Problem 938

Exhausting a Colour — P(R,B) via log-gamma closed form. P(24690, 12345).

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Performance comparison

Flow source

# Project Euler 938
# Exhausting a Colour — P(R,B) via log-gamma closed form. P(24690, 12345).

extern {
    function lgamma(x: f64) -> f64
    function log(x: f64) -> f64
    function exp(x: f64) -> f64
    function log1p(x: f64) -> f64
}

function log_add_exp(log_x: f64, log_y: f64, has_x: i32) -> f64 {
    if has_x == 0 { return log_y }
    let mut a: f64 = log_x
    let mut b: f64 = log_y
    if b > a {
        let t: f64 = a
        a = b
        b = t
    }
    return a + log1p(exp(b - a))
}

function probability_black(R: i64, B: i64) -> f64 {
    if B <= 0 { return 0.0 }
    if R <= 0 { return 1.0 }
    if (R & 1) == 1 { return 0.0 }
    let a: i64 = R / 2
    let b: i64 = B
    if a == 0 { return 1.0 }
    let log4: f64 = log(4.0)
    let m: i64 = a - 1
    let mut log_u: f64 = 0.0
    let mut has: i32 = 0
    let mut k: i64 = 1
    while k <= b {
        let log_g: f64 = lgamma((2 * k + 1) as f64) - 2.0 * lgamma((k + 1) as f64) - (k as f64) * log4
        let n: i64 = a + b - k - 1
        let log_binom: f64 = lgamma((n + 1) as f64) - lgamma((m + 1) as f64) - lgamma((n - m + 1) as f64)
        log_u = log_add_exp(log_u, log_g + log_binom, has)
        has = 1
        k = k + 1
    }
    let log_C: f64 = lgamma((a + b) as f64 + 0.5) - lgamma(a as f64 + 0.5) - lgamma((b + 1) as f64)
    return exp(log_u - log_C)
}

function main() -> i32 {
    printf("%.10f\n", probability_black(24690, 12345))
    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; }

double lgamma(double x);
double log1p(double x);
double log_add_exp_f64_f64_i32(double log_x, double log_y, int32_t has_x);
double probability_black_i64_i64(int64_t R, int64_t B);
int32_t main(void);





double log_add_exp_f64_f64_i32(double log_x, double log_y, int32_t has_x) {
    if (has_x == 0) {
        return log_y;
    }
    double a = log_x;
    double b = log_y;
    if (b > a) {
        double t = a;
        a = b;
        b = t;
    }
    return (a + log1p(exp((b - a))));
}

double probability_black_i64_i64(int64_t R, int64_t B) {
    if (B <= 0) {
        return 0.0;
    }
    if (R <= 0) {
        return 1.0;
    }
    if ((R & 1) == 1) {
        return 0.0;
    }
    int64_t a = FLOW_CHECKED_DIV((R), (2));
    int64_t b = B;
    if (a == 0) {
        return 1.0;
    }
    double log4 = log(4.0);
    int64_t m = (a - 1);
    double log_u = 0.0;
    int32_t has = 0;
    int64_t k = 1;
    while (k <= b) {
        double log_g = ((lgamma(((double)(((2 * k) + 1)))) - (2.0 * lgamma(((double)((k + 1)))))) - (((double)(k)) * log4));
        int64_t n = (((a + b) - k) - 1);
        double log_binom = ((lgamma(((double)((n + 1)))) - lgamma(((double)((m + 1))))) - lgamma(((double)(((n - m) + 1)))));
        log_u = log_add_exp_f64_f64_i32(log_u, (log_g + log_binom), has);
        has = 1;
        k = (k + 1);
    }
    double log_C = ((lgamma((((double)((a + b))) + 0.5)) - lgamma((((double)(a)) + 0.5))) - lgamma(((double)((b + 1)))));
    return exp((log_u - log_C));
}

