6 // Minds our p's and q's. The two last computed convergents.
11 typedef struct pqset_s
*pqset_ptr
;
12 typedef struct pqset_s pqset_t
[1];
14 void pqset_init(pqset_t pq
) {
21 void pqset_clear(pqset_t pq
) {
28 void pqset_neg(pqset_t pq
) {
29 mpz_neg(pq
->p
, pq
->p
);
30 mpz_neg(pq
->q
, pq
->q
);
31 mpz_neg(pq
->pold
, pq
->pold
);
32 mpz_neg(pq
->qold
, pq
->qold
);
35 void pqset_print(pqset_t pq
) {
36 gmp_printf("p's: %Zd %Zd\n", pq
->pold
, pq
->p
);
37 gmp_printf("q's: %Zd %Zd\n", pq
->qold
, pq
->q
);
40 // Compute the next convergent for regular continued fractions.
41 void pqset_regular_recur(pqset_t pq
, mpz_t denom
) {
42 mpz_addmul(pq
->pold
, denom
, pq
->p
);
43 mpz_swap(pq
->pold
, pq
->p
);
44 mpz_addmul(pq
->qold
, denom
, pq
->q
);
45 mpz_swap(pq
->qold
, pq
->q
);
48 // Compute the next convergent for nonregular continued fractions.
49 void pqset_nonregular_recur(pqset_t pq
, mpz_t num
, mpz_t denom
) {
50 mpz_mul(pq
->pold
, pq
->pold
, num
);
51 mpz_addmul(pq
->pold
, pq
->p
, denom
);
52 mpz_swap(pq
->pold
, pq
->p
);
53 mpz_mul(pq
->qold
, pq
->qold
, num
);
54 mpz_addmul(pq
->qold
, pq
->q
, denom
);
55 mpz_swap(pq
->qold
, pq
->q
);
58 // Get rid of nontrivial GCD for {p, q, pold, qold}.
59 // t0 and t1 are temporary variables.
60 void pqset_remove_gcd(pqset_ptr pq
, mpz_t t0
, mpz_t t1
) {
61 mpz_gcd(t0
, pq
->p
, pq
->q
);
62 mpz_gcd(t1
, pq
->pold
, pq
->qold
);
64 if (mpz_cmp_ui(t0
, 1)) {
65 mpz_divexact(pq
->pold
, pq
->pold
, t0
);
66 mpz_divexact(pq
->qold
, pq
->qold
, t0
);
67 mpz_divexact(pq
->p
, pq
->p
, t0
);
68 mpz_divexact(pq
->q
, pq
->q
, t0
);
72 // A Mobius transformation: four coefficients and the input.
73 // TODO: Use an array of size 4.
74 struct mobius_data_s
{
78 typedef struct mobius_data_s
*mobius_data_ptr
;
80 void pqset_set_mobius(pqset_t pq
, mobius_data_ptr md
) {
81 mpz_set(pq
->pold
, md
->b
); mpz_set(pq
->p
, md
->a
);
82 mpz_set(pq
->qold
, md
->d
); mpz_set(pq
->q
, md
->c
);
85 // Compute convergents of Mobius function applied to a regular
86 // continued fraction.
87 static void *mobius_convergent(cf_t cf
) {
88 mobius_data_ptr md
= cf_data(cf
);
89 cf_t input
= md
->input
;
92 pqset_set_mobius(pq
, md
);
98 pqset_regular_recur(pq
, denom
);
113 // Start a thread that, when signalled, computes the convergents of a Mobius
114 // transformation of a continued fraction.
115 cf_t
cf_new_mobius_convergent(cf_t x
, mpz_t a
, mpz_t b
, mpz_t c
, mpz_t d
) {
116 mobius_data_ptr md
= malloc(sizeof(*md
));
117 mpz_init(md
->a
); mpz_init(md
->b
); mpz_init(md
->c
); mpz_init(md
->d
);
118 mpz_set(md
->a
, a
); mpz_set(md
->b
, b
); mpz_set(md
->c
, c
); mpz_set(md
->d
, d
);
120 return cf_new(mobius_convergent
, md
);
123 // Start a thread that, when signalled, computes the convergents of a continued
125 cf_t
cf_new_convergent(cf_t x
) {
127 mpz_init(one
); mpz_init(zero
);
128 mpz_set_ui(one
, 1); mpz_set_ui(zero
, 0);
129 cf_t res
= cf_new_mobius_convergent(x
, one
, zero
, zero
, one
);
130 mpz_clear(one
); mpz_clear(zero
);
134 // Compute nonregular convergents of a Mobius function applied
135 // to a nonregular continued fraction.
