Problem 134

Sum of S(p1,p2) for consecutive primes with 5 ≤ p1 ≤ 10^6.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 134
# Sum of S(p1,p2) for consecutive primes with 5 ≤ p1 ≤ 10^6.

function tens(x: i64) -> i64 {
    let mut r: i64 = 1
    while r <= x { r = r * 10 }
    return r
}

# return (x * inv(m1)) % m2 style via extended gcd: find x with x*m1 ≡ small (mod m2)?
# S ends with digits of p1 and divisible by p2: S = k*m2 + 0, S ≡ p1 (mod m1) where m1=tens(p1)
# So k*p2 ≡ p1 (mod m1) => k ≡ p1 * inv(p2) (mod m1)
function mod_inverse(a0: i64, mod: i64) -> i64 {
    let mut a: i64 = a0 % mod
    if a < 0 { a = a + mod }
    let mut t: i64 = 0
    let mut newt: i64 = 1
    let mut r: i64 = mod
    let mut newr: i64 = a
    while newr != 0 {
        let q: i64 = r / newr
        let tmp: i64 = newt
        newt = t - q * newt
        t = tmp
        let tmp2: i64 = newr
        newr = r - q * newr
        r = tmp2
    }
    if t < 0 { t = t + mod }
    return t
}

function S(p1: i64, p2: i64) -> i64 {
    let m1: i64 = tens(p1)
    let inv: i64 = mod_inverse(p2 % m1, m1)
    let k: i64 = (p1 * inv) % m1
    return k * p2
}

function main() -> i32 {
    let limit: i64 = 1000000
    # sieve primes up to limit + some
    let slim: i64 = limit + 1000
    # collect primes
    let mut primes_cap: i64 = 80000
    # simple trial generation
    let mut prev: i64 = 3
    let mut total: i64 = 0
    let mut n: i64 = 5
    while true {
        let mut prime: bool = true
        let mut d: i64 = 3
        while d * d <= n {
            if n % d == 0 { prime = false; break }
            d = d + 2
        }
        if prime {
            if prev >= 5 && prev <= limit {
                total = total + S(prev, n)
            }
            if n > limit { break }
            prev = n
        }
        n = n + 2
    }
    printf("%lld\n", total)
    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; }

int64_t tens_i64(int64_t x);
int64_t mod_inverse_i64_i64(int64_t a0, int64_t mod);
int64_t S_i64_i64(int64_t p1, int64_t p2);
int32_t main(void);

int64_t tens_i64(int64_t x) {
    int64_t r = 1;
    while (r <= x) {
        r = (r * 10);
    }
    return r;
}

int64_t mod_inverse_i64_i64(int64_t a0, int64_t mod) {
    int64_t a = FLOW_CHECKED_MOD((a0), (mod));
    if (a < 0) {
        a = (a + mod);
    }
    int64_t t = 0;
    int64_t newt = 1;
    int64_t r = mod;
    int64_t newr = a;
    while (newr != 0) {
        int64_t q = FLOW_CHECKED_DIV((r), (newr));
        int64_t tmp = newt;
        newt = (t - (q * newt));
        t = tmp;
        int64_t tmp2 = newr;
        newr = (r - (q * newr));
        r = tmp2;
    }
    if (t < 0) {
        t = (t + mod);
    }
    return t;
}

int64_t S_i64_i64(int64_t p1, int64_t p2) {
    int64_t m1 = tens_i64(p1);
    int64_t inv = mod_inverse_i64_i64(FLOW_CHECKED_MOD((p2), (m1)), m1);
    int64_t k = FLOW_CHECKED_MOD(((p1 * inv)), (m1));
    return (k * p2);
}