int32_t main(void) {
    printf("%.10f\n", probability_black_i64_i64(24690, 12345));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func private @lgamma(f64) -> f64
  func.func private @log(f64) -> f64
  func.func private @exp(f64) -> f64
  func.func private @log1p(f64) -> f64
  func.func @log_add_exp(%arg0: f64, %arg1: f64, %arg2: i32) -> f64 {
    %0 = arith.constant 0 : i32
    %1 = arith.cmpi eq, %arg2, %0 : i32
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      func.return %arg1 : f64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x f64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %3 : f64, !llvm.ptr
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x f64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %5 : f64, !llvm.ptr
    %6 = llvm.load %5 : !llvm.ptr -> f64
    %7 = llvm.load %3 : !llvm.ptr -> f64
    %8 = arith.cmpf ogt, %6, %7 : f64
    cf.cond_br %8, ^bb3, ^bb4
    ^bb3:
      %9 = llvm.load %3 : !llvm.ptr -> f64
      %10 = llvm.load %5 : !llvm.ptr -> f64
      llvm.store %10, %3 : f64, !llvm.ptr
      llvm.store %9, %5 : f64, !llvm.ptr
      cf.br ^bb5
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %11 = llvm.load %3 : !llvm.ptr -> f64
    %13 = llvm.load %5 : !llvm.ptr -> f64
    %14 = llvm.load %3 : !llvm.ptr -> f64
    %15 = arith.subf %13, %14 : f64
    %16 = math.exp %15 : f64
    %12 = func.call @log1p(%16) : (f64) -> f64
    %17 = arith.addf %11, %12 : f64
    func.return %17 : f64
  }
  func.func @probability_black(%arg0: i64, %arg1: i64) -> f64 {
    %18 = arith.constant 0 : i32
    %20 = arith.extsi %18 : i32 to i64
    %19 = arith.cmpi sle, %arg1, %20 : i64
    cf.cond_br %19, ^bb6, ^bb7
    ^bb6:
      %21 = arith.constant 0.0 : f32
      %22 = arith.extf %21 : f32 to f64
      func.return %22 : f64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %23 = arith.constant 0 : i32
    %25 = arith.extsi %23 : i32 to i64
    %24 = arith.cmpi sle, %arg0, %25 : i64
    cf.cond_br %24, ^bb9, ^bb10
    ^bb9:
      %26 = arith.constant 1.0 : f32
      %27 = arith.extf %26 : f32 to f64
      func.return %27 : f64
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %28 = arith.constant 1 : i32
    %30 = arith.extsi %28 : i32 to i64
    %29 = arith.andi %arg0, %30 : i64
    %31 = arith.constant 1 : i32
    %33 = arith.extsi %31 : i32 to i64
    %32 = arith.cmpi eq, %29, %33 : i64
    cf.cond_br %32, ^bb12, ^bb13
    ^bb12:
      %34 = arith.constant 0.0 : f32
      %35 = arith.extf %34 : f32 to f64
      func.return %35 : f64
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %36 = arith.constant 2 : i32
    %38 = arith.extsi %36 : i32 to i64
    %37 = arith.divsi %arg0, %38 : i64
    %39 = arith.constant 0 : i32
    %41 = arith.extsi %39 : i32 to i64
    %40 = arith.cmpi eq, %37, %41 : i64
    cf.cond_br %40, ^bb15, ^bb16
    ^bb15:
      %42 = arith.constant 1.0 : f32
      %43 = arith.extf %42 : f32 to f64
      func.return %43 : f64
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %44 = arith.constant 4.0 : f32
    %45 = math.log %44 : f32
    %46 = arith.extf %45 : f32 to f64
    %47 = arith.constant 1 : i32
    %49 = arith.extsi %47 : i32 to i64
    %48 = arith.subi %37, %49 : i64
    %50 = arith.constant 0.0 : f32
    %51 = arith.extf %50 : f32 to f64
    %52 = llvm.mlir.constant(1 : i64) : i64
    %53 = llvm.alloca %52 x f64 : (i64) -> !llvm.ptr
    llvm.store %51, %53 : f64, !llvm.ptr
    %54 = arith.constant 0 : i32
    %55 = llvm.mlir.constant(1 : i64) : i64
    %56 = llvm.alloca %55 x i32 : (i64) -> !llvm.ptr
    llvm.store %54, %56 : i32, !llvm.ptr
    %57 = arith.constant 1 : i32
    %58 = arith.extsi %57 : i32 to i64
    %59 = llvm.mlir.constant(1 : i64) : i64
    %60 = llvm.alloca %59 x i64 : (i64) -> !llvm.ptr
    llvm.store %58, %60 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %61 = llvm.load %60 : !llvm.ptr -> i64
    %62 = arith.cmpi sle, %61, %arg1 : i64
