# Project Euler 975
# Winding walk on turning points of H(a,b,x) over prime pairs.
# Port of the C reference solver to pure Flow.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function cos(x: f64) -> f64
function sin(x: f64) -> f64
function fabs(x: f64) -> f64
}
const PI: f64 = 3.14159265358979323846
const MAXC: i64 = 4096
function gcd_int(a: i64, b: i64) -> i64 {
if a < 0 { a = -a }
if b < 0 { b = -b }
while b != 0 {
let t: i64 = a % b
a = b
b = t
}
return a
}
function iabs(x: i64) -> i64 {
if x < 0 { return -x }
return x
}
function fmaxv(a: f64, b: f64) -> f64 {
if a > b { return a }
return b
}
function fminv(a: f64, b: f64) -> f64 {
if a < b { return a }
return b
}
# candidate points stored in global buffers
let mut g_num: ptr<i64> = null
let mut g_den: ptr<i64> = null
let mut g_signs: ptr<i64> = null
let mut g_kept_num: ptr<i64> = null
let mut g_kept_den: ptr<i64> = null
function make_normalized(num: i64, den: i64, idx: i64) -> void {
let g: i64 = gcd_int(num, den)
g_num[idx] = num / g
g_den[idx] = den / g
}
function height_val(a: i64, b: i64, num: i64, den: i64) -> f64 {
if num == 0 { return 0.0 }
if num == den { return 1.0 }
let x: f64 = (num as f64) / (den as f64)
let z: f64 = 0.5 - ((b as f64) * cos((a as f64) * PI * x) + (a as f64) * cos((b as f64) * PI * x)) / (2.0 * ((a + b) as f64))
if z < 0.0 {
if z > -1e-14 { return 0.0 }
}
if z > 1.0 {
if z < 1.0 + 1e-14 { return 1.0 }
}
return z
}
function deriv_sign(a: i64, b: i64, ln: i64, ld: i64, rn: i64, rd: i64) -> i64 {
let x: f64 = ((ln * rd + rn * ld) as f64) / (2.0 * ((ld * rd) as f64))
let value: f64 = sin(((a + b) as f64) * PI * x * 0.5) * cos((iabs(a - b) as f64) * PI * x * 0.5)
if value > 0.0 { return 1 }
return -1
}
# selection sort candidate points by value num/den ascending
function sort_cand2(nc: i64) -> void {
let mut i: i64 = 0
while i < nc {
let mut best: i64 = i
let mut j: i64 = i + 1
while j < nc {
# compare g_num[j]/g_den[j] < g_num[best]/g_den[best]
if g_num[j] * g_den[best] < g_num[best] * g_den[j] {
best = j
}
j = j + 1
}
if best != i {
let tn: i64 = g_num[i]
let td: i64 = g_den[i]
g_num[i] = g_num[best]
g_den[i] = g_den[best]
g_num[best] = tn
g_den[best] = td
}
i = i + 1
}
}
function turning_values(a: i64, b: i64, tv: ptr<f64>) -> i64 {
let s: i64 = a + b
let delta: i64 = iabs(a - b)
let mut nc: i64 = 0
let mut k: i64 = 0
while k <= s / 2 {
make_normalized(2 * k, s, nc)
nc = nc + 1
k = k + 1
}
k = 0
while k < delta / 2 {
make_normalized(2 * k + 1, delta, nc)
nc = nc + 1
k = k + 1
}
sort_cand2(nc)
# dedupe
let mut unique: i64 = 1
let mut i: i64 = 1
while i < nc {
if g_num[i] != g_num[unique - 1] || g_den[i] != g_den[unique - 1] {
g_num[unique] = g_num[i]
g_den[unique] = g_den[i]
unique = unique + 1
}
i = i + 1
}
nc = unique
i = 0
while i < nc - 1 {
g_signs[i] = deriv_sign(a, b, g_num[i], g_den[i], g_num[i + 1], g_den[i + 1])
i = i + 1
}
let mut nk: i64 = 0
g_kept_num[nk] = g_num[0]
g_kept_den[nk] = g_den[0]
nk = nk + 1
i = 1
while i < nc - 1 {
if g_signs[i - 1] != g_signs[i] {
