Problem 341

Sum of Golomb self-describing sequence values at cubes 1^3..999999^3.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 341
# Sum of Golomb self-describing sequence values at cubes 1^3..999999^3.

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

function main() -> i32 {
    let limit: i64 = 1000000
    let cubic_limit: i64 = limit * limit * limit
    let cap: i64 = 12000000
    let golomb: ptr<i32> = calloc(cap, 4)
    if golomb == null { return 1 }
    golomb[1] = 1
    let mut products: i64 = 1
    let mut i: i64 = 2
    while products < cubic_limit {
        let gi: i32 = 1 + golomb[i - (golomb[golomb[i - 1]] as i64)]
        golomb[i] = gi
        products = products + (gi as i64) * i
        i = i + 1
    }
    let gmax: i64 = i

    let mut total: i64 = 0
    let mut last_sums: i64 = 0
    let mut sums: i64 = 1
    let mut last_products: i64 = 0
    products = 1
    let mut index: i64 = 1
    i = 1
    while i < limit {
        let n: i64 = i * i * i
        while products < n {
            index = index + 1
            last_sums = sums
            sums = sums + (golomb[index] as i64)
            last_products = products
            products = products + (golomb[index] as i64) * index
        }
        let from_v: i64 = last_products
        let to_v: i64 = products
        let ratio: f64 = ((n - from_v) as f64) / ((to_v - from_v) as f64)
        let low: i64 = last_sums
        let high: i64 = sums
        let offset: i64 = ceil(((high - low) as f64) * ratio) as i64
        total = total + offset + low
        i = i + 1
    }
    printf("%lld\n", total)
    free(golomb)
    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 = 1000000;
    int64_t cubic_limit = ((limit * limit) * limit);
    int64_t cap = 12000000;
    int32_t* golomb = (int32_t*)(calloc(cap, 4));
    if (golomb == NULL) {
        return 1;
    }
    golomb[1] = 1;
    int64_t products = 1;
    int64_t i = 2;
    while (products < cubic_limit) {
        int32_t gi = (1 + golomb[(i - ((int64_t)(golomb[golomb[(i - 1)]])))]);
        golomb[i] = gi;
        products = (products + (((int64_t)(gi)) * i));
        i = (i + 1);
    }
    int64_t gmax = i;
    int64_t total = 0;
    int64_t last_sums = 0;
    int64_t sums = 1;
    int64_t last_products = 0;
    products = 1;
    int64_t index = 1;
    i = 1;
    while (i < limit) {
        int64_t n = ((i * i) * i);
        while (products < n) {
            index = (index + 1);
            last_sums = sums;
            sums = (sums + ((int64_t)(golomb[index])));
            last_products = products;
            products = (products + (((int64_t)(golomb[index])) * index));
        }
        int64_t from_v = last_products;
        int64_t to_v = products;
        double ratio = (((double)((n - from_v))) / ((double)((to_v - from_v))));
        int64_t low = last_sums;
        int64_t high = sums;
        int64_t offset = ((int64_t)(ceil((((double)((high - low))) * ratio))));
        total = ((total + offset) + low);
        i = (i + 1);
    }
    printf("%lld\n", total);
    free(golomb);
    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 private @ceil(f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 1000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.muli %1, %1 : i64
    %3 = arith.muli %2, %1 : i64
    %4 = arith.constant 12000000 : i32
    %5 = arith.extsi %4 : i32 to i64
