Problem 235

Find r where s(r) = -6e11 for arithmetic-geometric series.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 235
# Find r where s(r) = -6e11 for arithmetic-geometric series.

function s(r: f64) -> f64 {
    let mut result: f64 = 0.0
    let mut x: f64 = 1.0
    let mut k: i32 = 1
    while k <= 5000 {
        result = result + (900.0 - 3.0 * (k as f64)) * x
        x = x * r
        k = k + 1
    }
    return result
}

function main() -> i32 {
    let mut lower: f64 = 0.0
    let mut upper: f64 = 2.0
    let mut iter: i32 = 0
    while iter < 80 {
        let mid: f64 = (upper + lower) / 2.0
        if s(mid) < 0.0 - 600000000000.0 {
            upper = mid
        } else {
            lower = mid
        }
        iter = iter + 1
    }
    printf("%.12f\n", (upper + lower) / 2.0)
    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 s_f64(double r);
int32_t main(void);

double s_f64(double r) {
    double result = 0.0;
    double x = 1.0;
    int32_t k = 1;
    while (k <= 5000) {
        result = (result + ((900.0 - (3.0 * ((double)(k)))) * x));
        x = (x * r);
        k = (k + 1);
    }
    return result;
}

int32_t main(void) {
    double lower = 0.0;
    double upper = 2.0;
    int32_t iter = 0;
    while (iter < 80) {
        double mid = ((upper + lower) / 2.0);
        if (s_f64(mid) < (0.0 - 600000000000.0)) {
            upper = mid;
        } else {
            lower = mid;
        }
        iter = (iter + 1);
    }
    printf("%.12f\n", ((upper + lower) / 2.0));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.12f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func @s(%arg0: f64) -> f64 {
    %0 = arith.constant 0.0 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x f64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : f64, !llvm.ptr
    %4 = arith.constant 1.0 : f32
    %5 = arith.extf %4 : f32 to f64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x f64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : f64, !llvm.ptr
    %8 = arith.constant 1 : i32
    %9 = llvm.mlir.constant(1 : i64) : i64
    %10 = llvm.alloca %9 x i32 : (i64) -> !llvm.ptr
    llvm.store %8, %10 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %11 = llvm.load %10 : !llvm.ptr -> i32
    %12 = arith.constant 5000 : i32
    %13 = arith.cmpi sle, %11, %12 : i32
    cf.cond_br %13, ^bb1, ^bb2
    ^bb1:
      %14 = llvm.load %3 : !llvm.ptr -> f64
      %15 = arith.constant 900.0 : f32
      %16 = arith.constant 3.0 : f32
      %17 = llvm.load %10 : !llvm.ptr -> i32
      %18 = arith.sitofp %17 : i32 to f64
      %20 = arith.extf %16 : f32 to f64
      %19 = arith.mulf %20, %18 : f64
      %22 = arith.extf %15 : f32 to f64
      %21 = arith.subf %22, %19 : f64
      %23 = llvm.load %7 : !llvm.ptr -> f64
      %24 = arith.mulf %21, %23 : f64
      %25 = arith.addf %14, %24 : f64
      llvm.store %25, %3 : f64, !llvm.ptr
      %26 = llvm.load %7 : !llvm.ptr -> f64
      %27 = arith.mulf %26, %arg0 : f64
      llvm.store %27, %7 : f64, !llvm.ptr
      %28 = llvm.load %10 : !llvm.ptr -> i32
      %29 = arith.constant 1 : i32
      %30 = arith.addi %28, %29 : i32
      llvm.store %30, %10 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %31 = llvm.load %3 : !llvm.ptr -> f64
    func.return %31 : f64
  }
  func.func @main() -> i32 {
    %32 = arith.constant 0.0 : f32
    %33 = arith.extf %32 : f32 to f64
    %34 = llvm.mlir.constant(1 : i64) : i64
    %35 = llvm.alloca %34 x f64 : (i64) -> !llvm.ptr
    llvm.store %33, %35 : f64, !llvm.ptr
    %36 = arith.constant 2.0 : f32
    %37 = arith.extf %36 : f32 to f64
    %38 = llvm.mlir.constant(1 : i64) : i64
    %39 = llvm.alloca %38 x f64 : (i64) -> !llvm.ptr
    llvm.store %37, %39 : f64, !llvm.ptr
    %40 = arith.constant 0 : i32
    %41 = llvm.mlir.constant(1 : i64) : i64
    %42 = llvm.alloca %41 x i32 : (i64) -> !llvm.ptr
    llvm.store %40, %42 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %43 = llvm.load %42 : !llvm.ptr -> i32
    %44 = arith.constant 80 : i32
    %45 = arith.cmpi slt, %43, %44 : i32
    cf.cond_br %45, ^bb4, ^bb5
    ^bb4:
      %46 = llvm.load %39 : !llvm.ptr -> f64
      %47 = llvm.load %35 : !llvm.ptr -> f64
      %48 = arith.addf %46, %47 : f64
      %49 = arith.constant 2.0 : f32
      %51 = arith.extf %49 : f32 to f64
      %50 = arith.divf %48, %51 : f64
      %52 = func.call @s(%50) : (f64) -> f64
      %53 = arith.constant 0.0 : f32
      %54 = arith.constant 600000000000.0 : f32
      %55 = arith.subf %53, %54 : f32
      %57 = arith.extf %55 : f32 to f64
      %56 = arith.cmpf olt, %52, %57 : f64
      cf.cond_br %56, ^bb6, ^bb7
      ^bb6:
        llvm.store %50, %39 : f64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        llvm.store %50, %35 : f64, !llvm.ptr
        cf.br ^bb8
      ^bb8:
      %58 = llvm.load %42 : !llvm.ptr -> i32
      %59 = arith.constant 1 : i32
      %60 = arith.addi %58, %59 : i32
      llvm.store %60, %42 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %61 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %62 = llvm.load %39 : !llvm.ptr -> f64
    %63 = llvm.load %35 : !llvm.ptr -> f64
    %64 = arith.addf %62, %63 : f64
    %65 = arith.constant 2.0 : f32
    %67 = arith.extf %65 : f32 to f64
    %66 = arith.divf %64, %67 : f64
    %68 = llvm.call @printf(%61, %66) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %69 = arith.constant 0 : i32
    func.return %69 : i32
  }
}