Problem 901

Well Drilling — optimal increasing depths via admissibility boundary. E[T] = d1 + 1 + sum exp(-d_n) under d_{n+1} = exp(d_n - d_{n-1}).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 901
# Well Drilling — optimal increasing depths via admissibility boundary.
# E[T] = d1 + 1 + sum exp(-d_n) under d_{n+1} = exp(d_n - d_{n-1}).

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

function is_admissible(first: f64) -> i32 {
    let mut prev: f64 = 0.0
    let mut cur: f64 = first
    let mut step: i32 = 0
    while step < 200 {
        let gap: f64 = cur - prev
        if gap <= 0.0 { return 0 }
        if cur > 80.0 || gap > 80.0 { return 1 }
        prev = cur
        cur = exp(gap)
        step = step + 1
    }
    return 1
}

function expected_cost(first: f64) -> f64 {
    let mut prev: f64 = 0.0
    let mut cur: f64 = first
    let mut total: f64 = first + 1.0
    let mut step: i32 = 0
    while step < 200 {
        total = total + exp(0.0 - cur)
        if cur > 80.0 { break }
        let nxt: f64 = exp(cur - prev)
        prev = cur
        cur = nxt
        step = step + 1
    }
    return total
}

function upper_branch_boundary() -> f64 {
    let mut prev_x: f64 = 0.6
    let mut prev_ok: i32 = is_admissible(prev_x)
    let mut x: f64 = 0.61
    let mut low: f64 = 0.0
    let mut high: f64 = 0.0
    let mut found: i32 = 0
    while x <= 1.5 {
        let ok: i32 = is_admissible(x)
        if prev_ok == 0 && ok == 1 {
            low = prev_x
            high = x
            found = 1
            break
        }
        prev_x = x
        prev_ok = ok
        x = x + 0.01
    }
    if found == 0 { return 0.0 }
    let mut i: i32 = 0
    while i < 90 {
        let mid: f64 = (low + high) * 0.5
        if is_admissible(mid) == 1 {
            high = mid
        } else {
            low = mid
        }
        i = i + 1
    }
    return high
}

function main() -> i32 {
    printf("%.9f\n", expected_cost(upper_branch_boundary()))
    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 is_admissible_f64(double first);
double expected_cost_f64(double first);
double upper_branch_boundary(void);
int32_t main(void);


int32_t is_admissible_f64(double first) {
    double prev = 0.0;
    double cur = first;
    int32_t step = 0;
    while (step < 200) {
        double gap = (cur - prev);
        if (gap <= 0.0) {
            return 0;
        }
        if ((cur > 80.0 || gap > 80.0)) {
            return 1;
        }
        prev = cur;
        cur = exp(gap);
        step = (step + 1);
    }
    return 1;
}

double expected_cost_f64(double first) {
    double prev = 0.0;
    double cur = first;
    double total = (first + 1.0);
    int32_t step = 0;
    while (step < 200) {
        total = (total + exp((0.0 - cur)));
        if (cur > 80.0) {
            break;
        }
        double nxt = exp((cur - prev));
        prev = cur;
        cur = nxt;
        step = (step + 1);
    }
    return total;
}

double upper_branch_boundary(void) {
    double prev_x = 0.6;
    int32_t prev_ok = is_admissible_f64(prev_x);
    double x = 0.61;
    double low = 0.0;
    double high = 0.0;
    int32_t found = 0;
    while (x <= 1.5) {
        int32_t ok = is_admissible_f64(x);
        if ((prev_ok == 0 && ok == 1)) {
            low = prev_x;
            high = x;
            found = 1;
            break;
        }
        prev_x = x;
        prev_ok = ok;
        x = (x + 0.01);
    }
    if (found == 0) {
        return 0.0;
    }
    int32_t i = 0;
    while (i < 90) {
        double mid = ((low + high) * 0.5);
        if (is_admissible_f64(mid) == 1) {
            high = mid;
        } else {
            low = mid;
        }
        i = (i + 1);
    }
    return high;
}

