = (i + 1);
    }
    ways[0] = 1;
    int32_t pi = 0;
    while (pi < pc) {
        int32_t c = primes[pi];
        int32_t x = c;
        while (x < limit) {
            ways[x] = (ways[x] + ways[(x - c)]);
            x = (x + 1);
        }
        pi = (pi + 1);
    }
    int64_t ans = 0;
    i = 2;
    while (i < limit) {
        if (ways[i] > 5000) {
            ans = ((int64_t)(i));
            break;
        }
        i = (i + 1);
    }
    printf("%lld\n", ans);
    free(sieve);
    free(primes);
    free(ways);
    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 200 : i32
    %2 = arith.extsi %0 : i32 to i64
    %3 = arith.constant 1 : i32
    %4 = arith.extsi %3 : i32 to i64
    %1 = func.call @calloc(%2, %4) : (i64, i64) -> !llvm.ptr
    %6 = arith.extsi %0 : i32 to i64
    %7 = arith.constant 4 : i32
    %8 = arith.extsi %7 : i32 to i64
    %5 = func.call @calloc(%6, %8) : (i64, i64) -> !llvm.ptr
    %10 = arith.extsi %0 : i32 to i64
    %11 = arith.constant 8 : i32
    %12 = arith.extsi %11 : i32 to i64
    %9 = func.call @calloc(%10, %12) : (i64, i64) -> !llvm.ptr
    %13 = llvm.mlir.zero : !llvm.ptr
    %14 = llvm.icmp "eq" %1, %13 : !llvm.ptr
    %15 = scf.if %14 -> (i1) {
      %16 = arith.constant true
      scf.yield %16 : i1
    } else {
      %17 = llvm.mlir.zero : !llvm.ptr
      %18 = llvm.icmp "eq" %5, %17 : !llvm.ptr
      scf.yield %18 : i1
    }
    %19 = scf.if %15 -> (i1) {
      %20 = arith.constant true
      scf.yield %20 : i1
    } else {
      %21 = llvm.mlir.zero : !llvm.ptr
      %22 = llvm.icmp "eq" %9, %21 : !llvm.ptr
      scf.yield %22 : i1
    }
    cf.cond_br %19, ^bb0, ^bb1
    ^bb0:
      %23 = arith.constant 1 : i32
      func.return %23 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %24 = arith.constant 1 : i32
    %25 = arith.constant 0 : i32
    %26 = arith.trunci %24 : i32 to i8
    %27 = arith.extsi %25 : i32 to i64
    %28 = llvm.getelementptr %1[%27] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %26, %28 : i8, !llvm.ptr
    %29 = arith.constant 1 : i32
    %30 = arith.constant 1 : i32
    %31 = arith.trunci %29 : i32 to i8
    %32 = arith.extsi %30 : i32 to i64
    %33 = llvm.getelementptr %1[%32] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %31, %33 : i8, !llvm.ptr
    %34 = arith.constant 2 : i32
    %35 = llvm.mlir.constant(1 : i64) : i64
    %36 = llvm.alloca %35 x i32 : (i64) -> !llvm.ptr
    llvm.store %34, %36 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %37 = llvm.load %36 : !llvm.ptr -> i32
    %38 = llvm.load %36 : !llvm.ptr -> i32
    %39 = arith.muli %37, %38 : i32
    %40 = arith.cmpi slt, %39, %0 : i32
    cf.cond_br %40, ^bb4, ^bb5
    ^bb4:
      %42 = llvm.load %36 : !llvm.ptr -> i32
      %43 = arith.extsi %42 : i32 to i64
      %44 = llvm.getelementptr %1[%43] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %41 = llvm.load %44 : !llvm.ptr -> i8
      %45 = arith.constant 0 : i32
      %47 = arith.extsi %41 : i8 to i32
      %46 = arith.cmpi eq, %47, %45 : i32
      cf.cond_br %46, ^bb6, ^bb7
      ^bb6:
        %48 = llvm.load %36 : !llvm.ptr -> i32
        %49 = llvm.load %36 : !llvm.ptr -> i32
        %50 = arith.muli %48, %49 : i32
        %51 = llvm.mlir.constant(1 : i64) : i64
        %52 = llvm.alloca %51 x i32 : (i64) -> !llvm.ptr
