static int
mpfr_rem1 (mpfr_ptr rem, long *quo, mpfr_rnd_t rnd_q,
mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd)
{
mpfr_exp_t ex, ey;
int compare, inex, q_is_odd, sign, signx = MPFR_SIGN (x);
mpz_t mx, my, r;
int tiny = 0;
MPFR_ASSERTD (rnd_q == MPFR_RNDN || rnd_q == MPFR_RNDZ);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y)))
{
if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x)
|| MPFR_IS_ZERO (y))
{
/* for remquo, quo is undefined */
MPFR_SET_NAN (rem);
MPFR_RET_NAN;
}
else /* either y is Inf and x is 0 or non-special,
or x is 0 and y is non-special,
in both cases the quotient is zero. */
{
if (quo)
*quo = 0;
return mpfr_set (rem, x, rnd);
}
}
/* now neither x nor y is NaN, Inf or zero */
mpz_init (mx);
mpz_init (my);
mpz_init (r);
ex = mpfr_get_z_2exp (mx, x); /* x = mx*2^ex */
ey = mpfr_get_z_2exp (my, y); /* y = my*2^ey */
/* to get rid of sign problems, we compute it separately:
quo(-x,-y) = quo(x,y), rem(-x,-y) = -rem(x,y)
quo(-x,y) = -quo(x,y), rem(-x,y) = -rem(x,y)
thus quo = sign(x/y)*quo(|x|,|y|), rem = sign(x)*rem(|x|,|y|) */
sign = (signx == MPFR_SIGN (y)) ? 1 : -1;
mpz_abs (mx, mx);
mpz_abs (my, my);
q_is_odd = 0;
/* divide my by 2^k if possible to make operations mod my easier */
{
unsigned long k = mpz_scan1 (my, 0);
ey += k;
mpz_fdiv_q_2exp (my, my, k);
}
if (ex <= ey)
{
/* q = x/y = mx/(my*2^(ey-ex)) */
/* First detect cases where q=0, to avoid creating a huge number
my*2^(ey-ex): if sx = mpz_sizeinbase (mx, 2) and sy =
mpz_sizeinbase (my, 2), we have x < 2^(ex + sx) and
y >= 2^(ey + sy - 1), thus if ex + sx <= ey + sy - 1
the quotient is 0 */
if (ex + (mpfr_exp_t) mpz_sizeinbase (mx, 2) <
ey + (mpfr_exp_t) mpz_sizeinbase (my, 2))
{
tiny = 1;
mpz_set (r, mx);
mpz_set_ui (mx, 0);
}
else
{
mpz_mul_2exp (my, my, ey - ex); /* divide mx by my*2^(ey-ex) */
/* since mx > 0 and my > 0, we can use mpz_tdiv_qr in all cases */
mpz_tdiv_qr (mx, r, mx, my);
/* 0 <= |r| <= |my|, r has the same sign as mx */
}
if (rnd_q == MPFR_RNDN)
q_is_odd = mpz_tstbit (mx, 0);
if (quo) /* mx is the quotient */
{
mpz_tdiv_r_2exp (mx, mx, WANTED_BITS);
*quo = mpz_get_si (mx);
}
}
else /* ex > ey */
{
if (quo) /* remquo case */
/* for remquo, to get the low WANTED_BITS more bits of the quotient,
we first compute R = X mod Y*2^WANTED_BITS, where X and Y are
defined below. Then the low WANTED_BITS of the quotient are
floor(R/Y). */
mpz_mul_2exp (my, my, WANTED_BITS); /* 2^WANTED_BITS*Y */
else if (rnd_q == MPFR_RNDN) /* remainder case */
/* Let X = mx*2^(ex-ey) and Y = my. Then both X and Y are integers.
Assume X = R mod Y, then x = X*2^ey = R*2^ey mod (Y*2^ey=y).
To be able to perform the rounding, we need the least significant
bit of the quotient, i.e., one more bit in the remainder,
which is obtained by dividing by 2Y. */
mpz_mul_2exp (my, my, 1); /* 2Y */
mpz_set_ui (r, 2);
mpz_powm_ui (r, r, ex - ey, my); /* 2^(ex-ey) mod my */
mpz_mul (r, r, mx);
mpz_mod (r, r, my);
if (quo) /* now 0 <= r < 2^WANTED_BITS*Y */
{
mpz_fdiv_q_2exp (my, my, WANTED_BITS); /* back to Y */
mpz_tdiv_qr (mx, r, r, my);
/* oldr = mx*my + newr */
*quo = mpz_get_si (mx);
q_is_odd = *quo & 1;
}
else if (rnd_q == MPFR_RNDN) /* now 0 <= r < 2Y in the remainder case */
{
mpz_fdiv_q_2exp (my, my, 1); /* back to Y */
/* least significant bit of q */
q_is_odd = mpz_cmpabs (r, my) >= 0;
if (q_is_odd)
mpz_sub (r, r, my);
}
/* now 0 <= |r| < |my|, and if needed,
q_is_odd is the least significant bit of q */
}
if (mpz_cmp_ui (r, 0) == 0)
{
inex = mpfr_set_ui (rem, 0, MPFR_RNDN);
/* take into account sign of x */
if (signx < 0)
mpfr_neg (rem, rem, MPFR_RNDN);
}
else
{
if (rnd_q == MPFR_RNDN)
{
/* FIXME: the comparison 2*r < my could be done more efficiently
at the mpn level */
mpz_mul_2exp (r, r, 1);
/* if tiny=1, we should compare r with my*2^(ey-ex) */
if (tiny)
{
if (ex + (mpfr_exp_t) mpz_sizeinbase (r, 2) <
ey + (mpfr_exp_t) mpz_sizeinbase (my, 2))
compare = 0; /* r*2^ex < my*2^ey */
else
{
mpz_mul_2exp (my, my, ey - ex);
compare = mpz_cmpabs (r, my);
}
}
else
compare = mpz_cmpabs (r, my);
mpz_fdiv_q_2exp (r, r, 1);
compare = ((compare > 0) ||
((rnd_q == MPFR_RNDN) && (compare == 0) && q_is_odd));
/* if compare != 0, we need to subtract my to r, and add 1 to quo */
if (compare)
{
mpz_sub (r, r, my);
if (quo && (rnd_q == MPFR_RNDN))
*quo += 1;
}
}
/* take into account sign of x */
if (signx < 0)
mpz_neg (r, r);
inex = mpfr_set_z_2exp (rem, r, ex > ey ? ey : ex, rnd);
}
if (quo)
*quo *= sign;
mpz_clear (mx);
mpz_clear (my);
mpz_clear (r);
return inex;
}
/* Implements asymptotic expansion for jn or yn (formulae 9.2.5 and 9.2.6
from Abramowitz & Stegun).
Assumes |z| > p log(2)/2, where p is the target precision
(z can be negative only for jn).
Return 0 if the expansion does not converge enough (the value 0 as inexact
flag should not happen for normal input).
*/
static int
FUNCTION (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
{
mpfr_t s, c, P, Q, t, iz, err_t, err_s, err_u;
mpfr_prec_t w;
long k;
int inex, stop, diverge = 0;
mpfr_exp_t err2, err;
MPFR_ZIV_DECL (loop);
mpfr_init (c);
w = MPFR_PREC(res) + MPFR_INT_CEIL_LOG2(MPFR_PREC(res)) + 4;
MPFR_ZIV_INIT (loop, w);
for (;;)
{
mpfr_set_prec (c, w);
mpfr_init2 (s, w);
mpfr_init2 (P, w);
mpfr_init2 (Q, w);
mpfr_init2 (t, w);
mpfr_init2 (iz, w);
mpfr_init2 (err_t, 31);
mpfr_init2 (err_s, 31);
mpfr_init2 (err_u, 31);
/* Approximate sin(z) and cos(z). In the following, err <= k means that
the approximate value y and the true value x are related by
y = x * (1 + u)^k with |u| <= 2^(-w), following Higham's method. */
mpfr_sin_cos (s, c, z, MPFR_RNDN);
if (MPFR_IS_NEG(z))
mpfr_neg (s, s, MPFR_RNDN); /* compute jn/yn(|z|), fix sign later */
/* The absolute error on s/c is bounded by 1/2 ulp(1/2) <= 2^(-w-1). */
mpfr_add (t, s, c, MPFR_RNDN);
mpfr_sub (c, s, c, MPFR_RNDN);
mpfr_swap (s, t);
/* now s approximates sin(z)+cos(z), and c approximates sin(z)-cos(z),
with total absolute error bounded by 2^(1-w). */
/* precompute 1/(8|z|) */
mpfr_si_div (iz, MPFR_IS_POS(z) ? 1 : -1, z, MPFR_RNDN); /* err <= 1 */
mpfr_div_2ui (iz, iz, 3, MPFR_RNDN);
/* compute P and Q */
mpfr_set_ui (P, 1, MPFR_RNDN);
mpfr_set_ui (Q, 0, MPFR_RNDN);
mpfr_set_ui (t, 1, MPFR_RNDN); /* current term */
mpfr_set_ui (err_t, 0, MPFR_RNDN); /* error on t */
mpfr_set_ui (err_s, 0, MPFR_RNDN); /* error on P and Q (sum of errors) */
for (k = 1, stop = 0; stop < 4; k++)
{
/* compute next term: t(k)/t(k-1) = (2n+2k-1)(2n-2k+1)/(8kz) */
mpfr_mul_si (t, t, 2 * (n + k) - 1, MPFR_RNDN); /* err <= err_k + 1 */
mpfr_mul_si (t, t, 2 * (n - k) + 1, MPFR_RNDN); /* err <= err_k + 2 */
mpfr_div_ui (t, t, k, MPFR_RNDN); /* err <= err_k + 3 */
mpfr_mul (t, t, iz, MPFR_RNDN); /* err <= err_k + 5 */
/* the relative error on t is bounded by (1+u)^(5k)-1, which is
bounded by 6ku for 6ku <= 0.02: first |5 log(1+u)| <= |5.5u|
for |u| <= 0.15, then |exp(5.5u)-1| <= 6u for |u| <= 0.02. */
mpfr_mul_ui (err_t, t, 6 * k, MPFR_IS_POS(t) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDN); /* exact */
/* the absolute error on t is bounded by err_t * 2^(-w) */
mpfr_abs (err_u, t, MPFR_RNDU);
mpfr_mul_2ui (err_u, err_u, w, MPFR_RNDU); /* t * 2^w */
mpfr_add (err_u, err_u, err_t, MPFR_RNDU); /* max|t| * 2^w */
if (stop >= 2)
{
/* take into account the neglected terms: t * 2^w */
mpfr_div_2ui (err_s, err_s, w, MPFR_RNDU);
if (MPFR_IS_POS(t))
mpfr_add (err_s, err_s, t, MPFR_RNDU);
else
mpfr_sub (err_s, err_s, t, MPFR_RNDU);
mpfr_mul_2ui (err_s, err_s, w, MPFR_RNDU);
stop ++;
}
/* if k is odd, add to Q, otherwise to P */
else if (k & 1)
{
/* if k = 1 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (Q, Q, t, MPFR_RNDN);
else
mpfr_sub (Q, Q, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(Q): if EXP(err_u)
<= EXP(Q), since the current term is bounded by
err_u * 2^(-w), it is bounded by ulp(Q) */
if (MPFR_EXP(err_u) <= MPFR_EXP(Q))
stop ++;
else
