Problem 144

Laser reflections in an elliptical mirror until exit.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 144
# Laser reflections in an elliptical mirror until exit.

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

function main() -> i32 {
    let mut steps: i64 = 0
    let mut from_x: f64 = 0.0
    let mut from_y: f64 = 10.1
    let mut to_x: f64 = 1.4
    let mut to_y: f64 = 0.0 - 9.6

    while true {
        if to_x >= (0.0 - 0.01) && to_x <= 0.01 && to_y > 9.9 {
            break
        }

        let mut nx: f64 = 0.0 - 4.0 * to_x
        let mut ny: f64 = 0.0 - to_y
        let length: f64 = sqrt(nx * nx + ny * ny)
        nx = nx / length
        ny = ny / length

        let dx: f64 = to_x - from_x
        let dy: f64 = to_y - from_y

        let dot: f64 = dx * nx + dy * ny
        let rx: f64 = dx - 2.0 * dot * nx
        let ry: f64 = dy - 2.0 * dot * ny
        let slope: f64 = ry / rx

        from_x = to_x
        from_y = to_y

        to_x = (4.0 * from_x - slope * slope * from_x + 2.0 * slope * from_y) / (0.0 - 4.0 - slope * slope)
        to_y = slope * (to_x - from_x) + from_y
        steps = steps + 1
    }
    printf("%lld\n", steps)
    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 steps = 0;
    double from_x = 0.0;
    double from_y = 10.1;
    double to_x = 1.4;
    double to_y = (0.0 - 9.6);
    while (1) {
        if (((to_x >= (0.0 - 0.01) && to_x <= 0.01) && to_y > 9.9)) {
            break;
        }
        double nx = (0.0 - (4.0 * to_x));
        double ny = (0.0 - to_y);
        double length = sqrt(((nx * nx) + (ny * ny)));
        nx = (nx / length);
        ny = (ny / length);
        double dx = (to_x - from_x);
        double dy = (to_y - from_y);
        double dot = ((dx * nx) + (dy * ny));
        double rx = (dx - ((2.0 * dot) * nx));
        double ry = (dy - ((2.0 * dot) * ny));
        double slope = (ry / rx);
        from_x = to_x;
        from_y = to_y;
        to_x = ((((4.0 * from_x) - ((slope * slope) * from_x)) + ((2.0 * slope) * from_y)) / ((0.0 - 4.0) - (slope * slope)));
        to_y = ((slope * (to_x - from_x)) + from_y);
        steps = (steps + 1);
    }
    printf("%lld\n", steps);
    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 private @sqrt(f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 0 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    %4 = arith.constant 0.0 : 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 10.1 : f32
    %9 = arith.extf %8 : f32 to f64
    %10 = llvm.mlir.constant(1 : i64) : i64
    %11 = llvm.alloca %10 x f64 : (i64) -> !llvm.ptr
    llvm.store %9, %11 : f64, !llvm.ptr
    %12 = arith.constant 1.4 : 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 0.0 : f32
    %17 = arith.constant 9.6 : f32
    %18 = arith.subf %16, %17 : f32
    %19 = arith.extf %18 : f32 to f64
    %20 = llvm.mlir.constant(1 : i64) : i64
    %21 = llvm.alloca %20 x f64 : (i64) -> !llvm.ptr
    llvm.store %19, %21 : f64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %22 = arith.constant 1 : i1
    cf.cond_br %22, ^bb1, ^bb2
    ^bb1:
      %23 = llvm.load %15 : !llvm.ptr -> f64
      %24 = arith.constant 0.0 : f32
      %25 = arith.constant 0.01 : f32
      %26 = arith.subf %24, %25 : f32
      %28 = arith.extf %26 : f32 to f64
      %27 = arith.cmpf oge, %23, %28 : f64
      %29 = scf.if %27 -> (i1) {
        %30 = llvm.load %15 : !llvm.ptr -> f64
        %31 = arith.constant 0.01 : f32
        %33 = arith.extf %31 : f32 to f64
        %32 = arith.cmpf ole, %30, %33 : f64
        scf.yield %32 : i1
      } else {
        %34 = arith.constant false
        scf.yield %34 : i1
      }
      %35 = scf.if %29 -> (i1) {
        %36 = llvm.load %21 : !llvm.ptr -> f64
        %37 = arith.constant 9.9 : f32
        %39 = arith.extf %37 : f32 to f64
        %38 = arith.cmpf ogt, %36, %39 : f64
        scf.yield %38 : i1
      } else {
        %40 = arith.constant false
        scf.yield %40 : i1
      }
      cf.cond_br %35, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %41 = arith.constant 0.0 : f32
