Problem 460

An Ant on the Move — minimal excess climb DP + cruise at height h=d/2.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 460
# An Ant on the Move — minimal excess climb DP + cruise at height h=d/2.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function log(x: f64) -> f64
    function sqrt(x: f64) -> f64
    function hypot(x: f64, y: f64) -> f64
    function floor(x: f64) -> f64
}

function min_step_excess(y0: i64, y1: i64, h: i64, logs: ptr<f64>) -> f64 {
    let dy: f64 = (y1 - y0) as f64
    let v: f64 = dy / (logs[y1] - logs[y0])
    let hh: f64 = h as f64
    let denom: f64 = sqrt(hh * hh - v * v)
    let dx_star: f64 = dy * v / denom
    let k0: i64 = floor(dx_star) as i64
    let mut best: f64 = 1.0e300
    let mut t: i64 = 0
    while t < 2 {
        let dx: i64 = k0 + t
        if dx >= 0 {
            let val: f64 = hypot(dx as f64, dy) / v - (dx as f64) / hh
            if val < best { best = val }
        }
        t = t + 1
    }
    return best
}

function best_climb_excess(h: i64) -> f64 {
    let logs: ptr<f64> = calloc(h + 1, 8)
    let dp: ptr<f64> = calloc(h + 1, 8)
    if logs == null || dp == null { return 0.0 }
    let mut y: i64 = 1
    while y <= h {
        logs[y] = log(y as f64)
        dp[y] = 1.0e300
        y = y + 1
    }
    dp[1] = 0.0
    y = 2
    while y <= h {
        let M: i64 = (64 * h) / y + 2
        let mut y0_min: i64 = y - M
        if y0_min < 1 { y0_min = 1 }
        let mut best: f64 = 1.0e300
        let mut y0: i64 = y0_min
        while y0 < y {
            let cand: f64 = dp[y0] + min_step_excess(y0, y, h, logs)
            if cand < best { best = cand }
            y0 = y0 + 1
        }
        dp[y] = best
        y = y + 1
    }
    let ans: f64 = dp[h]
    free(dp)
    free(logs)
    return ans
}

function main() -> i32 {
    let d: i64 = 10000
    let h: i64 = d / 2
    let E: f64 = best_climb_excess(h)
    let ans: f64 = 2.0 * E + (d as f64) / (h as f64)
    printf("%.9f\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 hypot(double x, double y);
double min_step_excess_i64_i64_i64_ptr_f64(int64_t y0, int64_t y1, int64_t h, double* logs);
double best_climb_excess_i64(int64_t h);
int32_t main(void);







double min_step_excess_i64_i64_i64_ptr_f64(int64_t y0, int64_t y1, int64_t h, double* logs) {
    double dy = ((double)((y1 - y0)));
    double v = (dy / (logs[y1] - logs[y0]));
    double hh = ((double)(h));
    double denom = sqrt(((hh * hh) - (v * v)));
    double dx_star = ((dy * v) / denom);
    int64_t k0 = ((int64_t)(floor(dx_star)));
    double best = 1.0e300;
    int64_t t = 0;
    while (t < 2) {
        int64_t dx = (k0 + t);
        if (dx >= 0) {
            double val = ((hypot(((double)(dx)), dy) / v) - (((double)(dx)) / hh));
            if (val < best) {
                best = val;
            }
        }
        t = (t + 1);
    }
    return best;
}

double best_climb_excess_i64(int64_t h) {
    double* logs = (double*)(calloc((h + 1), 8));
    double* dp = (double*)(calloc((h + 1), 8));
    if ((logs == NULL || dp == NULL)) {
        return 0.0;
    }
    int64_t y = 1;
    while (y <= h) {
        logs[y] = log(((double)(y)));
        dp[y] = 1.0e300;
        y = (y + 1);
    }
    dp[1] = 0.0;
    y = 2;
    while (y <= h) {
        int64_t M = (FLOW_CHECKED_DIV(((64 * h)), (y)) + 2);
        int64_t y0_min = (y - M);
        if (y0_min < 1) {
            y0_min = 1;
        }
        double best = 1.0e300;
        int64_t y0 = y0_min;
        while (y0 < y) {
            double cand = (dp[y0] + min_step_excess_i64_i64_i64_ptr_f64(y0, y, h, logs));
            if (cand < best) {
                best = cand;
            }
            y0 = (y0 + 1);
        }
        dp[y] = best;
        y = (y + 1);
    }
    double ans = dp[h];
    free(dp);
    free(logs);
    return ans;
}

