Problem 499

St. Petersburg Lottery — p_15(10^9) via negative root of mgf equation.

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Performance comparison

Flow source

# Project Euler 499
# St. Petersburg Lottery — p_15(10^9) via negative root of mgf equation.

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

function expm1(x: f64) -> f64 {
    return exp(x) - 1.0
}

function f_expm1(t: f64, m: i32) -> f64 {
    let mut s: f64 = 0.0
    let mut c: f64 = 0.0
    let mut pow2: f64 = 1.0
    let mut weight: f64 = 0.5
    let mut k: i32 = 0
    while k < 200 {
        let term: f64 = weight * expm1(pow2 * t)
        let y: f64 = term - c
        let tmp: f64 = s + y
        c = (tmp - s) - y
        s = tmp
        if weight < 1.0e-27 { break }
        pow2 = pow2 * 2.0
        weight = weight * 0.5
        k = k + 1
    }
    return expm1((m as f64) * t) - s
}

function solve_t(m: i32) -> f64 {
    let mut hi: f64 = -1.0e-12
    let mut f_hi: f64 = f_expm1(hi, m)
    while f_hi <= 0.0 {
        hi = hi * 0.5
        f_hi = f_expm1(hi, m)
    }
    let mut lo: f64 = hi
    let mut f_lo: f64 = f_hi
    while f_lo > 0.0 {
        lo = lo * 2.0
        f_lo = f_expm1(lo, m)
    }
    let mut it: i32 = 0
    while it < 120 {
        let mid: f64 = (lo + hi) * 0.5
        let f_mid: f64 = f_expm1(mid, m)
        if f_mid > 0.0 {
            hi = mid
        } else {
            lo = mid
        }
        it = it + 1
    }
    return (lo + hi) * 0.5
}

function main() -> i32 {
    let m: i32 = 15
    let s: i64 = 1000000000
    let t: f64 = solve_t(m)
    let p: f64 = -expm1(t * ((s - (m as i64) + 1) as f64))
    printf("%.7f\n", p)
    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 expm1_f64(double x);
double f_expm1_f64_i32(double t, int32_t m);
double solve_t_i32(int32_t m);
int32_t main(void);


double expm1_f64(double x) {
    return (exp(x) - 1.0);
}

double f_expm1_f64_i32(double t, int32_t m) {
    double s = 0.0;
    double c = 0.0;
    double pow2 = 1.0;
    double weight = 0.5;
    int32_t k = 0;
    while (k < 200) {
        double term = (weight * expm1_f64((pow2 * t)));
        double y = (term - c);
        double tmp = (s + y);
        c = ((tmp - s) - y);
        s = tmp;
        if (weight < 1.0e-27) {
            break;
        }
        pow2 = (pow2 * 2.0);
        weight = (weight * 0.5);
        k = (k + 1);
    }
    return (expm1_f64((((double)(m)) * t)) - s);
}

double solve_t_i32(int32_t m) {
    double hi = (-1.0e-12);
    double f_hi = f_expm1_f64_i32(hi, m);
    while (f_hi <= 0.0) {
        hi = (hi * 0.5);
        f_hi = f_expm1_f64_i32(hi, m);
    }
    double lo = hi;
    double f_lo = f_hi;
    while (f_lo > 0.0) {
        lo = (lo * 2.0);
        f_lo = f_expm1_f64_i32(lo, m);
    }
    int32_t it = 0;
    while (it < 120) {
        double mid = ((lo + hi) * 0.5);
        double f_mid = f_expm1_f64_i32(mid, m);
        if (f_mid > 0.0) {
            hi = mid;
        } else {
            lo = mid;
        }
        it = (it + 1);
    }
    return ((lo + hi) * 0.5);
}

