Problem 029

Count distinct a^b for 2 <= a <= 100 and 2 <= b <= 100. Canonicalize each base as root^scale. Then a^b is uniquely identified by (root, scale * b), so no big integers are needed.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 029
# Count distinct a^b for 2 <= a <= 100 and 2 <= b <= 100.
#
# Canonicalize each base as root^scale.
# Then a^b is uniquely identified by (root, scale * b),
# so no big integers are needed.

struct Canonical { root: i32, exponent: i32 }

function ipow(base: i32, exp: i32) -> i32 {
    let mut result: i32 = 1

    for _ in 0 to exp {
        result = result * base
    }

    return result
}

function canonical_power(n: i32) -> Canonical {
    let mut result: Canonical = Canonical { root: n, exponent: 1 }

    for power in 2 to 7 {
        for candidate in 2 to n + 1 {
            let value: i32 = ipow(candidate, power)

            if value == n {
                result.root = candidate
                result.exponent = power
            }

            if value > n {
                break
            }
        }
    }

    return result
}

function solve() -> i32 {
    let mut seen: array<bool, 60701>
    let mut i: i32 = 0
    while i < 60701 {
        seen[i] = false
        i = i + 1
    }

    let mut count: i32 = 0

    for a in 2 to 101 {
        let c: Canonical = canonical_power(a)
        let root: i32 = c.root
        let scale: i32 = c.exponent

        for b in 2 to 101 {
            let key: i32 = root * 601 + scale * b

            if !seen[key] {
                seen[key] = true
                count = count + 1
            }
        }
    }

    return count
}

function main() -> i32 {
    println(solve())
    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; }

typedef struct Canonical Canonical;

struct Canonical {
    int32_t root;
    int32_t exponent;
};

int32_t ipow_i32_i32(int32_t base, int32_t exp);
Canonical canonical_power_i32(int32_t n);
int32_t solve(void);
int32_t main(void);

int32_t ipow_i32_i32(int32_t base, int32_t exp) {
    int32_t result = 1;
    int32_t __flow_step_1 = 1;
    for (int32_t _ = 0; (0 <= exp) ? _ < exp : _ > exp; _ += (0 <= exp) ? 1 : -1) {
        result = (result * base);
    }
    return result;
}

Canonical canonical_power_i32(int32_t n) {
    Canonical result = (Canonical){ .root = n, .exponent = 1 };
    int32_t __flow_step_2 = 1;
    for (int32_t power = 2; (2 <= 7) ? power < 7 : power > 7; power += (2 <= 7) ? 1 : -1) {
        int32_t __flow_step_3 = 1;
        for (int32_t candidate = 2; (2 <= (n + 1)) ? candidate < (n + 1) : candidate > (n + 1); candidate += (2 <= (n + 1)) ? 1 : -1) {
            int32_t value = ipow_i32_i32(candidate, power);
            if (value == n) {
                result.root = candidate;
                result.exponent = power;
            }
            if (value > n) {
                break;
            }
        }
    }
    return result;
}

int32_t solve(void) {
    bool seen[60701];
    int32_t i = 0;
    while (i < 60701) {
        seen[i] = 0;
        i = (i + 1);
    }
    int32_t count = 0;
    int32_t __flow_step_4 = 1;
    for (int32_t a = 2; (2 <= 101) ? a < 101 : a > 101; a += (2 <= 101) ? 1 : -1) {
        Canonical c = canonical_power_i32(a);
        int32_t root = c.root;
        int32_t scale = c.exponent;
        int32_t __flow_step_5 = 1;
        for (int32_t b = 2; (2 <= 101) ? b < 101 : b > 101; b += (2 <= 101) ? 1 : -1) {
            int32_t key = ((root * 601) + (scale * b));
            if ((!((((unsigned)(key) < 60701) ? seen[key] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(key), 60701), flow_fault_handler("array index out of bounds"), seen[0]))))) {
                seen[key] = 1;
                count = (count + 1);
            }
        }
    }
    return count;
}

