Problem 310

Nim Square losing positions for a,b,c ≤ 100000.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 310
# Nim Square losing positions for a,b,c ≤ 100000.

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

function main() -> i32 {
    let limit: i64 = 100000
    let mex: ptr<i32> = calloc(limit + 1, 4)
    let moves: ptr<i8> = calloc(80, 1)
    if mex == null || moves == null { return 1 }
    let mut size: i64 = 0
    while size <= limit {
        let mut mi: i64 = 0
        while mi < 80 {
            moves[mi] = 0
            mi = mi + 1
        }
        let mut i: i64 = 1
        while i * i <= size {
            moves[mex[size - i * i]] = 1
            i = i + 1
        }
        let mut available: i32 = 0
        while moves[available] == 1 {
            available = available + 1
        }
        mex[size] = available
        size = size + 1
    }
    let mut max_nim: i32 = 0
    size = 0
    while size <= limit {
        if mex[size] > max_nim { max_nim = mex[size] }
        size = size + 1
    }
    let mut next_pow: i64 = 1
    while next_pow < (max_nim as i64) {
        next_pow = next_pow * 2
    }
    let frequency: ptr<i64> = calloc(next_pow, 8)
    if frequency == null { return 1 }
    let mut num_lost: i64 = 0
    let mut a: i64 = limit
    while a >= 0 {
        let mut c: i64 = a
        while c <= limit {
            let idx: i64 = (mex[a] ^ mex[c]) as i64
            frequency[idx] = frequency[idx] + 1
            c = c + 1
        }
        num_lost = num_lost + frequency[mex[a]]
        a = a - 1
    }
    printf("%lld\n", num_lost)
    free(mex); free(moves); free(frequency)
    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 = 100000;
    int32_t* mex = (int32_t*)(calloc((limit + 1), 4));
    int8_t* moves = (int8_t*)(calloc(80, 1));
    if ((mex == NULL || moves == NULL)) {
        return 1;
    }
    int64_t size = 0;
    while (size <= limit) {
        int64_t mi = 0;
        while (mi < 80) {
            moves[mi] = 0;
            mi = (mi + 1);
        }
        int64_t i = 1;
        while ((i * i) <= size) {
            moves[mex[(size - (i * i))]] = 1;
            i = (i + 1);
        }
        int32_t available = 0;
        while (moves[available] == 1) {
            available = (available + 1);
        }
        mex[size] = available;
        size = (size + 1);
    }
    int32_t max_nim = 0;
    size = 0;
    while (size <= limit) {
        if (mex[size] > max_nim) {
            max_nim = mex[size];
        }
        size = (size + 1);
    }
    int64_t next_pow = 1;
    while (next_pow < ((int64_t)(max_nim))) {
        next_pow = (next_pow * 2);
    }
    int64_t* frequency = (int64_t*)(calloc(next_pow, 8));
    if (frequency == NULL) {
        return 1;
    }
    int64_t num_lost = 0;
    int64_t a = limit;
    while (a >= 0) {
        int64_t c = a;
        while (c <= limit) {
            int64_t idx = ((int64_t)((mex[a] ^ mex[c])));
            frequency[idx] = (frequency[idx] + 1);
            c = (c + 1);
        }
        num_lost = (num_lost + frequency[mex[a]]);
        a = (a - 1);
    }
    printf("%lld\n", num_lost);
    free(mex);
    free(moves);
    free(frequency);
    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 100000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %3 = arith.constant 1 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.addi %1, %5 : i64