stop = 0;
}
else
{
/* if k = 0 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (P, P, t, MPFR_RNDN);
else
mpfr_sub (P, P, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(P) */
if (MPFR_EXP(err_u) <= MPFR_EXP(P))
stop ++;
else
stop = 0;
}
mpfr_add (err_s, err_s, err_t, MPFR_RNDU);
/* the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w) */
/* stop when start to diverge */
if (stop < 2 &&
((MPFR_IS_POS(z) && mpfr_cmp_ui (z, (k + 1) / 2) < 0) ||
(MPFR_IS_NEG(z) && mpfr_cmp_si (z, - ((k + 1) / 2)) > 0)))
{
/* if we have to stop the series because it diverges, then
increasing the precision will most probably fail, since
we will stop to the same point, and thus compute a very
similar approximation */
diverge = 1;
stop = 2; /* force stop */
}
}
/* the sum of the total errors on P and Q is bounded by err_s * 2^(-w) */
/* Now combine: the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w), and the absolute error on s/c is bounded by 2^(1-w) */
if ((n & 1) == 0) /* n even: P * (sin + cos) + Q (cos - sin) for jn
Q * (sin + cos) + P (sin - cos) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#else
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_sub (s, s, c, MPFR_RNDN);
#else
mpfr_add (s, s, c, MPFR_RNDN);
#endif
}
else /* n odd: P * (sin - cos) + Q (cos + sin) for jn,
Q * (sin - cos) - P (cos + sin) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#else
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_add (s, s, c, MPFR_RNDN);
#else
mpfr_sub (s, c, s, MPFR_RNDN);
#endif
}
if ((n & 2) != 0)
mpfr_neg (s, s, MPFR_RNDN);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
/* the absolute error on s is bounded by P*err(s/c) + Q*err(s/c)
+ err(P)*(s/c) + err(Q)*(s/c) + 3 * 2^(err - w - 1)
<= (|P|+|Q|) * 2^(1-w) + err_s * 2^(1-w) + 2^err * 2^(1-w),
since |c|, |old_s| <= 2. */
err2 = (MPFR_EXP(P) >= MPFR_EXP(Q)) ? MPFR_EXP(P) + 2 : MPFR_EXP(Q) + 2;
/* (|P| + |Q|) * 2^(1 - w) <= 2^(err2 - w) */
err = MPFR_EXP(err_s) >= err ? MPFR_EXP(err_s) + 2 : err + 2;
/* err_s * 2^(1-w) + 2^old_err * 2^(1-w) <= 2^err * 2^(-w) */
err2 = (err >= err2) ? err + 1 : err2 + 1;
/* now the absolute error on s is bounded by 2^(err2 - w) */
/* multiply by sqrt(1/(Pi*z)) */
mpfr_const_pi (c, MPFR_RNDN); /* Pi, err <= 1 */
mpfr_mul (c, c, z, MPFR_RNDN); /* err <= 2 */
mpfr_si_div (c, MPFR_IS_POS(z) ? 1 : -1, c, MPFR_RNDN); /* err <= 3 */
mpfr_sqrt (c, c, MPFR_RNDN); /* err<=5/2, thus the absolute error is
bounded by 3*u*|c| for |u| <= 0.25 */
mpfr_mul (err_t, c, s, MPFR_SIGN(c)==MPFR_SIGN(s) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDU);
mpfr_mul_ui (err_t, err_t, 3, MPFR_RNDU);
/* 3*2^(-w)*|old_c|*|s| [see below] is bounded by err_t * 2^(-w) */
err2 += MPFR_EXP(c);
/* |old_c| * 2^(err2 - w) [see below] is bounded by 2^(err2-w) */
mpfr_mul (c, c, s, MPFR_RNDN); /* the absolute error on c is bounded by
1/2 ulp(c) + 3*2^(-w)*|old_c|*|s|
+ |old_c| * 2^(err2 - w) */
/* compute err_t * 2^(-w) + 1/2 ulp(c) = (err_t + 2^EXP(c)) * 2^(-w) */
err = (MPFR_EXP(err_t) > MPFR_EXP(c)) ? MPFR_EXP(err_t) + 1 : MPFR_EXP(c) + 1;
/* err_t * 2^(-w) + 1/2 ulp(c) <= 2^(err - w) */
/* now err_t * 2^(-w) bounds 1/2 ulp(c) + 3*2^(-w)*|old_c|*|s| */
err = (err >= err2) ? err + 1 : err2 + 1;
/* the absolute error on c is bounded by 2^(err - w) */
mpfr_clear (s);
mpfr_clear (P);
mpfr_clear (Q);
mpfr_clear (t);
mpfr_clear (iz);
mpfr_clear (err_t);
mpfr_clear (err_s);
mpfr_clear (err_u);
err -= MPFR_EXP(c);
if (MPFR_LIKELY (MPFR_CAN_ROUND (c, w - err, MPFR_PREC(res), r)))
break;
if (diverge != 0)
{
mpfr_set (c, z, r); /* will force inex=0 below, which means the
asymptotic expansion failed */
break;
}
MPFR_ZIV_NEXT (loop, w);
}
MPFR_ZIV_FREE (loop);
inex = (MPFR_IS_POS(z) || ((n & 1) == 0)) ? mpfr_set (res, c, r)
: mpfr_neg (res, c, r);
mpfr_clear (c);
return inex;
}
int
mpfr_digamma (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inex;
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, inex));
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 (MPFR_IS_POS(x)) /* Digamma(+Inf) = +Inf */
{
MPFR_SET_SAME_SIGN(y, x);
MPFR_SET_INF(y);
MPFR_RET(0);
}
else /* Digamma(-Inf) = NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
else /* Zero case */
{
/* the following works also in case of overlap */
MPFR_SET_INF(y);
MPFR_SET_OPPOSITE_SIGN(y, x);
mpfr_set_divby0 ();
MPFR_RET(0);
}
}
/* Digamma is undefined for negative integers */
if (MPFR_IS_NEG(x) && mpfr_integer_p (x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
/* now x is a normal number */
MPFR_SAVE_EXPO_MARK (expo);
/* for x very small, we have Digamma(x) = -1/x - gamma + O(x), more precisely
-1 < Digamma(x) + 1/x < 0 for -0.2 < x < 0.2, thus:
(i) either x is a power of two, then 1/x is exactly representable, and
as long as 1/2*ulp(1/x) > 1, we can conclude;
(ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then
|y + 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place.
Since |Digamma(x) + 1/x| <= 1, if 2^(-2n) ufp(y) >= 2, then
|y - Digamma(x)| >= 2^(-2n-1)ufp(y), and rounding -1/x gives the correct result.
If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
A sufficient condition is thus EXP(x) <= -2 MAX(PREC(x),PREC(Y)). */
if (MPFR_EXP(x) < -2)
{
if (MPFR_EXP(x) <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y)))
{
int signx = MPFR_SIGN(x);
inex = mpfr_si_div (y, -1, x, rnd_mode);
if (inex == 0) /* x is a power of two */
{ /* result always -1/x, except when rounding down */
if (rnd_mode == MPFR_RNDA)
rnd_mode = (signx > 0) ? MPFR_RNDD : MPFR_RNDU;
if (rnd_mode == MPFR_RNDZ)
rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD;
if (rnd_mode == MPFR_RNDU)
inex = 1;
else if (rnd_mode == MPFR_RNDD)
{
mpfr_nextbelow (y);
inex = -1;
}
else /* nearest */
inex = 1;
}
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
goto end;
}
}
if (MPFR_IS_NEG(x))
inex = mpfr_digamma_reflection (y, x, rnd_mode);
/* if x < 1/2 we use the reflection formula */
else if (MPFR_EXP(x) < 0)
inex = mpfr_digamma_reflection (y, x, rnd_mode);
else
inex = mpfr_digamma_positive (y, x, rnd_mode);
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inex, rnd_mode);
}
int
mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t xp, arcc, tmp;
mpfr_exp_t supplement;
mpfr_prec_t prec;
int sign, compared, inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
("acos[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec(acos), mpfr_log_prec, acos, inexact));
/* Singular cases */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
{
MPFR_SET_NAN (acos);
MPFR_RET_NAN;
}
else /* necessarily x=0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
/* acos(0)=Pi/2 */
MPFR_SAVE_EXPO_MARK (expo);
inexact = mpfr_const_pi (acos, rnd_mode);
mpfr_div_2ui (acos, acos, 1, rnd_mode); /* exact */
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (acos, inexact, rnd_mode);
}
}
/* Set x_p=|x| */
sign = MPFR_SIGN (x);
mpfr_init2 (xp, MPFR_PREC (x));
mpfr_abs (xp, x, MPFR_RNDN); /* Exact */
compared = mpfr_cmp_ui (xp, 1);
if (MPFR_UNLIKELY (compared >= 0))
{
mpfr_clear (xp);
if (compared > 0) /* acos(x) = NaN for x > 1 */
{
MPFR_SET_NAN(acos);
MPFR_RET_NAN;
}
else
{
if (MPFR_IS_POS_SIGN (sign)) /* acos(+1) = +0 */
return mpfr_set_ui (acos, 0, rnd_mode);
else /* acos(-1) = Pi */
return mpfr_const_pi (acos, rnd_mode);
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* Compute the supplement */
mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
if (MPFR_IS_POS_SIGN (sign))
supplement = 2 - 2 * MPFR_GET_EXP (xp);
else
supplement = 2 - MPFR_GET_EXP (xp);
mpfr_clear (xp);
prec = MPFR_PREC (acos);
prec += MPFR_INT_CEIL_LOG2(prec) + 10 + supplement;
/* VL: The following change concerning prec comes from r3145
"Optimize mpfr_acos by choosing a better initial precision."
but it doesn't seem to be correct and leads to problems (assertion
failure or very important inefficiency) with tiny arguments.