    cf.cond_br %62, ^bb19, ^bb20
    ^bb19:
      %64 = arith.constant 2 : i32
      %65 = llvm.load %60 : !llvm.ptr -> i64
      %67 = arith.extsi %64 : i32 to i64
      %66 = arith.muli %67, %65 : i64
      %68 = arith.constant 1 : i32
      %70 = arith.extsi %68 : i32 to i64
      %69 = arith.addi %66, %70 : i64
      %71 = arith.sitofp %69 : i64 to f64
      %63 = func.call @lgamma(%71) : (f64) -> f64
      %72 = arith.constant 2.0 : f32
      %74 = llvm.load %60 : !llvm.ptr -> i64
      %75 = arith.constant 1 : i32
      %77 = arith.extsi %75 : i32 to i64
      %76 = arith.addi %74, %77 : i64
      %78 = arith.sitofp %76 : i64 to f64
      %73 = func.call @lgamma(%78) : (f64) -> f64
      %80 = arith.extf %72 : f32 to f64
      %79 = arith.mulf %80, %73 : f64
      %81 = arith.subf %63, %79 : f64
      %82 = llvm.load %60 : !llvm.ptr -> i64
      %83 = arith.sitofp %82 : i64 to f64
      %84 = arith.mulf %83, %46 : f64
      %85 = arith.subf %81, %84 : f64
      %86 = arith.addi %37, %arg1 : i64
      %87 = llvm.load %60 : !llvm.ptr -> i64
      %88 = arith.subi %86, %87 : i64
      %89 = arith.constant 1 : i32
      %91 = arith.extsi %89 : i32 to i64
      %90 = arith.subi %88, %91 : i64
      %93 = arith.constant 1 : i32
      %95 = arith.extsi %93 : i32 to i64
      %94 = arith.addi %90, %95 : i64
      %96 = arith.sitofp %94 : i64 to f64
      %92 = func.call @lgamma(%96) : (f64) -> f64
      %98 = arith.constant 1 : i32
      %100 = arith.extsi %98 : i32 to i64
      %99 = arith.addi %48, %100 : i64
      %101 = arith.sitofp %99 : i64 to f64
      %97 = func.call @lgamma(%101) : (f64) -> f64
      %102 = arith.subf %92, %97 : f64
      %104 = arith.subi %90, %48 : i64
      %105 = arith.constant 1 : i32
      %107 = arith.extsi %105 : i32 to i64
      %106 = arith.addi %104, %107 : i64
      %108 = arith.sitofp %106 : i64 to f64
      %103 = func.call @lgamma(%108) : (f64) -> f64
      %109 = arith.subf %102, %103 : f64
      %111 = llvm.load %53 : !llvm.ptr -> f64
      %112 = arith.addf %85, %109 : f64
      %113 = llvm.load %56 : !llvm.ptr -> i32
      %110 = func.call @log_add_exp(%111, %112, %113) : (f64, f64, i32) -> f64
      llvm.store %110, %53 : f64, !llvm.ptr
      %114 = arith.constant 1 : i32
      llvm.store %114, %56 : i32, !llvm.ptr
      %115 = llvm.load %60 : !llvm.ptr -> i64
      %116 = arith.constant 1 : i32
      %118 = arith.extsi %116 : i32 to i64
      %117 = arith.addi %115, %118 : i64
      llvm.store %117, %60 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %120 = arith.addi %37, %arg1 : i64
    %121 = arith.sitofp %120 : i64 to f64
    %122 = arith.constant 0.5 : f32
    %124 = arith.extf %122 : f32 to f64
    %123 = arith.addf %121, %124 : f64
    %119 = func.call @lgamma(%123) : (f64) -> f64
    %126 = arith.sitofp %37 : i64 to f64
    %127 = arith.constant 0.5 : f32
    %129 = arith.extf %127 : f32 to f64
    %128 = arith.addf %126, %129 : f64
    %125 = func.call @lgamma(%128) : (f64) -> f64
    %130 = arith.subf %119, %125 : f64
    %132 = arith.constant 1 : i32
    %134 = arith.extsi %132 : i32 to i64
    %133 = arith.addi %arg1, %134 : i64
    %135 = arith.sitofp %133 : i64 to f64
    %131 = func.call @lgamma(%135) : (f64) -> f64
    %136 = arith.subf %130, %131 : f64
    %137 = llvm.load %53 : !llvm.ptr -> f64
    %138 = arith.subf %137, %136 : f64
    %139 = math.exp %138 : f64
    func.return %139 : f64
  }
  func.func @main() -> i32 {
    %140 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %142 = arith.constant 24690 : i32
    %143 = arith.constant 12345 : i32
    %144 = arith.extsi %142 : i32 to i64
    %145 = arith.extsi %143 : i32 to i64
    %141 = func.call @probability_black(%144, %145) : (i64, i64) -> f64
    %146 = llvm.call @printf(%140, %141) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %147 = arith.constant 0 : i32
    func.return %147 : i32
  }
}