int32_t main(void) {
    int64_t limit = 1000000;
    int64_t slim = (limit + 1000);
    int64_t primes_cap = 80000;
    int64_t prev = 3;
    int64_t total = 0;
    int64_t n = 5;
    while (1) {
        bool prime = 1;
        int64_t d = 3;
        while ((d * d) <= n) {
            if (FLOW_CHECKED_MOD((n), (d)) == 0) {
                prime = 0;
                break;
            }
            d = (d + 2);
        }
        if (prime) {
            if ((prev >= 5 && prev <= limit)) {
                total = (total + S_i64_i64(prev, n));
            }
            if (n > limit) {
                break;
            }
            prev = n;
        }
        n = (n + 2);
    }
    printf("%lld\n", total);
    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 @tens(%arg0: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %4 = llvm.load %3 : !llvm.ptr -> i64
    %5 = arith.cmpi sle, %4, %arg0 : i64
    cf.cond_br %5, ^bb1, ^bb2
    ^bb1:
      %6 = llvm.load %3 : !llvm.ptr -> i64
      %7 = arith.constant 10 : i32
      %9 = arith.extsi %7 : i32 to i64
      %8 = arith.muli %6, %9 : i64
      llvm.store %8, %3 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %10 = llvm.load %3 : !llvm.ptr -> i64
    func.return %10 : i64
  }
  func.func @mod_inverse(%arg0: i64, %arg1: i64) -> i64 {
    %11 = arith.remsi %arg0, %arg1 : i64
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %11, %13 : i64, !llvm.ptr
    %14 = llvm.load %13 : !llvm.ptr -> i64
    %15 = arith.constant 0 : i32
    %17 = arith.extsi %15 : i32 to i64
    %16 = arith.cmpi slt, %14, %17 : i64
    cf.cond_br %16, ^bb3, ^bb4
    ^bb3:
      %18 = llvm.load %13 : !llvm.ptr -> i64
      %19 = arith.addi %18, %arg1 : i64
      llvm.store %19, %13 : i64, !llvm.ptr
      cf.br ^bb5
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %20 = arith.constant 0 : i32
    %21 = arith.extsi %20 : i32 to i64
    %22 = llvm.mlir.constant(1 : i64) : i64
    %23 = llvm.alloca %22 x i64 : (i64) -> !llvm.ptr
    llvm.store %21, %23 : i64, !llvm.ptr
    %24 = arith.constant 1 : i32
    %25 = arith.extsi %24 : i32 to i64
    %26 = llvm.mlir.constant(1 : i64) : i64
    %27 = llvm.alloca %26 x i64 : (i64) -> !llvm.ptr
    llvm.store %25, %27 : i64, !llvm.ptr
    %28 = llvm.mlir.constant(1 : i64) : i64
    %29 = llvm.alloca %28 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %29 : i64, !llvm.ptr
    %30 = llvm.load %13 : !llvm.ptr -> i64
    %31 = llvm.mlir.constant(1 : i64) : i64
    %32 = llvm.alloca %31 x i64 : (i64) -> !llvm.ptr
    llvm.store %30, %32 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %33 = llvm.load %32 : !llvm.ptr -> i64
    %34 = arith.constant 0 : i32
    %36 = arith.extsi %34 : i32 to i64
    %35 = arith.cmpi ne, %33, %36 : i64
    cf.cond_br %35, ^bb7, ^bb8
    ^bb7:
      %37 = llvm.load %29 : !llvm.ptr -> i64
      %38 = llvm.load %32 : !llvm.ptr -> i64
      %39 = arith.divsi %37, %38 : i64
      %40 = llvm.load %27 : !llvm.ptr -> i64
      %41 = llvm.load %23 : !llvm.ptr -> i64
      %42 = llvm.load %27 : !llvm.ptr -> i64
      %43 = arith.muli %39, %42 : i64
      %44 = arith.subi %41, %43 : i64
      llvm.store %44, %27 : i64, !llvm.ptr
      llvm.store %40, %23 : i64, !llvm.ptr
      %45 = llvm.load %32 : !llvm.ptr -> i64
      %46 = llvm.load %29 : !llvm.ptr -> i64
      %47 = llvm.load %32 : !llvm.ptr -> i64
      %48 = arith.muli %39, %47 : i64
      %49 = arith.subi %46, %48 : i64
      llvm.store %49, %32 : i64, !llvm.ptr
      llvm.store %45, %29 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %50 = llvm.load %23 : !llvm.ptr -> i64
    %51 = arith.constant 0 : i32
    %53 = arith.extsi %51 : i32 to i64
    %52 = arith.cmpi slt, %50, %53 : i64
    cf.cond_br %52, ^bb9, ^bb10
    ^bb9:
      %54 = llvm.load %23 : !llvm.ptr -> i64
      %55 = arith.addi %54, %arg1 : i64
      llvm.store %55, %23 : i64, !llvm.ptr
      cf.br ^bb11
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %56 = llvm.load %23 : !llvm.ptr -> i64
    func.return %56 : i64
  }
  func.func @S(%arg0: i64, %arg1: i64) -> i64 {
    %57 = func.call @tens(%arg0) : (i64) -> i64
    %59 = arith.remsi %arg1, %57 : i64
    %58 = func.call @mod_inverse(%59, %57) : (i64, i64) -> i64
    %60 = arith.muli %arg0, %58 : i64
    %61 = arith.remsi %60, %57 : i64
    %62 = arith.muli %61, %arg1 : i64
    func.return %62 : i64
  }
  func.func @main() -> i32 {
