Problem 476

Circle Packing II — average max 3-circle area for triangles with perimeter ≤ 1803.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 476
# Circle Packing II — average max 3-circle area for triangles with perimeter ≤ 1803.

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

function main() -> i32 {
    let n: i64 = 1803
    let PI: f64 = 3.14159265358979323846
    let mut total_count: i64 = 0
    let n2: i64 = n / 2
    let mut a: i64 = 1
    while a <= n2 {
        total_count = total_count + a * (n - 2 * a + 1)
        a = a + 1
    }
    let mut total: f64 = 0.0
    a = 1
    while a <= n2 {
        let twoa: i64 = 2 * a
        let foura: i64 = 4 * a
        let mut b: i64 = a
        while b <= n - a {
            let s_ab: i64 = a + b
            let twos: i64 = 2 * s_ab
            let twob: i64 = 2 * b
            let fourb: i64 = 4 * b
            let mut x: i64 = 1
            while x <= a {
                let c: i64 = s_ab - x
                let t1: i64 = twoa - x
                let t2: i64 = twob - x
                let r2: f64 = ((x * t1 * t2) as f64) / (4.0 * ((twos - x) as f64))
                let sA: f64 = sqrt(((x * t1) as f64) / ((fourb * c) as f64))
                let kA: f64 = (1.0 - sA) / (1.0 + sA)
                let kA2: f64 = kA * kA
                let sB: f64 = sqrt(((x * t2) as f64) / ((foura * c) as f64))
                let mut factor: f64 = 0.0
                if sB <= (2.0 * sA) / (1.0 + sA * sA) {
                    let kB: f64 = (1.0 - sB) / (1.0 + sB)
                    let kB2: f64 = kB * kB
                    factor = 1.0 + kA2 + kB2
                } else {
                    factor = 1.0 + kA2 + kA2 * kA2
                }
                total = total + r2 * factor
                x = x + 1
            }
            b = b + 1
        }
        a = a + 1
    }
    let ans: f64 = PI * total / (total_count as f64)
    printf("%.5f\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; }

int32_t main(void);