int32_t main(void) {
    int64_t d = 10000;
    int64_t h = FLOW_CHECKED_DIV((d), (2));
    double E = best_climb_excess_i64(h);
    double ans = ((2.0 * E) + (((double)(d)) / ((double)(h))));
    printf("%.9f\n", ans);
    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 @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func private @log(f64) -> f64
  func.func private @sqrt(f64) -> f64
  func.func private @hypot(f64, f64) -> f64
  func.func private @floor(f64) -> f64
  func.func @min_step_excess(%arg0: i64, %arg1: i64, %arg2: i64, %arg3: !llvm.ptr) -> f64 {
    %0 = arith.subi %arg1, %arg0 : i64
    %1 = arith.sitofp %0 : i64 to f64
    %3 = llvm.getelementptr %arg3[%arg1] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %2 = llvm.load %3 : !llvm.ptr -> f64
    %5 = llvm.getelementptr %arg3[%arg0] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %4 = llvm.load %5 : !llvm.ptr -> f64
    %6 = arith.subf %2, %4 : f64
    %7 = arith.divf %1, %6 : f64
    %8 = arith.sitofp %arg2 : i64 to f64
    %9 = arith.mulf %8, %8 : f64
    %10 = arith.mulf %7, %7 : f64
    %11 = arith.subf %9, %10 : f64
    %12 = math.sqrt %11 : f64
    %13 = arith.mulf %1, %7 : f64
    %14 = arith.divf %13, %12 : f64
    %15 = func.call @floor(%14) : (f64) -> f64
    %16 = arith.fptosi %15 : f64 to i64
    %17 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
    %18 = arith.extf %17 : f32 to f64
    %19 = llvm.mlir.constant(1 : i64) : i64
    %20 = llvm.alloca %19 x f64 : (i64) -> !llvm.ptr
    llvm.store %18, %20 : f64, !llvm.ptr
    %21 = arith.constant 0 : i32
    %22 = arith.extsi %21 : i32 to i64
    %23 = llvm.mlir.constant(1 : i64) : i64
    %24 = llvm.alloca %23 x i64 : (i64) -> !llvm.ptr
    llvm.store %22, %24 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %25 = llvm.load %24 : !llvm.ptr -> i64
    %26 = arith.constant 2 : i32
    %28 = arith.extsi %26 : i32 to i64
    %27 = arith.cmpi slt, %25, %28 : i64
    cf.cond_br %27, ^bb1, ^bb2
    ^bb1:
      %29 = llvm.load %24 : !llvm.ptr -> i64
      %30 = arith.addi %16, %29 : i64
      %31 = arith.constant 0 : i32
      %33 = arith.extsi %31 : i32 to i64
      %32 = arith.cmpi sge, %30, %33 : i64
      cf.cond_br %32, ^bb3, ^bb4
      ^bb3:
        %35 = arith.sitofp %30 : i64 to f64
        %34 = func.call @hypot(%35, %1) : (f64, f64) -> f64
        %36 = arith.divf %34, %7 : f64
        %37 = arith.sitofp %30 : i64 to f64
        %38 = arith.divf %37, %8 : f64
        %39 = arith.subf %36, %38 : f64
        %40 = llvm.load %20 : !llvm.ptr -> f64
        %41 = arith.cmpf olt, %39, %40 : f64
        cf.cond_br %41, ^bb6, ^bb7
        ^bb6:
          llvm.store %39, %20 : f64, !llvm.ptr
          cf.br ^bb8
        ^bb7:
          cf.br ^bb8
        ^bb8:
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %42 = llvm.load %24 : !llvm.ptr -> i64
      %43 = arith.constant 1 : i32
      %45 = arith.extsi %43 : i32 to i64
      %44 = arith.addi %42, %45 : i64
      llvm.store %44, %24 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %46 = llvm.load %20 : !llvm.ptr -> f64
    func.return %46 : f64
  }
  func.func @best_climb_excess(%arg0: i64) -> f64 {
    %48 = arith.constant 1 : i32
    %50 = arith.extsi %48 : i32 to i64
    %49 = arith.addi %arg0, %50 : i64
    %51 = arith.constant 8 : i32
