Problem 148

Entries not divisible by 7 in the first one billion rows of Pascal's triangle.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 148
# Entries not divisible by 7 in the first one billion rows of Pascal's triangle.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

function main() -> i32 {
    let N: i64 = 1000000000
    let digs: ptr<i64> = calloc(20, 8)
    let pow28: ptr<i64> = calloc(20, 8)
    if digs == null || pow28 == null { return 1 }

    let mut n: i64 = N
    let mut len: i32 = 0
    # collect digits least-significant first then reverse
    let tmp: ptr<i64> = calloc(20, 8)
    if tmp == null { return 1 }
    while n > 0 {
        tmp[len] = n % 7
        n = n / 7
        len = len + 1
    }
    let mut i: i32 = 0
    while i < len {
        digs[i] = tmp[len - 1 - i]
        i = i + 1
    }

    pow28[0] = 1
    i = 1
    while i <= len {
        pow28[i] = pow28[i - 1] * 28
        i = i + 1
    }

    let mut total: i64 = 0
    let mut prefix: i64 = 1
    i = 0
    while i < len {
        let digit: i64 = digs[i]
        let remaining: i32 = len - i - 1
        let smaller: i64 = digit * (digit + 1) / 2
        total = total + prefix * smaller * pow28[remaining]
        prefix = prefix * (digit + 1)
        i = i + 1
    }

