Problem 485

Maximum Number of Divisors — S(10^8, 10^5) via τ sieve + most-recent window max.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 485
# Maximum Number of Divisors — S(10^8, 10^5) via τ sieve + most-recent window max.

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

function main() -> i32 {
    let LIMIT: i64 = 100000000
    let BLOCK: i64 = 100000

    let tau: ptr<i16> = calloc(LIMIT + 1, 2)
    if tau == null { return 1 }

    # O(n log n) divisor count sieve — correct for all n
    let mut i: i64 = 1
    while i <= LIMIT {
        let mut j: i64 = i
        while j <= LIMIT {
            tau[j] = ((tau[j] as i64) + 1) as i16
            j = j + i
        }
        i = i + 1
    }

    # most_recent[d] = latest index with tau == d; mr_len-1 is current window max
    let CAP: i64 = 1024
    let most_recent: ptr<i32> = calloc(CAP, 4)
    if most_recent == null { return 1 }
    let mut mr_len: i64 = 0

    i = 0
    while i < BLOCK {
        let current: i64 = tau[i] as i64
        if current >= mr_len {
            let mut t: i64 = mr_len
            while t <= current {
                most_recent[t] = 0
                t = t + 1
            }
            mr_len = current + 1
        }
        most_recent[current] = i as i32
        i = i + 1
    }

    let mut result: i64 = 0
    i = BLOCK
    while i <= LIMIT {
        let too_far: i64 = i - BLOCK
        while mr_len > 0 {
            if (most_recent[mr_len - 1] as i64) > too_far { break }
            mr_len = mr_len - 1
        }

        let current2: i64 = tau[i] as i64
        if current2 >= mr_len {
            let mut t2: i64 = mr_len
            while t2 <= current2 {
                most_recent[t2] = 0
                t2 = t2 + 1
            }
            mr_len = current2 + 1
        }
        most_recent[current2] = i as i32
        result = result + (mr_len - 1)
        i = i + 1
    }