g_kept_num[nk] = g_num[i]
g_kept_den[nk] = g_den[i]
nk = nk + 1
}
i = i + 1
}
g_kept_num[nk] = g_num[nc - 1]
g_kept_den[nk] = g_den[nc - 1]
nk = nk + 1
i = 0
while i < nk {
tv[i] = height_val(a, b, g_kept_num[i], g_kept_den[i])
i = i + 1
}
return nk
}
function F_func(a: i64, b: i64, c: i64, d: i64) -> f64 {
let za: ptr<f64> = calloc(MAXC, 8)
let zb: ptr<f64> = calloc(MAXC, 8)
let na: i64 = turning_values(a, b, za)
let nb: i64 = turning_values(c, d, zb)
let mut i: i64 = 0
let mut j: i64 = 0
let mut current: f64 = 0.0
let mut total: f64 = 0.0
let mut upward: i64 = 1
let eps: f64 = 1e-12
let max_steps: i64 = 4 * (na + nb) * (na + nb)
let mut step: i64 = 0
while step < max_steps {
if i < 0 || i >= na - 1 || j < 0 || j >= nb - 1 {
free(za as ptr<void>)
free(zb as ptr<void>)
return total
}
let a0: f64 = za[i]
let a1: f64 = za[i + 1]
let b0: f64 = zb[j]
let b1: f64 = zb[j + 1]
let lower: f64 = fmaxv(fminv(a0, a1), fminv(b0, b1))
let upper: f64 = fminv(fmaxv(a0, a1), fmaxv(b0, b1))
let nxt: f64 = 0.0
if upward != 0 { nxt = upper } else { nxt = lower }
total = total + fabs(nxt - current)
let mut advanced: i64 = 0
if fabs(nxt - a0) <= eps { i = i - 1; advanced = 1 }
else {
if fabs(nxt - a1) <= eps { i = i + 1; advanced = 1 }
}
if fabs(nxt - b0) <= eps { j = j - 1; advanced = 1 }
else {
if fabs(nxt - b1) <= eps { j = j + 1; advanced = 1 }
}
if advanced == 0 {
free(za as ptr<void>)
free(zb as ptr<void>)
return total
}
current = nxt
upward = 1 - upward
step = step + 1
}
free(za as ptr<void>)
free(zb as ptr<void>)
return total
}
function G_func(m: i64, n: i64) -> f64 {
let is_prime: ptr<i64> = calloc(n + 1, 8)
let mut p: i64 = 0
while p <= n {
is_prime[p] = 1
p = p + 1
}
is_prime[0] = 0
is_prime[1] = 0
p = 2
while p * p <= n {
if is_prime[p] != 0 {
let mut j: i64 = p * p
while j <= n {
is_prime[j] = 0
j = j + p
}
}
p = p + 1
}
let ps: ptr<i64> = calloc(256, 8)
let mut np: i64 = 0
p = m
while p <= n {
if is_prime[p] != 0 {
ps[np] = p
np = np + 1
}
p = p + 1
}
free(is_prime as ptr<void>)
let mut total: f64 = 0.0
let mut i: i64 = 0
while i < np {
let mut j: i64 = i + 1
while j < np {
let pp: i64 = ps[i]
let qq: i64 = ps[j]
total = total + F_func(pp, qq, pp, 2 * qq - pp)
j = j + 1
}
i = i + 1
}
free(ps as ptr<void>)
return total
}
function main() -> i32 {
g_num = calloc(MAXC, 8) as ptr<i64>
g_den = calloc(MAXC, 8) as ptr<i64>
g_signs = calloc(MAXC, 8) as ptr<i64>
g_kept_num = calloc(MAXC, 8) as ptr<i64>
g_kept_den = calloc(MAXC, 8) as ptr<i64>
printf("%.5f\n", G_func(500, 1000))
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 gcd_int_i64_i64(int64_t a, int64_t b);
int64_t iabs_i64(int64_t x);
double fmaxv_f64_f64(double a, double b);
double fminv_f64_f64(double a, double b);
void make_normalized_i64_i64_i64(int64_t num, int64_t den, int64_t idx);
double height_val_i64_i64_i64_i64(int64_t a, int64_t b, int64_t num, int64_t den);
int64_t deriv_sign_i64_i64_i64_i64_i64_i64(int64_t a, int64_t b, int64_t ln, int64_t ld, int64_t rn, int64_t rd);
void sort_cand2_i64(int64_t nc);
