1/* Internal function for converting integers to ASCII.
2 Copyright (C) 1994-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Torbjorn Granlund <tege@matematik.su.se>
5 and Ulrich Drepper <drepper@gnu.org>.
6
7 The GNU C Library is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Lesser General Public
9 License as published by the Free Software Foundation; either
10 version 2.1 of the License, or (at your option) any later version.
11
12 The GNU C Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Lesser General Public License for more details.
16
17 You should have received a copy of the GNU Lesser General Public
18 License along with the GNU C Library; if not, see
19 <https://www.gnu.org/licenses/>. */
20
21#include <gmp-mparam.h>
22#include <gmp.h>
23#include <limits.h>
24#include <stdlib/gmp-impl.h>
25#include <stdlib/longlong.h>
26
27#include <_itoa.h>
28
29
30/* Canonize environment. For some architectures not all values might
31 be defined in the GMP header files. */
32#ifndef UMUL_TIME
33# define UMUL_TIME 1
34#endif
35#ifndef UDIV_TIME
36# define UDIV_TIME 3
37#endif
38
39/* Control memory layout. */
40#ifdef PACK
41# undef PACK
42# define PACK __attribute__ ((packed))
43#else
44# define PACK
45#endif
46
47
48/* Declare local types. */
49struct base_table_t
50{
51#if (UDIV_TIME > 2 * UMUL_TIME)
52 mp_limb_t base_multiplier;
53#endif
54 char flag;
55 char post_shift;
56#if BITS_PER_MP_LIMB == 32
57 struct
58 {
59 char normalization_steps;
60 char ndigits;
61 mp_limb_t base PACK;
62#if UDIV_TIME > 2 * UMUL_TIME
63 mp_limb_t base_ninv PACK;
64#endif
65 } big;
66#endif
67};
68
69/* To reduce the memory needed we include some fields of the tables
70 only conditionally. */
71#if UDIV_TIME > 2 * UMUL_TIME
72# define SEL1(X) X,
73# define SEL2(X) ,X
74#else
75# define SEL1(X)
76# define SEL2(X)
77#endif
78
79
80/* We do not compile _itoa if we always can use _itoa_word. */
81#if _ITOA_NEEDED
82/* Local variables. */
83const struct base_table_t _itoa_base_table[] attribute_hidden =
84{
85# if BITS_PER_MP_LIMB == 64
86 /* 2 */ {SEL1(0ull) 1, 1},
87 /* 3 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 1},
88 /* 4 */ {SEL1(0ull) 1, 2},
89 /* 5 */ {SEL1(0xcccccccccccccccdull) 0, 2},
90 /* 6 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 2},
91 /* 7 */ {SEL1(0x2492492492492493ull) 1, 3},
92 /* 8 */ {SEL1(0ull) 1, 3},
93 /* 9 */ {SEL1(0xe38e38e38e38e38full) 0, 3},
94 /* 10 */ {SEL1(0xcccccccccccccccdull) 0, 3},
95 /* 11 */ {SEL1(0x2e8ba2e8ba2e8ba3ull) 0, 1},
96 /* 12 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 3},
97 /* 13 */ {SEL1(0x4ec4ec4ec4ec4ec5ull) 0, 2},
98 /* 14 */ {SEL1(0x2492492492492493ull) 1, 4},
99 /* 15 */ {SEL1(0x8888888888888889ull) 0, 3},
100 /* 16 */ {SEL1(0ull) 1, 4},
101 /* 17 */ {SEL1(0xf0f0f0f0f0f0f0f1ull) 0, 4},
102 /* 18 */ {SEL1(0xe38e38e38e38e38full) 0, 4},
103 /* 19 */ {SEL1(0xd79435e50d79435full) 0, 4},
104 /* 20 */ {SEL1(0xcccccccccccccccdull) 0, 4},
