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-rw-r--r--py/mpz.c1009
1 files changed, 1009 insertions, 0 deletions
diff --git a/py/mpz.c b/py/mpz.c
new file mode 100644
index 0000000000..ab049ba890
--- /dev/null
+++ b/py/mpz.c
@@ -0,0 +1,1009 @@
+#include <stdint.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+
+#include "misc.h"
+#include "mpconfig.h"
+#include "mpz.h"
+
+#if MICROPY_LONGINT_IMPL == MICROPY_LONGINT_IMPL_MPZ
+
+#define DIG_SIZE (15)
+#define DIG_MASK ((1 << DIG_SIZE) - 1)
+
+/*
+ definition of normalise:
+ ?
+*/
+
+/* compares i with j
+ returns sign(i - j)
+ assumes i, j are normalised
+*/
+int mpn_cmp(const mpz_dig_t *idig, uint ilen, const mpz_dig_t *jdig, uint jlen) {
+ if (ilen < jlen) { return -1; }
+ if (ilen > jlen) { return 1; }
+
+ for (idig += ilen, jdig += ilen; ilen > 0; --ilen) {
+ int cmp = *(--idig) - *(--jdig);
+ if (cmp < 0) { return -1; }
+ if (cmp > 0) { return 1; }
+ }
+
+ return 0;
+}
+
+/* computes i = j >> n
+ returns number of digits in i
+ assumes enough memory in i; assumes normalised j
+ can have i, j pointing to same memory
+*/
+uint mpn_shr(mpz_dig_t *idig, mpz_dig_t *jdig, uint jlen, uint n) {
+ uint n_whole = n / DIG_SIZE;
+ uint n_part = n % DIG_SIZE;
+
+ if (n_whole >= jlen) {
+ return 0;
+ }
+
+ jdig += n_whole;
+ jlen -= n_whole;
+
+ for (uint i = jlen; i > 0; --i, ++idig, ++jdig) {
+ mpz_dbl_dig_t d = *jdig;
+ if (i > 1)
+ d |= jdig[1] << DIG_SIZE;
+ d >>= n_part;
+ *idig = d & DIG_MASK;
+ }
+
+ if (idig[-1] == 0) {
+ --jlen;
+ }
+
+ return jlen;
+}
+
+/* computes i = j + k
+ returns number of digits in i
+ assumes enough memory in i; assumes normalised j, k; assumes jlen >= klen
+ can have i, j, k pointing to same memory
+*/
+uint mpn_add(mpz_dig_t *idig, const mpz_dig_t *jdig, uint jlen, const mpz_dig_t *kdig, uint klen) {
+ mpz_dig_t *oidig = idig;
+ mpz_dbl_dig_t carry = 0;
+
+ jlen -= klen;
+
+ for (; klen > 0; --klen, ++idig, ++jdig, ++kdig) {
+ carry += *jdig + *kdig;
+ *idig = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+ }
+
+ for (; jlen > 0; --jlen, ++idig, ++jdig) {
+ carry += *jdig;
+ *idig = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+ }
+
+ if (carry != 0) {
+ *idig++ = carry;
+ }
+
+ return idig - oidig;
+}
+
+/* computes i = j - k
+ returns number of digits in i
+ assumes enough memory in i; assumes normalised j, k; assumes j >= k
+ can have i, j, k pointing to same memory
+*/
+uint mpn_sub(mpz_dig_t *idig, const mpz_dig_t *jdig, uint jlen, const mpz_dig_t *kdig, uint klen) {
+ mpz_dig_t *oidig = idig;
+ mpz_dbl_dig_signed_t borrow = 0;
+
+ jlen -= klen;
+
+ for (; klen > 0; --klen, ++idig, ++jdig, ++kdig) {
+ borrow += *jdig - *kdig;
+ *idig = borrow & DIG_MASK;
+ borrow >>= DIG_SIZE;
+ }
+
+ for (; jlen > 0; --jlen, ++idig, ++kdig) {
+ borrow += *jdig;
