ext_comp.c 15 KB

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  1. /*
  2. (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
  3. See the copyright notice in the ACK home directory, in the file "Copyright".
  4. */
  5. /* $Id$ */
  6. /* extended precision arithmetic for the strtod() and cvt() routines */
  7. /* This may require some more work when long doubles get bigger than 8
  8. bytes. In this case, these routines may become obsolete. ???
  9. */
  10. #include "ext_fmt.h"
  11. #include <float.h>
  12. #include <errno.h>
  13. #include <ctype.h>
  14. static int b64_add(struct mantissa *e1, struct mantissa *e2);
  15. static b64_sft(struct mantissa *e1, int n);
  16. static
  17. mul_ext(struct EXTEND *e1, struct EXTEND *e2, struct EXTEND *e3)
  18. {
  19. /* Multiply the extended numbers e1 and e2, and put the
  20. result in e3.
  21. */
  22. register int i,j; /* loop control */
  23. unsigned short mp[4];
  24. unsigned short mc[4];
  25. unsigned short result[8]; /* result */
  26. register unsigned short *pres;
  27. /* first save the sign (XOR) */
  28. e3->sign = e1->sign ^ e2->sign;
  29. /* compute new exponent */
  30. e3->exp = e1->exp + e2->exp + 1;
  31. /* check for overflow/underflow ??? */
  32. /* 128 bit multiply of mantissas */
  33. /* assign unknown long formats */
  34. /* to known unsigned word formats */
  35. mp[0] = e1->m1 >> 16;
  36. mp[1] = (unsigned short) e1->m1;
  37. mp[2] = e1->m2 >> 16;
  38. mp[3] = (unsigned short) e1->m2;
  39. mc[0] = e2->m1 >> 16;
  40. mc[1] = (unsigned short) e2->m1;
  41. mc[2] = e2->m2 >> 16;
  42. mc[3] = (unsigned short) e2->m2;
  43. for (i = 8; i--;) {
  44. result[i] = 0;
  45. }
  46. /*
  47. * fill registers with their components
  48. */
  49. for(i=4, pres = &result[4];i--;pres--) if (mp[i]) {
  50. unsigned short k = 0;
  51. unsigned long mpi = mp[i];
  52. for(j=4;j--;) {
  53. unsigned long tmp = (unsigned long)pres[j] + k;
  54. if (mc[j]) tmp += mpi * mc[j];
  55. pres[j] = tmp;
  56. k = tmp >> 16;
  57. }
  58. pres[-1] = k;
  59. }
  60. if (! (result[0] & 0x8000)) {
  61. e3->exp--;
  62. for (i = 0; i <= 3; i++) {
  63. result[i] <<= 1;
  64. if (result[i+1]&0x8000) result[i] |= 1;
  65. }
  66. result[4] <<= 1;
  67. }
  68. /*
  69. * combine the registers to a total
  70. */
  71. e3->m1 = ((unsigned long)(result[0]) << 16) + result[1];
  72. e3->m2 = ((unsigned long)(result[2]) << 16) + result[3];
  73. if (result[4] & 0x8000) {
  74. if (++e3->m2 == 0) {
  75. if (++e3->m1 == 0) {
  76. e3->m1 = 0x80000000;
  77. e3->exp++;
  78. }
  79. }
  80. }
  81. }
  82. static
  83. add_ext(struct EXTEND *e1, struct EXTEND *e2, struct EXTEND *e3)
  84. {