int32_t main(void) {
    int32_t m = 15;
    int64_t s = 1000000000;
    double t = solve_t_i32(m);
    double p = (-expm1_f64((t * ((double)(((s - ((int64_t)(m))) + 1))))));
    printf("%.7f\n", p);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.7f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @exp(f64) -> f64
  func.func @expm1(%arg0: f64) -> f64 {
    %0 = math.exp %arg0 : f64
    %1 = arith.constant 1.0 : f32
    %3 = arith.extf %1 : f32 to f64
    %2 = arith.subf %0, %3 : f64
    func.return %2 : f64
  }
  func.func @f_expm1(%arg0: f64, %arg1: i32) -> f64 {
    %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 0.0 : 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 1.0 : 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 0.5 : f32
    %17 = arith.extf %16 : f32 to f64
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x f64 : (i64) -> !llvm.ptr
    llvm.store %17, %19 : f64, !llvm.ptr
    %20 = arith.constant 0 : i32
    %21 = llvm.mlir.constant(1 : i64) : i64
    %22 = llvm.alloca %21 x i32 : (i64) -> !llvm.ptr
    llvm.store %20, %22 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %23 = llvm.load %22 : !llvm.ptr -> i32
    %24 = arith.constant 200 : i32
    %25 = arith.cmpi slt, %23, %24 : i32
    cf.cond_br %25, ^bb1, ^bb2
    ^bb1:
      %26 = llvm.load %19 : !llvm.ptr -> f64
      %28 = llvm.load %15 : !llvm.ptr -> f64
      %29 = arith.mulf %28, %arg0 : f64
      %27 = func.call @expm1(%29) : (f64) -> f64
      %30 = arith.mulf %26, %27 : f64
      %31 = llvm.load %11 : !llvm.ptr -> f64
      %32 = arith.subf %30, %31 : f64
      %33 = llvm.load %7 : !llvm.ptr -> f64
      %34 = arith.addf %33, %32 : f64
      %35 = llvm.load %7 : !llvm.ptr -> f64
      %36 = arith.subf %34, %35 : f64
      %37 = arith.subf %36, %32 : f64
      llvm.store %37, %11 : f64, !llvm.ptr
      llvm.store %34, %7 : f64, !llvm.ptr
      %38 = llvm.load %19 : !llvm.ptr -> f64
      %39 = arith.constant 0 : f32
      %41 = arith.extf %39 : f32 to f64
      %40 = arith.cmpf olt, %38, %41 : f64
      cf.cond_br %40, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %42 = llvm.load %15 : !llvm.ptr -> f64
      %43 = arith.constant 2.0 : f32
      %45 = arith.extf %43 : f32 to f64
      %44 = arith.mulf %42, %45 : f64
      llvm.store %44, %15 : f64, !llvm.ptr
      %46 = llvm.load %19 : !llvm.ptr -> f64
      %47 = arith.constant 0.5 : f32
      %49 = arith.extf %47 : f32 to f64
      %48 = arith.mulf %46, %49 : f64
      llvm.store %48, %19 : f64, !llvm.ptr
      %50 = llvm.load %22 : !llvm.ptr -> i32
      %51 = arith.constant 1 : i32
      %52 = arith.addi %50, %51 : i32
      llvm.store %52, %22 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %54 = arith.sitofp %arg1 : i32 to f64
    %55 = arith.mulf %54, %arg0 : f64
    %53 = func.call @expm1(%55) : (f64) -> f64
    %56 = llvm.load %7 : !llvm.ptr -> f64
    %57 = arith.subf %53, %56 : f64
    func.return %57 : f64
  }
  func.func @solve_t(%arg0: i32) -> f64 {
    %58 = arith.constant 0 : f32
    %59 = arith.negf %58 : f32
    %60 = arith.extf %59 : f32 to f64
    %61 = llvm.mlir.constant(1 : i64) : i64
    %62 = llvm.alloca %61 x f64 : (i64) -> !llvm.ptr
    llvm.store %60, %62 : f64, !llvm.ptr
    %64 = llvm.load %62 : !llvm.ptr -> f64
    %63 = func.call @f_expm1(%64, %arg0) : (f64, i32) -> f64
    %65 = llvm.mlir.constant(1 : i64) : i64
    %66 = llvm.alloca %65 x f64 : (i64) -> !llvm.ptr
    llvm.store %63, %66 : f64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %67 = llvm.load %66 : !llvm.ptr -> f64
    %68 = arith.constant 0.0 : f32
    %70 = arith.extf %68 : f32 to f64
    %69 = arith.cmpf ole, %67, %70 : f64
    cf.cond_br %69, ^bb7, ^bb8
