int
mpfr_div_2ui (mpfr_ptr y, mpfr_srcptr x, unsigned long n, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC (("x[%#R]=%R n=%lu rnd=%d", x, x, n, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_set (y, x, rnd_mode);
else
{
mpfr_exp_t exp = MPFR_GET_EXP (x);
mpfr_uexp_t diffexp;
MPFR_SETRAW (inexact, y, x, exp, rnd_mode);
diffexp = (mpfr_uexp_t) exp - (mpfr_uexp_t) (__gmpfr_emin - 1);
if (MPFR_UNLIKELY (n >= diffexp)) /* exp - n <= emin - 1 */
{
if (rnd_mode == MPFR_RNDN &&
(n > diffexp || (inexact >= 0 && mpfr_powerof2_raw (y))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (y, rnd_mode, MPFR_SIGN (y));
}
/* exp - n >= emin (no underflow, no integer overflow) */
while (n > LONG_MAX)
{
n -= LONG_MAX;
exp -= LONG_MAX; /* note: signed values */
}
MPFR_SET_EXP (y, exp - (long) n);
}
MPFR_RET (inexact);
}
int
mpfr_ui_div (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
MPFR_LOG_FUNC
(("u=%lu x[%Pu]=%.*Rg rnd=%d",
u, mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg", mpfr_get_prec(y), mpfr_log_prec, y));
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x)) /* u/Inf = 0 */
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN(y,x);
MPFR_RET(0);
}
else /* u / 0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
if (u)
{
/* u > 0, so y = sign(x) * Inf */
MPFR_SET_SAME_SIGN(y, x);
MPFR_SET_INF(y);
mpfr_set_divby0 ();
MPFR_RET(0);
}
else
{
/* 0 / 0 */
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
}
else if (MPFR_LIKELY(u != 0))
{
MPFR_TMP_INIT1(up, uu, GMP_NUMB_BITS);
MPFR_ASSERTN(u == (mp_limb_t) u);
count_leading_zeros(cnt, (mp_limb_t) u);
up[0] = (mp_limb_t) u << cnt;
MPFR_SET_EXP (uu, GMP_NUMB_BITS - cnt);
return mpfr_div (y, uu, x, rnd_mode);
}
else /* u = 0, and x != 0 */
{
MPFR_SET_ZERO(y); /* if u=0, then set y to 0 */
MPFR_SET_SAME_SIGN(y, x); /* u considered as +0: sign(+0/x) = sign(x) */
MPFR_RET(0);
}
}
int
mpfr_sqrt_ui (mpfr_ptr r, unsigned long u, mpfr_rnd_t rnd_mode)
{
if (u)
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_TMP_INIT1 (up, uu, GMP_NUMB_BITS);
MPFR_ASSERTN (u == (mp_limb_t) u);
count_leading_zeros (cnt, (mp_limb_t) u);
*up = (mp_limb_t) u << cnt;
MPFR_SAVE_EXPO_MARK (expo);
MPFR_SET_EXP (uu, GMP_NUMB_BITS - cnt);
inex = mpfr_sqrt(r, uu, rnd_mode);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range(r, inex, rnd_mode);
}
else /* sqrt(0) = 0 */
{
MPFR_SET_ZERO(r);
MPFR_SET_POS(r);
MPFR_RET(0);
}
}
/*
* Set f to z, choosing the smallest precision for f
* so that z = f*(2^BPML)*zs*2^(RetVal)
*/
static int
set_z (mpfr_ptr f, mpz_srcptr z, mp_size_t *zs)
{
mp_limb_t *p;
mp_size_t s;
int c;
mp_prec_t pf;
MPFR_ASSERTD (mpz_sgn (z) != 0);
/* Remove useless ending 0 */
for (p = PTR (z), s = *zs = ABS (SIZ (z)) ; *p == 0; p++, s--)
MPFR_ASSERTD (s >= 0);
/* Get working precision */
count_leading_zeros (c, p[s-1]);
pf = s * BITS_PER_MP_LIMB - c;
if (pf < MPFR_PREC_MIN)
pf = MPFR_PREC_MIN;
mpfr_init2 (f, pf);
/* Copy Mantissa */
if (MPFR_LIKELY (c))
mpn_lshift (MPFR_MANT (f), p, s, c);
else
MPN_COPY (MPFR_MANT (f), p, s);
MPFR_SET_SIGN (f, mpz_sgn (z));
MPFR_SET_EXP (f, 0);
return -c;
}
int
mpfr_frexp (mpfr_exp_t *exp, mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
{
int inex;
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN; /* exp is unspecified */
}
else if (MPFR_IS_INF(x))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y,x);
MPFR_RET(0); /* exp is unspecified */
}
else
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN(y,x);
*exp = 0;
MPFR_RET(0);
}
}
inex = mpfr_set (y, x, rnd);
*exp = MPFR_GET_EXP (y);
MPFR_SET_EXP (y, 0);
return mpfr_check_range (y, inex, rnd);
}
int
mpfr_sub_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mp_rnd_t rnd_mode)
{
if (MPFR_LIKELY (u != 0)) /* if u=0, do nothing */
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_TMP_INIT1 (up, uu, BITS_PER_MP_LIMB);
MPFR_ASSERTN (u == (mp_limb_t) u);
count_leading_zeros (cnt, (mp_limb_t) u);
*up = (mp_limb_t) u << cnt;
/* Optimization note: Exponent save/restore operations may be
removed if mpfr_sub works even when uu is out-of-range. */
MPFR_SAVE_EXPO_MARK (expo);
MPFR_SET_EXP (uu, BITS_PER_MP_LIMB - cnt);
inex = mpfr_sub (y, x, uu, rnd_mode);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inex, rnd_mode);
}
else
return mpfr_set (y, x, rnd_mode);
}
int
mpfr_add_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode)
{
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg u=%lu rnd=%d",
mpfr_get_prec(x), mpfr_log_prec, x, u, rnd_mode),
("y[%Pu]=%.*Rg", mpfr_get_prec (y), mpfr_log_prec, y));
if (MPFR_LIKELY(u != 0) ) /* if u=0, do nothing */
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_TMP_INIT1 (up, uu, GMP_NUMB_BITS);
MPFR_ASSERTD (u == (mp_limb_t) u);
count_leading_zeros(cnt, (mp_limb_t) u);
up[0] = (mp_limb_t) u << cnt;
/* Optimization note: Exponent save/restore operations may be
removed if mpfr_add works even when uu is out-of-range. */
MPFR_SAVE_EXPO_MARK (expo);
MPFR_SET_EXP (uu, GMP_NUMB_BITS - cnt);
inex = mpfr_add(y, x, uu, rnd_mode);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range(y, inex, rnd_mode);
}
else
/* (unsigned long) 0 is assumed to be a real 0 (unsigned) */
return mpfr_set (y, x, rnd_mode);
}
int
mpfr_mul_2si (mpfr_ptr y, mpfr_srcptr x, long int n, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC (("x[%#R]=%R n=%ld rnd=%d", x, x, n, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_set (y, x, rnd_mode);
else
{
mpfr_exp_t exp = MPFR_GET_EXP (x);
MPFR_SETRAW (inexact, y, x, exp, rnd_mode);
if (MPFR_UNLIKELY( n > 0 && (__gmpfr_emax < MPFR_EMIN_MIN + n ||
exp > __gmpfr_emax - n)))
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(y));
else if (MPFR_UNLIKELY(n < 0 && (__gmpfr_emin > MPFR_EMAX_MAX + n ||
exp < __gmpfr_emin - n)))
{
if (rnd_mode == MPFR_RNDN &&
(__gmpfr_emin > MPFR_EMAX_MAX + (n + 1) ||
exp < __gmpfr_emin - (n + 1) ||
(inexact >= 0 && mpfr_powerof2_raw (y))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (y, rnd_mode, MPFR_SIGN(y));
}
MPFR_SET_EXP (y, exp + n);
}
MPFR_RET (inexact);
}
int
mpfr_div_2si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC (("x[%#R]=%R n=%ld rnd=%d", x, x, n, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
inexact = MPFR_UNLIKELY(y != x) ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_LIKELY( MPFR_IS_PURE_FP(y) ))
{
mp_exp_t exp = MPFR_GET_EXP (y);
if (MPFR_UNLIKELY( n > 0 && (__gmpfr_emin > MPFR_EMAX_MAX - n ||
exp < __gmpfr_emin + n)) )
{
if (rnd_mode == GMP_RNDN &&
(__gmpfr_emin > MPFR_EMAX_MAX - (n - 1) ||
exp < __gmpfr_emin + (n - 1) ||
(inexact >= 0 && mpfr_powerof2_raw (y))))
rnd_mode = GMP_RNDZ;
return mpfr_underflow (y, rnd_mode, MPFR_SIGN(y));
}
if (MPFR_UNLIKELY(n < 0 && (__gmpfr_emax < MPFR_EMIN_MIN - n ||
exp > __gmpfr_emax + n)) )
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(y));
