1/* Internal function for converting integers to ASCII.
2 Copyright (C) 1994-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <gmp-mparam.h>
20#include <gmp.h>
21#include <limits.h>
22#include <stdlib/gmp-impl.h>
23#include <stdlib/longlong.h>
24
25#include <_itoa.h>
26
27
28/* Canonize environment. For some architectures not all values might
29 be defined in the GMP header files. */
30#ifndef UMUL_TIME
31# define UMUL_TIME 1
32#endif
33#ifndef UDIV_TIME
34# define UDIV_TIME 3
35#endif
36
37/* Control memory layout. */
38#ifdef PACK
39# undef PACK
40# define PACK __attribute__ ((packed))
41#else
42# define PACK
43#endif
44
45
46/* Declare local types. */
47struct base_table_t
48{
49#if (UDIV_TIME > 2 * UMUL_TIME)
50 mp_limb_t base_multiplier;
51#endif
52 char flag;
53 char post_shift;
54#if BITS_PER_MP_LIMB == 32
55 struct
56 {
57 char normalization_steps;
58 char ndigits;
59 mp_limb_t base PACK;
60#if UDIV_TIME > 2 * UMUL_TIME
61 mp_limb_t base_ninv PACK;
62#endif
63 } big;
64#endif
65};
66
67/* To reduce the memory needed we include some fields of the tables
68 only conditionally. */
69#if UDIV_TIME > 2 * UMUL_TIME
70# define SEL1(X) X,
71# define SEL2(X) ,X
72#else
73# define SEL1(X)
74# define SEL2(X)
75#endif
76
77
78/* We do not compile _itoa if we always can use _itoa_word. */
79#if _ITOA_NEEDED
80/* Local variables. */
81const struct base_table_t _itoa_base_table[] attribute_hidden =
82{
83# if BITS_PER_MP_LIMB == 64
84 /* 2 */ {SEL1(0ull) 1, 1},
85 /* 3 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 1},
86 /* 4 */ {SEL1(0ull) 1, 2},
87 /* 5 */ {SEL1(0xcccccccccccccccdull) 0, 2},
88 /* 6 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 2},
89 /* 7 */ {SEL1(0x2492492492492493ull) 1, 3},
90 /* 8 */ {SEL1(0ull) 1, 3},
91 /* 9 */ {SEL1(0xe38e38e38e38e38full) 0, 3},
92 /* 10 */ {SEL1(0xcccccccccccccccdull) 0, 3},
93 /* 11 */ {SEL1(0x2e8ba2e8ba2e8ba3ull) 0, 1},
94 /* 12 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 3},
95 /* 13 */ {SEL1(0x4ec4ec4ec4ec4ec5ull) 0, 2},
96 /* 14 */ {SEL1(0x2492492492492493ull) 1, 4},
97 /* 15 */ {SEL1(0x8888888888888889ull) 0, 3},
98 /* 16 */ {SEL1(0ull) 1, 4},
99 /* 17 */ {SEL1(0xf0f0f0f0f0f0f0f1ull) 0, 4},
100 /* 18 */ {SEL1(0xe38e38e38e38e38full) 0, 4},
101 /* 19 */ {SEL1(0xd79435e50d79435full) 0, 4},
102 /* 20 */ {SEL1(0xcccccccccccccccdull) 0, 4},
103 /* 21 */ {SEL1(0x8618618618618619ull) 1, 5},
104 /* 22 */ {SEL1(0x2e8ba2e8ba2e8ba3ull) 0, 2},
105 /* 23 */ {SEL1(0x642c8590b21642c9ull) 1, 5},
106 /* 24 */ {SEL1(0xaaaaaaaaaaaaaaabull) 0, 4},
107 /* 25 */ {SEL1(0x47ae147ae147ae15ull) 1, 5},
108 /* 26 */ {SEL1(0x4ec4ec4ec4ec4ec5ull) 0, 3},
109 /* 27 */ {SEL1(0x97b425ed097b425full) 0, 4},
110 /* 28 */ {SEL1(0x2492492492492493ull) 1, 5},
111 /* 29 */ {SEL1(0x1a7b9611a7b9611bull) 1, 5},