    ^bb7:
      %71 = llvm.load %62 : !llvm.ptr -> f64
      %72 = arith.constant 0.5 : f32
      %74 = arith.extf %72 : f32 to f64
      %73 = arith.mulf %71, %74 : f64
      llvm.store %73, %62 : f64, !llvm.ptr
      %76 = llvm.load %62 : !llvm.ptr -> f64
      %75 = func.call @f_expm1(%76, %arg0) : (f64, i32) -> f64
      llvm.store %75, %66 : f64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %77 = llvm.load %62 : !llvm.ptr -> f64
    %78 = llvm.mlir.constant(1 : i64) : i64
    %79 = llvm.alloca %78 x f64 : (i64) -> !llvm.ptr
    llvm.store %77, %79 : f64, !llvm.ptr
    %80 = llvm.load %66 : !llvm.ptr -> f64
    %81 = llvm.mlir.constant(1 : i64) : i64
    %82 = llvm.alloca %81 x f64 : (i64) -> !llvm.ptr
    llvm.store %80, %82 : f64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %83 = llvm.load %82 : !llvm.ptr -> f64
    %84 = arith.constant 0.0 : f32
    %86 = arith.extf %84 : f32 to f64
    %85 = arith.cmpf ogt, %83, %86 : f64
    cf.cond_br %85, ^bb10, ^bb11
    ^bb10:
      %87 = llvm.load %79 : !llvm.ptr -> f64
      %88 = arith.constant 2.0 : f32
      %90 = arith.extf %88 : f32 to f64
      %89 = arith.mulf %87, %90 : f64
      llvm.store %89, %79 : f64, !llvm.ptr
      %92 = llvm.load %79 : !llvm.ptr -> f64
      %91 = func.call @f_expm1(%92, %arg0) : (f64, i32) -> f64
      llvm.store %91, %82 : f64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %93 = arith.constant 0 : i32
    %94 = llvm.mlir.constant(1 : i64) : i64
    %95 = llvm.alloca %94 x i32 : (i64) -> !llvm.ptr
    llvm.store %93, %95 : i32, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %96 = llvm.load %95 : !llvm.ptr -> i32
    %97 = arith.constant 120 : i32
    %98 = arith.cmpi slt, %96, %97 : i32
    cf.cond_br %98, ^bb13, ^bb14
    ^bb13:
      %99 = llvm.load %79 : !llvm.ptr -> f64
      %100 = llvm.load %62 : !llvm.ptr -> f64
      %101 = arith.addf %99, %100 : f64
      %102 = arith.constant 0.5 : f32
      %104 = arith.extf %102 : f32 to f64
      %103 = arith.mulf %101, %104 : f64
      %105 = func.call @f_expm1(%103, %arg0) : (f64, i32) -> f64
      %106 = arith.constant 0.0 : f32
      %108 = arith.extf %106 : f32 to f64
      %107 = arith.cmpf ogt, %105, %108 : f64
      cf.cond_br %107, ^bb15, ^bb16
      ^bb15:
        llvm.store %103, %62 : f64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        llvm.store %103, %79 : f64, !llvm.ptr
        cf.br ^bb17
      ^bb17:
      %109 = llvm.load %95 : !llvm.ptr -> i32
      %110 = arith.constant 1 : i32
      %111 = arith.addi %109, %110 : i32
      llvm.store %111, %95 : i32, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %112 = llvm.load %79 : !llvm.ptr -> f64
    %113 = llvm.load %62 : !llvm.ptr -> f64
    %114 = arith.addf %112, %113 : f64
    %115 = arith.constant 0.5 : f32
    %117 = arith.extf %115 : f32 to f64
    %116 = arith.mulf %114, %117 : f64
    func.return %116 : f64
  }
  func.func @main() -> i32 {
    %118 = arith.constant 15 : i32
    %119 = arith.constant 1000000000 : i32
    %120 = arith.extsi %119 : i32 to i64
    %121 = func.call @solve_t(%118) : (i32) -> f64
    %123 = arith.extsi %118 : i32 to i64
    %124 = arith.subi %120, %123 : i64
    %125 = arith.constant 1 : i32
    %127 = arith.extsi %125 : i32 to i64
    %126 = arith.addi %124, %127 : i64
    %128 = arith.sitofp %126 : i64 to f64
    %129 = arith.mulf %121, %128 : f64
    %122 = func.call @expm1(%129) : (f64) -> f64
    %130 = arith.negf %122 : f64
    %131 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %132 = llvm.call @printf(%131, %130) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %133 = arith.constant 0 : i32
    func.return %133 : i32
  }
}