Therefore, I've disabled it. */
/* If x ~ 2^-N, acos(x) ~ PI/2 - x - x^3/6
If Prec < 2*N, we can't round since x^3/6 won't be counted. */
#if 0
if (MPFR_PREC (acos) >= MPFR_PREC (x) && MPFR_GET_EXP (x) < 0)
{
mpfr_uexp_t pmin = (mpfr_uexp_t) (-2 * MPFR_GET_EXP (x)) + 5;
MPFR_ASSERTN (pmin <= MPFR_PREC_MAX);
if (prec < pmin)
prec = pmin;
}
#endif
mpfr_init2 (tmp, prec);
mpfr_init2 (arcc, prec);
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
/* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */
mpfr_sqr (tmp, x, MPFR_RNDN);
mpfr_ui_sub (tmp, 1, tmp, MPFR_RNDN);
mpfr_sqrt (tmp, tmp, MPFR_RNDN);
mpfr_div (tmp, x, tmp, MPFR_RNDN);
mpfr_atan (arcc, tmp, MPFR_RNDN);
mpfr_const_pi (tmp, MPFR_RNDN);
mpfr_div_2ui (tmp, tmp, 1, MPFR_RNDN);
mpfr_sub (arcc, tmp, arcc, MPFR_RNDN);
if (MPFR_LIKELY (MPFR_CAN_ROUND (arcc, prec - supplement,
MPFR_PREC (acos), rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
mpfr_set_prec (arcc, prec);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (acos, arcc, rnd_mode);
mpfr_clear (tmp);
mpfr_clear (arcc);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (acos, inexact, rnd_mode);
}
static void
overfl_exp10_0 (void)
{
mpfr_t x, y;
int emax, i, inex, rnd, err = 0;
mpfr_exp_t old_emax;
old_emax = mpfr_get_emax ();
mpfr_init2 (x, 8);
mpfr_init2 (y, 8);
for (emax = -1; emax <= 0; emax++)
{
mpfr_set_ui_2exp (y, 1, emax, MPFR_RNDN);
mpfr_nextbelow (y);
set_emax (emax); /* 1 is not representable. */
/* and if emax < 0, 1 - eps is not representable either. */
for (i = -1; i <= 1; i++)
RND_LOOP (rnd)
{
mpfr_set_si_2exp (x, i, -512 * ABS (i), MPFR_RNDN);
mpfr_clear_flags ();
inex = mpfr_exp10 (x, x, (mpfr_rnd_t) rnd);
if ((i >= 0 || emax < 0 || rnd == MPFR_RNDN || rnd == MPFR_RNDU) &&
! mpfr_overflow_p ())
{
printf ("Error in overfl_exp10_0 (i = %d, rnd = %s):\n"
" The overflow flag is not set.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
{
if (inex >= 0)
{
printf ("Error in overfl_exp10_0 (i = %d, rnd = %s):\n"
" The inexact value must be negative.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! mpfr_equal_p (x, y))
{
printf ("Error in overfl_exp10_0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of 0.11111111E%d.\n", emax);
err = 1;
}
}
else
{
if (inex <= 0)
{
printf ("Error in overfl_exp10_0 (i = %d, rnd = %s):\n"
" The inexact value must be positive.\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (! (mpfr_inf_p (x) && MPFR_SIGN (x) > 0))
{
printf ("Error in overfl_exp10_0 (i = %d, rnd = %s):\n"
" Got ", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_print_binary (x);
printf (" instead of +Inf.\n");
err = 1;
}
}
}
set_emax (old_emax);
}
if (err)
exit (1);
mpfr_clear (x);
mpfr_clear (y);
}
static int
mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
/* Old implementation */
int sign_product, cc, inexact;
mpfr_exp_t ax;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq, cq;
mp_size_t bn, cn, tn, k;
MPFR_TMP_DECL(marker);
/* deal with special cases */
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
if (MPFR_IS_INF(b))
{
if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
{
MPFR_SET_SIGN(a,sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
if (MPFR_NOTZERO(b))
{
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 * 0 is exact */
}
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
bq = MPFR_PREC(b);
cq = MPFR_PREC(c);
MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */
cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
/* <= k, thus no int overflow */
MPFR_ASSERTD(tn <= k);
/* Check for no size_t overflow*/
MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
MPFR_TMP_MARK(marker);
tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
/* multiplies two mantissa in temporary allocated space */
b1 = (MPFR_LIKELY(bn >= cn)) ?
mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
: mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);
/* now tmp[0]..tmp[k-1] contains the product of both mantissa,
with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */
b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */
/* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
tmp += k - tn;
if (MPFR_UNLIKELY(b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq,
MPFR_IS_NEG_SIGN(sign_product),
MPFR_PREC (a), rnd_mode, &inexact);
/* cc = 1 ==> result is a power of two */
if (MPFR_UNLIKELY(cc))
MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;
MPFR_TMP_FREE(marker);
{
mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
return mpfr_overflow (a, rnd_mode, sign_product);
if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
{
/* In the rounding to the nearest mode, if the exponent of the exact
result (i.e. before rounding, i.e. without taking cc into account)
is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
both arguments are powers of 2), then round to zero. */
if (rnd_mode == MPFR_RNDN &&
(ax + (mpfr_exp_t) b1 < __gmpfr_emin ||
(mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, sign_product);
}
MPFR_SET_EXP (a, ax2);
MPFR_SET_SIGN(a, sign_product);
}
MPFR_RET (inexact);
}
static void
test_overflow2 (void)
{
mpfr_t x, y, z, r;
int i, inex, rnd, err = 0;
mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0);
MPFR_SET_POS (x);
mpfr_setmin (x, mpfr_get_emax ()); /* x = [email protected] */
mpfr_set_si (y, -2, MPFR_RNDN); /* y = -2 */
/* The intermediate multiplication x * y will overflow. */
for (i = -9; i <= 9; i++)
RND_LOOP (rnd)
{
int inf, overflow;
inf = rnd == MPFR_RNDN || rnd == MPFR_RNDD || rnd == MPFR_RNDA;
overflow = inf || i <= 0;
inex = mpfr_set_si_2exp (z, i, mpfr_get_emin (), MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_clear_flags ();
/* One has: x * y = [email protected] exactly (but not representable). */
inex = mpfr_fma (r, x, y, z, (mpfr_rnd_t) rnd);
if (overflow ^ (mpfr_overflow_p () != 0))
{
printf ("Error in test_overflow2 (i = %d, %s): wrong overflow"
" flag (should be %d)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), overflow);
err = 1;
}
if (mpfr_nanflag_p ())
{
printf ("Error in test_overflow2 (i = %d, %s): NaN flag should"
" not be set\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
if (mpfr_nan_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): got NaN\n",
i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
else if (MPFR_SIGN (r) >= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong sign "
"(+ instead of -)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
err = 1;
}
else if (inf && ! mpfr_inf_p (r))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -Inf,"
" got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_dump (r);
err = 1;
}
else if (!inf && (mpfr_inf_p (r) ||
(mpfr_nextbelow (r), ! mpfr_inf_p (r))))
{
printf ("Error in test_overflow2 (i = %d, %s): expected -MAX,"
" got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpfr_dump (r);
err = 1;
}
if (inf ? inex >= 0 : inex <= 0)
{
printf ("Error in test_overflow2 (i = %d, %s): wrong inexact"
" flag (got %d)\n", i,
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex);
err = 1;
}
}
if (err)
exit (1);
mpfr_clears (x, y, z, r, (mpfr_ptr) 0);
}
int
main (void)
{
mpfr_t x, y;
float f, g, infp;
int i;
infp = (float) DBL_POS_INF;
if (infp * 0.5 != infp)
{
fprintf (stderr, "Error, FLT_MAX + FLT_MAX does not yield INFP\n");
fprintf (stderr, "(this is probably a compiler bug, please report)\n");
exit (1);
}
tests_start_mpfr ();
mpfr_init2 (x, 24);
mpfr_init2 (y, 24);
#if !defined(MPFR_ERRDIVZERO)
mpfr_set_nan (x);
f = mpfr_get_flt (x, MPFR_RNDN);
if (f == f)
{
printf ("Error for mpfr_get_flt(NaN)\n");
exit (1);
}
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_nan_p (x) == 0)
{
printf ("Error for mpfr_set_flt(NaN)\n");
exit (1);
}
mpfr_set_inf (x, 1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
mpfr_set_inf (x, -1);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_inf_p (x) == 0 || mpfr_sgn (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-Inf)):\n");
printf ("f=%f, expected -Inf\n", f);
printf ("got "); mpfr_dump (x);
exit (1);
}
#endif
mpfr_set_ui (x, 0, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) < 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(+0))\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_neg (x, x, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_zero_p (x) == 0 || MPFR_SIGN (x) > 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-0))\n");
exit (1);
}
mpfr_set_ui (x, 17, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_ui (x, 17) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(17))\n");
printf ("expected 17\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si (x, -42, MPFR_RNDN);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (x, f, MPFR_RNDN);
if (mpfr_cmp_si (x, -42) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(-42))\n");
printf ("expected -42\n");
printf ("got ");
mpfr_dump (x);
exit (1);
}
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextbelow (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextabove (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_prec (x, 53);
mpfr_set_si_2exp (x, 1, -126, MPFR_RNDN);
for (i = -126; i < 128; i++)
{
mpfr_nextabove (x);
f = mpfr_get_flt (x, MPFR_RNDN);
mpfr_nextbelow (x);
mpfr_set_flt (y, f, MPFR_RNDN);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error for mpfr_set_flt(mpfr_get_flt(x))\n");
printf ("expected "); mpfr_dump (x);
printf ("got "); mpfr_dump (y);
exit (1);
}
mpfr_mul_2exp (x, x, 1, MPFR_RNDN);
}
mpfr_set_si_2exp (x, 1, -150, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-150),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -151, MPFR_RNDN);
g = 0.0;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-151),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, -149, MPFR_RNDN);
g = FLT_MIN * FLT_EPSILON;
f = mpfr_get_flt (x, MPFR_RNDN);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^(-149),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#if !defined(MPFR_ERRDIVZERO)
f = mpfr_get_flt (x, MPFR_RNDN); /* 2^128 rounds to itself with extended
exponent range, we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128,RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
#endif
/* corner case: take x with 25 bits just below 2^128 */
mpfr_set_prec (x, 25);
mpfr_set_si_2exp (x, 1, 128, MPFR_RNDN);
mpfr_nextbelow (x);
g = FLT_MAX;
f = mpfr_get_flt (x, MPFR_RNDZ);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDZ)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDD);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDD)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDN); /* first round to 2^128 (even rule),
thus we should get +Inf */
g = infp;
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDN)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDU);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDU)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
f = mpfr_get_flt (x, MPFR_RNDA);
if (f != g)
{
printf ("Error for mpfr_get_flt(2^128*(1-2^(-25)),RNDA)\n");
printf ("expected %.8e, got %.8e\n", g, f);
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
tests_end_mpfr ();
return 0;
}
int
mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mpfr_rnd_t rnd)
{
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg n=%ld rnd=%d",
mpfr_get_prec (x), mpfr_log_prec, x, n, rnd),
("y[%Pu]=%.*Rg", mpfr_get_prec (y), mpfr_log_prec, y));
if (n >= 0)
return mpfr_pow_ui (y, x, n, rnd);
else
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else
{
int positive = MPFR_IS_POS (x) || ((unsigned long) n & 1) == 0;
if (MPFR_IS_INF (x))
MPFR_SET_ZERO (y);
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_INF (y);
mpfr_set_divby0 ();
}
if (positive)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET (0);
}
}
/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
{
mpfr_exp_t expx = MPFR_EXP (x) - 1, expy;
MPFR_ASSERTD (n < 0);
/* Warning: n * expx may overflow!