MPFR_SET_EXP (y, exp - n);
}
return inexact;
}
int
mpfr_ui_div (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x)) /* u/Inf = 0 */
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN(y,x);
MPFR_RET(0);
}
else /* u / 0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
if (u)
{
/* u > 0, so y = sign(x) * Inf */
MPFR_SET_SAME_SIGN(y, x);
MPFR_SET_INF(y);
MPFR_RET(0);
}
else
{
/* 0 / 0 */
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
}
else if (MPFR_LIKELY(u != 0))
{
MPFR_TMP_INIT1(up, uu, BITS_PER_MP_LIMB);
MPFR_ASSERTN(u == (mp_limb_t) u);
count_leading_zeros(cnt, (mp_limb_t) u);
up[0] = (mp_limb_t) u << cnt;
MPFR_SET_EXP (uu, BITS_PER_MP_LIMB - cnt);
return mpfr_div (y, uu, x, rnd_mode);
}
else /* u = 0, and x != 0 */
{
MPFR_SET_ZERO(y); /* if u=0, then set y to 0 */
MPFR_SET_SAME_SIGN(y, x); /* u considered as +0: sign(+0/x) = sign(x) */
MPFR_RET(0);
}
}
void
mpfr_setmin (mpfr_ptr x, mp_exp_t e)
{
mp_size_t xn;
mp_limb_t *xp;
MPFR_SET_EXP (x, e);
xn = (MPFR_PREC(x) - 1) / BITS_PER_MP_LIMB;
xp = MPFR_MANT(x);
xp[xn] = MPFR_LIMB_HIGHBIT;
MPN_ZERO(xp, xn);
}
static void
set_special (mpfr_ptr x, unsigned int select)
{
MPFR_ASSERTN (select < SPECIAL_MAX);
switch (select)
{
case 0:
MPFR_SET_NAN (x);
break;
case 1:
MPFR_SET_INF (x);
MPFR_SET_POS (x);
break;
case 2:
MPFR_SET_INF (x);
MPFR_SET_NEG (x);
break;
case 3:
MPFR_SET_ZERO (x);
MPFR_SET_POS (x);
break;
case 4:
MPFR_SET_ZERO (x);
MPFR_SET_NEG (x);
break;
case 5:
mpfr_set_str_binary (x, "1");
break;
case 6:
mpfr_set_str_binary (x, "-1");
break;
case 7:
mpfr_set_str_binary (x, "1e-1");
break;
case 8:
mpfr_set_str_binary (x, "1e+1");
break;
case 9:
mpfr_const_pi (x, MPFR_RNDN);
break;
case 10:
mpfr_const_pi (x, MPFR_RNDN);
MPFR_SET_EXP (x, MPFR_GET_EXP (x)-1);
break;
default:
mpfr_urandomb (x, RANDS);
if (randlimb () & 1)
mpfr_neg (x, x, MPFR_RNDN);
break;
}
}
double
mpfr_get_d_2exp (long *expptr, mpfr_srcptr src, mpfr_rnd_t rnd_mode)
{
double ret;
mpfr_exp_t exp;
mpfr_t tmp;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
{
int negative;
*expptr = 0;
if (MPFR_IS_NAN (src))
return MPFR_DBL_NAN;
negative = MPFR_IS_NEG (src);
if (MPFR_IS_INF (src))
return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP;
MPFR_ASSERTD (MPFR_IS_ZERO(src));
return negative ? DBL_NEG_ZERO : 0.0;
}
tmp[0] = *src; /* Hack copy mpfr_t */
MPFR_SET_EXP (tmp, 0);
ret = mpfr_get_d (tmp, rnd_mode);
if (MPFR_IS_PURE_FP(src))
{
exp = MPFR_GET_EXP (src);
/* rounding can give 1.0, adjust back to 0.5 <= abs(ret) < 1.0 */
if (ret == 1.0)
{
ret = 0.5;
exp++;
}
else if (ret == -1.0)
{
ret = -0.5;
exp++;
}
MPFR_ASSERTN ((ret >= 0.5 && ret < 1.0)
|| (ret <= -0.5 && ret > -1.0));
MPFR_ASSERTN (exp >= LONG_MIN && exp <= LONG_MAX);
}
else
exp = 0;
*expptr = exp;
return ret;
}
void
mpfr_setmax (mpfr_ptr x, mpfr_exp_t e)
{
mp_size_t xn, i;
int sh;
mp_limb_t *xp;
MPFR_SET_EXP (x, e);
xn = MPFR_LIMB_SIZE (x);
sh = (mpfr_prec_t) xn * GMP_NUMB_BITS - MPFR_PREC(x);
xp = MPFR_MANT(x);
xp[0] = MP_LIMB_T_MAX << sh;
for (i = 1; i < xn; i++)
xp[i] = MP_LIMB_T_MAX;
}
void
mpfr_setmax (mpfr_ptr x, mp_exp_t e)
{
mp_size_t xn, i;
int sh;
mp_limb_t *xp;
MPFR_SET_EXP (x, e);
xn = 1 + (MPFR_PREC(x) - 1) / BITS_PER_MP_LIMB;
sh = (mp_prec_t) xn * BITS_PER_MP_LIMB - MPFR_PREC(x);
xp = MPFR_MANT(x);
xp[0] = MP_LIMB_T_MAX << sh;
for (i = 1; i < xn; i++)
xp[i] = MP_LIMB_T_MAX;
}
int
mpfr_div_2ui (mpfr_ptr y, mpfr_srcptr x, unsigned long n, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC (("x[%#R]=%R n=%lu rnd=%d", x, x, n, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
/* Most of the times, this function is called with y==x */
inexact = MPFR_UNLIKELY(y != x) ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_LIKELY( MPFR_IS_PURE_FP(y)) )
{
/* n will have to be casted to long to make sure that the addition
and subtraction below (for overflow detection) are signed */
while (MPFR_UNLIKELY(n > LONG_MAX))
{
int inex2;
n -= LONG_MAX;
inex2 = mpfr_div_2ui(y, y, LONG_MAX, rnd_mode);
if (inex2)
return inex2; /* underflow */
}
/* MPFR_EMAX_MAX - (long) n is signed and doesn't lead to an integer
overflow; the first test useful so that the real test can't lead
to an integer overflow. */
{
mpfr_exp_t exp = MPFR_GET_EXP (y);
if (MPFR_UNLIKELY( __gmpfr_emin > MPFR_EMAX_MAX - (long) n ||
exp < __gmpfr_emin + (long) n) )
{
if (rnd_mode == MPFR_RNDN &&
(__gmpfr_emin > MPFR_EMAX_MAX - (long) (n - 1) ||
exp < __gmpfr_emin + (long) (n - 1) ||
(inexact >= 0 && mpfr_powerof2_raw (y))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (y, rnd_mode, MPFR_SIGN(y));
}
MPFR_SET_EXP(y, exp - (long) n);
}
}
return inexact;
}
double
virtual_timing_ai2 (struct speed_params *s)
{
double t;
unsigned i;
mpfr_t w, x;
mp_size_t size;
mpfr_t temp1, temp2;
SPEED_RESTRICT_COND (s->size >= MPFR_PREC_MIN);
SPEED_RESTRICT_COND (s->size <= MPFR_PREC_MAX);
size = (s->size-1)/GMP_NUMB_BITS+1;
s->xp[size-1] |= MPFR_LIMB_HIGHBIT;
MPFR_TMP_INIT1 (s->xp, x, s->size);
MPFR_SET_EXP (x, (mpfr_exp_t) s->r);
if (s->align_xp == 2) MPFR_SET_NEG (x);
mpfr_init2 (w, s->size);
speed_starttime ();
i = s->reps;
mpfr_init2 (temp1, MPFR_SMALL_PRECISION);
mpfr_init2 (temp2, MPFR_SMALL_PRECISION);
mpfr_set (temp1, x, MPFR_SMALL_PRECISION);
mpfr_set_si (temp2, MPFR_AI_THRESHOLD2, MPFR_RNDN);
mpfr_mul_ui (temp2, temp2, (unsigned int)MPFR_PREC (w), MPFR_RNDN);
if (MPFR_IS_NEG (x))
mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD1, MPFR_RNDN);
else
mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD3, MPFR_RNDN);
mpfr_add (temp1, temp1, temp2, MPFR_RNDN);
if (mpfr_cmp_si (temp1, MPFR_AI_SCALE) > 0)
t = 1.;
else
t = 1000.;
mpfr_clear (temp1);
mpfr_clear (temp2);
return t;
}
int
mpfr_ui_sub (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
MPFR_LOG_FUNC
(("u=%lu x[%Pu]=%.*Rg rnd=%d",
u, mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg", mpfr_get_prec(y), mpfr_log_prec, y));
if (MPFR_UNLIKELY (u == 0))
return mpfr_neg (y, x, rnd_mode);
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x))
{
/* u - Inf = -Inf and u - -Inf = +Inf */
MPFR_SET_INF(y);
MPFR_SET_OPPOSITE_SIGN(y,x);
MPFR_RET(0); /* +/-infinity is exact */
}
else /* x is zero */
/* u - 0 = u */
return mpfr_set_ui(y, u, rnd_mode);
}
else
{
MPFR_TMP_INIT1 (up, uu, GMP_NUMB_BITS);
MPFR_ASSERTN(u == (mp_limb_t) u);
count_leading_zeros (cnt, (mp_limb_t) u);
*up = (mp_limb_t) u << cnt;
MPFR_SET_EXP (uu, GMP_NUMB_BITS - cnt);
return mpfr_sub (y, uu, x, rnd_mode);
}
}
int
mpfr_mul_2ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int n, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg n=%lu rnd=%d",
mpfr_get_prec (x), mpfr_log_prec, x, n, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (y), mpfr_log_prec, y, inexact));
inexact = MPFR_UNLIKELY(y != x) ? mpfr_set (y, x, rnd_mode) : 0;
if (MPFR_LIKELY( MPFR_IS_PURE_FP(y)) )
{
