2011-03-30 05:46:40 -07:00
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/* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
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/* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
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/* Let x be the exact mathematical number defined by a decimal
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* string s. Then atof(s) is the round-nearest-even IEEE
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* floating point value.
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* Let y be an IEEE floating point value and let s be the string
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* printed as %.17g. Then atof(s) is exactly y.
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*/
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#include <u.h>
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#include <libc.h>
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static Lock _dtoalk[2];
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#define ACQUIRE_DTOA_LOCK(n) lock(&_dtoalk[n])
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#define FREE_DTOA_LOCK(n) unlock(&_dtoalk[n])
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#define PRIVATE_mem ((2000+sizeof(double)-1)/sizeof(double))
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static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
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#define FLT_ROUNDS 1
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#define DBL_DIG 15
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#define DBL_MAX_10_EXP 308
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#define DBL_MAX_EXP 1024
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#define FLT_RADIX 2
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#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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2014-06-12 11:14:12 -07:00
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#define fpword0(x) ((x).hi)
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#define fpword1(x) ((x).lo)
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2011-03-30 05:46:40 -07:00
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/* Ten_pmax = floor(P*log(2)/log(5)) */
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/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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#define Exp_shift 20
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#define Exp_shift1 20
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#define Exp_msk1 0x100000
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#define Exp_msk11 0x100000
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#define Exp_mask 0x7ff00000
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#define P 53
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#define Bias 1023
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#define Emin (-1022)
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#define Exp_1 0x3ff00000
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#define Exp_11 0x3ff00000
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#define Ebits 11
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#define Frac_mask 0xfffff
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#define Frac_mask1 0xfffff
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#define Ten_pmax 22
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#define Bletch 0x10
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#define Bndry_mask 0xfffff
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#define Bndry_mask1 0xfffff
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#define Sign_bit 0x80000000
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 14
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#define Int_max 14
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#define rounded_product(a,b) a *= b
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#define rounded_quotient(a,b) a /= b
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#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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#define Big1 0xffffffff
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#define FFFFFFFF 0xffffffffUL
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#undef ULint
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#define Kmax 15
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struct
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Bigint {
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struct Bigint *next;
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int k, maxwds, sign, wds;
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unsigned int x[1];
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};
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typedef struct Bigint Bigint;
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static Bigint *freelist[Kmax+1];
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static Bigint *
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Balloc(int k)
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{
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int x;
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Bigint * rv;
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unsigned int len;
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2014-06-12 11:14:12 -07:00
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assert(k < nelem(freelist));
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2011-03-30 05:46:40 -07:00
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ACQUIRE_DTOA_LOCK(0);
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if (rv = freelist[k]) {
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freelist[k] = rv->next;
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} else {
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x = 1 << k;
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len = (sizeof(Bigint) + (x - 1) * sizeof(unsigned int) + sizeof(double) -1)
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/ sizeof(double);
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if (pmem_next - private_mem + len <= PRIVATE_mem) {
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rv = (Bigint * )pmem_next;
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pmem_next += len;
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} else
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rv = (Bigint * )malloc(len * sizeof(double));
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rv->k = k;
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rv->maxwds = x;
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}
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FREE_DTOA_LOCK(0);
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rv->sign = rv->wds = 0;
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return rv;
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}
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static void
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Bfree(Bigint *v)
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{
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if (v) {
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ACQUIRE_DTOA_LOCK(0);
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v->next = freelist[v->k];
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freelist[v->k] = v;
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FREE_DTOA_LOCK(0);
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}
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}
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#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
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y->wds*sizeof(int) + 2*sizeof(int))
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static Bigint *
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multadd(Bigint *b, int m, int a) /* multiply by m and add a */
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{
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int i, wds;
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unsigned int carry, *x, y;
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unsigned int xi, z;
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Bigint * b1;
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wds = b->wds;
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x = b->x;
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i = 0;
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carry = a;
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do {
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xi = *x;
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y = (xi & 0xffff) * m + carry;
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z = (xi >> 16) * m + (y >> 16);
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carry = z >> 16;
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*x++ = (z << 16) + (y & 0xffff);
