Problem 817

Digits in Squares — sum M(p, p-d) for d=1..1e5 (i128 for large intervals).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 817
# Digits in Squares — sum M(p, p-d) for d=1..1e5 (i128 for large intervals).

function isqrt128(n: i128) -> i128 {
    if n < 2 { return n }
    let mut x: i128 = n
    let mut y: i128 = (x + 1) / 2
    while y < x {
        x = y
        y = (x + n / x) / 2
    }
    return x
}

function ceil_isqrt128(n: i128) -> i128 {
    if n <= 0 { return 0 }
    return isqrt128(n - 1) + 1
}

function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
    let mut r: i64 = 1
    let mut b: i64 = base0 % mod
    let mut e: i64 = exp0
    while e > 0 {
        if (e & 1) != 0 {
            r = ((r as i128) * (b as i128) % (mod as i128)) as i64
        }
        b = ((b as i128) * (b as i128) % (mod as i128)) as i64
        e = e >> 1
    }
    return r
}

function M_pd(p: i64, d: i64, exp_leg: i64, exp_sqrt: i64, p2: i128) -> i64 {
    let a: i64 = p - d
    let ls: i64 = modpow(a, exp_leg, p)
    if ls == 1 {
        let mut r: i64 = modpow(a, exp_sqrt, p)
        if r > p - r { r = p - r }
        return r
    }
    let dp: i128 = (d as i128) * (p as i128)
    let mut L: i128 = p2 - dp
    let p128: i128 = p as i128
    while 1 == 1 {
        let m: i128 = ceil_isqrt128(L)
        if m * m <= L + (p128 - 1) {
            return m as i64
        }
        L = L + p2
    }
    return 0
}

function solve() -> i64 {
    let p: i64 = 1000000007
    let exp_leg: i64 = (p - 1) / 2
    let exp_sqrt: i64 = (p + 1) / 4
    let p2: i128 = (p as i128) * (p as i128)
    let mut total: i64 = 0
    let mut d: i64 = 1
    while d <= 100000 {
        total = total + M_pd(p, d, exp_leg, exp_sqrt, p2)
        d = d + 1
    }
    return total
}

function main() -> i32 {
    printf("%lld\n", 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; }

__int128 isqrt128_i128(__int128 n);
__int128 ceil_isqrt128_i128(__int128 n);
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t M_pd_i64_i64_i64_i64_i128(int64_t p, int64_t d, int64_t exp_leg, int64_t exp_sqrt, __int128 p2);
int64_t solve(void);
int32_t main(void);

__int128 isqrt128_i128(__int128 n) {
    if (n < 2) {
        return n;
    }
    __int128 x = n;
    __int128 y = FLOW_CHECKED_DIV(((x + 1)), (2));
    while (y < x) {
        x = y;
        y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
    }
    return x;
}

__int128 ceil_isqrt128_i128(__int128 n) {
    if (n <= 0) {
        return 0;
    }
    return (isqrt128_i128((n - 1)) + 1);
}

int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
    int64_t r = 1;
    int64_t b = FLOW_CHECKED_MOD((base0), (mod));
    int64_t e = exp0;
    while (e > 0) {
        if ((e & 1) != 0) {
            r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
        }
        b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
        e = FLOW_CHECKED_SHR((e), (1));
    }
    return r;
}

int64_t M_pd_i64_i64_i64_i64_i128(int64_t p, int64_t d, int64_t exp_leg, int64_t exp_sqrt, __int128 p2) {
    int64_t a = (p - d);
    int64_t ls = modpow_i64_i64_i64(a, exp_leg, p);
    if (ls == 1) {
        int64_t r = modpow_i64_i64_i64(a, exp_sqrt, p);
        if (r > (p - r)) {
            r = (p - r);
        }
        return r;
    }
    __int128 dp = (((__int128)(d)) * ((__int128)(p)));
    __int128 L = (p2 - dp);
    __int128 p128 = ((__int128)(p));
    while (1 == 1) {
        __int128 m = ceil_isqrt128_i128(L);
        if ((m * m) <= (L + (p128 - 1))) {
            return ((int64_t)(m));
        }
        L = (L + p2);
    }
    return 0;
}

int64_t solve(void) {
    int64_t p = 1000000007;
    int64_t exp_leg = FLOW_CHECKED_DIV(((p - 1)), (2));
    int64_t exp_sqrt = FLOW_CHECKED_DIV(((p + 1)), (4));
    __int128 p2 = (((__int128)(p)) * ((__int128)(p)));
    int64_t total = 0;
    int64_t d = 1;
    while (d <= 100000) {
        total = (total + M_pd_i64_i64_i64_i64_i128(p, d, exp_leg, exp_sqrt, p2));
        d = (d + 1);
    }
    return total;
}