int32_t main(void) {
    int64_t n = 1803;
    double PI = 3.14159265358979323846;
    int64_t total_count = 0;
    int64_t n2 = FLOW_CHECKED_DIV((n), (2));
    int64_t a = 1;
    while (a <= n2) {
        total_count = (total_count + (a * ((n - (2 * a)) + 1)));
        a = (a + 1);
    }
    double total = 0.0;
    a = 1;
    while (a <= n2) {
        int64_t twoa = (2 * a);
        int64_t foura = (4 * a);
        int64_t b = a;
        while (b <= (n - a)) {
            int64_t s_ab = (a + b);
            int64_t twos = (2 * s_ab);
            int64_t twob = (2 * b);
            int64_t fourb = (4 * b);
            int64_t x = 1;
            while (x <= a) {
                int64_t c = (s_ab - x);
                int64_t t1 = (twoa - x);
                int64_t t2 = (twob - x);
                double r2 = (((double)(((x * t1) * t2))) / (4.0 * ((double)((twos - x)))));
                double sA = sqrt((((double)((x * t1))) / ((double)((fourb * c)))));
                double kA = ((1.0 - sA) / (1.0 + sA));
                double kA2 = (kA * kA);
                double sB = sqrt((((double)((x * t2))) / ((double)((foura * c)))));
                double factor = 0.0;
                if (sB <= ((2.0 * sA) / (1.0 + (sA * sA)))) {
                    double kB = ((1.0 - sB) / (1.0 + sB));
                    double kB2 = (kB * kB);
                    factor = ((1.0 + kA2) + kB2);
                } else {
                    factor = ((1.0 + kA2) + (kA2 * kA2));
                }
                total = (total + (r2 * factor));
                x = (x + 1);
            }
            b = (b + 1);
        }
        a = (a + 1);
    }
    double ans = ((PI * total) / ((double)(total_count)));
    printf("%.5f\n", ans);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.5f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @sqrt(f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 1803 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 3.14159265358979323846 : f32
    %3 = arith.extf %2 : f32 to f64
    %4 = arith.constant 0 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    %8 = arith.constant 2 : i32
    %10 = arith.extsi %8 : i32 to i64
    %9 = arith.divsi %1, %10 : i64
    %11 = arith.constant 1 : i32
    %12 = arith.extsi %11 : i32 to i64
    %13 = llvm.mlir.constant(1 : i64) : i64
    %14 = llvm.alloca %13 x i64 : (i64) -> !llvm.ptr
    llvm.store %12, %14 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %15 = llvm.load %14 : !llvm.ptr -> i64
    %16 = arith.cmpi sle, %15, %9 : i64
    cf.cond_br %16, ^bb1, ^bb2
    ^bb1:
      %17 = llvm.load %7 : !llvm.ptr -> i64
      %18 = llvm.load %14 : !llvm.ptr -> i64
      %19 = arith.constant 2 : i32
      %20 = llvm.load %14 : !llvm.ptr -> i64
      %22 = arith.extsi %19 : i32 to i64
      %21 = arith.muli %22, %20 : i64
      %23 = arith.subi %1, %21 : i64
      %24 = arith.constant 1 : i32
      %26 = arith.extsi %24 : i32 to i64
      %25 = arith.addi %23, %26 : i64
      %27 = arith.muli %18, %25 : i64
      %28 = arith.addi %17, %27 : i64
      llvm.store %28, %7 : i64, !llvm.ptr
      %29 = llvm.load %14 : !llvm.ptr -> i64
      %30 = arith.constant 1 : i32
      %32 = arith.extsi %30 : i32 to i64
      %31 = arith.addi %29, %32 : i64
      llvm.store %31, %14 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %33 = arith.constant 0.0 : f32
    %34 = arith.extf %33 : f32 to f64
    %35 = llvm.mlir.constant(1 : i64) : i64
    %36 = llvm.alloca %35 x f64 : (i64) -> !llvm.ptr
    llvm.store %34, %36 : f64, !llvm.ptr
    %37 = arith.constant 1 : i32
    %38 = arith.extsi %37 : i32 to i64
    llvm.store %38, %14 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %39 = llvm.load %14 : !llvm.ptr -> i64
    %40 = arith.cmpi sle, %39, %9 : i64
    cf.cond_br %40, ^bb4, ^bb5
    ^bb4:
      %41 = arith.constant 2 : i32
      %42 = llvm.load %14 : !llvm.ptr -> i64
      %44 = arith.extsi %41 : i32 to i64
      %43 = arith.muli %44, %42 : i64
      %45 = arith.constant 4 : i32
      %46 = llvm.load %14 : !llvm.ptr -> i64
      %48 = arith.extsi %45 : i32 to i64
      %47 = arith.muli %48, %46 : i64
      %49 = llvm.load %14 : !llvm.ptr -> i64
      %50 = llvm.mlir.constant(1 : i64) : i64
      %51 = llvm.alloca %50 x i64 : (i64) -> !llvm.ptr
      llvm.store %49, %51 : i64, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %52 = llvm.load %51 : !llvm.ptr -> i64
      %53 = llvm.load %14 : !llvm.ptr -> i64
      %54 = arith.subi %1, %53 : i64
      %55 = arith.cmpi sle, %52, %54 : i64
      cf.cond_br %55, ^bb7, ^bb8
      ^bb7:
        %56 = llvm.load %14 : !llvm.ptr -> i64
        %57 = llvm.load %51 : !llvm.ptr -> i64
        %58 = arith.addi %56, %57 : i64
        %59 = arith.constant 2 : i32
        %61 = arith.extsi %59 : i32 to i64
        %60 = arith.muli %61, %58 : i64
        %62 = arith.constant 2 : i32
        %63 = llvm.load %51 : !llvm.ptr -> i64
        %65 = arith.extsi %62 : i32 to i64
        %64 = arith.muli %65, %63 : i64
        %66 = arith.constant 4 : i32
        %67 = llvm.load %51 : !llvm.ptr -> i64
        %69 = arith.extsi %66 : i32 to i64
        %68 = arith.muli %69, %67 : i64
        %70 = arith.constant 1 : i32
        %71 = arith.extsi %70 : i32 to i64
