Problem 863

Different Dice — expected rolls to emulate n-sided die with d5/d6.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 863
# Different Dice — expected rolls to emulate n-sided die with d5/d6.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function fabs(x: f64) -> f64
}

function R(n: i64) -> f64 {
    let nxt5: ptr<i64> = calloc(n, 8)
    let nxt6: ptr<i64> = calloc(n, 8)
    let c5: ptr<f64> = calloc(n, 8)
    let c6: ptr<f64> = calloc(n, 8)
    let E: ptr<f64> = calloc(n, 8)
    let mut s: i64 = 1
    while s < n {
        let t5: i64 = 5 * s
        let r5: i64 = t5 % n
        nxt5[s] = r5
        if r5 == 0 { c5[s] = 0.0 } else { c5[s] = (r5 as f64) / (t5 as f64) }
        let t6: i64 = 6 * s
        let r6: i64 = t6 % n
        nxt6[s] = r6
        if r6 == 0 { c6[s] = 0.0 } else { c6[s] = (r6 as f64) / (t6 as f64) }
        s = s + 1
    }
    let mut iter: i64 = 0
    while iter < 10000 {
        let mut delta: f64 = 0.0
        s = n - 1
        while s > 0 {
            let v0: f64 = 1.0 + c5[s] * E[nxt5[s]]
            let v1: f64 = 1.0 + c6[s] * E[nxt6[s]]
            let mut neu: f64 = v0
            if v1 < v0 { neu = v1 }
            let diff: f64 = fabs(neu - E[s])
            if diff > delta { delta = diff }
            E[s] = neu
            s = s - 1
        }
        if delta < 1e-15 { break }
        iter = iter + 1
    }
    let ans: f64 = E[1]
    free(nxt5)
    free(nxt6)
    free(c5)
    free(c6)
    free(E)
    return ans
}

function main() -> i32 {
    let mut total: f64 = 0.0
    let mut k: i64 = 2
    while k <= 1000 {
        total = total + R(k)
        k = k + 1
    }
    printf("%.6f\n", total)
    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; }

double R_i64(int64_t n);
int32_t main(void);




double R_i64(int64_t n) {
    int64_t* nxt5 = (int64_t*)(calloc(n, 8));
    int64_t* nxt6 = (int64_t*)(calloc(n, 8));
    double* c5 = (double*)(calloc(n, 8));
    double* c6 = (double*)(calloc(n, 8));
    double* E = (double*)(calloc(n, 8));
    int64_t s = 1;
    while (s < n) {
        int64_t t5 = (5 * s);
        int64_t r5 = FLOW_CHECKED_MOD((t5), (n));
        nxt5[s] = r5;
        if (r5 == 0) {
            c5[s] = 0.0;
        } else {
            c5[s] = (((double)(r5)) / ((double)(t5)));
        }
        int64_t t6 = (6 * s);
        int64_t r6 = FLOW_CHECKED_MOD((t6), (n));
        nxt6[s] = r6;
        if (r6 == 0) {
            c6[s] = 0.0;
        } else {
            c6[s] = (((double)(r6)) / ((double)(t6)));
        }
        s = (s + 1);
    }
    int64_t iter = 0;
    while (iter < 10000) {
        double delta = 0.0;
        s = (n - 1);
        while (s > 0) {
            double v0 = (1.0 + (c5[s] * E[nxt5[s]]));
            double v1 = (1.0 + (c6[s] * E[nxt6[s]]));
            double neu = v0;
            if (v1 < v0) {
                neu = v1;
            }
            double diff = fabs((neu - E[s]));
            if (diff > delta) {
                delta = diff;
            }
            E[s] = neu;
            s = (s - 1);
        }
        if (delta < 1e-15) {
            break;
        }
        iter = (iter + 1);
    }
    double ans = E[1];
    free(nxt5);
    free(nxt6);
    free(c5);
    free(c6);
    free(E);
    return ans;
}

int32_t main(void) {
    double total = 0.0;
