1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969798991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157167177187197207217227237247257267277287297307317327337347357367377387397407417427437447457467477487497507517527537547557567577587597607617627637647657667677687697707717727737747757767777787797807817827837847857867877887897907917927937947957967977987998008018028038048058068078088098108118128138148158168178188198208218228238248258268278288298308318328338348358368378388398408418428438448458468478488498508518528538548558568578588598608618628638648658668678688698708718728738748758768778788798808818828838848858868878888898908918928938948958968978988999009019029039049059069079089099109119129139149159169179189199209219229239249259269279289299309319329339349359369379389399409419429439449459469479489499509519529539549559569579589599609619629639649659669679689699709719729739749759769779789799809819829839849859869879889899909919929939949959969979989991000100110021003100410051006100710081009101010111012101310141015101610171018101910201021102210231024102510261027102810291030103110321033103410351036103710381039104010411042104310441045104610471048104910501051105210531054105510561057105810591060106110621063106410651066106710681069107010711072107310741075107610771078107910801081108210831084108510861087108810891090109110921093109410951096109710981099110011011102110311041105110611071108110911101111111211131114111511161117111811191120112111221123112411251126112711281129113011311132113311341135113611371138113911401141114211431144114511461147114811491150115111521153115411551156115711581159116011611162116311641165116611671168116911701171117211731174117511761177117811791180118111821183118411851186118711881189119011911192119311941195119611971198119912001201120212031204120512061207120812091210121112121213121412151216121712181219122012211222122312241225122612271228122912301231123212331234123512361237123812391240124112421243124412451246124712481249125012511252125312541255125612571258125912601261126212631264126512661267126812691270127112721273127412751276127712781279128012811282128312841285128612871288128912901291129212931294129512961297129812991300130113021303130413051306130713081309131013111312131313141315131613171318131913201321132213231324132513261327132813291330133113321333133413351336133713381339134013411342134313441345134613471348134913501351135213531354135513561357135813591360136113621363136413651366136713681369137013711372137313741375137613771378137913801381138213831384138513861387138813891390139113921393139413951396139713981399140014011402140314041405140614071408140914101411141214131414141514161417141814191420142114221423142414251426142714281429143014311432143314341435143614371438143914401441144214431444144514461447144814491450145114521453145414551456145714581459146014611462146314641465146614671468146914701471147214731474147514761477147814791480148114821483148414851486148714881489149014911492149314941495149614971498149915001501150215031504150515061507150815091510151115121513151415151516151715181519152015211522152315241525152615271528152915301531153215331534153515361537153815391540154115421543154415451546154715481549155015511552155315541555155615571558155915601561156215631564156515661567156815691570157115721573157415751576157715781579158015811582158315841585158615871588158915901591159215931594159515961597159815991600160116021603160416051606160716081609161016111612161316141615161616171618161916201621162216231624162516261627162816291630163116321633163416351636163716381639164016411642164316441645164616471648164916501651165216531654165516561657165816591660166116621663166416651666166716681669167016711672167316741675167616771678167916801681168216831684168516861687168816891690169116921693169416951696169716981699170017011702170317041705170617071708170917101711171217131714171517161717171817191720172117221723172417251726172717281729173017311732173317341735173617371738173917401741174217431744174517461747174817491750175117521753175417551756175717581759176017611762176317641765176617671768176917701771177217731774177517761777177817791780178117821783178417851786178717881789179017911792179317941795179617971798179918001801180218031804180518061807180818091810181118121813181418151816 |
- /* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
- /* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
- #include "lib9.h"
- #ifdef __APPLE__
- #pragma clang diagnostic ignored "-Wlogical-op-parentheses"
- #pragma clang diagnostic ignored "-Wparentheses"
- #endif
- #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
- #define FREE_DTOA_LOCK(n) /*nothing*/
- /* let's provide reasonable defaults for usual implementation of IEEE f.p. */