*
* Some systems (apparently alpha-freebsd) abort with
* LONG_MIN / 1, and LONG_MIN / -1 is undefined.
* http://www.freebsd.org/cgi/query-pr.cgi?pr=72024
*
* Proof of the overflow checking. The expressions below are
* assumed to be on the rational numbers, but the word "overflow"
* still has its own meaning in the C context. / still denotes
* the integer (truncated) division, and // denotes the exact
* division.
* - First, (__gmpfr_emin - 1) / n and (__gmpfr_emax - 1) / n
* cannot overflow due to the constraints on the exponents of
* MPFR numbers.
* - If n = -1, then n * expx = - expx, which is representable
* because of the constraints on the exponents of MPFR numbers.
* - If expx = 0, then n * expx = 0, which is representable.
* - If n < -1 and expx > 0:
* + If expx > (__gmpfr_emin - 1) / n, then
* expx >= (__gmpfr_emin - 1) / n + 1
* > (__gmpfr_emin - 1) // n,
* and
* n * expx < __gmpfr_emin - 1,
* i.e.
* n * expx <= __gmpfr_emin - 2.
* This corresponds to an underflow, with a null result in
* the rounding-to-nearest mode.
* + If expx <= (__gmpfr_emin - 1) / n, then n * expx cannot
* overflow since 0 < expx <= (__gmpfr_emin - 1) / n and
* 0 > n * expx >= n * ((__gmpfr_emin - 1) / n)
* >= __gmpfr_emin - 1.
* - If n < -1 and expx < 0:
* + If expx < (__gmpfr_emax - 1) / n, then
* expx <= (__gmpfr_emax - 1) / n - 1
* < (__gmpfr_emax - 1) // n,
* and
* n * expx > __gmpfr_emax - 1,
* i.e.
* n * expx >= __gmpfr_emax.
* This corresponds to an overflow (2^(n * expx) has an
* exponent > __gmpfr_emax).
* + If expx >= (__gmpfr_emax - 1) / n, then n * expx cannot
* overflow since 0 > expx >= (__gmpfr_emax - 1) / n and
* 0 < n * expx <= n * ((__gmpfr_emax - 1) / n)
* <= __gmpfr_emax - 1.
* Note: one could use expx bounds based on MPFR_EXP_MIN and
* MPFR_EXP_MAX instead of __gmpfr_emin and __gmpfr_emax. The
* current bounds do not lead to noticeably slower code and
* allow us to avoid a bug in Sun's compiler for Solaris/x86
* (when optimizations are enabled); known affected versions:
* cc: Sun C 5.8 2005/10/13
* cc: Sun C 5.8 Patch 121016-02 2006/03/31
* cc: Sun C 5.8 Patch 121016-04 2006/10/18
*/
expy =
n != -1 && expx > 0 && expx > (__gmpfr_emin - 1) / n ?
MPFR_EMIN_MIN - 2 /* Underflow */ :
n != -1 && expx < 0 && expx < (__gmpfr_emax - 1) / n ?
MPFR_EMAX_MAX /* Overflow */ : n * expx;
return mpfr_set_si_2exp (y, n % 2 ? MPFR_INT_SIGN (x) : 1,
expy, rnd);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mpfr_prec_t Ny; /* target precision */
mpfr_prec_t Nt; /* working precision */
mpfr_rnd_t rnd1;
int size_n;
int inexact;
unsigned long abs_n;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
abs_n = - (unsigned long) n;
count_leading_zeros (size_n, (mp_limb_t) abs_n);
size_n = GMP_NUMB_BITS - size_n;
/* initial working precision */
Ny = MPFR_PREC (y);
Nt = Ny + size_n + 3 + MPFR_INT_CEIL_LOG2 (Ny);
MPFR_SAVE_EXPO_MARK (expo);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
/* We will compute rnd(rnd1(1/x) ^ |n|), where rnd1 is the rounding
toward sign(x), to avoid spurious overflow or underflow, as in
mpfr_pow_z. */
rnd1 = MPFR_EXP (x) < 1 ? MPFR_RNDZ :
(MPFR_SIGN (x) > 0 ? MPFR_RNDU : MPFR_RNDD);
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute (1/x)^|n| */
MPFR_BLOCK (flags, mpfr_ui_div (t, 1, x, rnd1));
MPFR_ASSERTD (! MPFR_UNDERFLOW (flags));
/* t = (1/x)*(1+theta) where |theta| <= 2^(-Nt) */
if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
goto overflow;
MPFR_BLOCK (flags, mpfr_pow_ui (t, t, abs_n, rnd));
/* t = (1/x)^|n|*(1+theta')^(|n|+1) where |theta'| <= 2^(-Nt).
If (|n|+1)*2^(-Nt) <= 1/2, which is satisfied as soon as
Nt >= bits(n)+2, then we can use Lemma \ref{lemma_graillat}
from algorithms.tex, which yields x^n*(1+theta) with
|theta| <= 2(|n|+1)*2^(-Nt), thus the error is bounded by
2(|n|+1) ulps <= 2^(bits(n)+2) ulps. */
if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
{
overflow:
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
MPFR_LOG_MSG (("overflow\n", 0));
return mpfr_overflow (y, rnd, abs_n & 1 ?
MPFR_SIGN (x) : MPFR_SIGN_POS);
}
if (MPFR_UNLIKELY (MPFR_UNDERFLOW (flags)))
{
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
MPFR_LOG_MSG (("underflow\n", 0));
if (rnd == MPFR_RNDN)
{
mpfr_t y2, nn;
/* We cannot decide now whether the result should be
rounded toward zero or away from zero. So, like
in mpfr_pow_pos_z, let's use the general case of
mpfr_pow in precision 2. */
MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
MPFR_EXP (x) - 1) != 0);
mpfr_init2 (y2, 2);
mpfr_init2 (nn, sizeof (long) * CHAR_BIT);
inexact = mpfr_set_si (nn, n, MPFR_RNDN);
MPFR_ASSERTN (inexact == 0);
inexact = mpfr_pow_general (y2, x, nn, rnd, 1,
(mpfr_save_expo_t *) NULL);
mpfr_clear (nn);
mpfr_set (y, y2, MPFR_RNDN);
mpfr_clear (y2);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW);
goto end;
}
else
{
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (y, rnd, abs_n & 1 ?
MPFR_SIGN (x) : MPFR_SIGN_POS);
}
}
/* error estimate -- see pow function in algorithms.ps */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - size_n - 2, Ny, rnd)))
break;
/* actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd);
mpfr_clear (t);
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd);
}
}
}
int
mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t c, xr;
mpfr_srcptr xx;
mpfr_exp_t expx, err;
mpfr_prec_t precy, m;
int inexact, sign, reduce;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
{
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);
}
}
/* sin(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
rnd_mode, {});
MPFR_SAVE_EXPO_MARK (expo);
/* Compute initial precision */
precy = MPFR_PREC (y);
if (precy >= MPFR_SINCOS_THRESHOLD)
return mpfr_sin_fast (y, x, rnd_mode);
m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13;
expx = MPFR_GET_EXP (x);
mpfr_init (c);
mpfr_init (xr);
MPFR_ZIV_INIT (loop, m);
for (;;)
{
/* first perform argument reduction modulo 2*Pi (if needed),
also helps to determine the sign of sin(x) */
if (expx >= 2) /* If Pi < x < 4, we need to reduce too, to determine
the sign of sin(x). For 2 <= |x| < Pi, we could avoid
the reduction. */
{
reduce = 1;
/* As expx + m - 1 will silently be converted into mpfr_prec_t
in the mpfr_set_prec call, the assert below may be useful to
avoid undefined behavior. */
MPFR_ASSERTN (expx + m - 1 <= MPFR_PREC_MAX);
mpfr_set_prec (c, expx + m - 1);
mpfr_set_prec (xr, m);
mpfr_const_pi (c, MPFR_RNDN);
mpfr_mul_2ui (c, c, 1, MPFR_RNDN);
mpfr_remainder (xr, x, c, MPFR_RNDN);
/* The analysis is similar to that of cos.c:
|xr - x - 2kPi| <= 2^(2-m). Thus we can decide the sign
of sin(x) if xr is at distance at least 2^(2-m) of both
0 and +/-Pi. */
mpfr_div_2ui (c, c, 1, MPFR_RNDN);
/* Since c approximates Pi with an error <= 2^(2-expx-m) <= 2^(-m),
it suffices to check that c - |xr| >= 2^(2-m). */
if (MPFR_SIGN (xr) > 0)
mpfr_sub (c, c, xr, MPFR_RNDZ);
else
mpfr_add (c, c, xr, MPFR_RNDZ);
if (MPFR_IS_ZERO(xr)
|| MPFR_EXP(xr) < (mpfr_exp_t) 3 - (mpfr_exp_t) m
|| MPFR_EXP(c) < (mpfr_exp_t) 3 - (mpfr_exp_t) m)
goto ziv_next;
/* |xr - x - 2kPi| <= 2^(2-m), thus |sin(xr) - sin(x)| <= 2^(2-m) */
xx = xr;
}
else /* the input argument is already reduced */
{
reduce = 0;
xx = x;
}
sign = MPFR_SIGN(xx);
/* now that the argument is reduced, precision m is enough */
mpfr_set_prec (c, m);
mpfr_cos (c, xx, MPFR_RNDZ); /* can't be exact */
mpfr_nexttoinf (c); /* now c = cos(x) rounded away */
mpfr_mul (c, c, c, MPFR_RNDU); /* away */
mpfr_ui_sub (c, 1, c, MPFR_RNDZ);
mpfr_sqrt (c, c, MPFR_RNDZ);
if (MPFR_IS_NEG_SIGN(sign))
MPFR_CHANGE_SIGN(c);
/* Warning: c may be 0! */
if (MPFR_UNLIKELY (MPFR_IS_ZERO (c)))
{
/* Huge cancellation: increase prec a lot! */
m = MAX (m, MPFR_PREC (x));
m = 2 * m;
}
else
{
/* the absolute error on c is at most 2^(3-m-EXP(c)),
plus 2^(2-m) if there was an argument reduction.
