Problem 892

Zebra Circles — sum D(n) for n<=1e7 mod 1234567891.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 892
# Zebra Circles — sum D(n) for n<=1e7 mod 1234567891.

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

const MOD: i64 = 1234567891
const N_MAX: i64 = 10000000

function solve() -> i64 {
    let r_max: i64 = N_MAX / 2
    let inv: ptr<i64> = calloc(r_max + 2, 8)
    inv[1] = 1
    for i in 2..(r_max + 2) {
        inv[i] = (MOD - ((MOD / i) * inv[MOD % i]) % MOD) % MOD
    }
    let inv2: i64 = (MOD + 1) / 2
    let mut b: i64 = 1
    let mut ans: i64 = 0
    for r in 0..(r_max + 1) {
        let bb: i64 = ((b as i128) * (b as i128) % (MOD as i128)) as i64
        if r > 0 {
            ans = (ans + ((bb as i128) * (inv2 as i128) % (MOD as i128)) as i64) % MOD
        }
        if r > 0 && (2 * r + 1) <= N_MAX {
            let term: i64 = (((bb as i128) * ((2 * r) as i128) % (MOD as i128)) * (inv[r + 1] as i128) % (MOD as i128)) as i64
            ans = (ans + term) % MOD
        }
        if r < r_max {
            let inv_rp1: i64 = inv[r + 1]
            b = ((b as i128) * ((2 * r + 1) as i128) % (MOD as i128)) as i64
            b = ((b as i128) * ((2 * r + 2) as i128) % (MOD as i128)) as i64
            b = ((b as i128) * (inv_rp1 as i128) % (MOD as i128)) as i64
            b = ((b as i128) * (inv_rp1 as i128) % (MOD as i128)) as i64
        }
    }
    free(inv)
    return ans % MOD
}

function main() -> i32 {
    printf("%lld\n", solve())
    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 solve(void);
int32_t main(void);

static const int64_t MOD = 1234567891;
static const int64_t N_MAX = 10000000;



int64_t solve(void) {
    int64_t r_max = FLOW_CHECKED_DIV((N_MAX), (2));
    int64_t* inv = (int64_t*)(calloc((r_max + 2), 8));
    inv[1] = 1;
    int32_t __flow_step_1 = 1;
    for (int32_t i = 2; (2 <= (r_max + 2)) ? i < (r_max + 2) : i > (r_max + 2); i += (2 <= (r_max + 2)) ? 1 : -1) {
        inv[i] = FLOW_CHECKED_MOD(((MOD - FLOW_CHECKED_MOD(((FLOW_CHECKED_DIV((MOD), (i)) * inv[FLOW_CHECKED_MOD((MOD), (i))])), (MOD)))), (MOD));
    }
    int64_t inv2 = FLOW_CHECKED_DIV(((MOD + 1)), (2));
    int64_t b = 1;
    int64_t ans = 0;
    int32_t __flow_step_2 = 1;
    for (int32_t r = 0; (0 <= (r_max + 1)) ? r < (r_max + 1) : r > (r_max + 1); r += (0 <= (r_max + 1)) ? 1 : -1) {
        int64_t bb = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(MOD))))));
        if (r > 0) {
            ans = FLOW_CHECKED_MOD(((ans + ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(bb)) * ((__int128)(inv2)))), (((__int128)(MOD)))))))), (MOD));
        }
        if ((r > 0 && ((2 * r) + 1) <= N_MAX)) {
            int64_t term = ((int64_t)(FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((((__int128)(bb)) * ((__int128)((2 * r))))), (((__int128)(MOD)))) * ((__int128)(inv[(r + 1)])))), (((__int128)(MOD))))));
            ans = FLOW_CHECKED_MOD(((ans + term)), (MOD));
        }
        if (r < r_max) {
            int64_t inv_rp1 = inv[(r + 1)];
            b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(((2 * r) + 1))))), (((__int128)(MOD))))));