/* n will have to be casted to long to make sure that the addition
and subtraction below (for overflow detection) are signed */
while (MPFR_UNLIKELY(n > LONG_MAX))
{
int inex2;
n -= LONG_MAX;
inex2 = mpfr_mul_2ui(y, y, LONG_MAX, rnd_mode);
if (inex2)
return inex2; /* overflow */
}
/* MPFR_EMIN_MIN + (long) n is signed and doesn't lead to an overflow;
the first test useful so that the real test can't lead to an
overflow. */
{
mpfr_exp_t exp = MPFR_GET_EXP (y);
if (MPFR_UNLIKELY( __gmpfr_emax < MPFR_EMIN_MIN + (long) n ||
exp > __gmpfr_emax - (long) n))
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(y));
MPFR_SET_EXP (y, exp + (long) n);
}
}
return inexact;
}
int
mpfr_ui_sub (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
if (MPFR_UNLIKELY (u == 0))
return mpfr_neg (y, x, rnd_mode);
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x))
{
/* u - Inf = -Inf and u - -Inf = +Inf */
MPFR_SET_INF(y);
MPFR_SET_OPPOSITE_SIGN(y,x);
MPFR_RET(0); /* +/-infinity is exact */
}
else /* x is zero */
/* u - 0 = u */
return mpfr_set_ui(y, u, rnd_mode);
}
else
{
MPFR_TMP_INIT1 (up, uu, BITS_PER_MP_LIMB);
MPFR_ASSERTN(u == (mp_limb_t) u);
count_leading_zeros (cnt, (mp_limb_t) u);
*up = (mp_limb_t) u << cnt;
MPFR_SET_EXP (uu, BITS_PER_MP_LIMB - cnt);
return mpfr_sub (y, uu, x, rnd_mode);
}
}
MPFR_HOT_FUNCTION_ATTR int
mpfr_div_2si (mpfr_ptr y, mpfr_srcptr x, long int n, mpfr_rnd_t rnd_mode)
{
int inexact;
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg n=%ld rnd=%d",
mpfr_get_prec(x), mpfr_log_prec, x, n, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec(y), mpfr_log_prec, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_set (y, x, rnd_mode);
else
{
mpfr_exp_t exp = MPFR_GET_EXP (x);
MPFR_SETRAW (inexact, y, x, exp, rnd_mode);
if (MPFR_UNLIKELY( n > 0 && (__gmpfr_emin > MPFR_EMAX_MAX - n ||
exp < __gmpfr_emin + n)) )
{
if (rnd_mode == MPFR_RNDN &&
(__gmpfr_emin > MPFR_EMAX_MAX - (n - 1) ||
exp < __gmpfr_emin + (n - 1) ||
((MPFR_IS_NEG (y) ? inexact <= 0 : inexact >= 0) &&
mpfr_powerof2_raw (y))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (y, rnd_mode, MPFR_SIGN(y));
}
else if (MPFR_UNLIKELY(n <= 0 && (__gmpfr_emax < MPFR_EMIN_MIN - n ||
exp > __gmpfr_emax + n)) )
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(y));
MPFR_SET_EXP (y, exp - n);
}
MPFR_RET (inexact);
}
int
mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpz_t m;
mpfr_exp_t e, r, sh;
mpfr_prec_t n, size_m, tmp;
int inexact, negative;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (
("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
inexact));
/* special values */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
/* case 0: cbrt(+/- 0) = +/- 0 */
else /* x is necessarily 0 */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
}
/* General case */
MPFR_SAVE_EXPO_MARK (expo);
mpz_init (m);
e = mpfr_get_z_2exp (m, x); /* x = m * 2^e */
if ((negative = MPFR_IS_NEG(x)))
mpz_neg (m, m);
r = e % 3;
if (r < 0)
r += 3;
/* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */
MPFR_MPZ_SIZEINBASE2 (size_m, m);
n = MPFR_PREC (y) + (rnd_mode == MPFR_RNDN);
/* we want 3*n-2 <= size_m + 3*sh + r <= 3*n
i.e. 3*sh + size_m + r <= 3*n */
sh = (3 * (mpfr_exp_t) n - (mpfr_exp_t) size_m - r) / 3;
sh = 3 * sh + r;
if (sh >= 0)
{
mpz_mul_2exp (m, m, sh);
e = e - sh;
}
else if (r > 0)
{
mpz_mul_2exp (m, m, r);
e = e - r;
}
/* invariant: x = m*2^e, with e divisible by 3 */
/* we reuse the variable m to store the cube root, since it is not needed
any more: we just need to know if the root is exact */
inexact = mpz_root (m, m, 3) == 0;
MPFR_MPZ_SIZEINBASE2 (tmp, m);
sh = tmp - n;
if (sh > 0) /* we have to flush to 0 the last sh bits from m */
{
inexact = inexact || ((mpfr_exp_t) mpz_scan1 (m, 0) < sh);
mpz_fdiv_q_2exp (m, m, sh);
e += 3 * sh;
}
if (inexact)
{
if (negative)
rnd_mode = MPFR_INVERT_RND (rnd_mode);
if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA
|| (rnd_mode == MPFR_RNDN && mpz_tstbit (m, 0)))
inexact = 1, mpz_add_ui (m, m, 1);
else
inexact = -1;
}
/* either inexact is not zero, and the conversion is exact, i.e. inexact
is not changed; or inexact=0, and inexact is set only when
rnd_mode=MPFR_RNDN and bit (n+1) from m is 1 */
inexact += mpfr_set_z (y, m, MPFR_RNDN);
MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3);
if (negative)
{
MPFR_CHANGE_SIGN (y);
inexact = -inexact;
}
mpz_clear (m);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
int
mpfr_mul_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode)
{
mp_limb_t *yp;
mp_size_t xn;
int cnt, inexact;
MPFR_TMP_DECL (marker);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (u != 0)
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* infinity is exact */
}
else /* 0 * infinity */
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
}
else if (MPFR_UNLIKELY (u <= 1))
{
if (u < 1)
{
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
else
return mpfr_set (y, x, rnd_mode);
}
else if (MPFR_UNLIKELY (IS_POW2 (u)))
return mpfr_mul_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode);
yp = MPFR_MANT (y);
xn = MPFR_LIMB_SIZE (x);
MPFR_ASSERTD (xn < MP_SIZE_T_MAX);
MPFR_TMP_MARK(marker);
yp = MPFR_TMP_LIMBS_ALLOC (xn + 1);
MPFR_ASSERTN (u == (mp_limb_t) u);
yp[xn] = mpn_mul_1 (yp, MPFR_MANT (x), xn, u);
/* x * u is stored in yp[xn], ..., yp[0] */
/* since the case u=1 was treated above, we have u >= 2, thus
yp[xn] >= 1 since x was msb-normalized */
MPFR_ASSERTD (yp[xn] != 0);
if (MPFR_LIKELY (MPFR_LIMB_MSB (yp[xn]) == 0))
{
count_leading_zeros (cnt, yp[xn]);
mpn_lshift (yp, yp, xn + 1, cnt);
}
else
{
cnt = 0;
}
/* now yp[xn], ..., yp[0] is msb-normalized too, and has at most
PREC(x) + (GMP_NUMB_BITS - cnt) non-zero bits */
MPFR_RNDRAW (inexact, y, yp, (mpfr_prec_t) (xn + 1) * GMP_NUMB_BITS,
rnd_mode, MPFR_SIGN (x), cnt -- );
MPFR_TMP_FREE (marker);
cnt = GMP_NUMB_BITS - cnt;
if (MPFR_UNLIKELY (__gmpfr_emax < MPFR_EMAX_MIN + cnt
|| MPFR_GET_EXP (x) > __gmpfr_emax - cnt))
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(x));
MPFR_SET_EXP (y, MPFR_GET_EXP (x) + cnt);
MPFR_SET_SAME_SIGN (y, x);
return inexact;
}
int
mpfr_rint (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
int sign;
int rnd_away;
mp_exp_t exp;
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ))
{
if (MPFR_IS_NAN(u))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
MPFR_SET_SAME_SIGN(r, u);
if (MPFR_IS_INF(u))
{
MPFR_SET_INF(r);
MPFR_RET(0); /* infinity is exact */
}
else /* now u is zero */
{
MPFR_ASSERTD(MPFR_IS_ZERO(u));
MPFR_SET_ZERO(r);
MPFR_RET(0); /* zero is exact */
}
}
MPFR_SET_SAME_SIGN (r, u); /* Does nothing if r==u */
sign = MPFR_INT_SIGN (u);
exp = MPFR_GET_EXP (u);
rnd_away =
rnd_mode == GMP_RNDD ? sign < 0 :
rnd_mode == GMP_RNDU ? sign > 0 :
rnd_mode == GMP_RNDZ ? 0 : -1;
/* rnd_away:
1 if round away from zero,
0 if round to zero,
-1 if not decided yet.
