Problem 804

Counting Binary Quadratic Representations — T(10^16).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 804
# Counting Binary Quadratic Representations — T(10^16).

function isqrt(n: i64) -> i64 {
    if n < 2 { return n }
    let mut x: i64 = n
    let mut y: i64 = (x + 1) / 2
    while y < x {
        x = y
        y = (x + n / x) / 2
    }
    return x
}

function T(N: i64) -> i64 {
    if N <= 0 { return 0 }
    let A: i64 = 4 * N
    let B: i64 = 163
    let ymax: i64 = isqrt(A / B)
    let t0: i64 = isqrt(A)
    let mut total: i64 = t0 + 1 - (t0 & 1)
    let mut By2: i64 = 0
    let mut Bdelta: i64 = B
    let twoB: i64 = 2 * B
    let mut y: i64 = 1
    while y <= ymax {
        By2 = By2 + Bdelta
        Bdelta = Bdelta + twoB
        let t: i64 = isqrt(A - By2)
        let mut c: i64 = 0
        if (y & 1) != 0 {
            c = t + (t & 1)
        } else {
            c = t + 1 - (t & 1)
        }
        total = total + 2 * c
        y = y + 1
    }
    return total - 1
}

function main() -> i32 {
    printf("%lld\n", T(10000000000000000))
    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 isqrt_i64(int64_t n);
int64_t T_i64(int64_t N);
int32_t main(void);

int64_t isqrt_i64(int64_t n) {
    if (n < 2) {
        return n;
    }
    int64_t x = n;
    int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
    while (y < x) {
        x = y;
        y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
    }
    return x;
}

int64_t T_i64(int64_t N) {
    if (N <= 0) {
        return 0;
    }
    int64_t A = (4 * N);
    int64_t B = 163;
    int64_t ymax = isqrt_i64(FLOW_CHECKED_DIV((A), (B)));
    int64_t t0 = isqrt_i64(A);
    int64_t total = ((t0 + 1) - (t0 & 1));
    int64_t By2 = 0;
    int64_t Bdelta = B;
    int64_t twoB = (2 * B);
    int64_t y = 1;
    while (y <= ymax) {
        By2 = (By2 + Bdelta);
        Bdelta = (Bdelta + twoB);
        int64_t t = isqrt_i64((A - By2));
        int64_t c = 0;
        if ((y & 1) != 0) {
            c = (t + (t & 1));
        } else {
            c = ((t + 1) - (t & 1));
        }
        total = (total + (2 * c));
        y = (y + 1);
    }
    return (total - 1);
}