  85. /* Add two extended numbers e1 and e2, and put the result
  86. in e3
  87. */
  88. struct EXTEND ce2;
  89. int diff;
  90. if ((e2->m1 | e2->m2) == 0L) {
  91. *e3 = *e1;
  92. return;
  93. }
  94. if ((e1->m1 | e1->m2) == 0L) {
  95. *e3 = *e2;
  96. return;
  97. }
  98. ce2 = *e2;
  99. *e3 = *e1;
  100. e1 = &ce2;
  101. /* adjust mantissas to equal power */
  102. diff = e3->exp - e1->exp;
  103. if (diff < 0) {
  104. diff = -diff;
  105. e3->exp += diff;
  106. b64_sft(&(e3->mantissa), diff);
  107. }
  108. else if (diff > 0) {
  109. e1->exp += diff;
  110. b64_sft(&(e1->mantissa), diff);
  111. }
  112. if (e1->sign != e3->sign) {
  113. /* e3 + e1 = e3 - (-e1) */
  114. if (e1->m1 > e3->m1 ||
  115. (e1->m1 == e3->m1 && e1->m2 > e3->m2)) {
  116. /* abs(e1) > abs(e3) */
  117. if (e3->m2 > e1->m2) {
  118. e1->m1 -= 1; /* carry in */
  119. }
  120. e1->m1 -= e3->m1;
  121. e1->m2 -= e3->m2;
  122. *e3 = *e1;
  123. }
  124. else {
  125. if (e1->m2 > e3->m2)
  126. e3->m1 -= 1; /* carry in */
  127. e3->m1 -= e1->m1;
  128. e3->m2 -= e1->m2;
  129. }
  130. }
  131. else {
  132. if (b64_add(&e3->mantissa,&e1->mantissa)) {/* addition carry */
  133. b64_sft(&e3->mantissa,1);/* shift mantissa one bit RIGHT */
  134. e3->m1 |= 0x80000000L; /* set max bit */
  135. e3->exp++; /* increase the exponent */
  136. }
  137. }
  138. if ((e3->m2 | e3->m1) != 0L) {
  139. /* normalize */
  140. if (e3->m1 == 0L) {
  141. e3->m1 = e3->m2; e3->m2 = 0L; e3->exp -= 32;
  142. }
  143. if (!(e3->m1 & 0x80000000)) {
  144. unsigned long l = 0x40000000;
  145. int cnt = -1;
  146. while (! (l & e3->m1)) {
  147. l >>= 1; cnt--;
  148. }
  149. e3->exp += cnt;
  150. b64_sft(&(e3->mantissa), cnt);
  151. }
  152. }
  153. }
  154. static int
  155. cmp_ext(struct EXTEND *e1, struct EXTEND *e2)
  156. {
  157. struct EXTEND tmp;
  158. e2->sign = ! e2->sign;
  159. add_ext(e1, e2, &tmp);
  160. e2->sign = ! e2->sign;
  161. if (tmp.m1 == 0 && tmp.m2 == 0) return 0;
  162. if (tmp.sign) return -1;
  163. return 1;
  164. }
  165. static
  166. b64_sft(struct mantissa *e1, int n)
  167. {
  168. if (n > 0) {
  169. if (n > 63) {
  170. e1->l_32 = 0;
  171. e1->h_32 = 0;
  172. return;
  173. }
  174. if (n >= 32) {
  175. e1->l_32 = e1->h_32;
  176. e1->h_32 = 0;
  177. n -= 32;
  178. }
  179. if (n > 0) {
  180. e1->l_32 >>= n;
  181. if (e1->h_32 != 0) {
  182. e1->l_32 |= (e1->h_32 << (32 - n));
  183. e1->h_32 >>= n;
  184. }
  185. }
  186. return;
  187. }
  188. n = -n;
  189. if (n > 0) {
  190. if (n > 63) {
  191. e1->l_32 = 0;
  192. e1->h_32 = 0;
  193. return;
  194. }
  195. if (n >= 32) {
  196. e1->h_32 = e1->l_32;
  197. e1->l_32 = 0;
  198. n -= 32;
  199. }
  200. if (n > 0) {
  201. e1->h_32 <<= n;