*/
if (MPFR_UNLIKELY (exp <= 0)) /* 0 < |u| < 1 ==> round |u| to 0 or 1 */
{
/* Note: in the GMP_RNDN mode, 0.5 must be rounded to 0. */
if (rnd_away != 0 &&
(rnd_away > 0 ||
(exp == 0 && (rnd_mode == GMP_RNDNA ||
!mpfr_powerof2_raw (u)))))
{
mp_limb_t *rp;
mp_size_t rm;
rp = MPFR_MANT(r);
rm = (MPFR_PREC(r) - 1) / BITS_PER_MP_LIMB;
rp[rm] = MPFR_LIMB_HIGHBIT;
MPN_ZERO(rp, rm);
MPFR_SET_EXP (r, 1); /* |r| = 1 */
MPFR_RET(sign > 0 ? 2 : -2);
}
else
{
MPFR_SET_ZERO(r); /* r = 0 */
MPFR_RET(sign > 0 ? -2 : 2);
}
}
else /* exp > 0, |u| >= 1 */
{
mp_limb_t *up, *rp;
mp_size_t un, rn, ui;
int sh, idiff;
int uflags;
/*
* uflags will contain:
* _ 0 if u is an integer representable in r,
* _ 1 if u is an integer not representable in r,
* _ 2 if u is not an integer.
*/
up = MPFR_MANT(u);
rp = MPFR_MANT(r);
un = MPFR_LIMB_SIZE(u);
rn = MPFR_LIMB_SIZE(r);
MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (r));
MPFR_SET_EXP (r, exp); /* Does nothing if r==u */
if ((exp - 1) / BITS_PER_MP_LIMB >= un)
{
ui = un;
idiff = 0;
uflags = 0; /* u is an integer, representable or not in r */
}
else
{
mp_size_t uj;
ui = (exp - 1) / BITS_PER_MP_LIMB + 1; /* #limbs of the int part */
MPFR_ASSERTD (un >= ui);
uj = un - ui; /* lowest limb of the integer part */
idiff = exp % BITS_PER_MP_LIMB; /* #int-part bits in up[uj] or 0 */
uflags = idiff == 0 || (up[uj] << idiff) == 0 ? 0 : 2;
if (uflags == 0)
while (uj > 0)
if (up[--uj] != 0)
{
uflags = 2;
break;
}
}
if (ui > rn)
{
/* More limbs in the integer part of u than in r.
Just round u with the precision of r. */
MPFR_ASSERTD (rp != up && un > rn);
MPN_COPY (rp, up + (un - rn), rn); /* r != u */
if (rnd_away < 0)
{
/* This is a rounding to nearest mode (GMP_RNDN or GMP_RNDNA).
Decide the rounding direction here. */
if (rnd_mode == GMP_RNDN &&
(rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
{ /* halfway cases rounded toward zero */
mp_limb_t a, b;
/* a: rounding bit and some of the following bits */
/* b: boundary for a (weight of the rounding bit in a) */
if (sh != 0)
{
a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
b = MPFR_LIMB_ONE << (sh - 1);
}
else
{
a = up[un - rn - 1];
b = MPFR_LIMB_HIGHBIT;
}
rnd_away = a > b;
if (a == b)
{
mp_size_t i;
for (i = un - rn - 1 - (sh == 0); i >= 0; i--)
if (up[i] != 0)
{
rnd_away = 1;
break;
}
}
}
else /* halfway cases rounded away from zero */
rnd_away = /* rounding bit */
((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
(sh == 0 && (up[un - rn - 1] & MPFR_LIMB_HIGHBIT) != 0));
}
if (uflags == 0)
{ /* u is an integer; determine if it is representable in r */
if (sh != 0 && rp[0] << (BITS_PER_MP_LIMB - sh) != 0)
uflags = 1; /* u is not representable in r */
else
{
mp_size_t i;
for (i = un - rn - 1; i >= 0; i--)
if (up[i] != 0)
{
uflags = 1; /* u is not representable in r */
break;
}
}
}
}
else /* ui <= rn */
{
mp_size_t uj, rj;
int ush;
uj = un - ui; /* lowest limb of the integer part in u */
rj = rn - ui; /* lowest limb of the integer part in r */
if (MPFR_LIKELY (rp != up))
MPN_COPY(rp + rj, up + uj, ui);
/* Ignore the lowest rj limbs, all equal to zero. */
rp += rj;
rn = ui;
/* number of fractional bits in whole rp[0] */
ush = idiff == 0 ? 0 : BITS_PER_MP_LIMB - idiff;
if (rj == 0 && ush < sh)
{
/* If u is an integer (uflags == 0), we need to determine
if it is representable in r, i.e. if its sh - ush bits
in the non-significant part of r are all 0. */
if (uflags == 0 && (rp[0] & ((MPFR_LIMB_ONE << sh) -
(MPFR_LIMB_ONE << ush))) != 0)
uflags = 1; /* u is an integer not representable in r */
}
else /* The integer part of u fits in r, we'll round to it. */
sh = ush;
if (rnd_away < 0)
{
/* This is a rounding to nearest mode.
Decide the rounding direction here. */
if (uj == 0 && sh == 0)
rnd_away = 0; /* rounding bit = 0 (not represented in u) */
else if (rnd_mode == GMP_RNDN &&
(rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
{ /* halfway cases rounded toward zero */
mp_limb_t a, b;
/* a: rounding bit and some of the following bits */
/* b: boundary for a (weight of the rounding bit in a) */
if (sh != 0)
{
a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
b = MPFR_LIMB_ONE << (sh - 1);
}
else
{
MPFR_ASSERTD (uj >= 1); /* see above */
a = up[uj - 1];
b = MPFR_LIMB_HIGHBIT;
}
rnd_away = a > b;
if (a == b)
{
mp_size_t i;
for (i = uj - 1 - (sh == 0); i >= 0; i--)
if (up[i] != 0)
{
rnd_away = 1;
break;
}
}
}
else /* halfway cases rounded away from zero */
rnd_away = /* rounding bit */
((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
(sh == 0 && (MPFR_ASSERTD (uj >= 1),
up[uj - 1] & MPFR_LIMB_HIGHBIT) != 0));
}
/* Now we can make the low rj limbs to 0 */
MPN_ZERO (rp-rj, rj);
}
if (sh != 0)
rp[0] &= MP_LIMB_T_MAX << sh;
/* If u is a representable integer, there is no rounding. */
if (uflags == 0)
MPFR_RET(0);
MPFR_ASSERTD (rnd_away >= 0); /* rounding direction is defined */
if (rnd_away && mpn_add_1(rp, rp, rn, MPFR_LIMB_ONE << sh))
{
if (exp == __gmpfr_emax)
return mpfr_overflow(r, rnd_mode, MPFR_SIGN(r)) >= 0 ?
uflags : -uflags;
else
{
MPFR_SET_EXP(r, exp + 1);
rp[rn-1] = MPFR_LIMB_HIGHBIT;
}
}
MPFR_RET (rnd_away ^ (sign < 0) ? uflags : -uflags);
} /* exp > 0, |u| >= 1 */
}
/* Exact product. The number a is assumed to have enough allocated memory,
where the trailing bits are regarded as being part of the input numbers
(no reallocation is attempted and no check is performed as MPFR_TMP_INIT
could have been used). The arguments b and c may actually be UBF numbers
(mpfr_srcptr can be seen a bit like void *, but is stronger).
This function does not change the flags, except in case of NaN. */
void
mpfr_ubf_mul_exact (mpfr_ubf_ptr a, mpfr_srcptr b, mpfr_srcptr c)
{
MPFR_LOG_FUNC
(("b[%Pu]=%.*Rg c[%Pu]=%.*Rg",
mpfr_get_prec (b), mpfr_log_prec, b,
mpfr_get_prec (c), mpfr_log_prec, c),
("a[%Pu]=%.*Rg",
mpfr_get_prec (a), mpfr_log_prec, a));
MPFR_ASSERTD ((mpfr_ptr) a != b);
MPFR_ASSERTD ((mpfr_ptr) a != c);
MPFR_SIGN (a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_ARE_SINGULAR (b, c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
MPFR_SET_NAN (a);
else if (MPFR_IS_INF (b))
{
if (MPFR_NOTZERO (c))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_ZERO (a);
}
}
else
{
mpfr_exp_t e;
mp_size_t bn, cn;
mpfr_limb_ptr ap;
mp_limb_t u, v;
int m;
/* Note about the code below: For the choice of the precision of
* the result a, one could choose PREC(b) + PREC(c), instead of
* taking whole limbs into account, but in most cases where one
* would gain one limb, one would need to copy the significand
* instead of a no-op (see the mul.c code).
