mirror of https://github.com/PrimeDecomp/prime.git
602 lines
14 KiB
C
602 lines
14 KiB
C
#include <ansi_fp.h>
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#include <ctype.h>
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#include <float.h>
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#include <math.h>
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static int __count_trailing_zerol(unsigned long x) {
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int result = 0;
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int bits_not_checked = sizeof(unsigned long) * 8;
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int n = bits_not_checked / 2;
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int mask_size = n;
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unsigned long mask = (~0UL) >> (bits_not_checked - n);
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while (bits_not_checked) {
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if (!(x & mask)) {
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result += mask_size;
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x >>= mask_size;
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bits_not_checked -= mask_size;
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} else if (mask == 1)
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break;
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if (n > 1)
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n /= 2;
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if (mask > 1) {
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mask >>= n;
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mask_size -= n;
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}
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}
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return result;
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}
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static int __count_trailing_zero(double x) {
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unsigned long* l = (unsigned long*)&x;
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if (l[1] != 0)
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return __count_trailing_zerol(l[1]);
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return (int)(sizeof(unsigned long) * 8 + __count_trailing_zerol(l[0] | 0x00100000));
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}
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static int __must_round(const decimal* d, int pos) {
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unsigned char const* i = d->sig.text + pos;
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if (*i > 5)
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return 1;
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if (*i < 5)
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return -1;
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{
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unsigned char const* e = d->sig.text + d->sig.length;
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for (++i; i < e; ++i)
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if (*i != 0)
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return 1;
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}
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if (d->sig.text[pos - 1] & 1)
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return 1;
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return -1;
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}
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static void __dorounddecup(decimal* d, int digits) {
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unsigned char* b = d->sig.text;
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unsigned char* i = b + digits - 1;
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while (1) {
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if (*i < 9) {
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(*i)++;
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break;
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}
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if (i == b) {
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*i = 1;
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d->exp++;
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break;
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}
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*i-- = 0;
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}
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}
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static void __rounddec(decimal* d, int digits) {
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if (digits <= 0 || digits >= d->sig.length)
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return;
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{
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int r = __must_round(d, digits);
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d->sig.length = (unsigned char)digits;
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if (r < 0)
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return;
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}
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__dorounddecup(d, digits);
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}
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static void __ull2dec(decimal* result, unsigned long long integer) {
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result->sgn = 0;
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if (integer == 0) {
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result->exp = 0;
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result->sig.length = 1;
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result->sig.text[0] = 0;
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return;
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}
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if (integer < 0) {
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integer = -integer;
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result->sgn = 1;
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}
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result->sig.length = 0;
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for (; integer != 0; integer /= 10)
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result->sig.text[result->sig.length++] = (unsigned char)(integer % 10);
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{
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unsigned char* i = result->sig.text;
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unsigned char* j = result->sig.text + result->sig.length;
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for (; i < --j; ++i) {
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unsigned char t = *i;
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*i = *j;
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*j = t;
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}
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}
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result->exp = (short)(result->sig.length - 1);
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}
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static void __timesdec(decimal* result, const decimal* x, const decimal* y) {
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unsigned long accumulator = 0;
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unsigned char mantissa[2 * SIGDIGLEN];
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int i = x->sig.length + y->sig.length - 1;
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unsigned char* ip = mantissa + i + 1;
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unsigned char* ep = ip;
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result->sgn = 0;
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for (; i > 0; --i) {
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int k = y->sig.length - 1;
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int j = i - k - 1;
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int l;
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int t;
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unsigned char const *jp, *kp;
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if (j < 0) {
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j = 0;
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k = i - 1;
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}
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jp = x->sig.text + j;
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kp = y->sig.text + k;
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l = k + 1;
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t = x->sig.length - j;
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if (l > t)
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l = t;
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for (; l > 0; --l, ++jp, --kp)
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accumulator += (unsigned long)(*jp) * *kp;
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*--ip = (unsigned char)(accumulator % 10);
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accumulator /= 10;
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}
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result->exp = (short)(x->exp + y->exp);
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if (accumulator > 0) {
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*--ip = (unsigned char)accumulator;
