Problem 444

S_20(10^14) = C(N+k,k)*(H_{N+k}-H_k) in scientific notation.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 444
# S_20(10^14) = C(N+k,k)*(H_{N+k}-H_k) in scientific notation.

extern {
    function log(x: f64) -> f64
    function pow(x: f64, y: f64) -> f64
}

function main() -> i32 {
    let N: f64 = 100000000000000.0
    let K: i32 = 20
    let mut log_binom: f64 = 0.0
    let mut i: i32 = 1
    while i <= K {
        log_binom = log_binom + log(N + (i as f64)) - log(i as f64)
        i = i + 1
    }
    let GAMMA: f64 = 0.5772156649015328606
    let n1: f64 = N + (K as f64)
    let inv: f64 = 1.0 / n1
    let inv2: f64 = inv * inv
    let inv4: f64 = inv2 * inv2
    let inv6: f64 = inv4 * inv2
    let inv8: f64 = inv4 * inv4
    let inv10: f64 = inv8 * inv2
    let Hnk: f64 = log(n1) + GAMMA + inv / 2.0 - inv2 / 12.0 + inv4 / 120.0 - inv6 / 252.0 + inv8 / 240.0 - 5.0 * inv10 / 660.0
    let H20: f64 = 3.597739657143682
    let diff: f64 = Hnk - H20
    let log_ans: f64 = log_binom + log(diff)
    let LN10: f64 = 2.302585092994046
    let log10_ans: f64 = log_ans / LN10
    let mut exp10: i64 = log10_ans as i64
    if (exp10 as f64) > log10_ans {
        exp10 = exp10 - 1
    }
    let mant: f64 = pow(10.0, log10_ans - (exp10 as f64))
    let scaled: f64 = mant * 1000000000.0 + 0.5
    let mut iscaled: i64 = scaled as i64
    if iscaled >= 10000000000 {
        iscaled = iscaled / 10
        exp10 = exp10 + 1
    }
    let whole: i64 = iscaled / 1000000000
    let frac: i64 = iscaled % 1000000000
    printf("%lld.%09llde%lld\n", whole, frac, exp10)
    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) {
    double N = 100000000000000.0;
    int32_t K = 20;
    double log_binom = 0.0;
    int32_t i = 1;
    while (i <= K) {
        log_binom = ((log_binom + log((N + ((double)(i))))) - log(((double)(i))));
        i = (i + 1);
    }
    double GAMMA = 0.5772156649015328606;
    double n1 = (N + ((double)(K)));
    double inv = (1.0 / n1);
    double inv2 = (inv * inv);
    double inv4 = (inv2 * inv2);
    double inv6 = (inv4 * inv2);
    double inv8 = (inv4 * inv4);
    double inv10 = (inv8 * inv2);
    double Hnk = (((((((log(n1) + GAMMA) + (inv / 2.0)) - (inv2 / 12.0)) + (inv4 / 120.0)) - (inv6 / 252.0)) + (inv8 / 240.0)) - ((5.0 * inv10) / 660.0));
    double H20 = 3.597739657143682;
    double diff = (Hnk - H20);
    double log_ans = (log_binom + log(diff));
    double LN10 = 2.302585092994046;
    double log10_ans = (log_ans / LN10);
    int64_t exp10 = ((int64_t)(log10_ans));
    if (((double)(exp10)) > log10_ans) {
        exp10 = (exp10 - 1);
    }
    double mant = pow(10.0, (log10_ans - ((double)(exp10))));
    double scaled = ((mant * 1000000000.0) + 0.5);
    int64_t iscaled = ((int64_t)(scaled));
    if (iscaled >= 10000000000) {
        iscaled = FLOW_CHECKED_DIV((iscaled), (10));
        exp10 = (exp10 + 1);
    }
    int64_t whole = FLOW_CHECKED_DIV((iscaled), (1000000000));
    int64_t frac = FLOW_CHECKED_MOD((iscaled), (1000000000));