int32_t main(void) {
    printf("%lld\n", solve());
    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 @isqrt128(%arg0: i128) -> i128 {
    %0 = arith.constant 2 : i32
    %2 = arith.trunci %arg0 : i128 to i64
    %3 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi slt, %2, %3 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      func.return %arg0 : i128
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i128 : (i64) -> !llvm.ptr
    llvm.store %arg0, %5 : i128, !llvm.ptr
    %6 = llvm.load %5 : !llvm.ptr -> i128
    %7 = arith.constant 1 : i32
    %9 = arith.trunci %6 : i128 to i64
    %10 = arith.extsi %7 : i32 to i64
    %8 = arith.addi %9, %10 : i64
    %11 = arith.constant 2 : i32
    %13 = arith.extsi %11 : i32 to i64
    %12 = arith.divsi %8, %13 : i64
    %14 = arith.extsi %12 : i64 to i128
    %15 = llvm.mlir.constant(1 : i64) : i64
    %16 = llvm.alloca %15 x i128 : (i64) -> !llvm.ptr
    llvm.store %14, %16 : i128, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %17 = llvm.load %16 : !llvm.ptr -> i128
    %18 = llvm.load %5 : !llvm.ptr -> i128
    %20 = arith.trunci %17 : i128 to i64
    %21 = arith.trunci %18 : i128 to i64
    %19 = arith.cmpi slt, %20, %21 : i64
    cf.cond_br %19, ^bb4, ^bb5
    ^bb4:
      %22 = llvm.load %16 : !llvm.ptr -> i128
      llvm.store %22, %5 : i128, !llvm.ptr
      %23 = llvm.load %5 : !llvm.ptr -> i128
      %24 = llvm.load %5 : !llvm.ptr -> i128
      %26 = arith.trunci %arg0 : i128 to i64
      %27 = arith.trunci %24 : i128 to i64
      %25 = arith.divsi %26, %27 : i64
      %29 = arith.trunci %23 : i128 to i64
      %28 = arith.addi %29, %25 : i64
      %30 = arith.constant 2 : i32
      %32 = arith.extsi %30 : i32 to i64
      %31 = arith.divsi %28, %32 : i64
      %33 = arith.extsi %31 : i64 to i128
      llvm.store %33, %16 : i128, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %34 = llvm.load %5 : !llvm.ptr -> i128
    func.return %34 : i128
  }
  func.func @ceil_isqrt128(%arg0: i128) -> i128 {
    %35 = arith.constant 0 : i32
    %37 = arith.trunci %arg0 : i128 to i64
    %38 = arith.extsi %35 : i32 to i64
    %36 = arith.cmpi sle, %37, %38 : i64
    cf.cond_br %36, ^bb6, ^bb7
    ^bb6:
      %39 = arith.constant 0 : i32
      %40 = arith.extsi %39 : i32 to i128
      func.return %40 : i128
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %42 = arith.constant 1 : i32
    %44 = arith.trunci %arg0 : i128 to i64
    %45 = arith.extsi %42 : i32 to i64
    %43 = arith.subi %44, %45 : i64
    %46 = arith.extsi %43 : i64 to i128
    %41 = func.call @isqrt128(%46) : (i128) -> i128
    %47 = arith.constant 1 : i32
    %49 = arith.trunci %41 : i128 to i64
    %50 = arith.extsi %47 : i32 to i64
    %48 = arith.addi %49, %50 : i64
    %51 = arith.extsi %48 : i64 to i128
    func.return %51 : i128
  }
  func.func @modpow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %52 = arith.constant 1 : i32
    %53 = arith.extsi %52 : i32 to i64
    %54 = llvm.mlir.constant(1 : i64) : i64
    %55 = llvm.alloca %54 x i64 : (i64) -> !llvm.ptr
    llvm.store %53, %55 : i64, !llvm.ptr
    %56 = arith.remsi %arg0, %arg2 : i64
    %57 = llvm.mlir.constant(1 : i64) : i64
    %58 = llvm.alloca %57 x i64 : (i64) -> !llvm.ptr
    llvm.store %56, %58 : i64, !llvm.ptr
    %59 = llvm.mlir.constant(1 : i64) : i64
    %60 = llvm.alloca %59 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %60 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %61 = llvm.load %60 : !llvm.ptr -> i64
    %62 = arith.constant 0 : i32
    %64 = arith.extsi %62 : i32 to i64