- #ifndef DBL_DIG
- #define DBL_DIG 15
- #endif
- #ifndef DBL_MAX_10_EXP
- #define DBL_MAX_10_EXP 308
- #endif
- #ifndef DBL_MAX_EXP
- #define DBL_MAX_EXP 1024
- #endif
- #ifndef FLT_RADIX
- #define FLT_RADIX 2
- #endif
- #ifndef FLT_ROUNDS
- #define FLT_ROUNDS 1
- #endif
- #ifndef Storeinc
- #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
- #endif
- #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
- #ifdef USE_FPdbleword
- #define word0(x) ((FPdbleword*)&x)->hi
- #define word1(x) ((FPdbleword*)&x)->lo
- #else
- #ifdef __LITTLE_ENDIAN
- #define word0(x) ((unsigned long *)&x)[1]
- #define word1(x) ((unsigned long *)&x)[0]
- #else
- #define word0(x) ((unsigned long *)&x)[0]
- #define word1(x) ((unsigned long *)&x)[1]
- #endif
- #endif
- /* #define P DBL_MANT_DIG */
- /* Ten_pmax = floor(P*log(2)/log(5)) */
- /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
- /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
- /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
- #define Exp_shift 20
- #define Exp_shift1 20
- #define Exp_msk1 0x100000
- #define Exp_msk11 0x100000
- #define Exp_mask 0x7ff00000
- #define P 53
- #define Bias 1023
- #define Emin (-1022)
- #define Exp_1 0x3ff00000
- #define Exp_11 0x3ff00000
- #define Ebits 11
- #define Frac_mask 0xfffff
- #define Frac_mask1 0xfffff
- #define Ten_pmax 22
- #define Bletch 0x10
- #define Bndry_mask 0xfffff
- #define Bndry_mask1 0xfffff
- #define LSB 1
- #define Sign_bit 0x80000000
- #define Log2P 1
- #define Tiny0 0
- #define Tiny1 1
- #define Quick_max 14
- #define Int_max 14
- #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
- #define Avoid_Underflow
- #define rounded_product(a,b) a *= b
- #define rounded_quotient(a,b) a /= b
- #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
- #define Big1 0xffffffff
- #define Kmax 15
- struct
- Bigint {
- struct Bigint *next;
- int k, maxwds, sign, wds;
- unsigned long x[1];
- };
- typedef struct Bigint Bigint;
- static Bigint *freelist[Kmax+1];
- static Bigint *
- Balloc(int k)
- {
- int x;
- Bigint * rv;
- ACQUIRE_DTOA_LOCK(0);
- if (rv = freelist[k]) {
- freelist[k] = rv->next;
- } else {
- x = 1 << k;
- rv = (Bigint * )malloc(sizeof(Bigint) + (x - 1) * sizeof(unsigned long));
- if(rv == nil)
- return nil;
- rv->k = k;
- rv->maxwds = x;
- }
- FREE_DTOA_LOCK(0);
- rv->sign = rv->wds = 0;
- return rv;
- }
- static void
- Bfree(Bigint *v)
- {
- if (v) {
- ACQUIRE_DTOA_LOCK(0);
- v->next = freelist[v->k];
- freelist[v->k] = v;
- FREE_DTOA_LOCK(0);
- }
- }
- #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
- y->wds*sizeof(long) + 2*sizeof(int))
- static Bigint *
- multadd(Bigint *b, int m, int a) /* multiply by m and add a */
- {
- int i, wds;
- unsigned long * x, y;
- unsigned long xi, z;
- Bigint * b1;
- wds = b->wds;
- x = b->x;
- i = 0;
- do {
- xi = *x;
- y = (xi & 0xffff) * m + a;
- z = (xi >> 16) * m + (y >> 16);
- a = (int)(z >> 16);
- *x++ = (z << 16) + (y & 0xffff);
- } while (++i < wds);
- if (a) {
- if (wds >= b->maxwds) {
- b1 = Balloc(b->k + 1);
- Bcopy(b1, b);
- Bfree(b);
- b = b1;
- }
- b->x[wds++] = a;
- b->wds = wds;
- }
- return b;
- }
- static Bigint *
- s2b(const char *s, int nd0, int nd, unsigned long y9)
- {
- Bigint * b;
- int i, k;
- long x, y;
- x = (nd + 8) / 9;
- for (k = 0, y = 1; x > y; y <<= 1, k++)
- ;
- b = Balloc(k);
- b->x[0] = y9;
- b->wds = 1;
- i = 9;
- if (9 < nd0) {
- s += 9;
- do
- b = multadd(b, 10, *s++ - '0');
- while (++i < nd0);
- s++;
- } else
- s += 10;
- for (; i < nd; i++)
- b = multadd(b, 10, *s++ - '0');
- return b;
- }
- static int
- hi0bits(register unsigned long x)
- {
- register int k = 0;
- if (!(x & 0xffff0000)) {
- k = 16;
- x <<= 16;
- }
- if (!(x & 0xff000000)) {
- k += 8;
- x <<= 8;
- }
- if (!(x & 0xf0000000)) {
- k += 4;
- x <<= 4;
- }
- if (!(x & 0xc0000000)) {
- k += 2;
- x <<= 2;
- }
- if (!(x & 0x80000000)) {
- k++;
- if (!(x & 0x40000000))
- return 32;
- }
- return k;
- }
- static int
- lo0bits(unsigned long *y)
- {
- register int k;
- register unsigned long x = *y;
- if (x & 7) {
- if (x & 1)
- return 0;
- if (x & 2) {
- *y = x >> 1;
- return 1;
- }
- *y = x >> 2;
- return 2;
- }
- k = 0;
- if (!(x & 0xffff)) {
- k = 16;
- x >>= 16;
- }
- if (!(x & 0xff)) {
- k += 8;
- x >>= 8;
- }
- if (!(x & 0xf)) {
- k += 4;
- x >>= 4;
- }
- if (!(x & 0x3)) {
- k += 2;
- x >>= 2;
- }
- if (!(x & 1)) {
- k++;
- x >>= 1;
- if (!x & 1)
- return 32;
- }
- *y = x;
- return k;
- }
- static Bigint *
- i2b(int i)
- {
- Bigint * b;
- b = Balloc(1);
- b->x[0] = i;
- b->wds = 1;
- return b;
- }
- static Bigint *
- mult(Bigint *a, Bigint *b)
- {
- Bigint * c;
- int k, wa, wb, wc;
- unsigned long carry, y, z;
