Problem 232

The Race: optimal strategy win probability.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 232
# The Race: optimal strategy win probability.

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

let mut CACHE: ptr<f64> = null
let mut MAXS: i32 = 0

function two_wins(need_one: i32, need_two: i32) -> f64 {
    if need_two == 0 { return 1.0 }
    if need_one == 0 { return 0.0 }
    let idx: i64 = ((need_one - 1) as i64) * (MAXS as i64) + ((need_two - 1) as i64)
    if CACHE[idx] >= 0.0 { return CACHE[idx] }
    let mut best: f64 = 0.0
    let mut bet: i32 = 1
    while true {
        let win2: f64 = 0.5 / (bet as f64)
        let lose2: f64 = 1.0 - win2
        let mut next_two: i32 = need_two - bet
        if need_two < bet { next_two = 0 }
        let mut current: f64 = 0.5 * win2 * two_wins(need_one - 1, next_two)
        current = current + 0.5 * win2 * two_wins(need_one, next_two)
        current = current + 0.5 * lose2 * two_wins(need_one - 1, need_two)
        current = current / (1.0 - 0.5 * lose2)
        if best < current { best = current }
        if next_two == 0 { break }
        bet = bet * 2
    }
    CACHE[idx] = best
    return best
}

function main() -> i32 {
    MAXS = 100
    CACHE = calloc((MAXS as i64) * (MAXS as i64), 8)
    if CACHE == null { return 1 }
    let mut i: i64 = 0
    let N: i64 = (MAXS as i64) * (MAXS as i64)
    while i < N {
        CACHE[i] = 0.0 - 1.0
        i = i + 1
    }
    let result: f64 = 0.5 * two_wins(MAXS - 1, MAXS) + 0.5 * two_wins(MAXS, MAXS)
    printf("%.8f\n", result)
    free(CACHE)
    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 two_wins_i32_i32(int32_t need_one, int32_t need_two);
int32_t main(void);

/* Module statics */
static double* CACHE = NULL;
static int32_t MAXS = 0;



double two_wins_i32_i32(int32_t need_one, int32_t need_two) {
    if (need_two == 0) {
        return 1.0;
    }
    if (need_one == 0) {
        return 0.0;
    }
    int64_t idx = ((((int64_t)((need_one - 1))) * ((int64_t)(MAXS))) + ((int64_t)((need_two - 1))));
    if (CACHE[idx] >= 0.0) {
        return CACHE[idx];
    }
    double best = 0.0;
    int32_t bet = 1;
    while (1) {
        double win2 = (0.5 / ((double)(bet)));
        double lose2 = (1.0 - win2);
        int32_t next_two = (need_two - bet);
        if (need_two < bet) {
            next_two = 0;
        }
        double current = ((0.5 * win2) * two_wins_i32_i32((need_one - 1), next_two));
        current = (current + ((0.5 * win2) * two_wins_i32_i32(need_one, next_two)));
        current = (current + ((0.5 * lose2) * two_wins_i32_i32((need_one - 1), need_two)));
        current = (current / (1.0 - (0.5 * lose2)));
        if (best < current) {
            best = current;
        }
        if (next_two == 0) {
            break;
        }
        bet = (bet * 2);
    }
    CACHE[idx] = best;
    return best;
}