    %63 = arith.constant 1000000 : i32
    %64 = arith.extsi %63 : i32 to i64
    %65 = arith.constant 1000 : i32
    %67 = arith.extsi %65 : i32 to i64
    %66 = arith.addi %64, %67 : i64
    %68 = arith.constant 80000 : i32
    %69 = arith.extsi %68 : i32 to i64
    %70 = llvm.mlir.constant(1 : i64) : i64
    %71 = llvm.alloca %70 x i64 : (i64) -> !llvm.ptr
    llvm.store %69, %71 : i64, !llvm.ptr
    %72 = arith.constant 3 : i32
    %73 = arith.extsi %72 : i32 to i64
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x i64 : (i64) -> !llvm.ptr
    llvm.store %73, %75 : i64, !llvm.ptr
    %76 = arith.constant 0 : i32
    %77 = arith.extsi %76 : i32 to i64
    %78 = llvm.mlir.constant(1 : i64) : i64
    %79 = llvm.alloca %78 x i64 : (i64) -> !llvm.ptr
    llvm.store %77, %79 : i64, !llvm.ptr
    %80 = arith.constant 5 : i32
    %81 = arith.extsi %80 : i32 to i64
    %82 = llvm.mlir.constant(1 : i64) : i64
    %83 = llvm.alloca %82 x i64 : (i64) -> !llvm.ptr
    llvm.store %81, %83 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %84 = arith.constant 1 : i1
    cf.cond_br %84, ^bb13, ^bb14
    ^bb13:
      %85 = arith.constant 1 : i1
      %86 = llvm.mlir.constant(1 : i64) : i64
      %87 = llvm.alloca %86 x i1 : (i64) -> !llvm.ptr
      llvm.store %85, %87 : i1, !llvm.ptr
      %88 = arith.constant 3 : i32
      %89 = arith.extsi %88 : i32 to i64
      %90 = llvm.mlir.constant(1 : i64) : i64
      %91 = llvm.alloca %90 x i64 : (i64) -> !llvm.ptr
      llvm.store %89, %91 : i64, !llvm.ptr
      cf.br ^bb15
      ^bb15:
      %92 = llvm.load %91 : !llvm.ptr -> i64
      %93 = llvm.load %91 : !llvm.ptr -> i64
      %94 = arith.muli %92, %93 : i64
      %95 = llvm.load %83 : !llvm.ptr -> i64
      %96 = arith.cmpi sle, %94, %95 : i64
      cf.cond_br %96, ^bb16, ^bb17
      ^bb16:
        %97 = llvm.load %83 : !llvm.ptr -> i64
        %98 = llvm.load %91 : !llvm.ptr -> i64
        %99 = arith.remsi %97, %98 : i64
        %100 = arith.constant 0 : i32
        %102 = arith.extsi %100 : i32 to i64
        %101 = arith.cmpi eq, %99, %102 : i64
        cf.cond_br %101, ^bb18, ^bb19
        ^bb18:
          %103 = arith.constant 0 : i1
          llvm.store %103, %87 : i1, !llvm.ptr
          cf.br ^bb17
        ^bb19:
          cf.br ^bb20
        ^bb20:
        %104 = llvm.load %91 : !llvm.ptr -> i64
        %105 = arith.constant 2 : i32
        %107 = arith.extsi %105 : i32 to i64
        %106 = arith.addi %104, %107 : i64
        llvm.store %106, %91 : i64, !llvm.ptr
        cf.br ^bb15
      ^bb17:
      %108 = llvm.load %87 : !llvm.ptr -> i1
      cf.cond_br %108, ^bb21, ^bb22
      ^bb21:
        %109 = llvm.load %75 : !llvm.ptr -> i64
        %110 = arith.constant 5 : i32
        %112 = arith.extsi %110 : i32 to i64
        %111 = arith.cmpi sge, %109, %112 : i64
        %113 = scf.if %111 -> (i1) {
          %114 = llvm.load %75 : !llvm.ptr -> i64
          %115 = arith.cmpi sle, %114, %64 : i64
          scf.yield %115 : i1
        } else {
          %116 = arith.constant false
          scf.yield %116 : i1
        }
        cf.cond_br %113, ^bb24, ^bb25
        ^bb24:
          %117 = llvm.load %79 : !llvm.ptr -> i64
          %119 = llvm.load %75 : !llvm.ptr -> i64
          %120 = llvm.load %83 : !llvm.ptr -> i64
          %118 = func.call @S(%119, %120) : (i64, i64) -> i64
          %121 = arith.addi %117, %118 : i64
          llvm.store %121, %79 : i64, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          cf.br ^bb26
        ^bb26:
        %122 = llvm.load %83 : !llvm.ptr -> i64
        %123 = arith.cmpi sgt, %122, %64 : i64
        cf.cond_br %123, ^bb27, ^bb28
        ^bb27:
          cf.br ^bb14
        ^bb28:
          cf.br ^bb29
        ^bb29:
        %124 = llvm.load %83 : !llvm.ptr -> i64
        llvm.store %124, %75 : i64, !llvm.ptr
        cf.br ^bb23
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %125 = llvm.load %83 : !llvm.ptr -> i64
      %126 = arith.constant 2 : i32
      %128 = arith.extsi %126 : i32 to i64
      %127 = arith.addi %125, %128 : i64
      llvm.store %127, %83 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %129 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %130 = llvm.load %79 : !llvm.ptr -> i64
    %131 = llvm.call @printf(%129, %130) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %132 = arith.constant 0 : i32
    func.return %132 : i32
  }
}