- unsigned long * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
- unsigned long z2;
- if (a->wds < b->wds) {
- c = a;
- a = b;
- b = c;
- }
- k = a->k;
- wa = a->wds;
- wb = b->wds;
- wc = wa + wb;
- if (wc > a->maxwds)
- k++;
- c = Balloc(k);
- for (x = c->x, xa = x + wc; x < xa; x++)
- *x = 0;
- xa = a->x;
- xae = xa + wa;
- xb = b->x;
- xbe = xb + wb;
- xc0 = c->x;
- for (; xb < xbe; xb++, xc0++) {
- if (y = *xb & 0xffff) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
- carry = z >> 16;
- z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
- carry = z2 >> 16;
- Storeinc(xc, z2, z);
- } while (x < xae);
- *xc = carry;
- }
- if (y = *xb >> 16) {
- x = xa;
- xc = xc0;
- carry = 0;
- z2 = *xc;
- do {
- z = (*x & 0xffff) * y + (*xc >> 16) + carry;
- carry = z >> 16;
- Storeinc(xc, z, z2);
- z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
- carry = z2 >> 16;
- } while (x < xae);
- *xc = z2;
- }
- }
- for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc)
- ;
- c->wds = wc;
- return c;
- }
- static Bigint *p5s;
- static Bigint *
- pow5mult(Bigint *b, int k)
- {
- Bigint * b1, *p5, *p51;
- int i;
- static int p05[3] = {
- 5, 25, 125 };
- if (i = k & 3)
- b = multadd(b, p05[i-1], 0);
- if (!(k >>= 2))
- return b;
- if (!(p5 = p5s)) {
- /* first time */
- ACQUIRE_DTOA_LOCK(1);
- if (!(p5 = p5s)) {
- p5 = p5s = i2b(625);
- p5->next = 0;
- }
- FREE_DTOA_LOCK(1);
- }
- for (; ; ) {
- if (k & 1) {
- b1 = mult(b, p5);
- Bfree(b);
- b = b1;
- }
- if (!(k >>= 1))
- break;
- if (!(p51 = p5->next)) {
- ACQUIRE_DTOA_LOCK(1);
- if (!(p51 = p5->next)) {
- p51 = p5->next = mult(p5, p5);
- p51->next = 0;
- }
- FREE_DTOA_LOCK(1);
- }
- p5 = p51;
- }
- return b;
- }
- static Bigint *
- lshift(Bigint *b, int k)
- {
- int i, k1, n, n1;
- Bigint * b1;
- unsigned long * x, *x1, *xe, z;
- n = k >> 5;
- k1 = b->k;
- n1 = n + b->wds + 1;
- for (i = b->maxwds; n1 > i; i <<= 1)
- k1++;
- b1 = Balloc(k1);
- x1 = b1->x;
- for (i = 0; i < n; i++)
- *x1++ = 0;
- x = b->x;
- xe = x + b->wds;
- if (k &= 0x1f) {
- k1 = 32 - k;
- z = 0;
- do {
- *x1++ = *x << k | z;
- z = *x++ >> k1;
- } while (x < xe);
- if (*x1 = z)
- ++n1;
- } else
- do
- *x1++ = *x++;
- while (x < xe);
- b1->wds = n1 - 1;
- Bfree(b);
- return b1;
- }
- static int
- cmp(Bigint *a, Bigint *b)
- {
- unsigned long * xa, *xa0, *xb, *xb0;
- int i, j;
- i = a->wds;
- j = b->wds;
- if (i -= j)
- return i;
- xa0 = a->x;
- xa = xa0 + j;
- xb0 = b->x;
- xb = xb0 + j;
- for (; ; ) {
- if (*--xa != *--xb)
- return * xa < *xb ? -1 : 1;
- if (xa <= xa0)
- break;
- }
- return 0;
- }
- static Bigint *
- diff(Bigint *a, Bigint *b)
- {
- Bigint * c;
- int i, wa, wb;
- long borrow, y; /* We need signed shifts here. */
- unsigned long * xa, *xae, *xb, *xbe, *xc;
- long z;
- i = cmp(a, b);
- if (!i) {
- c = Balloc(0);
- c->wds = 1;
- c->x[0] = 0;
- return c;
- }
- if (i < 0) {
- c = a;
- a = b;
- b = c;
- i = 1;
- } else
- i = 0;
- c = Balloc(a->k);
- c->sign = i;
- wa = a->wds;
- xa = a->x;
- xae = xa + wa;
- wb = b->wds;
- xb = b->x;
- xbe = xb + wb;
- xc = c->x;
- borrow = 0;
- do {
- y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(xc, z, y);
- } while (xb < xbe);
- while (xa < xae) {
- y = (*xa & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*xa++ >> 16) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(xc, z, y);
- }
- while (!*--xc)
- wa--;
- c->wds = wa;
- return c;
- }
- static double
- ulp(double x)
- {
- register long L;
- double a;
- L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
- #ifndef Sudden_Underflow
- if (L > 0) {
- #endif
- word0(a) = L;
- word1(a) = 0;
- #ifndef Sudden_Underflow
- } else {
- L = -L >> Exp_shift;
- if (L < Exp_shift) {
- word0(a) = 0x80000 >> L;
- word1(a) = 0;
- } else {
- word0(a) = 0;
- L -= Exp_shift;
- word1(a) = L >= 31 ? 1 : 1 << 31 - L;
- }
- }
- #endif
- return a;
- }
- static double
- b2d(Bigint *a, int *e)
- {
- unsigned long * xa, *xa0, w, y, z;
- int k;
- double d;
- #define d0 word0(d)
- #define d1 word1(d)
- xa0 = a->x;
- xa = xa0 + a->wds;
- y = *--xa;
- k = hi0bits(y);
- *e = 32 - k;
- if (k < Ebits) {
- d0 = Exp_1 | y >> Ebits - k;
- w = xa > xa0 ? *--xa : 0;
- d1 = y << (32 - Ebits) + k | w >> Ebits - k;
- goto ret_d;
- }
- z = xa > xa0 ? *--xa : 0;
- if (k -= Ebits) {
- d0 = Exp_1 | y << k | z >> 32 - k;
- y = xa > xa0 ? *--xa : 0;
- d1 = z << k | y >> 32 - k;
- } else {
- d0 = Exp_1 | y;
- d1 = z;
- }
- ret_d:
- #undef d0
- #undef d1
- return d;
- }
- static Bigint *
- d2b(double d, int *e, int *bits)
- {
- Bigint * b;
- int de, i, k;
- unsigned long * x, y, z;
- #define d0 word0(d)
- #define d1 word1(d)
- b = Balloc(1);
- x = b->x;
- z = d0 & Frac_mask;
- d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