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} while (++i < wds);
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if (carry) {
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if (wds >= b->maxwds) {
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b1 = Balloc(b->k + 1);
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Bcopy(b1, b);
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Bfree(b);
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b = b1;
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}
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b->x[wds++] = carry;
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b->wds = wds;
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}
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return b;
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}
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static int
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hi0bits(register unsigned int x)
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{
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register int k = 0;
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if (!(x & 0xffff0000)) {
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k = 16;
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x <<= 16;
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}
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if (!(x & 0xff000000)) {
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k += 8;
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x <<= 8;
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}
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if (!(x & 0xf0000000)) {
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k += 4;
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x <<= 4;
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}
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if (!(x & 0xc0000000)) {
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k += 2;
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x <<= 2;
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}
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if (!(x & 0x80000000)) {
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k++;
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if (!(x & 0x40000000))
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return 32;
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}
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return k;
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}
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static int
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lo0bits(unsigned int *y)
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{
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register int k;
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register unsigned int x = *y;
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if (x & 7) {
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if (x & 1)
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return 0;
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if (x & 2) {
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*y = x >> 1;
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return 1;
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}
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*y = x >> 2;
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return 2;
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}
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k = 0;
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if (!(x & 0xffff)) {
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k = 16;
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x >>= 16;
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}
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if (!(x & 0xff)) {
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k += 8;
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x >>= 8;
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}
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if (!(x & 0xf)) {
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k += 4;
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x >>= 4;
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}
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if (!(x & 0x3)) {
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k += 2;
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x >>= 2;
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}
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if (!(x & 1)) {
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k++;
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x >>= 1;
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if (!x & 1)
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return 32;
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}
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*y = x;
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return k;
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}
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static Bigint *
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i2b(int i)
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{
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Bigint * b;
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b = Balloc(1);
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b->x[0] = i;
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b->wds = 1;
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return b;
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}
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static Bigint *
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mult(Bigint *a, Bigint *b)
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{
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Bigint * c;
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int k, wa, wb, wc;
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unsigned int * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
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unsigned int y;
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unsigned int carry, z;
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unsigned int z2;
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if (a->wds < b->wds) {
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c = a;
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a = b;
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b = c;
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}
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k = a->k;
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wa = a->wds;
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wb = b->wds;
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wc = wa + wb;
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if (wc > a->maxwds)
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k++;
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c = Balloc(k);
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for (x = c->x, xa = x + wc; x < xa; x++)
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*x = 0;
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xa = a->x;
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xae = xa + wa;
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xb = b->x;
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xbe = xb + wb;
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xc0 = c->x;
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for (; xb < xbe; xb++, xc0++) {
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if (y = *xb & 0xffff) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
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carry = z >> 16;
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z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
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carry = z2 >> 16;
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Storeinc(xc, z2, z);
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} while (x < xae);
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*xc = carry;
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}
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if (y = *xb >> 16) {
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x = xa;
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xc = xc0;
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carry = 0;
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z2 = *xc;
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do {
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z = (*x & 0xffff) * y + (*xc >> 16) + carry;
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carry = z >> 16;
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Storeinc(xc, z, z2);
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z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
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carry = z2 >> 16;
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} while (x < xae);