+ *idig = borrow & DIG_MASK;
+ borrow >>= DIG_SIZE;
+ }
+
+ for (--idig; idig >= oidig && *idig == 0; --idig) {
+ }
+
+ return idig + 1 - oidig;
+}
+
+/* computes i = i * d1 + d2
+ returns number of digits in i
+ assumes enough memory in i; assumes normalised i; assumes dmul != 0
+*/
+uint mpn_mul_dig_add_dig(mpz_dig_t *idig, uint ilen, mpz_dig_t dmul, mpz_dig_t dadd) {
+ mpz_dig_t *oidig = idig;
+ mpz_dbl_dig_t carry = dadd;
+
+ for (; ilen > 0; --ilen, ++idig) {
+ carry += *idig * dmul; // will never overflow so long as DIG_SIZE <= WORD_SIZE / 2
+ *idig = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+ }
+
+ if (carry != 0) {
+ *idig++ = carry;
+ }
+
+ return idig - oidig;
+}
+
+/* computes i = j * k
+ returns number of digits in i
+ assumes enough memory in i; assumes i is zeroed; assumes normalised j, k
+ can have j, k point to same memory
+*/
+uint mpn_mul(mpz_dig_t *idig, mpz_dig_t *jdig, uint jlen, mpz_dig_t *kdig, uint klen) {
+ mpz_dig_t *oidig = idig;
+ uint ilen = 0;
+
+ for (; klen > 0; --klen, ++idig, ++kdig) {
+ mpz_dig_t *id = idig;
+ mpz_dbl_dig_t carry = 0;
+
+ uint jl = jlen;
+ for (mpz_dig_t *jd = jdig; jl > 0; --jl, ++jd, ++id) {
+ carry += *id + *jd * *kdig; // will never overflow so long as DIG_SIZE <= WORD_SIZE / 2
+ *id = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+ }
+
+ if (carry != 0) {
+ *id++ = carry;
+ }
+
+ ilen = id - oidig;
+ }
+
+ return ilen;
+}
+
+/* natural_div - quo * den + new_num = old_num (ie num is replaced with rem)
+ assumes den != 0
+ assumes num_dig has enough memory to be extended by 1 digit
+ assumes quo_dig has enough memory (as many digits as num)
+ assumes quo_dig is filled with zeros
+ modifies den_dig memory, but restors it to original state at end
+*/
+
+void mpn_div(mpz_dig_t *num_dig, machine_uint_t *num_len, mpz_dig_t *den_dig, machine_uint_t den_len, mpz_dig_t *quo_dig, machine_uint_t *quo_len) {
+ mpz_dig_t *orig_num_dig = num_dig;
+ mpz_dig_t *orig_quo_dig = quo_dig;
+ mpz_dig_t norm_shift = 0;
+ mpz_dbl_dig_t lead_den_digit;
+
+ // handle simple cases
+ {
+ int cmp = mpn_cmp(num_dig, *num_len, den_dig, den_len);
+ if (cmp == 0) {
+ *num_len = 0;
+ quo_dig[0] = 1;
+ *quo_len = 1;
+ return;
+ } else if (cmp < 0) {
+ // numerator remains the same
+ *quo_len = 0;
+ return;
+ }
+ }
+
+ // count number of leading zeros in leading digit of denominator
+ {
+ mpz_dig_t d = den_dig[den_len - 1];
+ while ((d & (1 << (DIG_SIZE - 1))) == 0) {
+ d <<= 1;
+ ++norm_shift;
+ }
+ }
+
+ // normalise denomenator (leading bit of leading digit is 1)
+ for (mpz_dig_t *den = den_dig, carry = 0; den < den_dig + den_len; ++den) {
+ mpz_dig_t d = *den;
+ *den = ((d << norm_shift) | carry) & DIG_MASK;
+ carry = d >> (DIG_SIZE - norm_shift);
+ }
+
+ // now need to shift numerator by same amount as denominator