- #ifdef Sudden_Underflow
- de = (int)(d0 >> Exp_shift);
- z |= Exp_msk11;
- #else
- if (de = (int)(d0 >> Exp_shift))
- z |= Exp_msk1;
- #endif
- if (y = d1) {
- if (k = lo0bits(&y)) {
- x[0] = y | z << 32 - k;
- z >>= k;
- } else
- x[0] = y;
- i = b->wds = (x[1] = z) ? 2 : 1;
- } else {
- k = lo0bits(&z);
- x[0] = z;
- i = b->wds = 1;
- k += 32;
- }
- #ifndef Sudden_Underflow
- if (de) {
- #endif
- *e = de - Bias - (P - 1) + k;
- *bits = P - k;
- #ifndef Sudden_Underflow
- } else {
- *e = de - Bias - (P - 1) + 1 + k;
- *bits = 32 * i - hi0bits(x[i-1]);
- }
- #endif
- return b;
- }
- #undef d0
- #undef d1
- static double
- ratio(Bigint *a, Bigint *b)
- {
- double da, db;
- int k, ka, kb;
- da = b2d(a, &ka);
- db = b2d(b, &kb);
- k = ka - kb + 32 * (a->wds - b->wds);
- if (k > 0)
- word0(da) += k * Exp_msk1;
- else {
- k = -k;
- word0(db) += k * Exp_msk1;
- }
- return da / db;
- }
- static const double
- tens[] = {
- 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
- 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
- 1e20, 1e21, 1e22
- };
- static const double
- bigtens[] = {
- 1e16, 1e32, 1e64, 1e128, 1e256 };
- static const double tinytens[] = {
- 1e-16, 1e-32, 1e-64, 1e-128,
- 9007199254740992.e-256
- };
- /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
- /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
- #define Scale_Bit 0x10
- #define n_bigtens 5
- #define NAN_WORD0 0x7ff80000
- #define NAN_WORD1 0
- static int
- match(const char **sp, char *t)
- {
- int c, d;
- const char * s = *sp;
- while (d = *t++) {
- if ((c = *++s) >= 'A' && c <= 'Z')
- c += 'a' - 'A';
- if (c != d)
- return 0;
- }
- *sp = s + 1;
- return 1;
- }
- double
- strtod(const char *s00, char **se)
- {
- int scale;
- int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
- e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
- const char * s, *s0, *s1;
- double aadj, aadj1, adj, rv, rv0;
- long L;
- unsigned long y, z;
- Bigint * bb, *bb1, *bd, *bd0, *bs, *delta;
- sign = nz0 = nz = 0;
- rv = 0.;
- for (s = s00; ; s++)
- switch (*s) {
- case '-':
- sign = 1;
- /* no break */
- case '+':
- if (*++s)
- goto break2;
- /* no break */
- case 0:
- s = s00;
- goto ret;
- case '\t':
- case '\n':
- case '\v':
- case '\f':
- case '\r':
- case ' ':
- continue;
- default:
- goto break2;
- }
- break2:
- if (*s == '0') {
- nz0 = 1;
- while (*++s == '0')
- ;
- if (!*s)
- goto ret;
- }
- s0 = s;
- y = z = 0;
- for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
- if (nd < 9)
- y = 10 * y + c - '0';
- else if (nd < 16)
- z = 10 * z + c - '0';
- nd0 = nd;
- if (c == '.') {
- c = *++s;
- if (!nd) {
- for (; c == '0'; c = *++s)
- nz++;
- if (c > '0' && c <= '9') {
- s0 = s;
- nf += nz;
- nz = 0;
- goto have_dig;
- }
- goto dig_done;
- }
- for (; c >= '0' && c <= '9'; c = *++s) {
- have_dig:
- nz++;
- if (c -= '0') {
- nf += nz;
- for (i = 1; i < nz; i++)
- if (nd++ < 9)
- y *= 10;
- else if (nd <= DBL_DIG + 1)
- z *= 10;
- if (nd++ < 9)
- y = 10 * y + c;
- else if (nd <= DBL_DIG + 1)
- z = 10 * z + c;
- nz = 0;
- }
- }
- }
- dig_done:
- e = 0;
- if (c == 'e' || c == 'E') {
- if (!nd && !nz && !nz0) {
- s = s00;
- goto ret;
- }
- s00 = s;
- esign = 0;
- switch (c = *++s) {
- case '-':
- esign = 1;
- case '+':
- c = *++s;
- }
- if (c >= '0' && c <= '9') {
- while (c == '0')
- c = *++s;
- if (c > '0' && c <= '9') {
- L = c - '0';
- s1 = s;
- while ((c = *++s) >= '0' && c <= '9')
- L = 10 * L + c - '0';
- if (s - s1 > 8 || L > 19999)
- /* Avoid confusion from exponents
- * so large that e might overflow.
- */
- e = 19999; /* safe for 16 bit ints */
- else
- e = (int)L;
- if (esign)
- e = -e;
- } else
- e = 0;
- } else
- s = s00;
- }
- if (!nd) {
- if (!nz && !nz0) {
- /* Check for Nan and Infinity */
- switch (c) {
- case 'i':
- case 'I':
- if (match(&s, "nfinity")) {
- word0(rv) = 0x7ff00000;
- word1(rv) = 0;
- goto ret;
- }
- break;
- case 'n':
- case 'N':
- if (match(&s, "an")) {
- word0(rv) = NAN_WORD0;
- word1(rv) = NAN_WORD1;
- goto ret;
- }
- }
- s = s00;
- }
- goto ret;
- }
- e1 = e -= nf;
- /* Now we have nd0 digits, starting at s0, followed by a
- * decimal point, followed by nd-nd0 digits. The number we're
- * after is the integer represented by those digits times
- * 10**e */
- if (!nd0)
- nd0 = nd;
- k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
- rv = y;
- if (k > 9)
- rv = tens[k - 9] * rv + z;
- bd0 = 0;
- if (nd <= DBL_DIG
- && FLT_ROUNDS == 1
- ) {
- if (!e)
- goto ret;
- if (e > 0) {
- if (e <= Ten_pmax) {
- /* rv = */ rounded_product(rv, tens[e]);
- goto ret;
- }
- i = DBL_DIG - nd;
- if (e <= Ten_pmax + i) {
- /* A fancier test would sometimes let us do
- * this for larger i values.