    printf("%lld\n", total)
    free(tmp)
    free(pow28)
    free(digs)
    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) {
    int64_t N = 1000000000;
    int64_t* digs = (int64_t*)(calloc(20, 8));
    int64_t* pow28 = (int64_t*)(calloc(20, 8));
    if ((digs == NULL || pow28 == NULL)) {
        return 1;
    }
    int64_t n = N;
    int32_t len = 0;
    int64_t* tmp = (int64_t*)(calloc(20, 8));
    if (tmp == NULL) {
        return 1;
    }
    while (n > 0) {
        tmp[len] = FLOW_CHECKED_MOD((n), (7));
        n = FLOW_CHECKED_DIV((n), (7));
        len = (len + 1);
    }
    int32_t i = 0;
    while (i < len) {
        digs[i] = tmp[((len - 1) - i)];
        i = (i + 1);
    }
    pow28[0] = 1;
    i = 1;
    while (i <= len) {
        pow28[i] = (pow28[(i - 1)] * 28);
        i = (i + 1);
    }
    int64_t total = 0;
    int64_t prefix = 1;
    i = 0;
    while (i < len) {
        int64_t digit = digs[i];
        int32_t remaining = ((len - i) - 1);
        int64_t smaller = FLOW_CHECKED_DIV(((digit * (digit + 1))), (2));
        total = (total + ((prefix * smaller) * pow28[remaining]));
        prefix = (prefix * (digit + 1));
        i = (i + 1);
    }
    printf("%lld\n", total);
    free(tmp);
    free(pow28);
    free(digs);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\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 @main() -> i32 {
    %0 = arith.constant 1000000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %3 = arith.constant 20 : i32
    %4 = arith.constant 8 : i32
    %5 = arith.extsi %3 : i32 to i64
    %6 = arith.extsi %4 : i32 to i64
    %2 = func.call @calloc(%5, %6) : (i64, i64) -> !llvm.ptr
    %8 = arith.constant 20 : i32
    %9 = arith.constant 8 : i32
    %10 = arith.extsi %8 : i32 to i64
    %11 = arith.extsi %9 : i32 to i64
    %7 = func.call @calloc(%10, %11) : (i64, i64) -> !llvm.ptr
    %12 = llvm.mlir.zero : !llvm.ptr
    %13 = llvm.icmp "eq" %2, %12 : !llvm.ptr
    %14 = scf.if %13 -> (i1) {
      %15 = arith.constant true
      scf.yield %15 : i1
    } else {
      %16 = llvm.mlir.zero : !llvm.ptr
      %17 = llvm.icmp "eq" %7, %16 : !llvm.ptr
      scf.yield %17 : i1
    }
    cf.cond_br %14, ^bb0, ^bb1
    ^bb0:
      %18 = arith.constant 1 : i32
      func.return %18 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %19 = llvm.mlir.constant(1 : i64) : i64
    %20 = llvm.alloca %19 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %20 : i64, !llvm.ptr
    %21 = arith.constant 0 : i32
    %22 = llvm.mlir.constant(1 : i64) : i64
    %23 = llvm.alloca %22 x i32 : (i64) -> !llvm.ptr
    llvm.store %21, %23 : i32, !llvm.ptr
    %25 = arith.constant 20 : i32
    %26 = arith.constant 8 : i32
    %27 = arith.extsi %25 : i32 to i64
    %28 = arith.extsi %26 : i32 to i64
    %24 = func.call @calloc(%27, %28) : (i64, i64) -> !llvm.ptr
    %29 = llvm.mlir.zero : !llvm.ptr
    %30 = llvm.icmp "eq" %24, %29 : !llvm.ptr
    cf.cond_br %30, ^bb3, ^bb4
    ^bb3:
      %31 = arith.constant 1 : i32
      func.return %31 : i32
    ^bb4:
      cf.br ^bb5
    ^bb5:
    cf.br ^bb6
    ^bb6:
    %32 = llvm.load %20 : !llvm.ptr -> i64
    %33 = arith.constant 0 : i32
    %35 = arith.extsi %33 : i32 to i64
    %34 = arith.cmpi sgt, %32, %35 : i64
    cf.cond_br %34, ^bb7, ^bb8
    ^bb7:
      %36 = llvm.load %20 : !llvm.ptr -> i64
      %37 = arith.constant 7 : i32
      %39 = arith.extsi %37 : i32 to i64
      %38 = arith.remsi %36, %39 : i64
      %40 = llvm.load %23 : !llvm.ptr -> i32
      %41 = arith.extsi %40 : i32 to i64
      %42 = llvm.getelementptr %24[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %38, %42 : i64, !llvm.ptr
      %43 = llvm.load %20 : !llvm.ptr -> i64
      %44 = arith.constant 7 : i32
      %46 = arith.extsi %44 : i32 to i64
      %45 = arith.divsi %43, %46 : i64
      llvm.store %45, %20 : i64, !llvm.ptr
      %47 = llvm.load %23 : !llvm.ptr -> i32
      %48 = arith.constant 1 : i32
      %49 = arith.addi %47, %48 : i32
      llvm.store %49, %23 : i32, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %50 = arith.constant 0 : i32
    %51 = llvm.mlir.constant(1 : i64) : i64
    %52 = llvm.alloca %51 x i32 : (i64) -> !llvm.ptr
    llvm.store %50, %52 : i32, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %53 = llvm.load %52 : !llvm.ptr -> i32
    %54 = llvm.load %23 : !llvm.ptr -> i32
    %55 = arith.cmpi slt, %53, %54 : i32
    cf.cond_br %55, ^bb10, ^bb11
    ^bb10:
      %57 = llvm.load %23 : !llvm.ptr -> i32
      %58 = arith.constant 1 : i32
      %59 = arith.subi %57, %58 : i32
      %60 = llvm.load %52 : !llvm.ptr -> i32
      %61 = arith.subi %59, %60 : i32