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*xc = z2;
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}
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}
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for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc)
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;
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c->wds = wc;
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return c;
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}
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static Bigint *p5s;
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static Bigint *
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pow5mult(Bigint *b, int k)
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{
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Bigint * b1, *p5, *p51;
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int i;
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static int p05[3] = {
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5, 25, 125 };
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if (i = k & 3)
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b = multadd(b, p05[i-1], 0);
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if (!(k >>= 2))
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return b;
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if (!(p5 = p5s)) {
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/* first time */
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ACQUIRE_DTOA_LOCK(1);
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if (!(p5 = p5s)) {
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p5 = p5s = i2b(625);
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p5->next = 0;
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}
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FREE_DTOA_LOCK(1);
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}
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for (; ; ) {
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if (k & 1) {
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b1 = mult(b, p5);
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Bfree(b);
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b = b1;
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}
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if (!(k >>= 1))
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break;
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if (!(p51 = p5->next)) {
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ACQUIRE_DTOA_LOCK(1);
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if (!(p51 = p5->next)) {
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p51 = p5->next = mult(p5, p5);
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p51->next = 0;
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}
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FREE_DTOA_LOCK(1);
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}
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p5 = p51;
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}
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return b;
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}
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static Bigint *
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lshift(Bigint *b, int k)
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{
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int i, k1, n, n1;
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Bigint * b1;
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unsigned int * x, *x1, *xe, z;
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n = k >> 5;
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k1 = b->k;
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n1 = n + b->wds + 1;
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for (i = b->maxwds; n1 > i; i <<= 1)
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k1++;
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b1 = Balloc(k1);
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x1 = b1->x;
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for (i = 0; i < n; i++)
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*x1++ = 0;
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x = b->x;
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xe = x + b->wds;
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if (k &= 0x1f) {
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k1 = 32 - k;
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z = 0;
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do {
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*x1++ = *x << k | z;
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z = *x++ >> k1;
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} while (x < xe);
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if (*x1 = z)
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++n1;
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} else
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do
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*x1++ = *x++;
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while (x < xe);
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b1->wds = n1 - 1;
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Bfree(b);
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return b1;
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}
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static int
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cmp(Bigint *a, Bigint *b)
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{
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unsigned int * xa, *xa0, *xb, *xb0;
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int i, j;
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i = a->wds;
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j = b->wds;
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if (i -= j)
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return i;
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xa0 = a->x;
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|
|
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;
|
|
|
|
unsigned int * xa, *xae, *xb, *xbe, *xc;
|
|
|
|
unsigned int borrow, y;
|
|
|
|
unsigned int 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 & 0x10000) >> 16;
|
|
|
|
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
Storeinc(xc, z, y);
|
|
|
|
} while (xb < xbe);
|
|
|
|
while (xa < xae) {
|
|
|
|
y = (*xa & 0xffff) - borrow;
|
|
|
|
borrow = (y & 0x10000) >> 16;
|
|
|
|
z = (*xa++ >> 16) - borrow;
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
Storeinc(xc, z, y);
|
|
|
|
}
|
|
|
|
while (!*--xc)
|
|
|
|
wa--;
|
|
|
|
c->wds = wa;
|
|
|
|
return c;
|
|
|
|
}
|
|
|
|
|
2014-06-12 11:14:12 -07:00
|
|
|
static FPdbleword
|
2011-03-30 05:46:40 -07:00
|
|
|
b2d(Bigint *a, int *e)
|
|
|
|
{
|
|
|
|
unsigned int * xa, *xa0, w, y, z;
|
|
|
|
int k;
|
|
|
|
#define d0 fpword0(d)
|
|
|
|
#define d1 fpword1(d)
|
2014-06-12 11:14:12 -07:00
|
|
|
FPdbleword d;
|
2011-03-30 05:46:40 -07:00
|
|
|
|
|
|
|
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 *
|
2014-06-12 11:14:12 -07:00
|
|
|
d2b(FPdbleword d, int *e, int *bits)
|
2011-03-30 05:46:40 -07:00
|
|
|
{
|
|
|
|
Bigint * b;
|
2014-06-12 11:14:12 -07:00
|
|
|
int de, k;
|
2011-03-30 05:46:40 -07:00
|
|
|
unsigned int * x, y, z;
|
2014-06-12 11:14:12 -07:00
|
|
|
#define d0 d.hi
|
|
|
|
#define d1 d.lo
|
2011-03-30 05:46:40 -07:00
|
|
|
|
|
|
|
b = Balloc(1);
|
|
|
|
x = b->x;
|
|
|
|
|
|
|
|
z = d0 & Frac_mask;
|
|
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
|
|
de = (int)(d0 >> Exp_shift);
|
|
|
|
z |= Exp_msk11;
|
|
|
|
if (y = d1) {
|
|
|
|
if (k = lo0bits(&y)) {
|
|
|
|
x[0] = y | z << 32 - k;
|
|
|
|
z >>= k;
|
|
|
|
} else
|
|
|
|
x[0] = y;
|
2014-06-12 11:14:12 -07:00
|
|
|
b->wds = (x[1] = z) ? 2 : 1;
|
2011-03-30 05:46:40 -07:00
|
|
|
} else {
|
|
|
|
k = lo0bits(&z);
|
|
|
|
x[0] = z;
|
2014-06-12 11:14:12 -07:00
|
|
|
b->wds = 1;
|
2011-03-30 05:46:40 -07:00
|
|
|
k += 32;
|
|
|
|
}
|
|
|
|
*e = de - Bias - (P - 1) + k;
|
|
|
|
*bits = P - k;
|
|
|
|
return b;
|
|
|
|
}
|
|
|
|
|
|
|
|
#undef d0
|
|
|
|
#undef d1
|
|
|
|
|
|
|
|
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 };
|
|
|
|
|
|
|
|
/* 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
|
|
|
|
quorem(Bigint *b, Bigint *S)
|
|
|
|
{
|
|
|
|
int n;
|
|
|
|
unsigned int * bx, *bxe, q, *sx, *sxe;
|
|
|
|
unsigned int borrow, carry, y, ys;
|
|
|
|
unsigned int si, z, 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 & 0x10000) >> 16;
|
|
|
|
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
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 & 0x10000) >> 16;
|
|
|
|
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
|
|
|
borrow = (z & 0x10000) >> 16;
|
|
|
|
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 int);
|
|
|
|
for (k = 0;
|
|
|
|
sizeof(Bigint) - sizeof(unsigned int) - 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 int
|
|
|
|
* calculation.