  202. if (e1->l_32 != 0) {
  203. e1->h_32 |= (e1->l_32 >> (32 - n));
  204. e1->l_32 <<= n;
  205. }
  206. }
  207. }
  208. }
  209. static int
  210. b64_add(struct mantissa *e1, struct mantissa *e2)
  211. /*
  212. * pointers to 64 bit 'registers'
  213. */
  214. {
  215. register int overflow;
  216. int carry;
  217. /* add higher pair of 32 bits */
  218. overflow = ((unsigned long) 0xFFFFFFFF - e1->h_32 < e2->h_32);
  219. e1->h_32 += e2->h_32;
  220. /* add lower pair of 32 bits */
  221. carry = ((unsigned long) 0xFFFFFFFF - e1->l_32 < e2->l_32);
  222. e1->l_32 += e2->l_32;
  223. if ((carry) && (++e1->h_32 == 0))
  224. return(1); /* had a 64 bit overflow */
  225. else
  226. return(overflow); /* return status from higher add */
  227. }
  228. /* The following tables can be computed with the following bc(1)
  229. program:
  230. obase=16
  231. scale=0
  232. define t(x){
  233. auto a, b, c
  234. a=2;b=1;c=2^32;n=1
  235. while(a<x) {
  236. b=a;n+=n;a*=a
  237. }
  238. n/=2
  239. a=b
  240. while(b<x) {
  241. a=b;b*=c;n+=32
  242. }
  243. n-=32
  244. b=a
  245. while(a<x) {
  246. b=a;a+=a;n+=1
  247. }
  248. n-=1
  249. x*=16^16
  250. b=x%a
  251. x/=a
  252. if(a<=(2*b)) x+=1
  253. obase=10
  254. n
  255. obase=16
  256. return(x)
  257. }
  258. for (i=1;i<28;i++) {
  259. t(10^i)
  260. }
  261. 0
  262. for (i=1;i<20;i++) {
  263. t(10^(28*i))
  264. }
  265. 0
  266. define r(x){
  267. auto a, b, c
  268. a=2;b=1;c=2^32;n=1
  269. while(a<x) {
  270. b=a;n+=n;a*=a
  271. }
  272. n/=2
  273. a=b
  274. while(b<x) {
  275. a=b;b*=c;n+=32
  276. }
  277. n-=32
  278. b=a
  279. while(a<x) {
  280. b=a;a+=a;n+=1
  281. }
  282. a=b
  283. a*=16^16
  284. b=a%x
  285. a/=x
  286. if(x<=(2*b)) a+=1
  287. obase=10
  288. -n
  289. obase=16
  290. return(a)
  291. }
  292. for (i=1;i<28;i++) {
  293. r(10^i)
  294. }
  295. 0
  296. for (i=1;i<20;i++) {
  297. r(10^(28*i))
  298. }
  299. 0
  300. */
  301. static struct EXTEND ten_powers[] = { /* representation of 10 ** i */
  302. { 0, 0, 0x80000000, 0 },
  303. { 0, 3, 0xA0000000, 0 },
  304. { 0, 6, 0xC8000000, 0 },
  305. { 0, 9, 0xFA000000, 0 },
  306. { 0, 13, 0x9C400000, 0 },
  307. { 0, 16, 0xC3500000, 0 },
  308. { 0, 19, 0xF4240000, 0 },
  309. { 0, 23, 0x98968000, 0 },
  310. { 0, 26, 0xBEBC2000, 0 },
  311. { 0, 29, 0xEE6B2800, 0 },
  312. { 0, 33, 0x9502F900, 0 },
  313. { 0, 36, 0xBA43B740, 0 },
  314. { 0, 39, 0xE8D4A510, 0 },
  315. { 0, 43, 0x9184E72A, 0 },
  316. { 0, 46, 0xB5E620F4, 0x80000000 },
  317. { 0, 49, 0xE35FA931, 0xA0000000 },
  318. { 0, 53, 0x8E1BC9BF, 0x04000000 },
  319. { 0, 56, 0xB1A2BC2E, 0xC5000000 },
  320. { 0, 59, 0xDE0B6B3A, 0x76400000 },