        llvm.store %50, %52 : i32, !llvm.ptr
        cf.br ^bb9
        ^bb9:
        %53 = llvm.load %52 : !llvm.ptr -> i32
        %54 = arith.cmpi slt, %53, %0 : i32
        cf.cond_br %54, ^bb10, ^bb11
        ^bb10:
          %55 = arith.constant 1 : i32
          %56 = llvm.load %52 : !llvm.ptr -> i32
          %57 = arith.trunci %55 : i32 to i8
          %58 = arith.extsi %56 : i32 to i64
          %59 = llvm.getelementptr %1[%58] : (!llvm.ptr, i64) -> !llvm.ptr, i8
          llvm.store %57, %59 : i8, !llvm.ptr
          %60 = llvm.load %52 : !llvm.ptr -> i32
          %61 = llvm.load %36 : !llvm.ptr -> i32
          %62 = arith.addi %60, %61 : i32
          llvm.store %62, %52 : i32, !llvm.ptr
          cf.br ^bb9
        ^bb11:
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %63 = llvm.load %36 : !llvm.ptr -> i32
      %64 = arith.constant 1 : i32
      %65 = arith.addi %63, %64 : i32
      llvm.store %65, %36 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %66 = arith.constant 0 : i32
    %67 = llvm.mlir.constant(1 : i64) : i64
    %68 = llvm.alloca %67 x i32 : (i64) -> !llvm.ptr
    llvm.store %66, %68 : i32, !llvm.ptr
    %69 = arith.constant 2 : i32
    %70 = llvm.mlir.constant(1 : i64) : i64
    %71 = llvm.alloca %70 x i32 : (i64) -> !llvm.ptr
    llvm.store %69, %71 : i32, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %72 = llvm.load %71 : !llvm.ptr -> i32
    %73 = arith.cmpi slt, %72, %0 : i32
    cf.cond_br %73, ^bb13, ^bb14
    ^bb13:
      %75 = llvm.load %71 : !llvm.ptr -> i32
      %76 = arith.extsi %75 : i32 to i64
      %77 = llvm.getelementptr %1[%76] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %74 = llvm.load %77 : !llvm.ptr -> i8
      %78 = arith.constant 0 : i32
      %80 = arith.extsi %74 : i8 to i32
      %79 = arith.cmpi eq, %80, %78 : i32
      cf.cond_br %79, ^bb15, ^bb16
      ^bb15:
        %81 = llvm.load %71 : !llvm.ptr -> i32
        %82 = llvm.load %68 : !llvm.ptr -> i32
        %83 = arith.extsi %82 : i32 to i64
        %84 = llvm.getelementptr %5[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %81, %84 : i32, !llvm.ptr
        %85 = llvm.load %68 : !llvm.ptr -> i32
        %86 = arith.constant 1 : i32
        %87 = arith.addi %85, %86 : i32
        llvm.store %87, %68 : i32, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      %88 = llvm.load %71 : !llvm.ptr -> i32
      %89 = arith.constant 1 : i32
      %90 = arith.addi %88, %89 : i32
      llvm.store %90, %71 : i32, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %91 = arith.constant 1 : i32
    %92 = arith.constant 0 : i32
    %93 = arith.extsi %91 : i32 to i64
    %94 = arith.extsi %92 : i32 to i64
    %95 = llvm.getelementptr %9[%94] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %93, %95 : i64, !llvm.ptr
    %96 = arith.constant 0 : i32
    %97 = llvm.mlir.constant(1 : i64) : i64
    %98 = llvm.alloca %97 x i32 : (i64) -> !llvm.ptr
    llvm.store %96, %98 : i32, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %99 = llvm.load %98 : !llvm.ptr -> i32
    %100 = llvm.load %68 : !llvm.ptr -> i32
    %101 = arith.cmpi slt, %99, %100 : i32
    cf.cond_br %101, ^bb19, ^bb20
    ^bb19:
      %103 = llvm.load %98 : !llvm.ptr -> i32
      %104 = arith.extsi %103 : i32 to i64