- */
- e -= i;
- rv *= tens[i];
- /* rv = */ rounded_product(rv, tens[e]);
- goto ret;
- }
- } else if (e >= -Ten_pmax) {
- /* rv = */ rounded_quotient(rv, tens[-e]);
- goto ret;
- }
- }
- e1 += nd - k;
- scale = 0;
- /* Get starting approximation = rv * 10**e1 */
- if (e1 > 0) {
- if (i = e1 & 15)
- rv *= tens[i];
- if (e1 &= ~15) {
- if (e1 > DBL_MAX_10_EXP) {
- ovfl:
- /* Can't trust HUGE_VAL */
- word0(rv) = Exp_mask;
- word1(rv) = 0;
- if (bd0)
- goto retfree;
- goto ret;
- }
- if (e1 >>= 4) {
- for (j = 0; e1 > 1; j++, e1 >>= 1)
- if (e1 & 1)
- rv *= bigtens[j];
- /* The last multiplication could overflow. */
- word0(rv) -= P * Exp_msk1;
- rv *= bigtens[j];
- if ((z = word0(rv) & Exp_mask)
- > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
- goto ovfl;
- if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
- /* set to largest number */
- /* (Can't trust DBL_MAX) */
- word0(rv) = Big0;
- word1(rv) = Big1;
- } else
- word0(rv) += P * Exp_msk1;
- }
- }
- } else if (e1 < 0) {
- e1 = -e1;
- if (i = e1 & 15)
- rv /= tens[i];
- if (e1 &= ~15) {
- e1 >>= 4;
- if (e1 >= 1 << n_bigtens)
- goto undfl;
- if (e1 & Scale_Bit)
- scale = P;
- for (j = 0; e1 > 0; j++, e1 >>= 1)
- if (e1 & 1)
- rv *= tinytens[j];
- if (!rv) {
- undfl:
- rv = 0.;
- if (bd0)
- goto retfree;
- goto ret;
- }
- }
- }
- /* Now the hard part -- adjusting rv to the correct value.*/
- /* Put digits into bd: true value = bd * 10^e */
- bd0 = s2b(s0, nd0, nd, y);
- for (; ; ) {
- bd = Balloc(bd0->k);
- Bcopy(bd, bd0);
- bb = d2b(rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
- bs = i2b(1);
- if (e >= 0) {
- bb2 = bb5 = 0;
- bd2 = bd5 = e;
- } else {
- bb2 = bb5 = -e;
- bd2 = bd5 = 0;
- }
- if (bbe >= 0)
- bb2 += bbe;
- else
- bd2 -= bbe;
- bs2 = bb2;
- #ifdef Sudden_Underflow
- j = P + 1 - bbbits;
- #else
- i = bbe + bbbits - 1; /* logb(rv) */
- if (i < Emin) /* denormal */
- j = bbe + (P - Emin);
- else
- j = P + 1 - bbbits;
- #endif
- bb2 += j;
- bd2 += j;
- bd2 += scale;
- i = bb2 < bd2 ? bb2 : bd2;
- if (i > bs2)
- i = bs2;
- if (i > 0) {
- bb2 -= i;
- bd2 -= i;
- bs2 -= i;
- }
- if (bb5 > 0) {
- bs = pow5mult(bs, bb5);
- bb1 = mult(bs, bb);
- Bfree(bb);
- bb = bb1;
- }
- if (bb2 > 0)
- bb = lshift(bb, bb2);
- if (bd5 > 0)
- bd = pow5mult(bd, bd5);
- if (bd2 > 0)
- bd = lshift(bd, bd2);
- if (bs2 > 0)
- bs = lshift(bs, bs2);
- delta = diff(bb, bd);
- dsign = delta->sign;
- delta->sign = 0;
- i = cmp(delta, bs);
- if (i < 0) {
- /* Error is less than half an ulp -- check for
- * special case of mantissa a power of two.
- */
- if (dsign || word1(rv) || word0(rv) & Bndry_mask
- || (word0(rv) & Exp_mask) <= Exp_msk1
- ) {
- if (!delta->x[0] && delta->wds == 1)
- dsign = 2;
- break;
- }
- delta = lshift(delta, Log2P);
- if (cmp(delta, bs) > 0)
- goto drop_down;
- break;
- }
- if (i == 0) {
- /* exactly half-way between */
- if (dsign) {
- if ((word0(rv) & Bndry_mask1) == Bndry_mask1
- && word1(rv) == 0xffffffff) {
- /*boundary case -- increment exponent*/
- word0(rv) = (word0(rv) & Exp_mask)
- + Exp_msk1
- ;
- word1(rv) = 0;
- dsign = 0;
- break;
- }
- } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
- dsign = 2;
- drop_down:
- /* boundary case -- decrement exponent */
- #ifdef Sudden_Underflow
- L = word0(rv) & Exp_mask;
- if (L <= Exp_msk1)
- goto undfl;
- L -= Exp_msk1;
- #else
- L = (word0(rv) & Exp_mask) - Exp_msk1;
- #endif
- word0(rv) = L | Bndry_mask1;
- word1(rv) = 0xffffffff;
- break;
- }
- if (!(word1(rv) & LSB))
- break;
- if (dsign)
- rv += ulp(rv);
- else {
- rv -= ulp(rv);
- #ifndef Sudden_Underflow
- if (!rv)
- goto undfl;
- #endif
- }
- dsign = 1 - dsign;
- break;
- }
- if ((aadj = ratio(delta, bs)) <= 2.) {
- if (dsign)
- aadj = aadj1 = 1.;
- else if (word1(rv) || word0(rv) & Bndry_mask) {
- #ifndef Sudden_Underflow
- if (word1(rv) == Tiny1 && !word0(rv))
- goto undfl;
- #endif
- aadj = 1.;
- aadj1 = -1.;
- } else {
- /* special case -- power of FLT_RADIX to be */
- /* rounded down... */
- if (aadj < 2. / FLT_RADIX)
- aadj = 1. / FLT_RADIX;
- else
- aadj *= 0.5;
- aadj1 = -aadj;
- }
- } else {
- aadj *= 0.5;
- aadj1 = dsign ? aadj : -aadj;
- if (FLT_ROUNDS == 0)
- aadj1 += 0.5;
- }
- y = word0(rv) & Exp_mask;
- /* Check for overflow */
- if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
- rv0 = rv;
- word0(rv) -= P * Exp_msk1;
- adj = aadj1 * ulp(rv);
- rv += adj;
- if ((word0(rv) & Exp_mask) >=
- Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
- if (word0(rv0) == Big0 && word1(rv0) == Big1)
- goto ovfl;
- word0(rv) = Big0;
- word1(rv) = Big1;
- goto cont;
- } else
- word0(rv) += P * Exp_msk1;
- } else {
- #ifdef Sudden_Underflow
- if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
- rv0 = rv;
- word0(rv) += P * Exp_msk1;
- adj = aadj1 * ulp(rv);
- rv += adj;
- if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
- if (word0(rv0) == Tiny0
- && word1(rv0) == Tiny1)
- goto undfl;
- word0(rv) = Tiny0;
- word1(rv) = Tiny1;
- goto cont;
- } else
- word0(rv) -= P * Exp_msk1;
- } else {
- adj = aadj1 * ulp(rv);
- rv += adj;
- }
- #else
- /* Compute adj so that the IEEE rounding rules will
- * correctly round rv + adj in some half-way cases.