            b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(((2 * r) + 2))))), (((__int128)(MOD))))));
            b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(inv_rp1)))), (((__int128)(MOD))))));
            b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(inv_rp1)))), (((__int128)(MOD))))));
        }
    }
    free(inv);
    return FLOW_CHECKED_MOD((ans), (MOD));
}

int32_t main(void) {
    printf("%lld\n", solve());
    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: MOD
  llvm.mlir.global internal constant @MOD(1234567891 : i64) : i64
  // Constant: N_MAX
  llvm.mlir.global internal constant @N_MAX(10000000 : i64) : i64
  func.func @solve() -> i64 {
    %0 = llvm.mlir.addressof @N_MAX : !llvm.ptr
    %1 = llvm.load %0 : !llvm.ptr -> i64
    %2 = arith.constant 2 : i32
    %4 = arith.extsi %2 : i32 to i64
    %3 = arith.divsi %1, %4 : i64
    %6 = arith.constant 2 : i32
    %8 = arith.extsi %6 : i32 to i64
    %7 = arith.addi %3, %8 : i64
    %9 = arith.constant 8 : i32
    %10 = arith.extsi %9 : i32 to i64
    %5 = func.call @calloc(%7, %10) : (i64, i64) -> !llvm.ptr
    %11 = arith.constant 1 : i32
    %12 = arith.constant 1 : i32
    %13 = arith.extsi %11 : i32 to i64
    %14 = arith.extsi %12 : i32 to i64
    %15 = llvm.getelementptr %5[%14] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %13, %15 : i64, !llvm.ptr
    %16 = arith.constant 2 : i32
    %17 = arith.constant 2 : i32
    %19 = arith.extsi %17 : i32 to i64
    %18 = arith.addi %3, %19 : i64
    %20 = arith.index_cast %16 : i32 to index
    %21 = arith.index_cast %18 : i32 to index
    %23 = arith.constant 1 : index
    %24 = arith.constant -1 : index
    %25 = arith.cmpi sle, %20, %21 : index
    %22 = arith.select %25, %23, %24 : index
    cf.br ^bb0(%20 : index)
    ^bb0(%26: index):
    %27 = arith.cmpi slt, %26, %21 : index
    %28 = arith.cmpi sgt, %26, %21 : index
    %29 = arith.select %25, %27, %28 : i1
    cf.cond_br %29, ^bb1(%26 : index), ^bb2(%26 : index)
    ^bb1(%30: index):
      %31 = llvm.mlir.addressof @MOD : !llvm.ptr
      %32 = llvm.load %31 : !llvm.ptr -> i64
      %33 = llvm.mlir.addressof @MOD : !llvm.ptr
      %34 = llvm.load %33 : !llvm.ptr -> i64
      %36 = arith.trunci %34 : i64 to i32
      %37 = arith.index_cast %30 : index to i32
      %35 = arith.divsi %36, %37 : i32
      %39 = llvm.mlir.addressof @MOD : !llvm.ptr
      %40 = llvm.load %39 : !llvm.ptr -> i64
      %42 = arith.trunci %40 : i64 to i32
      %43 = arith.index_cast %30 : index to i32
      %41 = arith.remsi %42, %43 : i32
      %44 = arith.extsi %41 : i32 to i64
      %45 = llvm.getelementptr %5[%44] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %38 = llvm.load %45 : !llvm.ptr -> i64
      %47 = arith.extsi %35 : i32 to i64
      %46 = arith.muli %47, %38 : i64
      %48 = llvm.mlir.addressof @MOD : !llvm.ptr
      %49 = llvm.load %48 : !llvm.ptr -> i64
      %50 = arith.remsi %46, %49 : i64
      %51 = arith.subi %32, %50 : i64
      %52 = llvm.mlir.addressof @MOD : !llvm.ptr
      %53 = llvm.load %52 : !llvm.ptr -> i64