    %52 = arith.extsi %51 : i32 to i64
    %47 = func.call @calloc(%49, %52) : (i64, i64) -> !llvm.ptr
    %54 = arith.constant 1 : i32
    %56 = arith.extsi %54 : i32 to i64
    %55 = arith.addi %arg0, %56 : i64
    %57 = arith.constant 8 : i32
    %58 = arith.extsi %57 : i32 to i64
    %53 = func.call @calloc(%55, %58) : (i64, i64) -> !llvm.ptr
    %59 = llvm.mlir.zero : !llvm.ptr
    %60 = llvm.icmp "eq" %47, %59 : !llvm.ptr
    %61 = scf.if %60 -> (i1) {
      %62 = arith.constant true
      scf.yield %62 : i1
    } else {
      %63 = llvm.mlir.zero : !llvm.ptr
      %64 = llvm.icmp "eq" %53, %63 : !llvm.ptr
      scf.yield %64 : i1
    }
    cf.cond_br %61, ^bb9, ^bb10
    ^bb9:
      %65 = arith.constant 0.0 : f32
      %66 = arith.extf %65 : f32 to f64
      func.return %66 : f64
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %67 = arith.constant 1 : i32
    %68 = arith.extsi %67 : i32 to i64
    %69 = llvm.mlir.constant(1 : i64) : i64
    %70 = llvm.alloca %69 x i64 : (i64) -> !llvm.ptr
    llvm.store %68, %70 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %71 = llvm.load %70 : !llvm.ptr -> i64
    %72 = arith.cmpi sle, %71, %arg0 : i64
    cf.cond_br %72, ^bb13, ^bb14
    ^bb13:
      %73 = llvm.load %70 : !llvm.ptr -> i64
      %74 = arith.sitofp %73 : i64 to f64
      %75 = math.log %74 : f64
      %76 = llvm.load %70 : !llvm.ptr -> i64
      %77 = llvm.getelementptr %47[%76] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %75, %77 : f64, !llvm.ptr
      %78 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
      %79 = llvm.load %70 : !llvm.ptr -> i64
      %80 = arith.extf %78 : f32 to f64
      %81 = llvm.getelementptr %53[%79] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %80, %81 : f64, !llvm.ptr
      %82 = llvm.load %70 : !llvm.ptr -> i64
      %83 = arith.constant 1 : i32
      %85 = arith.extsi %83 : i32 to i64
      %84 = arith.addi %82, %85 : i64
      llvm.store %84, %70 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %86 = arith.constant 0.0 : f32
    %87 = arith.constant 1 : i32
    %88 = arith.extf %86 : f32 to f64
    %89 = arith.extsi %87 : i32 to i64
    %90 = llvm.getelementptr %53[%89] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %88, %90 : f64, !llvm.ptr
    %91 = arith.constant 2 : i32
    %92 = arith.extsi %91 : i32 to i64
    llvm.store %92, %70 : i64, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %93 = llvm.load %70 : !llvm.ptr -> i64
    %94 = arith.cmpi sle, %93, %arg0 : i64
    cf.cond_br %94, ^bb16, ^bb17
    ^bb16:
      %95 = arith.constant 64 : i32
      %97 = arith.extsi %95 : i32 to i64
      %96 = arith.muli %97, %arg0 : i64
      %98 = llvm.load %70 : !llvm.ptr -> i64
      %99 = arith.divsi %96, %98 : i64
      %100 = arith.constant 2 : i32
      %102 = arith.extsi %100 : i32 to i64
      %101 = arith.addi %99, %102 : i64
      %103 = llvm.load %70 : !llvm.ptr -> i64
      %104 = arith.subi %103, %101 : i64
      %105 = llvm.mlir.constant(1 : i64) : i64
      %106 = llvm.alloca %105 x i64 : (i64) -> !llvm.ptr
      llvm.store %104, %106 : i64, !llvm.ptr
      %107 = llvm.load %106 : !llvm.ptr -> i64
      %108 = arith.constant 1 : i32
      %110 = arith.extsi %108 : i32 to i64
      %109 = arith.cmpi slt, %107, %110 : i64
      cf.cond_br %109, ^bb18, ^bb19