+ // first, increase length of numerator in case we need more room to shift
+ num_dig[*num_len] = 0;
+ ++(*num_len);
+ for (mpz_dig_t *num = num_dig, carry = 0; num < num_dig + *num_len; ++num) {
+ mpz_dig_t n = *num;
+ *num = ((n << norm_shift) | carry) & DIG_MASK;
+ carry = n >> (DIG_SIZE - norm_shift);
+ }
+
+ // cache the leading digit of the denominator
+ lead_den_digit = den_dig[den_len - 1];
+
+ // point num_dig to last digit in numerator
+ num_dig += *num_len - 1;
+
+ // calculate number of digits in quotient
+ *quo_len = *num_len - den_len;
+
+ // point to last digit to store for quotient
+ quo_dig += *quo_len - 1;
+
+ // keep going while we have enough digits to divide
+ while (*num_len > den_len) {
+ mpz_dbl_dig_t quo = (*num_dig << DIG_SIZE) | num_dig[-1];
+
+ // get approximate quotient
+ quo /= lead_den_digit;
+
+ // multiply quo by den and subtract from num get remainder
+ {
+ mpz_dbl_dig_signed_t borrow = 0;
+
+ for (mpz_dig_t *n = num_dig - den_len, *d = den_dig; n < num_dig; ++n, ++d) {
+ borrow += *n - quo * *d; // will overflow if DIG_SIZE >= 16
+ *n = borrow & DIG_MASK;
+ borrow >>= DIG_SIZE;
+ }
+ borrow += *num_dig; // will overflow if DIG_SIZE >= 16
+ *num_dig = borrow & DIG_MASK;
+ borrow >>= DIG_SIZE;
+
+ // adjust quotient if it is too big
+ for (; borrow != 0; --quo) {
+ mpz_dbl_dig_t carry = 0;
+ for (mpz_dig_t *n = num_dig - den_len, *d = den_dig; n < num_dig; ++n, ++d) {
+ carry += *n + *d;
+ *n = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+ }
+ carry += *num_dig;
+ *num_dig = carry & DIG_MASK;
+ carry >>= DIG_SIZE;
+
+ borrow += carry;
+ }
+ }
+
+ // store this digit of the quotient
+ *quo_dig = quo & DIG_MASK;
+ --quo_dig;
+
+ // move down to next digit of numerator
+ --num_dig;
+ --(*num_len);
+ }
+
+ // unnormalise denomenator
+ for (mpz_dig_t *den = den_dig + den_len - 1, carry = 0; den >= den_dig; --den) {
+ mpz_dig_t d = *den;
+ *den = ((d >> norm_shift) | carry) & DIG_MASK;
+ carry = d << (DIG_SIZE - norm_shift);
+ }
+
+ // unnormalise numerator (remainder now)
+ for (mpz_dig_t *num = orig_num_dig + *num_len - 1, carry = 0; num >= orig_num_dig; --num) {
+ mpz_dig_t n = *num;
+ *num = ((n >> norm_shift) | carry) & DIG_MASK;
+ carry = n << (DIG_SIZE - norm_shift);
+ }
+
+ // strip trailing zeros
+
+ while (*quo_len > 0 && orig_quo_dig[*quo_len - 1] == 0) {
+ --(*quo_len);
+ }
+
+ while (*num_len > 0 && orig_num_dig[*num_len - 1] == 0) {
+ --(*num_len);
+ }
+}
+
+#define MIN_ALLOC (4)
+#define ALIGN_ALLOC (2)
+#define NUM_DIG_FOR_INT (sizeof(int) * 8 / DIG_SIZE + 1)
+
+static const uint log_base2_floor[] = {
+ 0,
+ 0, 1, 1, 2,
+ 2, 2, 2, 3,
+ 3, 3, 3, 3,
+ 3, 3, 3, 4,
+ 4, 4, 4, 4,
+ 4, 4, 4, 4,
+ 4, 4, 4, 4,
+ 4, 4, 4, 5
+};
+
+bool mpz_int_is_sml_int(int i) {
+ return -(1 << DIG_SIZE) < i && i < (1 << DIG_SIZE);
+}
+
+void mpz_init_zero(mpz_t *z) {