      %54 = arith.remsi %51, %53 : i64
      %55 = arith.index_cast %30 : index to i64
      %56 = llvm.getelementptr %5[%55] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %54, %56 : i64, !llvm.ptr
      %57 = arith.addi %30, %22 : index
      cf.br ^bb0(%57 : index)
    ^bb2(%58: index):
    %59 = llvm.mlir.addressof @MOD : !llvm.ptr
    %60 = llvm.load %59 : !llvm.ptr -> i64
    %61 = arith.constant 1 : i32
    %63 = arith.extsi %61 : i32 to i64
    %62 = arith.addi %60, %63 : i64
    %64 = arith.constant 2 : i32
    %66 = arith.extsi %64 : i32 to i64
    %65 = arith.divsi %62, %66 : i64
    %67 = arith.constant 1 : i32
    %68 = arith.extsi %67 : i32 to i64
    %69 = llvm.mlir.constant(1 : i64) : i64
    %70 = llvm.alloca %69 x i64 : (i64) -> !llvm.ptr
    llvm.store %68, %70 : i64, !llvm.ptr
    %71 = arith.constant 0 : i32
    %72 = arith.extsi %71 : i32 to i64
    %73 = llvm.mlir.constant(1 : i64) : i64
    %74 = llvm.alloca %73 x i64 : (i64) -> !llvm.ptr
    llvm.store %72, %74 : i64, !llvm.ptr
    %75 = arith.constant 0 : i32
    %76 = arith.constant 1 : i32
    %78 = arith.extsi %76 : i32 to i64
    %77 = arith.addi %3, %78 : i64
    %79 = arith.index_cast %75 : i32 to index
    %80 = arith.index_cast %77 : i32 to index
    %82 = arith.constant 1 : index
    %83 = arith.constant -1 : index
    %84 = arith.cmpi sle, %79, %80 : index
    %81 = arith.select %84, %82, %83 : index
    cf.br ^bb3(%79 : index)
    ^bb3(%85: index):
    %86 = arith.cmpi slt, %85, %80 : index
    %87 = arith.cmpi sgt, %85, %80 : index
    %88 = arith.select %84, %86, %87 : i1
    cf.cond_br %88, ^bb4(%85 : index), ^bb5(%85 : index)
    ^bb4(%89: index):
      %90 = llvm.load %70 : !llvm.ptr -> i64
      %91 = arith.extsi %90 : i64 to i128
      %92 = llvm.load %70 : !llvm.ptr -> i64
      %93 = arith.extsi %92 : i64 to i128
      %95 = arith.trunci %91 : i128 to i64
      %96 = arith.trunci %93 : i128 to i64
      %94 = arith.muli %95, %96 : i64
      %97 = llvm.mlir.addressof @MOD : !llvm.ptr
      %98 = llvm.load %97 : !llvm.ptr -> i64
      %99 = arith.extsi %98 : i64 to i128
      %101 = arith.trunci %99 : i128 to i64
      %100 = arith.remsi %94, %101 : i64
      %102 = arith.constant 0 : i32
      %104 = arith.index_cast %89 : index to i32
      %103 = arith.cmpi sgt, %104, %102 : i32
      cf.cond_br %103, ^bb6, ^bb7
      ^bb6:
        %105 = llvm.load %74 : !llvm.ptr -> i64
        %106 = arith.extsi %100 : i64 to i128
        %107 = arith.extsi %65 : i64 to i128
        %109 = arith.trunci %106 : i128 to i64
        %110 = arith.trunci %107 : i128 to i64
        %108 = arith.muli %109, %110 : i64
        %111 = llvm.mlir.addressof @MOD : !llvm.ptr
        %112 = llvm.load %111 : !llvm.ptr -> i64
        %113 = arith.extsi %112 : i64 to i128
        %115 = arith.trunci %113 : i128 to i64
        %114 = arith.remsi %108, %115 : i64
        %116 = arith.addi %105, %114 : i64
        %117 = llvm.mlir.addressof @MOD : !llvm.ptr
        %118 = llvm.load %117 : !llvm.ptr -> i64
        %119 = arith.remsi %116, %118 : i64