112 /* 30 */ {SEL1(0x8888888888888889ull) 0, 4},
113 /* 31 */ {SEL1(0x0842108421084211ull) 1, 5},
114 /* 32 */ {SEL1(0ull) 1, 5},
115 /* 33 */ {SEL1(0x0f83e0f83e0f83e1ull) 0, 1},
116 /* 34 */ {SEL1(0xf0f0f0f0f0f0f0f1ull) 0, 5},
117 /* 35 */ {SEL1(0xea0ea0ea0ea0ea0full) 0, 5},
118 /* 36 */ {SEL1(0xe38e38e38e38e38full) 0, 5}
119# endif
120# if BITS_PER_MP_LIMB == 32
121 /* 2 */ {SEL1(0ul) 1, 1, {0, 31, 0x80000000ul SEL2(0xfffffffful)}},
122 /* 3 */ {SEL1(0xaaaaaaabul) 0, 1, {0, 20, 0xcfd41b91ul SEL2(0x3b563c24ul)}},
123 /* 4 */ {SEL1(0ul) 1, 2, {1, 15, 0x40000000ul SEL2(0xfffffffful)}},
124 /* 5 */ {SEL1(0xcccccccdul) 0, 2, {1, 13, 0x48c27395ul SEL2(0xc25c2684ul)}},
125 /* 6 */ {SEL1(0xaaaaaaabul) 0, 2, {0, 12, 0x81bf1000ul SEL2(0xf91bd1b6ul)}},
126 /* 7 */ {SEL1(0x24924925ul) 1, 3, {1, 11, 0x75db9c97ul SEL2(0x1607a2cbul)}},
127 /* 8 */ {SEL1(0ul) 1, 3, {1, 10, 0x40000000ul SEL2(0xfffffffful)}},
128 /* 9 */ {SEL1(0x38e38e39ul) 0, 1, {0, 10, 0xcfd41b91ul SEL2(0x3b563c24ul)}},
129 /* 10 */ {SEL1(0xcccccccdul) 0, 3, {2, 9, 0x3b9aca00ul SEL2(0x12e0be82ul)}},
130 /* 11 */ {SEL1(0xba2e8ba3ul) 0, 3, {0, 9, 0x8c8b6d2bul SEL2(0xd24cde04ul)}},
131 /* 12 */ {SEL1(0xaaaaaaabul) 0, 3, {3, 8, 0x19a10000ul SEL2(0x3fa39ab5ul)}},
132 /* 13 */ {SEL1(0x4ec4ec4ful) 0, 2, {2, 8, 0x309f1021ul SEL2(0x50f8ac5ful)}},
133 /* 14 */ {SEL1(0x24924925ul) 1, 4, {1, 8, 0x57f6c100ul SEL2(0x74843b1eul)}},
134 /* 15 */ {SEL1(0x88888889ul) 0, 3, {0, 8, 0x98c29b81ul SEL2(0xad0326c2ul)}},
135 /* 16 */ {SEL1(0ul) 1, 4, {3, 7, 0x10000000ul SEL2(0xfffffffful)}},
136 /* 17 */ {SEL1(0xf0f0f0f1ul) 0, 4, {3, 7, 0x18754571ul SEL2(0x4ef0b6bdul)}},
137 /* 18 */ {SEL1(0x38e38e39ul) 0, 2, {2, 7, 0x247dbc80ul SEL2(0xc0fc48a1ul)}},
138 /* 19 */ {SEL1(0xaf286bcbul) 1, 5, {2, 7, 0x3547667bul SEL2(0x33838942ul)}},
139 /* 20 */ {SEL1(0xcccccccdul) 0, 4, {1, 7, 0x4c4b4000ul SEL2(0xad7f29abul)}},
140 /* 21 */ {SEL1(0x86186187ul) 1, 5, {1, 7, 0x6b5a6e1dul SEL2(0x313c3d15ul)}},
141 /* 22 */ {SEL1(0xba2e8ba3ul) 0, 4, {0, 7, 0x94ace180ul SEL2(0xb8cca9e0ul)}},
142 /* 23 */ {SEL1(0xb21642c9ul) 0, 4, {0, 7, 0xcaf18367ul SEL2(0x42ed6de9ul)}},
143 /* 24 */ {SEL1(0xaaaaaaabul) 0, 4, {4, 6, 0x0b640000ul SEL2(0x67980e0bul)}},
144 /* 25 */ {SEL1(0x51eb851ful) 0, 3, {4, 6, 0x0e8d4a51ul SEL2(0x19799812ul)}},
145 /* 26 */ {SEL1(0x4ec4ec4ful) 0, 3, {3, 6, 0x1269ae40ul SEL2(0xbce85396ul)}},
146 /* 27 */ {SEL1(0x2f684bdbul) 1, 5, {3, 6, 0x17179149ul SEL2(0x62c103a9ul)}},
147 /* 28 */ {SEL1(0x24924925ul) 1, 5, {3, 6, 0x1cb91000ul SEL2(0x1d353d43ul)}},
148 /* 29 */ {SEL1(0x8d3dcb09ul) 0, 4, {2, 6, 0x23744899ul SEL2(0xce1deceaul)}},
149 /* 30 */ {SEL1(0x88888889ul) 0, 4, {2, 6, 0x2b73a840ul SEL2(0x790fc511ul)}},
150 /* 31 */ {SEL1(0x08421085ul) 1, 5, {2, 6, 0x34e63b41ul SEL2(0x35b865a0ul)}},
151 /* 32 */ {SEL1(0ul) 1, 5, {1, 6, 0x40000000ul SEL2(0xfffffffful)}},
