6 // sqrt(2) = [1; 2, 2, ...]
7 static void *sqrt2(cf_t cf
) {
16 return cf_new_const(sqrt2
);
19 // e = [2; 1, 2, 1, 1, 4, 1, ...]
20 static void *e_expansion(cf_t cf
) {
34 return cf_new_const(e_expansion
);
37 // 4/pi = 1 + 1/(3 + 4/(5 + 9/(7 + 16/(9 + ...))))
38 static void *pi_arctan_sequence(cf_t cf
) {
48 mpz_add_ui(denom
, denom
, 2);
50 mpz_add(num
, num
, denom
);
59 static void *regularized_pi(cf_t cf
) {
61 mpz_init(a
); mpz_init(b
); mpz_init(c
); mpz_init(d
);
62 mpz_set_ui(a
, 0); mpz_set_ui(b
, 4);
63 mpz_set_ui(c
, 1); mpz_set_ui(d
, 0);
64 cf_t nonregpi
= cf_new(pi_arctan_sequence
, NULL
);
65 cf_t conv
= cf_new_nonregular_to_cf(nonregpi
, a
, b
, c
, d
);
75 mpz_clear(a
); mpz_clear(b
); mpz_clear(c
); mpz_clear(d
);
80 return cf_new_const(regularized_pi
);
83 // tan 1 = [1; 1, 1, 3, 1, 5, ...]
84 static void *tan1_expansion(cf_t cf
) {
97 return cf_new_const(tan1_expansion
);
100 // exp(z) = 1 + z/(1 - z/(2 + z/(3 - z/(2 + z/(5 - z/(2 + z/ ...))))))
101 void *exp_expansion(cf_t cf
) {
102 mpz_ptr z
= cf_data(cf
);
121 // tanh n = z/(1 + z^2/(3 + z^2/(5 + z^2/...)))
122 static void *gauss_tanh_expansion(cf_t cf
) {
123 mpz_ptr z
= cf_data(cf
);
126 mpz_init(odd
); mpz_init(z2
);
134 mpz_add_ui(odd
, odd
, 2);
137 mpz_clear(odd
); mpz_clear(z2
);
143 // tan n = z/(1 - z^2/(3 - z^2/(5 - z^2/...)))
144 static void *gauss_tan_expansion(cf_t cf
) {
145 mpz_ptr z
= cf_data(cf
);
148 mpz_init(odd
); mpz_init(z2
);
157 mpz_add_ui(odd
, odd
, 2);
160 mpz_clear(odd
); mpz_clear(z2
);
166 cf_t
cf_new_one_arg(void *(*fun
)(cf_t
), mpz_t z
) {
167 mpz_ptr p
= malloc(sizeof(*p
));
170 return cf_new(fun
, p
);
177 typedef struct funarg_s
*funarg_ptr
;
179 static void *one_arg_nonreg(cf_t cf
) {
180 funarg_ptr p
= cf_data(cf
);
182 mpz_init(a
); mpz_init(b
); mpz_init(c
); mpz_init(d
);
183 mpz_set_ui(a
, 1); mpz_set_ui(b
, 0);
184 mpz_set_ui(c
, 0); mpz_set_ui(d
, 1);
185 mpz_ptr copy
= malloc(sizeof(*copy
));
187 mpz_set(copy
, p
->arg
);
188 cf_t nonreg
= cf_new(p
->fun
, copy
);
189 cf_t conv
= cf_new_nonregular_to_cf(nonreg
, a
, b
, c
, d
);
199 mpz_clear(a
); mpz_clear(b
); mpz_clear(c
); mpz_clear(d
);
206 cf_t
cf_new_one_arg_nonreg(void *(*fun
)(cf_t
), mpz_t z
) {
207 funarg_ptr p
= malloc(sizeof(*p
));
211 return cf_new(one_arg_nonreg
, p
);
214 cf_t
cf_new_epow(mpz_t pow
) {
215 return cf_new_one_arg_nonreg(exp_expansion
, pow
);
218 cf_t
cf_new_tanh(mpz_t z
) {
219 return cf_new_one_arg_nonreg(gauss_tanh_expansion
, z
);
222 cf_t
cf_new_tan(mpz_t z
) {
223 return cf_new_one_arg_nonreg(gauss_tan_expansion
, z
);