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| | /* Big numbers for Emacs.
Copyright 2018 Free Software Foundation, Inc.
This file is part of GNU Emacs.
GNU Emacs is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.
GNU Emacs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>. */
#include <config.h>
#include "bignum.h"
#include "lisp.h"
#include <math.h>
#include <stdlib.h>
/* mpz global temporaries. Making them global saves the trouble of
properly using mpz_init and mpz_clear on temporaries even when
storage is exhausted. Admittedly this is not ideal. An mpz value
in a temporary is made permanent by mpz_swapping it with a bignum's
value. Although typically at most two temporaries are needed,
rounding_driver and rounddiv_q need four altogther. */
mpz_t mpz[4];
static void *
xrealloc_for_gmp (void *ptr, size_t ignore, size_t size)
{
return xrealloc (ptr, size);
}
static void
xfree_for_gmp (void *ptr, size_t ignore)
{
xfree (ptr);
}
void
init_bignum (void)
{
eassert (mp_bits_per_limb == GMP_NUMB_BITS);
integer_width = 1 << 16;
mp_set_memory_functions (xmalloc, xrealloc_for_gmp, xfree_for_gmp);
for (int i = 0; i < ARRAYELTS (mpz); i++)
mpz_init (mpz[i]);
}
/* Return the value of the Lisp bignum N, as a double. */
double
bignum_to_double (Lisp_Object n)
{
return mpz_get_d_rounded (XBIGNUM (n)->value);
}
/* Return D, converted to a Lisp integer. Discard any fraction.
Signal an error if D cannot be converted. */
Lisp_Object
double_to_integer (double d)
{
if (!isfinite (d))
overflow_error ();
mpz_set_d (mpz[0], d);
return make_integer_mpz ();
}
/* Return a Lisp integer equal to mpz[0], which has BITS bits and which
must not be in fixnum range. Set mpz[0] to a junk value. */
static Lisp_Object
make_bignum_bits (size_t bits)
{
/* The documentation says integer-width should be nonnegative, so
a single comparison suffices even though 'bits' is unsigned. */
if (integer_width < bits)
overflow_error ();
struct Lisp_Bignum *b = ALLOCATE_PSEUDOVECTOR (struct Lisp_Bignum, value,
PVEC_BIGNUM);
mpz_init (b->value);
mpz_swap (b->value, mpz[0]);
return make_lisp_ptr (b, Lisp_Vectorlike);
}
/* Return a Lisp integer equal to mpz[0], which must not be in fixnum range.
Set mpz[0] to a junk value. */
static Lisp_Object
make_bignum (void)
{
return make_bignum_bits (mpz_sizeinbase (mpz[0], 2));
}
/* Return a Lisp integer equal to N, which must not be in fixnum range. */
Lisp_Object
make_bigint (intmax_t n)
{
eassert (FIXNUM_OVERFLOW_P (n));
mpz_set_intmax (mpz[0], n);
return make_bignum ();
}
Lisp_Object
make_biguint (uintmax_t n)
{
eassert (FIXNUM_OVERFLOW_P (n));
mpz_set_uintmax (mpz[0], n);
return make_bignum ();
}
/* Return a Lisp integer with value taken from mpz[0].
Set mpz[0] to a junk value. */
Lisp_Object
make_integer_mpz (void)
{
size_t bits = mpz_sizeinbase (mpz[0], 2);
if (bits <= FIXNUM_BITS)
{
EMACS_INT v = 0;
int i = 0, shift = 0;
do
{
EMACS_INT limb = mpz_getlimbn (mpz[0], i++);
v += limb << shift;
shift += GMP_NUMB_BITS;
}
while (shift < bits);
if (mpz_sgn (mpz[0]) < 0)
v = -v;
if (!FIXNUM_OVERFLOW_P (v))
return make_fixnum (v);
}
return make_bignum_bits (bits);
}
/* Set RESULT to V. This code is for when intmax_t is wider than long. */
void
mpz_set_intmax_slow (mpz_t result, intmax_t v)
{
int maxlimbs = (INTMAX_WIDTH + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
mp_limb_t *limb = mpz_limbs_write (result, maxlimbs);
int n = 0;
uintmax_t u = v;
bool negative = v < 0;
if (negative)
{
uintmax_t two = 2;
u = -u & ((two << (UINTMAX_WIDTH - 1)) - 1);
}
do
{
limb[n++] = u;
u = GMP_NUMB_BITS < UINTMAX_WIDTH ? u >> GMP_NUMB_BITS : 0;
}
while (u != 0);
mpz_limbs_finish (result, negative ? -n : n);
}
void
mpz_set_uintmax_slow (mpz_t result, uintmax_t v)
{
int maxlimbs = (UINTMAX_WIDTH + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
mp_limb_t *limb = mpz_limbs_write (result, maxlimbs);
int n = 0;
do
{
limb[n++] = v;
v = GMP_NUMB_BITS < INTMAX_WIDTH ? v >> GMP_NUMB_BITS : 0;
}
while (v != 0);
mpz_limbs_finish (result, n);
}
/* If Z fits into *PI, store its value there and return true.