+ z->alloc = 0;
+ z->neg = 0;
+ z->len = 0;
+ z->dig = NULL;
+}
+
+void mpz_init_from_int(mpz_t *z, machine_int_t val) {
+ mpz_init_zero(z);
+ mpz_set_from_int(z, val);
+}
+
+void mpz_deinit(mpz_t *z) {
+ if (z != NULL) {
+ m_del(mpz_dig_t, z->dig, z->alloc);
+ }
+}
+
+mpz_t *mpz_zero(void) {
+ mpz_t *z = m_new_obj(mpz_t);
+ mpz_init_zero(z);
+ return z;
+}
+
+mpz_t *mpz_from_int(machine_int_t val) {
+ mpz_t *z = mpz_zero();
+ mpz_set_from_int(z, val);
+ return z;
+}
+
+mpz_t *mpz_from_str(const char *str, uint len, bool neg, uint base) {
+ mpz_t *z = mpz_zero();
+ mpz_set_from_str(z, str, len, neg, base);
+ return z;
+}
+
+void mpz_free(mpz_t *z) {
+ if (z != NULL) {
+ m_del(mpz_dig_t, z->dig, z->alloc);
+ m_del_obj(mpz_t, z);
+ }
+}
+
+STATIC void mpz_need_dig(mpz_t *z, uint need) {
+ uint alloc;
+ if (need < MIN_ALLOC) {
+ alloc = MIN_ALLOC;
+ } else {
+ alloc = (need + ALIGN_ALLOC) & (~(ALIGN_ALLOC - 1));
+ }
+
+ if (z->dig == NULL || z->alloc < alloc) {
+ z->dig = m_renew(mpz_dig_t, z->dig, z->alloc, alloc);
+ z->alloc = alloc;
+ }
+}
+
+mpz_t *mpz_clone(const mpz_t *src) {
+ mpz_t *z = m_new_obj(mpz_t);
+ z->alloc = src->alloc;
+ z->neg = src->neg;
+ z->len = src->len;
+ if (src->dig == NULL) {
+ z->dig = NULL;
+ } else {
+ z->dig = m_new(mpz_dig_t, z->alloc);
+ memcpy(z->dig, src->dig, src->alloc * sizeof(mpz_dig_t));
+ }
+ return z;
+}
+
+void mpz_set(mpz_t *dest, const mpz_t *src) {
+ mpz_need_dig(dest, src->len);
+ dest->neg = src->neg;
+ dest->len = src->len;
+ memcpy(dest->dig, src->dig, src->len * sizeof(mpz_dig_t));
+}
+
+void mpz_set_from_int(mpz_t *z, machine_int_t val) {
+ mpz_need_dig(z, NUM_DIG_FOR_INT);
+
+ if (val < 0) {
+ z->neg = 1;
+ val = -val;
+ } else {
+ z->neg = 0;
+ }
+
+ z->len = 0;
+ while (val > 0) {
+ z->dig[z->len++] = val & DIG_MASK;
+ val >>= DIG_SIZE;
+ }
+}
+
+// returns number of bytes from str that were processed
+uint mpz_set_from_str(mpz_t *z, const char *str, uint len, bool neg, uint base) {
+ assert(base < 36);
+
+ const char *cur = str;
+ const char *top = str + len;
+
+ mpz_need_dig(z, len * 8 / DIG_SIZE + 1);
+
+ if (neg) {
+ z->neg = 1;
+ } else {
+ z->neg = 0;
+ }
+
+ z->len = 0;
+ for (; cur < top; ++cur) { // XXX UTF8 next char
+ //uint v = char_to_numeric(cur#); // XXX UTF8 get char
+ uint v = *cur;
+ if ('0' <= v && v <= '9') {
+ v -= '0';
+ } else if ('A' <= v && v <= 'Z') {
+ v -= 'A' - 10;
+ } else if ('a' <= v && v <= 'z') {
+ v -= 'a' - 10;
+ } else {
+ break;
+ }
+ if (v >= base) {
+ break;
+ }
+ z->len = mpn_mul_dig_add_dig(z->dig, z->len, base, v);
+ }
+
+ return cur - str;
+}
+
+bool mpz_is_zero(const mpz_t *z) {
+ return z->len == 0;
+}
+
+bool mpz_is_pos(const mpz_t *z) {
+ return z->len > 0 && z->neg == 0;
+}
+
+bool mpz_is_neg(const mpz_t *z) {
+ return z->len > 0 && z->neg != 0;
+}
+