      %105 = llvm.getelementptr %5[%104] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %102 = llvm.load %105 : !llvm.ptr -> i32
      %106 = llvm.mlir.constant(1 : i64) : i64
      %107 = llvm.alloca %106 x i32 : (i64) -> !llvm.ptr
      llvm.store %102, %107 : i32, !llvm.ptr
      cf.br ^bb21
      ^bb21:
      %108 = llvm.load %107 : !llvm.ptr -> i32
      %109 = arith.cmpi slt, %108, %0 : i32
      cf.cond_br %109, ^bb22, ^bb23
      ^bb22:
        %111 = llvm.load %107 : !llvm.ptr -> i32
        %112 = arith.extsi %111 : i32 to i64
        %113 = llvm.getelementptr %9[%112] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %110 = llvm.load %113 : !llvm.ptr -> i64
        %115 = llvm.load %107 : !llvm.ptr -> i32
        %116 = arith.subi %115, %102 : i32
        %117 = arith.extsi %116 : i32 to i64
        %118 = llvm.getelementptr %9[%117] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %114 = llvm.load %118 : !llvm.ptr -> i64
        %119 = arith.addi %110, %114 : i64
        %120 = llvm.load %107 : !llvm.ptr -> i32
        %121 = arith.extsi %120 : i32 to i64
        %122 = llvm.getelementptr %9[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %119, %122 : i64, !llvm.ptr
        %123 = llvm.load %107 : !llvm.ptr -> i32
        %124 = arith.constant 1 : i32
        %125 = arith.addi %123, %124 : i32
        llvm.store %125, %107 : i32, !llvm.ptr
        cf.br ^bb21
      ^bb23:
      %126 = llvm.load %98 : !llvm.ptr -> i32
      %127 = arith.constant 1 : i32
      %128 = arith.addi %126, %127 : i32
      llvm.store %128, %98 : i32, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %129 = arith.constant 0 : i32
    %130 = arith.extsi %129 : i32 to i64
    %131 = llvm.mlir.constant(1 : i64) : i64
    %132 = llvm.alloca %131 x i64 : (i64) -> !llvm.ptr
    llvm.store %130, %132 : i64, !llvm.ptr
    %133 = arith.constant 2 : i32
    llvm.store %133, %71 : i32, !llvm.ptr
    cf.br ^bb24
    ^bb24:
    %134 = llvm.load %71 : !llvm.ptr -> i32
    %135 = arith.cmpi slt, %134, %0 : i32
    cf.cond_br %135, ^bb25, ^bb26
    ^bb25:
      %137 = llvm.load %71 : !llvm.ptr -> i32
      %138 = arith.extsi %137 : i32 to i64
      %139 = llvm.getelementptr %9[%138] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %136 = llvm.load %139 : !llvm.ptr -> i64
      %140 = arith.constant 5000 : i32
      %142 = arith.extsi %140 : i32 to i64
      %141 = arith.cmpi sgt, %136, %142 : i64
      cf.cond_br %141, ^bb27, ^bb28
      ^bb27:
        %143 = llvm.load %71 : !llvm.ptr -> i32
        %144 = arith.extsi %143 : i32 to i64
        llvm.store %144, %132 : i64, !llvm.ptr
        cf.br ^bb26
      ^bb28:
        cf.br ^bb29
      ^bb29:
      %145 = llvm.load %71 : !llvm.ptr -> i32
      %146 = arith.constant 1 : i32
      %147 = arith.addi %145, %146 : i32
      llvm.store %147, %71 : i32, !llvm.ptr
      cf.br ^bb24
    ^bb26:
    %148 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %149 = llvm.load %132 : !llvm.ptr -> i64
    %150 = llvm.call @printf(%148, %149) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%1) : (!llvm.ptr) -> ()
    func.call @free(%5) : (!llvm.ptr) -> ()
    func.call @free(%9) : (!llvm.ptr) -> ()
    %154 = arith.constant 0 : i32
    func.return %154 : i32
  }
}