      %62 = arith.extsi %61 : i32 to i64
      %63 = llvm.getelementptr %24[%62] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %56 = llvm.load %63 : !llvm.ptr -> i64
      %64 = llvm.load %52 : !llvm.ptr -> i32
      %65 = arith.extsi %64 : i32 to i64
      %66 = llvm.getelementptr %2[%65] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %56, %66 : i64, !llvm.ptr
      %67 = llvm.load %52 : !llvm.ptr -> i32
      %68 = arith.constant 1 : i32
      %69 = arith.addi %67, %68 : i32
      llvm.store %69, %52 : i32, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %70 = arith.constant 1 : i32
    %71 = arith.constant 0 : i32
    %72 = arith.extsi %70 : i32 to i64
    %73 = arith.extsi %71 : i32 to i64
    %74 = llvm.getelementptr %7[%73] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %72, %74 : i64, !llvm.ptr
    %75 = arith.constant 1 : i32
    llvm.store %75, %52 : i32, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %76 = llvm.load %52 : !llvm.ptr -> i32
    %77 = llvm.load %23 : !llvm.ptr -> i32
    %78 = arith.cmpi sle, %76, %77 : i32
    cf.cond_br %78, ^bb13, ^bb14
    ^bb13:
      %80 = llvm.load %52 : !llvm.ptr -> i32
      %81 = arith.constant 1 : i32
      %82 = arith.subi %80, %81 : i32
      %83 = arith.extsi %82 : i32 to i64
      %84 = llvm.getelementptr %7[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %79 = llvm.load %84 : !llvm.ptr -> i64
      %85 = arith.constant 28 : i32
      %87 = arith.extsi %85 : i32 to i64
      %86 = arith.muli %79, %87 : i64
      %88 = llvm.load %52 : !llvm.ptr -> i32
      %89 = arith.extsi %88 : i32 to i64
      %90 = llvm.getelementptr %7[%89] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %86, %90 : i64, !llvm.ptr
      %91 = llvm.load %52 : !llvm.ptr -> i32
      %92 = arith.constant 1 : i32
      %93 = arith.addi %91, %92 : i32
      llvm.store %93, %52 : i32, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %94 = arith.constant 0 : i32
    %95 = arith.extsi %94 : i32 to i64
    %96 = llvm.mlir.constant(1 : i64) : i64
    %97 = llvm.alloca %96 x i64 : (i64) -> !llvm.ptr
    llvm.store %95, %97 : i64, !llvm.ptr
    %98 = arith.constant 1 : i32
    %99 = arith.extsi %98 : i32 to i64
    %100 = llvm.mlir.constant(1 : i64) : i64
    %101 = llvm.alloca %100 x i64 : (i64) -> !llvm.ptr
    llvm.store %99, %101 : i64, !llvm.ptr
    %102 = arith.constant 0 : i32
    llvm.store %102, %52 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %103 = llvm.load %52 : !llvm.ptr -> i32
    %104 = llvm.load %23 : !llvm.ptr -> i32
    %105 = arith.cmpi slt, %103, %104 : i32
    cf.cond_br %105, ^bb16, ^bb17
    ^bb16:
      %107 = llvm.load %52 : !llvm.ptr -> i32
      %108 = arith.extsi %107 : i32 to i64
      %109 = llvm.getelementptr %2[%108] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %106 = llvm.load %109 : !llvm.ptr -> i64
      %110 = llvm.load %23 : !llvm.ptr -> i32
      %111 = llvm.load %52 : !llvm.ptr -> i32
      %112 = arith.subi %110, %111 : i32
      %113 = arith.constant 1 : i32
      %114 = arith.subi %112, %113 : i32
      %115 = arith.constant 1 : i32
      %117 = arith.extsi %115 : i32 to i64
      %116 = arith.addi %106, %117 : i64
      %118 = arith.muli %106, %116 : i64
      %119 = arith.constant 2 : i32
      %121 = arith.extsi %119 : i32 to i64
      %120 = arith.divsi %118, %121 : i64
      %122 = llvm.load %97 : !llvm.ptr -> i64
      %123 = llvm.load %101 : !llvm.ptr -> i64
      %124 = arith.muli %123, %120 : i64
      %126 = arith.extsi %114 : i32 to i64
      %127 = llvm.getelementptr %7[%126] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %125 = llvm.load %127 : !llvm.ptr -> i64
      %128 = arith.muli %124, %125 : i64
      %129 = arith.addi %122, %128 : i64
      llvm.store %129, %97 : i64, !llvm.ptr
      %130 = llvm.load %101 : !llvm.ptr -> i64
      %131 = arith.constant 1 : i32
      %133 = arith.extsi %131 : i32 to i64
      %132 = arith.addi %106, %133 : i64
      %134 = arith.muli %130, %132 : i64
      llvm.store %134, %101 : i64, !llvm.ptr
      %135 = llvm.load %52 : !llvm.ptr -> i32
      %136 = arith.constant 1 : i32
      %137 = arith.addi %135, %136 : i32
      llvm.store %137, %52 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %138 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %139 = llvm.load %97 : !llvm.ptr -> i64
    %140 = llvm.call @printf(%138, %139) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%24) : (!llvm.ptr) -> ()
    func.call @free(%7) : (!llvm.ptr) -> ()
    func.call @free(%2) : (!llvm.ptr) -> ()
    %144 = arith.constant 0 : i32
    func.return %144 : i32
  }
}