+bool mpz_is_odd(const mpz_t *z) {
+ return z->len > 0 && (z->dig[0] & 1) != 0;
+}
+
+bool mpz_is_even(const mpz_t *z) {
+ return z->len == 0 || (z->dig[0] & 1) == 0;
+}
+
+int mpz_cmp(const mpz_t *z1, const mpz_t *z2) {
+ int cmp = z2->neg - z1->neg;
+ if (cmp != 0) {
+ return cmp;
+ }
+ cmp = mpn_cmp(z1->dig, z1->len, z2->dig, z2->len);
+ if (z1->neg != 0) {
+ cmp = -cmp;
+ }
+ return cmp;
+}
+
+int mpz_cmp_sml_int(const mpz_t *z, int sml_int) {
+ int cmp;
+ if (z->neg == 0) {
+ if (sml_int < 0) return 1;
+ if (sml_int == 0) {
+ if (z->len == 0) return 0;
+ return 1;
+ }
+ if (z->len == 0) return -1;
+ assert(sml_int < (1 << DIG_SIZE));
+ if (z->len != 1) return 1;
+ cmp = z->dig[0] - sml_int;
+ } else {
+ if (sml_int > 0) return -1;
+ if (sml_int == 0) {
+ if (z->len == 0) return 0;
+ return -1;
+ }
+ if (z->len == 0) return 1;
+ assert(sml_int > -(1 << DIG_SIZE));
+ if (z->len != 1) return -1;
+ cmp = -z->dig[0] - sml_int;
+ }
+ if (cmp < 0) return -1;
+ if (cmp > 0) return 1;
+ return 0;
+}
+
+/* not finished
+mpz_t *mpz_shl(mpz_t *dest, const mpz_t *lhs, int rhs)
+{
+ if (dest != lhs)
+ dest = mpz_set(dest, lhs);
+
+ if (dest.len == 0 || rhs == 0)
+ return dest;
+
+ if (rhs < 0)
+ return mpz_shr(dest, dest, -rhs);
+
+ printf("mpz_shl: not implemented\n");
+
+ return dest;
+}
+
+mpz_t *mpz_shr(mpz_t *dest, const mpz_t *lhs, int rhs)
+{
+ if (dest != lhs)
+ dest = mpz_set(dest, lhs);
+
+ if (dest.len == 0 || rhs == 0)
+ return dest;
+
+ if (rhs < 0)
+ return mpz_shl(dest, dest, -rhs);
+
+ dest.len = mpn_shr(dest.len, dest.dig, rhs);
+ dest.dig[dest.len .. dest->alloc] = 0;
+
+ return dest;
+}
+*/
+
+
+#if 0
+these functions are unused
+
+/* returns abs(z)
+*/
+mpz_t *mpz_abs(const mpz_t *z) {
+ mpz_t *z2 = mpz_clone(z);
+ z2->neg = 0;
+ return z2;
+}
+
+/* returns -z
+*/
+mpz_t *mpz_neg(const mpz_t *z) {
+ mpz_t *z2 = mpz_clone(z);
+ z2->neg = 1 - z2->neg;
+ return z2;
+}
+
+/* returns lhs + rhs
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_add(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t *z = mpz_zero();
+ mpz_add_inpl(z, lhs, rhs);
+ return z;
+}
+
+/* returns lhs - rhs
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_sub(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t *z = mpz_zero();
+ mpz_sub_inpl(z, lhs, rhs);
+ return z;
+}
+
+/* returns lhs * rhs
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_mul(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t *z = mpz_zero();
+ mpz_mul_inpl(z, lhs, rhs);
+ return z;
+}
+
+/* returns lhs ** rhs
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_pow(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t *z = mpz_zero();
+ mpz_pow_inpl(z, lhs, rhs);
+ return z;
+}
+#endif
+
+/* computes dest = abs(z)
+ can have dest, z the same
+*/
+void mpz_abs_inpl(mpz_t *dest, const mpz_t *z) {