      %42 = arith.constant 4.0 : f32
      %43 = llvm.load %15 : !llvm.ptr -> f64
      %45 = arith.extf %42 : f32 to f64
      %44 = arith.mulf %45, %43 : f64
      %47 = arith.extf %41 : f32 to f64
      %46 = arith.subf %47, %44 : f64
      %48 = llvm.mlir.constant(1 : i64) : i64
      %49 = llvm.alloca %48 x f64 : (i64) -> !llvm.ptr
      llvm.store %46, %49 : f64, !llvm.ptr
      %50 = arith.constant 0.0 : f32
      %51 = llvm.load %21 : !llvm.ptr -> f64
      %53 = arith.extf %50 : f32 to f64
      %52 = arith.subf %53, %51 : f64
      %54 = llvm.mlir.constant(1 : i64) : i64
      %55 = llvm.alloca %54 x f64 : (i64) -> !llvm.ptr
      llvm.store %52, %55 : f64, !llvm.ptr
      %56 = llvm.load %49 : !llvm.ptr -> f64
      %57 = llvm.load %49 : !llvm.ptr -> f64
      %58 = arith.mulf %56, %57 : f64
      %59 = llvm.load %55 : !llvm.ptr -> f64
      %60 = llvm.load %55 : !llvm.ptr -> f64
      %61 = arith.mulf %59, %60 : f64
      %62 = arith.addf %58, %61 : f64
      %63 = math.sqrt %62 : f64
      %64 = llvm.load %49 : !llvm.ptr -> f64
      %65 = arith.divf %64, %63 : f64
      llvm.store %65, %49 : f64, !llvm.ptr
      %66 = llvm.load %55 : !llvm.ptr -> f64
      %67 = arith.divf %66, %63 : f64
      llvm.store %67, %55 : f64, !llvm.ptr
      %68 = llvm.load %15 : !llvm.ptr -> f64
      %69 = llvm.load %7 : !llvm.ptr -> f64
      %70 = arith.subf %68, %69 : f64
      %71 = llvm.load %21 : !llvm.ptr -> f64
      %72 = llvm.load %11 : !llvm.ptr -> f64
      %73 = arith.subf %71, %72 : f64
      %74 = llvm.load %49 : !llvm.ptr -> f64
      %75 = arith.mulf %70, %74 : f64
      %76 = llvm.load %55 : !llvm.ptr -> f64
      %77 = arith.mulf %73, %76 : f64
      %78 = arith.addf %75, %77 : f64
      %79 = arith.constant 2.0 : f32
      %81 = arith.extf %79 : f32 to f64
      %80 = arith.mulf %81, %78 : f64
      %82 = llvm.load %49 : !llvm.ptr -> f64
      %83 = arith.mulf %80, %82 : f64
      %84 = arith.subf %70, %83 : f64
      %85 = arith.constant 2.0 : f32
      %87 = arith.extf %85 : f32 to f64
      %86 = arith.mulf %87, %78 : f64
      %88 = llvm.load %55 : !llvm.ptr -> f64
      %89 = arith.mulf %86, %88 : f64
      %90 = arith.subf %73, %89 : f64
      %91 = arith.divf %90, %84 : f64
      %92 = llvm.load %15 : !llvm.ptr -> f64
      llvm.store %92, %7 : f64, !llvm.ptr
      %93 = llvm.load %21 : !llvm.ptr -> f64
      llvm.store %93, %11 : f64, !llvm.ptr
      %94 = arith.constant 4.0 : f32
      %95 = llvm.load %7 : !llvm.ptr -> f64
      %97 = arith.extf %94 : f32 to f64
      %96 = arith.mulf %97, %95 : f64
      %98 = arith.mulf %91, %91 : f64
      %99 = llvm.load %7 : !llvm.ptr -> f64
      %100 = arith.mulf %98, %99 : f64
      %101 = arith.subf %96, %100 : f64
      %102 = arith.constant 2.0 : f32
      %104 = arith.extf %102 : f32 to f64
      %103 = arith.mulf %104, %91 : f64
      %105 = llvm.load %11 : !llvm.ptr -> f64
      %106 = arith.mulf %103, %105 : f64
      %107 = arith.addf %101, %106 : f64
      %108 = arith.constant 0.0 : f32
      %109 = arith.constant 4.0 : f32
      %110 = arith.subf %108, %109 : f32
      %111 = arith.mulf %91, %91 : f64
      %113 = arith.extf %110 : f32 to f64
      %112 = arith.subf %113, %111 : f64
      %114 = arith.divf %107, %112 : f64
      llvm.store %114, %15 : f64, !llvm.ptr
      %115 = llvm.load %15 : !llvm.ptr -> f64
      %116 = llvm.load %7 : !llvm.ptr -> f64
      %117 = arith.subf %115, %116 : f64
      %118 = arith.mulf %91, %117 : f64
      %119 = llvm.load %11 : !llvm.ptr -> f64
      %120 = arith.addf %118, %119 : f64
      llvm.store %120, %21 : f64, !llvm.ptr
      %121 = llvm.load %3 : !llvm.ptr -> i64
      %122 = arith.constant 1 : i32
      %124 = arith.extsi %122 : i32 to i64
      %123 = arith.addi %121, %124 : i64
      llvm.store %123, %3 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %125 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %126 = llvm.load %3 : !llvm.ptr -> i64
    %127 = llvm.call @printf(%125, %126) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %128 = arith.constant 0 : i32
    func.return %128 : i32
  }
}