Problem 870

Transition values T(i) computed via g-base generation. Uses logarithmic representation of b values to avoid bignum, since b values grow exponentially. The ratio b_k/b[i_ptr-1] converges and f64 precision suffices for 10 decimal places.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 870: Stone Game IV
# Transition values T(i) computed via g-base generation.
# Uses logarithmic representation of b values to avoid bignum,
# since b values grow exponentially. The ratio b_k/b[i_ptr-1]
# converges and f64 precision suffices for 10 decimal places.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>)
    function printf(fmt: ptr<i8>, ...) -> i32
    function log(x: f64) -> f64
    function exp(x: f64) -> f64
    function log1p(x: f64) -> f64
}

const MAX_STEPS: i32 = 3000

function next_transition(q: f64) -> f64 {
    let log_b: ptr<f64> = calloc((MAX_STEPS + 2) as i64, 8)
    log_b[0] = 0.0
    let mut len_: i32 = 1
    let mut i_ptr: i32 = 0
    let mut best_ratio: f64 = 0.0
    let mut have_best: i32 = 0
    let log_q: f64 = log(q)
    let mut step: i32 = 0
    while step < MAX_STEPS {
        let log_bk: f64 = log_b[len_ - 1]
        let target: f64 = log_bk - log_q
        # advance i_ptr until log_b[i_ptr] >= target
        while i_ptr < len_ {
            if log_b[i_ptr] >= target - 1e-10 { break }
            i_ptr = i_ptr + 1
        }
        if i_ptr >= len_ { break }
        if i_ptr > 0 {
            let ratio: f64 = exp(log_bk - log_b[i_ptr - 1])
            if have_best == 0 || ratio < best_ratio {
                best_ratio = ratio
                have_best = 1
            }
        }
        # b[len] = bk + b[i_ptr] => log = log_bk + log1p(exp(log_b[i_ptr] - log_bk))
        let diff: f64 = log_b[i_ptr] - log_bk
        log_b[len_] = log_bk + log1p(exp(diff))
        len_ = len_ + 1
        step = step + 1
    }
    free(log_b as ptr<void>)
    if have_best == 0 { return 1.0 }
    return best_ratio
}

function main() -> i32 {
    let mut q: f64 = 1.0
    let mut i: i32 = 0
    while i < 123455 {
        q = next_transition(q)
        i = i + 1
    }
    printf("%.10f\n", q)
    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 log1p(double x);
double next_transition_f64(double q);
int32_t main(void);

static const int32_t MAX_STEPS = 3000;







double next_transition_f64(double q) {
    double* log_b = (double*)(calloc(((int64_t)((MAX_STEPS + 2))), 8));
    log_b[0] = 0.0;
    int32_t len_ = 1;
    int32_t i_ptr = 0;
    double best_ratio = 0.0;
    int32_t have_best = 0;
    double log_q = log(q);
    int32_t step = 0;
    while (step < MAX_STEPS) {
        double log_bk = log_b[(len_ - 1)];
        double target = (log_bk - log_q);
        while (i_ptr < len_) {
            if (log_b[i_ptr] >= (target - 1e-10)) {
                break;
            }
            i_ptr = (i_ptr + 1);
        }
        if (i_ptr >= len_) {
            break;
        }
        if (i_ptr > 0) {
            double ratio = exp((log_bk - log_b[(i_ptr - 1)]));
            if ((have_best == 0 || ratio < best_ratio)) {
                best_ratio = ratio;
                have_best = 1;
            }
        }
        double diff = (log_b[i_ptr] - log_bk);
        log_b[len_] = (log_bk + log1p(exp(diff)));
        len_ = (len_ + 1);
        step = (step + 1);
    }
    free(((void*)(log_b)));
    if (have_best == 0) {
        return 1.0;
    }
    return best_ratio;
}