- * If rv * ulp(rv) is denormalized (i.e.,
- * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
- * trouble from bits lost to denormalization;
- * example: 1.2e-307 .
- */
- if (y <= (P - 1) * Exp_msk1 && aadj >= 1.) {
- aadj1 = (double)(int)(aadj + 0.5);
- if (!dsign)
- aadj1 = -aadj1;
- }
- adj = aadj1 * ulp(rv);
- rv += adj;
- #endif
- }
- z = word0(rv) & Exp_mask;
- if (!scale)
- if (y == z) {
- /* Can we stop now? */
- L = aadj;
- aadj -= L;
- /* The tolerances below are conservative. */
- if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
- if (aadj < .4999999 || aadj > .5000001)
- break;
- } else if (aadj < .4999999 / FLT_RADIX)
- break;
- }
- cont:
- Bfree(bb);
- Bfree(bd);
- Bfree(bs);
- Bfree(delta);
- }
- if (scale) {
- if ((word0(rv) & Exp_mask) <= P * Exp_msk1
- && word1(rv) & 1
- && dsign != 2)
- if (dsign)
- rv += ulp(rv);
- else
- word1(rv) &= ~1;
- word0(rv0) = Exp_1 - P * Exp_msk1;
- word1(rv0) = 0;
- rv *= rv0;
- }
- retfree:
- Bfree(bb);
- Bfree(bd);
- Bfree(bs);
- Bfree(bd0);
- Bfree(delta);
- ret:
- if (se)
- *se = (char *)s;
- return sign ? -rv : rv;
- }
- static int
- quorem(Bigint *b, Bigint *S)
- {
- int n;
- long borrow, y;
- unsigned long carry, q, ys;
- unsigned long * bx, *bxe, *sx, *sxe;
- long z;
- unsigned long si, zs;
- n = S->wds;
- if (b->wds < n)
- return 0;
- sx = S->x;
- sxe = sx + --n;
- bx = b->x;
- bxe = bx + n;
- q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
- if (q) {
- borrow = 0;
- carry = 0;
- do {
- si = *sx++;
- ys = (si & 0xffff) * q + carry;
- zs = (si >> 16) * q + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(bx, z, y);
- } while (sx <= sxe);
- if (!*bxe) {
- bx = b->x;
- while (--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- if (cmp(b, S) >= 0) {
- q++;
- borrow = 0;
- carry = 0;
- bx = b->x;
- sx = S->x;
- do {
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend(borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend(borrow, z);
- Storeinc(bx, z, y);
- } while (sx <= sxe);
- bx = b->x;
- bxe = bx + n;
- if (!*bxe) {
- while (--bxe > bx && !*bxe)
- --n;
- b->wds = n;
- }
- }
- return q;
- }
- static char *
- rv_alloc(int i)
- {
- int j, k, *r;
- j = sizeof(unsigned long);
- for (k = 0;
- sizeof(Bigint) - sizeof(unsigned long) - sizeof(int) + j <= i;
- j <<= 1)
- k++;
- r = (int * )Balloc(k);
- *r = k;
- return
- (char *)(r + 1);
- }
- static char *
- nrv_alloc(char *s, char **rve, int n)
- {
- char *rv, *t;
- t = rv = rv_alloc(n);
- while (*t = *s++)
- t++;
- if (rve)
- *rve = t;
- return rv;
- }
- /* freedtoa(s) must be used to free values s returned by dtoa
- * when MULTIPLE_THREADS is #defined. It should be used in all cases,
- * but for consistency with earlier versions of dtoa, it is optional
- * when MULTIPLE_THREADS is not defined.
- */
- void
- freedtoa(char *s)
- {
- Bigint * b = (Bigint * )((int *)s - 1);
- b->maxwds = 1 << (b->k = *(int * )b);
- Bfree(b);
- }
- /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
- *
- * Inspired by "How to Print Floating-Point Numbers Accurately" by
- * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
- *
- * Modifications:
- * 1. Rather than iterating, we use a simple numeric overestimate
- * to determine k = floor(log10(d)). We scale relevant
- * quantities using O(log2(k)) rather than O(k) multiplications.
- * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
- * try to generate digits strictly left to right. Instead, we
- * compute with fewer bits and propagate the carry if necessary
- * when rounding the final digit up. This is often faster.
- * 3. Under the assumption that input will be rounded nearest,
- * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
- * That is, we allow equality in stopping tests when the
- * round-nearest rule will give the same floating-point value
- * as would satisfaction of the stopping test with strict
- * inequality.
- * 4. We remove common factors of powers of 2 from relevant
- * quantities.
- * 5. When converting floating-point integers less than 1e16,
- * we use floating-point arithmetic rather than resorting
- * to multiple-precision integers.
- * 6. When asked to produce fewer than 15 digits, we first try
- * to get by with floating-point arithmetic; we resort to
- * multiple-precision integer arithmetic only if we cannot
- * guarantee that the floating-point calculation has given
- * the correctly rounded result. For k requested digits and
- * "uniformly" distributed input, the probability is
- * something like 10^(k-15) that we must resort to the long
- * calculation.
- */
- char *
- dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
- {
- /* Arguments ndigits, decpt, sign are similar to those
- of ecvt and fcvt; trailing zeros are suppressed from
- the returned string. If not null, *rve is set to point
- to the end of the return value. If d is +-Infinity or NaN,
- then *decpt is set to 9999.
- mode:
- 0 ==> shortest string that yields d when read in
- and rounded to nearest.
- 1 ==> like 0, but with Steele & White stopping rule;
- e.g. with IEEE P754 arithmetic , mode 0 gives
- 1e23 whereas mode 1 gives 9.999999999999999e22.
- 2 ==> max(1,ndigits) significant digits. This gives a
- return value similar to that of ecvt, except
- that trailing zeros are suppressed.
