Problem 197

u_{n+1}=floor(2^(30.403243784-u_n^2))*1e-9; find u_n+u_{n+1} at n=10^12.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 197
# u_{n+1}=floor(2^(30.403243784-u_n^2))*1e-9; find u_n+u_{n+1} at n=10^12.

extern {
    function pow(x: f64, y: f64) -> f64
    function floor(x: f64) -> f64
}

function f(x: f64) -> f64 {
    return floor(pow(2.0, 30.403243784 - x * x)) * 0.000000001
}

function main() -> i32 {
    let mut a: f64 = -1.0
    let mut i: i32 = 0
    while i < 2000 {
        a = f(a)
        i = i + 1
    }
    let b: f64 = f(a)
    printf("%.9f\n", a + b)
    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; }

double f_f64(double x);
int32_t main(void);



double f_f64(double x) {
    return (floor(pow(2.0, (30.403243784 - (x * x)))) * 0.000000001);
}

int32_t main(void) {
    double a = (-1.0);
    int32_t i = 0;
    while (i < 2000) {
        a = f_f64(a);
        i = (i + 1);
    }
    double b = f_f64(a);
    printf("%.9f\n", (a + b));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.9f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @pow(f64, f64) -> f64
  func.func private @floor(f64) -> f64
  func.func @f(%arg0: f64) -> f64 {
    %2 = arith.constant 2.0 : f32
    %3 = arith.constant 30.403243784 : f32
    %4 = arith.mulf %arg0, %arg0 : f64
    %6 = arith.extf %3 : f32 to f64
    %5 = arith.subf %6, %4 : f64
    %7 = arith.extf %2 : f32 to f64
    %1 = func.call @pow(%7, %5) : (f64, f64) -> f64
    %0 = func.call @floor(%1) : (f64) -> f64
    %8 = arith.constant 0.000000001 : f32
    %10 = arith.extf %8 : f32 to f64
    %9 = arith.mulf %0, %10 : f64
    func.return %9 : f64
  }
  func.func @main() -> i32 {
    %11 = arith.constant 1.0 : f32
    %12 = arith.negf %11 : f32
    %13 = arith.extf %12 : f32 to f64
    %14 = llvm.mlir.constant(1 : i64) : i64
    %15 = llvm.alloca %14 x f64 : (i64) -> !llvm.ptr
    llvm.store %13, %15 : f64, !llvm.ptr
    %16 = arith.constant 0 : i32
    %17 = llvm.mlir.constant(1 : i64) : i64
    %18 = llvm.alloca %17 x i32 : (i64) -> !llvm.ptr
    llvm.store %16, %18 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %19 = llvm.load %18 : !llvm.ptr -> i32
    %20 = arith.constant 2000 : i32
    %21 = arith.cmpi slt, %19, %20 : i32
    cf.cond_br %21, ^bb1, ^bb2
    ^bb1:
      %23 = llvm.load %15 : !llvm.ptr -> f64
      %22 = func.call @f(%23) : (f64) -> f64
      llvm.store %22, %15 : f64, !llvm.ptr
      %24 = llvm.load %18 : !llvm.ptr -> i32
      %25 = arith.constant 1 : i32
      %26 = arith.addi %24, %25 : i32
      llvm.store %26, %18 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %28 = llvm.load %15 : !llvm.ptr -> f64
    %27 = func.call @f(%28) : (f64) -> f64
    %29 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %30 = llvm.load %15 : !llvm.ptr -> f64
    %31 = arith.addf %30, %27 : f64
    %32 = llvm.call @printf(%29, %31) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %33 = arith.constant 0 : i32
    func.return %33 : i32
  }
}