152 /* 33 */ {SEL1(0x3e0f83e1ul) 0, 3, {1, 6, 0x4cfa3cc1ul SEL2(0xa9aed1b3ul)}},
153 /* 34 */ {SEL1(0xf0f0f0f1ul) 0, 5, {1, 6, 0x5c13d840ul SEL2(0x63dfc229ul)}},
154 /* 35 */ {SEL1(0xd41d41d5ul) 1, 6, {1, 6, 0x6d91b519ul SEL2(0x2b0fee30ul)}},
155 /* 36 */ {SEL1(0x38e38e39ul) 0, 3, {0, 6, 0x81bf1000ul SEL2(0xf91bd1b6ul)}}
156# endif
157};
158#endif
159
160char *
161_itoa_word (_ITOA_WORD_TYPE value, char *buflim,
162 unsigned int base, int upper_case)
163{
164 const char *digits = (upper_case
165 ? _itoa_upper_digits
166 : _itoa_lower_digits);
167
168 switch (base)
169 {
170#define SPECIAL(Base) \
171 case Base: \
172 do \
173 *--buflim = digits[value % Base]; \
174 while ((value /= Base) != 0); \
175 break
176
177 SPECIAL (10);
178 SPECIAL (16);
179 SPECIAL (8);
180 default:
181 do
182 *--buflim = digits[value % base];
183 while ((value /= base) != 0);
184 }
185 return buflim;
186}
187#undef SPECIAL
188
189
190#if _ITOA_NEEDED
191char *
192_itoa (unsigned long long int value, char *buflim, unsigned int base,
193 int upper_case)
194{
195 const char *digits = (upper_case
196 ? _itoa_upper_digits
197 : _itoa_lower_digits);
198 const struct base_table_t *brec = &_itoa_base_table[base - 2];
199
200 switch (base)
201 {
202# define RUN_2N(BITS) \
203 do \
204 { \
205 /* `unsigned long long int' always has 64 bits. */ \
206 mp_limb_t work_hi = value >> (64 - BITS_PER_MP_LIMB); \
207 \
208 if (BITS_PER_MP_LIMB == 32) \
209 { \
210 if (work_hi != 0) \
211 { \
212 mp_limb_t work_lo; \
213 int cnt; \
214 \
215 work_lo = value & 0xfffffffful; \
216 for (cnt = BITS_PER_MP_LIMB / BITS; cnt > 0; --cnt) \
217 { \
218 *--buflim = digits[work_lo & ((1ul << BITS) - 1)]; \
219 work_lo >>= BITS; \
220 } \
221 if (BITS_PER_MP_LIMB % BITS != 0) \
222 { \
223 work_lo \
224 |= ((work_hi \
225 & ((1 << (BITS - BITS_PER_MP_LIMB%BITS)) \
226 - 1)) \
227 << BITS_PER_MP_LIMB % BITS); \
228 work_hi >>= BITS - BITS_PER_MP_LIMB % BITS; \
229 if (work_hi == 0) \
230 work_hi = work_lo; \
231 else \
232 *--buflim = digits[work_lo]; \
233 } \
234 } \
235 else \
236 work_hi = value & 0xfffffffful; \
237 } \
238 do \
239 { \
240 *--buflim = digits[work_hi & ((1 << BITS) - 1)]; \
241 work_hi >>= BITS; \
242 } \
243 while (work_hi != 0); \
244 } \
245 while (0)
246 case 8:
247 RUN_2N (3);
248 break;
249
250 case 16:
251 RUN_2N (4);
252 break;
253
254 default:
255 {
256 char *bufend = buflim;
257# if BITS_PER_MP_LIMB == 64
258 mp_limb_t base_multiplier = brec->base_multiplier;
259 if (brec->flag)
260 while (value != 0)
261 {
262 mp_limb_t quo, rem, x;
263 mp_limb_t dummy __attribute__ ((unused));
264
265 umul_ppmm (x, dummy, value, base_multiplier);
266 quo = (x + ((value - x) >> 1)) >> (brec->post_shift - 1);
267 rem = value - quo * base;
268 *--buflim = digits[rem];
269 value = quo;
270 }
271 else