int32_t main(void) {
    FLOW_LOG("%d\n", solve());
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%d\n\00") {addr_space = 0 : i32} : !llvm.array<4 x i8>
  // Struct: Canonical
  // Fields:
  //   root: i32
  //   exponent: i32
  func.func @ipow(%arg0: i32, %arg1: i32) -> i32 {
    %0 = arith.constant 1 : i32
    %1 = llvm.mlir.constant(1 : i64) : i64
    %2 = llvm.alloca %1 x i32 : (i64) -> !llvm.ptr
    llvm.store %0, %2 : i32, !llvm.ptr
    %3 = arith.constant 0 : i32
    %4 = arith.index_cast %3 : i32 to index
    %5 = arith.index_cast %arg1 : i32 to index
    %7 = arith.constant 1 : index
    %8 = arith.constant -1 : index
    %9 = arith.cmpi sle, %4, %5 : index
    %6 = arith.select %9, %7, %8 : index
    cf.br ^bb0(%4 : index)
    ^bb0(%10: index):
    %11 = arith.cmpi slt, %10, %5 : index
    %12 = arith.cmpi sgt, %10, %5 : index
    %13 = arith.select %9, %11, %12 : i1
    cf.cond_br %13, ^bb1(%10 : index), ^bb2(%10 : index)
    ^bb1(%14: index):
      %15 = llvm.load %2 : !llvm.ptr -> i32
      %16 = arith.muli %15, %arg0 : i32
      llvm.store %16, %2 : i32, !llvm.ptr
      %17 = arith.addi %14, %6 : index
      cf.br ^bb0(%17 : index)
    ^bb2(%18: index):
    %19 = llvm.load %2 : !llvm.ptr -> i32
    func.return %19 : i32
  }
  func.func @canonical_power(%arg0: i32) -> !llvm.struct<(i32, i32)> {
    %20 = llvm.mlir.undef : !llvm.struct<(i32, i32)>
    %21 = llvm.insertvalue %arg0, %20[0] : !llvm.struct<(i32, i32)>
    %22 = arith.constant 1 : i32
    %23 = llvm.insertvalue %22, %21[1] : !llvm.struct<(i32, i32)>
    %24 = llvm.mlir.constant(1 : i64) : i64
    %25 = llvm.alloca %24 x !llvm.struct<(i32, i32)> : (i64) -> !llvm.ptr
    llvm.store %23, %25 : !llvm.struct<(i32, i32)>, !llvm.ptr
    %26 = arith.constant 2 : i32
    %27 = arith.constant 7 : i32
    %28 = arith.index_cast %26 : i32 to index
    %29 = arith.index_cast %27 : i32 to index
    %31 = arith.constant 1 : index
    %32 = arith.constant -1 : index
    %33 = arith.cmpi sle, %28, %29 : index
    %30 = arith.select %33, %31, %32 : index
    cf.br ^bb3(%28 : index)
    ^bb3(%34: index):
    %35 = arith.cmpi slt, %34, %29 : index
    %36 = arith.cmpi sgt, %34, %29 : index
    %37 = arith.select %33, %35, %36 : i1
    cf.cond_br %37, ^bb4(%34 : index), ^bb5(%34 : index)
    ^bb4(%38: index):
      %39 = arith.constant 2 : i32
      %40 = arith.constant 1 : i32
      %41 = arith.addi %arg0, %40 : i32
      %42 = arith.index_cast %39 : i32 to index
      %43 = arith.index_cast %41 : i32 to index
      %45 = arith.constant 1 : index
      %46 = arith.constant -1 : index
      %47 = arith.cmpi sle, %42, %43 : index
      %44 = arith.select %47, %45, %46 : index
      cf.br ^bb6(%42 : index)
      ^bb6(%48: index):
      %49 = arith.cmpi slt, %48, %43 : index
      %50 = arith.cmpi sgt, %48, %43 : index
      %51 = arith.select %47, %49, %50 : i1
      cf.cond_br %51, ^bb7(%48 : index), ^bb8(%48 : index)
      ^bb7(%52: index):
        %54 = arith.index_cast %52 : index to i32
        %55 = arith.index_cast %38 : index to i32
        %53 = func.call @ipow(%54, %55) : (i32, i32) -> i32
        %56 = arith.cmpi eq, %53, %arg0 : i32
        cf.cond_br %56, ^bb9, ^bb10
        ^bb9:
          %57 = arith.index_cast %52 : index to i32
