Problem 371

Expected number of plates until 000/500 pair (mod 1000).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 371
# Expected number of plates until 000/500 pair (mod 1000).

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

function main() -> i32 {
    let num_plates: i32 = 1000
    let max_have: i32 = num_plates / 2 - 1
    let plates: f64 = num_plates as f64

    let have500: ptr<f64> = calloc((max_have + 1) as i64, 8)
    let no500: ptr<f64> = calloc((max_have + 1) as i64, 8)
    if have500 == null || no500 == null { return 1 }

    let mut prob_duplicate: f64 = (max_have as f64) / plates
    let prob_zero: f64 = 1.0 / plates
    let prob_500: f64 = 1.0 / plates
    let mut prob_unchanged: f64 = prob_duplicate + prob_zero

    have500[max_have] = 1.0 / (1.0 - prob_unchanged)
    no500[max_have] = (1.0 + prob_500 * have500[max_have]) / (1.0 - prob_unchanged)

    let mut have: i32 = max_have - 1
    while have >= 0 {
        let num_new: f64 = plates - 2.0 * (have as f64) - 2.0
        let prob_new: f64 = num_new / plates
        prob_duplicate = (have as f64) / plates
        prob_unchanged = prob_duplicate + prob_zero
        have500[have] = (1.0 + prob_new * have500[have + 1]) / (1.0 - prob_unchanged)
        no500[have] = (1.0 + prob_500 * have500[have] + prob_new * no500[have + 1]) / (1.0 - prob_unchanged)
        have = have - 1
    }