Since EXP(c) <= 1, 3-m-EXP(c) >= 2-m, thus the error
is at most 2^(3-m-EXP(c)) in case of argument reduction. */
err = 2 * MPFR_GET_EXP (c) + (mpfr_exp_t) m - 3 - (reduce != 0);
if (MPFR_CAN_ROUND (c, err, precy, rnd_mode))
break;
/* check for huge cancellation (Near 0) */
if (err < (mpfr_exp_t) MPFR_PREC (y))
m += MPFR_PREC (y) - err;
/* Check if near 1 */
if (MPFR_GET_EXP (c) == 1)
m += m;
}
ziv_next:
/* Else generic increase */
MPFR_ZIV_NEXT (loop, m);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, c, rnd_mode);
/* inexact cannot be 0, since this would mean that c was representable
within the target precision, but in that case mpfr_can_round will fail */
mpfr_clear (c);
mpfr_clear (xr);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
int
main (int argc, char *argv[])
{
mpfr_t x, y;
unsigned long k, bd, nc, i;
char *str, *str2;
mpfr_exp_t e;
int base, logbase, prec, baseprec, ret, obase;
tests_start_mpfr ();
if (argc >= 2) /* tset_str <string> [<prec>] [<ibase>] [<obase>] */
{
prec = (argc >= 3) ? atoi (argv[2]) : 53;
base = (argc >= 4) ? atoi (argv[3]) : 2;
obase = (argc >= 5) ? atoi (argv[4]) : 10;
mpfr_init2 (x, prec);
mpfr_set_str (x, argv[1], base, MPFR_RNDN);
mpfr_out_str (stdout, obase, 0, x, MPFR_RNDN);
puts ("");
mpfr_clear (x);
return 0;
}
mpfr_init2 (x, 2);
nc = (argc > 1) ? atoi(argv[1]) : 53;
if (nc < 100)
nc = 100;
bd = randlimb () & 8;
str2 = str = (char*) (*__gmp_allocate_func) (nc);
if (bd)
{
for(k = 1; k <= bd; k++)
*(str2++) = (randlimb () & 1) + '0';
}
else
*(str2++) = '0';
*(str2++) = '.';
for (k = 1; k < nc - 17 - bd; k++)
*(str2++) = '0' + (char) (randlimb () & 1);
*(str2++) = 'e';
sprintf (str2, "%d", (int) (randlimb () & INT_MAX) + INT_MIN/2);
mpfr_set_prec (x, nc + 10);
mpfr_set_str_binary (x, str);
mpfr_set_prec (x, 54);
mpfr_set_str_binary (x, "0.100100100110110101001010010101111000001011100100101010E-529");
mpfr_init2 (y, 54);
mpfr_set_str (y, "[email protected]", 16, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1a):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str_binary (x, "0.111111101101110010111010100110000111011001010100001101E-529");
mpfr_set_str (y, "0.fedcba98765434P-529", 16, MPFR_RNDN);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (1b):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, nc);
mpfr_set_prec (x, 53);
mpfr_set_str_binary (x, "+110101100.01010000101101000000100111001000101011101110E00");
mpfr_set_str_binary (x, "1.0");
if (mpfr_cmp_ui (x, 1))
{
printf ("Error in mpfr_set_str_binary for s=1.0\n");
mpfr_clear(x);
mpfr_clear(y);
exit(1);
}
mpfr_set_str_binary (x, "+0000");
mpfr_set_str_binary (x, "+0000E0");
mpfr_set_str_binary (x, "0000E0");
if (mpfr_cmp_ui (x, 0))
{
printf ("Error in mpfr_set_str_binary for s=0.0\n");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (x, "+243495834958.53452345E1", 10, MPFR_RNDN);
mpfr_set_str (x, "9007199254740993", 10, MPFR_RNDN);
mpfr_set_str (x, "9007199254740992", 10, MPFR_RNDU);
mpfr_set_str (x, "9007199254740992", 10, MPFR_RNDD);
mpfr_set_str (x, "9007199254740992", 10, MPFR_RNDZ);
/* check a random number printed and read is not modified */
prec = 53;
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
for (i=0;i<N;i++)
{
mpfr_rnd_t rnd;
mpfr_urandomb (x, RANDS);
rnd = RND_RAND ();
logbase = (randlimb () % 5) + 1;
base = 1 << logbase;
/* Warning: the number of bits needed to print exactly a number of
'prec' bits in base 2^logbase may be greater than ceil(prec/logbase),
for example 0.11E-1 in base 2 cannot be written exactly with only
one digit in base 4 */
if (base == 2)
baseprec = prec;
else
baseprec = 1 + (prec - 2 + logbase) / logbase;
str = mpfr_get_str (NULL, &e, base, baseprec, x, rnd);
mpfr_set_str (y, str, base, rnd);
MPFR_EXP(y) += logbase * (e - strlen (str));
if (mpfr_cmp (x, y))
{
printf ("mpfr_set_str o mpfr_get_str <> id for rnd_mode=%s\n",
mpfr_print_rnd_mode (rnd));
printf ("x=");
mpfr_print_binary (x);
puts ("");
printf ("s=%s, exp=%d, base=%d\n", str, (int) e, base);
printf ("y=");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
(*__gmp_free_func) (str, strlen (str) + 1);
}
for (i = 2; i <= 62; i++)
{
if (mpfr_set_str (x, "@[email protected](garbage)", i, MPFR_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on @[email protected](garbage)\n");
exit (1);
}
/*
if (mpfr_set_str (x, "@[email protected]", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on @[email protected]\n");
exit (1);
}
if (mpfr_set_str (x, "[email protected]@garbage", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on [email protected]@garbage\n");
exit (1);
}
if (mpfr_set_str (x, "[email protected]@garbage", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on [email protected]@garbage\n");
exit (1);
}
*/
if (i > 16)
continue;
if (mpfr_set_str (x, "NaN", i, MPFR_RNDN) != 0 ||
!mpfr_nan_p(x))
{
printf ("mpfr_set_str failed on NaN\n");
exit (1);
}
if (mpfr_set_str (x, "Inf", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on Inf\n");
exit (1);
}
if (mpfr_set_str (x, "-Inf", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) > 0)
{
printf ("mpfr_set_str failed on -Inf\n");
exit (1);
}
if (mpfr_set_str (x, "+Inf", i, MPFR_RNDN) != 0 ||
!mpfr_inf_p(x) || MPFR_SIGN(x) < 0)
{
printf ("mpfr_set_str failed on +Inf\n");
exit (1);
}
}
/* check that mpfr_set_str works for uppercase letters too */
mpfr_set_prec (x, 10);
mpfr_set_str (x, "B", 16, MPFR_RNDN);
if (mpfr_cmp_ui (x, 11) != 0)
{
printf ("mpfr_set_str does not work for uppercase letters\n");
exit (1);
}
/* start of tests added by Alain Delplanque */
/* in this example an overflow can occur */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.0E-532");
mpfr_set_str (y, "[email protected]", 10, MPFR_RNDU);
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (2):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* in this example, I think there was a pb in the old function :
result of mpfr_set_str_old for the same number , but with more
precision is: 1.111111111110000000000000000111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100111000100001100000010101100111010e184
this result is the same as mpfr_set_str */
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111110000000000000000111111111111111111111111110000000001E184");
mpfr_set_str (y, "[email protected]", 27, MPFR_RNDU);
/* y = 49027884868983130654865109690613178467841148597221480052 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (3):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* not exact rounding in mpfr_set_str
same number with more precision is : 1.111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011011111101000001101110110010101101000010100110011101110010001110e195
this result is the same as mpfr_set_str */
/* problem was : can_round was call with MPFR_RNDN round mode,
so can_round use an error : 1/2 * 2^err * ulp(y)
instead of 2^err * ulp(y)
I have increase err by 1 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111111111111111111111111000000000000000000000000000000000001e195");
mpfr_set_str (y, "[email protected]", 21, MPFR_RNDU);
/* y = 100433627392042473064661483711179345482301462325708736552078 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (4):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* may be an error in mpfr_set_str_old
with more precision : 1.111111100000001111110000000000011111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110111101010001110111011000010111001011100110110e180 */
mpfr_set_prec (x, 64); /* it was round down instead of up */
mpfr_set_prec (y, 64);
mpfr_set_str_binary (x, "1.111111100000001111110000000000011111011111111111111111111111111e180");
mpfr_set_str (y, "[email protected]", 23, MPFR_RNDZ);
/* y = 3053110535624388280648330929253842828159081875986159414 */
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (5):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "[email protected]", 28, MPFR_RNDU);
/* y = 196159429139499688661464718784226062699788036696626429952 */
mpfr_set_str_binary (x, "0.1111111111111111111111111111111000000000000011100000001111100001E187");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (6):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_str (y, "[email protected]", 24, MPFR_RNDZ);
/* y = 52652933527468502324759448399183654588831274530295083078827114496 */
mpfr_set_str_binary (x, "0.1111111111111100000000001000000000000000000011111111111111101111E215");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (7):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