136 static void *nonregular_mobius_convergent(cf_t cf
) {
137 mobius_data_ptr md
= cf_data(cf
);
138 cf_t input
= md
->input
;
139 pqset_t pq
; pqset_init(pq
); pqset_set_mobius(pq
, md
);
140 mpz_t num
; mpz_init(num
);
141 mpz_t denom
; mpz_init(denom
);
142 mpz_t t0
, t1
; mpz_init(t0
); mpz_init(t1
);
144 pqset_nonregular_recur(pq
, num
, denom
);
145 pqset_remove_gcd(pq
, t0
, t1
);
151 cf_get(denom
, input
);
155 cf_get(denom
, input
);
162 mpz_clear(md
->a
); mpz_clear(md
->b
); mpz_clear(md
->c
); mpz_clear(md
->d
);
163 mpz_clear(t0
); mpz_clear(t1
);
168 cf_t
cf_new_nonregular_mobius_convergent(cf_t x
, mpz_t a
, mpz_t b
, mpz_t c
, mpz_t d
) {
169 mobius_data_ptr md
= malloc(sizeof(*md
));
170 mpz_init(md
->a
); mpz_init(md
->b
); mpz_init(md
->c
); mpz_init(md
->d
);
171 mpz_set(md
->a
, a
); mpz_set(md
->b
, b
); mpz_set(md
->c
, c
); mpz_set(md
->d
, d
);
173 return cf_new(nonregular_mobius_convergent
, md
);
176 static void *mobius_nonregular_throughput(cf_t cf
) {
177 mobius_data_ptr md
= cf_data(cf
);
178 cf_t input
= md
->input
;
179 pqset_t pq
; pqset_init(pq
); pqset_set_mobius(pq
, md
);
180 mpz_t num
; mpz_init(num
);
181 mpz_t denom
; mpz_init(denom
);
182 mpz_t t0
, t1
, t2
; mpz_init(t2
); mpz_init(t1
); mpz_init(t0
);
184 pqset_nonregular_recur(pq
, num
, denom
);
185 pqset_remove_gcd(pq
, t0
, t1
);
187 if (mpz_sgn(pq
->qold
)) {
188 mpz_fdiv_qr(t1
, t0
, pq
->pold
, pq
->qold
);
189 mpz_mul(t2
, t1
, pq
->q
);
191 if (mpz_cmp(t2
, pq
->p
) <= 0) {
192 mpz_add(t2
, t2
, pq
->q
);
193 if (mpz_cmp(t2
, pq
->p
) > 0) {
194 // Output continued fraction term.
196 // Subtract: remainder of p/q.
197 mpz_sub(t2
, t2
, pq
->p
);
198 mpz_sub(t2
, pq
->q
, t2
);
200 mpz_set(pq
->pold
, pq
->qold
);
201 mpz_set(pq
->qold
, t0
);
202 mpz_set(pq
->p
, pq
->q
);
211 cf_get(denom
, input
);
216 cf_get(denom
, input
);
223 mpz_clear(md
->a
); mpz_clear(md
->b
); mpz_clear(md
->c
); mpz_clear(md
->d
);
225 mpz_clear(t2
); mpz_clear(t1
); mpz_clear(t0
);
229 cf_t
cf_new_nonregular_to_cf(cf_t x
, mpz_t a
, mpz_t b
, mpz_t c
, mpz_t d
) {
230 mobius_data_ptr md
= malloc(sizeof(*md
));
231 mpz_init(md
->a
); mpz_init(md
->b
); mpz_init(md
->c
); mpz_init(md
->d
);
232 mpz_set(md
->a
, a
); mpz_set(md
->b
, b
); mpz_set(md
->c
, c
); mpz_set(md
->d
, d
);
234 return cf_new(mobius_nonregular_throughput
, md
);
237 static void *mobius_decimal(cf_t cf
) {
238 mobius_data_ptr md
= cf_data(cf
);
239 cf_t input
= md
->input
;
240 pqset_t pq
; pqset_init(pq
); pqset_set_mobius(pq
, md
);
241 mpz_t denom
; mpz_init(denom
);
242 mpz_t t0
, t1
, t2
; mpz_init(t2
); mpz_init(t1
); mpz_init(t0
);
244 // Determine the sign.
245 while (mpz_sgn(pq
->pold
) != mpz_sgn(pq
->p
)
246 || mpz_sgn(pq
->qold
) != mpz_sgn(pq
->q
)) {
247 cf_get(denom
, input
);
248 pqset_regular_recur(pq
, denom
);
250 if (mpz_sgn(pq
->qold
) < 0) {
251 mpz_neg(pq
->qold
, pq
->qold
);
252 mpz_neg(pq
->q
, pq
->q
);
255 if (mpz_sgn(pq
->pold
) < 0) {
256 mpz_neg(pq
->pold
, pq
->pold
);
257 mpz_neg(pq
->p
, pq
->p
);
262 pqset_regular_recur(pq
, denom
);
264 // If the denominator is zero, we can't do anything yet.
265 if (mpz_sgn(pq
->qold
)) {
266 // Each term except possibly the first is one of {0, ..., 9}.