|
|
|
|
*/
|
|
|
|
|
|
|
|
char *
|
2014-06-12 11:14:12 -07:00
|
|
|
dtoa(double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
|
2011-03-30 05:46:40 -07:00
|
|
|
{
|
|
|
|
/* 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;
|
|
|
|
int L;
|
|
|
|
Bigint * b, *b1, *delta, *mlo=nil, *mhi, *S;
|
2014-06-12 11:14:12 -07:00
|
|
|
double ds;
|
|
|
|
FPdbleword d, d2, eps;
|
2011-03-30 05:46:40 -07:00
|
|
|
char *s, *s0;
|
|
|
|
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x = _d;
|
2011-03-30 05:46:40 -07:00
|
|
|
if (fpword0(d) & Sign_bit) {
|
|
|
|
/* set sign for everything, including 0's and NaNs */
|
|
|
|
*sign = 1;
|
|
|
|
fpword0(d) &= ~Sign_bit; /* clear sign bit */
|
|
|
|
} else
|
|
|
|
*sign = 0;
|
|
|
|
|
|
|
|
if ((fpword0(d) & Exp_mask) == Exp_mask) {
|
|
|
|
/* Infinity or NaN */
|
|
|
|
*decpt = 9999;
|
|
|
|
if (!fpword1(d) && !(fpword0(d) & 0xfffff))
|
|
|
|
return nrv_alloc("Infinity", rve, 8);
|
|
|
|
return nrv_alloc("NaN", rve, 3);
|
|
|
|
}
|
2014-06-12 11:14:12 -07:00
|
|
|
if (!d.x) {
|
2011-03-30 05:46:40 -07:00
|
|
|
*decpt = 1;
|
|
|
|
return nrv_alloc("0", rve, 1);
|
|
|
|
}
|
|
|
|
|
|
|
|
b = d2b(d, &be, &bbits);
|
|
|
|
i = (int)(fpword0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
|
|
|
|
d2 = d;
|
|
|
|
fpword0(d2) &= Frac_mask1;
|
|
|
|
fpword0(d2) |= Exp_11;
|
|
|
|
|
|
|
|
/* 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;
|
2014-06-12 11:14:12 -07:00
|
|
|
ds = (d2.x - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
|
2011-03-30 05:46:40 -07:00
|
|
|
k = (int)ds;
|
|
|
|
if (ds < 0. && ds != k)
|
|
|
|
k--; /* want k = floor(ds) */
|
|
|
|
k_check = 1;
|
|
|
|
if (k >= 0 && k <= Ten_pmax) {
|
2014-06-12 11:14:12 -07:00
|
|
|
if (d.x < tens[k])
|
2011-03-30 05:46:40 -07:00
|
|
|
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:
|
2014-06-12 11:14:12 -07:00
|
|
|
default:
|
2011-03-30 05:46:40 -07:00
|
|
|
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;
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x /= bigtens[n_bigtens-1];
|
2011-03-30 05:46:40 -07:00
|
|
|
ieps++;
|
|
|
|
}
|
|
|
|
for (; j; j >>= 1, i++)
|
|
|
|
if (j & 1) {
|
|
|
|
ieps++;
|
|
|
|
ds *= bigtens[i];
|
|
|
|
}
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x /= ds;
|
2011-03-30 05:46:40 -07:00
|
|
|
} else if (j1 = -k) {
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x *= tens[j1 & 0xf];
|
2011-03-30 05:46:40 -07:00
|
|
|
for (j = j1 >> 4; j; j >>= 1, i++)
|
|
|
|
if (j & 1) {
|
|
|
|
ieps++;
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x *= bigtens[i];
|
2011-03-30 05:46:40 -07:00
|
|
|
}
|
|
|
|
}
|
2014-06-12 11:14:12 -07:00
|
|
|
if (k_check && d.x < 1. && ilim > 0) {
|
2011-03-30 05:46:40 -07:00
|
|
|
if (ilim1 <= 0)
|
|
|
|
goto fast_failed;