        %72 = llvm.mlir.constant(1 : i64) : i64
        %73 = llvm.alloca %72 x i64 : (i64) -> !llvm.ptr
        llvm.store %71, %73 : i64, !llvm.ptr
        cf.br ^bb9
        ^bb9:
        %74 = llvm.load %73 : !llvm.ptr -> i64
        %75 = llvm.load %14 : !llvm.ptr -> i64
        %76 = arith.cmpi sle, %74, %75 : i64
        cf.cond_br %76, ^bb10, ^bb11
        ^bb10:
          %77 = llvm.load %73 : !llvm.ptr -> i64
          %78 = arith.subi %58, %77 : i64
          %79 = llvm.load %73 : !llvm.ptr -> i64
          %80 = arith.subi %43, %79 : i64
          %81 = llvm.load %73 : !llvm.ptr -> i64
          %82 = arith.subi %64, %81 : i64
          %83 = llvm.load %73 : !llvm.ptr -> i64
          %84 = arith.muli %83, %80 : i64
          %85 = arith.muli %84, %82 : i64
          %86 = arith.sitofp %85 : i64 to f64
          %87 = arith.constant 4.0 : f32
          %88 = llvm.load %73 : !llvm.ptr -> i64
          %89 = arith.subi %60, %88 : i64
          %90 = arith.sitofp %89 : i64 to f64
          %92 = arith.extf %87 : f32 to f64
          %91 = arith.mulf %92, %90 : f64
          %93 = arith.divf %86, %91 : f64
          %94 = llvm.load %73 : !llvm.ptr -> i64
          %95 = arith.muli %94, %80 : i64
          %96 = arith.sitofp %95 : i64 to f64
          %97 = arith.muli %68, %78 : i64
          %98 = arith.sitofp %97 : i64 to f64
          %99 = arith.divf %96, %98 : f64
          %100 = math.sqrt %99 : f64
          %101 = arith.constant 1.0 : f32
          %103 = arith.extf %101 : f32 to f64
          %102 = arith.subf %103, %100 : f64
          %104 = arith.constant 1.0 : f32
          %106 = arith.extf %104 : f32 to f64
          %105 = arith.addf %106, %100 : f64
          %107 = arith.divf %102, %105 : f64
          %108 = arith.mulf %107, %107 : f64
          %109 = llvm.load %73 : !llvm.ptr -> i64
          %110 = arith.muli %109, %82 : i64
          %111 = arith.sitofp %110 : i64 to f64
          %112 = arith.muli %47, %78 : i64
          %113 = arith.sitofp %112 : i64 to f64
          %114 = arith.divf %111, %113 : f64
          %115 = math.sqrt %114 : f64
          %116 = arith.constant 0.0 : f32
          %117 = arith.extf %116 : f32 to f64
          %118 = llvm.mlir.constant(1 : i64) : i64
          %119 = llvm.alloca %118 x f64 : (i64) -> !llvm.ptr
          llvm.store %117, %119 : f64, !llvm.ptr
          %120 = arith.constant 2.0 : f32
          %122 = arith.extf %120 : f32 to f64
          %121 = arith.mulf %122, %100 : f64
          %123 = arith.constant 1.0 : f32
          %124 = arith.mulf %100, %100 : f64
          %126 = arith.extf %123 : f32 to f64
          %125 = arith.addf %126, %124 : f64
          %127 = arith.divf %121, %125 : f64
          %128 = arith.cmpf ole, %115, %127 : f64
          cf.cond_br %128, ^bb12, ^bb13
          ^bb12:
            %129 = arith.constant 1.0 : f32
            %131 = arith.extf %129 : f32 to f64
            %130 = arith.subf %131, %115 : f64
            %132 = arith.constant 1.0 : f32
            %134 = arith.extf %132 : f32 to f64
            %133 = arith.addf %134, %115 : f64
            %135 = arith.divf %130, %133 : f64
            %136 = arith.mulf %135, %135 : f64
            %137 = arith.constant 1.0 : f32
            %139 = arith.extf %137 : f32 to f64
            %138 = arith.addf %139, %108 : f64
            %140 = arith.addf %138, %136 : f64
            llvm.store %140, %119 : f64, !llvm.ptr
            cf.br ^bb14
          ^bb13:
            %141 = arith.constant 1.0 : f32
            %143 = arith.extf %141 : f32 to f64
            %142 = arith.addf %143, %108 : f64
            %144 = arith.mulf %108, %108 : f64
            %145 = arith.addf %142, %144 : f64
            llvm.store %145, %119 : f64, !llvm.ptr
            cf.br ^bb14
          ^bb14:
          %146 = llvm.load %36 : !llvm.ptr -> f64
          %147 = llvm.load %119 : !llvm.ptr -> f64
          %148 = arith.mulf %93, %147 : f64
          %149 = arith.addf %146, %148 : f64
          llvm.store %149, %36 : f64, !llvm.ptr
          %150 = llvm.load %73 : !llvm.ptr -> i64
          %151 = arith.constant 1 : i32
          %153 = arith.extsi %151 : i32 to i64
          %152 = arith.addi %150, %153 : i64
          llvm.store %152, %73 : i64, !llvm.ptr
          cf.br ^bb9
        ^bb11:
        %154 = llvm.load %51 : !llvm.ptr -> i64
        %155 = arith.constant 1 : i32
        %157 = arith.extsi %155 : i32 to i64
        %156 = arith.addi %154, %157 : i64
        llvm.store %156, %51 : i64, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %158 = llvm.load %14 : !llvm.ptr -> i64
      %159 = arith.constant 1 : i32
      %161 = arith.extsi %159 : i32 to i64
      %160 = arith.addi %158, %161 : i64
      llvm.store %160, %14 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %162 = llvm.load %36 : !llvm.ptr -> f64
    %163 = arith.mulf %3, %162 : f64
    %164 = llvm.load %7 : !llvm.ptr -> i64
    %165 = arith.sitofp %164 : i64 to f64
    %166 = arith.divf %163, %165 : f64
    %167 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %168 = llvm.call @printf(%167, %166) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %169 = arith.constant 0 : i32
    func.return %169 : i32
  }
}