    printf("%lld.%09llde%lld\n", whole, frac, exp10);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld.%09llde%lld\n\00") {addr_space = 0 : i32} : !llvm.array<18 x i8>
  func.func private @log(f64) -> f64
  func.func private @pow(f64, f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 100000000000000.0 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = arith.constant 20 : i32
    %3 = arith.constant 0.0 : f32
    %4 = arith.extf %3 : f32 to f64
    %5 = llvm.mlir.constant(1 : i64) : i64
    %6 = llvm.alloca %5 x f64 : (i64) -> !llvm.ptr
    llvm.store %4, %6 : f64, !llvm.ptr
    %7 = arith.constant 1 : i32
    %8 = llvm.mlir.constant(1 : i64) : i64
    %9 = llvm.alloca %8 x i32 : (i64) -> !llvm.ptr
    llvm.store %7, %9 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %10 = llvm.load %9 : !llvm.ptr -> i32
    %11 = arith.cmpi sle, %10, %2 : i32
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %12 = llvm.load %6 : !llvm.ptr -> f64
      %13 = llvm.load %9 : !llvm.ptr -> i32
      %14 = arith.sitofp %13 : i32 to f64
      %15 = arith.addf %1, %14 : f64
      %16 = math.log %15 : f64
      %17 = arith.addf %12, %16 : f64
      %18 = llvm.load %9 : !llvm.ptr -> i32
      %19 = arith.sitofp %18 : i32 to f64
      %20 = math.log %19 : f64
      %21 = arith.subf %17, %20 : f64
      llvm.store %21, %6 : f64, !llvm.ptr
      %22 = llvm.load %9 : !llvm.ptr -> i32
      %23 = arith.constant 1 : i32
      %24 = arith.addi %22, %23 : i32
      llvm.store %24, %9 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %25 = arith.constant 0.5772156649015328606 : f32
    %26 = arith.extf %25 : f32 to f64
    %27 = arith.sitofp %2 : i32 to f64
    %28 = arith.addf %1, %27 : f64
    %29 = arith.constant 1.0 : f32
    %31 = arith.extf %29 : f32 to f64
    %30 = arith.divf %31, %28 : f64
    %32 = arith.mulf %30, %30 : f64
    %33 = arith.mulf %32, %32 : f64
    %34 = arith.mulf %33, %32 : f64
    %35 = arith.mulf %33, %33 : f64
    %36 = arith.mulf %35, %32 : f64
    %37 = math.log %28 : f64
    %38 = arith.addf %37, %26 : f64
    %39 = arith.constant 2.0 : f32
    %41 = arith.extf %39 : f32 to f64
    %40 = arith.divf %30, %41 : f64
    %42 = arith.addf %38, %40 : f64
    %43 = arith.constant 12.0 : f32
    %45 = arith.extf %43 : f32 to f64
    %44 = arith.divf %32, %45 : f64
    %46 = arith.subf %42, %44 : f64
    %47 = arith.constant 120.0 : f32
    %49 = arith.extf %47 : f32 to f64
    %48 = arith.divf %33, %49 : f64
    %50 = arith.addf %46, %48 : f64
    %51 = arith.constant 252.0 : f32
    %53 = arith.extf %51 : f32 to f64
    %52 = arith.divf %34, %53 : f64
    %54 = arith.subf %50, %52 : f64
    %55 = arith.constant 240.0 : f32
    %57 = arith.extf %55 : f32 to f64
    %56 = arith.divf %35, %57 : f64
    %58 = arith.addf %54, %56 : f64
    %59 = arith.constant 5.0 : f32
    %61 = arith.extf %59 : f32 to f64
    %60 = arith.mulf %61, %36 : f64
    %62 = arith.constant 660.0 : f32
    %64 = arith.extf %62 : f32 to f64
