cf.h

   1 // Requires gmp.h
   2 //
   3 // Opaque interface to continued fractions object.
   4
   5 #ifndef __CF_H__
   6 #define __CF_H__
   7
   8 struct cf_s;
   9 typedef struct cf_s *cf_t;
  10
  11 cf_t cf_new(void *(*func)(cf_t), void *data);
  12 static inline cf_t cf_new_const(void *(*func)(cf_t)) {
  13   return cf_new(func, NULL);
  14 }
  15 void cf_free(cf_t cf);
  16
  17 void cf_set_sign(cf_t cf, int sign);
  18 int cf_sign(cf_t cf);
  19 int cf_flip_sign(cf_t cf);
  20 void cf_get(mpz_t z, cf_t cf);
  21 void cf_put(cf_t cf, mpz_t z);
  22 void cf_put_int(cf_t cf, int n);
  23
  24 int cf_wait(cf_t cf);
  25
  26 void *cf_data(cf_t cf);
  27
  28 void cf_signal(cf_t cf); // For tee.
  29 void cf_wait_special(cf_t cf);
  30
  31 // From cf_tee.c:
  32 //
  33 void cf_tee(cf_t *out_array, cf_t in);
  34
  35 // From cf_mobius.c:
  36 //
  37 // Compute convergents of a simple continued fraction x.
  38 // Outputs p then q on channel, where p/q is the last convergent computed.
  39 cf_t cf_new_cf_convergent(cf_t x);
  40 // Compute decimal representation of a simple continued fraction x.
  41 // Outputs integer part first, then digits one at a time.
  42 cf_t cf_new_cf_to_decimal(cf_t x);
  43
  44 // Compute convergents of (a x + b)/(c x + d)
  45 // where x is a regular continued fraction.
  46 cf_t cf_new_mobius_convergent(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  47 cf_t cf_new_mobius_to_decimal(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  48 cf_t cf_new_mobius_to_cf(cf_t x, mpz_t z[4]);
  49
  50 // Compute convergents of (a x + b)/(c x + d)
  51 // where x is a nonregular continued fraction.
  52 cf_t cf_new_nonregular_mobius_convergent(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  53 // Input: Mobius transformation and nonregular continued fraction.
  54 // Output: Regular continued fraction. Assumes input fraction is well-behaved.
  55 cf_t cf_new_nonregular_to_cf(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  56 // Does both of the above at once. Seems slow.
  57 cf_t cf_new_nonregular_mobius_to_decimal(cf_t x, mpz_t a[4]);
  58
  59 cf_t cf_new_const_nonregular(void *(*fun)(cf_t));
  60 cf_t cf_new_one_arg_nonregular(void *(*fun)(cf_t), mpz_t z);
  61
  62 // Well-known continued fraction expansions.
  63 // cf_famous.c:
  64 // e:
  65 cf_t cf_new_sqrt2();
  66 cf_t cf_new_sqrt5();
  67 cf_t cf_new_e();
  68 cf_t cf_new_pi();
  69 cf_t cf_new_tan1();
  70 cf_t cf_new_epow(mpz_t pow);
  71 cf_t cf_new_tanh(mpz_t z);
  72
  73 // This won't work because my code cannot handle negative denominators,
  74 // and also assumes the sequence of convergents alternatively overshoot
  75 // and undershoots the target. The tan expansion leads to a sequence of
  76 // strictly increasing convergents (for positive input).
  77 cf_t cf_new_tan(mpz_t z);
  78
  79 // Gosper's method for computing bihomographic functions of continued fractions.
  80 cf_t cf_new_bihom(cf_t x, cf_t y, mpz_t a[8]);
  81 cf_t cf_new_add(cf_t x, cf_t y);
  82 cf_t cf_new_sub(cf_t x, cf_t y);
  83 cf_t cf_new_mul(cf_t x, cf_t y);
  84 cf_t cf_new_div(cf_t x, cf_t y);
  85
  86 void mpz8_init(mpz_t z[8]);
  87 void mpz8_clear(mpz_t z[8]);
  88 void mpz8_set_int(mpz_t z[8],
  89     int a, int b, int c, int d,
  90     int e, int f, int g, int h);
  91 void mpz8_set_add(mpz_t z[8]);
  92 void mpz8_set_sub(mpz_t z[8]);
  93 void mpz8_set_mul(mpz_t z[8]);
  94 void mpz8_set_div(mpz_t z[8]);
  95
  96 // From taylor.c:
  97 cf_t cf_new_sin1();
  98 cf_t cf_new_cos1();
  99
 100 // From newton.c:
 101 // Use Newton's method to find solutions of:
 102 //
 103 //     a0 xy + a1 x + a2 y + a3
 104 // y = ------------------------
 105 //     a4 xy - a0 x + a5 y - a2
 106 cf_t cf_new_newton(cf_t x, mpz_t a[6], mpz_t lower);
 107 cf_t cf_new_sqrt(cf_t x);
 108 cf_t cf_new_sqrt_int(int a, int b);
 109 cf_t cf_new_sqrt_pq(mpz_t zp, mpz_t zq);
 110
 111 #endif  // __CF_H__