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Py: Complete implementation of mpz_ and or xor for negative arguments #1810

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dbd852d
Complete implementation of mpz_ and or xor for negative arguments
dcurrie Jan 31, 2016
f7cdb8f
py: code size optimizations in mpz and_neg or_neg xor_neg
dcurrie Feb 1, 2016
14b46e2
py: save a few more __text bytes in mpz_neg_and_or_xor
dcurrie Feb 1, 2016
30b3cb7
py: fix comments in py/mpz.c per code review
dcurrie Feb 1, 2016
3ea800d
py: compile time option MICROPY_MPZ_BITWISE_SPEEDIER for benchmarking
dcurrie Feb 1, 2016
5ce8baa
Merge branch 'master' into mpz_neg_and_or_xor
dcurrie Feb 1, 2016
233e47c
py: rename MICROPY_MPZ_BITWISE_SPEEDIER to MICROPY_MPZ_BITWISE_FAST
dcurrie Feb 2, 2016
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261 changes: 201 additions & 60 deletions py/mpz.c
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Original file line number Diff line number Diff line change
Expand Up @@ -29,9 +29,6 @@

#include "py/mpz.h"

// this is only needed for mp_not_implemented, which should eventually be removed
#include "py/runtime.h"

#if MICROPY_LONGINT_IMPL == MICROPY_LONGINT_IMPL_MPZ

#define DIG_SIZE (MPZ_DIG_SIZE)
Expand Down Expand Up @@ -199,6 +196,16 @@ STATIC mp_uint_t mpn_sub(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen,
return idig + 1 - oidig;
}

STATIC mp_uint_t mpn_trimmed_length(mpz_dig_t *oidig, mpz_dig_t *idig) {
// remove trailing zeros
for (--idig; idig >= oidig && *idig == 0; --idig) {
}

return idig + 1 - oidig;
}

#if MICROPY_MPZ_BITWISE_FAST

/* computes i = j & k
returns number of digits in i
assumes enough memory in i; assumes normalised j, k; assumes jlen >= klen (jlen argument not needed)
Expand All @@ -218,34 +225,43 @@ STATIC mp_uint_t mpn_and(mpz_dig_t *idig, const mpz_dig_t *jdig, const mpz_dig_t
return idig + 1 - oidig;
}

/* computes i = j & -k = j & (~k + 1)
#endif

/* i = -((-j) & (-k)) = ~((~j + 1) & (~k + 1)) + 1
i = (j & (-k)) = (j & (~k + 1)) = ( j & (~k + 1))
i = ((-j) & k) = ((~j + 1) & k) = ((~j + 1) & k )
computes general form:
i = (im ^ (((j ^ jm) + jc) & ((k ^ km) + kc))) + ic where Xm = Xc == 0 ? 0 : DIG_MASK
returns number of digits in i
assumes enough memory in i; assumes normalised j, k
assumes enough memory in i; assumes normalised j, k; assumes length j >= length k
can have i, j, k pointing to same memory
*/
STATIC mp_uint_t mpn_and_neg(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen, const mpz_dig_t *kdig, mp_uint_t klen) {
STATIC mp_uint_t mpn_and_neg(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen, const mpz_dig_t *kdig, mp_uint_t klen,
mpz_dbl_dig_t carryi, mpz_dbl_dig_t carryj, mpz_dbl_dig_t carryk) {
mpz_dig_t *oidig = idig;
mpz_dbl_dig_t carry = 1;
mpz_dig_t imask = (0 == carryi) ? 0 : DIG_MASK;
mpz_dig_t jmask = (0 == carryj) ? 0 : DIG_MASK;
mpz_dig_t kmask = (0 == carryk) ? 0 : DIG_MASK;

for (; jlen > 0 && klen > 0; --jlen, --klen, ++idig, ++jdig, ++kdig) {
carry += *kdig ^ DIG_MASK;
*idig = (*jdig & carry) & DIG_MASK;
carry >>= DIG_SIZE;
for (; jlen > 0; ++idig, ++jdig) {
carryj += *jdig ^ jmask;
carryk += (--klen <= --jlen) ? (*kdig++ ^ kmask) : kmask;
carryi += ((carryj & carryk) ^ imask) & DIG_MASK;
*idig = carryi & DIG_MASK;
carryk >>= DIG_SIZE;
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This is not good. DIG_SIZE is usually the number of bits in mpz_dig_t (eg 16, uint16_t) and so this shift is undefined by the C standard.

