Problem 957

Point Genesis — closed form for maximal blue points g(16).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 957
# Point Genesis — closed form for maximal blue points g(16).

function g(n: i64) -> i64 {
    let sign: i64 = 1
    if (n & 1) != 0 { sign = -1 }
    let one: i128 = 1
    let pow2n: i128 = one << (n as i32)
    let pow2_2n: i128 = one << ((2 * n) as i32)
    let pow2_3n: i128 = one << ((3 * n) as i32)
    let pow2_4n: i128 = one << ((4 * n) as i32)
    let m2n: i128 = pow2n * (sign as i128)
    let mut numer: i128 = 0
    numer = numer + (11 as i128) * pow2_4n
    numer = numer + (132 as i128) * pow2_3n
    numer = numer + (564 as i128) * pow2_2n
    numer = numer + (1008 as i128) * pow2n
    numer = numer - (384 as i128) * (sign as i128)
    numer = numer - (128 as i128) * m2n
    numer = numer + (768 as i128)
    return (numer / (864 as i128)) as i64
}

function main() -> i32 {
    printf("%lld\n", g(16))
    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 g_i64(int64_t n);
int32_t main(void);

int64_t g_i64(int64_t n) {
    int64_t sign = 1;
    if ((n & 1) != 0) {
        sign = (-1);
    }
    __int128 one = 1;
    __int128 pow2n = FLOW_CHECKED_SHL((one), (((int32_t)(n))));
    __int128 pow2_2n = FLOW_CHECKED_SHL((one), (((int32_t)((2 * n)))));
    __int128 pow2_3n = FLOW_CHECKED_SHL((one), (((int32_t)((3 * n)))));
    __int128 pow2_4n = FLOW_CHECKED_SHL((one), (((int32_t)((4 * n)))));
    __int128 m2n = (pow2n * ((__int128)(sign)));
    __int128 numer = 0;
    numer = (numer + (((__int128)(11)) * pow2_4n));
    numer = (numer + (((__int128)(132)) * pow2_3n));
    numer = (numer + (((__int128)(564)) * pow2_2n));
    numer = (numer + (((__int128)(1008)) * pow2n));
    numer = (numer - (((__int128)(384)) * ((__int128)(sign))));
    numer = (numer - (((__int128)(128)) * m2n));
    numer = (numer + ((__int128)(768)));
    return ((int64_t)(FLOW_CHECKED_DIV((numer), (((__int128)(864))))));
}

