Problem 120

Sum of r_max for 3 ≤ a ≤ 1000, where r_max is max remainder of (a-1)^n + (a+1)^n mod a^2. For odd n: 2*a*n mod a^2 → max when n = a-1 if a odd? r_max = a^2 - a if a even? Actually r_max = 2*a*((a-1)/2) = a*(a-1) if a odd? Known: r_max = a * a - 2*a if? Formula: r_max = 2*a*floor((a-1)/2)

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 120
# Sum of r_max for 3 ≤ a ≤ 1000, where r_max is max remainder of
# (a-1)^n + (a+1)^n mod a^2.

# For odd n: 2*a*n mod a^2 → max when n = a-1 if a odd? 
# r_max = a^2 - a if a even? Actually r_max = 2*a*((a-1)/2) = a*(a-1) if a odd? 
# Known: r_max = a * a - 2*a if? Formula: r_max = 2*a*floor((a-1)/2)

function main() -> i32 {
    let mut total: i64 = 0
    let mut a: i64 = 3
    while a <= 1000 {
        total = total + 2 * a * ((a - 1) / 2)
        a = a + 1
    }
    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; }

int32_t main(void);

int32_t main(void) {
    int64_t total = 0;
    int64_t a = 3;
    while (a <= 1000) {
        total = (total + ((2 * a) * FLOW_CHECKED_DIV(((a - 1)), (2))));
        a = (a + 1);
    }
    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 @main() -> i32 {
    %0 = arith.constant 0 : 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
    %4 = arith.constant 3 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %8 = llvm.load %7 : !llvm.ptr -> i64
    %9 = arith.constant 1000 : i32
    %11 = arith.extsi %9 : i32 to i64
    %10 = arith.cmpi sle, %8, %11 : i64
    cf.cond_br %10, ^bb1, ^bb2
    ^bb1:
      %12 = llvm.load %3 : !llvm.ptr -> i64
      %13 = arith.constant 2 : i32
      %14 = llvm.load %7 : !llvm.ptr -> i64
      %16 = arith.extsi %13 : i32 to i64
      %15 = arith.muli %16, %14 : i64
      %17 = llvm.load %7 : !llvm.ptr -> i64
      %18 = arith.constant 1 : i32
      %20 = arith.extsi %18 : i32 to i64
      %19 = arith.subi %17, %20 : i64
      %21 = arith.constant 2 : i32
      %23 = arith.extsi %21 : i32 to i64
      %22 = arith.divsi %19, %23 : i64
      %24 = arith.muli %15, %22 : i64
      %25 = arith.addi %12, %24 : i64
      llvm.store %25, %3 : i64, !llvm.ptr
      %26 = llvm.load %7 : !llvm.ptr -> i64
      %27 = arith.constant 1 : i32
      %29 = arith.extsi %27 : i32 to i64
      %28 = arith.addi %26, %29 : i64
      llvm.store %28, %7 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %30 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %31 = llvm.load %3 : !llvm.ptr -> i64
    %32 = llvm.call @printf(%30, %31) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %33 = arith.constant 0 : i32
    func.return %33 : i32
  }
}