        llvm.store %119, %74 : i64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %120 = arith.constant 0 : i32
      %122 = arith.index_cast %89 : index to i32
      %121 = arith.cmpi sgt, %122, %120 : i32
      %123 = scf.if %121 -> (i1) {
        %124 = arith.constant 2 : i32
        %126 = arith.index_cast %89 : index to i32
        %125 = arith.muli %124, %126 : i32
        %127 = arith.constant 1 : i32
        %128 = arith.addi %125, %127 : i32
        %129 = llvm.mlir.addressof @N_MAX : !llvm.ptr
        %130 = llvm.load %129 : !llvm.ptr -> i64
        %132 = arith.extsi %128 : i32 to i64
        %131 = arith.cmpi sle, %132, %130 : i64
        scf.yield %131 : i1
      } else {
        %133 = arith.constant false
        scf.yield %133 : i1
      }
      cf.cond_br %123, ^bb9, ^bb10
      ^bb9:
        %134 = arith.extsi %100 : i64 to i128
        %135 = arith.constant 2 : i32
        %137 = arith.index_cast %89 : index to i32
        %136 = arith.muli %135, %137 : i32
        %138 = arith.extsi %136 : i32 to i128
        %140 = arith.trunci %134 : i128 to i64
        %141 = arith.trunci %138 : i128 to i64
        %139 = arith.muli %140, %141 : i64
        %142 = llvm.mlir.addressof @MOD : !llvm.ptr
        %143 = llvm.load %142 : !llvm.ptr -> i64
        %144 = arith.extsi %143 : i64 to i128
        %146 = arith.trunci %144 : i128 to i64
        %145 = arith.remsi %139, %146 : i64
        %148 = arith.constant 1 : i32
        %150 = arith.index_cast %89 : index to i32
        %149 = arith.addi %150, %148 : i32
        %151 = arith.extsi %149 : i32 to i64
        %152 = llvm.getelementptr %5[%151] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %147 = llvm.load %152 : !llvm.ptr -> i64
        %153 = arith.extsi %147 : i64 to i128
        %155 = arith.trunci %153 : i128 to i64
        %154 = arith.muli %145, %155 : i64
        %156 = llvm.mlir.addressof @MOD : !llvm.ptr
        %157 = llvm.load %156 : !llvm.ptr -> i64
        %158 = arith.extsi %157 : i64 to i128
        %160 = arith.trunci %158 : i128 to i64
        %159 = arith.remsi %154, %160 : i64
        %161 = llvm.load %74 : !llvm.ptr -> i64
        %162 = arith.addi %161, %159 : i64
        %163 = llvm.mlir.addressof @MOD : !llvm.ptr
        %164 = llvm.load %163 : !llvm.ptr -> i64
        %165 = arith.remsi %162, %164 : i64
        llvm.store %165, %74 : i64, !llvm.ptr
        cf.br ^bb11
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %167 = arith.index_cast %89 : index to i32
      %168 = arith.trunci %3 : i64 to i32
      %166 = arith.cmpi slt, %167, %168 : i32
      cf.cond_br %166, ^bb12, ^bb13
      ^bb12:
        %170 = arith.constant 1 : i32
        %172 = arith.index_cast %89 : index to i32
        %171 = arith.addi %172, %170 : i32
        %173 = arith.extsi %171 : i32 to i64
        %174 = llvm.getelementptr %5[%173] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %169 = llvm.load %174 : !llvm.ptr -> i64
        %175 = llvm.load %70 : !llvm.ptr -> i64
        %176 = arith.extsi %175 : i64 to i128
        %177 = arith.constant 2 : i32
        %179 = arith.index_cast %89 : index to i32
        %178 = arith.muli %177, %179 : i32
