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. */
47 struct 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. */
81 const 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
160 #if IS_IN (libc)
161 char *
162 _itoa_word (_ITOA_WORD_TYPE value, char *buflim,
163 unsigned int base, int upper_case)
164 {
165 const char *digits = (upper_case
166 ? _itoa_upper_digits
167 : _itoa_lower_digits);
168
169 switch (base)
170 {
171 #define SPECIAL(Base) \
172 case Base: \
173 do \
174 *--buflim = digits[value % Base]; \
175 while ((value /= Base) != 0); \
176 break
177
178 SPECIAL (10);
179 SPECIAL (16);
180 SPECIAL (8);
181 default:
182 do
183 *--buflim = digits[value % base];
184 while ((value /= base) != 0);
185 }
186 return buflim;
187 }
188 #undef SPECIAL
189 #endif /* IS_IN (libc) */
190
191
192 #if _ITOA_NEEDED
193 char *
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
458 char *
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
470 char *
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