    int64_t k = 2;
    while (k <= 1000) {
        total = (total + R_i64(k));
        k = (k + 1);
    }
    printf("%.6f\n", total);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.6f\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 private @fabs(f64) -> f64
  func.func @R(%arg0: i64) -> f64 {
    %1 = arith.constant 8 : i32
    %2 = arith.extsi %1 : i32 to i64
    %0 = func.call @calloc(%arg0, %2) : (i64, i64) -> !llvm.ptr
    %4 = arith.constant 8 : i32
    %5 = arith.extsi %4 : i32 to i64
    %3 = func.call @calloc(%arg0, %5) : (i64, i64) -> !llvm.ptr
    %7 = arith.constant 8 : i32
    %8 = arith.extsi %7 : i32 to i64
    %6 = func.call @calloc(%arg0, %8) : (i64, i64) -> !llvm.ptr
    %10 = arith.constant 8 : i32
    %11 = arith.extsi %10 : i32 to i64
    %9 = func.call @calloc(%arg0, %11) : (i64, i64) -> !llvm.ptr
    %13 = arith.constant 8 : i32
    %14 = arith.extsi %13 : i32 to i64
    %12 = func.call @calloc(%arg0, %14) : (i64, i64) -> !llvm.ptr
    %15 = arith.constant 1 : i32
    %16 = arith.extsi %15 : i32 to i64
    %17 = llvm.mlir.constant(1 : i64) : i64
    %18 = llvm.alloca %17 x i64 : (i64) -> !llvm.ptr
    llvm.store %16, %18 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %19 = llvm.load %18 : !llvm.ptr -> i64
    %20 = arith.cmpi slt, %19, %arg0 : i64
    cf.cond_br %20, ^bb1, ^bb2
    ^bb1:
      %21 = arith.constant 5 : i32
      %22 = llvm.load %18 : !llvm.ptr -> i64
      %24 = arith.extsi %21 : i32 to i64
      %23 = arith.muli %24, %22 : i64
      %25 = arith.remsi %23, %arg0 : i64
      %26 = llvm.load %18 : !llvm.ptr -> i64
      %27 = llvm.getelementptr %0[%26] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %25, %27 : i64, !llvm.ptr
      %28 = arith.constant 0 : i32
      %30 = arith.extsi %28 : i32 to i64
      %29 = arith.cmpi eq, %25, %30 : i64
      cf.cond_br %29, ^bb3, ^bb4
      ^bb3:
        %31 = arith.constant 0.0 : f32
        %32 = llvm.load %18 : !llvm.ptr -> i64
        %33 = arith.extf %31 : f32 to f64
        %34 = llvm.getelementptr %6[%32] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %33, %34 : f64, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        %35 = arith.sitofp %25 : i64 to f64
        %36 = arith.sitofp %23 : i64 to f64
        %37 = arith.divf %35, %36 : f64
        %38 = llvm.load %18 : !llvm.ptr -> i64
        %39 = llvm.getelementptr %6[%38] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %37, %39 : f64, !llvm.ptr
        cf.br ^bb5
      ^bb5:
      %40 = arith.constant 6 : i32
      %41 = llvm.load %18 : !llvm.ptr -> i64
      %43 = arith.extsi %40 : i32 to i64
      %42 = arith.muli %43, %41 : i64
      %44 = arith.remsi %42, %arg0 : i64
      %45 = llvm.load %18 : !llvm.ptr -> i64
      %46 = llvm.getelementptr %3[%45] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %44, %46 : i64, !llvm.ptr
      %47 = arith.constant 0 : i32
      %49 = arith.extsi %47 : i32 to i64
      %48 = arith.cmpi eq, %44, %49 : i64
      cf.cond_br %48, ^bb6, ^bb7
      ^bb6:
        %50 = arith.constant 0.0 : f32
        %51 = llvm.load %18 : !llvm.ptr -> i64
        %52 = arith.extf %50 : f32 to f64
        %53 = llvm.getelementptr %9[%51] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %52, %53 : f64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        %54 = arith.sitofp %44 : i64 to f64