272 while (value != 0)
273 {
274 mp_limb_t quo, rem, x;
275 mp_limb_t dummy __attribute__ ((unused));
276
277 umul_ppmm (x, dummy, value, base_multiplier);
278 quo = x >> brec->post_shift;
279 rem = value - quo * base;
280 *--buflim = digits[rem];
281 value = quo;
282 }
283# endif
284# if BITS_PER_MP_LIMB == 32
285 mp_limb_t t[3];
286 int n;
287
288 /* First convert x0 to 1-3 words in base s->big.base.
289 Optimize for frequent cases of 32 bit numbers. */
290 if ((mp_limb_t) (value >> 32) >= 1)
291 {
292# if UDIV_TIME > 2 * UMUL_TIME || UDIV_NEEDS_NORMALIZATION
293 int big_normalization_steps = brec->big.normalization_steps;
294 mp_limb_t big_base_norm
295 = brec->big.base << big_normalization_steps;
296# endif
297 if ((mp_limb_t) (value >> 32) >= brec->big.base)
298 {
299 mp_limb_t x1hi, x1lo, r;
300 /* If you want to optimize this, take advantage of
301 that the quotient in the first udiv_qrnnd will
302 always be very small. It might be faster just to
303 subtract in a tight loop. */
304
305# if UDIV_TIME > 2 * UMUL_TIME
306 mp_limb_t x, xh, xl;
307
308 if (big_normalization_steps == 0)
309 xh = 0;
310 else
311 xh = (mp_limb_t) (value >> (64 - big_normalization_steps));
312 xl = (mp_limb_t) (value >> (32 - big_normalization_steps));
313 udiv_qrnnd_preinv (x1hi, r, xh, xl, big_base_norm,
314 brec->big.base_ninv);
315
316 xl = ((mp_limb_t) value) << big_normalization_steps;
317 udiv_qrnnd_preinv (x1lo, x, r, xl, big_base_norm,
318 brec->big.base_ninv);
319 t[2] = x >> big_normalization_steps;
320
321 if (big_normalization_steps == 0)
322 xh = x1hi;
323 else
324 xh = ((x1hi << big_normalization_steps)
325 | (x1lo >> (32 - big_normalization_steps)));
326 xl = x1lo << big_normalization_steps;
327 udiv_qrnnd_preinv (t[0], x, xh, xl, big_base_norm,
328 brec->big.base_ninv);
329 t[1] = x >> big_normalization_steps;
330# elif UDIV_NEEDS_NORMALIZATION
331 mp_limb_t x, xh, xl;
332
333 if (big_normalization_steps == 0)
334 xh = 0;
335 else
336 xh = (mp_limb_t) (value >> 64 - big_normalization_steps);
337 xl = (mp_limb_t) (value >> 32 - big_normalization_steps);
338 udiv_qrnnd (x1hi, r, xh, xl, big_base_norm);
339
340 xl = ((mp_limb_t) value) << big_normalization_steps;
341 udiv_qrnnd (x1lo, x, r, xl, big_base_norm);
342 t[2] = x >> big_normalization_steps;
343
344 if (big_normalization_steps == 0)
345 xh = x1hi;
346 else
347 xh = ((x1hi << big_normalization_steps)
348 | (x1lo >> 32 - big_normalization_steps));
349 xl = x1lo << big_normalization_steps;
350 udiv_qrnnd (t[0], x, xh, xl, big_base_norm);
351 t[1] = x >> big_normalization_steps;
352# else
353 udiv_qrnnd (x1hi, r, 0, (mp_limb_t) (value >> 32),
354 brec->big.base);
355 udiv_qrnnd (x1lo, t[2], r, (mp_limb_t) value, brec->big.base);
356 udiv_qrnnd (t[0], t[1], x1hi, x1lo, brec->big.base);
357# endif
358 n = 3;