        %180 = arith.constant 1 : i32
        %181 = arith.addi %178, %180 : i32
        %182 = arith.extsi %181 : i32 to i128
        %184 = arith.trunci %176 : i128 to i64
        %185 = arith.trunci %182 : i128 to i64
        %183 = arith.muli %184, %185 : i64
        %186 = llvm.mlir.addressof @MOD : !llvm.ptr
        %187 = llvm.load %186 : !llvm.ptr -> i64
        %188 = arith.extsi %187 : i64 to i128
        %190 = arith.trunci %188 : i128 to i64
        %189 = arith.remsi %183, %190 : i64
        llvm.store %189, %70 : i64, !llvm.ptr
        %191 = llvm.load %70 : !llvm.ptr -> i64
        %192 = arith.extsi %191 : i64 to i128
        %193 = arith.constant 2 : i32
        %195 = arith.index_cast %89 : index to i32
        %194 = arith.muli %193, %195 : i32
        %196 = arith.constant 2 : i32
        %197 = arith.addi %194, %196 : i32
        %198 = arith.extsi %197 : i32 to i128
        %200 = arith.trunci %192 : i128 to i64
        %201 = arith.trunci %198 : i128 to i64
        %199 = arith.muli %200, %201 : i64
        %202 = llvm.mlir.addressof @MOD : !llvm.ptr
        %203 = llvm.load %202 : !llvm.ptr -> i64
        %204 = arith.extsi %203 : i64 to i128
        %206 = arith.trunci %204 : i128 to i64
        %205 = arith.remsi %199, %206 : i64
        llvm.store %205, %70 : i64, !llvm.ptr
        %207 = llvm.load %70 : !llvm.ptr -> i64
        %208 = arith.extsi %207 : i64 to i128
        %209 = arith.extsi %169 : i64 to i128
        %211 = arith.trunci %208 : i128 to i64
        %212 = arith.trunci %209 : i128 to i64
        %210 = arith.muli %211, %212 : i64
        %213 = llvm.mlir.addressof @MOD : !llvm.ptr
        %214 = llvm.load %213 : !llvm.ptr -> i64
        %215 = arith.extsi %214 : i64 to i128
        %217 = arith.trunci %215 : i128 to i64
        %216 = arith.remsi %210, %217 : i64
        llvm.store %216, %70 : i64, !llvm.ptr
        %218 = llvm.load %70 : !llvm.ptr -> i64
        %219 = arith.extsi %218 : i64 to i128
        %220 = arith.extsi %169 : i64 to i128
        %222 = arith.trunci %219 : i128 to i64
        %223 = arith.trunci %220 : i128 to i64
        %221 = arith.muli %222, %223 : i64
        %224 = llvm.mlir.addressof @MOD : !llvm.ptr
        %225 = llvm.load %224 : !llvm.ptr -> i64
        %226 = arith.extsi %225 : i64 to i128
        %228 = arith.trunci %226 : i128 to i64
        %227 = arith.remsi %221, %228 : i64
        llvm.store %227, %70 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %229 = arith.addi %89, %81 : index
      cf.br ^bb3(%229 : index)
    ^bb5(%230: index):
    func.call @free(%5) : (!llvm.ptr) -> ()
    %232 = llvm.load %74 : !llvm.ptr -> i64
    %233 = llvm.mlir.addressof @MOD : !llvm.ptr
    %234 = llvm.load %233 : !llvm.ptr -> i64
    %235 = arith.remsi %232, %234 : i64
    func.return %235 : i64
  }
  func.func @main() -> i32 {
    %236 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %237 = func.call @solve() : () -> i64
    %238 = llvm.call @printf(%236, %237) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %239 = arith.constant 0 : i32
    func.return %239 : i32
  }
}