Problem 702

Jumping Flea — S(N) via modular-multiplication inversion counts.

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Performance comparison

Flow source

# Project Euler 702
# Jumping Flea — S(N) via modular-multiplication inversion counts.

function inv_count(x0: i64, m: i64) -> i64 {
    if m <= 2 { return 0 }
    let mut x: i64 = x0 % m
    if x <= 1 { return 0 }
    if x == m - 1 { return (m - 1) * (m - 2) / 2 }
    let t: i64 = m / x
    let y: i64 = m - t * x
    let block: i64 = (t * (t + 1) / 2) * (x * (x - 1) / 2)
    return block + (t + 1) * inv_count(x, y) - t * inv_count(x, x - y)
}

function g(x: i64, m: i64) -> i64 {
    if m <= 2 { return 0 }
    return (m - 1) * (m - 2) - inv_count(x, m)
}

function bit_length(n0: i64) -> i64 {
    let mut n: i64 = n0
    let mut d: i64 = 0
    while n > 0 {
        n = n >> 1
        d = d + 1
    }
    return d
}

function S(N: i64) -> i64 {
    let D: i64 = bit_length(N)
    let mut total: i64 = (N * (3 * N + 1) / 2) * (D + 1)
    let mut d: i64 = 2
    while d <= D {
        total = total - g(N, 1 << d)
        d = d + 1
    }
    total = total + 2 * g(N, (1 << D) - N)
    return total
}

function main() -> i32 {
    printf("%lld\n", S(123456789))
    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 inv_count_i64_i64(int64_t x0, int64_t m);
int64_t g_i64_i64(int64_t x, int64_t m);
int64_t bit_length_i64(int64_t n0);
int64_t S_i64(int64_t N);
int32_t main(void);

int64_t inv_count_i64_i64(int64_t x0, int64_t m) {
    if (m <= 2) {
        return 0;
    }
    int64_t x = FLOW_CHECKED_MOD((x0), (m));
    if (x <= 1) {
        return 0;
    }
    if (x == (m - 1)) {
        return FLOW_CHECKED_DIV((((m - 1) * (m - 2))), (2));
    }
    int64_t t = FLOW_CHECKED_DIV((m), (x));
    int64_t y = (m - (t * x));
    int64_t block = (FLOW_CHECKED_DIV(((t * (t + 1))), (2)) * FLOW_CHECKED_DIV(((x * (x - 1))), (2)));
    return ((block + ((t + 1) * inv_count_i64_i64(x, y))) - (t * inv_count_i64_i64(x, (x - y))));
}

int64_t g_i64_i64(int64_t x, int64_t m) {
    if (m <= 2) {
        return 0;
    }
    return (((m - 1) * (m - 2)) - inv_count_i64_i64(x, m));
}

int64_t bit_length_i64(int64_t n0) {
    int64_t n = n0;
    int64_t d = 0;
    while (n > 0) {
        n = FLOW_CHECKED_SHR((n), (1));
        d = (d + 1);
    }
    return d;
}

int64_t S_i64(int64_t N) {
    int64_t D = bit_length_i64(N);
    int64_t total = (FLOW_CHECKED_DIV(((N * ((3 * N) + 1))), (2)) * (D + 1));
    int64_t d = 2;
    while (d <= D) {
        total = (total - g_i64_i64(N, FLOW_CHECKED_SHL((1), (d))));
        d = (d + 1);
    }
    total = (total + (2 * g_i64_i64(N, (FLOW_CHECKED_SHL((1), (D)) - N))));
    return total;
}