        %55 = arith.sitofp %42 : i64 to f64
        %56 = arith.divf %54, %55 : f64
        %57 = llvm.load %18 : !llvm.ptr -> i64
        %58 = llvm.getelementptr %9[%57] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %56, %58 : f64, !llvm.ptr
        cf.br ^bb8
      ^bb8:
      %59 = llvm.load %18 : !llvm.ptr -> i64
      %60 = arith.constant 1 : i32
      %62 = arith.extsi %60 : i32 to i64
      %61 = arith.addi %59, %62 : i64
      llvm.store %61, %18 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %63 = arith.constant 0 : 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
    cf.br ^bb9
    ^bb9:
    %67 = llvm.load %66 : !llvm.ptr -> i64
    %68 = arith.constant 10000 : i32
    %70 = arith.extsi %68 : i32 to i64
    %69 = arith.cmpi slt, %67, %70 : i64
    cf.cond_br %69, ^bb10, ^bb11
    ^bb10:
      %71 = arith.constant 0.0 : f32
      %72 = arith.extf %71 : f32 to f64
      %73 = llvm.mlir.constant(1 : i64) : i64
      %74 = llvm.alloca %73 x f64 : (i64) -> !llvm.ptr
      llvm.store %72, %74 : f64, !llvm.ptr
      %75 = arith.constant 1 : i32
      %77 = arith.extsi %75 : i32 to i64
      %76 = arith.subi %arg0, %77 : i64
      llvm.store %76, %18 : i64, !llvm.ptr
      cf.br ^bb12
      ^bb12:
      %78 = llvm.load %18 : !llvm.ptr -> i64
      %79 = arith.constant 0 : i32
      %81 = arith.extsi %79 : i32 to i64
      %80 = arith.cmpi sgt, %78, %81 : i64
      cf.cond_br %80, ^bb13, ^bb14
      ^bb13:
        %82 = arith.constant 1.0 : f32
        %84 = llvm.load %18 : !llvm.ptr -> i64
        %85 = llvm.getelementptr %6[%84] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %83 = llvm.load %85 : !llvm.ptr -> f64
        %88 = llvm.load %18 : !llvm.ptr -> i64
        %89 = llvm.getelementptr %0[%88] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %87 = llvm.load %89 : !llvm.ptr -> i64
        %90 = llvm.getelementptr %12[%87] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %86 = llvm.load %90 : !llvm.ptr -> f64
        %91 = arith.mulf %83, %86 : f64
        %93 = arith.extf %82 : f32 to f64
        %92 = arith.addf %93, %91 : f64
        %94 = arith.constant 1.0 : f32
        %96 = llvm.load %18 : !llvm.ptr -> i64
        %97 = llvm.getelementptr %9[%96] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %95 = llvm.load %97 : !llvm.ptr -> f64
        %100 = llvm.load %18 : !llvm.ptr -> i64
        %101 = llvm.getelementptr %3[%100] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %99 = llvm.load %101 : !llvm.ptr -> i64
        %102 = llvm.getelementptr %12[%99] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %98 = llvm.load %102 : !llvm.ptr -> f64
        %103 = arith.mulf %95, %98 : f64
        %105 = arith.extf %94 : f32 to f64
        %104 = arith.addf %105, %103 : f64
        %106 = llvm.mlir.constant(1 : i64) : i64
        %107 = llvm.alloca %106 x f64 : (i64) -> !llvm.ptr
        llvm.store %92, %107 : f64, !llvm.ptr
        %108 = arith.cmpf olt, %104, %92 : f64
        cf.cond_br %108, ^bb15, ^bb16
        ^bb15:
          llvm.store %104, %107 : f64, !llvm.ptr
          cf.br ^bb17
        ^bb16:
          cf.br ^bb17
        ^bb17:
        %109 = llvm.load %107 : !llvm.ptr -> f64
        %111 = llvm.load %18 : !llvm.ptr -> i64