105 /* 21 */ {SEL1(0x8618618618618619ull) 1, 5},
106 /* 22 */ {SEL1(0x2e8ba2e8ba2e8ba3ull) 0, 2},
107 /* 23 */ {SEL1(0x642c8590b21642c9ull) 1, 5},
108 /* 24 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 4},
109 /* 25 */ {SEL1(0x47ae147ae147ae15ull) 1, 5},
110 /* 26 */ {SEL1(0x4ec4ec4ec4ec4ec5ull) 0, 3},
111 /* 27 */ {SEL1(0x97b425ed097b425full) 0, 4},
112 /* 28 */ {SEL1(0x2492492492492493ull) 1, 5},
113 /* 29 */ {SEL1(0x1a7b9611a7b9611bull) 1, 5},
114 /* 30 */ {SEL1(0x8888888888888889ull) 0, 4},
115 /* 31 */ {SEL1(0x0842108421084211ull) 1, 5},
116 /* 32 */ {SEL1(0ull) 1, 5},
117 /* 33 */ {SEL1(0x0f83e0f83e0f83e1ull) 0, 1},
118 /* 34 */ {SEL1(0xf0f0f0f0f0f0f0f1ull) 0, 5},
119 /* 35 */ {SEL1(0xea0ea0ea0ea0ea0full) 0, 5},
120 /* 36 */ {SEL1(0xe38e38e38e38e38full) 0, 5}
121# endif
122# if BITS_PER_MP_LIMB == 32
123 /* 2 */ {SEL1(0ul) 1, 1, {0, 31, 0x80000000ul SEL2(0xfffffffful)}},
124 /* 3 */ {SEL1(0xaaaaaaabul) 0, 1, {0, 20, 0xcfd41b91ul SEL2(0x3b563c24ul)}},
125 /* 4 */ {SEL1(0ul) 1, 2, {1, 15, 0x40000000ul SEL2(0xfffffffful)}},
126 /* 5 */ {SEL1(0xcccccccdul) 0, 2, {1, 13, 0x48c27395ul SEL2(0xc25c2684ul)}},
127 /* 6 */ {SEL1(0xaaaaaaabul) 0, 2, {0, 12, 0x81bf1000ul SEL2(0xf91bd1b6ul)}},
128 /* 7 */ {SEL1(0x24924925ul) 1, 3, {1, 11, 0x75db9c97ul SEL2(0x1607a2cbul)}},
129 /* 8 */ {SEL1(0ul) 1, 3, {1, 10, 0x40000000ul SEL2(0xfffffffful)}},
130 /* 9 */ {SEL1(0x38e38e39ul) 0, 1, {0, 10, 0xcfd41b91ul SEL2(0x3b563c24ul)}},
131 /* 10 */ {SEL1(0xcccccccdul) 0, 3, {2, 9, 0x3b9aca00ul SEL2(0x12e0be82ul)}},
132 /* 11 */ {SEL1(0xba2e8ba3ul) 0, 3, {0, 9, 0x8c8b6d2bul SEL2(0xd24cde04ul)}},
133 /* 12 */ {SEL1(0xaaaaaaabul) 0, 3, {3, 8, 0x19a10000ul SEL2(0x3fa39ab5ul)}},
134 /* 13 */ {SEL1(0x4ec4ec4ful) 0, 2, {2, 8, 0x309f1021ul SEL2(0x50f8ac5ful)}},
135 /* 14 */ {SEL1(0x24924925ul) 1, 4, {1, 8, 0x57f6c100ul SEL2(0x74843b1eul)}},
136 /* 15 */ {SEL1(0x88888889ul) 0, 3, {0, 8, 0x98c29b81ul SEL2(0xad0326c2ul)}},
137 /* 16 */ {SEL1(0ul) 1, 4, {3, 7, 0x10000000ul SEL2(0xfffffffful)}},
138 /* 17 */ {SEL1(0xf0f0f0f1ul) 0, 4, {3, 7, 0x18754571ul SEL2(0x4ef0b6bdul)}},
139 /* 18 */ {SEL1(0x38e38e39ul) 0, 2, {2, 7, 0x247dbc80ul SEL2(0xc0fc48a1ul)}},
140 /* 19 */ {SEL1(0xaf286bcbul) 1, 5, {2, 7, 0x3547667bul SEL2(0x33838942ul)}},
141 /* 20 */ {SEL1(0xcccccccdul) 0, 4, {1, 7, 0x4c4b4000ul SEL2(0xad7f29abul)}},
142 /* 21 */ {SEL1(0x86186187ul) 1, 5, {1, 7, 0x6b5a6e1dul SEL2(0x313c3d15ul)}},
143 /* 22 */ {SEL1(0xba2e8ba3ul) 0, 4, {0, 7, 0x94ace180ul SEL2(0xb8cca9e0ul)}},
144 /* 23 */ {SEL1(0xb21642c9ul) 0, 4, {0, 7, 0xcaf18367ul SEL2(0x42ed6de9ul)}},
145 /* 24 */ {SEL1(0xaaaaaaabul) 0, 4, {4, 6, 0x0b640000ul SEL2(0x67980e0bul)}},
146 /* 25 */ {SEL1(0x51eb851ful) 0, 3, {4, 6, 0x0e8d4a51ul SEL2(0x19799812ul)}},
147 /* 26 */ {SEL1(0x4ec4ec4ful) 0, 3, {3, 6, 0x1269ae40ul SEL2(0xbce85396ul)}},
148 /* 27 */ {SEL1(0x2f684bdbul) 1, 5, {3, 6, 0x17179149ul SEL2(0x62c103a9ul)}},