359 }
360 else
361 {
362# if UDIV_TIME > 2 * UMUL_TIME
363 mp_limb_t x;
364
365 value <<= brec->big.normalization_steps;
366 udiv_qrnnd_preinv (t[0], x, (mp_limb_t) (value >> 32),
367 (mp_limb_t) value, big_base_norm,
368 brec->big.base_ninv);
369 t[1] = x >> brec->big.normalization_steps;
370# elif UDIV_NEEDS_NORMALIZATION
371 mp_limb_t x;
372
373 value <<= big_normalization_steps;
374 udiv_qrnnd (t[0], x, (mp_limb_t) (value >> 32),
375 (mp_limb_t) value, big_base_norm);
376 t[1] = x >> big_normalization_steps;
377# else
378 udiv_qrnnd (t[0], t[1], (mp_limb_t) (value >> 32),
379 (mp_limb_t) value, brec->big.base);
380# endif
381 n = 2;
382 }
383 }
384 else
385 {
386 t[0] = value;
387 n = 1;
388 }
389
390 /* Convert the 1-3 words in t[], word by word, to ASCII. */
391 do
392 {
393 mp_limb_t ti = t[--n];
394 int ndig_for_this_limb = 0;
395
396# if UDIV_TIME > 2 * UMUL_TIME
397 mp_limb_t base_multiplier = brec->base_multiplier;
398 if (brec->flag)
399 while (ti != 0)
400 {
401 mp_limb_t quo, rem, x;
402 mp_limb_t dummy __attribute__ ((unused));
403
404 umul_ppmm (x, dummy, ti, base_multiplier);
405 quo = (x + ((ti - x) >> 1)) >> (brec->post_shift - 1);
406 rem = ti - quo * base;
407 *--buflim = digits[rem];
408 ti = quo;
409 ++ndig_for_this_limb;
410 }
411 else
412 while (ti != 0)
413 {
414 mp_limb_t quo, rem, x;
415 mp_limb_t dummy __attribute__ ((unused));
416
417 umul_ppmm (x, dummy, ti, base_multiplier);
418 quo = x >> brec->post_shift;
419 rem = ti - quo * base;
420 *--buflim = digits[rem];
421 ti = quo;
422 ++ndig_for_this_limb;
423 }
424# else
425 while (ti != 0)
426 {
427 mp_limb_t quo, rem;
428
429 quo = ti / base;
430 rem = ti % base;
431 *--buflim = digits[rem];
432 ti = quo;
433 ++ndig_for_this_limb;
434 }
435# endif
436 /* If this wasn't the most significant word, pad with zeros. */
437 if (n != 0)
438 while (ndig_for_this_limb < brec->big.ndigits)
439 {
440 *--buflim = '0';
441 ++ndig_for_this_limb;
442 }
443 }
444 while (n != 0);
445# endif
446 if (buflim == bufend)
447 *--buflim = '0';
448 }
449 break;
450 }
451
452 return buflim;
453}
454#endif
455
456char *
457_fitoa_word (_ITOA_WORD_TYPE value, char *buf, unsigned int base,
458 int upper_case)
459{
460 char tmpbuf[sizeof (value) * 4]; /* Worst case length: base 2. */
461 char *cp = _itoa_word (value, tmpbuf + sizeof (value) * 4, base, upper_case);
462 while (cp < tmpbuf + sizeof (value) * 4)
463 *buf++ = *cp++;
464 return buf;
465}
466
467#if _ITOA_NEEDED
468char *
469_fitoa (unsigned long long value, char *buf, unsigned int base, int upper_case)
470{
471 char tmpbuf[sizeof (value) * 4]; /* Worst case length: base 2. */
472 char *cp = _itoa (value, tmpbuf + sizeof (value) * 4, base, upper_case);
473 while (cp < tmpbuf + sizeof (value) * 4)
474 *buf++ = *cp++;
475 return buf;
476}
477#endif
478