    %7 = arith.constant 4 : i32
    %8 = arith.extsi %7 : i32 to i64
    %6 = func.call @calloc(%5, %8) : (i64, i64) -> !llvm.ptr
    %9 = llvm.mlir.zero : !llvm.ptr
    %10 = llvm.icmp "eq" %6, %9 : !llvm.ptr
    cf.cond_br %10, ^bb0, ^bb1
    ^bb0:
      %11 = arith.constant 1 : i32
      func.return %11 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %12 = arith.constant 1 : i32
    %13 = arith.constant 1 : i32
    %14 = arith.extsi %13 : i32 to i64
    %15 = llvm.getelementptr %6[%14] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    llvm.store %12, %15 : i32, !llvm.ptr
    %16 = arith.constant 1 : i32
    %17 = arith.extsi %16 : i32 to i64
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x i64 : (i64) -> !llvm.ptr
    llvm.store %17, %19 : i64, !llvm.ptr
    %20 = arith.constant 2 : 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 %19 : !llvm.ptr -> i64
    %25 = arith.cmpi slt, %24, %3 : i64
    cf.cond_br %25, ^bb4, ^bb5
    ^bb4:
      %26 = arith.constant 1 : i32
      %28 = llvm.load %23 : !llvm.ptr -> i64
      %31 = llvm.load %23 : !llvm.ptr -> i64
      %32 = arith.constant 1 : i32
      %34 = arith.extsi %32 : i32 to i64
      %33 = arith.subi %31, %34 : i64
      %35 = llvm.getelementptr %6[%33] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %30 = llvm.load %35 : !llvm.ptr -> i32
      %36 = arith.extsi %30 : i32 to i64
      %37 = llvm.getelementptr %6[%36] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %29 = llvm.load %37 : !llvm.ptr -> i32
      %38 = arith.extsi %29 : i32 to i64
      %39 = arith.subi %28, %38 : i64
      %40 = llvm.getelementptr %6[%39] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %27 = llvm.load %40 : !llvm.ptr -> i32
      %41 = arith.addi %26, %27 : i32
      %42 = llvm.load %23 : !llvm.ptr -> i64
      %43 = llvm.getelementptr %6[%42] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %41, %43 : i32, !llvm.ptr
      %44 = llvm.load %19 : !llvm.ptr -> i64
      %45 = arith.extsi %41 : i32 to i64
      %46 = llvm.load %23 : !llvm.ptr -> i64
      %47 = arith.muli %45, %46 : i64
      %48 = arith.addi %44, %47 : i64
      llvm.store %48, %19 : i64, !llvm.ptr
      %49 = llvm.load %23 : !llvm.ptr -> i64
      %50 = arith.constant 1 : i32
      %52 = arith.extsi %50 : i32 to i64
      %51 = arith.addi %49, %52 : i64
      llvm.store %51, %23 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %53 = llvm.load %23 : !llvm.ptr -> i64
    %54 = arith.constant 0 : i32
    %55 = arith.extsi %54 : i32 to i64
    %56 = llvm.mlir.constant(1 : i64) : i64
    %57 = llvm.alloca %56 x i64 : (i64) -> !llvm.ptr
    llvm.store %55, %57 : i64, !llvm.ptr
    %58 = arith.constant 0 : i32
    %59 = arith.extsi %58 : i32 to i64
    %60 = llvm.mlir.constant(1 : i64) : i64
    %61 = llvm.alloca %60 x i64 : (i64) -> !llvm.ptr
    llvm.store %59, %61 : i64, !llvm.ptr
    %62 = arith.constant 1 : i32
    %63 = arith.extsi %62 : i32 to i64
    %64 = llvm.mlir.constant(1 : i64) : i64
    %65 = llvm.alloca %64 x i64 : (i64) -> !llvm.ptr
    llvm.store %63, %65 : i64, !llvm.ptr
    %66 = arith.constant 0 : i32
    %67 = arith.extsi %66 : i32 to i64
    %68 = llvm.mlir.constant(1 : i64) : i64
    %69 = llvm.alloca %68 x i64 : (i64) -> !llvm.ptr
    llvm.store %67, %69 : i64, !llvm.ptr
    %70 = arith.constant 1 : i32
    %71 = arith.extsi %70 : i32 to i64
    llvm.store %71, %19 : i64, !llvm.ptr