int32_t main(void) {
    printf("%.9f\n", expected_cost_f64(upper_branch_boundary()));
    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 @exp(f64) -> f64
  func.func @is_admissible(%arg0: f64) -> i32 {
    %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 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x f64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %5 : f64, !llvm.ptr
    %6 = arith.constant 0 : i32
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i32 : (i64) -> !llvm.ptr
    llvm.store %6, %8 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %9 = llvm.load %8 : !llvm.ptr -> i32
    %10 = arith.constant 200 : i32
    %11 = arith.cmpi slt, %9, %10 : i32
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %12 = llvm.load %5 : !llvm.ptr -> f64
      %13 = llvm.load %3 : !llvm.ptr -> f64
      %14 = arith.subf %12, %13 : f64
      %15 = arith.constant 0.0 : f32
      %17 = arith.extf %15 : f32 to f64
      %16 = arith.cmpf ole, %14, %17 : f64
      cf.cond_br %16, ^bb3, ^bb4
      ^bb3:
        %18 = arith.constant 0 : i32
        func.return %18 : i32
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %19 = llvm.load %5 : !llvm.ptr -> f64
      %20 = arith.constant 80.0 : f32
      %22 = arith.extf %20 : f32 to f64
      %21 = arith.cmpf ogt, %19, %22 : f64
      %23 = scf.if %21 -> (i1) {
        %24 = arith.constant true
        scf.yield %24 : i1
      } else {
        %25 = arith.constant 80.0 : f32
        %27 = arith.extf %25 : f32 to f64
        %26 = arith.cmpf ogt, %14, %27 : f64
        scf.yield %26 : i1
      }
      cf.cond_br %23, ^bb6, ^bb7
      ^bb6:
        %28 = arith.constant 1 : i32
        func.return %28 : i32
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %29 = llvm.load %5 : !llvm.ptr -> f64
      llvm.store %29, %3 : f64, !llvm.ptr
      %30 = math.exp %14 : f64
      llvm.store %30, %5 : f64, !llvm.ptr
      %31 = llvm.load %8 : !llvm.ptr -> i32
      %32 = arith.constant 1 : i32
      %33 = arith.addi %31, %32 : i32
      llvm.store %33, %8 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %34 = arith.constant 1 : i32
    func.return %34 : i32
  }
  func.func @expected_cost(%arg0: f64) -> f64 {
    %35 = arith.constant 0.0 : f32
    %36 = arith.extf %35 : f32 to f64
    %37 = llvm.mlir.constant(1 : i64) : i64
    %38 = llvm.alloca %37 x f64 : (i64) -> !llvm.ptr
    llvm.store %36, %38 : f64, !llvm.ptr
    %39 = llvm.mlir.constant(1 : i64) : i64
    %40 = llvm.alloca %39 x f64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %40 : f64, !llvm.ptr
    %41 = arith.constant 1.0 : f32
    %43 = arith.extf %41 : f32 to f64
    %42 = arith.addf %arg0, %43 : f64
    %44 = llvm.mlir.constant(1 : i64) : i64
    %45 = llvm.alloca %44 x f64 : (i64) -> !llvm.ptr
    llvm.store %42, %45 : f64, !llvm.ptr
    %46 = arith.constant 0 : i32
    %47 = llvm.mlir.constant(1 : i64) : i64
    %48 = llvm.alloca %47 x i32 : (i64) -> !llvm.ptr
    llvm.store %46, %48 : i32, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %49 = llvm.load %48 : !llvm.ptr -> i32
    %50 = arith.constant 200 : i32
    %51 = arith.cmpi slt, %49, %50 : i32
    cf.cond_br %51, ^bb10, ^bb11
    ^bb10:
      %52 = llvm.load %45 : !llvm.ptr -> f64
      %53 = arith.constant 0.0 : f32
      %54 = llvm.load %40 : !llvm.ptr -> f64
      %56 = arith.extf %53 : f32 to f64
      %55 = arith.subf %56, %54 : f64
      %57 = math.exp %55 : f64
      %58 = arith.addf %52, %57 : f64
      llvm.store %58, %45 : f64, !llvm.ptr
      %59 = llvm.load %40 : !llvm.ptr -> f64
      %60 = arith.constant 80.0 : f32
      %62 = arith.extf %60 : f32 to f64
      %61 = arith.cmpf ogt, %59, %62 : f64
      cf.cond_br %61, ^bb12, ^bb13
      ^bb12:
        cf.br ^bb11
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %63 = llvm.load %40 : !llvm.ptr -> f64
      %64 = llvm.load %38 : !llvm.ptr -> f64
      %65 = arith.subf %63, %64 : f64
      %66 = math.exp %65 : f64
      %67 = llvm.load %40 : !llvm.ptr -> f64
      llvm.store %67, %38 : f64, !llvm.ptr
      llvm.store %66, %40 : f64, !llvm.ptr
      %68 = llvm.load %48 : !llvm.ptr -> i32
      %69 = arith.constant 1 : i32
      %70 = arith.addi %68, %69 : i32
      llvm.store %70, %48 : i32, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %71 = llvm.load %45 : !llvm.ptr -> f64
    func.return %71 : f64
  }
  func.func @upper_branch_boundary() -> f64 {
    %72 = arith.constant 0.6 : f32
    %73 = arith.extf %72 : f32 to f64
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x f64 : (i64) -> !llvm.ptr