    %63 = arith.cmpi sgt, %61, %64 : i64
    cf.cond_br %63, ^bb10, ^bb11
    ^bb10:
      %65 = llvm.load %60 : !llvm.ptr -> i64
      %66 = arith.constant 1 : i32
      %68 = arith.extsi %66 : i32 to i64
      %67 = arith.andi %65, %68 : i64
      %69 = arith.constant 0 : i32
      %71 = arith.extsi %69 : i32 to i64
      %70 = arith.cmpi ne, %67, %71 : i64
      cf.cond_br %70, ^bb12, ^bb13
      ^bb12:
        %72 = llvm.load %55 : !llvm.ptr -> i64
        %73 = arith.extsi %72 : i64 to i128
        %74 = llvm.load %58 : !llvm.ptr -> i64
        %75 = arith.extsi %74 : i64 to i128
        %77 = arith.trunci %73 : i128 to i64
        %78 = arith.trunci %75 : i128 to i64
        %76 = arith.muli %77, %78 : i64
        %79 = arith.extsi %arg2 : i64 to i128
        %81 = arith.trunci %79 : i128 to i64
        %80 = arith.remsi %76, %81 : i64
        llvm.store %80, %55 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %82 = llvm.load %58 : !llvm.ptr -> i64
      %83 = arith.extsi %82 : i64 to i128
      %84 = llvm.load %58 : !llvm.ptr -> i64
      %85 = arith.extsi %84 : i64 to i128
      %87 = arith.trunci %83 : i128 to i64
      %88 = arith.trunci %85 : i128 to i64
      %86 = arith.muli %87, %88 : i64
      %89 = arith.extsi %arg2 : i64 to i128
      %91 = arith.trunci %89 : i128 to i64
      %90 = arith.remsi %86, %91 : i64
      llvm.store %90, %58 : i64, !llvm.ptr
      %92 = llvm.load %60 : !llvm.ptr -> i64
      %93 = arith.constant 1 : i32
      %95 = arith.extsi %93 : i32 to i64
      %94 = arith.shrsi %92, %95 : i64
      llvm.store %94, %60 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %96 = llvm.load %55 : !llvm.ptr -> i64
    func.return %96 : i64
  }
  func.func @M_pd(%arg0: i64, %arg1: i64, %arg2: i64, %arg3: i64, %arg4: i128) -> i64 {
    %97 = arith.subi %arg0, %arg1 : i64
    %98 = func.call @modpow(%97, %arg2, %arg0) : (i64, i64, i64) -> i64
    %99 = arith.constant 1 : i32
    %101 = arith.extsi %99 : i32 to i64
    %100 = arith.cmpi eq, %98, %101 : i64
    cf.cond_br %100, ^bb15, ^bb16
    ^bb15:
      %102 = func.call @modpow(%97, %arg3, %arg0) : (i64, i64, i64) -> i64
      %103 = llvm.mlir.constant(1 : i64) : i64
      %104 = llvm.alloca %103 x i64 : (i64) -> !llvm.ptr
      llvm.store %102, %104 : i64, !llvm.ptr
      %105 = llvm.load %104 : !llvm.ptr -> i64
      %106 = llvm.load %104 : !llvm.ptr -> i64
      %107 = arith.subi %arg0, %106 : i64
      %108 = arith.cmpi sgt, %105, %107 : i64
      cf.cond_br %108, ^bb18, ^bb19
      ^bb18:
        %109 = llvm.load %104 : !llvm.ptr -> i64
        %110 = arith.subi %arg0, %109 : i64
        llvm.store %110, %104 : i64, !llvm.ptr
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %111 = llvm.load %104 : !llvm.ptr -> i64
      func.return %111 : i64
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %112 = arith.extsi %arg1 : i64 to i128
    %113 = arith.extsi %arg0 : i64 to i128
    %115 = arith.trunci %112 : i128 to i64
    %116 = arith.trunci %113 : i128 to i64
    %114 = arith.muli %115, %116 : i64
    %117 = arith.extsi %114 : i64 to i128
    %119 = arith.trunci %arg4 : i128 to i64
    %120 = arith.trunci %117 : i128 to i64
    %118 = arith.subi %119, %120 : i64
    %121 = arith.extsi %118 : i64 to i128
    %122 = llvm.mlir.constant(1 : i64) : i64
    %123 = llvm.alloca %122 x i128 : (i64) -> !llvm.ptr
    llvm.store %121, %123 : i128, !llvm.ptr
    %124 = arith.extsi %arg0 : i64 to i128
    cf.br ^bb21
    ^bb21:
    %125 = arith.constant 1 : i32
    %126 = arith.constant 1 : i32
    %127 = arith.cmpi eq, %125, %126 : i32