        %112 = llvm.getelementptr %12[%111] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %110 = llvm.load %112 : !llvm.ptr -> f64
        %113 = arith.subf %109, %110 : f64
        %114 = math.absf %113 : f64
        %115 = llvm.load %74 : !llvm.ptr -> f64
        %116 = arith.cmpf ogt, %114, %115 : f64
        cf.cond_br %116, ^bb18, ^bb19
        ^bb18:
          llvm.store %114, %74 : f64, !llvm.ptr
          cf.br ^bb20
        ^bb19:
          cf.br ^bb20
        ^bb20:
        %117 = llvm.load %107 : !llvm.ptr -> f64
        %118 = llvm.load %18 : !llvm.ptr -> i64
        %119 = llvm.getelementptr %12[%118] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %117, %119 : f64, !llvm.ptr
        %120 = llvm.load %18 : !llvm.ptr -> i64
        %121 = arith.constant 1 : i32
        %123 = arith.extsi %121 : i32 to i64
        %122 = arith.subi %120, %123 : i64
        llvm.store %122, %18 : i64, !llvm.ptr
        cf.br ^bb12
      ^bb14:
      %124 = llvm.load %74 : !llvm.ptr -> f64
      %125 = arith.constant 0 : f32
      %127 = arith.extf %125 : f32 to f64
      %126 = arith.cmpf olt, %124, %127 : f64
      cf.cond_br %126, ^bb21, ^bb22
      ^bb21:
        cf.br ^bb11
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %128 = llvm.load %66 : !llvm.ptr -> i64
      %129 = arith.constant 1 : i32
      %131 = arith.extsi %129 : i32 to i64
      %130 = arith.addi %128, %131 : i64
      llvm.store %130, %66 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %133 = arith.constant 1 : i32
    %134 = arith.extsi %133 : i32 to i64
    %135 = llvm.getelementptr %12[%134] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %132 = llvm.load %135 : !llvm.ptr -> f64
    func.call @free(%0) : (!llvm.ptr) -> ()
    func.call @free(%3) : (!llvm.ptr) -> ()
    func.call @free(%6) : (!llvm.ptr) -> ()
    func.call @free(%9) : (!llvm.ptr) -> ()
    func.call @free(%12) : (!llvm.ptr) -> ()
    func.return %132 : f64
  }
  func.func @main() -> i32 {
    %141 = arith.constant 0.0 : f32
    %142 = arith.extf %141 : f32 to f64
    %143 = llvm.mlir.constant(1 : i64) : i64
    %144 = llvm.alloca %143 x f64 : (i64) -> !llvm.ptr
    llvm.store %142, %144 : f64, !llvm.ptr
    %145 = arith.constant 2 : i32
    %146 = arith.extsi %145 : i32 to i64
    %147 = llvm.mlir.constant(1 : i64) : i64
    %148 = llvm.alloca %147 x i64 : (i64) -> !llvm.ptr
    llvm.store %146, %148 : i64, !llvm.ptr
    cf.br ^bb24
    ^bb24:
    %149 = llvm.load %148 : !llvm.ptr -> i64
    %150 = arith.constant 1000 : i32
    %152 = arith.extsi %150 : i32 to i64
    %151 = arith.cmpi sle, %149, %152 : i64
    cf.cond_br %151, ^bb25, ^bb26
    ^bb25:
      %153 = llvm.load %144 : !llvm.ptr -> f64
      %155 = llvm.load %148 : !llvm.ptr -> i64
      %154 = func.call @R(%155) : (i64) -> f64
      %156 = arith.addf %153, %154 : f64
      llvm.store %156, %144 : f64, !llvm.ptr
      %157 = llvm.load %148 : !llvm.ptr -> i64
      %158 = arith.constant 1 : i32
      %160 = arith.extsi %158 : i32 to i64
      %159 = arith.addi %157, %160 : i64
      llvm.store %159, %148 : i64, !llvm.ptr
      cf.br ^bb24
    ^bb26:
    %161 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %162 = llvm.load %144 : !llvm.ptr -> f64
    %163 = llvm.call @printf(%161, %162) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %164 = arith.constant 0 : i32
    func.return %164 : i32
  }
}