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carryk is a mpz_dbl_dig_t as are all the carryX

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Ah, yes, correct! I was looking at the type of the masks....

carryj >>= DIG_SIZE;
carryi >>= DIG_SIZE;
}

for (; jlen > 0; --jlen, ++idig, ++jdig) {
carry += DIG_MASK;
*idig = (*jdig & carry) & DIG_MASK;
carry >>= DIG_SIZE;
if (0 != carryi) {
*idig++ = carryi;
}

// remove trailing zeros
for (--idig; idig >= oidig && *idig == 0; --idig) {
}

return idig + 1 - oidig;
return mpn_trimmed_length(oidig, idig);
}

#if MICROPY_MPZ_BITWISE_FAST

/* computes i = j | k
returns number of digits in i
assumes enough memory in i; assumes normalised j, k; assumes jlen >= klen
Expand All @@ -267,6 +283,10 @@ STATIC mp_uint_t mpn_or(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen,
return idig - oidig;
}

#endif

#if MICROPY_MPZ_BITWISE_FAST

/* computes i = j ^ k
returns number of digits in i
assumes enough memory in i; assumes normalised j, k; assumes jlen >= klen
Expand All @@ -292,6 +312,102 @@ STATIC mp_uint_t mpn_xor(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen,
return idig + 1 - oidig;
}

#endif

/* i = (-j) ^ (-k) = ~(j - 1) ^ ~(k - 1) = (j - 1) ^ (k - 1)
i = -(j ^ (-k)) = -(j ^ ~(k - 1)) = ~(j ^ ~(k - 1)) + 1 = (j ^ (k - 1)) + 1
i = -((-j) ^ k) = -(~(j - 1) ^ k) = ~(~(j - 1) ^ k) + 1 = ((j - 1) ^ k) + 1
computes general form:
i = ((j - 1 + jc) ^ (k - 1 + kc)) + ic
returns number of digits in i
assumes enough memory in i; assumes normalised j, k; assumes length j >= length k
can have i, j, k pointing to same memory
*/
STATIC mp_uint_t mpn_xor_neg(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen, const mpz_dig_t *kdig, mp_uint_t klen,
mpz_dbl_dig_t carryi, mpz_dbl_dig_t carryj, mpz_dbl_dig_t carryk) {
mpz_dig_t *oidig = idig;

for (; jlen > 0; ++idig, ++jdig) {
carryj += *jdig + DIG_MASK;
carryk += (--klen <= --jlen) ? (*kdig++ + DIG_MASK) : DIG_MASK;
carryi += (carryj ^ carryk) & DIG_MASK;
*idig = carryi & DIG_MASK;
carryk >>= DIG_SIZE;
carryj >>= DIG_SIZE;
carryi >>= DIG_SIZE;
}

if (0 != carryi) {
*idig++ = carryi;
}

return mpn_trimmed_length(oidig, idig);
}

/* i = -((-j) | (-k)) = ~((~j + 1) | (~k + 1)) + 1
i = -(j | (-k)) = -(j | (~k + 1)) = ~( j | (~k + 1)) + 1
i = -((-j) | k) = -((~j + 1) | k) = ~((~j + 1) | k ) + 1
computes general form:
i = ~(((j ^ jm) + jc) | ((k ^ km) + kc)) + 1 where Xm = Xc == 0 ? 0 : DIG_MASK
returns number of digits in i
assumes enough memory in i; assumes normalised j, k; assumes length j >= length k
can have i, j, k pointing to same memory
*/

#if MICROPY_MPZ_BITWISE_FAST

STATIC mp_uint_t mpn_or_neg(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen, const mpz_dig_t *kdig, mp_uint_t klen,
mpz_dbl_dig_t carryj, mpz_dbl_dig_t carryk) {
mpz_dig_t *oidig = idig;
mpz_dbl_dig_t carryi = 1;
mpz_dig_t jmask = (0 == carryj) ? 0 : DIG_MASK;
mpz_dig_t kmask = (0 == carryk) ? 0 : DIG_MASK;

for (; jlen > 0; ++idig, ++jdig) {
carryj += *jdig ^ jmask;
carryk += (--klen <= --jlen) ? (*kdig++ ^ kmask) : kmask;
carryi += ((carryj | carryk) ^ DIG_MASK) & DIG_MASK;
*idig = carryi & DIG_MASK;
carryk >>= DIG_SIZE;
carryj >>= DIG_SIZE;
carryi >>= DIG_SIZE;
}

if (0 != carryi) {
*idig++ = carryi;
}

return mpn_trimmed_length(oidig, idig);
}

#else

STATIC mp_uint_t mpn_or_neg(mpz_dig_t *idig, const mpz_dig_t *jdig, mp_uint_t jlen, const mpz_dig_t *kdig, mp_uint_t klen,
mpz_dbl_dig_t carryi, mpz_dbl_dig_t carryj, mpz_dbl_dig_t carryk) {
mpz_dig_t *oidig = idig;
mpz_dig_t imask = (0 == carryi) ? 0 : DIG_MASK;
mpz_dig_t jmask = (0 == carryj) ? 0 : DIG_MASK;
mpz_dig_t kmask = (0 == carryk) ? 0 : DIG_MASK;

for (; jlen > 0; ++idig, ++jdig) {
carryj += *jdig ^ jmask;
carryk += (--klen <= --jlen) ? (*kdig++ ^ kmask) : kmask;
carryi += ((carryj | carryk) ^ imask) & DIG_MASK;
*idig = carryi & DIG_MASK;
carryk >>= DIG_SIZE;
carryj >>= DIG_SIZE;
carryi >>= DIG_SIZE;
}