149 /* 28 */ {SEL1(0x24924925ul) 1, 5, {3, 6, 0x1cb91000ul SEL2(0x1d353d43ul)}},
150 /* 29 */ {SEL1(0x8d3dcb09ul) 0, 4, {2, 6, 0x23744899ul SEL2(0xce1deceaul)}},
151 /* 30 */ {SEL1(0x88888889ul) 0, 4, {2, 6, 0x2b73a840ul SEL2(0x790fc511ul)}},
152 /* 31 */ {SEL1(0x08421085ul) 1, 5, {2, 6, 0x34e63b41ul SEL2(0x35b865a0ul)}},
153 /* 32 */ {SEL1(0ul) 1, 5, {1, 6, 0x40000000ul SEL2(0xfffffffful)}},
154 /* 33 */ {SEL1(0x3e0f83e1ul) 0, 3, {1, 6, 0x4cfa3cc1ul SEL2(0xa9aed1b3ul)}},
155 /* 34 */ {SEL1(0xf0f0f0f1ul) 0, 5, {1, 6, 0x5c13d840ul SEL2(0x63dfc229ul)}},
156 /* 35 */ {SEL1(0xd41d41d5ul) 1, 6, {1, 6, 0x6d91b519ul SEL2(0x2b0fee30ul)}},
157 /* 36 */ {SEL1(0x38e38e39ul) 0, 3, {0, 6, 0x81bf1000ul SEL2(0xf91bd1b6ul)}}
158# endif
159};
160#endif
161
162char *
163_itoa_word (_ITOA_WORD_TYPE value, char *buflim,
164 unsigned int base, int upper_case)
165{
166 const char *digits = (upper_case
167 ? _itoa_upper_digits
168 : _itoa_lower_digits);
169
170 switch (base)
171 {
172#define SPECIAL(Base) \
173 case Base: \
174 do \
175 *--buflim = digits[value % Base]; \
176 while ((value /= Base) != 0); \
177 break
178
179 SPECIAL (10);
180 SPECIAL (16);
181 SPECIAL (8);
182 default:
183 do
184 *--buflim = digits[value % base];
185 while ((value /= base) != 0);
186 }
187 return buflim;
188}
189#undef SPECIAL
190
191
192#if _ITOA_NEEDED
193char *
194_itoa (unsigned long long int value, char *buflim, unsigned int base,
195 int upper_case)
196{
197 const char *digits = (upper_case
198 ? _itoa_upper_digits
199 : _itoa_lower_digits);
200 const struct base_table_t *brec = &_itoa_base_table[base - 2];
201
202 switch (base)
203 {
204# define RUN_2N(BITS) \
205 do \
206 { \
207 /* `unsigned long long int' always has 64 bits. */ \
208 mp_limb_t work_hi = value >> (64 - BITS_PER_MP_LIMB); \
209 \
210 if (BITS_PER_MP_LIMB == 32) \
211 { \
212 if (work_hi != 0) \
213 { \
214 mp_limb_t work_lo; \
215 int cnt; \
216 \
217 work_lo = value & 0xfffffffful; \
218 for (cnt = BITS_PER_MP_LIMB / BITS; cnt > 0; --cnt) \
219 { \
220 *--buflim = digits[work_lo & ((1ul << BITS) - 1)]; \
221 work_lo >>= BITS; \
222 } \
223 if (BITS_PER_MP_LIMB % BITS != 0) \
224 { \
225 work_lo \
226 |= ((work_hi \
227 & ((1 << (BITS - BITS_PER_MP_LIMB%BITS)) \
228 - 1)) \
229 << BITS_PER_MP_LIMB % BITS); \
230 work_hi >>= BITS - BITS_PER_MP_LIMB % BITS; \
231 if (work_hi == 0) \
232 work_hi = work_lo; \
233 else \
234 *--buflim = digits[work_lo]; \
235 } \
236 } \
237 else \
238 work_hi = value & 0xfffffffful; \
239 } \
240 do \
241 { \
242 *--buflim = digits[work_hi & ((1 << BITS) - 1)]; \
243 work_hi >>= BITS; \
244 } \
245 while (work_hi != 0); \
246 } \
247 while (0)
248 case 8:
249 RUN_2N (3);
250 break;
251
252 case 16:
253 RUN_2N (4);
254 break;
255
256 default:
257 {
258 char *bufend = buflim;
259# if BITS_PER_MP_LIMB == 64
260 mp_limb_t base_multiplier = brec->base_multiplier;
261 if (brec->flag)
262 while (value != 0)
263 {
264 mp_limb_t quo, rem, x;
