Problem 512

Sums of Totients of Powers — odd-totient prefix G(5e8).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 512
# Sums of Totients of Powers — odd-totient prefix G(5e8).

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

const CAP: i64 = 2097152
const TARGET: i64 = 500000000

function odd_part_sum(n0: i64) -> i64 {
    let mut n: i64 = n0
    let mut total: i64 = 0
    while n > 0 {
        let odd_count: i64 = (n + 1) / 2
        total = total + odd_count * odd_count
        n = n / 2
    }
    return total
}

function hslot(key: i64, keys: ptr<i64>, used: ptr<i8>) -> i64 {
    let mut h: i64 = key % CAP
    if h < 0 { h = h + CAP }
    while used[h] == 1 && keys[h] != key {
        h = h + 1
        if h == CAP { h = 0 }
    }
    return h
}

function odd_totient(n: i64, keys: ptr<i64>, vals: ptr<i64>, used: ptr<i8>) -> i64 {
    if n <= 0 { return 0 }
    let s: i64 = hslot(n, keys, used)
    if used[s] == 1 { return vals[s] }
    let mut total: i64 = odd_part_sum(n)
    let mut lo: i64 = 2
    while lo <= n {
        let q: i64 = n / lo
        let hi: i64 = n / q
        total = total - (hi - lo + 1) * odd_totient(q, keys, vals, used)
        lo = hi + 1
    }
    used[s] = 1
    keys[s] = n
    vals[s] = total
    return total
}

function main() -> i32 {
    let keys: ptr<i64> = calloc(CAP, 8)
    let vals: ptr<i64> = calloc(CAP, 8)
    let used: ptr<i8> = calloc(CAP, 1)
    if keys == null || vals == null || used == null { return 1 }
    let ans: i64 = odd_totient(TARGET, keys, vals, used)
    printf("%lld\n", ans)
    free(keys); free(vals); free(used)
    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; }

int64_t odd_part_sum_i64(int64_t n0);
int64_t hslot_i64_ptr_i64_ptr_i8(int64_t key, int64_t* keys, int8_t* used);
int64_t odd_totient_i64_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* keys, int64_t* vals, int8_t* used);
int32_t main(void);

static const int64_t CAP = 2097152;
static const int64_t TARGET = 500000000;



int64_t odd_part_sum_i64(int64_t n0) {
    int64_t n = n0;
    int64_t total = 0;
    while (n > 0) {
        int64_t odd_count = FLOW_CHECKED_DIV(((n + 1)), (2));
        total = (total + (odd_count * odd_count));
        n = FLOW_CHECKED_DIV((n), (2));
    }
    return total;
}

int64_t hslot_i64_ptr_i64_ptr_i8(int64_t key, int64_t* keys, int8_t* used) {
    int64_t h = FLOW_CHECKED_MOD((key), (CAP));
    if (h < 0) {
        h = (h + CAP);
    }
    while ((used[h] == 1 && keys[h] != key)) {
        h = (h + 1);
        if (h == CAP) {
            h = 0;
        }
    }
    return h;
}

int64_t odd_totient_i64_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* keys, int64_t* vals, int8_t* used) {
    if (n <= 0) {
        return 0;
    }
    int64_t s = hslot_i64_ptr_i64_ptr_i8(n, keys, used);
    if (used[s] == 1) {
        return vals[s];
    }
    int64_t total = odd_part_sum_i64(n);
    int64_t lo = 2;
    while (lo <= n) {
        int64_t q = FLOW_CHECKED_DIV((n), (lo));
        int64_t hi = FLOW_CHECKED_DIV((n), (q));
        total = (total - (((hi - lo) + 1) * odd_totient_i64_ptr_i64_ptr_i64_ptr_i8(q, keys, vals, used)));
        lo = (hi + 1);
    }
    used[s] = 1;
    keys[s] = n;
    vals[s] = total;
    return total;
}