int32_t main(void) {
    printf("%lld\n", g_i64(16));
    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 @g(%arg0: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 1 : i32
    %4 = arith.extsi %2 : i32 to i64
    %3 = arith.andi %arg0, %4 : i64
    %5 = arith.constant 0 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.cmpi ne, %3, %7 : i64
    %8 = scf.if %6 -> (i64) {
      %9 = arith.constant 1 : i32
      %11 = arith.constant 0 : i32
      %10 = arith.subi %11, %9 : i32
      %12 = arith.extsi %10 : i32 to i64
      scf.yield %12 : i64
    } else {
      scf.yield %1 : i64
    }
    %13 = arith.constant 1 : i32
    %14 = arith.extsi %13 : i32 to i128
    %15 = arith.trunci %arg0 : i64 to i32
    %17 = arith.trunci %14 : i128 to i64
    %18 = arith.extsi %15 : i32 to i64
    %16 = arith.shli %17, %18 : i64
    %19 = arith.extsi %16 : i64 to i128
    %20 = arith.constant 2 : i32
    %22 = arith.extsi %20 : i32 to i64
    %21 = arith.muli %22, %arg0 : i64
    %23 = arith.trunci %21 : i64 to i32
    %25 = arith.trunci %14 : i128 to i64
    %26 = arith.extsi %23 : i32 to i64
    %24 = arith.shli %25, %26 : i64
    %27 = arith.extsi %24 : i64 to i128
    %28 = arith.constant 3 : i32
    %30 = arith.extsi %28 : i32 to i64
    %29 = arith.muli %30, %arg0 : i64
    %31 = arith.trunci %29 : i64 to i32
    %33 = arith.trunci %14 : i128 to i64
    %34 = arith.extsi %31 : i32 to i64
    %32 = arith.shli %33, %34 : i64
    %35 = arith.extsi %32 : i64 to i128
    %36 = arith.constant 4 : i32
    %38 = arith.extsi %36 : i32 to i64
    %37 = arith.muli %38, %arg0 : i64
    %39 = arith.trunci %37 : i64 to i32
    %41 = arith.trunci %14 : i128 to i64
    %42 = arith.extsi %39 : i32 to i64
    %40 = arith.shli %41, %42 : i64
    %43 = arith.extsi %40 : i64 to i128
    %44 = arith.extsi %8 : i64 to i128
    %46 = arith.trunci %19 : i128 to i64
    %47 = arith.trunci %44 : i128 to i64
    %45 = arith.muli %46, %47 : i64
    %48 = arith.extsi %45 : i64 to i128
    %49 = arith.constant 0 : i32
    %50 = arith.extsi %49 : i32 to i128
    %51 = llvm.mlir.constant(1 : i64) : i64
    %52 = llvm.alloca %51 x i128 : (i64) -> !llvm.ptr
    llvm.store %50, %52 : i128, !llvm.ptr
    %53 = llvm.load %52 : !llvm.ptr -> i128
    %54 = arith.constant 11 : i32
    %55 = arith.extsi %54 : i32 to i128
    %57 = arith.trunci %55 : i128 to i64
    %58 = arith.trunci %43 : i128 to i64
    %56 = arith.muli %57, %58 : i64
    %60 = arith.trunci %53 : i128 to i64
    %59 = arith.addi %60, %56 : i64
    %61 = arith.extsi %59 : i64 to i128
    llvm.store %61, %52 : i128, !llvm.ptr
    %62 = llvm.load %52 : !llvm.ptr -> i128
    %63 = arith.constant 132 : i32
    %64 = arith.extsi %63 : i32 to i128
    %66 = arith.trunci %64 : i128 to i64
    %67 = arith.trunci %35 : i128 to i64
    %65 = arith.muli %66, %67 : i64
    %69 = arith.trunci %62 : i128 to i64
    %68 = arith.addi %69, %65 : i64
    %70 = arith.extsi %68 : i64 to i128
    llvm.store %70, %52 : i128, !llvm.ptr
    %71 = llvm.load %52 : !llvm.ptr -> i128
    %72 = arith.constant 564 : i32
    %73 = arith.extsi %72 : i32 to i128
    %75 = arith.trunci %73 : i128 to i64
    %76 = arith.trunci %27 : i128 to i64
    %74 = arith.muli %75, %76 : i64
    %78 = arith.trunci %71 : i128 to i64
    %77 = arith.addi %78, %74 : i64
    %79 = arith.extsi %77 : i64 to i128
    llvm.store %79, %52 : i128, !llvm.ptr
    %80 = llvm.load %52 : !llvm.ptr -> i128
    %81 = arith.constant 1008 : i32
    %82 = arith.extsi %81 : i32 to i128
    %84 = arith.trunci %82 : i128 to i64
    %85 = arith.trunci %19 : i128 to i64
    %83 = arith.muli %84, %85 : i64
    %87 = arith.trunci %80 : i128 to i64
    %86 = arith.addi %87, %83 : i64
    %88 = arith.extsi %86 : i64 to i128
    llvm.store %88, %52 : i128, !llvm.ptr
    %89 = llvm.load %52 : !llvm.ptr -> i128
    %90 = arith.constant 384 : i32
    %91 = arith.extsi %90 : i32 to i128
    %92 = arith.extsi %8 : i64 to i128
    %94 = arith.trunci %91 : i128 to i64
    %95 = arith.trunci %92 : i128 to i64
    %93 = arith.muli %94, %95 : i64
    %97 = arith.trunci %89 : i128 to i64
    %96 = arith.subi %97, %93 : i64
    %98 = arith.extsi %96 : i64 to i128
    llvm.store %98, %52 : i128, !llvm.ptr
    %99 = llvm.load %52 : !llvm.ptr -> i128
    %100 = arith.constant 128 : i32
    %101 = arith.extsi %100 : i32 to i128
    %103 = arith.trunci %101 : i128 to i64
    %104 = arith.trunci %48 : i128 to i64
    %102 = arith.muli %103, %104 : i64
    %106 = arith.trunci %99 : i128 to i64
    %105 = arith.subi %106, %102 : i64
    %107 = arith.extsi %105 : i64 to i128
    llvm.store %107, %52 : i128, !llvm.ptr
    %108 = llvm.load %52 : !llvm.ptr -> i128
    %109 = arith.constant 768 : i32
    %110 = arith.extsi %109 : i32 to i128
    %112 = arith.trunci %108 : i128 to i64
    %113 = arith.trunci %110 : i128 to i64
    %111 = arith.addi %112, %113 : i64
    %114 = arith.extsi %111 : i64 to i128
    llvm.store %114, %52 : i128, !llvm.ptr
    %115 = llvm.load %52 : !llvm.ptr -> i128
    %116 = arith.constant 864 : i32
    %117 = arith.extsi %116 : i32 to i128
    %119 = arith.trunci %115 : i128 to i64
    %120 = arith.trunci %117 : i128 to i64
    %118 = arith.divsi %119, %120 : i64
    func.return %118 : i64
  }
  func.func @main() -> i32 {
    %121 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %123 = arith.constant 16 : i32
    %124 = arith.extsi %123 : i32 to i64
    %122 = func.call @g(%124) : (i64) -> i64
    %125 = llvm.call @printf(%121, %122) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %126 = arith.constant 0 : i32
    func.return %126 : i32
  }
}