      ^bb18:
        %111 = arith.constant 1 : i32
        %112 = arith.extsi %111 : i32 to i64
        llvm.store %112, %106 : i64, !llvm.ptr
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %113 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
      %114 = arith.extf %113 : f32 to f64
      %115 = llvm.mlir.constant(1 : i64) : i64
      %116 = llvm.alloca %115 x f64 : (i64) -> !llvm.ptr
      llvm.store %114, %116 : f64, !llvm.ptr
      %117 = llvm.load %106 : !llvm.ptr -> i64
      %118 = llvm.mlir.constant(1 : i64) : i64
      %119 = llvm.alloca %118 x i64 : (i64) -> !llvm.ptr
      llvm.store %117, %119 : i64, !llvm.ptr
      cf.br ^bb21
      ^bb21:
      %120 = llvm.load %119 : !llvm.ptr -> i64
      %121 = llvm.load %70 : !llvm.ptr -> i64
      %122 = arith.cmpi slt, %120, %121 : i64
      cf.cond_br %122, ^bb22, ^bb23
      ^bb22:
        %124 = llvm.load %119 : !llvm.ptr -> i64
        %125 = llvm.getelementptr %53[%124] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %123 = llvm.load %125 : !llvm.ptr -> f64
        %127 = llvm.load %119 : !llvm.ptr -> i64
        %128 = llvm.load %70 : !llvm.ptr -> i64
        %126 = func.call @min_step_excess(%127, %128, %arg0, %47) : (i64, i64, i64, !llvm.ptr) -> f64
        %129 = arith.addf %123, %126 : f64
        %130 = llvm.load %116 : !llvm.ptr -> f64
        %131 = arith.cmpf olt, %129, %130 : f64
        cf.cond_br %131, ^bb24, ^bb25
        ^bb24:
          llvm.store %129, %116 : f64, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          cf.br ^bb26
        ^bb26:
        %132 = llvm.load %119 : !llvm.ptr -> i64
        %133 = arith.constant 1 : i32
        %135 = arith.extsi %133 : i32 to i64
        %134 = arith.addi %132, %135 : i64
        llvm.store %134, %119 : i64, !llvm.ptr
        cf.br ^bb21
      ^bb23:
      %136 = llvm.load %116 : !llvm.ptr -> f64
      %137 = llvm.load %70 : !llvm.ptr -> i64
      %138 = llvm.getelementptr %53[%137] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %136, %138 : f64, !llvm.ptr
      %139 = llvm.load %70 : !llvm.ptr -> i64
      %140 = arith.constant 1 : i32
      %142 = arith.extsi %140 : i32 to i64
      %141 = arith.addi %139, %142 : i64
      llvm.store %141, %70 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %144 = llvm.getelementptr %53[%arg0] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    %143 = llvm.load %144 : !llvm.ptr -> f64
    func.call @free(%53) : (!llvm.ptr) -> ()
    func.call @free(%47) : (!llvm.ptr) -> ()
    func.return %143 : f64
  }
  func.func @main() -> i32 {
    %147 = arith.constant 10000 : i32
    %148 = arith.extsi %147 : i32 to i64
    %149 = arith.constant 2 : i32
    %151 = arith.extsi %149 : i32 to i64
    %150 = arith.divsi %148, %151 : i64
    %152 = func.call @best_climb_excess(%150) : (i64) -> f64
    %153 = arith.constant 2.0 : f32
    %155 = arith.extf %153 : f32 to f64
    %154 = arith.mulf %155, %152 : f64
    %156 = arith.sitofp %148 : i64 to f64
    %157 = arith.sitofp %150 : i64 to f64
    %158 = arith.divf %156, %157 : f64
    %159 = arith.addf %154, %158 : f64
    %160 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %161 = llvm.call @printf(%160, %159) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %162 = arith.constant 0 : i32
    func.return %162 : i32
  }
}