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result->exp++;
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}
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for (i = 0; i < SIGDIGLEN && ip < ep; ++i, ++ip)
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result->sig.text[i] = *ip;
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result->sig.length = (unsigned char)i;
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if (ip < ep && *ip >= 5) {
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if (*ip == 5) {
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unsigned char* jp = ip + 1;
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for (; jp < ep; ++jp)
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if (*jp != 0)
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goto round;
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if ((*(ip - 1) & 1) == 0)
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return;
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}
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round:
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__dorounddecup(result, result->sig.length);
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}
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}
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static void __str2dec(decimal* d, const char* s, short exp) {
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int i;
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d->exp = exp;
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d->sgn = 0;
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for (i = 0; i < SIGDIGLEN && *s != 0;)
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d->sig.text[i++] = (unsigned char)(*s++ - '0');
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d->sig.length = (unsigned char)i;
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if (*s != 0) {
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if (*s < 5)
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return;
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{
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const char* p = s + 1;
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for (; *p != 0; ++p)
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if (*p != '0')
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goto round;
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if ((d->sig.text[i - 1] & 1) == 0)
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return;
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}
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round:
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__dorounddecup(d, d->sig.length);
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}
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}
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static void __two_exp(decimal* result, short exp) {
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switch (exp) {
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case -64:
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__str2dec(result, "542101086242752217003726400434970855712890625", -20);
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return;
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case -53:
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__str2dec(result, "11102230246251565404236316680908203125", -16);
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return;
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case -32:
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__str2dec(result, "23283064365386962890625", -10);
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return;
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case -16:
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__str2dec(result, "152587890625", -5);
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return;
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case -8:
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__str2dec(result, "390625", -3);
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return;
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case -7:
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__str2dec(result, "78125", -3);
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return;
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case -6:
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__str2dec(result, "15625", -2);
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return;
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case -5:
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__str2dec(result, "3125", -2);
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return;
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case -4:
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__str2dec(result, "625", -2);
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return;
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case -3:
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__str2dec(result, "125", -1);
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return;
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case -2:
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__str2dec(result, "25", -1);
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return;
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case -1:
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__str2dec(result, "5", -1);
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return;
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case 0:
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__str2dec(result, "1", 0);
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return;
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case 1:
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__str2dec(result, "2", 0);
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return;
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case 2:
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__str2dec(result, "4", 0);
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return;
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case 3:
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__str2dec(result, "8", 0);
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return;
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case 4:
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__str2dec(result, "16", 1);
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return;
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case 5:
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__str2dec(result, "32", 1);
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return;
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case 6:
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__str2dec(result, "64", 1);
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return;
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case 7:
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__str2dec(result, "128", 2);
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return;
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case 8:
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__str2dec(result, "256", 2);
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return;
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}
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{
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decimal x2;
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__two_exp(&x2, (short)(exp / 2));
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__timesdec(result, &x2, &x2);
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}
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if (exp & 1) {
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decimal temp = *result;
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if (exp > 0) {
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decimal two;
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__str2dec(&two, "2", 0);
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__timesdec(result, &temp, &two);
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} else {
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decimal one_half;
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__str2dec(&one_half, "5", -1);
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__timesdec(result, &temp, &one_half);
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}
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}
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}
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static int __equals_dec(const decimal* x, const decimal* y) {
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if (x->sig.text[0] == 0) {
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if (y->sig.text[0] == 0)
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return 1;
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return 0;
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}
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if (y->sig.text[0] == 0) {
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if (x->sig.text[0] == 0)
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return 1;
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return 0;
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}
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if (x->exp == y->exp) {
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int i;
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int l = x->sig.length;
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if (l > y->sig.length)
