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 // cf_mobius.c:
  29
  30 // Compute convergents of a simple continued fraction x.
  31 // Outputs p then q on channel, where p/q is the last convergent computed.
  32 cf_t cf_new_cf_convergent(cf_t x);
  33 // Compute decimal representation of a simple continued fraction x.
  34 // Outputs integer part first, then digits one at a time.
  35 cf_t cf_new_cf_to_decimal(cf_t x);
  36
  37 // Compute convergents of (a x + b)/(c x + d)
  38 // where x is a regular continued fraction.
  39 cf_t cf_new_mobius_convergent(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  40 cf_t cf_new_mobius_to_decimal(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  41 cf_t cf_new_mobius_to_cf(cf_t x, mpz_t z[4]);
  42
  43 // Compute convergents of (a x + b)/(c x + d)
  44 // where x is a nonregular continued fraction.
  45 cf_t cf_new_nonregular_mobius_convergent(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  46 // Input: Mobius transformation and nonregular continued fraction.
  47 // Output: Regular continued fraction. Assumes input fraction is well-behaved.
  48 cf_t cf_new_nonregular_to_cf(cf_t x, mpz_t a, mpz_t b, mpz_t c, mpz_t d);
  49 // Does both of the above at once. Seems slow.
  50 cf_t cf_new_nonregular_mobius_to_decimal(cf_t x, mpz_t a[4]);
  51
  52 // Well-known continued fraction expansions.
  53 // cf_famous.c:
  54 // e:
  55 cf_t cf_new_sqrt2();
  56 cf_t cf_new_e();
  57 cf_t cf_new_pi();
  58 cf_t cf_new_tan1();
  59 cf_t cf_new_epow(mpz_t pow);
  60 cf_t cf_new_tanh(mpz_t z);
  61
  62 // This won't work because my code cannot handle negative denominators,
  63 // and also assumes the sequence of convergents alternatively overshoot
  64 // and undershoots the target. The tan expansion leads to a sequence of
  65 // strictly increasing convergents (for positive input).
  66 cf_t cf_new_tan(mpz_t z);
  67
  68 // Gosper's method for computing bihomographic functions of continued fractions.
  69 cf_t cf_new_bihom(cf_t x, cf_t y, mpz_t a[8]);
  70
  71 // From taylor.c:
  72 cf_t cf_new_sin1();
  73 cf_t cf_new_cos1();
  74
  75 // From newton.c:
  76 // Use Newton's method to find solutions of:
  77 //
  78 //     a0 xy + a1 x + a2 y + a3
  79 // y = ------------------------
  80 //     a4 xy - a0 x + a5 y - a2
  81 cf_t cf_new_newton(cf_t x, mpz_t a[6], mpz_t lower);
  82 cf_t cf_new_sqrt(cf_t x);
  83
  84 #endif  // __CF_H__