* But in the case MPFR_LIMB_MSB (u) == 0, if the result fits in
* an-1 limbs, one could actually do
* mpn_rshift (ap, ap, k, GMP_NUMB_BITS - 1)
* instead of
* mpn_lshift (ap, ap, k, 1)
* to gain one limb (and reduce the precision), replacing a shift
* by another one. Would this be interesting?
*/
bn = MPFR_LIMB_SIZE (b);
cn = MPFR_LIMB_SIZE (c);
ap = MPFR_MANT (a);
u = (bn >= cn) ?
mpn_mul (ap, MPFR_MANT (b), bn, MPFR_MANT (c), cn) :
mpn_mul (ap, MPFR_MANT (c), cn, MPFR_MANT (b), bn);
if (MPFR_UNLIKELY (MPFR_LIMB_MSB (u) == 0))
{
m = 1;
MPFR_DBGRES (v = mpn_lshift (ap, ap, bn + cn, 1));
MPFR_ASSERTD (v == 0);
}
else
m = 0;
if (! MPFR_IS_UBF (b) && ! MPFR_IS_UBF (c) &&
(e = MPFR_GET_EXP (b) + MPFR_GET_EXP (c) - m,
MPFR_EXP_IN_RANGE (e)))
{
MPFR_SET_EXP (a, e);
}
else
{
mpz_t be, ce;
mpz_init (MPFR_ZEXP (a));
/* This may involve copies of mpz_t, but exponents should not be
very large integers anyway. */
mpfr_get_zexp (be, b);
mpfr_get_zexp (ce, c);
mpz_add (MPFR_ZEXP (a), be, ce);
mpz_clear (be);
mpz_clear (ce);
mpz_sub_ui (MPFR_ZEXP (a), MPFR_ZEXP (a), m);
MPFR_SET_UBF (a);
}
}
}
long double
mpfr_get_ld (mpfr_srcptr x, mp_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return (long double) mpfr_get_d (x, rnd_mode);
else /* now x is a normal non-zero number */
{
long double r; /* result */
long double m;
double s; /* part of result */
mp_exp_t sh; /* exponent shift, so that x/2^sh is in the double range */
mpfr_t y, z;
int sign;
/* first round x to the target long double precision, so that
all subsequent operations are exact (this avoids double rounding
problems) */
mpfr_init2 (y, MPFR_LDBL_MANT_DIG);
mpfr_init2 (z, IEEE_DBL_MANT_DIG);
mpfr_set (y, x, rnd_mode);
sh = MPFR_GET_EXP (y);
sign = MPFR_SIGN (y);
MPFR_SET_EXP (y, 0);
MPFR_SET_POS (y);
r = 0.0;
do {
s = mpfr_get_d (y, GMP_RNDN); /* high part of y */
r += (long double) s;
mpfr_set_d (z, s, GMP_RNDN); /* exact */
mpfr_sub (y, y, z, GMP_RNDN); /* exact */
} while (!MPFR_IS_ZERO (y));
mpfr_clear (z);
mpfr_clear (y);
/* we now have to multiply back by 2^sh */
MPFR_ASSERTD (r > 0);
if (sh != 0)
{
/* An overflow may occurs (example: 0.5*2^1024) */
while (r < 1.0)
{
r += r;
sh--;
}
if (sh > 0)
m = 2.0;
else
{
m = 0.5;
sh = -sh;
}
for (;;)
{
if (sh % 2)
r = r * m;
sh >>= 1;
if (sh == 0)
break;
m = m * m;
}
}
if (sign < 0)
r = -r;
return r;
}
}
int
mpfr_set_uj_2exp (mpfr_t x, uintmax_t j, intmax_t e, mp_rnd_t rnd)
{
unsigned int cnt, i;
mp_size_t k, len;
mp_limb_t limb;
mp_limb_t yp[sizeof(uintmax_t) / sizeof(mp_limb_t)];
mpfr_t y;
unsigned long uintmax_bit_size = sizeof(uintmax_t) * CHAR_BIT;
unsigned long bpml = BITS_PER_MP_LIMB % uintmax_bit_size;
/* Special case */
if (j == 0)
{
MPFR_SET_POS(x);
MPFR_SET_ZERO(x);
MPFR_RET(0);
}
MPFR_ASSERTN (sizeof(uintmax_t) % sizeof(mp_limb_t) == 0);
/* Create an auxillary var */
MPFR_TMP_INIT1 (yp, y, uintmax_bit_size);
k = numberof (yp);
if (k == 1)
limb = yp[0] = j;
else
{
/* Note: either BITS_PER_MP_LIMB = uintmax_bit_size, then k = 1 the
shift j >>= bpml is never done, or BITS_PER_MP_LIMB < uintmax_bit_size
and bpml = BITS_PER_MP_LIMB. */
for (i = 0; i < k; i++, j >>= bpml)
yp[i] = j; /* Only the low bits are copied */
/* Find the first limb not equal to zero. */
do
{
MPFR_ASSERTD (k > 0);
limb = yp[--k];
}
while (limb == 0);
k++;
}
count_leading_zeros(cnt, limb);
len = numberof (yp) - k;
/* Normalize it: len = number of last 0 limb, k number of non-zero limbs */
if (MPFR_LIKELY(cnt))
mpn_lshift (yp+len, yp, k, cnt); /* Normalize the High Limb*/
else if (len != 0)
MPN_COPY_DECR (yp+len, yp, k); /* Must use DECR */
if (len != 0)
/* Note: when numberof(yp)==1, len is constant and null, so the compiler
can optimize out this code. */
{
if (len == 1)
yp[0] = (mp_limb_t) 0;
else
MPN_ZERO (yp, len); /* Zeroing the last limbs */
}
e += k * BITS_PER_MP_LIMB - cnt; /* Update Expo */
MPFR_ASSERTD (MPFR_LIMB_MSB(yp[numberof (yp) - 1]) != 0);
/* Check expo underflow / overflow (can't use mpfr_check_range) */
if (MPFR_UNLIKELY(e < __gmpfr_emin))
{
/* The following test is necessary because in the rounding to the
* nearest mode, mpfr_underflow always rounds away from 0. In
* this rounding mode, we need to round to 0 if:
* _ |x| < 2^(emin-2), or
* _ |x| = 2^(emin-2) and the absolute value of the exact
* result is <= 2^(emin-2). */
if (rnd == GMP_RNDN && (e+1 < __gmpfr_emin || mpfr_powerof2_raw(y)))
rnd = GMP_RNDZ;
return mpfr_underflow (x, rnd, MPFR_SIGN_POS);
}
if (MPFR_UNLIKELY(e > __gmpfr_emax))
return mpfr_overflow (x, rnd, MPFR_SIGN_POS);
MPFR_SET_EXP (y, e);
/* Final: set x to y (rounding if necessary) */
return mpfr_set (x, y, rnd);
}
/* y <- exp(p/2^r) within 1 ulp, using 2^m terms from the series
Assume |p/2^r| < 1.
We use the following binary splitting formula:
P(a,b) = p if a+1=b, P(a,c)*P(c,b) otherwise
Q(a,b) = a*2^r if a+1=b [except Q(0,1)=1], Q(a,c)*Q(c,b) otherwise
T(a,b) = P(a,b) if a+1=b, Q(c,b)*T(a,c)+P(a,c)*T(c,b) otherwise
Then exp(p/2^r) ~ T(0,i)/Q(0,i) for i so that (p/2^r)^i/i! is small enough.
Since P(a,b) = p^(b-a), and we consider only values of b-a of the form 2^j,
we don't need to compute P(), we only precompute p^(2^j) in the ptoj[] array
below.
Since Q(a,b) is divisible by 2^(r*(b-a-1)), we don't compute the power of
two part.