  321. { 0, 63, 0x8AC72304, 0x89E80000 },
  322. { 0, 66, 0xAD78EBC5, 0xAC620000 },
  323. { 0, 69, 0xD8D726B7, 0x177A8000 },
  324. { 0, 73, 0x87867832, 0x6EAC9000 },
  325. { 0, 76, 0xA968163F, 0x0A57B400 },
  326. { 0, 79, 0xD3C21BCE, 0xCCEDA100 },
  327. { 0, 83, 0x84595161, 0x401484A0 },
  328. { 0, 86, 0xA56FA5B9, 0x9019A5C8 },
  329. { 0, 89, 0xCECB8F27, 0xF4200F3A }
  330. };
  331. static struct EXTEND big_ten_powers[] = { /* representation of 10 ** (28*i) */
  332. { 0, 0, 0x80000000, 0 },
  333. { 0, 93, 0x813F3978, 0xF8940984 },
  334. { 0, 186, 0x82818F12, 0x81ED44A0 },
  335. { 0, 279, 0x83C7088E, 0x1AAB65DB },
  336. { 0, 372, 0x850FADC0, 0x9923329E },
  337. { 0, 465, 0x865B8692, 0x5B9BC5C2 },
  338. { 0, 558, 0x87AA9AFF, 0x79042287 },
  339. { 0, 651, 0x88FCF317, 0xF22241E2 },
  340. { 0, 744, 0x8A5296FF, 0xE33CC930 },
  341. { 0, 837, 0x8BAB8EEF, 0xB6409C1A },
  342. { 0, 930, 0x8D07E334, 0x55637EB3 },
  343. { 0, 1023, 0x8E679C2F, 0x5E44FF8F },
  344. { 0, 1116, 0x8FCAC257, 0x558EE4E6 },
  345. { 0, 1209, 0x91315E37, 0xDB165AA9 },
  346. { 0, 1302, 0x929B7871, 0xDE7F22B9 },
  347. { 0, 1395, 0x940919BB, 0xD4620B6D },
  348. { 0, 1488, 0x957A4AE1, 0xEBF7F3D4 },
  349. { 0, 1581, 0x96EF14C6, 0x454AA840 },
  350. { 0, 1674, 0x98678061, 0x27ECE4F5 },
  351. { 0, 1767, 0x99E396C1, 0x3A3ACFF2 }
  352. };
  353. static struct EXTEND r_ten_powers[] = { /* representation of 10 ** -i */
  354. { 0, 0, 0x80000000, 0 },
  355. { 0, -4, 0xCCCCCCCC, 0xCCCCCCCD },
  356. { 0, -7, 0xA3D70A3D, 0x70A3D70A },
  357. { 0, -10, 0x83126E97, 0x8D4FDF3B },
  358. { 0, -14, 0xD1B71758, 0xE219652C },
  359. { 0, -17, 0xA7C5AC47, 0x1B478423 },
  360. { 0, -20, 0x8637BD05, 0xAF6C69B6 },
  361. { 0, -24, 0xD6BF94D5, 0xE57A42BC },
  362. { 0, -27, 0xABCC7711, 0x8461CEFD },
  363. { 0, -30, 0x89705F41, 0x36B4A597 },
  364. { 0, -34, 0xDBE6FECE, 0xBDEDD5BF },
  365. { 0, -37, 0xAFEBFF0B, 0xCB24AAFF },
  366. { 0, -40, 0x8CBCCC09, 0x6F5088CC },
  367. { 0, -44, 0xE12E1342, 0x4BB40E13 },
  368. { 0, -47, 0xB424DC35, 0x095CD80F },
  369. { 0, -50, 0x901D7CF7, 0x3AB0ACD9 },
  370. { 0, -54, 0xE69594BE, 0xC44DE15B },
  371. { 0, -57, 0xB877AA32, 0x36A4B449 },
  372. { 0, -60, 0x9392EE8E, 0x921D5D07 },
  373. { 0, -64, 0xEC1E4A7D, 0xB69561A5 },
  374. { 0, -67, 0xBCE50864, 0x92111AEB },
  375. { 0, -70, 0x971DA050, 0x74DA7BEF },
  376. { 0, -74, 0xF1C90080, 0xBAF72CB1 },
  377. { 0, -77, 0xC16D9A00, 0x95928A27 },
  378. { 0, -80, 0x9ABE14CD, 0x44753B53 },
  379. { 0, -84, 0xF79687AE, 0xD3EEC551 },
  380. { 0, -87, 0xC6120625, 0x76589DDB },
  381. { 0, -90, 0x9E74D1B7, 0x91E07E48 }
  382. };
  383. static struct EXTEND r_big_ten_powers[] = { /* representation of 10 ** -(28*i) */
  384. { 0, 0, 0x80000000, 0 },