    printf("%lld\n", result)
    free(most_recent)
    free(tau)
    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 = 100000000;
    int64_t BLOCK = 100000;
    int16_t* tau = (int16_t*)(calloc((LIMIT + 1), 2));
    if (tau == NULL) {
        return 1;
    }
    int64_t i = 1;
    while (i <= LIMIT) {
        int64_t j = i;
        while (j <= LIMIT) {
            tau[j] = ((int16_t)((((int64_t)(tau[j])) + 1)));
            j = (j + i);
        }
        i = (i + 1);
    }
    int64_t CAP = 1024;
    int32_t* most_recent = (int32_t*)(calloc(CAP, 4));
    if (most_recent == NULL) {
        return 1;
    }
    int64_t mr_len = 0;
    i = 0;
    while (i < BLOCK) {
        int64_t current = ((int64_t)(tau[i]));
        if (current >= mr_len) {
            int64_t t = mr_len;
            while (t <= current) {
                most_recent[t] = 0;
                t = (t + 1);
            }
            mr_len = (current + 1);
        }
        most_recent[current] = ((int32_t)(i));
        i = (i + 1);
    }
    int64_t result = 0;
    i = BLOCK;
    while (i <= LIMIT) {
        int64_t too_far = (i - BLOCK);
        while (mr_len > 0) {
            if (((int64_t)(most_recent[(mr_len - 1)])) > too_far) {
                break;
            }
            mr_len = (mr_len - 1);
        }
        int64_t current2 = ((int64_t)(tau[i]));
        if (current2 >= mr_len) {
            int64_t t2 = mr_len;
            while (t2 <= current2) {
                most_recent[t2] = 0;
                t2 = (t2 + 1);
            }
            mr_len = (current2 + 1);
        }
        most_recent[current2] = ((int32_t)(i));
        result = (result + (mr_len - 1));
        i = (i + 1);
    }
    printf("%lld\n", result);
    free(most_recent);
    free(tau);
    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 @main() -> i32 {
    %0 = arith.constant 100000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 100000 : i32
    %3 = arith.extsi %2 : i32 to i64
    %5 = arith.constant 1 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.addi %1, %7 : i64
    %8 = arith.constant 2 : i32
    %9 = arith.extsi %8 : i32 to i64
    %4 = func.call @calloc(%6, %9) : (i64, i64) -> !llvm.ptr
    %10 = llvm.mlir.zero : !llvm.ptr
    %11 = llvm.icmp "eq" %4, %10 : !llvm.ptr
    cf.cond_br %11, ^bb0, ^bb1
    ^bb0:
      %12 = arith.constant 1 : i32
      func.return %12 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %13 = arith.constant 1 : i32
    %14 = arith.extsi %13 : i32 to i64
    %15 = llvm.mlir.constant(1 : i64) : i64
    %16 = llvm.alloca %15 x i64 : (i64) -> !llvm.ptr
    llvm.store %14, %16 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %17 = llvm.load %16 : !llvm.ptr -> i64
    %18 = arith.cmpi sle, %17, %1 : i64
    cf.cond_br %18, ^bb4, ^bb5
    ^bb4:
      %19 = llvm.load %16 : !llvm.ptr -> i64
      %20 = llvm.mlir.constant(1 : i64) : i64
      %21 = llvm.alloca %20 x i64 : (i64) -> !llvm.ptr
      llvm.store %19, %21 : i64, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %22 = llvm.load %21 : !llvm.ptr -> i64
      %23 = arith.cmpi sle, %22, %1 : i64
      cf.cond_br %23, ^bb7, ^bb8
      ^bb7:
        %25 = llvm.load %21 : !llvm.ptr -> i64
        %26 = llvm.getelementptr %4[%25] : (!llvm.ptr, i64) -> !llvm.ptr, i16
        %24 = llvm.load %26 : !llvm.ptr -> i16
        %27 = arith.extsi %24 : i16 to i64
        %28 = arith.constant 1 : i32
        %30 = arith.extsi %28 : i32 to i64
        %29 = arith.addi %27, %30 : i64
        %31 = arith.trunci %29 : i64 to i16
        %32 = llvm.load %21 : !llvm.ptr -> i64
        %33 = llvm.getelementptr %4[%32] : (!llvm.ptr, i64) -> !llvm.ptr, i16
        llvm.store %31, %33 : i16, !llvm.ptr
        %34 = llvm.load %21 : !llvm.ptr -> i64
        %35 = llvm.load %16 : !llvm.ptr -> i64
        %36 = arith.addi %34, %35 : i64
        llvm.store %36, %21 : i64, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %37 = llvm.load %16 : !llvm.ptr -> i64
      %38 = arith.constant 1 : i32
      %40 = arith.extsi %38 : i32 to i64
      %39 = arith.addi %37, %40 : i64
      llvm.store %39, %16 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %41 = arith.constant 1024 : i32
    %42 = arith.extsi %41 : i32 to i64
    %44 = arith.constant 4 : i32
    %45 = arith.extsi %44 : i32 to i64
    %43 = func.call @calloc(%42, %45) : (i64, i64) -> !llvm.ptr
    %46 = llvm.mlir.zero : !llvm.ptr
    %47 = llvm.icmp "eq" %43, %46 : !llvm.ptr
    cf.cond_br %47, ^bb9, ^bb10
    ^bb9:
      %48 = arith.constant 1 : i32
      func.return %48 : i32
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %49 = arith.constant 0 : i32
    %50 = arith.extsi %49 : i32 to i64
    %51 = llvm.mlir.constant(1 : i64) : i64
    %52 = llvm.alloca %51 x i64 : (i64) -> !llvm.ptr
    llvm.store %50, %52 : i64, !llvm.ptr
    %53 = arith.constant 0 : i32
    %54 = arith.extsi %53 : i32 to i64
    llvm.store %54, %16 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %55 = llvm.load %16 : !llvm.ptr -> i64
    %56 = arith.cmpi slt, %55, %3 : i64
    cf.cond_br %56, ^bb13, ^bb14
    ^bb13:
      %58 = llvm.load %16 : !llvm.ptr -> i64
      %59 = llvm.getelementptr %4[%58] : (!llvm.ptr, i64) -> !llvm.ptr, i16
      %57 = llvm.load %59 : !llvm.ptr -> i16
      %60 = arith.extsi %57 : i16 to i64
      %61 = llvm.load %52 : !llvm.ptr -> i64
      %62 = arith.cmpi sge, %60, %61 : i64
      cf.cond_br %62, ^bb15, ^bb16
      ^bb15:
        %63 = llvm.load %52 : !llvm.ptr -> i64