- 3 ==> through ndigits past the decimal point. This
- gives a return value similar to that from fcvt,
- except that trailing zeros are suppressed, and
- ndigits can be negative.
- 4-9 should give the same return values as 2-3, i.e.,
- 4 <= mode <= 9 ==> same return as mode
- 2 + (mode & 1). These modes are mainly for
- debugging; often they run slower but sometimes
- faster than modes 2-3.
- 4,5,8,9 ==> left-to-right digit generation.
- 6-9 ==> don't try fast floating-point estimate
- (if applicable).
- Values of mode other than 0-9 are treated as mode 0.
- Sufficient space is allocated to the return value
- to hold the suppressed trailing zeros.
- */
- int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
- j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
- spec_case, try_quick;
- long L;
- #ifndef Sudden_Underflow
- int denorm;
- unsigned long x;
- #endif
- Bigint * b, *b1, *delta, *mlo, *mhi, *S;
- double d2, ds, eps;
- char *s, *s0;
- if (word0(d) & Sign_bit) {
- /* set sign for everything, including 0's and NaNs */
- *sign = 1;
- word0(d) &= ~Sign_bit; /* clear sign bit */
- } else
- *sign = 0;
- if ((word0(d) & Exp_mask) == Exp_mask) {
- /* Infinity or NaN */
- *decpt = 9999;
- if (!word1(d) && !(word0(d) & 0xfffff))
- return nrv_alloc("Infinity", rve, 8);
- return nrv_alloc("NaN", rve, 3);
- }
- if (!d) {
- *decpt = 1;
- return nrv_alloc("0", rve, 1);
- }
- b = d2b(d, &be, &bbits);
- #ifdef Sudden_Underflow
- i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
- #else
- if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))) {
- #endif
- word0(d2) = (word0(d) & Frac_mask1) | Exp_11;
- word1(d2) = word1(d);
- /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
- * log10(x) = log(x) / log(10)
- * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
- * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
- *
- * This suggests computing an approximation k to log10(d) by
- *
- * k = (i - Bias)*0.301029995663981
- * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
- *
- * We want k to be too large rather than too small.
- * The error in the first-order Taylor series approximation
- * is in our favor, so we just round up the constant enough
- * to compensate for any error in the multiplication of
- * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
- * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
- * adding 1e-13 to the constant term more than suffices.
- * Hence we adjust the constant term to 0.1760912590558.
- * (We could get a more accurate k by invoking log10,
- * but this is probably not worthwhile.)
- */
- i -= Bias;
- #ifndef Sudden_Underflow
- denorm = 0;
- } else {
- /* d is denormalized */
- i = bbits + be + (Bias + (P - 1) - 1);
- x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
- : word1(d) << 32 - i;
- d2 = x;
- word0(d2) -= 31 * Exp_msk1; /* adjust exponent */
- i -= (Bias + (P - 1) - 1) + 1;
- denorm = 1;
- }
- #endif
- ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
- k = (int)ds;
- if (ds < 0. && ds != k)
- k--; /* want k = floor(ds) */
- k_check = 1;
- if (k >= 0 && k <= Ten_pmax) {
- if (d < tens[k])
- k--;
- k_check = 0;
- }
- j = bbits - i - 1;
- if (j >= 0) {
- b2 = 0;
- s2 = j;
- } else {
- b2 = -j;
- s2 = 0;
- }
- if (k >= 0) {
- b5 = 0;
- s5 = k;
- s2 += k;
- } else {
- b2 -= k;
- b5 = -k;
- s5 = 0;
- }
- if (mode < 0 || mode > 9)
- mode = 0;
- try_quick = 1;
- if (mode > 5) {
- mode -= 4;
- try_quick = 0;
- }
- leftright = 1;
- switch (mode) {
- case 0:
- case 1:
- ilim = ilim1 = -1;
- i = 18;
- ndigits = 0;
- break;
- case 2:
- leftright = 0;
- /* no break */
- case 4:
- if (ndigits <= 0)
- ndigits = 1;
- ilim = ilim1 = i = ndigits;
- break;
- case 3:
- leftright = 0;
- /* no break */
- case 5:
- i = ndigits + k + 1;
- ilim = i;
- ilim1 = i - 1;
- if (i <= 0)
- i = 1;
- }
- s = s0 = rv_alloc(i);
- if (ilim >= 0 && ilim <= Quick_max && try_quick) {
- /* Try to get by with floating-point arithmetic. */
- i = 0;
- d2 = d;
- k0 = k;
- ilim0 = ilim;
- ieps = 2; /* conservative */
- if (k > 0) {
- ds = tens[k&0xf];
- j = k >> 4;
- if (j & Bletch) {
- /* prevent overflows */
- j &= Bletch - 1;
- d /= bigtens[n_bigtens-1];
- ieps++;
- }
- for (; j; j >>= 1, i++)
- if (j & 1) {
- ieps++;
- ds *= bigtens[i];
- }
- d /= ds;
- } else if (j1 = -k) {
- d *= tens[j1 & 0xf];
- for (j = j1 >> 4; j; j >>= 1, i++)
- if (j & 1) {
- ieps++;
- d *= bigtens[i];
- }
- }
- if (k_check && d < 1. && ilim > 0) {
- if (ilim1 <= 0)
- goto fast_failed;
- ilim = ilim1;
- k--;
- d *= 10.;
- ieps++;
- }
- eps = ieps * d + 7.;
- word0(eps) -= (P - 1) * Exp_msk1;
- if (ilim == 0) {
- S = mhi = 0;
- d -= 5.;
- if (d > eps)
- goto one_digit;
- if (d < -eps)
- goto no_digits;
- goto fast_failed;
- }
- /* Generate ilim digits, then fix them up. */
- eps *= tens[ilim-1];
- for (i = 1; ; i++, d *= 10.) {
- L = d;
- d -= L;
- *s++ = '0' + (int)L;
- if (i == ilim) {
- if (d > 0.5 + eps)
- goto bump_up;
- else if (d < 0.5 - eps) {
- while (*--s == '0')
- ;
- s++;
- goto ret1;
- }
- break;
- }
- }
- fast_failed:
- s = s0;
- d = d2;
- k = k0;
- ilim = ilim0;
- }
- /* Do we have a "small" integer? */
- if (be >= 0 && k <= Int_max) {
- /* Yes. */
- ds = tens[k];
- if (ndigits < 0 && ilim <= 0) {
- S = mhi = 0;
- if (ilim < 0 || d <= 5 * ds)
- goto no_digits;
- goto one_digit;
- }
- for (i = 1; ; i++) {
- L = d / ds;
- d -= L * ds;
- *s++ = '0' + (int)L;
- if (i == ilim) {
- d += d;
- if (d > ds || d == ds && L & 1) {
- bump_up:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s = '0';
- break;
- }
- ++ * s++;
- }
- break;
- }
- if (!(d *= 10.))