          %58 = llvm.getelementptr %25[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i32, i32)>
          llvm.store %57, %58 : i32, !llvm.ptr
          %59 = arith.index_cast %38 : index to i32
          %60 = llvm.getelementptr %25[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i32, i32)>
          llvm.store %59, %60 : i32, !llvm.ptr
          cf.br ^bb11
        ^bb10:
          cf.br ^bb11
        ^bb11:
        %61 = arith.cmpi sgt, %53, %arg0 : i32
        cf.cond_br %61, ^bb12, ^bb13
        ^bb12:
          cf.br ^bb8(%52 : index)
        ^bb13:
          cf.br ^bb14
        ^bb14:
        %62 = arith.addi %52, %44 : index
        cf.br ^bb6(%62 : index)
      ^bb8(%63: index):
      %64 = arith.addi %38, %30 : index
      cf.br ^bb3(%64 : index)
    ^bb5(%65: index):
    %66 = llvm.load %25 : !llvm.ptr -> !llvm.struct<(i32, i32)>
    %67 = llvm.mlir.undef : !llvm.struct<(i32, i32)>
    %68 = llvm.extractvalue %66[0] : !llvm.struct<(i32, i32)>
    %69 = llvm.insertvalue %68, %67[0] : !llvm.struct<(i32, i32)>
    %70 = llvm.extractvalue %66[1] : !llvm.struct<(i32, i32)>
    %71 = llvm.insertvalue %70, %69[1] : !llvm.struct<(i32, i32)>
    %72 = llvm.mlir.constant(1 : i64) : i64
    %73 = llvm.alloca %72 x !llvm.struct<(i32, i32)> : (i64) -> !llvm.ptr
    llvm.store %71, %73 : !llvm.struct<(i32, i32)>, !llvm.ptr
    %74 = llvm.load %73 : !llvm.ptr -> !llvm.struct<(i32, i32)>
    func.return %74 : !llvm.struct<(i32, i32)>
  }
  func.func @solve() -> i32 {
    %75 = memref.alloca() {type = memref<60701xi1>} : memref<60701xbool>
    %76 = arith.constant 0 : i32
    %77 = llvm.mlir.constant(1 : i64) : i64
    %78 = llvm.alloca %77 x i32 : (i64) -> !llvm.ptr
    llvm.store %76, %78 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %79 = llvm.load %78 : !llvm.ptr -> i32
    %80 = arith.constant 60701 : i32
    %81 = arith.cmpi slt, %79, %80 : i32
    cf.cond_br %81, ^bb16, ^bb17
    ^bb16:
      %82 = arith.constant 0 : i1
      %83 = llvm.load %78 : !llvm.ptr -> i32
      %84 = arith.index_cast %83 : i32 to index
      memref.store %82, %75[%84] : memref<60701xi1>
      %85 = llvm.load %78 : !llvm.ptr -> i32
      %86 = arith.constant 1 : i32
      %87 = arith.addi %85, %86 : i32
      llvm.store %87, %78 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %88 = arith.constant 0 : i32
    %89 = llvm.mlir.constant(1 : i64) : i64
    %90 = llvm.alloca %89 x i32 : (i64) -> !llvm.ptr
    llvm.store %88, %90 : i32, !llvm.ptr
    %91 = arith.constant 2 : i32
    %92 = arith.constant 101 : i32
    %93 = arith.index_cast %91 : i32 to index
    %94 = arith.index_cast %92 : i32 to index
    %96 = arith.constant 1 : index
    %97 = arith.constant -1 : index
    %98 = arith.cmpi sle, %93, %94 : index
    %95 = arith.select %98, %96, %97 : index
    cf.br ^bb18(%93 : index)
    ^bb18(%99: index):
    %100 = arith.cmpi slt, %99, %94 : index
    %101 = arith.cmpi sgt, %99, %94 : index
    %102 = arith.select %98, %100, %101 : i1
    cf.cond_br %102, ^bb19(%99 : index), ^bb20(%99 : index)
    ^bb19(%103: index):
      %105 = arith.index_cast %103 : index to i32
      %104 = func.call @canonical_power(%105) : (i32) -> !llvm.struct<(i32, i32)>
      %106 = llvm.mlir.undef : !llvm.struct<(i32, i32)>