int32_t main(void) {
    MAXS = 100;
    CACHE = calloc((((int64_t)(MAXS)) * ((int64_t)(MAXS))), 8);
    if (CACHE == NULL) {
        return 1;
    }
    int64_t i = 0;
    int64_t N = (((int64_t)(MAXS)) * ((int64_t)(MAXS)));
    while (i < N) {
        CACHE[i] = (0.0 - 1.0);
        i = (i + 1);
    }
    double result = ((0.5 * two_wins_i32_i32((MAXS - 1), MAXS)) + (0.5 * two_wins_i32_i32(MAXS, MAXS)));
    printf("%.8f\n", result);
    free(CACHE);
    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) -> ()
  // Module static: CACHE
  llvm.mlir.global internal @CACHE() {addr_space = 0 : i32} : !llvm.ptr {
    %0 = llvm.mlir.zero : !llvm.ptr
    llvm.return %0 : !llvm.ptr
  }
  // Module static: MAXS
  llvm.mlir.global internal @MAXS(0 : i32) : i32
  func.func @two_wins(%arg0: i32, %arg1: i32) -> f64 {
    %1 = arith.constant 0 : i32
    %2 = arith.cmpi eq, %arg1, %1 : i32
    cf.cond_br %2, ^bb0, ^bb1
    ^bb0:
      %3 = arith.constant 1.0 : f32
      %4 = arith.extf %3 : f32 to f64
      func.return %4 : f64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %5 = arith.constant 0 : i32
    %6 = arith.cmpi eq, %arg0, %5 : i32
    cf.cond_br %6, ^bb3, ^bb4
    ^bb3:
      %7 = arith.constant 0.0 : f32
      %8 = arith.extf %7 : f32 to f64
      func.return %8 : f64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %9 = arith.constant 1 : i32
    %10 = arith.subi %arg0, %9 : i32
    %11 = arith.extsi %10 : i32 to i64
    %12 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %13 = llvm.load %12 : !llvm.ptr -> i32
    %14 = arith.extsi %13 : i32 to i64
    %15 = arith.muli %11, %14 : i64
    %16 = arith.constant 1 : i32
    %17 = arith.subi %arg1, %16 : i32
    %18 = arith.extsi %17 : i32 to i64
    %19 = arith.addi %15, %18 : i64
    %21 = llvm.mlir.addressof @CACHE : !llvm.ptr
    %22 = llvm.load %21 : !llvm.ptr -> !llvm.ptr
    %23 = llvm.getelementptr %22[%19] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %20 = llvm.load %23 : !llvm.ptr -> f64
    %24 = arith.constant 0.0 : f32
    %26 = arith.extf %24 : f32 to f64
    %25 = arith.cmpf oge, %20, %26 : f64
    cf.cond_br %25, ^bb6, ^bb7
    ^bb6:
      %28 = llvm.mlir.addressof @CACHE : !llvm.ptr
      %29 = llvm.load %28 : !llvm.ptr -> !llvm.ptr
      %30 = llvm.getelementptr %29[%19] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %27 = llvm.load %30 : !llvm.ptr -> f64
      func.return %27 : f64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %31 = arith.constant 0.0 : f32
    %32 = arith.extf %31 : f32 to f64
    %33 = llvm.mlir.constant(1 : i64) : i64
    %34 = llvm.alloca %33 x f64 : (i64) -> !llvm.ptr
    llvm.store %32, %34 : f64, !llvm.ptr
    %35 = arith.constant 1 : i32
    %36 = llvm.mlir.constant(1 : i64) : i64
    %37 = llvm.alloca %36 x i32 : (i64) -> !llvm.ptr
    llvm.store %35, %37 : i32, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %38 = arith.constant 1 : i1
    cf.cond_br %38, ^bb10, ^bb11
    ^bb10:
      %39 = arith.constant 0.5 : f32
      %40 = llvm.load %37 : !llvm.ptr -> i32
      %41 = arith.sitofp %40 : i32 to f64
      %43 = arith.extf %39 : f32 to f64
      %42 = arith.divf %43, %41 : f64
      %44 = arith.constant 1.0 : f32
      %46 = arith.extf %44 : f32 to f64
      %45 = arith.subf %46, %42 : f64
      %47 = llvm.load %37 : !llvm.ptr -> i32
      %48 = arith.subi %arg1, %47 : i32
      %49 = llvm.mlir.constant(1 : i64) : i64