    %6 = arith.constant 4 : i32
    %7 = arith.extsi %6 : i32 to i64
    %2 = func.call @calloc(%4, %7) : (i64, i64) -> !llvm.ptr
    %9 = arith.constant 80 : i32
    %10 = arith.constant 1 : i32
    %11 = arith.extsi %9 : i32 to i64
    %12 = arith.extsi %10 : i32 to i64
    %8 = func.call @calloc(%11, %12) : (i64, i64) -> !llvm.ptr
    %13 = llvm.mlir.zero : !llvm.ptr
    %14 = llvm.icmp "eq" %2, %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" %8, %17 : !llvm.ptr
      scf.yield %18 : i1
    }
    cf.cond_br %15, ^bb0, ^bb1
    ^bb0:
      %19 = arith.constant 1 : i32
      func.return %19 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %20 = arith.constant 0 : i32
    %21 = arith.extsi %20 : i32 to i64
    %22 = llvm.mlir.constant(1 : i64) : i64
    %23 = llvm.alloca %22 x i64 : (i64) -> !llvm.ptr
    llvm.store %21, %23 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %24 = llvm.load %23 : !llvm.ptr -> i64
    %25 = arith.cmpi sle, %24, %1 : i64
    cf.cond_br %25, ^bb4, ^bb5
    ^bb4:
      %26 = arith.constant 0 : i32
      %27 = arith.extsi %26 : i32 to i64
      %28 = llvm.mlir.constant(1 : i64) : i64
      %29 = llvm.alloca %28 x i64 : (i64) -> !llvm.ptr
      llvm.store %27, %29 : i64, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %30 = llvm.load %29 : !llvm.ptr -> i64
      %31 = arith.constant 80 : i32
      %33 = arith.extsi %31 : i32 to i64
      %32 = arith.cmpi slt, %30, %33 : i64
      cf.cond_br %32, ^bb7, ^bb8
      ^bb7:
        %34 = arith.constant 0 : i32
        %35 = llvm.load %29 : !llvm.ptr -> i64
        %36 = arith.trunci %34 : i32 to i8
        %37 = llvm.getelementptr %8[%35] : (!llvm.ptr, i64) -> !llvm.ptr, i8
        llvm.store %36, %37 : i8, !llvm.ptr
        %38 = llvm.load %29 : !llvm.ptr -> i64
        %39 = arith.constant 1 : i32
        %41 = arith.extsi %39 : i32 to i64
        %40 = arith.addi %38, %41 : i64
        llvm.store %40, %29 : i64, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %42 = arith.constant 1 : i32
      %43 = arith.extsi %42 : i32 to i64
      %44 = llvm.mlir.constant(1 : i64) : i64
      %45 = llvm.alloca %44 x i64 : (i64) -> !llvm.ptr
      llvm.store %43, %45 : i64, !llvm.ptr
      cf.br ^bb9
      ^bb9:
      %46 = llvm.load %45 : !llvm.ptr -> i64
      %47 = llvm.load %45 : !llvm.ptr -> i64
      %48 = arith.muli %46, %47 : i64
      %49 = llvm.load %23 : !llvm.ptr -> i64
      %50 = arith.cmpi sle, %48, %49 : i64
      cf.cond_br %50, ^bb10, ^bb11
      ^bb10:
        %51 = arith.constant 1 : i32
        %53 = llvm.load %23 : !llvm.ptr -> i64
        %54 = llvm.load %45 : !llvm.ptr -> i64
        %55 = llvm.load %45 : !llvm.ptr -> i64
        %56 = arith.muli %54, %55 : i64
        %57 = arith.subi %53, %56 : i64
        %58 = llvm.getelementptr %2[%57] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %52 = llvm.load %58 : !llvm.ptr -> i32
        %59 = arith.trunci %51 : i32 to i8
        %60 = arith.extsi %52 : i32 to i64
        %61 = llvm.getelementptr %8[%60] : (!llvm.ptr, i64) -> !llvm.ptr, i8
        llvm.store %59, %61 : i8, !llvm.ptr
        %62 = llvm.load %45 : !llvm.ptr -> i64
        %63 = arith.constant 1 : i32
        %65 = arith.extsi %63 : i32 to i64
        %64 = arith.addi %62, %65 : i64
        llvm.store %64, %45 : i64, !llvm.ptr
        cf.br ^bb9
