Problem 449

Chocolate volume on ellipsoid a=3, b=1, thickness 1.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 449
# Chocolate volume on ellipsoid a=3, b=1, thickness 1.

extern {
    function sqrt(x: f64) -> f64
    function atan(x: f64) -> f64
    function atanh(x: f64) -> f64
}

function main() -> i32 {
    let PI: f64 = 3.14159265358979323846
    let A: f64 = 3.0
    let C: f64 = 1.0
    let t: f64 = 1.0
    let e: f64 = sqrt(1.0 - (C * C) / (A * A))
    let S: f64 = 2.0 * PI * A * A * (1.0 + (C * C / (A * A)) * (atanh(e) / e))
    let M: f64 = 2.0 * PI * C + (2.0 * PI * A / e) * atan((A * e) / C)
    let ans: f64 = S * t + M * t * t + (4.0 * PI / 3.0) * t * t * t
    printf("%.8f\n", ans)
    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 atan(double x);
double atanh(double x);
int32_t main(void);




int32_t main(void) {
    double PI = 3.14159265358979323846;
    double A = 3.0;
    double C = 1.0;
    double t = 1.0;
    double e = sqrt((1.0 - ((C * C) / (A * A))));
    double S = ((((2.0 * PI) * A) * A) * (1.0 + (((C * C) / (A * A)) * (atanh(e) / e))));
    double M = (((2.0 * PI) * C) + ((((2.0 * PI) * A) / e) * atan(((A * e) / C))));
    double ans = (((S * t) + ((M * t) * t)) + (((((4.0 * PI) / 3.0) * t) * t) * t));
    printf("%.8f\n", ans);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.8f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @sqrt(f64) -> f64
  func.func private @atan(f64) -> f64
  func.func private @atanh(f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 3.14159265358979323846 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = arith.constant 3.0 : f32
    %3 = arith.extf %2 : f32 to f64
    %4 = arith.constant 1.0 : f32
    %5 = arith.extf %4 : f32 to f64
    %6 = arith.constant 1.0 : f32
    %7 = arith.extf %6 : f32 to f64
    %8 = arith.constant 1.0 : f32
    %9 = arith.mulf %5, %5 : f64
    %10 = arith.mulf %3, %3 : f64
    %11 = arith.divf %9, %10 : f64
    %13 = arith.extf %8 : f32 to f64
    %12 = arith.subf %13, %11 : f64
    %14 = math.sqrt %12 : f64
    %15 = arith.constant 2.0 : f32
    %17 = arith.extf %15 : f32 to f64
    %16 = arith.mulf %17, %1 : f64
    %18 = arith.mulf %16, %3 : f64
    %19 = arith.mulf %18, %3 : f64
    %20 = arith.constant 1.0 : f32
    %21 = arith.mulf %5, %5 : f64
    %22 = arith.mulf %3, %3 : f64
    %23 = arith.divf %21, %22 : f64
    %24 = func.call @atanh(%14) : (f64) -> f64
    %25 = arith.divf %24, %14 : f64
    %26 = arith.mulf %23, %25 : f64
    %28 = arith.extf %20 : f32 to f64
    %27 = arith.addf %28, %26 : f64
    %29 = arith.mulf %19, %27 : f64
    %30 = arith.constant 2.0 : f32
    %32 = arith.extf %30 : f32 to f64
    %31 = arith.mulf %32, %1 : f64
    %33 = arith.mulf %31, %5 : f64
    %34 = arith.constant 2.0 : f32
    %36 = arith.extf %34 : f32 to f64
    %35 = arith.mulf %36, %1 : f64
    %37 = arith.mulf %35, %3 : f64
    %38 = arith.divf %37, %14 : f64
    %40 = arith.mulf %3, %14 : f64
    %41 = arith.divf %40, %5 : f64
    %39 = func.call @atan(%41) : (f64) -> f64
    %42 = arith.mulf %38, %39 : f64
    %43 = arith.addf %33, %42 : f64
    %44 = arith.mulf %29, %7 : f64
    %45 = arith.mulf %43, %7 : f64
    %46 = arith.mulf %45, %7 : f64
    %47 = arith.addf %44, %46 : f64
    %48 = arith.constant 4.0 : f32
    %50 = arith.extf %48 : f32 to f64
    %49 = arith.mulf %50, %1 : f64
    %51 = arith.constant 3.0 : f32
    %53 = arith.extf %51 : f32 to f64
    %52 = arith.divf %49, %53 : f64
    %54 = arith.mulf %52, %7 : f64
    %55 = arith.mulf %54, %7 : f64
    %56 = arith.mulf %55, %7 : f64
    %57 = arith.addf %47, %56 : f64
    %58 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %59 = llvm.call @printf(%58, %57) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %60 = arith.constant 0 : i32
    func.return %60 : i32
  }
}