      %50 = llvm.alloca %49 x i32 : (i64) -> !llvm.ptr
      llvm.store %48, %50 : i32, !llvm.ptr
      %51 = llvm.load %37 : !llvm.ptr -> i32
      %52 = arith.cmpi slt, %arg1, %51 : i32
      cf.cond_br %52, ^bb12, ^bb13
      ^bb12:
        %53 = arith.constant 0 : i32
        llvm.store %53, %50 : i32, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %54 = arith.constant 0.5 : f32
      %56 = arith.extf %54 : f32 to f64
      %55 = arith.mulf %56, %42 : f64
      %58 = arith.constant 1 : i32
      %59 = arith.subi %arg0, %58 : i32
      %60 = llvm.load %50 : !llvm.ptr -> i32
      %57 = func.call @two_wins(%59, %60) : (i32, i32) -> f64
      %61 = arith.mulf %55, %57 : f64
      %62 = llvm.mlir.constant(1 : i64) : i64
      %63 = llvm.alloca %62 x f64 : (i64) -> !llvm.ptr
      llvm.store %61, %63 : f64, !llvm.ptr
      %64 = llvm.load %63 : !llvm.ptr -> f64
      %65 = arith.constant 0.5 : f32
      %67 = arith.extf %65 : f32 to f64
      %66 = arith.mulf %67, %42 : f64
      %69 = llvm.load %50 : !llvm.ptr -> i32
      %68 = func.call @two_wins(%arg0, %69) : (i32, i32) -> f64
      %70 = arith.mulf %66, %68 : f64
      %71 = arith.addf %64, %70 : f64
      llvm.store %71, %63 : f64, !llvm.ptr
      %72 = llvm.load %63 : !llvm.ptr -> f64
      %73 = arith.constant 0.5 : f32
      %75 = arith.extf %73 : f32 to f64
      %74 = arith.mulf %75, %45 : f64
      %77 = arith.constant 1 : i32
      %78 = arith.subi %arg0, %77 : i32
      %76 = func.call @two_wins(%78, %arg1) : (i32, i32) -> f64
      %79 = arith.mulf %74, %76 : f64
      %80 = arith.addf %72, %79 : f64
      llvm.store %80, %63 : f64, !llvm.ptr
      %81 = llvm.load %63 : !llvm.ptr -> f64
      %82 = arith.constant 1.0 : f32
      %83 = arith.constant 0.5 : f32
      %85 = arith.extf %83 : f32 to f64
      %84 = arith.mulf %85, %45 : f64
      %87 = arith.extf %82 : f32 to f64
      %86 = arith.subf %87, %84 : f64
      %88 = arith.divf %81, %86 : f64
      llvm.store %88, %63 : f64, !llvm.ptr
      %89 = llvm.load %34 : !llvm.ptr -> f64
      %90 = llvm.load %63 : !llvm.ptr -> f64
      %91 = arith.cmpf olt, %89, %90 : f64
      cf.cond_br %91, ^bb15, ^bb16
      ^bb15:
        %92 = llvm.load %63 : !llvm.ptr -> f64
        llvm.store %92, %34 : f64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      %93 = llvm.load %50 : !llvm.ptr -> i32
      %94 = arith.constant 0 : i32
      %95 = arith.cmpi eq, %93, %94 : i32
      cf.cond_br %95, ^bb18, ^bb19
      ^bb18:
        cf.br ^bb11
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %96 = llvm.load %37 : !llvm.ptr -> i32
      %97 = arith.constant 2 : i32
      %98 = arith.muli %96, %97 : i32
      llvm.store %98, %37 : i32, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %99 = llvm.load %34 : !llvm.ptr -> f64
    %100 = llvm.mlir.addressof @CACHE : !llvm.ptr
    %101 = llvm.load %100 : !llvm.ptr -> !llvm.ptr
    %102 = llvm.getelementptr %101[%19] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %99, %102 : f64, !llvm.ptr
    %103 = llvm.load %34 : !llvm.ptr -> f64
    func.return %103 : f64
  }
  func.func @main() -> i32 {
    %104 = arith.constant 100 : i32
    %105 = llvm.mlir.addressof @MAXS : !llvm.ptr
    llvm.store %104, %105 : i32, !llvm.ptr
    %107 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %108 = llvm.load %107 : !llvm.ptr -> i32
    %109 = arith.extsi %108 : i32 to i64