int32_t main(void) {
    int64_t* keys = (int64_t*)(calloc(CAP, 8));
    int64_t* vals = (int64_t*)(calloc(CAP, 8));
    int8_t* used = (int8_t*)(calloc(CAP, 1));
    if (((keys == NULL || vals == NULL) || used == NULL)) {
        return 1;
    }
    int64_t ans = odd_totient_i64_ptr_i64_ptr_i64_ptr_i8(TARGET, keys, vals, used);
    printf("%lld\n", ans);
    free(keys);
    free(vals);
    free(used);
    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) -> ()
  // Constant: CAP
  llvm.mlir.global internal constant @CAP(2097152 : i64) : i64
  // Constant: TARGET
  llvm.mlir.global internal constant @TARGET(500000000 : i64) : i64
  func.func @odd_part_sum(%arg0: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %1 : i64, !llvm.ptr
    %2 = arith.constant 0 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %3, %5 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %6 = llvm.load %1 : !llvm.ptr -> i64
    %7 = arith.constant 0 : i32
    %9 = arith.extsi %7 : i32 to i64
    %8 = arith.cmpi sgt, %6, %9 : i64
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %10 = llvm.load %1 : !llvm.ptr -> i64
      %11 = arith.constant 1 : i32
      %13 = arith.extsi %11 : i32 to i64
      %12 = arith.addi %10, %13 : i64
      %14 = arith.constant 2 : i32
      %16 = arith.extsi %14 : i32 to i64
      %15 = arith.divsi %12, %16 : i64
      %17 = llvm.load %5 : !llvm.ptr -> i64
      %18 = arith.muli %15, %15 : i64
      %19 = arith.addi %17, %18 : i64
      llvm.store %19, %5 : i64, !llvm.ptr
      %20 = llvm.load %1 : !llvm.ptr -> i64
      %21 = arith.constant 2 : i32
      %23 = arith.extsi %21 : i32 to i64
      %22 = arith.divsi %20, %23 : i64
      llvm.store %22, %1 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %24 = llvm.load %5 : !llvm.ptr -> i64
    func.return %24 : i64
  }
  func.func @hslot(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr) -> i64 {
    %25 = llvm.mlir.addressof @CAP : !llvm.ptr
    %26 = llvm.load %25 : !llvm.ptr -> i64
    %27 = arith.remsi %arg0, %26 : i64
    %28 = llvm.mlir.constant(1 : i64) : i64
    %29 = llvm.alloca %28 x i64 : (i64) -> !llvm.ptr
    llvm.store %27, %29 : i64, !llvm.ptr
    %30 = llvm.load %29 : !llvm.ptr -> i64
    %31 = arith.constant 0 : i32
    %33 = arith.extsi %31 : i32 to i64
    %32 = arith.cmpi slt, %30, %33 : i64
    cf.cond_br %32, ^bb3, ^bb4
    ^bb3:
      %34 = llvm.load %29 : !llvm.ptr -> i64
      %35 = llvm.mlir.addressof @CAP : !llvm.ptr
      %36 = llvm.load %35 : !llvm.ptr -> i64
      %37 = arith.addi %34, %36 : i64
      llvm.store %37, %29 : i64, !llvm.ptr
      cf.br ^bb5
    ^bb4:
      cf.br ^bb5
    ^bb5:
    cf.br ^bb6
    ^bb6:
    %39 = llvm.load %29 : !llvm.ptr -> i64
    %40 = llvm.getelementptr %arg2[%39] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %38 = llvm.load %40 : !llvm.ptr -> i8
    %41 = arith.constant 1 : i32
    %43 = arith.extsi %38 : i8 to i32
    %42 = arith.cmpi eq, %43, %41 : i32
    %44 = scf.if %42 -> (i1) {
      %46 = llvm.load %29 : !llvm.ptr -> i64
      %47 = llvm.getelementptr %arg1[%46] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %45 = llvm.load %47 : !llvm.ptr -> i64
      %48 = arith.cmpi ne, %45, %arg0 : i64
      scf.yield %48 : i1
    } else {
      %49 = arith.constant false
      scf.yield %49 : i1
    }
    cf.cond_br %44, ^bb7, ^bb8
    ^bb7:
      %50 = llvm.load %29 : !llvm.ptr -> i64
      %51 = arith.constant 1 : i32
      %53 = arith.extsi %51 : i32 to i64
      %52 = arith.addi %50, %53 : i64
      llvm.store %52, %29 : i64, !llvm.ptr
      %54 = llvm.load %29 : !llvm.ptr -> i64
      %55 = llvm.mlir.addressof @CAP : !llvm.ptr
      %56 = llvm.load %55 : !llvm.ptr -> i64
      %57 = arith.cmpi eq, %54, %56 : i64
      cf.cond_br %57, ^bb9, ^bb10
      ^bb9:
        %58 = arith.constant 0 : i32
        %59 = arith.extsi %58 : i32 to i64
        llvm.store %59, %29 : i64, !llvm.ptr
        cf.br ^bb11
      ^bb10:
        cf.br ^bb11
      ^bb11:
      cf.br ^bb6
    ^bb8:
    %60 = llvm.load %29 : !llvm.ptr -> i64
    func.return %60 : i64
  }
  func.func @odd_totient(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr, %arg3: !llvm.ptr) -> i64 {
    %61 = arith.constant 0 : i32
    %63 = arith.extsi %61 : i32 to i64
    %62 = arith.cmpi sle, %arg0, %63 : i64
    cf.cond_br %62, ^bb12, ^bb13
    ^bb12:
      %64 = arith.constant 0 : i32
      %65 = arith.extsi %64 : i32 to i64
      func.return %65 : i64
