mobius_test.c

   1 #include <stdio.h>
   2 #include <stdlib.h>
   3 #include <gmp.h>
   4 #include "cf.h"
   5 #include "test.h"
   6
   7 static void *sqrt2(cf_t cf) {
   8   cf_put_int(cf, 1);
   9   while(cf_wait(cf)) {
  10     cf_put_int(cf, 2);
  11   }
  12   return NULL;
  13 }
  14
  15 // Converges extremely slowly.
  16 static void *slow_pi(cf_t cf) {
  17   mpz_t num, denom, t;
  18   mpz_init(num);
  19   mpz_init(denom);
  20   mpz_init(t);
  21
  22   mpz_set_ui(denom, 3);
  23   cf_put(cf, denom);
  24
  25   mpz_set_ui(num, 1);
  26   cf_put(cf, num);
  27   mpz_set_ui(t, 8);
  28
  29   mpz_set_ui(denom, 6);
  30   while(cf_wait(cf)) {
  31     cf_put(cf, denom);
  32     mpz_add(num, num, t);
  33     cf_put(cf, num);
  34     mpz_add_ui(t, t, 8);
  35   }
  36
  37   mpz_clear(num);
  38   mpz_clear(denom);
  39   mpz_clear(t);
  40   return NULL;
  41 }
  42
  43 int main() {
  44   cf_t x, conv;
  45   x = cf_new_const(sqrt2);
  46   conv = cf_new_cf_convergent(x);
  47
  48   mpz_t p, q;
  49   mpz_init(p);
  50   mpz_init(q);
  51
  52   cf_get(p, conv);
  53   EXPECT(!mpz_cmp_ui(p, 1));
  54   cf_get(q, conv);
  55   EXPECT(!mpz_cmp_ui(q, 1));
  56
  57   cf_get(p, conv);
  58   EXPECT(!mpz_cmp_ui(p, 3));
  59   cf_get(q, conv);
  60   EXPECT(!mpz_cmp_ui(q, 2));
  61
  62   cf_get(p, conv);
  63   EXPECT(!mpz_cmp_ui(p, 7));
  64   cf_get(q, conv);
  65   EXPECT(!mpz_cmp_ui(q, 5));
  66
  67   cf_get(p, conv);
  68   EXPECT(!mpz_cmp_ui(p, 17));
  69   cf_get(q, conv);
  70   EXPECT(!mpz_cmp_ui(q, 12));
  71
  72   mpz_clear(p);
  73   mpz_clear(q);
  74   cf_free(conv);
  75   cf_free(x);
  76
  77   mpz_t z[4];
  78   for (int i = 0; i < 4; i++) mpz_init(z[i]);
  79   // Identity Mobius transformation.
  80   mpz_set_si(z[0], 1);
  81   mpz_set_si(z[3], 1);
  82   mpz_t digit;
  83   mpz_init(digit);
  84
  85   x = cf_new_const(slow_pi);
  86   conv = cf_new_nonregular_mobius_to_decimal(x, z);
  87   cf_get(digit, conv);
  88   EXPECT(!mpz_cmp_ui(digit, 3));
  89   cf_get(digit, conv);
  90   EXPECT(!mpz_cmp_ui(digit, 1));
  91   cf_get(digit, conv);
  92   EXPECT(!mpz_cmp_ui(digit, 4));
  93   cf_get(digit, conv);
  94   EXPECT(!mpz_cmp_ui(digit, 1));
  95   cf_get(digit, conv);
  96   EXPECT(!mpz_cmp_ui(digit, 5));
  97   cf_get(digit, conv);
  98   EXPECT(!mpz_cmp_ui(digit, 9));
  99   cf_get(digit, conv);
 100   EXPECT(!mpz_cmp_ui(digit, 2));
 101
 102   mpz_clear(digit);
 103   cf_free(x);
 104   cf_free(conv);
 105
 106   x = cf_new_const(sqrt2);
 107   cf_t mob;
 108   mob = cf_new_mobius_to_cf(x, z);
 109   CF_EXPECT_DEC(mob, "1.4142135623730");
 110   cf_free(mob);
 111   cf_free(x);
 112   x = cf_new_const(sqrt2);
 113   // (x - 2)/(-3x + 4)
 114   // Works out to be 1 + sqrt(2).
 115   mpz_set_si(z[0], 1);
 116   mpz_set_si(z[1], -2);
 117   mpz_set_si(z[2], -3);
 118   mpz_set_si(z[3], 4);
 119   mob = cf_new_mobius_to_cf(x, z);
 120   CF_EXPECT_DEC(mob, "2.4142135623730");
 121   cf_free(x);
 122   cf_free(mob);
 123   for (int i = 0; i < 4; i++) mpz_clear(z[i]);
 124
 125   return 0;
 126 }