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l = y->sig.length;
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for (i = 0; i < l; ++i)
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if (x->sig.text[i] != y->sig.text[i])
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return 0;
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if (l == x->sig.length) {
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for (; i < y->sig.length; ++i)
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if (y->sig.text[i] != 0)
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return 0;
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} else {
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for (; i < x->sig.length; ++i)
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if (x->sig.text[i] != 0)
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return 0;
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}
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return 1;
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}
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return 0;
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}
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static int __less_dec(const decimal* x, const decimal* y) {
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if (x->sig.text[0] == 0) {
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if (y->sig.text[0] != 0)
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return 1;
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return 0;
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}
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if (y->sig.text[0] == 0)
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return 0;
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if (x->exp == y->exp) {
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int i;
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int l = x->sig.length;
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if (l > y->sig.length)
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l = y->sig.length;
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for (i = 0; i < l; ++i) {
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if (x->sig.text[i] < y->sig.text[i])
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return 1;
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if (y->sig.text[i] < x->sig.text[i])
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return 0;
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}
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if (l == x->sig.length) {
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for (; i < y->sig.length; ++i)
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if (y->sig.text[i] != 0)
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return 1;
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}
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return 0;
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}
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return x->exp < y->exp;
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}
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static void __minus_dec(decimal* z, const decimal* x, const decimal* y) {
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int zlen, dexp;
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unsigned char *ib, *i, *ie;
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unsigned char const *jb, *j, *jn;
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*z = *x;
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if (y->sig.text[0] == 0)
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return;
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zlen = z->sig.length;
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if (zlen < y->sig.length)
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zlen = y->sig.length;
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dexp = z->exp - y->exp;
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zlen += dexp;
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if (zlen > SIGDIGLEN)
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zlen = SIGDIGLEN;
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while (z->sig.length < zlen)
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z->sig.text[z->sig.length++] = 0;
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ib = z->sig.text;
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i = ib + zlen;
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if (y->sig.length + dexp < zlen)
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i = ib + (y->sig.length + dexp);
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jb = y->sig.text;
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j = jb + (i - ib - dexp);
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jn = j;
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while (i > ib && j > jb) {
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--i;
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--j;
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if (*i < *j) {
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unsigned char* k = i - 1;
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while (*k == 0)
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--k;
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while (k != i) {
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--*k;
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*++k += 10;
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}
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}
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*i -= *j;
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}
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if (jn - jb < y->sig.length) {
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int round_down = 0;
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if (*jn < 5)
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round_down = 1;
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else if (*jn == 5) {
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unsigned char const* je = y->sig.text + y->sig.length;
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for (j = jn + 1; j < je; ++j)
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if (*j != 0)
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goto done;
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i = ib + (jn - jb) + dexp - 1;
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if (*i & 1)
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round_down = 1;
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}
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if (round_down) {
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if (*i < 1) {
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unsigned char* k = i - 1;
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while (*k == 0)
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--k;
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while (k != i) {
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--*k;
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*++k += 10;
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}
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}
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*i -= 1;
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}
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}
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done:
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for (i = ib; *i == 0; ++i) {
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}
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if (i > ib) {
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unsigned char dl = (unsigned char)(i - ib);
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z->exp -= dl;
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ie = ib + z->sig.length;
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for (; i < ie; ++i, ++ib)
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*ib = *i;
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z->sig.length -= dl;
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}
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ib = z->sig.text;
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for (i = ib + z->sig.length; i > ib;) {
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--i;
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if (*i != 0)
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break;
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}
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z->sig.length = (unsigned char)(i - ib + 1);
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}
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static void __num2dec_internal(decimal* d, double x) {
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char sgn = signbit(x) != 0;
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if (x == 0.0) {
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d->sgn = sgn;
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d->exp = 0;
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d->sig.length = 1;
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d->sig.text[0] = 0;
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return;
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}
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if (!isfinite(x)) {
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d->sgn = sgn;
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d->exp = 0;
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d->sig.length = 1;