|
|
|
|
ilim = ilim1;
|
|
|
|
k--;
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x *= 10.;
|
2011-03-30 05:46:40 -07:00
|
|
|
ieps++;
|
|
|
|
}
|
2014-06-12 11:14:12 -07:00
|
|
|
eps.x = ieps * d.x + 7.;
|
2011-03-30 05:46:40 -07:00
|
|
|
fpword0(eps) -= (P - 1) * Exp_msk1;
|
|
|
|
if (ilim == 0) {
|
|
|
|
S = mhi = 0;
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x -= 5.;
|
|
|
|
if (d.x > eps.x)
|
2011-03-30 05:46:40 -07:00
|
|
|
goto one_digit;
|
2014-06-12 11:14:12 -07:00
|
|
|
if (d.x < -eps.x)
|
2011-03-30 05:46:40 -07:00
|
|
|
goto no_digits;
|
|
|
|
goto fast_failed;
|
|
|
|
}
|
|
|
|
/* Generate ilim digits, then fix them up. */
|
2014-06-12 11:14:12 -07:00
|
|
|
eps.x *= tens[ilim-1];
|
|
|
|
for (i = 1; ; i++, d.x *= 10.) {
|
|
|
|
L = d.x;
|
|
|
|
d.x -= L;
|
2011-03-30 05:46:40 -07:00
|
|
|
*s++ = '0' + (int)L;
|
|
|
|
if (i == ilim) {
|
2014-06-12 11:14:12 -07:00
|
|
|
if (d.x > 0.5 + eps.x)
|
2011-03-30 05:46:40 -07:00
|
|
|
goto bump_up;
|
2014-06-12 11:14:12 -07:00
|
|
|
else if (d.x < 0.5 - eps.x) {
|
2011-03-30 05:46:40 -07:00
|
|
|
while (*--s == '0')
|
|
|
|
;
|
|
|
|
s++;
|
|
|
|
goto ret1;
|
|
|
|
}
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
fast_failed:
|
|
|
|
s = s0;
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x = d2.x;
|
2011-03-30 05:46:40 -07:00
|
|
|
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;
|
2014-06-12 11:14:12 -07:00
|
|
|
if (ilim < 0 || d.x <= 5 * ds)
|
2011-03-30 05:46:40 -07:00
|
|
|
goto no_digits;
|
|
|
|
goto one_digit;
|
|
|
|
}
|
|
|
|
for (i = 1; ; i++) {
|
2014-06-12 11:14:12 -07:00
|
|
|
L = d.x / ds;
|
|
|
|
d.x -= L * ds;
|
2011-03-30 05:46:40 -07:00
|
|
|
*s++ = '0' + (int)L;
|
|
|
|
if (i == ilim) {
|
2014-06-12 11:14:12 -07:00
|
|
|
d.x += d.x;
|
|
|
|
if (d.x > ds || d.x == ds && L & 1) {
|
2011-03-30 05:46:40 -07:00
|
|
|
bump_up:
|
|
|
|
while (*--s == '9')
|
|
|
|
if (s == s0) {
|
|
|
|
k++;
|
|
|
|
*s = '0';
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
++ * s++;
|
|
|
|
}
|
|
|
|
break;
|
|
|
|
}
|
2014-06-12 11:14:12 -07:00
|
|
|
if (!(d.x *= 10.))
|
2011-03-30 05:46:40 -07:00
|
|
|
break;
|
|
|
|
}
|
|
|
|
goto ret1;
|
|
|
|
}
|
|
|
|
|
|
|
|
m2 = b2;
|
|
|
|
m5 = b5;
|
|
|
|
mhi = mlo = 0;
|
|
|
|
if (leftright) {
|
|
|
|
if (mode < 2) {
|
|
|
|
i =
|
|
|
|
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 (!fpword1(d) && !(fpword0(d) & Bndry_mask)
|
|
|
|
) {
|
|
|
|
/* 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 && !(fpword1(d) & 1)) {
|
|
|
|
if (dig == '9')
|
|
|
|
goto round_9_up;
|
|
|
|
if (j > 0)
|
|
|
|
dig++;
|
|
|
|
*s++ = dig;
|
|
|
|
goto ret;
|
|
|
|
}
|
|
|
|
if (j < 0 || j == 0 && !mode
|
|
|
|
&& !(fpword1(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;
|
|
|
|
}
|
|
|
|
|