+ if (dest != z) {
+ mpz_set(dest, z);
+ }
+ dest->neg = 0;
+}
+
+/* computes dest = -z
+ can have dest, z the same
+*/
+void mpz_neg_inpl(mpz_t *dest, const mpz_t *z) {
+ if (dest != z) {
+ mpz_set(dest, z);
+ }
+ dest->neg = 1 - dest->neg;
+}
+
+/* computes dest = lhs + rhs
+ can have dest, lhs, rhs the same
+*/
+void mpz_add_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
+ if (mpn_cmp(lhs->dig, lhs->len, rhs->dig, rhs->len) < 0) {
+ const mpz_t *temp = lhs;
+ lhs = rhs;
+ rhs = temp;
+ }
+
+ if (lhs->neg == rhs->neg) {
+ mpz_need_dig(dest, lhs->len + 1);
+ dest->len = mpn_add(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
+ } else {
+ mpz_need_dig(dest, lhs->len);
+ dest->len = mpn_sub(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
+ }
+
+ dest->neg = lhs->neg;
+}
+
+/* computes dest = lhs - rhs
+ can have dest, lhs, rhs the same
+*/
+void mpz_sub_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
+ bool neg = false;
+
+ if (mpn_cmp(lhs->dig, lhs->len, rhs->dig, rhs->len) < 0) {
+ const mpz_t *temp = lhs;
+ lhs = rhs;
+ rhs = temp;
+ neg = true;
+ }
+
+ if (lhs->neg != rhs->neg) {
+ mpz_need_dig(dest, lhs->len + 1);
+ dest->len = mpn_add(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
+ } else {
+ mpz_need_dig(dest, lhs->len);
+ dest->len = mpn_sub(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
+ }
+
+ if (neg) {
+ dest->neg = 1 - lhs->neg;
+ } else {
+ dest->neg = lhs->neg;
+ }
+}
+
+/* computes dest = lhs * rhs
+ can have dest, lhs, rhs the same
+*/
+void mpz_mul_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs)
+{
+ if (lhs->len == 0 || rhs->len == 0) {
+ return mpz_set_from_int(dest, 0);
+ }
+
+ mpz_t *temp = NULL;
+ if (lhs == dest) {
+ lhs = temp = mpz_clone(lhs);
+ if (rhs == dest) {
+ rhs = lhs;
+ }
+ } else if (rhs == dest) {
+ rhs = temp = mpz_clone(rhs);
+ }
+
+ mpz_need_dig(dest, lhs->len + rhs->len); // min mem l+r-1, max mem l+r
+ memset(dest->dig, 0, dest->alloc * sizeof(mpz_dig_t));
+ dest->len = mpn_mul(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
+
+ if (lhs->neg == rhs->neg) {
+ dest->neg = 0;
+ } else {
+ dest->neg = 1;
+ }
+
+ mpz_free(temp);
+}
+
+/* computes dest = lhs ** rhs
+ can have dest, lhs, rhs the same
+*/
+void mpz_pow_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
+ if (lhs->len == 0 || rhs->neg != 0) {
+ return mpz_set_from_int(dest, 0);
+ }
+
+ if (rhs->len == 0) {
+ return mpz_set_from_int(dest, 1);
+ }
+
+ mpz_t *x = mpz_clone(lhs);
+ mpz_t *n = mpz_clone(rhs);
+
+ mpz_set_from_int(dest, 1);
+
+ while (n->len > 0) {
+ if (mpz_is_odd(n)) {
+ mpz_mul_inpl(dest, dest, x);
+ }
+ mpz_mul_inpl(x, x, x);
+ n->len = mpn_shr(n->dig, n->dig, n->len, 1);
+ }
+
+ mpz_free(x);
+ mpz_free(n);
+}
+
+/* computes gcd(z1, z2)
+ based on Knuth's modified gcd algorithm (I think?)