int32_t main(void) {
    printf("%lld\n", S_i64(123456789));
    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 @inv_count(%arg0: i64, %arg1: i64) -> i64 {
    %0 = arith.constant 2 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi sle, %arg1, %2 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      %3 = arith.constant 0 : i32
      %4 = arith.extsi %3 : i32 to i64
      func.return %4 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %5 = arith.remsi %arg0, %arg1 : i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    %8 = llvm.load %7 : !llvm.ptr -> i64
    %9 = arith.constant 1 : i32
    %11 = arith.extsi %9 : i32 to i64
    %10 = arith.cmpi sle, %8, %11 : i64
    cf.cond_br %10, ^bb3, ^bb4
    ^bb3:
      %12 = arith.constant 0 : i32
      %13 = arith.extsi %12 : i32 to i64
      func.return %13 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %14 = llvm.load %7 : !llvm.ptr -> i64
    %15 = arith.constant 1 : i32
    %17 = arith.extsi %15 : i32 to i64
    %16 = arith.subi %arg1, %17 : i64
    %18 = arith.cmpi eq, %14, %16 : i64
    cf.cond_br %18, ^bb6, ^bb7
    ^bb6:
      %19 = arith.constant 1 : i32
      %21 = arith.extsi %19 : i32 to i64
      %20 = arith.subi %arg1, %21 : i64
      %22 = arith.constant 2 : i32
      %24 = arith.extsi %22 : i32 to i64
      %23 = arith.subi %arg1, %24 : i64
      %25 = arith.muli %20, %23 : i64
      %26 = arith.constant 2 : i32
      %28 = arith.extsi %26 : i32 to i64
      %27 = arith.divsi %25, %28 : i64
      func.return %27 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %29 = llvm.load %7 : !llvm.ptr -> i64
    %30 = arith.divsi %arg1, %29 : i64
    %31 = llvm.load %7 : !llvm.ptr -> i64
    %32 = arith.muli %30, %31 : i64
    %33 = arith.subi %arg1, %32 : i64
    %34 = arith.constant 1 : i32
    %36 = arith.extsi %34 : i32 to i64
    %35 = arith.addi %30, %36 : i64
    %37 = arith.muli %30, %35 : i64
    %38 = arith.constant 2 : i32
    %40 = arith.extsi %38 : i32 to i64
    %39 = arith.divsi %37, %40 : i64
    %41 = llvm.load %7 : !llvm.ptr -> i64
    %42 = llvm.load %7 : !llvm.ptr -> i64
    %43 = arith.constant 1 : i32
    %45 = arith.extsi %43 : i32 to i64
    %44 = arith.subi %42, %45 : i64
    %46 = arith.muli %41, %44 : i64
    %47 = arith.constant 2 : i32
    %49 = arith.extsi %47 : i32 to i64
    %48 = arith.divsi %46, %49 : i64
    %50 = arith.muli %39, %48 : i64
    %51 = arith.constant 1 : i32
    %53 = arith.extsi %51 : i32 to i64
    %52 = arith.addi %30, %53 : i64
    %55 = llvm.load %7 : !llvm.ptr -> i64
    %54 = func.call @inv_count(%55, %33) : (i64, i64) -> i64
    %56 = arith.muli %52, %54 : i64
    %57 = arith.addi %50, %56 : i64
    %59 = llvm.load %7 : !llvm.ptr -> i64
    %60 = llvm.load %7 : !llvm.ptr -> i64
    %61 = arith.subi %60, %33 : i64
    %58 = func.call @inv_count(%59, %61) : (i64, i64) -> i64
    %62 = arith.muli %30, %58 : i64
    %63 = arith.subi %57, %62 : i64
    func.return %63 : i64
  }
  func.func @g(%arg0: i64, %arg1: i64) -> i64 {
    %64 = arith.constant 2 : i32
    %66 = arith.extsi %64 : i32 to i64
    %65 = arith.cmpi sle, %arg1, %66 : i64
    cf.cond_br %65, ^bb9, ^bb10
    ^bb9:
      %67 = arith.constant 0 : i32
      %68 = arith.extsi %67 : i32 to i64
      func.return %68 : i64
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %69 = arith.constant 1 : i32
    %71 = arith.extsi %69 : i32 to i64
    %70 = arith.subi %arg1, %71 : i64
    %72 = arith.constant 2 : i32
    %74 = arith.extsi %72 : i32 to i64
    %73 = arith.subi %arg1, %74 : i64
    %75 = arith.muli %70, %73 : i64
    %76 = func.call @inv_count(%arg0, %arg1) : (i64, i64) -> i64
    %77 = arith.subi %75, %76 : i64
    func.return %77 : i64