    printf("%.8f\n", no500[0])
    free(no500)
    free(have500)
    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 num_plates = 1000;
    int32_t max_have = (FLOW_CHECKED_DIV((num_plates), (2)) - 1);
    double plates = ((double)(num_plates));
    double* have500 = (double*)(calloc(((int64_t)((max_have + 1))), 8));
    double* no500 = (double*)(calloc(((int64_t)((max_have + 1))), 8));
    if ((have500 == NULL || no500 == NULL)) {
        return 1;
    }
    double prob_duplicate = (((double)(max_have)) / plates);
    double prob_zero = (1.0 / plates);
    double prob_500 = (1.0 / plates);
    double prob_unchanged = (prob_duplicate + prob_zero);
    have500[max_have] = (1.0 / (1.0 - prob_unchanged));
    no500[max_have] = ((1.0 + (prob_500 * have500[max_have])) / (1.0 - prob_unchanged));
    int32_t have = (max_have - 1);
    while (have >= 0) {
        double num_new = ((plates - (2.0 * ((double)(have)))) - 2.0);
        double prob_new = (num_new / plates);
        prob_duplicate = (((double)(have)) / plates);
        prob_unchanged = (prob_duplicate + prob_zero);
        have500[have] = ((1.0 + (prob_new * have500[(have + 1)])) / (1.0 - prob_unchanged));
        no500[have] = (((1.0 + (prob_500 * have500[have])) + (prob_new * no500[(have + 1)])) / (1.0 - prob_unchanged));
        have = (have - 1);
    }
    printf("%.8f\n", no500[0]);
    free(no500);
    free(have500);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.8f\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 1000 : i32
    %1 = arith.constant 2 : i32
    %2 = arith.divsi %0, %1 : i32
    %3 = arith.constant 1 : i32
    %4 = arith.subi %2, %3 : i32
    %5 = arith.sitofp %0 : i32 to f64
    %7 = arith.constant 1 : i32
    %8 = arith.addi %4, %7 : i32
    %9 = arith.extsi %8 : i32 to i64
    %10 = arith.constant 8 : i32
    %11 = arith.extsi %10 : i32 to i64
    %6 = func.call @calloc(%9, %11) : (i64, i64) -> !llvm.ptr
    %13 = arith.constant 1 : i32
    %14 = arith.addi %4, %13 : i32
    %15 = arith.extsi %14 : i32 to i64
    %16 = arith.constant 8 : i32
    %17 = arith.extsi %16 : i32 to i64
    %12 = func.call @calloc(%15, %17) : (i64, i64) -> !llvm.ptr
    %18 = llvm.mlir.zero : !llvm.ptr
    %19 = llvm.icmp "eq" %6, %18 : !llvm.ptr
    %20 = scf.if %19 -> (i1) {
      %21 = arith.constant true
      scf.yield %21 : i1
    } else {
      %22 = llvm.mlir.zero : !llvm.ptr
      %23 = llvm.icmp "eq" %12, %22 : !llvm.ptr
      scf.yield %23 : i1
    }
    cf.cond_br %20, ^bb0, ^bb1
    ^bb0:
      %24 = arith.constant 1 : i32
      func.return %24 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %25 = arith.sitofp %4 : i32 to f64
    %26 = arith.divf %25, %5 : f64
    %27 = llvm.mlir.constant(1 : i64) : i64
    %28 = llvm.alloca %27 x f64 : (i64) -> !llvm.ptr
    llvm.store %26, %28 : f64, !llvm.ptr
    %29 = arith.constant 1.0 : f32
    %31 = arith.extf %29 : f32 to f64
    %30 = arith.divf %31, %5 : f64
    %32 = arith.constant 1.0 : f32
    %34 = arith.extf %32 : f32 to f64
    %33 = arith.divf %34, %5 : f64
    %35 = llvm.load %28 : !llvm.ptr -> f64
    %36 = arith.addf %35, %30 : f64
    %37 = llvm.mlir.constant(1 : i64) : i64
    %38 = llvm.alloca %37 x f64 : (i64) -> !llvm.ptr
    llvm.store %36, %38 : f64, !llvm.ptr
    %39 = arith.constant 1.0 : f32
    %40 = arith.constant 1.0 : f32
    %41 = llvm.load %38 : !llvm.ptr -> f64
    %43 = arith.extf %40 : f32 to f64
    %42 = arith.subf %43, %41 : f64
    %45 = arith.extf %39 : f32 to f64
    %44 = arith.divf %45, %42 : f64
    %46 = arith.extsi %4 : i32 to i64
    %47 = llvm.getelementptr %6[%46] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %44, %47 : f64, !llvm.ptr
    %48 = arith.constant 1.0 : f32
    %50 = arith.extsi %4 : i32 to i64
    %51 = llvm.getelementptr %6[%50] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %49 = llvm.load %51 : !llvm.ptr -> f64
    %52 = arith.mulf %33, %49 : f64
    %54 = arith.extf %48 : f32 to f64
    %53 = arith.addf %54, %52 : f64
    %55 = arith.constant 1.0 : f32
    %56 = llvm.load %38 : !llvm.ptr -> f64
    %58 = arith.extf %55 : f32 to f64
    %57 = arith.subf %58, %56 : f64
    %59 = arith.divf %53, %57 : f64
    %60 = arith.extsi %4 : i32 to i64
    %61 = llvm.getelementptr %12[%60] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %59, %61 : f64, !llvm.ptr
    %62 = arith.constant 1 : i32
    %63 = arith.subi %4, %62 : i32
    %64 = llvm.mlir.constant(1 : i64) : i64
    %65 = llvm.alloca %64 x i32 : (i64) -> !llvm.ptr
    llvm.store %63, %65 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %66 = llvm.load %65 : !llvm.ptr -> i32
    %67 = arith.constant 0 : i32
    %68 = arith.cmpi sge, %66, %67 : i32
    cf.cond_br %68, ^bb4, ^bb5
    ^bb4:
      %69 = arith.constant 2.0 : f32
      %70 = llvm.load %65 : !llvm.ptr -> i32
      %71 = arith.sitofp %70 : i32 to f64
      %73 = arith.extf %69 : f32 to f64
      %72 = arith.mulf %73, %71 : f64
      %74 = arith.subf %5, %72 : f64
      %75 = arith.constant 2.0 : f32
      %77 = arith.extf %75 : f32 to f64
      %76 = arith.subf %74, %77 : f64
      %78 = arith.divf %76, %5 : f64
      %79 = llvm.load %65 : !llvm.ptr -> i32
      %80 = arith.sitofp %79 : i32 to f64
      %81 = arith.divf %80, %5 : f64
      llvm.store %81, %28 : f64, !llvm.ptr
      %82 = llvm.load %28 : !llvm.ptr -> f64
      %83 = arith.addf %82, %30 : f64
      llvm.store %83, %38 : f64, !llvm.ptr
      %84 = arith.constant 1.0 : f32
      %86 = llvm.load %65 : !llvm.ptr -> i32
      %87 = arith.constant 1 : i32
      %88 = arith.addi %86, %87 : i32
      %89 = arith.extsi %88 : i32 to i64
      %90 = llvm.getelementptr %6[%89] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %85 = llvm.load %90 : !llvm.ptr -> f64
      %91 = arith.mulf %78, %85 : f64
      %93 = arith.extf %84 : f32 to f64
      %92 = arith.addf %93, %91 : f64
      %94 = arith.constant 1.0 : f32
      %95 = llvm.load %38 : !llvm.ptr -> f64
      %97 = arith.extf %94 : f32 to f64
      %96 = arith.subf %97, %95 : f64
      %98 = arith.divf %92, %96 : f64
      %99 = llvm.load %65 : !llvm.ptr -> i32
      %100 = arith.extsi %99 : i32 to i64
      %101 = llvm.getelementptr %6[%100] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %98, %101 : f64, !llvm.ptr
      %102 = arith.constant 1.0 : f32
      %104 = llvm.load %65 : !llvm.ptr -> i32
      %105 = arith.extsi %104 : i32 to i64
      %106 = llvm.getelementptr %6[%105] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %103 = llvm.load %106 : !llvm.ptr -> f64
      %107 = arith.mulf %33, %103 : f64
      %109 = arith.extf %102 : f32 to f64
      %108 = arith.addf %109, %107 : f64
      %111 = llvm.load %65 : !llvm.ptr -> i32
      %112 = arith.constant 1 : i32
      %113 = arith.addi %111, %112 : i32
      %114 = arith.extsi %113 : i32 to i64
      %115 = llvm.getelementptr %12[%114] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %110 = llvm.load %115 : !llvm.ptr -> f64
      %116 = arith.mulf %78, %110 : f64
      %117 = arith.addf %108, %116 : f64
      %118 = arith.constant 1.0 : f32
      %119 = llvm.load %38 : !llvm.ptr -> f64
      %121 = arith.extf %118 : f32 to f64
      %120 = arith.subf %121, %119 : f64
      %122 = arith.divf %117, %120 : f64
      %123 = llvm.load %65 : !llvm.ptr -> i32
      %124 = arith.extsi %123 : i32 to i64
      %125 = llvm.getelementptr %12[%124] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %122, %125 : f64, !llvm.ptr
      %126 = llvm.load %65 : !llvm.ptr -> i32
      %127 = arith.constant 1 : i32
      %128 = arith.subi %126, %127 : i32
      llvm.store %128, %65 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %129 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %131 = arith.constant 0 : i32
    %132 = arith.extsi %131 : i32 to i64
    %133 = llvm.getelementptr %12[%132] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %130 = llvm.load %133 : !llvm.ptr -> f64
    %134 = llvm.call @printf(%129, %130) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    func.call @free(%12) : (!llvm.ptr) -> ()
    func.call @free(%6) : (!llvm.ptr) -> ()
    %137 = arith.constant 0 : i32
    func.return %137 : i32
  }
}