    %72 = arith.constant 1 : i32
    %73 = arith.extsi %72 : i32 to i64
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x i64 : (i64) -> !llvm.ptr
    llvm.store %73, %75 : i64, !llvm.ptr
    %76 = arith.constant 1 : i32
    %77 = arith.extsi %76 : i32 to i64
    llvm.store %77, %23 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %78 = llvm.load %23 : !llvm.ptr -> i64
    %79 = arith.cmpi slt, %78, %1 : i64
    cf.cond_br %79, ^bb7, ^bb8
    ^bb7:
      %80 = llvm.load %23 : !llvm.ptr -> i64
      %81 = llvm.load %23 : !llvm.ptr -> i64
      %82 = arith.muli %80, %81 : i64
      %83 = llvm.load %23 : !llvm.ptr -> i64
      %84 = arith.muli %82, %83 : i64
      cf.br ^bb9
      ^bb9:
      %85 = llvm.load %19 : !llvm.ptr -> i64
      %86 = arith.cmpi slt, %85, %84 : i64
      cf.cond_br %86, ^bb10, ^bb11
      ^bb10:
        %87 = llvm.load %75 : !llvm.ptr -> i64
        %88 = arith.constant 1 : i32
        %90 = arith.extsi %88 : i32 to i64
        %89 = arith.addi %87, %90 : i64
        llvm.store %89, %75 : i64, !llvm.ptr
        %91 = llvm.load %65 : !llvm.ptr -> i64
        llvm.store %91, %61 : i64, !llvm.ptr
        %92 = llvm.load %65 : !llvm.ptr -> i64
        %94 = llvm.load %75 : !llvm.ptr -> i64
        %95 = llvm.getelementptr %6[%94] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %93 = llvm.load %95 : !llvm.ptr -> i32
        %96 = arith.extsi %93 : i32 to i64
        %97 = arith.addi %92, %96 : i64
        llvm.store %97, %65 : i64, !llvm.ptr
        %98 = llvm.load %19 : !llvm.ptr -> i64
        llvm.store %98, %69 : i64, !llvm.ptr
        %99 = llvm.load %19 : !llvm.ptr -> i64
        %101 = llvm.load %75 : !llvm.ptr -> i64
        %102 = llvm.getelementptr %6[%101] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %100 = llvm.load %102 : !llvm.ptr -> i32
        %103 = arith.extsi %100 : i32 to i64
        %104 = llvm.load %75 : !llvm.ptr -> i64
        %105 = arith.muli %103, %104 : i64
        %106 = arith.addi %99, %105 : i64
        llvm.store %106, %19 : i64, !llvm.ptr
        cf.br ^bb9
      ^bb11:
      %107 = llvm.load %69 : !llvm.ptr -> i64
      %108 = llvm.load %19 : !llvm.ptr -> i64
      %109 = arith.subi %84, %107 : i64
      %110 = arith.sitofp %109 : i64 to f64
      %111 = arith.subi %108, %107 : i64
      %112 = arith.sitofp %111 : i64 to f64
      %113 = arith.divf %110, %112 : f64
      %114 = llvm.load %61 : !llvm.ptr -> i64
      %115 = llvm.load %65 : !llvm.ptr -> i64
      %117 = arith.subi %115, %114 : i64
      %118 = arith.sitofp %117 : i64 to f64
      %119 = arith.mulf %118, %113 : f64
      %116 = func.call @ceil(%119) : (f64) -> f64
      %120 = arith.fptosi %116 : f64 to i64
      %121 = llvm.load %57 : !llvm.ptr -> i64
      %122 = arith.addi %121, %120 : i64
      %123 = arith.addi %122, %114 : i64
      llvm.store %123, %57 : i64, !llvm.ptr
      %124 = llvm.load %23 : !llvm.ptr -> i64
      %125 = arith.constant 1 : i32
      %127 = arith.extsi %125 : i32 to i64
      %126 = arith.addi %124, %127 : i64
      llvm.store %126, %23 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %128 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %129 = llvm.load %57 : !llvm.ptr -> i64
    %130 = llvm.call @printf(%128, %129) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%6) : (!llvm.ptr) -> ()
    %132 = arith.constant 0 : i32
    func.return %132 : i32
  }
}