    %110 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %111 = llvm.load %110 : !llvm.ptr -> i32
    %112 = arith.extsi %111 : i32 to i64
    %113 = arith.muli %109, %112 : i64
    %114 = arith.constant 8 : i32
    %115 = arith.extsi %114 : i32 to i64
    %106 = func.call @calloc(%113, %115) : (i64, i64) -> !llvm.ptr
    %116 = llvm.mlir.addressof @CACHE : !llvm.ptr
    llvm.store %106, %116 : !llvm.ptr, !llvm.ptr
    %117 = llvm.mlir.addressof @CACHE : !llvm.ptr
    %118 = llvm.load %117 : !llvm.ptr -> !llvm.ptr
    %119 = llvm.mlir.zero : !llvm.ptr
    %120 = llvm.icmp "eq" %118, %119 : !llvm.ptr
    cf.cond_br %120, ^bb21, ^bb22
    ^bb21:
      %121 = arith.constant 1 : i32
      func.return %121 : i32
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %122 = arith.constant 0 : i32
    %123 = arith.extsi %122 : i32 to i64
    %124 = llvm.mlir.constant(1 : i64) : i64
    %125 = llvm.alloca %124 x i64 : (i64) -> !llvm.ptr
    llvm.store %123, %125 : i64, !llvm.ptr
    %126 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %127 = llvm.load %126 : !llvm.ptr -> i32
    %128 = arith.extsi %127 : i32 to i64
    %129 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %130 = llvm.load %129 : !llvm.ptr -> i32
    %131 = arith.extsi %130 : i32 to i64
    %132 = arith.muli %128, %131 : i64
    cf.br ^bb24
    ^bb24:
    %133 = llvm.load %125 : !llvm.ptr -> i64
    %134 = arith.cmpi slt, %133, %132 : i64
    cf.cond_br %134, ^bb25, ^bb26
    ^bb25:
      %135 = arith.constant 0.0 : f32
      %136 = arith.constant 1.0 : f32
      %137 = arith.subf %135, %136 : f32
      %138 = llvm.mlir.addressof @CACHE : !llvm.ptr
      %139 = llvm.load %138 : !llvm.ptr -> !llvm.ptr
      %140 = llvm.load %125 : !llvm.ptr -> i64
      %141 = arith.extf %137 : f32 to f64
      %142 = llvm.getelementptr %139[%140] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %141, %142 : f64, !llvm.ptr
      %143 = llvm.load %125 : !llvm.ptr -> i64
      %144 = arith.constant 1 : i32
      %146 = arith.extsi %144 : i32 to i64
      %145 = arith.addi %143, %146 : i64
      llvm.store %145, %125 : i64, !llvm.ptr
      cf.br ^bb24
    ^bb26:
    %147 = arith.constant 0.5 : f32
    %149 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %150 = llvm.load %149 : !llvm.ptr -> i32
    %151 = arith.constant 1 : i32
    %152 = arith.subi %150, %151 : i32
    %153 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %154 = llvm.load %153 : !llvm.ptr -> i32
    %148 = func.call @two_wins(%152, %154) : (i32, i32) -> f64
    %156 = arith.extf %147 : f32 to f64
    %155 = arith.mulf %156, %148 : f64
    %157 = arith.constant 0.5 : f32
    %159 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %160 = llvm.load %159 : !llvm.ptr -> i32
    %161 = llvm.mlir.addressof @MAXS : !llvm.ptr
    %162 = llvm.load %161 : !llvm.ptr -> i32
    %158 = func.call @two_wins(%160, %162) : (i32, i32) -> f64
    %164 = arith.extf %157 : f32 to f64
    %163 = arith.mulf %164, %158 : f64
    %165 = arith.addf %155, %163 : f64
    %166 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %167 = llvm.call @printf(%166, %165) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %169 = llvm.mlir.addressof @CACHE : !llvm.ptr
    %170 = llvm.load %169 : !llvm.ptr -> !llvm.ptr
    func.call @free(%170) : (!llvm.ptr) -> ()
    %171 = arith.constant 0 : i32
    func.return %171 : i32
  }
}