    %63 = arith.divf %60, %64 : f64
    %65 = arith.subf %58, %63 : f64
    %66 = arith.constant 3.597739657143682 : f32
    %67 = arith.extf %66 : f32 to f64
    %68 = arith.subf %65, %67 : f64
    %69 = llvm.load %6 : !llvm.ptr -> f64
    %70 = math.log %68 : f64
    %71 = arith.addf %69, %70 : f64
    %72 = arith.constant 2.302585092994046 : f32
    %73 = arith.extf %72 : f32 to f64
    %74 = arith.divf %71, %73 : f64
    %75 = arith.fptosi %74 : f64 to i64
    %76 = llvm.mlir.constant(1 : i64) : i64
    %77 = llvm.alloca %76 x i64 : (i64) -> !llvm.ptr
    llvm.store %75, %77 : i64, !llvm.ptr
    %78 = llvm.load %77 : !llvm.ptr -> i64
    %79 = arith.sitofp %78 : i64 to f64
    %80 = arith.cmpf ogt, %79, %74 : f64
    cf.cond_br %80, ^bb3, ^bb4
    ^bb3:
      %81 = llvm.load %77 : !llvm.ptr -> i64
      %82 = arith.constant 1 : i32
      %84 = arith.extsi %82 : i32 to i64
      %83 = arith.subi %81, %84 : i64
      llvm.store %83, %77 : i64, !llvm.ptr
      cf.br ^bb5
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %86 = arith.constant 10.0 : f32
    %87 = llvm.load %77 : !llvm.ptr -> i64
    %88 = arith.sitofp %87 : i64 to f64
    %89 = arith.subf %74, %88 : f64
    %90 = arith.extf %86 : f32 to f64
    %85 = func.call @pow(%90, %89) : (f64, f64) -> f64
    %91 = arith.constant 1000000000.0 : f32
    %93 = arith.extf %91 : f32 to f64
    %92 = arith.mulf %85, %93 : f64
    %94 = arith.constant 0.5 : f32
    %96 = arith.extf %94 : f32 to f64
    %95 = arith.addf %92, %96 : f64
    %97 = arith.fptosi %95 : f64 to i64
    %98 = llvm.mlir.constant(1 : i64) : i64
    %99 = llvm.alloca %98 x i64 : (i64) -> !llvm.ptr
    llvm.store %97, %99 : i64, !llvm.ptr
    %100 = llvm.load %99 : !llvm.ptr -> i64
    %101 = arith.constant 5705032704 : i32
    %103 = arith.extsi %101 : i32 to i64
    %102 = arith.cmpi sge, %100, %103 : i64
    cf.cond_br %102, ^bb6, ^bb7
    ^bb6:
      %104 = llvm.load %99 : !llvm.ptr -> i64
      %105 = arith.constant 10 : i32
      %107 = arith.extsi %105 : i32 to i64
      %106 = arith.divsi %104, %107 : i64
      llvm.store %106, %99 : i64, !llvm.ptr
      %108 = llvm.load %77 : !llvm.ptr -> i64
      %109 = arith.constant 1 : i32
      %111 = arith.extsi %109 : i32 to i64
      %110 = arith.addi %108, %111 : i64
      llvm.store %110, %77 : i64, !llvm.ptr
      cf.br ^bb8
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %112 = llvm.load %99 : !llvm.ptr -> i64
    %113 = arith.constant 1000000000 : i32
    %115 = arith.extsi %113 : i32 to i64
    %114 = arith.divsi %112, %115 : i64
    %116 = llvm.load %99 : !llvm.ptr -> i64
    %117 = arith.constant 1000000000 : i32
    %119 = arith.extsi %117 : i32 to i64
    %118 = arith.remsi %116, %119 : i64
    %120 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %121 = llvm.load %77 : !llvm.ptr -> i64
    %122 = llvm.call @printf(%120, %114, %118, %121) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64, i64, i64) -> i32
    %123 = arith.constant 0 : i32
    func.return %123 : i32
  }
}