/* worst cases for rounding to nearest in double precision */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str (y, "5e125", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10111101000101110110011000100000101001010000000111111E418");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (8):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "69e267", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10000101101111100101101100000110010011001010011011010E894");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (9):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "623e100", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10110010000001010011000101111001110101000001111011111E342");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (10):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "3571e263", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10110001001100100010011000110000111010100000110101010E886");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (11):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "75569e-254", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10101101001000110001011011001000111000110101010110011E-827");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (12):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "920657e-23", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10101001110101001100110000101110110111101111001101100E-56");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (13):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "9210917e80", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11101101000100011001000110100011111100110000000110010E289");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (14):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "87575437e-309", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.11110000001110011001000000110000000100000010101101100E-1000");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (15):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "245540327e122", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E434");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (16):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "491080654e122", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10001101101100010001100011110000110001100010111001011E435");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (17):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
mpfr_set_str (y, "83356057653e193", 10, MPFR_RNDN);
mpfr_set_str_binary (x, "0.10101010001001110011011011010111011100010101000011000E678");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_set_str (18):\n");
mpfr_print_binary (x);
puts ("");
mpfr_print_binary (y);
puts ("");
mpfr_clear (x);
mpfr_clear (y);
exit (1);
}
CHECK53(y, "83356057653e193", MPFR_RNDN, x,
"0.10101010001001110011011011010111011100010101000011000E678",
18);
CHECK53(y, "619534293513e124", MPFR_RNDN, x,
"0.10001000011000010000000110000001111111110000011110001e452",
19);
CHECK53(y, "3142213164987e-294", MPFR_RNDN, x,
"0.11101001101000000100111011111101111001010001001101111e-935",
20);
CHECK53(y, "36167929443327e-159", MPFR_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-483",
21);
CHECK53(y, "904198236083175e-161", MPFR_RNDN, x,
"0.11100111001110111110000101011001100110010100011111100e-485",
22);
CHECK53(y, "3743626360493413e-165", MPFR_RNDN, x,
"0.11000100000100011101001010111101011011011111011111001e-496",
23);
CHECK53(y, "94080055902682397e-242", MPFR_RNDN, x,
"0.10110010010011000000111100011100111100110011011001010e-747",
24);
CHECK53(y, "7e-303", MPFR_RNDD, x,
"0.10011001100111001000100110001110001000110111110001011e-1003",
25);
CHECK53(y, "7e-303", MPFR_RNDU, x,
"0.10011001100111001000100110001110001000110111110001100e-1003",
26);
CHECK53(y, "93e-234", MPFR_RNDD, x,
"0.10010011110110010111001001111001000010000000001110101E-770",
27);
CHECK53(y, "93e-234", MPFR_RNDU, x,
"0.10010011110110010111001001111001000010000000001110110E-770",
28);
CHECK53(y, "755e174", MPFR_RNDD, x,
"0.10111110110010011000110010011111101111000111111000101E588",
29);
CHECK53(y, "755e174", MPFR_RNDU, x,
"0.10111110110010011000110010011111101111000111111000110E588",
30);
CHECK53(y, "8699e-276", MPFR_RNDD, x,
"0.10010110100101101111100100100011011101100110100101100E-903",
31);
CHECK53(y, "8699e-276", MPFR_RNDU, x,
"0.10010110100101101111100100100011011101100110100101101E-903",
32);
CHECK53(y, "82081e41", MPFR_RNDD, x,
"0.10111000000010000010111011111001111010100011111001011E153",
33);
CHECK53(y, "82081e41", MPFR_RNDU, x,
"0.10111000000010000010111011111001111010100011111001100E153",
34);
CHECK53(y, "584169e229", MPFR_RNDD, x,
"0.11101011001010111000001011001110111000111100110101010E780",
35);
CHECK53(y, "584169e229", MPFR_RNDU, x,
"0.11101011001010111000001011001110111000111100110101011E780",
36);
CHECK53(y, "5783893e-128", MPFR_RNDD, x,
"0.10011000111100000110011110000101100111110011101110100E-402",
37);
CHECK53(y, "5783893e-128", MPFR_RNDU, x,
"0.10011000111100000110011110000101100111110011101110101E-402",
38);
CHECK53(y, "87575437e-310", MPFR_RNDD, x,
"0.11000000001011100000110011110011010000000010001010110E-1003",
39);
CHECK53(y, "87575437e-310", MPFR_RNDU, x,
"0.11000000001011100000110011110011010000000010001010111E-1003",
40);
CHECK53(y, "245540327e121", MPFR_RNDD, x,
"0.11100010101101001111010010110100011100000100101000100E430",
41);
CHECK53(y, "245540327e121", MPFR_RNDU, x,
"0.11100010101101001111010010110100011100000100101000101E430",
42);
CHECK53(y, "9078555839e-109", MPFR_RNDD, x,
"0.11111110001010111010110000110011100110001010011101101E-329",
43);
CHECK53(y, "9078555839e-109", MPFR_RNDU, x,
"0.11111110001010111010110000110011100110001010011101110E-329",
44);
CHECK53(y, "42333842451e201", MPFR_RNDD, x,
"0.10000000110001001101000100110110111110101011101011111E704",
45);
CHECK53(y, "42333842451e201", MPFR_RNDU, x,
"0.10000000110001001101000100110110111110101011101100000E704",
46);
CHECK53(y, "778380362293e218", MPFR_RNDD, x,
"0.11001101010111000001001100001100110010000001010010010E764",
47);
CHECK53(y, "778380362293e218", MPFR_RNDU, x,
"0.11001101010111000001001100001100110010000001010010011E764",
48);
CHECK53(y, "7812878489261e-179", MPFR_RNDD, x,
"0.10010011011011010111001111011101111101101101001110100E-551",
49);
CHECK53(y, "7812878489261e-179", MPFR_RNDU, x,
"0.10010011011011010111001111011101111101101101001110101E-551",
50);
CHECK53(y, "77003665618895e-73", MPFR_RNDD, x,
"0.11000101111110111111001111111101001101111000000101001E-196",
51);
CHECK53(y, "77003665618895e-73", MPFR_RNDU, x,
"0.11000101111110111111001111111101001101111000000101010E-196",
52);
CHECK53(y, "834735494917063e-300", MPFR_RNDD, x,
"0.11111110001101100001001101111100010011001110111010001E-947",
53);
CHECK53(y, "834735494917063e-300", MPFR_RNDU, x,
"0.11111110001101100001001101111100010011001110111010010E-947",
54);
CHECK53(y, "6182410494241627e-119", MPFR_RNDD, x,
"0.10001101110010110010001011000010001000101110100000111E-342",
55);
CHECK53(y, "6182410494241627e-119", MPFR_RNDU, x,
"0.10001101110010110010001011000010001000101110100001000E-342",
56);
CHECK53(y, "26153245263757307e49", MPFR_RNDD, x,
"0.10011110111100000000001011011110101100010000011011110E218",
57);
CHECK53(y, "26153245263757307e49", MPFR_RNDU, x,
"0.10011110111100000000001011011110101100010000011011111E218",
58);
/* to check this problem : I convert limb (10--0 or 101--1) into base b
with more than mp_bits_per_limb digits,
so when convert into base 2 I should have
the limb that I have choose */
/* this use mpfr_get_str */
{
size_t nb_digit = mp_bits_per_limb;
mp_limb_t check_limb[2] = {MPFR_LIMB_HIGHBIT, ~(MPFR_LIMB_HIGHBIT >> 1)};
int base[3] = {10, 16, 19};
mpfr_rnd_t rnd[3] = {MPFR_RNDU, MPFR_RNDN, MPFR_RNDD};
int cbase, climb, crnd;
char *str;
mpfr_set_prec (x, mp_bits_per_limb); /* x and y have only one limb */
mpfr_set_prec (y, mp_bits_per_limb);
str = (char*) (*__gmp_allocate_func) (N + 20);
mpfr_set_ui (x, 1, MPFR_RNDN); /* ensures that x is not NaN or Inf */
for (; nb_digit < N; nb_digit *= 10)
for (cbase = 0; cbase < 3; cbase++)
for (climb = 0; climb < 2; climb++)
for (crnd = 0; crnd < 3; crnd++)
{
char *str1;
mpfr_exp_t exp;
*(MPFR_MANT(x)) = check_limb[climb];
MPFR_EXP(x) = 0;
mpfr_get_str (str + 2, &exp, base[cbase],
nb_digit, x, rnd[crnd]);
str[0] = '-';
str[(str[2] == '-')] = '0';
str[(str[2] == '-') + 1] = '.';
for (str1 = str; *str1 != 0; str1++)
;
sprintf (str1, "@%i", (int) exp);
mpfr_set_str (y, str, base[cbase], rnd[2 - crnd]);
if (mpfr_cmp (x, y) != 0)
{
printf ("Error in mpfr_set_str for nb_digit=%u, base=%d, "
"rnd=%s:\n", (unsigned int) nb_digit, base[cbase],
mpfr_print_rnd_mode (rnd[crnd]));
printf ("instead of: ");
mpfr_print_binary (x);
puts ("");
printf ("return : ");
mpfr_print_binary (y);
puts ("");
exit (1);
}
}
(*__gmp_free_func) (str, N + 20);
}
/* end of tests added by Alain Delplanque */
/* check that flags are correctly cleared */
mpfr_set_nan (x);
mpfr_set_str (x, "+0.0", 10, MPFR_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) < 0)
{
printf ("x <- +0.0 failed after x=NaN\n");
exit (1);
}
mpfr_set_str (x, "-0.0", 10, MPFR_RNDN);
if (!mpfr_number_p(x) || mpfr_cmp_ui (x, 0) != 0 || mpfr_sgn (x) > 0)
{
printf ("x <- -0.0 failed after x=NaN\n");
exit (1);
}
/* check invalid input */
ret = mpfr_set_str (x, "1E10toto", 10, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1p10toto", 16, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "", 16, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "+", 16, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "-", 16, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "this_is_an_invalid_number_in_base_36", 36, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
ret = mpfr_set_str (x, "1.2.3", 10, MPFR_RNDN);
MPFR_ASSERTN (ret == -1);
mpfr_set_prec (x, 135);
ret = mpfr_set_str (x, "thisisavalidnumberinbase36", 36, MPFR_RNDN);
mpfr_set_prec (y, 135);
