ext_comp.c 15 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688
  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. /* $Header$ */
  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 (sizeof(ten_powers)/sizeof(ten_powers[0]))
  406. #define BTP (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(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 = 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 = s - 1;
  463. if (c == 'E' || c == 'e') {
  464. int exp1 = 0;
  465. int sign = 1;
  466. switch(*s) {
  467. case '-':
  468. sign = -1;
  469. case '+':
  470. s++;
  471. }
  472. if (c = *s, isdigit(c)) {
  473. do {
  474. int tmp;
  475. exp1 = 10 * exp1 + (c - '0');
  476. if ((tmp = sign * exp1 + exp) > MAX_EXP ||
  477. tmp < -MAX_EXP) {
  478. errno = ERANGE;
  479. }
  480. } while (c = *++s, isdigit(c));
  481. if (ss) *ss = s;
  482. }
  483. exp += sign * exp1;
  484. if (errno == ERANGE) exp = sign * MAX_EXP;
  485. }
  486. if (e->m1 == 0 && e->m2 == 0) return;
  487. e->exp = 63;
  488. while (! (e->m1 & 0x80000000)) {
  489. b64_sft(&(e->mantissa),-1);
  490. e->exp--;
  491. }
  492. add_exponent(e, exp);
  493. }
  494. #include <math.h>
  495. #define NDIGITS 128
  496. char *
  497. _ext_str_cvt(struct EXTEND *e, int ndigit, int *decpt, int *sign, int ecvtflag)
  498. {
  499. /* Like cvt(), but for extended precision */
  500. static char buf[NDIGITS+1];
  501. register char *p = buf;
  502. register char *pe;
  503. if (ndigit < 0) ndigit = 0;
  504. if (ndigit > NDIGITS) ndigit = NDIGITS;
  505. pe = &buf[ndigit];
  506. buf[0] = '\0';
  507. *sign = 0;
  508. if (e->sign) {
  509. *sign = 1;
  510. e->sign = 0;
  511. }
  512. *decpt = 0;
  513. if (e->m1 != 0) {
  514. register struct EXTEND *pp = &big_ten_powers[1];
  515. while(cmp_ext(e,pp) >= 0) pp++;
  516. pp--;
  517. mul_ext(e,&r_big_ten_powers[pp-big_ten_powers],e);
  518. *decpt += (pp - big_ten_powers) * TP;
  519. pp = &ten_powers[1];
  520. while(pp < &ten_powers[TP] && cmp_ext(e, pp) >= 0) pp++;
  521. pp--;
  522. mul_ext(e, &r_ten_powers[pp-ten_powers], e);
  523. *decpt += pp - ten_powers;
  524. if (cmp_ext(e, &ten_powers[0]) < 0) {
  525. pp = &r_big_ten_powers[1];
  526. while(cmp_ext(e,pp) < 0) pp++;
  527. pp--;
  528. mul_ext(e, &big_ten_powers[pp - r_big_ten_powers], e);
  529. *decpt -= (pp - r_big_ten_powers) * TP;
  530. /* here, value >= 10 ** -28 */
  531. mul_ext(e, &ten_powers[1], e);
  532. (*decpt)--;
  533. pp = &r_ten_powers[0];
  534. while(cmp_ext(e, pp) < 0) pp++;
  535. mul_ext(e, &ten_powers[pp - r_ten_powers], e);
  536. *decpt -= pp - r_ten_powers;
  537. }
  538. (*decpt)++; /* because now value in [1.0, 10.0) */
  539. }
  540. if (! ecvtflag) {
  541. /* for fcvt() we need ndigit digits behind the dot */
  542. pe += *decpt;
  543. if (pe > &buf[NDIGITS]) pe = &buf[NDIGITS];
  544. }
  545. while (p <= pe) {
  546. if (e->exp >= 0 && e->m1 != 0) {
  547. struct EXTEND x;
  548. x.m2 = 0; x.exp = e->exp;
  549. x.sign = 1;
  550. x.m1 = e->m1>>(31-e->exp);
  551. *p++ = (x.m1) + '0';
  552. if (x.m1) {
  553. x.m1 = x.m1 << (31-e->exp);
  554. add_ext(e, &x, e);
  555. }
  556. }
  557. else *p++ = '0';
  558. if (e->m1) mul_ext(e, &ten_powers[1], e);
  559. }
  560. if (pe >= buf) {
  561. p = pe;
  562. *p += 5; /* round of at the end */
  563. while (*p > '9') {
  564. *p = '0';
  565. if (p > buf) ++*--p;
  566. else {
  567. *p = '1';
  568. ++*decpt;
  569. if (! ecvtflag) {
  570. /* maybe add another digit at the end,
  571. because the point was shifted right
  572. */
  573. if (pe > buf) *pe = '0';
  574. pe++;
  575. }
  576. }
  577. }
  578. *pe = '\0';
  579. }
  580. return buf;
  581. }
  582. _dbl_ext_cvt(double value, struct EXTEND *e)
  583. {
  584. /* Convert double to extended
  585. */
  586. int exponent;
  587. register int i;
  588. value = frexp(value, &exponent);
  589. e->sign = value < 0.0;
  590. if (e->sign) value = -value;
  591. e->exp = exponent - 1;
  592. e->m1 = 0;
  593. e->m2 = 0;
  594. for (i = 64; i > 0 && value != 0; i--) {
  595. double ipart;
  596. b64_sft(&(e->mantissa),-1);
  597. value = modf(2.0*value, &ipart);
  598. if (ipart) {
  599. e->m2 |= 1;
  600. }
  601. }
  602. if (i > 0) b64_sft(&(e->mantissa),-i);
  603. }
  604. static struct EXTEND max_d;
  605. static struct EXTEND min_d;
  606. double
  607. _ext_dbl_cvt(struct EXTEND *e)
  608. {
  609. /* Convert extended to double
  610. */
  611. double f;
  612. int sign = e->sign;
  613. e->sign = 0;
  614. if (e->m1 == 0 && e->m2 == 0) {
  615. return 0.0;
  616. }
  617. if (max_d.exp == 0) {
  618. _dbl_ext_cvt(DBL_MAX, &max_d);
  619. _dbl_ext_cvt(DBL_MIN, &min_d);
  620. }
  621. if (cmp_ext(e, &min_d) < 0) {
  622. f = 0.0;
  623. errno = ERANGE;
  624. }
  625. else if (cmp_ext(&max_d, e) < 0) {
  626. f = HUGE_VAL;
  627. errno = ERANGE;
  628. }
  629. else f = ldexp(ldexp((double)e->m1, 32) + (double)e->m2, e->exp-63);
  630. if (sign) f = -f;
  631. return f;
  632. }