        %64 = llvm.mlir.constant(1 : i64) : i64
        %65 = llvm.alloca %64 x i64 : (i64) -> !llvm.ptr
        llvm.store %63, %65 : i64, !llvm.ptr
        cf.br ^bb18
        ^bb18:
        %66 = llvm.load %65 : !llvm.ptr -> i64
        %67 = arith.cmpi sle, %66, %60 : i64
        cf.cond_br %67, ^bb19, ^bb20
        ^bb19:
          %68 = arith.constant 0 : i32
          %69 = llvm.load %65 : !llvm.ptr -> i64
          %70 = llvm.getelementptr %43[%69] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %68, %70 : i32, !llvm.ptr
          %71 = llvm.load %65 : !llvm.ptr -> i64
          %72 = arith.constant 1 : i32
          %74 = arith.extsi %72 : i32 to i64
          %73 = arith.addi %71, %74 : i64
          llvm.store %73, %65 : i64, !llvm.ptr
          cf.br ^bb18
        ^bb20:
        %75 = arith.constant 1 : i32
        %77 = arith.extsi %75 : i32 to i64
        %76 = arith.addi %60, %77 : i64
        llvm.store %76, %52 : i64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      %78 = llvm.load %16 : !llvm.ptr -> i64
      %79 = arith.trunci %78 : i64 to i32
      %80 = llvm.getelementptr %43[%60] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %79, %80 : i32, !llvm.ptr
      %81 = llvm.load %16 : !llvm.ptr -> i64
      %82 = arith.constant 1 : i32
      %84 = arith.extsi %82 : i32 to i64
      %83 = arith.addi %81, %84 : i64
      llvm.store %83, %16 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %85 = arith.constant 0 : i32
    %86 = arith.extsi %85 : i32 to i64
    %87 = llvm.mlir.constant(1 : i64) : i64
    %88 = llvm.alloca %87 x i64 : (i64) -> !llvm.ptr
    llvm.store %86, %88 : i64, !llvm.ptr
    llvm.store %3, %16 : i64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %89 = llvm.load %16 : !llvm.ptr -> i64
    %90 = arith.cmpi sle, %89, %1 : i64
    cf.cond_br %90, ^bb22, ^bb23
    ^bb22:
      %91 = llvm.load %16 : !llvm.ptr -> i64
      %92 = arith.subi %91, %3 : i64
      cf.br ^bb24
      ^bb24:
      %93 = llvm.load %52 : !llvm.ptr -> i64
      %94 = arith.constant 0 : i32
      %96 = arith.extsi %94 : i32 to i64
      %95 = arith.cmpi sgt, %93, %96 : i64
      cf.cond_br %95, ^bb25, ^bb26
      ^bb25:
        %98 = llvm.load %52 : !llvm.ptr -> i64
        %99 = arith.constant 1 : i32
        %101 = arith.extsi %99 : i32 to i64
        %100 = arith.subi %98, %101 : i64
        %102 = llvm.getelementptr %43[%100] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %97 = llvm.load %102 : !llvm.ptr -> i32
        %103 = arith.extsi %97 : i32 to i64
        %104 = arith.cmpi sgt, %103, %92 : i64
        cf.cond_br %104, ^bb27, ^bb28
        ^bb27:
          cf.br ^bb26
        ^bb28:
          cf.br ^bb29
        ^bb29:
        %105 = llvm.load %52 : !llvm.ptr -> i64
        %106 = arith.constant 1 : i32
        %108 = arith.extsi %106 : i32 to i64
        %107 = arith.subi %105, %108 : i64
        llvm.store %107, %52 : i64, !llvm.ptr
        cf.br ^bb24
      ^bb26:
      %110 = llvm.load %16 : !llvm.ptr -> i64
      %111 = llvm.getelementptr %4[%110] : (!llvm.ptr, i64) -> !llvm.ptr, i16
      %109 = llvm.load %111 : !llvm.ptr -> i16
      %112 = arith.extsi %109 : i16 to i64
      %113 = llvm.load %52 : !llvm.ptr -> i64
      %114 = arith.cmpi sge, %112, %113 : i64
      cf.cond_br %114, ^bb30, ^bb31
      ^bb30:
        %115 = llvm.load %52 : !llvm.ptr -> i64
        %116 = llvm.mlir.constant(1 : i64) : i64
        %117 = llvm.alloca %116 x i64 : (i64) -> !llvm.ptr
        llvm.store %115, %117 : i64, !llvm.ptr
        cf.br ^bb33
        ^bb33:
        %118 = llvm.load %117 : !llvm.ptr -> i64
        %119 = arith.cmpi sle, %118, %112 : i64
        cf.cond_br %119, ^bb34, ^bb35
        ^bb34:
          %120 = arith.constant 0 : i32
          %121 = llvm.load %117 : !llvm.ptr -> i64
          %122 = llvm.getelementptr %43[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %120, %122 : i32, !llvm.ptr
          %123 = llvm.load %117 : !llvm.ptr -> i64
          %124 = arith.constant 1 : i32
          %126 = arith.extsi %124 : i32 to i64
          %125 = arith.addi %123, %126 : i64
          llvm.store %125, %117 : i64, !llvm.ptr
          cf.br ^bb33
        ^bb35:
        %127 = arith.constant 1 : i32
        %129 = arith.extsi %127 : i32 to i64
        %128 = arith.addi %112, %129 : i64
        llvm.store %128, %52 : i64, !llvm.ptr
        cf.br ^bb32
      ^bb31:
        cf.br ^bb32
      ^bb32:
      %130 = llvm.load %16 : !llvm.ptr -> i64
      %131 = arith.trunci %130 : i64 to i32
      %132 = llvm.getelementptr %43[%112] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %131, %132 : i32, !llvm.ptr
      %133 = llvm.load %88 : !llvm.ptr -> i64
      %134 = llvm.load %52 : !llvm.ptr -> i64
      %135 = arith.constant 1 : i32
      %137 = arith.extsi %135 : i32 to i64
      %136 = arith.subi %134, %137 : i64
      %138 = arith.addi %133, %136 : i64
      llvm.store %138, %88 : i64, !llvm.ptr
      %139 = llvm.load %16 : !llvm.ptr -> i64
      %140 = arith.constant 1 : i32
      %142 = arith.extsi %140 : i32 to i64
      %141 = arith.addi %139, %142 : i64
      llvm.store %141, %16 : i64, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %143 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %144 = llvm.load %88 : !llvm.ptr -> i64
    %145 = llvm.call @printf(%143, %144) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%43) : (!llvm.ptr) -> ()
    func.call @free(%4) : (!llvm.ptr) -> ()
    %148 = arith.constant 0 : i32
    func.return %148 : i32
  }
}