+ gcd(z1, z2) >= 0
+ gcd(0, 0) = 0
+ gcd(z, 0) = abs(z)
+*/
+mpz_t *mpz_gcd(const mpz_t *z1, const mpz_t *z2) {
+ if (z1->len == 0) {
+ mpz_t *a = mpz_clone(z2);
+ a->neg = 0;
+ return a;
+ } else if (z2->len == 0) {
+ mpz_t *a = mpz_clone(z1);
+ a->neg = 0;
+ return a;
+ }
+
+ mpz_t *a = mpz_clone(z1);
+ mpz_t *b = mpz_clone(z2);
+ mpz_t c; mpz_init_zero(&c);
+ a->neg = 0;
+ b->neg = 0;
+
+ for (;;) {
+ if (mpz_cmp(a, b) < 0) {
+ if (a->len == 0) {
+ mpz_free(a);
+ mpz_deinit(&c);
+ return b;
+ }
+ mpz_t *t = a; a = b; b = t;
+ }
+ if (!(b->len >= 2 || (b->len == 1 && b->dig[0] > 1))) { // compute b > 0; could be mpz_cmp_small_int(b, 1) > 0
+ break;
+ }
+ mpz_set(&c, b);
+ do {
+ mpz_add_inpl(&c, &c, &c);
+ } while (mpz_cmp(&c, a) <= 0);
+ c.len = mpn_shr(c.dig, c.dig, c.len, 1);
+ mpz_sub_inpl(a, a, &c);
+ }
+
+ mpz_deinit(&c);
+
+ if (b->len == 1 && b->dig[0] == 1) { // compute b == 1; could be mpz_cmp_small_int(b, 1) == 0
+ mpz_free(a);
+ return b;
+ } else {
+ mpz_free(b);
+ return a;
+ }
+}
+
+/* computes lcm(z1, z2)
+ = abs(z1) / gcd(z1, z2) * abs(z2)
+ lcm(z1, z1) >= 0
+ lcm(0, 0) = 0
+ lcm(z, 0) = 0
+*/
+mpz_t *mpz_lcm(const mpz_t *z1, const mpz_t *z2)
+{
+ if (z1->len == 0 || z2->len == 0)
+ return mpz_zero();
+
+ mpz_t *gcd = mpz_gcd(z1, z2);
+ mpz_t *quo = mpz_zero();
+ mpz_t *rem = mpz_zero();
+ mpz_divmod_inpl(quo, rem, z1, gcd);
+ mpz_mul_inpl(rem, quo, z2);
+ mpz_free(gcd);
+ mpz_free(quo);
+ rem->neg = 0;
+ return rem;
+}
+
+/* computes new integers in quo and rem such that:
+ quo * rhs + rem = lhs
+ 0 <= rem < rhs
+ can have lhs, rhs the same
+*/
+void mpz_divmod(const mpz_t *lhs, const mpz_t *rhs, mpz_t **quo, mpz_t **rem) {
+ *quo = mpz_zero();
+ *rem = mpz_zero();
+ mpz_divmod_inpl(*quo, *rem, lhs, rhs);
+}
+
+/* computes new integers in quo and rem such that:
+ quo * rhs + rem = lhs
+ 0 <= rem < rhs
+ can have lhs, rhs the same
+*/
+void mpz_divmod_inpl(mpz_t *dest_quo, mpz_t *dest_rem, const mpz_t *lhs, const mpz_t *rhs) {
+ if (rhs->len == 0) {
+ mpz_set_from_int(dest_quo, 0);
+ mpz_set_from_int(dest_rem, 0);
+ return;
+ }
+
+ mpz_need_dig(dest_quo, lhs->len + 1); // +1 necessary?
+ memset(dest_quo->dig, 0, (lhs->len + 1) * sizeof(mpz_dig_t));
+ dest_quo->len = 0;
+ mpz_need_dig(dest_rem, lhs->len + 1); // +1 necessary?