*/
static void
mpfr_exp_rational (mpfr_ptr y, mpz_ptr p, long r, int m,
mpz_t *Q, mp_prec_t *mult)
{
unsigned long n, i, j;
mpz_t *S, *ptoj;
mp_prec_t *log2_nb_terms;
mp_exp_t diff, expo;
mp_prec_t precy = MPFR_PREC(y), prec_i_have, prec_ptoj;
int k, l;
MPFR_ASSERTN ((size_t) m < sizeof (long) * CHAR_BIT - 1);
S = Q + (m+1);
ptoj = Q + 2*(m+1); /* ptoj[i] = mantissa^(2^i) */
log2_nb_terms = mult + (m+1);
/* Normalize p */
MPFR_ASSERTD (mpz_cmp_ui (p, 0) != 0);
n = mpz_scan1 (p, 0); /* number of trailing zeros in p */
mpz_tdiv_q_2exp (p, p, n);
r -= n; /* since |p/2^r| < 1 and p >= 1, r >= 1 */
/* Set initial var */
mpz_set (ptoj[0], p);
for (k = 1; k < m; k++)
mpz_mul (ptoj[k], ptoj[k-1], ptoj[k-1]); /* ptoj[k] = p^(2^k) */
mpz_set_ui (Q[0], 1);
mpz_set_ui (S[0], 1);
k = 0;
mult[0] = 0; /* the multiplier P[k]/Q[k] for the remaining terms
satisfies P[k]/Q[k] <= 2^(-mult[k]) */
log2_nb_terms[0] = 0; /* log2(#terms) [exact in 1st loop where 2^k] */
prec_i_have = 0;
/* Main Loop */
n = 1UL << m;
for (i = 1; (prec_i_have < precy) && (i < n); i++)
{
/* invariant: Q[0]*Q[1]*...*Q[k] equals i! */
k++;
log2_nb_terms[k] = 0; /* 1 term */
mpz_set_ui (Q[k], i + 1);
mpz_set_ui (S[k], i + 1);
j = i + 1; /* we have computed j = i+1 terms so far */
l = 0;
while ((j & 1) == 0) /* combine and reduce */
{
/* invariant: S[k] corresponds to 2^l consecutive terms */
mpz_mul (S[k], S[k], ptoj[l]);
mpz_mul (S[k-1], S[k-1], Q[k]);
/* Q[k] corresponds to 2^l consecutive terms too.
Since it does not contains the factor 2^(r*2^l),
when going from l to l+1 we need to multiply
by 2^(r*2^(l+1))/2^(r*2^l) = 2^(r*2^l) */
mpz_mul_2exp (S[k-1], S[k-1], r << l);
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (Q[k-1], Q[k-1], Q[k]);
log2_nb_terms[k-1] ++; /* number of terms in S[k-1]
is a power of 2 by construction */
MPFR_MPZ_SIZEINBASE2 (prec_i_have, Q[k]);
MPFR_MPZ_SIZEINBASE2 (prec_ptoj, ptoj[l]);
mult[k-1] += prec_i_have + (r << l) - prec_ptoj - 1;
prec_i_have = mult[k] = mult[k-1];
/* since mult[k] >= mult[k-1] + nbits(Q[k]),
we have Q[0]*...*Q[k] <= 2^mult[k] = 2^prec_i_have */
l ++;
j >>= 1;
k --;
}
}
/* accumulate all products in S[0] and Q[0]. Warning: contrary to above,
here we do not have log2_nb_terms[k-1] = log2_nb_terms[k]+1. */
l = 0; /* number of accumulated terms in the right part S[k]/Q[k] */
while (k > 0)
{
j = log2_nb_terms[k-1];
mpz_mul (S[k], S[k], ptoj[j]);
mpz_mul (S[k-1], S[k-1], Q[k]);
l += 1 << log2_nb_terms[k];
mpz_mul_2exp (S[k-1], S[k-1], r * l);
mpz_add (S[k-1], S[k-1], S[k]);
mpz_mul (Q[k-1], Q[k-1], Q[k]);
k--;
}
/* Q[0] now equals i! */
MPFR_MPZ_SIZEINBASE2 (prec_i_have, S[0]);
diff = (mp_exp_t) prec_i_have - 2 * (mp_exp_t) precy;
expo = diff;
if (diff >= 0)
mpz_div_2exp (S[0], S[0], diff);
else
mpz_mul_2exp (S[0], S[0], -diff);
MPFR_MPZ_SIZEINBASE2 (prec_i_have, Q[0]);
diff = (mp_exp_t) prec_i_have - (mp_prec_t) precy;
expo -= diff;
if (diff > 0)
mpz_div_2exp (Q[0], Q[0], diff);
else
mpz_mul_2exp (Q[0], Q[0], -diff);
mpz_tdiv_q (S[0], S[0], Q[0]);
mpfr_set_z (y, S[0], GMP_RNDD);
MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo - r * (i - 1) );
}
int
mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t bx,cx;
mpfr_uexp_t d;
mpfr_prec_t p, sh, cnt;
mp_size_t n;
mp_limb_t *ap, *bp, *cp;
mp_limb_t limb;
int inexact;
mp_limb_t bcp,bcp1; /* Cp and C'p+1 */
mp_limb_t bbcp = (mp_limb_t) -1, bbcp1 = (mp_limb_t) -1; /* Cp+1 and C'p+2,
gcc claims that they might be used uninitialized. We fill them with invalid
values, which should produce a failure if so. See README.dev file. */
MPFR_TMP_DECL(marker);
MPFR_TMP_MARK(marker);
MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c));
MPFR_ASSERTD(MPFR_IS_PURE_FP(b));
MPFR_ASSERTD(MPFR_IS_PURE_FP(c));
/* Read prec and num of limbs */
p = MPFR_PREC (b);
n = MPFR_PREC2LIMBS (p);
/* Fast cmp of |b| and |c|*/
bx = MPFR_GET_EXP (b);
cx = MPFR_GET_EXP (c);
if (MPFR_UNLIKELY(bx == cx))
{
mp_size_t k = n - 1;
/* Check mantissa since exponent are equals */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
while (k>=0 && MPFR_UNLIKELY(bp[k] == cp[k]))
k--;
if (MPFR_UNLIKELY(k < 0))
/* b == c ! */
{
/* Return exact number 0 */
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET(0);
}
else if (bp[k] > cp[k])
goto BGreater;
else
{
MPFR_ASSERTD(bp[k]<cp[k]);
goto CGreater;
}
}
else if (MPFR_UNLIKELY(bx < cx))
{
/* Swap b and c and set sign */
mpfr_srcptr t;
mpfr_exp_t tx;
CGreater:
MPFR_SET_OPPOSITE_SIGN(a,b);
t = b; b = c; c = t;
tx = bx; bx = cx; cx = tx;
}
else
{
/* b > c */
BGreater:
MPFR_SET_SAME_SIGN(a,b);
}
/* Now b > c */
MPFR_ASSERTD(bx >= cx);
d = (mpfr_uexp_t) bx - cx;
DEBUG (printf ("New with diff=%lu\n", (unsigned long) d));
if (MPFR_UNLIKELY(d <= 1))
{
if (MPFR_LIKELY(d < 1))
{
/* <-- b -->
<-- c --> : exact sub */
ap = MPFR_MANT(a);
mpn_sub_n (ap, MPFR_MANT(b), MPFR_MANT(c), n);
/* Normalize */
ExactNormalize:
limb = ap[n-1];
if (MPFR_LIKELY(limb))
{
/* First limb is not zero. */
count_leading_zeros(cnt, limb);
/* cnt could be == 0 <= SubD1Lose */
if (MPFR_LIKELY(cnt))
{
mpn_lshift(ap, ap, n, cnt); /* Normalize number */
bx -= cnt; /* Update final expo */
}
/* Last limb should be ok */
MPFR_ASSERTD(!(ap[0] & MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
else
{
/* First limb is zero */
mp_size_t k = n-1, len;
/* Find the first limb not equal to zero.