Return false otherwise. */
bool
mpz_to_intmax (mpz_t const z, intmax_t *pi)
{
ptrdiff_t bits = mpz_sizeinbase (z, 2);
bool negative = mpz_sgn (z) < 0;
if (bits < INTMAX_WIDTH)
{
intmax_t v = 0;
int i = 0, shift = 0;
do
{
intmax_t limb = mpz_getlimbn (z, i++);
v += limb << shift;
shift += GMP_NUMB_BITS;
}
while (shift < bits);
*pi = negative ? -v : v;
return true;
}
if (bits == INTMAX_WIDTH && INTMAX_MIN < -INTMAX_MAX && negative
&& mpz_scan1 (z, 0) == INTMAX_WIDTH - 1)
{
*pi = INTMAX_MIN;
return true;
}
return false;
}
bool
mpz_to_uintmax (mpz_t const z, uintmax_t *pi)
{
if (mpz_sgn (z) < 0)
return false;
ptrdiff_t bits = mpz_sizeinbase (z, 2);
if (UINTMAX_WIDTH < bits)
return false;
uintmax_t v = 0;
int i = 0, shift = 0;
do
{
uintmax_t limb = mpz_getlimbn (z, i++);
v += limb << shift;
shift += GMP_NUMB_BITS;
}
while (shift < bits);
*pi = v;
return true;
}
/* Return the value of the bignum X if it fits, 0 otherwise.
A bignum cannot be zero, so 0 indicates failure reliably. */
intmax_t
bignum_to_intmax (Lisp_Object x)
{
intmax_t i;
return mpz_to_intmax (XBIGNUM (x)->value, &i) ? i : 0;
}
uintmax_t
bignum_to_uintmax (Lisp_Object x)
{
uintmax_t i;
return mpz_to_uintmax (XBIGNUM (x)->value, &i) ? i : 0;
}
/* Yield an upper bound on the buffer size needed to contain a C
string representing the NUM in base BASE. This includes any
preceding '-' and the terminating null. */
static ptrdiff_t
mpz_bufsize (mpz_t const num, int base)
{
return mpz_sizeinbase (num, base) + 2;
}
ptrdiff_t
bignum_bufsize (Lisp_Object num, int base)
{
return mpz_bufsize (XBIGNUM (num)->value, base);
}
/* Convert NUM to a nearest double, as opposed to mpz_get_d which
truncates toward zero. */
double
mpz_get_d_rounded (mpz_t const num)
{
ptrdiff_t size = mpz_bufsize (num, 10);
/* Use mpz_get_d as a shortcut for a bignum so small that rounding
errors cannot occur, which is possible if EMACS_INT (not counting
sign) has fewer bits than a double significand. */
if (! ((FLT_RADIX == 2 && DBL_MANT_DIG <= FIXNUM_BITS - 1)
|| (FLT_RADIX == 16 && DBL_MANT_DIG * 4 <= FIXNUM_BITS - 1))
&& size <= DBL_DIG + 2)
return mpz_get_d (num);
USE_SAFE_ALLOCA;
char *buf = SAFE_ALLOCA (size);
mpz_get_str (buf, 10, num);
double result = strtod (buf, NULL);
SAFE_FREE ();
return result;
}
/* Store into BUF (of size SIZE) the value of NUM as a base-BASE string.
If BASE is negative, use upper-case digits in base -BASE.
Return the string's length.
SIZE must equal bignum_bufsize (NUM, abs (BASE)). */
ptrdiff_t
bignum_to_c_string (char *buf, ptrdiff_t size, Lisp_Object num, int base)
{
eassert (bignum_bufsize (num, abs (base)) == size);
mpz_get_str (buf, base, XBIGNUM (num)->value);
ptrdiff_t n = size - 2;
return !buf[n - 1] ? n - 1 : n + !!buf[n];
}
/* Convert NUM to a base-BASE Lisp string.
If BASE is negative, use upper-case digits in base -BASE. */
Lisp_Object
bignum_to_string (Lisp_Object num, int base)
{
ptrdiff_t size = bignum_bufsize (num, abs (base));
USE_SAFE_ALLOCA;
char *str = SAFE_ALLOCA (size);
ptrdiff_t len = bignum_to_c_string (str, size, num, base);
Lisp_Object result = make_unibyte_string (str, len);
SAFE_FREE ();
return result;
}
/* Create a bignum by scanning NUM, with digits in BASE.
NUM must consist of an optional '-', a nonempty sequence
of base-BASE digits, and a terminating null byte, and
the represented number must not be in fixnum range. */
Lisp_Object
make_bignum_str (char const *num, int base)
{
struct Lisp_Bignum *b = ALLOCATE_PSEUDOVECTOR (struct Lisp_Bignum, value,
PVEC_BIGNUM);
mpz_init (b->value);
int check = mpz_set_str (b->value, num, base);
eassert (check == 0);
return make_lisp_ptr (b, Lisp_Vectorlike);
}
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