265 mp_limb_t dummy __attribute__ ((unused));
266
267 umul_ppmm (x, dummy, value, base_multiplier);
268 quo = (x + ((value - x) >> 1)) >> (brec->post_shift - 1);
269 rem = value - quo * base;
270 *--buflim = digits[rem];
271 value = quo;
272 }
273 else
274 while (value != 0)
275 {
276 mp_limb_t quo, rem, x;
277 mp_limb_t dummy __attribute__ ((unused));
278
279 umul_ppmm (x, dummy, value, base_multiplier);
280 quo = x >> brec->post_shift;
281 rem = value - quo * base;
282 *--buflim = digits[rem];
283 value = quo;
284 }
285# endif
286# if BITS_PER_MP_LIMB == 32
287 mp_limb_t t[3];
288 int n;
289
290 /* First convert x0 to 1-3 words in base s->big.base.
291 Optimize for frequent cases of 32 bit numbers. */
292 if ((mp_limb_t) (value >> 32) >= 1)
293 {
294# if UDIV_TIME > 2 * UMUL_TIME || UDIV_NEEDS_NORMALIZATION
295 int big_normalization_steps = brec->big.normalization_steps;
296 mp_limb_t big_base_norm
297 = brec->big.base << big_normalization_steps;
298# endif
299 if ((mp_limb_t) (value >> 32) >= brec->big.base)
300 {
301 mp_limb_t x1hi, x1lo, r;
302 /* If you want to optimize this, take advantage of
303 that the quotient in the first udiv_qrnnd will
304 always be very small. It might be faster just to
305 subtract in a tight loop. */
306
307# if UDIV_TIME > 2 * UMUL_TIME
308 mp_limb_t x, xh, xl;
309
310 if (big_normalization_steps == 0)
311 xh = 0;
312 else
313 xh = (mp_limb_t) (value >> (64 - big_normalization_steps));
314 xl = (mp_limb_t) (value >> (32 - big_normalization_steps));
315 udiv_qrnnd_preinv (x1hi, r, xh, xl, big_base_norm,
316 brec->big.base_ninv);
317
318 xl = ((mp_limb_t) value) << big_normalization_steps;
319 udiv_qrnnd_preinv (x1lo, x, r, xl, big_base_norm,
320 brec->big.base_ninv);
321 t[2] = x >> big_normalization_steps;
322
323 if (big_normalization_steps == 0)
324 xh = x1hi;
325 else
326 xh = ((x1hi << big_normalization_steps)
327 | (x1lo >> (32 - big_normalization_steps)));
328 xl = x1lo << big_normalization_steps;
329 udiv_qrnnd_preinv (t[0], x, xh, xl, big_base_norm,
330 brec->big.base_ninv);
331 t[1] = x >> big_normalization_steps;
332# elif UDIV_NEEDS_NORMALIZATION
333 mp_limb_t x, xh, xl;
334
335 if (big_normalization_steps == 0)
336 xh = 0;
337 else
338 xh = (mp_limb_t) (value >> 64 - big_normalization_steps);
339 xl = (mp_limb_t) (value >> 32 - big_normalization_steps);
340 udiv_qrnnd (x1hi, r, xh, xl, big_base_norm);
341
342 xl = ((mp_limb_t) value) << big_normalization_steps;
343 udiv_qrnnd (x1lo, x, r, xl, big_base_norm);
344 t[2] = x >> big_normalization_steps;
345
346 if (big_normalization_steps == 0)
347 xh = x1hi;
348 else
349 xh = ((x1hi << big_normalization_steps)
350 | (x1lo >> 32 - big_normalization_steps));
351 xl = x1lo << big_normalization_steps;
352 udiv_qrnnd (t[0], x, xh, xl, big_base_norm);
353 t[1] = x >> big_normalization_steps;
354# else
355 udiv_qrnnd (x1hi, r, 0, (mp_limb_t) (value >> 32),
356 brec->big.base);