    llvm.store %73, %75 : f64, !llvm.ptr
    %77 = llvm.load %75 : !llvm.ptr -> f64
    %76 = func.call @is_admissible(%77) : (f64) -> i32
    %78 = llvm.mlir.constant(1 : i64) : i64
    %79 = llvm.alloca %78 x i32 : (i64) -> !llvm.ptr
    llvm.store %76, %79 : i32, !llvm.ptr
    %80 = arith.constant 0.61 : f32
    %81 = arith.extf %80 : f32 to f64
    %82 = llvm.mlir.constant(1 : i64) : i64
    %83 = llvm.alloca %82 x f64 : (i64) -> !llvm.ptr
    llvm.store %81, %83 : f64, !llvm.ptr
    %84 = arith.constant 0.0 : f32
    %85 = arith.extf %84 : f32 to f64
    %86 = llvm.mlir.constant(1 : i64) : i64
    %87 = llvm.alloca %86 x f64 : (i64) -> !llvm.ptr
    llvm.store %85, %87 : f64, !llvm.ptr
    %88 = arith.constant 0.0 : f32
    %89 = arith.extf %88 : f32 to f64
    %90 = llvm.mlir.constant(1 : i64) : i64
    %91 = llvm.alloca %90 x f64 : (i64) -> !llvm.ptr
    llvm.store %89, %91 : f64, !llvm.ptr
    %92 = arith.constant 0 : i32
    %93 = llvm.mlir.constant(1 : i64) : i64
    %94 = llvm.alloca %93 x i32 : (i64) -> !llvm.ptr
    llvm.store %92, %94 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %95 = llvm.load %83 : !llvm.ptr -> f64
    %96 = arith.constant 1.5 : f32
    %98 = arith.extf %96 : f32 to f64
    %97 = arith.cmpf ole, %95, %98 : f64
    cf.cond_br %97, ^bb16, ^bb17
    ^bb16:
      %100 = llvm.load %83 : !llvm.ptr -> f64
      %99 = func.call @is_admissible(%100) : (f64) -> i32
      %101 = llvm.load %79 : !llvm.ptr -> i32
      %102 = arith.constant 0 : i32
      %103 = arith.cmpi eq, %101, %102 : i32
      %104 = scf.if %103 -> (i1) {
        %105 = arith.constant 1 : i32
        %106 = arith.cmpi eq, %99, %105 : i32
        scf.yield %106 : i1
      } else {
        %107 = arith.constant false
        scf.yield %107 : i1
      }
      cf.cond_br %104, ^bb18, ^bb19
      ^bb18:
        %108 = llvm.load %75 : !llvm.ptr -> f64
        llvm.store %108, %87 : f64, !llvm.ptr
        %109 = llvm.load %83 : !llvm.ptr -> f64
        llvm.store %109, %91 : f64, !llvm.ptr
        %110 = arith.constant 1 : i32
        llvm.store %110, %94 : i32, !llvm.ptr
        cf.br ^bb17
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %111 = llvm.load %83 : !llvm.ptr -> f64
      llvm.store %111, %75 : f64, !llvm.ptr
      llvm.store %99, %79 : i32, !llvm.ptr
      %112 = llvm.load %83 : !llvm.ptr -> f64
      %113 = arith.constant 0.01 : f32
      %115 = arith.extf %113 : f32 to f64
      %114 = arith.addf %112, %115 : f64
      llvm.store %114, %83 : f64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %116 = llvm.load %94 : !llvm.ptr -> i32
    %117 = arith.constant 0 : i32
    %118 = arith.cmpi eq, %116, %117 : i32
    cf.cond_br %118, ^bb21, ^bb22
    ^bb21:
      %119 = arith.constant 0.0 : f32
      %120 = arith.extf %119 : f32 to f64
      func.return %120 : f64
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %121 = arith.constant 0 : i32
    %122 = llvm.mlir.constant(1 : i64) : i64
    %123 = llvm.alloca %122 x i32 : (i64) -> !llvm.ptr
    llvm.store %121, %123 : i32, !llvm.ptr
    cf.br ^bb24
    ^bb24:
    %124 = llvm.load %123 : !llvm.ptr -> i32
    %125 = arith.constant 90 : i32
    %126 = arith.cmpi slt, %124, %125 : i32
    cf.cond_br %126, ^bb25, ^bb26
    ^bb25:
      %127 = llvm.load %87 : !llvm.ptr -> f64
      %128 = llvm.load %91 : !llvm.ptr -> f64
      %129 = arith.addf %127, %128 : f64
      %130 = arith.constant 0.5 : f32
      %132 = arith.extf %130 : f32 to f64
      %131 = arith.mulf %129, %132 : f64
      %133 = func.call @is_admissible(%131) : (f64) -> i32
      %134 = arith.constant 1 : i32
      %135 = arith.cmpi eq, %133, %134 : i32
      cf.cond_br %135, ^bb27, ^bb28
      ^bb27:
        llvm.store %131, %91 : f64, !llvm.ptr
        cf.br ^bb29
      ^bb28:
        llvm.store %131, %87 : f64, !llvm.ptr
        cf.br ^bb29
      ^bb29:
      %136 = llvm.load %123 : !llvm.ptr -> i32
      %137 = arith.constant 1 : i32
      %138 = arith.addi %136, %137 : i32
      llvm.store %138, %123 : i32, !llvm.ptr
      cf.br ^bb24
    ^bb26:
    %139 = llvm.load %91 : !llvm.ptr -> f64
    func.return %139 : f64
  }
  func.func @main() -> i32 {
    %140 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %142 = func.call @upper_branch_boundary() : () -> f64
    %141 = func.call @expected_cost(%142) : (f64) -> f64
    %143 = llvm.call @printf(%140, %141) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %144 = arith.constant 0 : i32
    func.return %144 : i32
  }
}