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %66 = func.call @hslot(%arg0, %arg1, %arg3) : (i64, !llvm.ptr, !llvm.ptr) -> i64
    %68 = llvm.getelementptr %arg3[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %67 = llvm.load %68 : !llvm.ptr -> i8
    %69 = arith.constant 1 : i32
    %71 = arith.extsi %67 : i8 to i32
    %70 = arith.cmpi eq, %71, %69 : i32
    cf.cond_br %70, ^bb15, ^bb16
    ^bb15:
      %73 = llvm.getelementptr %arg2[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %72 = llvm.load %73 : !llvm.ptr -> i64
      func.return %72 : i64
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %74 = func.call @odd_part_sum(%arg0) : (i64) -> i64
    %75 = llvm.mlir.constant(1 : i64) : i64
    %76 = llvm.alloca %75 x i64 : (i64) -> !llvm.ptr
    llvm.store %74, %76 : i64, !llvm.ptr
    %77 = arith.constant 2 : i32
    %78 = arith.extsi %77 : i32 to i64
    %79 = llvm.mlir.constant(1 : i64) : i64
    %80 = llvm.alloca %79 x i64 : (i64) -> !llvm.ptr
    llvm.store %78, %80 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %81 = llvm.load %80 : !llvm.ptr -> i64
    %82 = arith.cmpi sle, %81, %arg0 : i64
    cf.cond_br %82, ^bb19, ^bb20
    ^bb19:
      %83 = llvm.load %80 : !llvm.ptr -> i64
      %84 = arith.divsi %arg0, %83 : i64
      %85 = arith.divsi %arg0, %84 : i64
      %86 = llvm.load %76 : !llvm.ptr -> i64
      %87 = llvm.load %80 : !llvm.ptr -> i64
      %88 = arith.subi %85, %87 : i64
      %89 = arith.constant 1 : i32
      %91 = arith.extsi %89 : i32 to i64
      %90 = arith.addi %88, %91 : i64
      %92 = func.call @odd_totient(%84, %arg1, %arg2, %arg3) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
      %93 = arith.muli %90, %92 : i64
      %94 = arith.subi %86, %93 : i64
      llvm.store %94, %76 : i64, !llvm.ptr
      %95 = arith.constant 1 : i32
      %97 = arith.extsi %95 : i32 to i64
      %96 = arith.addi %85, %97 : i64
      llvm.store %96, %80 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %98 = arith.constant 1 : i32
    %99 = arith.trunci %98 : i32 to i8
    %100 = llvm.getelementptr %arg3[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %99, %100 : i8, !llvm.ptr
    %101 = llvm.getelementptr %arg1[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg0, %101 : i64, !llvm.ptr
    %102 = llvm.load %76 : !llvm.ptr -> i64
    %103 = llvm.getelementptr %arg2[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %102, %103 : i64, !llvm.ptr
    %104 = llvm.load %76 : !llvm.ptr -> i64
    func.return %104 : i64
  }
  func.func @main() -> i32 {
    %106 = llvm.mlir.addressof @CAP : !llvm.ptr
    %107 = llvm.load %106 : !llvm.ptr -> i64
    %108 = arith.constant 8 : i32
    %109 = arith.extsi %108 : i32 to i64
    %105 = func.call @calloc(%107, %109) : (i64, i64) -> !llvm.ptr
    %111 = llvm.mlir.addressof @CAP : !llvm.ptr
    %112 = llvm.load %111 : !llvm.ptr -> i64
    %113 = arith.constant 8 : i32
    %114 = arith.extsi %113 : i32 to i64
    %110 = func.call @calloc(%112, %114) : (i64, i64) -> !llvm.ptr
    %116 = llvm.mlir.addressof @CAP : !llvm.ptr
    %117 = llvm.load %116 : !llvm.ptr -> i64
    %118 = arith.constant 1 : i32
    %119 = arith.extsi %118 : i32 to i64
    %115 = func.call @calloc(%117, %119) : (i64, i64) -> !llvm.ptr
    %120 = llvm.mlir.zero : !llvm.ptr
    %121 = llvm.icmp "eq" %105, %120 : !llvm.ptr
    %122 = scf.if %121 -> (i1) {
      %123 = arith.constant true
      scf.yield %123 : i1
    } else {
      %124 = llvm.mlir.zero : !llvm.ptr
      %125 = llvm.icmp "eq" %110, %124 : !llvm.ptr
      scf.yield %125 : i1
    }
    %126 = scf.if %122 -> (i1) {
      %127 = arith.constant true
      scf.yield %127 : i1
    } else {
      %128 = llvm.mlir.zero : !llvm.ptr
      %129 = llvm.icmp "eq" %115, %128 : !llvm.ptr
      scf.yield %129 : i1
    }
    cf.cond_br %126, ^bb21, ^bb22
    ^bb21:
      %130 = arith.constant 1 : i32
      func.return %130 : i32
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %132 = llvm.mlir.addressof @TARGET : !llvm.ptr
    %133 = llvm.load %132 : !llvm.ptr -> i64
    %131 = func.call @odd_totient(%133, %105, %110, %115) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
    %134 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %135 = llvm.call @printf(%134, %131) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%105) : (!llvm.ptr) -> ()
    func.call @free(%110) : (!llvm.ptr) -> ()
    func.call @free(%115) : (!llvm.ptr) -> ()
    %139 = arith.constant 0 : i32
    func.return %139 : i32
  }
}