int32_t main(void) {
    printf("%lld\n", T_i64(10000000000000000));
    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 @isqrt(%arg0: i64) -> i64 {
    %0 = arith.constant 2 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi slt, %arg0, %2 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      func.return %arg0 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %3 = llvm.mlir.constant(1 : i64) : i64
    %4 = llvm.alloca %3 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %4 : i64, !llvm.ptr
    %5 = llvm.load %4 : !llvm.ptr -> i64
    %6 = arith.constant 1 : i32
    %8 = arith.extsi %6 : i32 to i64
    %7 = arith.addi %5, %8 : i64
    %9 = arith.constant 2 : i32
    %11 = arith.extsi %9 : i32 to i64
    %10 = arith.divsi %7, %11 : i64
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %10, %13 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %14 = llvm.load %13 : !llvm.ptr -> i64
    %15 = llvm.load %4 : !llvm.ptr -> i64
    %16 = arith.cmpi slt, %14, %15 : i64
    cf.cond_br %16, ^bb4, ^bb5
    ^bb4:
      %17 = llvm.load %13 : !llvm.ptr -> i64
      llvm.store %17, %4 : i64, !llvm.ptr
      %18 = llvm.load %4 : !llvm.ptr -> i64
      %19 = llvm.load %4 : !llvm.ptr -> i64
      %20 = arith.divsi %arg0, %19 : i64
      %21 = arith.addi %18, %20 : i64
      %22 = arith.constant 2 : i32
      %24 = arith.extsi %22 : i32 to i64
      %23 = arith.divsi %21, %24 : i64
      llvm.store %23, %13 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %25 = llvm.load %4 : !llvm.ptr -> i64
    func.return %25 : i64
  }
  func.func @T(%arg0: i64) -> i64 {
    %26 = arith.constant 0 : i32
    %28 = arith.extsi %26 : i32 to i64
    %27 = arith.cmpi sle, %arg0, %28 : i64
    cf.cond_br %27, ^bb6, ^bb7
    ^bb6:
      %29 = arith.constant 0 : i32
      %30 = arith.extsi %29 : i32 to i64
      func.return %30 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %31 = arith.constant 4 : i32
    %33 = arith.extsi %31 : i32 to i64
    %32 = arith.muli %33, %arg0 : i64
    %34 = arith.constant 163 : i32
    %35 = arith.extsi %34 : i32 to i64
    %37 = arith.divsi %32, %35 : i64
    %36 = func.call @isqrt(%37) : (i64) -> i64
    %38 = func.call @isqrt(%32) : (i64) -> i64
    %39 = arith.constant 1 : i32
    %41 = arith.extsi %39 : i32 to i64
    %40 = arith.addi %38, %41 : i64
    %42 = arith.constant 1 : i32
    %44 = arith.extsi %42 : i32 to i64
    %43 = arith.andi %38, %44 : i64
    %45 = arith.subi %40, %43 : i64
    %46 = llvm.mlir.constant(1 : i64) : i64
    %47 = llvm.alloca %46 x i64 : (i64) -> !llvm.ptr
    llvm.store %45, %47 : i64, !llvm.ptr
    %48 = arith.constant 0 : i32
    %49 = arith.extsi %48 : i32 to i64
    %50 = llvm.mlir.constant(1 : i64) : i64
    %51 = llvm.alloca %50 x i64 : (i64) -> !llvm.ptr
    llvm.store %49, %51 : i64, !llvm.ptr
    %52 = llvm.mlir.constant(1 : i64) : i64
    %53 = llvm.alloca %52 x i64 : (i64) -> !llvm.ptr
    llvm.store %35, %53 : i64, !llvm.ptr
    %54 = arith.constant 2 : i32
    %56 = arith.extsi %54 : i32 to i64
    %55 = arith.muli %56, %35 : i64
    %57 = arith.constant 1 : i32
    %58 = arith.extsi %57 : i32 to i64
    %59 = llvm.mlir.constant(1 : i64) : i64
    %60 = llvm.alloca %59 x i64 : (i64) -> !llvm.ptr
    llvm.store %58, %60 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %61 = llvm.load %60 : !llvm.ptr -> i64
    %62 = arith.cmpi sle, %61, %36 : i64
    cf.cond_br %62, ^bb10, ^bb11
    ^bb10:
      %63 = llvm.load %51 : !llvm.ptr -> i64
      %64 = llvm.load %53 : !llvm.ptr -> i64
      %65 = arith.addi %63, %64 : i64
      llvm.store %65, %51 : i64, !llvm.ptr
      %66 = llvm.load %53 : !llvm.ptr -> i64
      %67 = arith.addi %66, %55 : i64
      llvm.store %67, %53 : i64, !llvm.ptr
      %69 = llvm.load %51 : !llvm.ptr -> i64
      %70 = arith.subi %32, %69 : i64
      %68 = func.call @isqrt(%70) : (i64) -> i64
      %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 = llvm.load %60 : !llvm.ptr -> i64
      %76 = arith.constant 1 : i32
      %78 = arith.extsi %76 : i32 to i64
      %77 = arith.andi %75, %78 : i64
      %79 = arith.constant 0 : i32
      %81 = arith.extsi %79 : i32 to i64
      %80 = arith.cmpi ne, %77, %81 : i64
      cf.cond_br %80, ^bb12, ^bb13
      ^bb12:
        %82 = arith.constant 1 : i32
        %84 = arith.extsi %82 : i32 to i64
        %83 = arith.andi %68, %84 : i64
        %85 = arith.addi %68, %83 : i64
        llvm.store %85, %74 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        %86 = arith.constant 1 : i32
        %88 = arith.extsi %86 : i32 to i64
        %87 = arith.addi %68, %88 : i64
        %89 = arith.constant 1 : i32
        %91 = arith.extsi %89 : i32 to i64
        %90 = arith.andi %68, %91 : i64
        %92 = arith.subi %87, %90 : i64
        llvm.store %92, %74 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb14:
      %93 = llvm.load %47 : !llvm.ptr -> i64
      %94 = arith.constant 2 : i32
      %95 = llvm.load %74 : !llvm.ptr -> i64
      %97 = arith.extsi %94 : i32 to i64
      %96 = arith.muli %97, %95 : i64
      %98 = arith.addi %93, %96 : i64
      llvm.store %98, %47 : i64, !llvm.ptr
      %99 = llvm.load %60 : !llvm.ptr -> i64
      %100 = arith.constant 1 : i32
      %102 = arith.extsi %100 : i32 to i64
      %101 = arith.addi %99, %102 : i64
      llvm.store %101, %60 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %103 = llvm.load %47 : !llvm.ptr -> i64
    %104 = arith.constant 1 : i32
    %106 = arith.extsi %104 : i32 to i64
    %105 = arith.subi %103, %106 : i64
    func.return %105 : i64
  }
  func.func @main() -> i32 {
    %107 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %109 = arith.constant 9999995705032704 : i32
    %110 = arith.extsi %109 : i32 to i64
    %108 = func.call @T(%110) : (i64) -> i64
    %111 = llvm.call @printf(%107, %108) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %112 = arith.constant 0 : i32
    func.return %112 : i32
  }
}