  385. { 0, -94, 0xFD87B5F2, 0x8300CA0E },
  386. { 0, -187, 0xFB158592, 0xBE068D2F },
  387. { 0, -280, 0xF8A95FCF, 0x88747D94 },
  388. { 0, -373, 0xF64335BC, 0xF065D37D },
  389. { 0, -466, 0xF3E2F893, 0xDEC3F126 },
  390. { 0, -559, 0xF18899B1, 0xBC3F8CA2 },
  391. { 0, -652, 0xEF340A98, 0x172AACE5 },
  392. { 0, -745, 0xECE53CEC, 0x4A314EBE },
  393. { 0, -838, 0xEA9C2277, 0x23EE8BCB },
  394. { 0, -931, 0xE858AD24, 0x8F5C22CA },
  395. { 0, -1024, 0xE61ACF03, 0x3D1A45DF },
  396. { 0, -1117, 0xE3E27A44, 0x4D8D98B8 },
  397. { 0, -1210, 0xE1AFA13A, 0xFBD14D6E },
  398. { 0, -1303, 0xDF82365C, 0x497B5454 },
  399. { 0, -1396, 0xDD5A2C3E, 0xAB3097CC },
  400. { 0, -1489, 0xDB377599, 0xB6074245 },
  401. { 0, -1582, 0xD91A0545, 0xCDB51186 },
  402. { 0, -1675, 0xD701CE3B, 0xD387BF48 },
  403. { 0, -1768, 0xD4EEC394, 0xD6258BF8 }
  404. };
  405. #define TP (int)(sizeof(ten_powers)/sizeof(ten_powers[0]))
  406. #define BTP (int)(sizeof(big_ten_powers)/sizeof(big_ten_powers[0]))
  407. #define MAX_EXP (TP * BTP - 1)
  408. static
  409. add_exponent(struct EXTEND *e, int exp)
  410. {
  411. int neg = exp < 0;
  412. int divsz, modsz;
  413. struct EXTEND x;
  414. if (neg) exp = -exp;
  415. divsz = exp / TP;
  416. modsz = exp % TP;
  417. if (neg) {
  418. mul_ext(e, &r_ten_powers[modsz], &x);
  419. mul_ext(&x, &r_big_ten_powers[divsz], e);
  420. }
  421. else {
  422. mul_ext(e, &ten_powers[modsz], &x);
  423. mul_ext(&x, &big_ten_powers[divsz], e);
  424. }
  425. }
  426. _str_ext_cvt(const char *s, char **ss, struct EXTEND *e)
  427. {
  428. /* Like strtod, but for extended precision */
  429. register int c;
  430. int dotseen = 0;
  431. int digitseen = 0;
  432. int exp = 0;
  433. if (ss) *ss = (char *)s;
  434. while (isspace(*s)) s++;
  435. e->sign = 0;
  436. e->exp = 0;
  437. e->m1 = e->m2 = 0;
  438. c = *s;
  439. switch(c) {
  440. case '-':
  441. e->sign = 1;
  442. case '+':
  443. s++;
  444. }
  445. while (c = *s++, isdigit(c) || (c == '.' && ! dotseen++)) {
  446. if (c == '.') continue;
  447. digitseen = 1;
  448. if (e->m1 <= (unsigned long)(0xFFFFFFFF)/10) {
  449. struct mantissa a1;
  450. a1 = e->mantissa;
  451. b64_sft(&(e->mantissa), -3);
  452. b64_sft(&a1, -1);
  453. b64_add(&(e->mantissa), &a1);
  454. a1.h_32 = 0;
  455. a1.l_32 = c - '0';
  456. b64_add(&(e->mantissa), &a1);
  457. }
  458. else exp++;
  459. if (dotseen) exp--;
  460. }
  461. if (! digitseen) return;
  462. if (ss) *ss = (char *)s - 1;
  463. if (c == 'E' || c == 'e') {
  464. int exp1 = 0;
  465. int sign = 1;
  466. int exp_overflow = 0;
  467. switch(*s) {
  468. case '-':
  469. sign = -1;
  470. case '+':
  471. s++;
  472. }
  473. if (c = *s, isdigit(c)) {
  474. do {