mpfr_set_str (y, "23833565676460972739462619524519814462546", 10, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp (x, y) == 0 && ret == 0);
/* coverage test for set_str_binary */
mpfr_set_str_binary (x, "NaN");
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_str_binary (x, "Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "+Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_str_binary (x, "-Inf");
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_prec (x, 3);
mpfr_set_str_binary (x, "0.01E2");
MPFR_ASSERTN(mpfr_cmp_ui (x, 1) == 0);
mpfr_set_str_binary (x, "-0.01E2");
MPFR_ASSERTN(mpfr_cmp_si (x, -1) == 0);
mpfr_clear (x);
mpfr_clear (y);
check_underflow ();
bug20081028 ();
tests_end_mpfr ();
return 0;
}
/// Returns sign of the number
inline int sign() const { return MPFR_SIGN(val); }
int
main (void)
{
mpfr_t x, y, z;
int i, j, k;
tests_start_mpfr ();
mpfr_init (x);
mpfr_init (y);
mpfr_init (z);
for (i = 0; i <= 1; i++)
for (j = 0; j <= 1; j++)
for (k = 0; k <= 5; k++)
{
mpfr_set_nan (x);
i ? MPFR_SET_NEG (x) : MPFR_SET_POS (x);
mpfr_set_nan (y);
j ? MPFR_SET_NEG (y) : MPFR_SET_POS (y);
copysign_variant (z, x, y, GMP_RNDN, k);
if (MPFR_SIGN (z) != MPFR_SIGN (y) || !mpfr_nanflag_p ())
{
printf ("Error in mpfr_copysign (%cNaN, %cNaN)\n",
i ? '-' : '+', j ? '-' : '+');
exit (1);
}
mpfr_set_si (x, i ? -1250 : 1250, GMP_RNDN);
mpfr_set_nan (y);
j ? MPFR_SET_NEG (y) : MPFR_SET_POS (y);
copysign_variant (z, x, y, GMP_RNDN, k);
if (i != j)
mpfr_neg (x, x, GMP_RNDN);
if (! mpfr_equal_p (z, x) || mpfr_nanflag_p ())
{
printf ("Error in mpfr_copysign (%c1250, %cNaN)\n",
i ? '-' : '+', j ? '-' : '+');
exit (1);
}
mpfr_set_si (x, i ? -1250 : 1250, GMP_RNDN);
mpfr_set_si (y, j ? -1717 : 1717, GMP_RNDN);
copysign_variant (z, x, y, GMP_RNDN, k);
if (i != j)
mpfr_neg (x, x, GMP_RNDN);
if (! mpfr_equal_p (z, x) || mpfr_nanflag_p ())
{
printf ("Error in mpfr_copysign (%c1250, %c1717)\n",
i ? '-' : '+', j ? '-' : '+');
exit (1);
}
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
tests_end_mpfr ();
return 0;
}
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));
}
static void
check_for_zero (void)
{
/* Check that 0 is unsigned! */
mpq_t q;
mpz_t z;
mpfr_t x;
int r;
mpfr_sign_t i;
mpfr_init (x);
mpz_init (z);
mpq_init (q);
mpz_set_ui (z, 0);
mpq_set_ui (q, 0, 1);
MPFR_SET_ZERO (x);
RND_LOOP (r)
{
for (i = MPFR_SIGN_NEG ; i <= MPFR_SIGN_POS ;
i+=MPFR_SIGN_POS-MPFR_SIGN_NEG)
{
MPFR_SET_SIGN(x, i);
mpfr_add_z (x, x, z, (mpfr_rnd_t) r);
if (!MPFR_IS_ZERO(x) || MPFR_SIGN(x)!=i)
{
printf("GMP Zero errors for add_z & rnd=%s & s=%d\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
mpfr_dump (x);
exit (1);
}
mpfr_sub_z (x, x, z, (mpfr_rnd_t) r);
if (!MPFR_IS_ZERO(x) || MPFR_SIGN(x)!=i)
{
printf("GMP Zero errors for sub_z & rnd=%s & s=%d\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
mpfr_dump (x);
exit (1);
}
mpfr_mul_z (x, x, z, (mpfr_rnd_t) r);
if (!MPFR_IS_ZERO(x) || MPFR_SIGN(x)!=i)
{
printf("GMP Zero errors for mul_z & rnd=%s & s=%d\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
mpfr_dump (x);
exit (1);
}
mpfr_add_q (x, x, q, (mpfr_rnd_t) r);
if (!MPFR_IS_ZERO(x) || MPFR_SIGN(x)!=i)
{
printf("GMP Zero errors for add_q & rnd=%s & s=%d\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
mpfr_dump (x);
exit (1);
}
mpfr_sub_q (x, x, q, (mpfr_rnd_t) r);
if (!MPFR_IS_ZERO(x) || MPFR_SIGN(x)!=i)
{
printf("GMP Zero errors for sub_q & rnd=%s & s=%d\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r), i);
mpfr_dump (x);
exit (1);
}
}
}
mpq_clear (q);
mpz_clear (z);
mpfr_clear (x);
}
int
mpfr_add (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
("a[%#R]=%R", a, a));
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
/* neither b nor c is NaN here */
else if (MPFR_IS_INF(b))
{
if (!MPFR_IS_INF(c) || MPFR_SIGN(b) == MPFR_SIGN(c))
{
MPFR_SET_INF(a);
MPFR_SET_SAME_SIGN(a, b);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
MPFR_SET_INF(a);
MPFR_SET_SAME_SIGN(a, c);
MPFR_RET(0); /* exact */
}
/* now either b or c is zero */
else if (MPFR_IS_ZERO(b))
{
if (MPFR_IS_ZERO(c))
{
/* for round away, we take the same convention for 0 + 0
as for round to zero or to nearest: it always gives +0,
except (-0) + (-0) = -0. */
MPFR_SET_SIGN(a,
(rnd_mode != MPFR_RNDD ?
((MPFR_IS_NEG(b) && MPFR_IS_NEG(c)) ? -1 : 1) :
((MPFR_IS_POS(b) && MPFR_IS_POS(c)) ? 1 : -1)));
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 + 0 is exact */
}
return mpfr_set (a, c, rnd_mode);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(c));
return mpfr_set (a, b, rnd_mode);
}
}
MPFR_ASSERTD(MPFR_IS_PURE_FP(b) && MPFR_IS_PURE_FP(c));
if (MPFR_UNLIKELY(MPFR_SIGN(b) != MPFR_SIGN(c)))
{ /* signs differ, it's a subtraction */
if (MPFR_LIKELY(MPFR_PREC(a) == MPFR_PREC(b)
&& MPFR_PREC(b) == MPFR_PREC(c)))
return mpfr_sub1sp(a,b,c,rnd_mode);
else
return mpfr_sub1(a, b, c, rnd_mode);
}
else
{ /* signs are equal, it's an addition */
if (MPFR_LIKELY(MPFR_PREC(a) == MPFR_PREC(b)
&& MPFR_PREC(b) == MPFR_PREC(c)))
if (MPFR_GET_EXP(b) < MPFR_GET_EXP(c))
return mpfr_add1sp(a, c, b, rnd_mode);
else
return mpfr_add1sp(a, b, c, rnd_mode);
else
if (MPFR_GET_EXP(b) < MPFR_GET_EXP(c))
return mpfr_add1(a, c, b, rnd_mode);
else
return mpfr_add1(a, b, c, rnd_mode);
}
}
int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
int sign, inexact;
mpfr_exp_t ax, ax2;
mp_limb_t *tmp;
mp_limb_t b1;
mpfr_prec_t bq, cq;
mp_size_t bn, cn, tn, k;
MPFR_TMP_DECL (marker);
MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
("a[%#R]=%R inexact=%d", a, a, inexact));
/* deal with special cases */
if (MPFR_ARE_SINGULAR (b, c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_IS_INF (b))
{
if (!MPFR_IS_ZERO (c))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET (0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN (a, sign);
MPFR_SET_ZERO (a);
MPFR_RET (0);
}
}
sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
/* Note: the exponent of the exact result will be e = bx + cx + ec with
ec in {-1,0,1} and the following assumes that e is representable. */
/* FIXME: Useful since we do an exponent check after ?
* It is useful iff the precision is big, there is an overflow
* and we are doing further mults...*/
#ifdef HUGE
if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1))
return mpfr_overflow (a, rnd_mode, sign);
if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2))
return mpfr_underflow (a, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
sign);
#endif
bq = MPFR_PREC (b);
cq = MPFR_PREC (c);
MPFR_ASSERTD (bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */
cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */
/* Check for no size_t overflow*/
MPFR_ASSERTD ((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
MPFR_TMP_MARK (marker);
tmp = (mp_limb_t *) MPFR_TMP_ALLOC ((size_t) k * BYTES_PER_MP_LIMB);
/* multiplies two mantissa in temporary allocated space */
if (MPFR_UNLIKELY (bn < cn))
{
mpfr_srcptr z = b;
mp_size_t zn = bn;
b = c;
bn = cn;
c = z;
cn = zn;
}
MPFR_ASSERTD (bn >= cn);
if (MPFR_LIKELY (bn <= 2))
{
if (bn == 1)
{
/* 1 limb * 1 limb */
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
b1 = tmp[1];
}
else if (MPFR_UNLIKELY (cn == 1))
{
/* 2 limbs * 1 limb */
mp_limb_t t;
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
umul_ppmm (tmp[2], t, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t);
b1 = tmp[2];
}
else
{
/* 2 limbs * 2 limbs */
mp_limb_t t1, t2, t3;
/* First 2 limbs * 1 limb */
umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
umul_ppmm (tmp[2], t1, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t1);
/* Second, the other 2 limbs * 1 limb product */
umul_ppmm (t1, t2, MPFR_MANT (b)[0], MPFR_MANT (c)[1]);
umul_ppmm (tmp[3], t3, MPFR_MANT (b)[1], MPFR_MANT (c)[1]);
add_ssaaaa (tmp[3], t1, tmp[3], t1, 0, t3);
/* Sum those two partial products */
add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], t1, t2);
tmp[3] += (tmp[2] < t1);
b1 = tmp[3];
}
b1 >>= (GMP_NUMB_BITS - 1);
tmp += k - tn;
if (MPFR_UNLIKELY (b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
}
else
/* Mulders' mulhigh. Disable if squaring, since it is not tuned for
such a case */
if (MPFR_UNLIKELY (bn > MPFR_MUL_THRESHOLD && b != c))
int
mpfr_rint (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
int sign;
int rnd_away;
mpfr_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 == MPFR_RNDD ? sign < 0 :
rnd_mode == MPFR_RNDU ? sign > 0 :
rnd_mode == MPFR_RNDZ ? 0 :
rnd_mode == MPFR_RNDA ? 1 :
-1; /* round to nearest-even (RNDN) or nearest-away (RNDNA) */
/* 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 MPFR_RNDN mode, 0.5 must be rounded to 0. */
if (rnd_away != 0 &&
(rnd_away > 0 ||
(exp == 0 && (rnd_mode == MPFR_RNDNA ||
!mpfr_powerof2_raw (u)))))
{
mp_limb_t *rp;
mp_size_t rm;
rp = MPFR_MANT(r);
rm = (MPFR_PREC(r) - 1) / GMP_NUMB_BITS;
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) / GMP_NUMB_BITS >= un)
{
ui = un;
idiff = 0;
uflags = 0; /* u is an integer, representable or not in r */
}
else
{
mp_size_t uj;
ui = (exp - 1) / GMP_NUMB_BITS + 1; /* #limbs of the int part */
MPFR_ASSERTD (un >= ui);
uj = un - ui; /* lowest limb of the integer part */
idiff = exp % GMP_NUMB_BITS; /* #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 (MPFR_RNDN or MPFR_RNDNA).
