Problem 503

Compromise or Persist — F(10^6) via backward rank-threshold DP.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 503
# Compromise or Persist — F(10^6) via backward rank-threshold DP.

function main() -> i32 {
    let N: i32 = 1000000
    let mut x_next: f64 = 0.5
    let mut t: i32 = N - 1
    while t >= 1 {
        let tp1: f64 = (t + 1) as f64
        let y: f64 = x_next
        let mut K: i32 = (y * tp1) as i32
        if K > t { K = t }
        while K > 0 && ((K as f64) / tp1) > y + 1.0e-15 {
            K = K - 1
        }
        while K < t && (((K + 1) as f64) / tp1) <= y - 1.0e-15 {
            K = K + 1
        }
        let sumk: f64 = (K as f64) * ((K + 1) as f64) / 2.0
        let x_t: f64 = (sumk / tp1 + ((t - K) as f64) * y) / (t as f64)
        x_next = x_t
        t = t - 1
    }
    let ans: f64 = x_next * ((N + 1) as f64)
    printf("%.10f\n", ans)
    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 N = 1000000;
    double x_next = 0.5;
    int32_t t = (N - 1);
    while (t >= 1) {
        double tp1 = ((double)((t + 1)));
        double y = x_next;
        int32_t K = ((int32_t)((y * tp1)));
        if (K > t) {
            K = t;
        }
        while ((K > 0 && (((double)(K)) / tp1) > (y + 1.0e-15))) {
            K = (K - 1);
        }
        while ((K < t && (((double)((K + 1))) / tp1) <= (y - 1.0e-15))) {
            K = (K + 1);
        }
        double sumk = ((((double)(K)) * ((double)((K + 1)))) / 2.0);
        double x_t = (((sumk / tp1) + (((double)((t - K))) * y)) / ((double)(t)));
        x_next = x_t;
        t = (t - 1);
    }
    double ans = (x_next * ((double)((N + 1))));
    printf("%.10f\n", ans);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func @main() -> i32 {
    %0 = arith.constant 1000000 : i32
    %1 = arith.constant 0.5 : f32
    %2 = arith.extf %1 : f32 to f64
    %3 = llvm.mlir.constant(1 : i64) : i64
    %4 = llvm.alloca %3 x f64 : (i64) -> !llvm.ptr
    llvm.store %2, %4 : f64, !llvm.ptr
    %5 = arith.constant 1 : i32
    %6 = arith.subi %0, %5 : i32
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i32 : (i64) -> !llvm.ptr
    llvm.store %6, %8 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %9 = llvm.load %8 : !llvm.ptr -> i32
    %10 = arith.constant 1 : i32
    %11 = arith.cmpi sge, %9, %10 : i32
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %12 = llvm.load %8 : !llvm.ptr -> i32
      %13 = arith.constant 1 : i32
      %14 = arith.addi %12, %13 : i32
      %15 = arith.sitofp %14 : i32 to f64
      %16 = llvm.load %4 : !llvm.ptr -> f64
      %17 = arith.mulf %16, %15 : f64
      %18 = arith.fptosi %17 : f64 to i32
      %19 = llvm.mlir.constant(1 : i64) : i64
      %20 = llvm.alloca %19 x i32 : (i64) -> !llvm.ptr
      llvm.store %18, %20 : i32, !llvm.ptr
      %21 = llvm.load %20 : !llvm.ptr -> i32
      %22 = llvm.load %8 : !llvm.ptr -> i32
      %23 = arith.cmpi sgt, %21, %22 : i32
      cf.cond_br %23, ^bb3, ^bb4
      ^bb3:
        %24 = llvm.load %8 : !llvm.ptr -> i32
        llvm.store %24, %20 : i32, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      cf.br ^bb6
      ^bb6:
      %25 = llvm.load %20 : !llvm.ptr -> i32
      %26 = arith.constant 0 : i32
      %27 = arith.cmpi sgt, %25, %26 : i32
      %28 = scf.if %27 -> (i1) {
        %29 = llvm.load %20 : !llvm.ptr -> i32
        %30 = arith.sitofp %29 : i32 to f64
        %31 = arith.divf %30, %15 : f64
        %32 = arith.constant 0 : f32
        %34 = arith.extf %32 : f32 to f64
        %33 = arith.addf %16, %34 : f64
        %35 = arith.cmpf ogt, %31, %33 : f64
        scf.yield %35 : i1
      } else {
        %36 = arith.constant false
        scf.yield %36 : i1
      }
      cf.cond_br %28, ^bb7, ^bb8
      ^bb7:
        %37 = llvm.load %20 : !llvm.ptr -> i32
        %38 = arith.constant 1 : i32
        %39 = arith.subi %37, %38 : i32
        llvm.store %39, %20 : i32, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      cf.br ^bb9
      ^bb9:
      %40 = llvm.load %20 : !llvm.ptr -> i32
      %41 = llvm.load %8 : !llvm.ptr -> i32
      %42 = arith.cmpi slt, %40, %41 : i32
      %43 = scf.if %42 -> (i1) {
        %44 = llvm.load %20 : !llvm.ptr -> i32
        %45 = arith.constant 1 : i32
        %46 = arith.addi %44, %45 : i32
        %47 = arith.sitofp %46 : i32 to f64
        %48 = arith.divf %47, %15 : f64
        %49 = arith.constant 0 : f32
        %51 = arith.extf %49 : f32 to f64
        %50 = arith.subf %16, %51 : f64
        %52 = arith.cmpf ole, %48, %50 : f64
        scf.yield %52 : i1
      } else {
        %53 = arith.constant false
        scf.yield %53 : i1
      }
      cf.cond_br %43, ^bb10, ^bb11
      ^bb10:
        %54 = llvm.load %20 : !llvm.ptr -> i32
        %55 = arith.constant 1 : i32
        %56 = arith.addi %54, %55 : i32
        llvm.store %56, %20 : i32, !llvm.ptr
        cf.br ^bb9
      ^bb11:
      %57 = llvm.load %20 : !llvm.ptr -> i32
      %58 = arith.sitofp %57 : i32 to f64
      %59 = llvm.load %20 : !llvm.ptr -> i32
      %60 = arith.constant 1 : i32
      %61 = arith.addi %59, %60 : i32
      %62 = arith.sitofp %61 : i32 to f64
      %63 = arith.mulf %58, %62 : f64
      %64 = arith.constant 2.0 : f32
      %66 = arith.extf %64 : f32 to f64
      %65 = arith.divf %63, %66 : f64
      %67 = arith.divf %65, %15 : f64
      %68 = llvm.load %8 : !llvm.ptr -> i32
      %69 = llvm.load %20 : !llvm.ptr -> i32
      %70 = arith.subi %68, %69 : i32
      %71 = arith.sitofp %70 : i32 to f64
      %72 = arith.mulf %71, %16 : f64
      %73 = arith.addf %67, %72 : f64
      %74 = llvm.load %8 : !llvm.ptr -> i32
      %75 = arith.sitofp %74 : i32 to f64
      %76 = arith.divf %73, %75 : f64
      llvm.store %76, %4 : f64, !llvm.ptr
      %77 = llvm.load %8 : !llvm.ptr -> i32
      %78 = arith.constant 1 : i32
      %79 = arith.subi %77, %78 : i32
      llvm.store %79, %8 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %80 = llvm.load %4 : !llvm.ptr -> f64
    %81 = arith.constant 1 : i32
    %82 = arith.addi %0, %81 : i32
    %83 = arith.sitofp %82 : i32 to f64
    %84 = arith.mulf %80, %83 : f64
    %85 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %86 = llvm.call @printf(%85, %84) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %87 = arith.constant 0 : i32
    func.return %87 : i32
  }
}