- break;
- }
- goto ret1;
- }
- m2 = b2;
- m5 = b5;
- mhi = mlo = 0;
- if (leftright) {
- if (mode < 2) {
- i =
- #ifndef Sudden_Underflow
- denorm ? be + (Bias + (P - 1) - 1 + 1) :
- #endif
- 1 + P - bbits;
- } else {
- j = ilim - 1;
- if (m5 >= j)
- m5 -= j;
- else {
- s5 += j -= m5;
- b5 += j;
- m5 = 0;
- }
- if ((i = ilim) < 0) {
- m2 -= i;
- i = 0;
- }
- }
- b2 += i;
- s2 += i;
- mhi = i2b(1);
- }
- if (m2 > 0 && s2 > 0) {
- i = m2 < s2 ? m2 : s2;
- b2 -= i;
- m2 -= i;
- s2 -= i;
- }
- if (b5 > 0) {
- if (leftright) {
- if (m5 > 0) {
- mhi = pow5mult(mhi, m5);
- b1 = mult(mhi, b);
- Bfree(b);
- b = b1;
- }
- if (j = b5 - m5)
- b = pow5mult(b, j);
- } else
- b = pow5mult(b, b5);
- }
- S = i2b(1);
- if (s5 > 0)
- S = pow5mult(S, s5);
- /* Check for special case that d is a normalized power of 2. */
- spec_case = 0;
- if (mode < 2) {
- if (!word1(d) && !(word0(d) & Bndry_mask)
- #ifndef Sudden_Underflow
- && word0(d) & Exp_mask
- #endif
- ) {
- /* The special case */
- b2 += Log2P;
- s2 += Log2P;
- spec_case = 1;
- }
- }
- /* Arrange for convenient computation of quotients:
- * shift left if necessary so divisor has 4 leading 0 bits.
- *
- * Perhaps we should just compute leading 28 bits of S once
- * and for all and pass them and a shift to quorem, so it
- * can do shifts and ors to compute the numerator for q.
- */
- if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
- i = 32 - i;
- if (i > 4) {
- i -= 4;
- b2 += i;
- m2 += i;
- s2 += i;
- } else if (i < 4) {
- i += 28;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- if (b2 > 0)
- b = lshift(b, b2);
- if (s2 > 0)
- S = lshift(S, s2);
- if (k_check) {
- if (cmp(b, S) < 0) {
- k--;
- b = multadd(b, 10, 0); /* we botched the k estimate */
- if (leftright)
- mhi = multadd(mhi, 10, 0);
- ilim = ilim1;
- }
- }
- if (ilim <= 0 && mode > 2) {
- if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
- /* no digits, fcvt style */
- no_digits:
- k = -1 - ndigits;
- goto ret;
- }
- one_digit:
- *s++ = '1';
- k++;
- goto ret;
- }
- if (leftright) {
- if (m2 > 0)
- mhi = lshift(mhi, m2);
- /* Compute mlo -- check for special case
- * that d is a normalized power of 2.
- */
- mlo = mhi;
- if (spec_case) {
- mhi = Balloc(mhi->k);
- Bcopy(mhi, mlo);
- mhi = lshift(mhi, Log2P);
- }
- for (i = 1; ; i++) {
- dig = quorem(b, S) + '0';
- /* Do we yet have the shortest decimal string
- * that will round to d?
- */
- j = cmp(b, mlo);
- delta = diff(S, mhi);
- j1 = delta->sign ? 1 : cmp(b, delta);
- Bfree(delta);
- if (j1 == 0 && !mode && !(word1(d) & 1)) {
- if (dig == '9')
- goto round_9_up;
- if (j > 0)
- dig++;
- *s++ = dig;
- goto ret;
- }
- if (j < 0 || j == 0 && !mode
- && !(word1(d) & 1)
- ) {
- if (j1 > 0) {
- b = lshift(b, 1);
- j1 = cmp(b, S);
- if ((j1 > 0 || j1 == 0 && dig & 1)
- && dig++ == '9')
- goto round_9_up;
- }
- *s++ = dig;
- goto ret;
- }
- if (j1 > 0) {
- if (dig == '9') { /* possible if i == 1 */
- round_9_up:
- *s++ = '9';
- goto roundoff;
- }
- *s++ = dig + 1;
- goto ret;
- }
- *s++ = dig;
- if (i == ilim)
- break;
- b = multadd(b, 10, 0);
- if (mlo == mhi)
- mlo = mhi = multadd(mhi, 10, 0);
- else {
- mlo = multadd(mlo, 10, 0);
- mhi = multadd(mhi, 10, 0);
- }
- }
- } else
- for (i = 1; ; i++) {
- *s++ = dig = quorem(b, S) + '0';
- if (i >= ilim)
- break;
- b = multadd(b, 10, 0);
- }
- /* Round off last digit */
- b = lshift(b, 1);
- j = cmp(b, S);
- if (j > 0 || j == 0 && dig & 1) {
- roundoff:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s++ = '1';
- goto ret;
- }
- ++ * s++;
- } else {
- while (*--s == '0')
- ;
- s++;
- }
- ret:
- Bfree(S);
- if (mhi) {
- if (mlo && mlo != mhi)
- Bfree(mlo);
- Bfree(mhi);
- }
- ret1:
- Bfree(b);
- *s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
- return s0;
- }
|