+ mpz_set(dest_rem, lhs);
+ //rhs->dig[rhs->len] = 0;
+ mpn_div(dest_rem->dig, &dest_rem->len, rhs->dig, rhs->len, dest_quo->dig, &dest_quo->len);
+
+ if (lhs->neg != rhs->neg) {
+ dest_quo->neg = 1;
+ }
+}
+
+#if 0
+these functions are unused
+
+/* computes floor(lhs / rhs)
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_div(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t *quo = mpz_zero();
+ mpz_t rem; mpz_init_zero(&rem);
+ mpz_divmod_inpl(quo, &rem, lhs, rhs);
+ mpz_deinit(&rem);
+ return quo;
+}
+
+/* computes lhs % rhs ( >= 0)
+ can have lhs, rhs the same
+*/
+mpz_t *mpz_mod(const mpz_t *lhs, const mpz_t *rhs) {
+ mpz_t quo; mpz_init_zero(&quo);
+ mpz_t *rem = mpz_zero();
+ mpz_divmod_inpl(&quo, rem, lhs, rhs);
+ mpz_deinit(&quo);
+ return rem;
+}
+#endif
+
+int mpz_as_int(const mpz_t *i) {
+ int val = 0;
+ mpz_dig_t *d = i->dig + i->len;
+
+ while (--d >= i->dig)
+ {
+ int oldval = val;
+ val = (val << DIG_SIZE) | *d;
+ if (val < oldval)
+ {
+ if (i->neg == 0) {
+ return 0x7fffffff;
+ } else {
+ return 0x80000000;
+ }
+ }
+ }
+
+ if (i->neg != 0) {
+ val = -val;
+ }
+
+ return val;
+}
+
+machine_float_t mpz_as_float(const mpz_t *i) {
+ machine_float_t val = 0;
+ mpz_dig_t *d = i->dig + i->len;
+
+ while (--d >= i->dig) {
+ val = val * (1 << DIG_SIZE) + *d;
+ }
+
+ if (i->neg != 0) {
+ val = -val;
+ }
+
+ return val;
+}
+
+uint mpz_as_str_size(const mpz_t *i, uint base) {
+ if (base < 2 || base > 32) {
+ return 0;
+ }
+
+ return i->len * DIG_SIZE / log_base2_floor[base] + 2 + 1; // +1 for null byte termination
+}
+
+char *mpz_as_str(const mpz_t *i, uint base) {
+ char *s = m_new(char, mpz_as_str_size(i, base));
+ mpz_as_str_inpl(i, base, s);
+ return s;
+}
+
+// assumes enough space as calculated by mpz_as_str_size
+// returns length of string, not including null byte
+uint mpz_as_str_inpl(const mpz_t *i, uint base, char *str) {
+ if (str == NULL || base < 2 || base > 32) {
+ str[0] = 0;
+ return 0;
+ }
+
+ uint ilen = i->len;
+
+ if (ilen == 0) {
+ str[0] = '0';
+ str[1] = 0;
+ return 1;
+ }
+
+ // make a copy of mpz digits
+ mpz_dig_t *dig = m_new(mpz_dig_t, ilen);
+ memcpy(dig, i->dig, ilen * sizeof(mpz_dig_t));
+
+ // convert
+ char *s = str;
+ bool done;
+ do {
+ mpz_dig_t *d = dig + ilen;
+ mpz_dbl_dig_t a = 0;
+
+ // compute next remainder
+ while (--d >= dig) {
+ a = (a << DIG_SIZE) | *d;
+ *d = a / base;
+ a %= base;
+ }
+
+ // convert to character
+ a += '0';
+ if (a > '9') {
+ a += 'a' - '9' - 1;
+ }
+ *s++ = a;
+
+ // check if number is zero
+ done = true;
+ for (d = dig; d < dig + ilen; ++d) {
+ if (*d != 0) {
+ done = false;
+ break;
+ }
+ }
+ } while (!done);
+
+ if (i->neg != 0) {
+ *s++ = '-';
+ }
+
+ // reverse string
+ for (char *u = str, *v = s - 1; u < v; ++u, --v) {
+ char temp = *u;
+ *u = *v;
+ *v = temp;
+ }
+
+ s[0] = 0; // null termination
+
+ return s - str;
+}
+
+#endif // MICROPY_LONGINT_IMPL == MICROPY_LONGINT_IMPL_MPZ
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