      ^bb11:
      %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
      cf.br ^bb12
      ^bb12:
      %70 = llvm.load %68 : !llvm.ptr -> i32
      %71 = arith.extsi %70 : i32 to i64
      %72 = llvm.getelementptr %8[%71] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %69 = llvm.load %72 : !llvm.ptr -> i8
      %73 = arith.constant 1 : i32
      %75 = arith.extsi %69 : i8 to i32
      %74 = arith.cmpi eq, %75, %73 : i32
      cf.cond_br %74, ^bb13, ^bb14
      ^bb13:
        %76 = llvm.load %68 : !llvm.ptr -> i32
        %77 = arith.constant 1 : i32
        %78 = arith.addi %76, %77 : i32
        llvm.store %78, %68 : i32, !llvm.ptr
        cf.br ^bb12
      ^bb14:
      %79 = llvm.load %68 : !llvm.ptr -> i32
      %80 = llvm.load %23 : !llvm.ptr -> i64
      %81 = llvm.getelementptr %2[%80] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %79, %81 : i32, !llvm.ptr
      %82 = llvm.load %23 : !llvm.ptr -> i64
      %83 = arith.constant 1 : i32
      %85 = arith.extsi %83 : i32 to i64
      %84 = arith.addi %82, %85 : i64
      llvm.store %84, %23 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %86 = arith.constant 0 : i32
    %87 = llvm.mlir.constant(1 : i64) : i64
    %88 = llvm.alloca %87 x i32 : (i64) -> !llvm.ptr
    llvm.store %86, %88 : i32, !llvm.ptr
    %89 = arith.constant 0 : i32
    %90 = arith.extsi %89 : i32 to i64
    llvm.store %90, %23 : i64, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %91 = llvm.load %23 : !llvm.ptr -> i64
    %92 = arith.cmpi sle, %91, %1 : i64
    cf.cond_br %92, ^bb16, ^bb17
    ^bb16:
      %94 = llvm.load %23 : !llvm.ptr -> i64
      %95 = llvm.getelementptr %2[%94] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %93 = llvm.load %95 : !llvm.ptr -> i32
      %96 = llvm.load %88 : !llvm.ptr -> i32
      %97 = arith.cmpi sgt, %93, %96 : i32
      cf.cond_br %97, ^bb18, ^bb19
      ^bb18:
        %99 = llvm.load %23 : !llvm.ptr -> i64
        %100 = llvm.getelementptr %2[%99] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %98 = llvm.load %100 : !llvm.ptr -> i32
        llvm.store %98, %88 : i32, !llvm.ptr
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %101 = llvm.load %23 : !llvm.ptr -> i64
      %102 = arith.constant 1 : i32
      %104 = arith.extsi %102 : i32 to i64
      %103 = arith.addi %101, %104 : i64
      llvm.store %103, %23 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %105 = arith.constant 1 : i32
    %106 = arith.extsi %105 : i32 to i64
    %107 = llvm.mlir.constant(1 : i64) : i64
    %108 = llvm.alloca %107 x i64 : (i64) -> !llvm.ptr
    llvm.store %106, %108 : i64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %109 = llvm.load %108 : !llvm.ptr -> i64
    %110 = llvm.load %88 : !llvm.ptr -> i32
    %111 = arith.extsi %110 : i32 to i64
    %112 = arith.cmpi slt, %109, %111 : i64
    cf.cond_br %112, ^bb22, ^bb23
    ^bb22:
      %113 = llvm.load %108 : !llvm.ptr -> i64
      %114 = arith.constant 2 : i32
      %116 = arith.extsi %114 : i32 to i64
      %115 = arith.muli %113, %116 : i64
      llvm.store %115, %108 : i64, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %118 = llvm.load %108 : !llvm.ptr -> i64
    %119 = arith.constant 8 : i32
    %120 = arith.extsi %119 : i32 to i64
    %117 = func.call @calloc(%118, %120) : (i64, i64) -> !llvm.ptr
    %121 = llvm.mlir.zero : !llvm.ptr