267 /* Naive attempt to expoit this didn't seem faster:
268 * (and I'd have to handle the first term properly)
271 for (i = 0; i <= 9; i++) {
272 if (mpz_cmp(t0, pq->p) > 0) break;
273 mpz_add(t0, t0, pq->q);
275 mpz_set_ui(pq->pold, i);
276 mpz_sub(t0, t0, pq->p);
277 mpz_sub(t0, pq->q, t0);
278 mpz_mul(pq->qold, pq->pold, pq->qnew);
281 mpz_fdiv_qr(t1
, t0
, pq
->pold
, pq
->qold
);
282 mpz_mul(t2
, t1
, pq
->q
);
283 if (mpz_cmp(t2
, pq
->p
) <= 0) {
284 mpz_add(t2
, t2
, pq
->q
);
285 if (mpz_cmp(t2
, pq
->p
) > 0) {
286 // Output a decimal digit.
288 // Compute t2 = remainder of p/q.
289 mpz_sub(t2
, t2
, pq
->p
);
290 mpz_sub(t2
, pq
->q
, t2
);
291 // Multiply numerator by 10.
292 mpz_mul_ui(pq
->pold
, t0
, 10);
293 mpz_mul_ui(pq
->p
, t2
, 10);
302 cf_get(denom
, input
);
307 mpz_clear(t0
); mpz_clear(t1
); mpz_clear(t2
);
308 mpz_clear(md
->a
); mpz_clear(md
->b
); mpz_clear(md
->c
); mpz_clear(md
->d
);
312 cf_t
cf_new_mobius_to_decimal(cf_t x
, mpz_t a
, mpz_t b
, mpz_t c
, mpz_t d
) {
313 mobius_data_ptr md
= malloc(sizeof(*md
));
314 mpz_init(md
->a
); mpz_init(md
->b
); mpz_init(md
->c
); mpz_init(md
->d
);
315 mpz_set(md
->a
, a
); mpz_set(md
->b
, b
); mpz_set(md
->c
, c
); mpz_set(md
->d
, d
);
317 return cf_new(mobius_decimal
, md
);
320 cf_t
cf_new_cf_to_decimal(cf_t x
) {
322 mpz_init(one
); mpz_init(zero
);
323 mpz_set_ui(one
, 1); mpz_set_ui(zero
, 0);
324 cf_t res
= cf_new_mobius_to_decimal(x
, one
, zero
, zero
, one
);
325 mpz_clear(one
); mpz_clear(zero
);
329 // This seems to be slower than regularizing the continued fraction
330 // and then converting to decimal.
331 static void *nonregular_mobius_decimal(cf_t cf
) {
332 mobius_data_ptr md
= cf_data(cf
);
333 cf_t input
= md
->input
;
334 pqset_t pq
; pqset_init(pq
); pqset_set_mobius(pq
, md
);
335 mpz_t num
; mpz_init(num
);
336 mpz_t denom
; mpz_init(denom
);
337 mpz_t t0
, t1
, t2
; mpz_init(t2
); mpz_init(t1
); mpz_init(t0
);
339 pqset_nonregular_recur(pq
, num
, denom
);
340 pqset_remove_gcd(pq
, t0
, t1
);
342 // If the denominator is zero, we can't do anything yet.
343 if (mpz_sgn(pq
->qold
)) {
344 mpz_fdiv_qr(t1
, t0
, pq
->pold
, pq
->qold
);
345 mpz_mul(t2
, t1
, pq
->q
);
346 if (mpz_cmp(t2
, pq
->p
) <= 0) {
347 mpz_add(t2
, t2
, pq
->q
);
348 if (mpz_cmp(t2
, pq
->p
) > 0) {
349 // Output a decimal digit.
351 // Subtract: remainder of p/q.
352 mpz_sub(t2
, t2
, pq
->p
);
353 mpz_sub(t2
, pq
->q
, t2
);
354 // Multiply numerator by 10.
355 mpz_mul_ui(pq
->pold
, t0
, 10);
356 mpz_mul_ui(pq
->p
, t2
, 10);
364 cf_get(denom
, input
);
369 cf_get(denom
, input
);
375 mpz_clear(t0
); mpz_clear(t1
); mpz_clear(t2
);
376 mpz_clear(md
->a
); mpz_clear(md
->b
); mpz_clear(md
->c
); mpz_clear(md
->d
);
381 cf_t
cf_new_nonregular_mobius_to_decimal(cf_t x
, mpz_t a
, mpz_t b
, mpz_t c
, mpz_t d
) {
382 mobius_data_ptr md
= malloc(sizeof(*md
));
383 mpz_init(md
->a
); mpz_init(md
->b
); mpz_init(md
->c
); mpz_init(md
->d
);
384 mpz_set(md
->a
, a
); mpz_set(md
->b
, b
); mpz_set(md
->c
, c
); mpz_set(md
->d
, d
);
386 return cf_new(nonregular_mobius_decimal
, md
);