357 udiv_qrnnd (x1lo, t[2], r, (mp_limb_t) value, brec->big.base);
358 udiv_qrnnd (t[0], t[1], x1hi, x1lo, brec->big.base);
359# endif
360 n = 3;
361 }
362 else
363 {
364# if UDIV_TIME > 2 * UMUL_TIME
365 mp_limb_t x;
366
367 value <<= brec->big.normalization_steps;
368 udiv_qrnnd_preinv (t[0], x, (mp_limb_t) (value >> 32),
369 (mp_limb_t) value, big_base_norm,
370 brec->big.base_ninv);
371 t[1] = x >> brec->big.normalization_steps;
372# elif UDIV_NEEDS_NORMALIZATION
373 mp_limb_t x;
374
375 value <<= big_normalization_steps;
376 udiv_qrnnd (t[0], x, (mp_limb_t) (value >> 32),
377 (mp_limb_t) value, big_base_norm);
378 t[1] = x >> big_normalization_steps;
379# else
380 udiv_qrnnd (t[0], t[1], (mp_limb_t) (value >> 32),
381 (mp_limb_t) value, brec->big.base);
382# endif
383 n = 2;
384 }
385 }
386 else
387 {
388 t[0] = value;
389 n = 1;
390 }
391
392 /* Convert the 1-3 words in t[], word by word, to ASCII. */
393 do
394 {
395 mp_limb_t ti = t[--n];
396 int ndig_for_this_limb = 0;
397
398# if UDIV_TIME > 2 * UMUL_TIME
399 mp_limb_t base_multiplier = brec->base_multiplier;
400 if (brec->flag)
401 while (ti != 0)
402 {
403 mp_limb_t quo, rem, x;
404 mp_limb_t dummy __attribute__ ((unused));
405
406 umul_ppmm (x, dummy, ti, base_multiplier);
407 quo = (x + ((ti - x) >> 1)) >> (brec->post_shift - 1);
408 rem = ti - quo * base;
409 *--buflim = digits[rem];
410 ti = quo;
411 ++ndig_for_this_limb;
412 }
413 else
414 while (ti != 0)
415 {
416 mp_limb_t quo, rem, x;
417 mp_limb_t dummy __attribute__ ((unused));
418
419 umul_ppmm (x, dummy, ti, base_multiplier);
420 quo = x >> brec->post_shift;
421 rem = ti - quo * base;
422 *--buflim = digits[rem];
423 ti = quo;
424 ++ndig_for_this_limb;
425 }
426# else
427 while (ti != 0)
428 {
429 mp_limb_t quo, rem;
430
431 quo = ti / base;
432 rem = ti % base;
433 *--buflim = digits[rem];
434 ti = quo;
435 ++ndig_for_this_limb;
436 }
437# endif
438 /* If this wasn't the most significant word, pad with zeros. */
439 if (n != 0)
440 while (ndig_for_this_limb < brec->big.ndigits)
441 {
442 *--buflim = '0';
443 ++ndig_for_this_limb;
444 }
445 }
446 while (n != 0);
447# endif
448 if (buflim == bufend)
449 *--buflim = '0';
450 }
451 break;
452 }
453
454 return buflim;
455}
456#endif
457
458char *
459_fitoa_word (_ITOA_WORD_TYPE value, char *buf, unsigned int base,
460 int upper_case)
461{
462 char tmpbuf[sizeof (value) * 4]; /* Worst case length: base 2. */
463 char *cp = _itoa_word (value, tmpbuf + sizeof (value) * 4, base, upper_case);
464 while (cp < tmpbuf + sizeof (value) * 4)
465 *buf++ = *cp++;
466 return buf;
467}
468
469#if _ITOA_NEEDED
470char *
471_fitoa (unsigned long long value, char *buf, unsigned int base, int upper_case)
472{
473 char tmpbuf[sizeof (value) * 4]; /* Worst case length: base 2. */
474 char *cp = _itoa (value, tmpbuf + sizeof (value) * 4, base, upper_case);
475 while (cp < tmpbuf + sizeof (value) * 4)
476 *buf++ = *cp++;
477 return buf;
478}
479#endif
480