  475. int tmp;
  476. exp1 = 10 * exp1 + (c - '0');
  477. if ((tmp = sign * exp1 + exp) > MAX_EXP ||
  478. tmp < -MAX_EXP) {
  479. exp_overflow = 1;
  480. }
  481. } while (c = *++s, isdigit(c));
  482. if (ss) *ss = (char *)s;
  483. }
  484. exp += sign * exp1;
  485. if (exp_overflow) {
  486. exp = sign * MAX_EXP;
  487. if (e->m1 != 0 || e->m2 != 0) errno = ERANGE;
  488. }
  489. }
  490. if (e->m1 == 0 && e->m2 == 0) return;
  491. e->exp = 63;
  492. while (! (e->m1 & 0x80000000)) {
  493. b64_sft(&(e->mantissa),-1);
  494. e->exp--;
  495. }
  496. add_exponent(e, exp);
  497. }
  498. #include <math.h>
  499. static
  500. ten_mult(struct EXTEND *e)
  501. {
  502. struct EXTEND e1 = *e;
  503. e1.exp++;
  504. e->exp += 3;
  505. add_ext(e, &e1, e);
  506. }
  507. #define NDIGITS 128
  508. #define NSIGNIFICANT 19
  509. char *
  510. _ext_str_cvt(struct EXTEND *e, int ndigit, int *decpt, int *sign, int ecvtflag)
  511. {
  512. /* Like cvt(), but for extended precision */
  513. static char buf[NDIGITS+1];
  514. struct EXTEND m;
  515. register char *p = buf;
  516. register char *pe;
  517. int findex = 0;
  518. if (ndigit < 0) ndigit = 0;
  519. if (ndigit > NDIGITS) ndigit = NDIGITS;
  520. pe = &buf[ndigit];
  521. buf[0] = '\0';
  522. *sign = 0;
  523. if (e->sign) {
  524. *sign = 1;
  525. e->sign = 0;
  526. }
  527. *decpt = 0;
  528. if (e->m1 != 0) {
  529. register struct EXTEND *pp = &big_ten_powers[1];
  530. while(cmp_ext(e,pp) >= 0) {
  531. pp++;
  532. findex = pp - big_ten_powers;
  533. if (findex >= BTP) break;
  534. }
  535. pp--;
  536. findex = pp - big_ten_powers;
  537. mul_ext(e,&r_big_ten_powers[findex],e);
  538. *decpt += findex * TP;
  539. pp = &ten_powers[1];
  540. while(pp < &ten_powers[TP] && cmp_ext(e, pp) >= 0) pp++;
  541. pp--;
  542. findex = pp - ten_powers;
  543. *decpt += findex;
  544. if (cmp_ext(e, &ten_powers[0]) < 0) {
  545. pp = &r_big_ten_powers[1];
  546. while(cmp_ext(e,pp) < 0) pp++;
  547. pp--;
  548. findex = pp - r_big_ten_powers;
  549. mul_ext(e, &big_ten_powers[findex], e);
  550. *decpt -= findex * TP;
  551. /* here, value >= 10 ** -28 */
  552. ten_mult(e);
  553. (*decpt)--;
  554. pp = &r_ten_powers[0];
  555. while(cmp_ext(e, pp) < 0) pp++;
  556. findex = pp - r_ten_powers;
  557. mul_ext(e, &ten_powers[findex], e);
  558. *decpt -= findex;
  559. findex = 0;
  560. }
  561. (*decpt)++; /* because now value in [1.0, 10.0) */
  562. }
  563. if (! ecvtflag) {
  564. /* for fcvt() we need ndigit digits behind the dot */
  565. pe += *decpt;
  566. if (pe > &buf[NDIGITS]) pe = &buf[NDIGITS];
  567. }
  568. m.exp = -62;
  569. m.sign = 0;
  570. m.m1 = 0xA0000000;
  571. m.m2 = 0;