    %122 = llvm.icmp "eq" %117, %121 : !llvm.ptr
    cf.cond_br %122, ^bb24, ^bb25
    ^bb24:
      %123 = arith.constant 1 : i32
      func.return %123 : i32
    ^bb25:
      cf.br ^bb26
    ^bb26:
    %124 = arith.constant 0 : i32
    %125 = arith.extsi %124 : i32 to i64
    %126 = llvm.mlir.constant(1 : i64) : i64
    %127 = llvm.alloca %126 x i64 : (i64) -> !llvm.ptr
    llvm.store %125, %127 : i64, !llvm.ptr
    %128 = llvm.mlir.constant(1 : i64) : i64
    %129 = llvm.alloca %128 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %129 : i64, !llvm.ptr
    cf.br ^bb27
    ^bb27:
    %130 = llvm.load %129 : !llvm.ptr -> i64
    %131 = arith.constant 0 : i32
    %133 = arith.extsi %131 : i32 to i64
    %132 = arith.cmpi sge, %130, %133 : i64
    cf.cond_br %132, ^bb28, ^bb29
    ^bb28:
      %134 = llvm.load %129 : !llvm.ptr -> i64
      %135 = llvm.mlir.constant(1 : i64) : i64
      %136 = llvm.alloca %135 x i64 : (i64) -> !llvm.ptr
      llvm.store %134, %136 : i64, !llvm.ptr
      cf.br ^bb30
      ^bb30:
      %137 = llvm.load %136 : !llvm.ptr -> i64
      %138 = arith.cmpi sle, %137, %1 : i64
      cf.cond_br %138, ^bb31, ^bb32
      ^bb31:
        %140 = llvm.load %129 : !llvm.ptr -> i64
        %141 = llvm.getelementptr %2[%140] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %139 = llvm.load %141 : !llvm.ptr -> i32
        %143 = llvm.load %136 : !llvm.ptr -> i64
        %144 = llvm.getelementptr %2[%143] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %142 = llvm.load %144 : !llvm.ptr -> i32
        %145 = arith.xori %139, %142 : i32
        %146 = arith.extsi %145 : i32 to i64
        %148 = llvm.getelementptr %117[%146] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %147 = llvm.load %148 : !llvm.ptr -> i64
        %149 = arith.constant 1 : i32
        %151 = arith.extsi %149 : i32 to i64
        %150 = arith.addi %147, %151 : i64
        %152 = llvm.getelementptr %117[%146] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %150, %152 : i64, !llvm.ptr
        %153 = llvm.load %136 : !llvm.ptr -> i64
        %154 = arith.constant 1 : i32
        %156 = arith.extsi %154 : i32 to i64
        %155 = arith.addi %153, %156 : i64
        llvm.store %155, %136 : i64, !llvm.ptr
        cf.br ^bb30
      ^bb32:
      %157 = llvm.load %127 : !llvm.ptr -> i64
      %160 = llvm.load %129 : !llvm.ptr -> i64
      %161 = llvm.getelementptr %2[%160] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %159 = llvm.load %161 : !llvm.ptr -> i32
      %162 = arith.extsi %159 : i32 to i64
      %163 = llvm.getelementptr %117[%162] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %158 = llvm.load %163 : !llvm.ptr -> i64
      %164 = arith.addi %157, %158 : i64
      llvm.store %164, %127 : i64, !llvm.ptr
      %165 = llvm.load %129 : !llvm.ptr -> i64
      %166 = arith.constant 1 : i32
      %168 = arith.extsi %166 : i32 to i64
      %167 = arith.subi %165, %168 : i64
      llvm.store %167, %129 : i64, !llvm.ptr
      cf.br ^bb27
    ^bb29:
    %169 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %170 = llvm.load %127 : !llvm.ptr -> i64
    %171 = llvm.call @printf(%169, %170) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%2) : (!llvm.ptr) -> ()
    func.call @free(%8) : (!llvm.ptr) -> ()
    func.call @free(%117) : (!llvm.ptr) -> ()
    %175 = arith.constant 0 : i32
    func.return %175 : i32
  }
}