  }
  func.func @bit_length(%arg0: i64) -> i64 {
    %78 = llvm.mlir.constant(1 : i64) : i64
    %79 = llvm.alloca %78 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %79 : i64, !llvm.ptr
    %80 = arith.constant 0 : i32
    %81 = arith.extsi %80 : i32 to i64
    %82 = llvm.mlir.constant(1 : i64) : i64
    %83 = llvm.alloca %82 x i64 : (i64) -> !llvm.ptr
    llvm.store %81, %83 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %84 = llvm.load %79 : !llvm.ptr -> i64
    %85 = arith.constant 0 : i32
    %87 = arith.extsi %85 : i32 to i64
    %86 = arith.cmpi sgt, %84, %87 : i64
    cf.cond_br %86, ^bb13, ^bb14
    ^bb13:
      %88 = llvm.load %79 : !llvm.ptr -> i64
      %89 = arith.constant 1 : i32
      %91 = arith.extsi %89 : i32 to i64
      %90 = arith.shrsi %88, %91 : i64
      llvm.store %90, %79 : i64, !llvm.ptr
      %92 = llvm.load %83 : !llvm.ptr -> i64
      %93 = arith.constant 1 : i32
      %95 = arith.extsi %93 : i32 to i64
      %94 = arith.addi %92, %95 : i64
      llvm.store %94, %83 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %96 = llvm.load %83 : !llvm.ptr -> i64
    func.return %96 : i64
  }
  func.func @S(%arg0: i64) -> i64 {
    %97 = func.call @bit_length(%arg0) : (i64) -> i64
    %98 = arith.constant 3 : i32
    %100 = arith.extsi %98 : i32 to i64
    %99 = arith.muli %100, %arg0 : i64
    %101 = arith.constant 1 : i32
    %103 = arith.extsi %101 : i32 to i64
    %102 = arith.addi %99, %103 : i64
    %104 = arith.muli %arg0, %102 : i64
    %105 = arith.constant 2 : i32
    %107 = arith.extsi %105 : i32 to i64
    %106 = arith.divsi %104, %107 : i64
    %108 = arith.constant 1 : i32
    %110 = arith.extsi %108 : i32 to i64
    %109 = arith.addi %97, %110 : i64
    %111 = arith.muli %106, %109 : i64
    %112 = llvm.mlir.constant(1 : i64) : i64
    %113 = llvm.alloca %112 x i64 : (i64) -> !llvm.ptr
    llvm.store %111, %113 : i64, !llvm.ptr
    %114 = arith.constant 2 : i32
    %115 = arith.extsi %114 : i32 to 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 ^bb15
    ^bb15:
    %118 = llvm.load %117 : !llvm.ptr -> i64
    %119 = arith.cmpi sle, %118, %97 : i64
    cf.cond_br %119, ^bb16, ^bb17
    ^bb16:
      %120 = llvm.load %113 : !llvm.ptr -> i64
      %122 = arith.constant 1 : i32
      %123 = llvm.load %117 : !llvm.ptr -> i64
      %125 = arith.extsi %122 : i32 to i64
      %124 = arith.shli %125, %123 : i64
      %121 = func.call @g(%arg0, %124) : (i64, i64) -> i64
      %126 = arith.subi %120, %121 : i64
      llvm.store %126, %113 : i64, !llvm.ptr
      %127 = llvm.load %117 : !llvm.ptr -> i64
      %128 = arith.constant 1 : i32
      %130 = arith.extsi %128 : i32 to i64
      %129 = arith.addi %127, %130 : i64
      llvm.store %129, %117 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %131 = llvm.load %113 : !llvm.ptr -> i64
    %132 = arith.constant 2 : i32
    %134 = arith.constant 1 : i32
    %136 = arith.extsi %134 : i32 to i64
    %135 = arith.shli %136, %97 : i64
    %137 = arith.subi %135, %arg0 : i64
    %133 = func.call @g(%arg0, %137) : (i64, i64) -> i64
    %139 = arith.extsi %132 : i32 to i64
    %138 = arith.muli %139, %133 : i64
    %140 = arith.addi %131, %138 : i64
    llvm.store %140, %113 : i64, !llvm.ptr
    %141 = llvm.load %113 : !llvm.ptr -> i64
    func.return %141 : i64
  }
  func.func @main() -> i32 {
    %142 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %144 = arith.constant 123456789 : i32
    %145 = arith.extsi %144 : i32 to i64
    %143 = func.call @S(%145) : (i64) -> i64
    %146 = llvm.call @printf(%142, %143) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %147 = arith.constant 0 : i32
    func.return %147 : i32
  }
}