  572. while (p <= pe) {
  573. struct EXTEND oneminm;
  574. if (p - pe > NSIGNIFICANT) {
  575. findex = 0;
  576. e->m1 = 0;
  577. }
  578. if (findex) {
  579. struct EXTEND tc, oldtc;
  580. int count = 0;
  581. oldtc.exp = 0;
  582. oldtc.sign = 0;
  583. oldtc.m1 = 0;
  584. oldtc.m2 = 0;
  585. tc = ten_powers[findex];
  586. while (cmp_ext(e, &tc) >= 0) {
  587. oldtc = tc;
  588. add_ext(&tc, &ten_powers[findex], &tc);
  589. count++;
  590. }
  591. *p++ = count + '0';
  592. oldtc.sign = 1;
  593. add_ext(e, &oldtc, e);
  594. findex--;
  595. continue;
  596. }
  597. if (e->m1) {
  598. m.sign = 1;
  599. add_ext(&ten_powers[0], &m, &oneminm);
  600. m.sign = 0;
  601. if (e->exp >= 0) {
  602. struct EXTEND x;
  603. x.m2 = 0; x.exp = e->exp;
  604. x.sign = 1;
  605. x.m1 = e->m1>>(31-e->exp);
  606. *p++ = (x.m1) + '0';
  607. x.m1 = x.m1 << (31-e->exp);
  608. add_ext(e, &x, e);
  609. }
  610. else *p++ = '0';
  611. /* Check that remainder is still significant */
  612. if (cmp_ext(&m, e) > 0 || cmp_ext(e, &oneminm) > 0) {
  613. if (e->m1 && e->exp >= -1) *(p-1) += 1;
  614. e->m1 = 0;
  615. continue;
  616. }
  617. ten_mult(&m);
  618. ten_mult(e);
  619. }
  620. else *p++ = '0';
  621. }
  622. if (pe >= buf) {
  623. p = pe;
  624. *p += 5; /* round of at the end */
  625. while (*p > '9') {
  626. *p = '0';
  627. if (p > buf) ++*--p;
  628. else {
  629. *p = '1';
  630. ++*decpt;
  631. if (! ecvtflag) {
  632. /* maybe add another digit at the end,
  633. because the point was shifted right
  634. */
  635. if (pe > buf) *pe = '0';
  636. pe++;
  637. }
  638. }
  639. }
  640. *pe = '\0';
  641. }
  642. return buf;
  643. }
  644. _dbl_ext_cvt(double value, struct EXTEND *e)
  645. {
  646. /* Convert double to extended
  647. */
  648. int exponent;
  649. value = frexp(value, &exponent);
  650. e->sign = value < 0.0;
  651. if (e->sign) value = -value;
  652. e->exp = exponent - 1;
  653. value *= 4294967296.0;
  654. e->m1 = value;
  655. value -= e->m1;
  656. value *= 4294967296.0;
  657. e->m2 = value;
  658. }
  659. static struct EXTEND max_d;
  660. double
  661. _ext_dbl_cvt(struct EXTEND *e)
  662. {
  663. /* Convert extended to double
  664. */
  665. double f;
  666. int sign = e->sign;
  667. e->sign = 0;
  668. if (e->m1 == 0 && e->m2 == 0) {
  669. return 0.0;
  670. }
  671. if (max_d.exp == 0) {
  672. _dbl_ext_cvt(DBL_MAX, &max_d);
  673. }
  674. if (cmp_ext(&max_d, e) < 0) {
  675. f = HUGE_VAL;
  676. errno = ERANGE;
  677. }
  678. else f = ldexp((double)e->m1*4294967296.0 + (double)e->m2, e->exp-63);
  679. if (sign) f = -f;
  680. if (f == 0.0 && (e->m1 != 0 || e->m2 != 0)) {
  681. errno = ERANGE;
  682. }
  683. return f;
  684. }