FIXME:It is assume it exists (since |b| > |c| and same prec)*/
do
{
MPFR_ASSERTD( k > 0 );
limb = ap[--k];
}
while (limb == 0);
MPFR_ASSERTD(limb != 0);
count_leading_zeros(cnt, limb);
k++;
len = n - k; /* Number of last limb */
MPFR_ASSERTD(k >= 0);
if (MPFR_LIKELY(cnt))
mpn_lshift(ap+len, ap, k, cnt); /* Normalize the High Limb*/
else
{
/* Must use DECR since src and dest may overlap & dest>=src*/
MPN_COPY_DECR(ap+len, ap, k);
}
MPN_ZERO(ap, len); /* Zeroing the last limbs */
bx -= cnt + len*GMP_NUMB_BITS; /* Update Expo */
/* Last limb should be ok */
MPFR_ASSERTD(!(ap[len]&MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
/* Check expo underflow */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
MPFR_TMP_FREE(marker);
/* inexact=0 */
DEBUG( printf("(D==0 Underflow)\n") );
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(/*inexact >= 0 &&*/ mpfr_powerof2_raw (a))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
/* No rounding is necessary since the result is exact */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
MPFR_TMP_FREE(marker);
return 0;
}
else /* if (d == 1) */
{
/* | <-- b -->
| <-- c --> */
mp_limb_t c0, mask;
mp_size_t k;
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* If we lose at least one bit, compute 2*b-c (Exact)
* else compute b-c/2 */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
k = n-1;
limb = bp[k] - cp[k]/2;
if (limb > MPFR_LIMB_HIGHBIT)
{
/* We can't lose precision: compute b-c/2 */
/* Shift c in the allocated temporary block */
SubD1NoLose:
c0 = cp[0] & (MPFR_LIMB_ONE<<sh);
cp = MPFR_TMP_LIMBS_ALLOC (n);
mpn_rshift(cp, MPFR_MANT(c), n, 1);
if (MPFR_LIKELY(c0 == 0))
{
/* Result is exact: no need of rounding! */
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
MPFR_SET_EXP(a, bx); /* No expo overflow! */
/* No truncate or normalize is needed */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
/* No rounding is necessary since the result is exact */
MPFR_TMP_FREE(marker);
return 0;
}
ap = MPFR_MANT(a);
mask = ~MPFR_LIMB_MASK(sh);
cp[0] &= mask; /* Delete last bit of c */
mpn_sub_n (ap, bp, cp, n);
MPFR_SET_EXP(a, bx); /* No expo overflow! */
MPFR_ASSERTD( !(ap[0] & ~mask) ); /* Check last bits */
/* No normalize is needed */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
/* Rounding is necessary since c0 = 1*/
/* Cp =-1 and C'p+1=0 */
bcp = 1; bcp1 = 0;
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
/* Even Rule apply: Check Ap-1 */
if (MPFR_LIKELY( (ap[0] & (MPFR_LIMB_ONE<<sh)) == 0) )
goto truncate;
else
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else
goto truncate;
}
else if (MPFR_LIKELY(limb < MPFR_LIMB_HIGHBIT))
{
/* We lose at least one bit of prec */
/* Calcul of 2*b-c (Exact) */
/* Shift b in the allocated temporary block */
SubD1Lose:
bp = MPFR_TMP_LIMBS_ALLOC (n);
mpn_lshift (bp, MPFR_MANT(b), n, 1);
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
bx--;
goto ExactNormalize;
}
else
{
/* Case: limb = 100000000000 */
/* Check while b[k] == c'[k] (C' is C shifted by 1) */
/* If b[k]<c'[k] => We lose at least one bit*/
/* If b[k]>c'[k] => We don't lose any bit */
/* If k==-1 => We don't lose any bit
AND the result is 100000000000 0000000000 00000000000 */
mp_limb_t carry;
do {
carry = cp[k]&MPFR_LIMB_ONE;
k--;
} while (k>=0 &&
bp[k]==(carry=cp[k]/2+(carry<<(GMP_NUMB_BITS-1))));
if (MPFR_UNLIKELY(k<0))
{
/*If carry then (sh==0 and Virtual c'[-1] > Virtual b[-1]) */
if (MPFR_UNLIKELY(carry)) /* carry = cp[0]&MPFR_LIMB_ONE */
{
/* FIXME: Can be faster? */
MPFR_ASSERTD(sh == 0);
goto SubD1Lose;
}
/* Result is a power of 2 */
ap = MPFR_MANT (a);
MPN_ZERO (ap, n);
ap[n-1] = MPFR_LIMB_HIGHBIT;
MPFR_SET_EXP (a, bx); /* No expo overflow! */
/* No Normalize is needed*/
/* No Rounding is needed */
MPFR_TMP_FREE (marker);
return 0;
}
/* carry = cp[k]/2+(cp[k-1]&1)<<(GMP_NUMB_BITS-1) = c'[k]*/
else if (bp[k] > carry)
goto SubD1NoLose;
else
{
MPFR_ASSERTD(bp[k]<carry);
goto SubD1Lose;
}
}
}
}
else if (MPFR_UNLIKELY(d >= p))
{
ap = MPFR_MANT(a);
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* We can't set A before since we use cp for rounding... */
/* Perform rounding: check if a=b or a=b-ulp(b) */
if (MPFR_UNLIKELY(d == p))
{
/* cp == -1 and c'p+1 = ? */
bcp = 1;
/* We need Cp+1 later for a very improbable case. */
bbcp = (MPFR_MANT(c)[n-1] & (MPFR_LIMB_ONE<<(GMP_NUMB_BITS-2)));
/* We need also C'p+1 for an even more unprobable case... */
if (MPFR_LIKELY( bbcp ))
bcp1 = 1;
else
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && cp[k]==0);
bcp1 = (k>=0);
}
else
bcp1 = 1;
}
DEBUG( printf("(D=P) Cp=-1 Cp+1=%d C'p+1=%d \n", bbcp!=0, bcp1!=0) );
bp = MPFR_MANT (b);
/* Even if src and dest overlap, it is ok using MPN_COPY */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_UNLIKELY( bcp && bcp1==0 ))
/* Cp=-1 and C'p+1=0: Even rule Apply! */
/* Check Ap-1 = Bp-1 */
if ((bp[0] & (MPFR_LIMB_ONE<<sh)) == 0)
{
MPN_COPY(ap, bp, n);
goto truncate;
}
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
{
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
else
{
MPN_COPY(ap, bp, n);
goto truncate;
}
}
else
{
/* Cp=0, Cp+1=-1 if d==p+1, C'p+1=-1 */
bcp = 0; bbcp = (d==p+1); bcp1 = 1;
DEBUG( printf("(D>P) Cp=%d Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0) );
/* Need to compute C'p+2 if d==p+1 and if rnd_mode=NEAREST
(Because of a very improbable case) */
if (MPFR_UNLIKELY(d==p+1 && rnd_mode==MPFR_RNDN))
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && cp[k]==0);
bbcp1 = (k>=0);
}
else
bbcp1 = 1;
DEBUG( printf("(D>P) C'p+2=%d\n", bbcp1!=0) );
}
/* Copy mantissa B in A */
MPN_COPY(ap, MPFR_MANT(b), n);
/* Round */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
goto truncate;
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else /* rnd_mode = AWAY */
goto truncate;
}
}
else
{
mpfr_uexp_t dm;
mp_size_t m;
mp_limb_t mask;
/* General case: 2 <= d < p */
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift c in temporary allocated place */
dm = d % GMP_NUMB_BITS;
m = d / GMP_NUMB_BITS;
if (MPFR_UNLIKELY(dm == 0))
{
/* dm = 0 and m > 0: Just copy */
MPFR_ASSERTD(m!=0);
MPN_COPY(cp, MPFR_MANT(c)+m, n-m);
MPN_ZERO(cp+n-m, m);
}
else if (MPFR_LIKELY(m == 0))
{
/* dm >=2 and m == 0: just shift */
MPFR_ASSERTD(dm >= 2);
mpn_rshift(cp, MPFR_MANT(c), n, dm);
}
else
{
/* dm > 0 and m > 0: shift and zero */
mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm);
MPN_ZERO(cp+n-m, m);
}
DEBUG( mpfr_print_mant_binary("Before", MPFR_MANT(c), p) );
DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) );
DEBUG( mpfr_print_mant_binary("After ", cp, p) );
/* Compute bcp=Cp and bcp1=C'p+1 */
if (MPFR_LIKELY(sh))
{
/* Try to compute them from C' rather than C (FIXME: Faster?) */
bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ;
if (MPFR_LIKELY( cp[0] & MPFR_LIMB_MASK(sh-1) ))
bcp1 = 1;
else
{
/* We can't compute C'p+1 from C'. Compute it from C */
/* Start from bit x=p-d+sh in mantissa C
(+sh since we have already looked sh bits in C'!) */
mpfr_prec_t x = p-d+sh-1;
if (MPFR_LIKELY(x>p))
/* We are already looked at all the bits of c, so C'p+1 = 0*/
bcp1 = 0;
else
{
mp_limb_t *tp = MPFR_MANT(c);
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
DEBUG (printf ("(First) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx,
(unsigned long) sx));
/* Looks at the last bits of limb kx (if sx=0 does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/
/*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx >= 0);
}
}
}
}
else
{
/* Compute Cp and C'p+1 from C with sh=0 */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=p-d in mantissa C */
mpfr_prec_t x = p-d;
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p >= d);
bcp = (tp[kx] & (MPFR_LIMB_ONE<<sx));
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx>=0);
}
}
DEBUG( printf("sh=%lu Cp=%d C'p+1=%d\n", sh, bcp!=0, bcp1!=0) );
/* Check if we can lose a bit, and if so compute Cp+1 and C'p+2 */
bp = MPFR_MANT(b);
if (MPFR_UNLIKELY((bp[n-1]-cp[n-1]) <= MPFR_LIMB_HIGHBIT))
{
/* We can lose a bit so we precompute Cp+1 and C'p+2 */
/* Test for trivial case: since C'p+1=0, Cp+1=0 and C'p+2 =0 */
if (MPFR_LIKELY(bcp1 == 0))
{
bbcp = 0;
bbcp1 = 0;
}
else /* bcp1 != 0 */
{
/* We can lose a bit:
compute Cp+1 and C'p+2 from mantissa C */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=(p+1)-d in mantissa C */
mpfr_prec_t x = p+1-d;
mp_size_t kx = n-1 - (x/GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p > d);
DEBUG (printf ("(pre) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx,
(unsigned long) sx));
bbcp = (tp[kx] & (MPFR_LIMB_ONE<<sx)) ;
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
/* If Cp+1=0, since C'p+1!=0, C'p+2=1 ! */
if (MPFR_LIKELY(bbcp==0 || (tp[kx]&MPFR_LIMB_MASK(sx))))
bbcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bbcp1 = (kx>=0);
DEBUG (printf ("(Pre) Scan done for %ld\n", (long) kx));
}
} /*End of Bcp1 != 0*/
DEBUG( printf("(Pre) Cp+1=%d C'p+2=%d\n", bbcp!=0, bbcp1!=0) );
} /* End of "can lose a bit" */
/* Clean shifted C' */
mask = ~MPFR_LIMB_MASK (sh);
cp[0] &= mask;
/* Subtract the mantissa c from b in a */
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
DEBUG( mpfr_print_mant_binary("Sub= ", ap, p) );
/* Normalize: we lose at max one bit*/
if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
{
/* High bit is not set and we have to fix it! */
/* Ap >= 010000xxx001 */
mpn_lshift(ap, ap, n, 1);
/* Ap >= 100000xxx010 */
if (MPFR_UNLIKELY(bcp!=0)) /* Check if Cp = -1 */
/* Since Cp == -1, we have to substract one more */
{
mpn_sub_1(ap, ap, n, MPFR_LIMB_ONE<<sh);
MPFR_ASSERTD(MPFR_LIMB_MSB(ap[n-1]) != 0);
}
/* Ap >= 10000xxx001 */
/* Final exponent -1 since we have shifted the mantissa */
bx--;
/* Update bcp and bcp1 */
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
MPFR_ASSERTN(bbcp1 != (mp_limb_t) -1);
bcp = bbcp;
bcp1 = bbcp1;
/* We dont't have anymore a valid Cp+1!