if (0 != carryi) {
*idig++ = carryi;
}

return mpn_trimmed_length(oidig, idig);
}

#endif

/* computes i = i * d1 + d2
returns number of digits in i
assumes enough memory in i; assumes normalised i; assumes dmul != 0
Expand Down Expand Up @@ -1097,81 +1213,106 @@ void mpz_sub_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
can have dest, lhs, rhs the same
*/
void mpz_and_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
if (lhs->neg == rhs->neg) {
if (lhs->neg == 0) {
// make sure lhs has the most digits
if (lhs->len < rhs->len) {
const mpz_t *temp = lhs;
lhs = rhs;
rhs = temp;
}
// do the and'ing
mpz_need_dig(dest, rhs->len);
dest->len = mpn_and(dest->dig, lhs->dig, rhs->dig, rhs->len);
dest->neg = 0;
} else {
// TODO both args are negative
mp_not_implemented("bignum and with negative args");
}
// make sure lhs has the most digits
if (lhs->len < rhs->len) {
const mpz_t *temp = lhs;
lhs = rhs;
rhs = temp;
}

#if MICROPY_MPZ_BITWISE_FAST

if ((0 == lhs->neg) && (0 == rhs->neg)) {
mpz_need_dig(dest, lhs->len);
dest->len = mpn_and(dest->dig, lhs->dig, rhs->dig, rhs->len);
dest->neg = 0;
} else {
// args have different sign
// make sure lhs is the positive arg
if (rhs->neg == 0) {
const mpz_t *temp = lhs;
lhs = rhs;
rhs = temp;
}
mpz_need_dig(dest, lhs->len + 1);
dest->len = mpn_and_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
assert(dest->len <= dest->alloc);
dest->neg = 0;
dest->len = mpn_and_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len,
lhs->neg == rhs->neg, 0 != lhs->neg, 0 != rhs->neg);
dest->neg = lhs->neg & rhs->neg;
}

#else

mpz_need_dig(dest, lhs->len + (lhs->neg || rhs->neg));
dest->len = mpn_and_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len,
(lhs->neg == rhs->neg) ? lhs->neg : 0, lhs->neg, rhs->neg);
dest->neg = lhs->neg & rhs->neg;

#endif
}

/* computes dest = lhs | rhs
can have dest, lhs, rhs the same
*/
void mpz_or_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
if (mpn_cmp(lhs->dig, lhs->len, rhs->dig, rhs->len) < 0) {
// make sure lhs has the most digits
if (lhs->len < rhs->len) {
const mpz_t *temp = lhs;
lhs = rhs;
rhs = temp;
}

if (lhs->neg == rhs->neg) {
#if MICROPY_MPZ_BITWISE_FAST

if ((0 == lhs->neg) && (0 == rhs->neg)) {
mpz_need_dig(dest, lhs->len);
dest->len = mpn_or(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
dest->neg = 0;
} else {
mpz_need_dig(dest, lhs->len);
// TODO
mp_not_implemented("bignum or with negative args");
// dest->len = mpn_or_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
mpz_need_dig(dest, lhs->len + 1);
dest->len = mpn_or_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len,
0 != lhs->neg, 0 != rhs->neg);
dest->neg = 1;
}

dest->neg = lhs->neg;
#else

mpz_need_dig(dest, lhs->len + (lhs->neg || rhs->neg));
dest->len = mpn_or_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len,
(lhs->neg || rhs->neg), lhs->neg, rhs->neg);
dest->neg = lhs->neg | rhs->neg;

#endif
}

/* computes dest = lhs ^ rhs
can have dest, lhs, rhs the same
*/
void mpz_xor_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
if (mpn_cmp(lhs->dig, lhs->len, rhs->dig, rhs->len) < 0) {
// make sure lhs has the most digits
if (lhs->len < rhs->len) {
const mpz_t *temp = lhs;
lhs = rhs;
rhs = temp;
}

#if MICROPY_MPZ_BITWISE_FAST

if (lhs->neg == rhs->neg) {
mpz_need_dig(dest, lhs->len);
dest->len = mpn_xor(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
if (lhs->neg == 0) {
dest->len = mpn_xor(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
} else {
dest->len = mpn_xor_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len, 0, 0, 0);
}
dest->neg = 0;
} else {
mpz_need_dig(dest, lhs->len);
// TODO
mp_not_implemented("bignum xor with negative args");
// dest->len = mpn_xor_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
mpz_need_dig(dest, lhs->len + 1);
dest->len = mpn_xor_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len, 1,
0 == lhs->neg, 0 == rhs->neg);
dest->neg = 1;
}

dest->neg = 0;
#else

mpz_need_dig(dest, lhs->len + (lhs->neg || rhs->neg));
dest->len = mpn_xor_neg(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len,
(lhs->neg != rhs->neg), 0 == lhs->neg, 0 == rhs->neg);
dest->neg = lhs->neg ^ rhs->neg;

#endif
}

/* computes dest = lhs * rhs
Expand Down
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