int64_t turning_values_i64_i64_ptr_f64(int64_t a, int64_t b, double* tv);
double F_func_i64_i64_i64_i64(int64_t a, int64_t b, int64_t c, int64_t d);
double G_func_i64_i64(int64_t m, int64_t n);
int32_t main(void);
static const double PI = 3.14159265358979323846;
static const int64_t MAXC = 4096;
/* Module statics */
static int64_t* g_num = NULL;
static int64_t* g_den = NULL;
static int64_t* g_signs = NULL;
static int64_t* g_kept_num = NULL;
static int64_t* g_kept_den = NULL;
int64_t gcd_int_i64_i64(int64_t a, int64_t b) {
if (a < 0) {
a = (-a);
}
if (b < 0) {
b = (-b);
}
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t iabs_i64(int64_t x) {
if (x < 0) {
return (-x);
}
return x;
}
double fmaxv_f64_f64(double a, double b) {
if (a > b) {
return a;
}
return b;
}
double fminv_f64_f64(double a, double b) {
if (a < b) {
return a;
}
return b;
}
void make_normalized_i64_i64_i64(int64_t num, int64_t den, int64_t idx) {
int64_t g = gcd_int_i64_i64(num, den);
g_num[idx] = FLOW_CHECKED_DIV((num), (g));
g_den[idx] = FLOW_CHECKED_DIV((den), (g));
}
double height_val_i64_i64_i64_i64(int64_t a, int64_t b, int64_t num, int64_t den) {
if (num == 0) {
return 0.0;
}
if (num == den) {
return 1.0;
}
double x = (((double)(num)) / ((double)(den)));
double z = (0.5 - (((((double)(b)) * cos(((((double)(a)) * PI) * x))) + (((double)(a)) * cos(((((double)(b)) * PI) * x)))) / (2.0 * ((double)((a + b))))));
if (z < 0.0) {
if (z > (-1e-14)) {
return 0.0;
}
}
if (z > 1.0) {
if (z < (1.0 + 1e-14)) {
return 1.0;
}
}
return z;
}
int64_t deriv_sign_i64_i64_i64_i64_i64_i64(int64_t a, int64_t b, int64_t ln, int64_t ld, int64_t rn, int64_t rd) {
double x = (((double)(((ln * rd) + (rn * ld)))) / (2.0 * ((double)((ld * rd)))));
double value = (sin((((((double)((a + b))) * PI) * x) * 0.5)) * cos((((((double)(iabs_i64((a - b)))) * PI) * x) * 0.5)));
if (value > 0.0) {
return 1;
}
return (-1);
}
void sort_cand2_i64(int64_t nc) {
int64_t i = 0;
while (i < nc) {
int64_t best = i;
int64_t j = (i + 1);
while (j < nc) {
if ((g_num[j] * g_den[best]) < (g_num[best] * g_den[j])) {
best = j;
}
j = (j + 1);
}
if (best != i) {
int64_t tn = g_num[i];
int64_t td = g_den[i];
g_num[i] = g_num[best];
g_den[i] = g_den[best];
g_num[best] = tn;
g_den[best] = td;
}
i = (i + 1);
}
}
int64_t turning_values_i64_i64_ptr_f64(int64_t a, int64_t b, double* tv) {
int64_t s = (a + b);
int64_t delta = iabs_i64((a - b));
int64_t nc = 0;
int64_t k = 0;
while (k <= FLOW_CHECKED_DIV((s), (2))) {
make_normalized_i64_i64_i64((2 * k), s, nc);
nc = (nc + 1);
k = (k + 1);
}
k = 0;
while (k < FLOW_CHECKED_DIV((delta), (2))) {
make_normalized_i64_i64_i64(((2 * k) + 1), delta, nc);
nc = (nc + 1);
k = (k + 1);
}
sort_cand2_i64(nc);
int64_t unique = 1;
int64_t i = 1;
while (i < nc) {
if ((g_num[i] != g_num[(unique - 1)] || g_den[i] != g_den[(unique - 1)])) {
g_num[unique] = g_num[i];
g_den[unique] = g_den[i];
unique = (unique + 1);
}
i = (i + 1);
}
nc = unique;
i = 0;
while (i < (nc - 1)) {