But since Ap >= 100000xxx001, the final sub can't unnormalize!*/
}
MPFR_ASSERTD( !(ap[0] & ~mask) );
/* Rounding */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_LIKELY(bcp==0))
goto truncate;
else if ((bcp1) || ((ap[0] & (MPFR_LIMB_ONE<<sh)) != 0))
goto sub_one_ulp;
else
goto truncate;
}
/* Update rounding mode */
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ && (MPFR_LIKELY(bcp || bcp1)))
goto sub_one_ulp;
goto truncate;
}
MPFR_RET_NEVER_GO_HERE ();
/* Sub one ulp to the result */
sub_one_ulp:
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
/* Result should be smaller than exact value: inexact=-1 */
inexact = -1;
/* Check normalisation */
if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
{
/* ap was a power of 2, and we lose a bit */
/* Now it is 0111111111111111111[00000 */
mpn_lshift(ap, ap, n, 1);
bx--;
/* And the lost bit x depends on Cp+1, and Cp */
/* Compute Cp+1 if it isn't already compute (ie d==1) */
/* FIXME: Is this case possible? */
if (MPFR_UNLIKELY(d == 1))
bbcp = 0;
DEBUG( printf("(SubOneUlp)Cp=%d, Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0));
/* Compute the last bit (Since we have shifted the mantissa)
we need one more bit!*/
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
if ( (rnd_mode == MPFR_RNDZ && bcp==0)
|| (rnd_mode==MPFR_RNDN && bbcp==0)
|| (bcp && bcp1==0) ) /*Exact result*/
{
ap[0] |= MPFR_LIMB_ONE<<sh;
if (rnd_mode == MPFR_RNDN)
inexact = 1;
DEBUG( printf("(SubOneUlp) Last bit set\n") );
}
/* Result could be exact if C'p+1 = 0 and rnd == Zero
since we have had one more bit to the result */
/* Fixme: rnd_mode == MPFR_RNDZ needed ? */
if (bcp1==0 && rnd_mode==MPFR_RNDZ)
{
DEBUG( printf("(SubOneUlp) Exact result\n") );
inexact = 0;
}
}
goto end_of_sub;
truncate:
/* Check if the result is an exact power of 2: 100000000000
in which cases, we could have to do sub_one_ulp due to some nasty reasons:
If Result is a Power of 2:
+ If rnd = AWAY,
| If Cp=-1 and C'p+1 = 0, SubOneUlp and the result is EXACT.
If Cp=-1 and C'p+1 =-1, SubOneUlp and the result is above.
Otherwise truncate
+ If rnd = NEAREST,
If Cp= 0 and Cp+1 =-1 and C'p+2=-1, SubOneUlp and the result is above
If cp=-1 and C'p+1 = 0, SubOneUlp and the result is exact.
Otherwise truncate.
X bit should always be set if SubOneUlp*/
if (MPFR_UNLIKELY(ap[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do {
k--;
} while (k>=0 && ap[k]==0);
if (MPFR_UNLIKELY(k<0))
{
/* It is a power of 2! */
/* Compute Cp+1 if it isn't already compute (ie d==1) */
/* FIXME: Is this case possible? */
if (d == 1)
bbcp=0;
DEBUG( printf("(Truncate) Cp=%d, Cp+1=%d C'p+1=%d C'p+2=%d\n", \
bcp!=0, bbcp!=0, bcp1!=0, bbcp1!=0) );
MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
MPFR_ASSERTN((rnd_mode != MPFR_RNDN) || (bcp != 0) || (bbcp == 0) || (bbcp1 != (mp_limb_t) -1));
if (((rnd_mode != MPFR_RNDZ) && bcp)
||
((rnd_mode == MPFR_RNDN) && (bcp == 0) && (bbcp) && (bbcp1)))
{
DEBUG( printf("(Truncate) Do sub\n") );
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
mpn_lshift(ap, ap, n, 1);
ap[0] |= MPFR_LIMB_ONE<<sh;
bx--;
/* FIXME: Explain why it works (or why not)... */
inexact = (bcp1 == 0) ? 0 : (rnd_mode==MPFR_RNDN) ? -1 : 1;
goto end_of_sub;
}
}
}
/* Calcul of Inexact flag.*/
inexact = MPFR_LIKELY(bcp || bcp1) ? 1 : 0;
end_of_sub:
/* Update Expo */
/* FIXME: Is this test really useful?
If d==0 : Exact case. This is never called.
if 1 < d < p : bx=MPFR_EXP(b) or MPFR_EXP(b)-1 > MPFR_EXP(c) > emin
if d == 1 : bx=MPFR_EXP(b). If we could lose any bits, the exact
normalisation is called.
if d >= p : bx=MPFR_EXP(b) >= MPFR_EXP(c) + p > emin
After SubOneUlp, we could have one bit less.
if 1 < d < p : bx >= MPFR_EXP(b)-2 >= MPFR_EXP(c) > emin
if d == 1 : bx >= MPFR_EXP(b)-1 = MPFR_EXP(c) > emin.
if d >= p : bx >= MPFR_EXP(b)-1 > emin since p>=2.
*/
MPFR_ASSERTD( bx >= __gmpfr_emin);
/*
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
DEBUG( printf("(Final Underflow)\n") );
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(inexact >= 0 && mpfr_powerof2_raw (a))))
rnd_mode = MPFR_RNDZ;
MPFR_TMP_FREE(marker);
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
*/
MPFR_SET_EXP (a, bx);
MPFR_TMP_FREE(marker);
MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
long double
mpfr_get_ld (mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return (long double) mpfr_get_d (x, rnd_mode);
else /* now x is a normal non-zero number */
{
long double r; /* result */
long double m;
double s; /* part of result */
mpfr_exp_t sh; /* exponent shift, so that x/2^sh is in the double range */
mpfr_t y, z;
int sign;
/* first round x to the target long double precision, so that
all subsequent operations are exact (this avoids double rounding
problems) */
mpfr_init2 (y, MPFR_LDBL_MANT_DIG);
mpfr_init2 (z, MPFR_LDBL_MANT_DIG);
/* Note about the precision of z: even though IEEE_DBL_MANT_DIG is
sufficient, z has been set to the same precision as y so that
the mpfr_sub below calls mpfr_sub1sp, which is faster than the
generic subtraction, even in this particular case (from tests
done by Patrick Pelissier on a 64-bit Core2 Duo against r7285).
But here there is an important cancellation in the subtraction.
TODO: get more information about what has been tested. */
mpfr_set (y, x, rnd_mode);
sh = MPFR_GET_EXP (y);
sign = MPFR_SIGN (y);
MPFR_SET_EXP (y, 0);
MPFR_SET_POS (y);
r = 0.0;
do {
s = mpfr_get_d (y, MPFR_RNDN); /* high part of y */
r += (long double) s;
mpfr_set_d (z, s, MPFR_RNDN); /* exact */
mpfr_sub (y, y, z, MPFR_RNDN); /* exact */
} while (!MPFR_IS_ZERO (y));
mpfr_clear (z);
mpfr_clear (y);
/* we now have to multiply back by 2^sh */
MPFR_ASSERTD (r > 0);
if (sh != 0)
{
/* An overflow may occurs (example: 0.5*2^1024) */
while (r < 1.0)
{
r += r;
sh--;
}
if (sh > 0)
m = 2.0;
else
{
m = 0.5;
sh = -sh;
}
for (;;)
{
if (sh % 2)
r = r * m;
sh >>= 1;
if (sh == 0)
break;
m = m * m;
}
}
if (sign < 0)
r = -r;
return r;
}
}