int32_t main(void) {
    double q = 1.0;
    int32_t i = 0;
    while (i < 123455) {
        q = next_transition_f64(q);
        i = (i + 1);
    }
    printf("%.10f\n", q);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10f\n\00") {addr_space = 0 : i32} : !llvm.array<7 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 @exp(f64) -> f64
  func.func private @log1p(f64) -> f64
  // Constant: MAX_STEPS
  llvm.mlir.global internal constant @MAX_STEPS(3000 : i32) : i32
  func.func @next_transition(%arg0: f64) -> f64 {
    %1 = llvm.mlir.addressof @MAX_STEPS : !llvm.ptr
    %2 = llvm.load %1 : !llvm.ptr -> i32
    %3 = arith.constant 2 : i32
    %4 = arith.addi %2, %3 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = arith.constant 8 : i32
    %7 = arith.extsi %6 : i32 to i64
    %0 = func.call @calloc(%5, %7) : (i64, i64) -> !llvm.ptr
    %8 = arith.constant 0.0 : f32
    %9 = arith.constant 0 : i32
    %10 = arith.extf %8 : f32 to f64
    %11 = arith.extsi %9 : i32 to i64
    %12 = llvm.getelementptr %0[%11] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %10, %12 : f64, !llvm.ptr
    %13 = arith.constant 1 : i32
    %14 = llvm.mlir.constant(1 : i64) : i64
    %15 = llvm.alloca %14 x i32 : (i64) -> !llvm.ptr
    llvm.store %13, %15 : i32, !llvm.ptr
    %16 = arith.constant 0 : i32
    %17 = llvm.mlir.constant(1 : i64) : i64
    %18 = llvm.alloca %17 x i32 : (i64) -> !llvm.ptr
    llvm.store %16, %18 : i32, !llvm.ptr
    %19 = arith.constant 0.0 : f32
    %20 = arith.extf %19 : f32 to f64
    %21 = llvm.mlir.constant(1 : i64) : i64
    %22 = llvm.alloca %21 x f64 : (i64) -> !llvm.ptr
    llvm.store %20, %22 : f64, !llvm.ptr
    %23 = arith.constant 0 : i32
    %24 = llvm.mlir.constant(1 : i64) : i64
    %25 = llvm.alloca %24 x i32 : (i64) -> !llvm.ptr
    llvm.store %23, %25 : i32, !llvm.ptr
    %26 = math.log %arg0 : f64
    %27 = arith.constant 0 : i32
    %28 = llvm.mlir.constant(1 : i64) : i64
    %29 = llvm.alloca %28 x i32 : (i64) -> !llvm.ptr
    llvm.store %27, %29 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %30 = llvm.load %29 : !llvm.ptr -> i32
    %31 = llvm.mlir.addressof @MAX_STEPS : !llvm.ptr
    %32 = llvm.load %31 : !llvm.ptr -> i32
    %33 = arith.cmpi slt, %30, %32 : i32
    cf.cond_br %33, ^bb1, ^bb2
    ^bb1:
      %35 = llvm.load %15 : !llvm.ptr -> i32
      %36 = arith.constant 1 : i32
      %37 = arith.subi %35, %36 : i32
      %38 = arith.extsi %37 : i32 to i64
      %39 = llvm.getelementptr %0[%38] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %34 = llvm.load %39 : !llvm.ptr -> f64
      %40 = arith.subf %34, %26 : f64
      cf.br ^bb3
      ^bb3:
      %41 = llvm.load %18 : !llvm.ptr -> i32
      %42 = llvm.load %15 : !llvm.ptr -> i32
      %43 = arith.cmpi slt, %41, %42 : i32
      cf.cond_br %43, ^bb4, ^bb5
      ^bb4:
        %45 = llvm.load %18 : !llvm.ptr -> i32
        %46 = arith.extsi %45 : i32 to i64
        %47 = llvm.getelementptr %0[%46] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %44 = llvm.load %47 : !llvm.ptr -> f64
        %48 = arith.constant 0.0000000001 : f32
        %50 = arith.extf %48 : f32 to f64
        %49 = arith.subf %40, %50 : f64
        %51 = arith.cmpf oge, %44, %49 : f64
        cf.cond_br %51, ^bb6, ^bb7
        ^bb6:
          cf.br ^bb5
        ^bb7:
          cf.br ^bb8
        ^bb8:
        %52 = llvm.load %18 : !llvm.ptr -> i32
        %53 = arith.constant 1 : i32
        %54 = arith.addi %52, %53 : i32
        llvm.store %54, %18 : i32, !llvm.ptr
        cf.br ^bb3
      ^bb5:
      %55 = llvm.load %18 : !llvm.ptr -> i32
      %56 = llvm.load %15 : !llvm.ptr -> i32
      %57 = arith.cmpi sge, %55, %56 : i32
      cf.cond_br %57, ^bb9, ^bb10
      ^bb9:
        cf.br ^bb2
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %58 = llvm.load %18 : !llvm.ptr -> i32