      %107 = llvm.extractvalue %104[0] : !llvm.struct<(i32, i32)>
      %108 = llvm.insertvalue %107, %106[0] : !llvm.struct<(i32, i32)>
      %109 = llvm.extractvalue %104[1] : !llvm.struct<(i32, i32)>
      %110 = llvm.insertvalue %109, %108[1] : !llvm.struct<(i32, i32)>
      %111 = llvm.mlir.constant(1 : i64) : i64
      %112 = llvm.alloca %111 x !llvm.struct<(i32, i32)> : (i64) -> !llvm.ptr
      llvm.store %110, %112 : !llvm.struct<(i32, i32)>, !llvm.ptr
      %113 = llvm.load %112 : !llvm.ptr -> !llvm.struct<(i32, i32)>
      %114 = llvm.mlir.constant(1 : i64) : i64
      %115 = llvm.alloca %114 x !llvm.struct<(i32, i32)> : (i64) -> !llvm.ptr
      llvm.store %113, %115 : !llvm.struct<(i32, i32)>, !llvm.ptr
      %116 = llvm.load %115 : !llvm.ptr -> !llvm.struct<(i32, i32)>
      %117 = llvm.getelementptr %115[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i32, i32)>
      %118 = llvm.load %117 : !llvm.ptr -> i32
      %119 = llvm.load %115 : !llvm.ptr -> !llvm.struct<(i32, i32)>
      %120 = llvm.getelementptr %115[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i32, i32)>
      %121 = llvm.load %120 : !llvm.ptr -> i32
      %122 = arith.constant 2 : i32
      %123 = arith.constant 101 : i32
      %124 = arith.index_cast %122 : i32 to index
      %125 = arith.index_cast %123 : i32 to index
      %127 = arith.constant 1 : index
      %128 = arith.constant -1 : index
      %129 = arith.cmpi sle, %124, %125 : index
      %126 = arith.select %129, %127, %128 : index
      cf.br ^bb21(%124 : index)
      ^bb21(%130: index):
      %131 = arith.cmpi slt, %130, %125 : index
      %132 = arith.cmpi sgt, %130, %125 : index
      %133 = arith.select %129, %131, %132 : i1
      cf.cond_br %133, ^bb22(%130 : index), ^bb23(%130 : index)
      ^bb22(%134: index):
        %135 = arith.constant 601 : i32
        %136 = arith.muli %118, %135 : i32
        %138 = arith.index_cast %134 : index to i32
        %137 = arith.muli %121, %138 : i32
        %139 = arith.addi %136, %137 : i32
        %141 = arith.index_cast %139 : i32 to index
        %140 = memref.load %75[%141] : memref<60701xi1>
        %143 = arith.constant 1 : i1
        %142 = arith.xori %140, %143 : i1
        cf.cond_br %142, ^bb24, ^bb25
        ^bb24:
          %145 = arith.constant 1 : i1
          %146 = arith.index_cast %139 : i32 to index
          memref.store %145, %75[%146] : memref<60701xi1>
          %147 = llvm.load %90 : !llvm.ptr -> i32
          %148 = arith.constant 1 : i32
          %149 = arith.addi %147, %148 : i32
          llvm.store %149, %90 : i32, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          cf.br ^bb26
        ^bb26:
        %150 = arith.addi %134, %126 : index
        cf.br ^bb21(%150 : index)
      ^bb23(%151: index):
      %152 = arith.addi %103, %95 : index
      cf.br ^bb18(%152 : index)
    ^bb20(%153: index):
    %154 = llvm.load %90 : !llvm.ptr -> i32
    func.return %154 : i32
  }
  func.func @main() -> i32 {
    %155 = func.call @solve() : () -> i32
    %156 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %157 = llvm.call @printf(%156, %155) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i32) -> i32
    %158 = arith.constant 0 : i32
    %159 = arith.constant 0 : i32
    func.return %159 : i32
  }
}