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d->sig.text[0] = (unsigned char)(isnan(x) ? 'N' : 'I');
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return;
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}
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if (sgn)
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x = -x;
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{
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int exp;
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double frac = frexp(x, &exp);
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short num_bits_extract = (short)(DBL_MANT_DIG - __count_trailing_zero(frac));
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double integer;
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decimal int_d, pow2_d;
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__two_exp(&pow2_d, (short)(exp - num_bits_extract));
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frac = modf(ldexp(frac, num_bits_extract), &integer);
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__ull2dec(&int_d, (unsigned long long)integer);
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__timesdec(d, &int_d, &pow2_d);
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d->sgn = sgn;
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}
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}
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void __num2dec(const decform* f, double x, decimal* d) {
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short digits = f->digits;
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int i;
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__num2dec_internal(d, x);
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if (d->sig.text[0] > 9)
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return;
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if (digits > SIGDIGLEN)
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digits = SIGDIGLEN;
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__rounddec(d, digits);
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while (d->sig.length < digits)
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d->sig.text[d->sig.length++] = 0;
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d->exp -= d->sig.length - 1;
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for (i = 0; i < d->sig.length; ++i)
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d->sig.text[i] += '0';
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}
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double __dec2num(const decimal* d) {
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if (d->sig.length <= 0)
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return copysign(0.0, d->sgn == 0 ? 1.0 : -1.0);
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switch (d->sig.text[0]) {
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case '0':
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return copysign(0.0, d->sgn == 0 ? 1.0 : -1.0);
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case 'I':
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return copysign((double)INFINITY, d->sgn == 0 ? 1.0 : -1.0);
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case 'N': {
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double result;
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unsigned long long* ll = (unsigned long long*)&result;
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*ll = 0x7FF0000000000000;
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if (d->sgn)
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*ll |= 0x8000000000000000;
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if (d->sig.length == 1)
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*ll |= 0x0008000000000000;
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else {
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unsigned char* p = (unsigned char*)&result + 1;
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int placed_non_zero = 0;
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int low = 1;
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int i;
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int e = d->sig.length;
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if (e > 14)
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e = 14;
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for (i = 1; i < e; ++i) {
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unsigned char c = d->sig.text[i];
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if (isdigit(c))
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c -= '0';
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else
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c = (unsigned char)(tolower(c) - 'a' + 10);
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if (c != 0)
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placed_non_zero = 1;
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if (low)
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*p++ |= c;
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else
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*p = (unsigned char)(c << 4);
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low = !low;
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}
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if (!placed_non_zero)
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*ll |= 0x0008000000000000;
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}
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return result;
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}
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}
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{
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static double pow_10[8] = {1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8};
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decimal dec = *d;
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unsigned char* i = dec.sig.text;
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unsigned char* e = i + dec.sig.length;
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double first_guess;
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int exponent;
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for (; i < e; ++i)
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*i -= '0';
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dec.exp += dec.sig.length - 1;
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exponent = dec.exp;
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i = dec.sig.text;
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first_guess = *i++;
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while (i < e) {
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unsigned long ival = 0;
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int j;
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double temp1, temp2;
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int ndig = (e - i) % 8;
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if (ndig == 0)
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ndig = 8;
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for (j = 0; j < ndig; ++j, ++i)
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ival = ival * 10 + *i;
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temp1 = first_guess * pow_10[ndig - 1];
|
|
temp2 = temp1 + ival;
|
|
if (ival != 0 && temp1 == temp2)
|
|
break;
|
|
first_guess = temp2;
|
|
exponent -= ndig;
|
|
}
|
|
if (exponent < 0)
|
|
first_guess /= pow(5.0, -exponent);
|
|
else
|
|
first_guess *= pow(5.0, exponent);
|
|
first_guess = ldexp(first_guess, exponent);
|
|
if (isinf(first_guess)) {
|
|
decimal max;
|
|
__str2dec(&max, "179769313486231580793729011405303420", 308);
|
|
if (__less_dec(&max, &dec))
|
|
goto done;
|
|
first_guess = DBL_MAX;
|
|
}
|
|
{
|
|
decimal feedback1;
|
|
__num2dec_internal(&feedback1, first_guess);
|
|
if (__equals_dec(&feedback1, &dec))
|
|
goto done;
|
|
if (__less_dec(&feedback1, &dec)) {
|
|
|
|
decimal feedback2, difflow, diffhigh;
|
|
double next_guess = nextafter(first_guess, (double)INFINITY);
|
|
if (isinf(next_guess)) {
|
|
first_guess = next_guess;
|
|
goto done;
|
|
}
|
|
__num2dec_internal(&feedback2, next_guess);
|
|
while (__less_dec(&feedback2, &dec)) {
|
|
feedback1 = feedback2;
|
|
first_guess = next_guess;
|
|
next_guess = nextafter(next_guess, (double)INFINITY);
|
|
if (isinf(next_guess)) {
|
|
first_guess = next_guess;
|
|
goto done;
|
|
}
|
|
__num2dec_internal(&feedback2, next_guess);
|
|
}
|
|
__minus_dec(&difflow, &dec, &feedback1);
|
|
__minus_dec(&diffhigh, &feedback2, &dec);
|
|
if (__equals_dec(&difflow, &diffhigh)) {
|
|
if (*(unsigned long long*)&first_guess & 1)
|
|
first_guess = next_guess;
|
|
} else if (!__less_dec(&difflow, &diffhigh))
|
|
first_guess = next_guess;
|
|
} else {
|
|
decimal feedback2, difflow, diffhigh;
|
|
double next_guess = nextafter(first_guess, (double)(-INFINITY));
|
|
__num2dec_internal(&feedback2, next_guess);
|
|
while (__less_dec(&dec, &feedback2)) {
|
|
feedback1 = feedback2;
|
|
first_guess = next_guess;
|
|
next_guess = nextafter(next_guess, (double)(-INFINITY));
|
|
__num2dec_internal(&feedback2, next_guess);
|
|
}
|
|
__minus_dec(&difflow, &dec, &feedback2);
|
|
__minus_dec(&diffhigh, &feedback1, &dec);
|
|
if (__equals_dec(&difflow, &diffhigh)) {
|
|
if (*(unsigned long long*)&first_guess & 1)
|
|
first_guess = next_guess;
|
|
} else if (__less_dec(&difflow, &diffhigh))
|
|
first_guess = next_guess;
|
|
}
|
|
}
|
|
done:
|
|
if (dec.sgn)
|
|
first_guess = -first_guess;
|
|
return first_guess;
|
|
}
|
|
}
|