      %59 = arith.constant 0 : i32
      %60 = arith.cmpi sgt, %58, %59 : i32
      cf.cond_br %60, ^bb12, ^bb13
      ^bb12:
        %62 = llvm.load %18 : !llvm.ptr -> i32
        %63 = arith.constant 1 : i32
        %64 = arith.subi %62, %63 : i32
        %65 = arith.extsi %64 : i32 to i64
        %66 = llvm.getelementptr %0[%65] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        %61 = llvm.load %66 : !llvm.ptr -> f64
        %67 = arith.subf %34, %61 : f64
        %68 = math.exp %67 : f64
        %69 = llvm.load %25 : !llvm.ptr -> i32
        %70 = arith.constant 0 : i32
        %71 = arith.cmpi eq, %69, %70 : i32
        %72 = scf.if %71 -> (i1) {
          %73 = arith.constant true
          scf.yield %73 : i1
        } else {
          %74 = llvm.load %22 : !llvm.ptr -> f64
          %75 = arith.cmpf olt, %68, %74 : f64
          scf.yield %75 : i1
        }
        cf.cond_br %72, ^bb15, ^bb16
        ^bb15:
          llvm.store %68, %22 : f64, !llvm.ptr
          %76 = arith.constant 1 : i32
          llvm.store %76, %25 : i32, !llvm.ptr
          cf.br ^bb17
        ^bb16:
          cf.br ^bb17
        ^bb17:
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %78 = llvm.load %18 : !llvm.ptr -> i32
      %79 = arith.extsi %78 : i32 to i64
      %80 = llvm.getelementptr %0[%79] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %77 = llvm.load %80 : !llvm.ptr -> f64
      %81 = arith.subf %77, %34 : f64
      %83 = math.exp %81 : f64
      %82 = func.call @log1p(%83) : (f64) -> f64
      %84 = arith.addf %34, %82 : f64
      %85 = llvm.load %15 : !llvm.ptr -> i32
      %86 = arith.extsi %85 : i32 to i64
      %87 = llvm.getelementptr %0[%86] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %84, %87 : f64, !llvm.ptr
      %88 = llvm.load %15 : !llvm.ptr -> i32
      %89 = arith.constant 1 : i32
      %90 = arith.addi %88, %89 : i32
      llvm.store %90, %15 : i32, !llvm.ptr
      %91 = llvm.load %29 : !llvm.ptr -> i32
      %92 = arith.constant 1 : i32
      %93 = arith.addi %91, %92 : i32
      llvm.store %93, %29 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    func.call @free(%0) : (!llvm.ptr) -> ()
    %95 = llvm.load %25 : !llvm.ptr -> i32
    %96 = arith.constant 0 : i32
    %97 = arith.cmpi eq, %95, %96 : i32
    cf.cond_br %97, ^bb18, ^bb19
    ^bb18:
      %98 = arith.constant 1.0 : f32
      %99 = arith.extf %98 : f32 to f64
      func.return %99 : f64
    ^bb19:
      cf.br ^bb20
    ^bb20:
    %100 = llvm.load %22 : !llvm.ptr -> f64
    func.return %100 : f64
  }
  func.func @main() -> i32 {
    %101 = arith.constant 1.0 : f32
    %102 = arith.extf %101 : f32 to f64
    %103 = llvm.mlir.constant(1 : i64) : i64
    %104 = llvm.alloca %103 x f64 : (i64) -> !llvm.ptr
    llvm.store %102, %104 : f64, !llvm.ptr
    %105 = arith.constant 0 : i32
    %106 = llvm.mlir.constant(1 : i64) : i64
    %107 = llvm.alloca %106 x i32 : (i64) -> !llvm.ptr
    llvm.store %105, %107 : i32, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %108 = llvm.load %107 : !llvm.ptr -> i32
    %109 = arith.constant 123455 : i32
    %110 = arith.cmpi slt, %108, %109 : i32
    cf.cond_br %110, ^bb22, ^bb23
    ^bb22:
      %112 = llvm.load %104 : !llvm.ptr -> f64
      %111 = func.call @next_transition(%112) : (f64) -> f64
      llvm.store %111, %104 : f64, !llvm.ptr
      %113 = llvm.load %107 : !llvm.ptr -> i32
      %114 = arith.constant 1 : i32
      %115 = arith.addi %113, %114 : i32
      llvm.store %115, %107 : i32, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %116 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %117 = llvm.load %104 : !llvm.ptr -> f64
    %118 = llvm.call @printf(%116, %117) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %119 = arith.constant 0 : i32
    func.return %119 : i32
  }
}