g_signs[i] = deriv_sign_i64_i64_i64_i64_i64_i64(a, b, g_num[i], g_den[i], g_num[(i + 1)], g_den[(i + 1)]);
i = (i + 1);
}
int64_t nk = 0;
g_kept_num[nk] = g_num[0];
g_kept_den[nk] = g_den[0];
nk = (nk + 1);
i = 1;
while (i < (nc - 1)) {
if (g_signs[(i - 1)] != g_signs[i]) {
g_kept_num[nk] = g_num[i];
g_kept_den[nk] = g_den[i];
nk = (nk + 1);
}
i = (i + 1);
}
g_kept_num[nk] = g_num[(nc - 1)];
g_kept_den[nk] = g_den[(nc - 1)];
nk = (nk + 1);
i = 0;
while (i < nk) {
tv[i] = height_val_i64_i64_i64_i64(a, b, g_kept_num[i], g_kept_den[i]);
i = (i + 1);
}
return nk;
}
double F_func_i64_i64_i64_i64(int64_t a, int64_t b, int64_t c, int64_t d) {
double* za = (double*)(calloc(MAXC, 8));
double* zb = (double*)(calloc(MAXC, 8));
int64_t na = turning_values_i64_i64_ptr_f64(a, b, za);
int64_t nb = turning_values_i64_i64_ptr_f64(c, d, zb);
int64_t i = 0;
int64_t j = 0;
double current = 0.0;
double total = 0.0;
int64_t upward = 1;
double eps = 1e-12;
int64_t max_steps = ((4 * (na + nb)) * (na + nb));
int64_t step = 0;
while (step < max_steps) {
if ((((i < 0 || i >= (na - 1)) || j < 0) || j >= (nb - 1))) {
free(((void*)(za)));
free(((void*)(zb)));
return total;
}
double a0 = za[i];
double a1 = za[(i + 1)];
double b0 = zb[j];
double b1 = zb[(j + 1)];
double lower = fmaxv_f64_f64(fminv_f64_f64(a0, a1), fminv_f64_f64(b0, b1));
double upper = fminv_f64_f64(fmaxv_f64_f64(a0, a1), fmaxv_f64_f64(b0, b1));
double nxt = 0.0;
if (upward != 0) {
nxt = upper;
} else {
nxt = lower;
}
total = (total + fabs((nxt - current)));
int64_t advanced = 0;
if (fabs((nxt - a0)) <= eps) {
i = (i - 1);
advanced = 1;
} else {
if (fabs((nxt - a1)) <= eps) {
i = (i + 1);
advanced = 1;
}
}
if (fabs((nxt - b0)) <= eps) {
j = (j - 1);
advanced = 1;
} else {
if (fabs((nxt - b1)) <= eps) {
j = (j + 1);
advanced = 1;
}
}
if (advanced == 0) {
free(((void*)(za)));
free(((void*)(zb)));
return total;
}
current = nxt;
upward = (1 - upward);
step = (step + 1);
}
free(((void*)(za)));
free(((void*)(zb)));
return total;
}
double G_func_i64_i64(int64_t m, int64_t n) {
int64_t* is_prime = (int64_t*)(calloc((n + 1), 8));
int64_t p = 0;
while (p <= n) {
is_prime[p] = 1;
p = (p + 1);
}
is_prime[0] = 0;
is_prime[1] = 0;
p = 2;
while ((p * p) <= n) {
if (is_prime[p] != 0) {
int64_t j = (p * p);
while (j <= n) {
is_prime[j] = 0;
j = (j + p);
}
}
p = (p + 1);
}
int64_t* ps = (int64_t*)(calloc(256, 8));
int64_t np = 0;
p = m;
while (p <= n) {
if (is_prime[p] != 0) {
ps[np] = p;
np = (np + 1);
}
p = (p + 1);
}
free(((void*)(is_prime)));
double total = 0.0;
int64_t i = 0;
while (i < np) {
int64_t j = (i + 1);
while (j < np) {
int64_t pp = ps[i];
int64_t qq = ps[j];
total = (total + F_func_i64_i64_i64_i64(pp, qq, pp, ((2 * qq) - pp)));
j = (j + 1);
}
i = (i + 1);
}
free(((void*)(ps)));
return total;
}
int32_t main(void) {
g_num = ((int64_t*)(calloc(MAXC, 8)));
g_den = ((int64_t*)(calloc(MAXC, 8)));
g_signs = ((int64_t*)(calloc(MAXC, 8)));
g_kept_num = ((int64_t*)(calloc(MAXC, 8)));
g_kept_den = ((int64_t*)(calloc(MAXC, 8)));
printf("%.5f\n", G_func_i64_i64(500, 1000));
return 0;
}