    cf.cond_br %127, ^bb22, ^bb23
    ^bb22:
      %129 = llvm.load %123 : !llvm.ptr -> i128
      %128 = func.call @ceil_isqrt128(%129) : (i128) -> i128
      %131 = arith.trunci %128 : i128 to i64
      %132 = arith.trunci %128 : i128 to i64
      %130 = arith.muli %131, %132 : i64
      %133 = llvm.load %123 : !llvm.ptr -> i128
      %134 = arith.constant 1 : i32
      %136 = arith.trunci %124 : i128 to i64
      %137 = arith.extsi %134 : i32 to i64
      %135 = arith.subi %136, %137 : i64
      %139 = arith.trunci %133 : i128 to i64
      %138 = arith.addi %139, %135 : i64
      %140 = arith.cmpi sle, %130, %138 : i64
      cf.cond_br %140, ^bb24, ^bb25
      ^bb24:
        %141 = arith.trunci %128 : i128 to i64
        func.return %141 : i64
      ^bb25:
        cf.br ^bb26
      ^bb26:
      %142 = llvm.load %123 : !llvm.ptr -> i128
      %144 = arith.trunci %142 : i128 to i64
      %145 = arith.trunci %arg4 : i128 to i64
      %143 = arith.addi %144, %145 : i64
      %146 = arith.extsi %143 : i64 to i128
      llvm.store %146, %123 : i128, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %147 = arith.constant 0 : i32
    %148 = arith.extsi %147 : i32 to i64
    func.return %148 : i64
  }
  func.func @solve() -> i64 {
    %149 = arith.constant 1000000007 : i32
    %150 = arith.extsi %149 : i32 to i64
    %151 = arith.constant 1 : i32
    %153 = arith.extsi %151 : i32 to i64
    %152 = arith.subi %150, %153 : i64
    %154 = arith.constant 2 : i32
    %156 = arith.extsi %154 : i32 to i64
    %155 = arith.divsi %152, %156 : i64
    %157 = arith.constant 1 : i32
    %159 = arith.extsi %157 : i32 to i64
    %158 = arith.addi %150, %159 : i64
    %160 = arith.constant 4 : i32
    %162 = arith.extsi %160 : i32 to i64
    %161 = arith.divsi %158, %162 : i64
    %163 = arith.extsi %150 : i64 to i128
    %164 = arith.extsi %150 : i64 to i128
    %166 = arith.trunci %163 : i128 to i64
    %167 = arith.trunci %164 : i128 to i64
    %165 = arith.muli %166, %167 : i64
    %168 = arith.extsi %165 : i64 to i128
    %169 = arith.constant 0 : i32
    %170 = arith.extsi %169 : i32 to i64
    %171 = llvm.mlir.constant(1 : i64) : i64
    %172 = llvm.alloca %171 x i64 : (i64) -> !llvm.ptr
    llvm.store %170, %172 : i64, !llvm.ptr
    %173 = arith.constant 1 : i32
    %174 = arith.extsi %173 : i32 to i64
    %175 = llvm.mlir.constant(1 : i64) : i64
    %176 = llvm.alloca %175 x i64 : (i64) -> !llvm.ptr
    llvm.store %174, %176 : i64, !llvm.ptr
    cf.br ^bb27
    ^bb27:
    %177 = llvm.load %176 : !llvm.ptr -> i64
    %178 = arith.constant 100000 : i32
    %180 = arith.extsi %178 : i32 to i64
    %179 = arith.cmpi sle, %177, %180 : i64
    cf.cond_br %179, ^bb28, ^bb29
    ^bb28:
      %181 = llvm.load %172 : !llvm.ptr -> i64
      %183 = llvm.load %176 : !llvm.ptr -> i64
      %182 = func.call @M_pd(%150, %183, %155, %161, %168) : (i64, i64, i64, i64, i128) -> i64
      %184 = arith.addi %181, %182 : i64
      llvm.store %184, %172 : i64, !llvm.ptr
      %185 = llvm.load %176 : !llvm.ptr -> i64
      %186 = arith.constant 1 : i32
      %188 = arith.extsi %186 : i32 to i64
      %187 = arith.addi %185, %188 : i64
      llvm.store %187, %176 : i64, !llvm.ptr
      cf.br ^bb27
    ^bb29:
    %189 = llvm.load %172 : !llvm.ptr -> i64
    func.return %189 : i64
  }
  func.func @main() -> i32 {
    %190 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %191 = func.call @solve() : () -> i64
    %192 = llvm.call @printf(%190, %191) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %193 = arith.constant 0 : i32
    func.return %193 : i32
  }
}