Decide the rounding direction here. */
if (rnd_mode == MPFR_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] << (GMP_NUMB_BITS - 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 : GMP_NUMB_BITS - 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 == MPFR_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 */
}
int
mpfr_sinh_cosh (mpfr_ptr sh, mpfr_ptr ch, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
{
mpfr_t x;
int inexact_sh, inexact_ch;
MPFR_ASSERTN (sh != ch);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("sh[%Pu]=%.*Rg ch[%Pu]=%.*Rg",
mpfr_get_prec (sh), mpfr_log_prec, sh,
mpfr_get_prec (ch), mpfr_log_prec, ch));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
{
if (MPFR_IS_NAN (xt))
{
MPFR_SET_NAN (ch);
MPFR_SET_NAN (sh);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (xt))
{
MPFR_SET_INF (sh);
MPFR_SET_SAME_SIGN (sh, xt);
MPFR_SET_INF (ch);
MPFR_SET_POS (ch);
MPFR_RET (0);
}
else /* xt is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (xt));
MPFR_SET_ZERO (sh); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN (sh, xt);
inexact_sh = 0;
inexact_ch = mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */
return INEX(inexact_sh,inexact_ch);
}
}
/* Warning: if we use MPFR_FAST_COMPUTE_IF_SMALL_INPUT here, make sure
that the code also works in case of overlap (see sin_cos.c) */
MPFR_TMP_INIT_ABS (x, xt);
{
mpfr_t s, c, ti;
mpfr_exp_t d;
mpfr_prec_t N; /* Precision of the intermediary variables */
long int err; /* Precision of error */
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_MARK (expo);
/* compute the precision of intermediary variable */
N = MPFR_PREC (ch);
N = MAX (N, MPFR_PREC (sh));
/* the optimal number of bits : see algorithms.ps */
N = N + MPFR_INT_CEIL_LOG2 (N) + 4;
/* initialise of intermediary variables */
MPFR_GROUP_INIT_3 (group, N, s, c, ti);
/* First computation of sinh_cosh */
MPFR_ZIV_INIT (loop, N);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute sinh_cosh */
MPFR_BLOCK (flags, mpfr_exp (s, x, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* exp(x) does overflow */
{
/* since cosh(x) >= exp(x), cosh(x) overflows too */
inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS);
/* sinh(x) may be representable */
inexact_sh = mpfr_sinh (sh, xt, rnd_mode);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
d = MPFR_GET_EXP (s);
mpfr_ui_div (ti, 1, s, MPFR_RNDU); /* 1/exp(x) */
mpfr_add (c, s, ti, MPFR_RNDU); /* exp(x) + 1/exp(x) */
mpfr_sub (s, s, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */
mpfr_div_2ui (c, c, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x)) */
mpfr_div_2ui (s, s, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
/* it may be that s is zero (in fact, it can only occur when exp(x)=1,
and thus ti=1 too) */
if (MPFR_IS_ZERO (s))
err = N; /* double the precision */
else
{
/* calculation of the error */
d = d - MPFR_GET_EXP (s) + 2;
/* error estimate: err = N-(__gmpfr_ceil_log2(1+pow(2,d)));*/
err = N - (MAX (d, 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (s, err, MPFR_PREC (sh),
rnd_mode) && \
MPFR_CAN_ROUND (c, err, MPFR_PREC (ch),
rnd_mode)))
{
inexact_sh = mpfr_set4 (sh, s, rnd_mode, MPFR_SIGN (xt));
inexact_ch = mpfr_set (ch, c, rnd_mode);
break;
}
}
/* actualisation of the precision */
N += err;
MPFR_ZIV_NEXT (loop, N);
MPFR_GROUP_REPREC_3 (group, N, s, c, ti);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
MPFR_SAVE_EXPO_FREE (expo);
}
/* now, let's raise the flags if needed */
inexact_sh = mpfr_check_range (sh, inexact_sh, rnd_mode);
inexact_ch = mpfr_check_range (ch, inexact_ch, rnd_mode);
return INEX(inexact_sh,inexact_ch);
}
static void
special (void)
{
mpfr_t x, y;
int i;
mpfr_init (x);
mpfr_init (y);
mpfr_set_nan (x);
test_expm1 (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error for expm1(NaN)\n");
exit (1);
}
mpfr_set_inf (x, 1);
test_expm1 (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error for expm1(+Inf)\n");
exit (1);
}
mpfr_set_inf (x, -1);
test_expm1 (y, x, MPFR_RNDN);
if (mpfr_cmp_si (y, -1))
{
printf ("Error for expm1(-Inf)\n");
exit (1);
}
mpfr_set_ui (x, 0, MPFR_RNDN);
test_expm1 (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error for expm1(+0)\n");
exit (1);
}
mpfr_neg (x, x, MPFR_RNDN);
test_expm1 (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) > 0)
{
printf ("Error for expm1(-0)\n");
exit (1);
}
/* Check overflow of expm1(x) */
mpfr_clear_flags ();
mpfr_set_str_binary (x, "1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) > 0);
MPFR_ASSERTN (mpfr_overflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDU);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) > 0);
MPFR_ASSERTN (mpfr_overflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDD);
MPFR_ASSERTN (!MPFR_IS_INF (x) && MPFR_SIGN (x) > 0);
MPFR_ASSERTN (mpfr_overflow_p ());
MPFR_ASSERTN (i == -1);
/* Check internal underflow of expm1 (x) */
mpfr_set_prec (x, 2);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDN);
MPFR_ASSERTN (mpfr_cmp_si (x, -1) == 0);
MPFR_ASSERTN (!mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_set_str_binary (x, "-1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDD);
MPFR_ASSERTN (mpfr_cmp_si (x, -1) == 0);
MPFR_ASSERTN (!mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_set_str_binary (x, "-1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDZ);
MPFR_ASSERTN (mpfr_cmp_str (x, "-0.11", 2, MPFR_RNDN) == 0);
MPFR_ASSERTN (!mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_set_str_binary (x, "-1.1E1000000000");
i = test_expm1 (x, x, MPFR_RNDU);
MPFR_ASSERTN (mpfr_cmp_str (x, "-0.11", 2, MPFR_RNDN) == 0);
MPFR_ASSERTN (!mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear (x);
mpfr_clear (y);
}
/* Usage: tzeta - generic tests
tzeta s prec rnd_mode - compute zeta(s) with precision 'prec'
and rounding mode 'mode' */
int
main (int argc, char *argv[])
{
mpfr_t s, y, z;
mpfr_prec_t prec;
mpfr_rnd_t rnd_mode;
int inex;
tests_start_mpfr ();
if (argc != 1 && argc != 4)
{
printf ("Usage: tzeta\n"
" or tzeta s prec rnd_mode\n");
exit (1);
}
if (argc == 4)
{
prec = atoi(argv[2]);
mpfr_init2 (s, prec);
mpfr_init2 (z, prec);
mpfr_set_str (s, argv[1], 10, MPFR_RNDN);
rnd_mode = (mpfr_rnd_t) atoi(argv[3]);
mpfr_zeta (z, s, rnd_mode);
mpfr_out_str (stdout, 10, 0, z, MPFR_RNDN);
printf ("\n");
mpfr_clear (s);
mpfr_clear (z);
return 0;
}
test1();
mpfr_init2 (s, MPFR_PREC_MIN);
mpfr_init2 (y, MPFR_PREC_MIN);
mpfr_init2 (z, MPFR_PREC_MIN);
/* the following seems to loop */
mpfr_set_prec (s, 6);
mpfr_set_prec (z, 6);
mpfr_set_str_binary (s, "1.10010e4");
mpfr_zeta (z, s, MPFR_RNDZ);
mpfr_set_prec (s, 53);
mpfr_set_prec (y, 53);
mpfr_set_prec (z, 53);
mpfr_set_ui (s, 1, MPFR_RNDN);
mpfr_clear_divby0();
mpfr_zeta (z, s, MPFR_RNDN);
if (!mpfr_inf_p (z) || MPFR_SIGN (z) < 0 || !mpfr_divby0_p())
{
printf ("Error in mpfr_zeta for s = 1 (should be +inf) with divby0 flag\n");
exit (1);
}
mpfr_set_str_binary (s, "0.1100011101110111111111111010000110010111001011001011");
mpfr_set_str_binary (y, "-0.11111101111011001001001111111000101010000100000100100E2");
mpfr_zeta (z, s, MPFR_RNDN);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (1,RNDN)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDZ);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (1,RNDZ)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDU);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (1,RNDU)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDD);
mpfr_nexttoinf (y);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (1,RNDD)\n");
exit (1);
}
mpfr_set_str_binary (s, "0.10001011010011100110010001100100001011000010011001011");
mpfr_set_str_binary (y, "-0.11010011010010101101110111011010011101111101111010110E1");
mpfr_zeta (z, s, MPFR_RNDN);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (2,RNDN)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDZ);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (2,RNDZ)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDU);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (2,RNDU)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDD);
mpfr_nexttoinf (y);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (2,RNDD)\n");
exit (1);
}
mpfr_set_str_binary (s, "0.1100111110100001111110111000110101111001011101000101");
mpfr_set_str_binary (y, "-0.10010111010110000111011111001101100001111011000001010E3");
mpfr_zeta (z, s, MPFR_RNDN);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (3,RNDN)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDD);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (3,RNDD)\n");
exit (1);
}
mpfr_nexttozero (y);
mpfr_zeta (z, s, MPFR_RNDZ);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (3,RNDZ)\n");
exit (1);
}
mpfr_zeta (z, s, MPFR_RNDU);
if (mpfr_cmp (z, y) != 0)
{
printf ("Error in mpfr_zeta (3,RNDU)\n");
exit (1);
}
mpfr_set_str (s, "-400000001", 10, MPFR_RNDZ);
mpfr_zeta (z, s, MPFR_RNDN);
if (!(mpfr_inf_p (z) && MPFR_SIGN(z) < 0))
{
printf ("Error in mpfr_zeta (-400000001)\n");
exit (1);
}
mpfr_set_str (s, "-400000003", 10, MPFR_RNDZ);
mpfr_zeta (z, s, MPFR_RNDN);
if (!(mpfr_inf_p (z) && MPFR_SIGN(z) > 0))
{
printf ("Error in mpfr_zeta (-400000003)\n");
exit (1);
}
mpfr_set_prec (s, 34);
mpfr_set_prec (z, 34);
mpfr_set_str_binary (s, "-1.111111100001011110000010001010000e-35");
mpfr_zeta (z, s, MPFR_RNDD);
mpfr_set_str_binary (s, "-1.111111111111111111111111111111111e-2");
if (mpfr_cmp (s, z))
{
printf ("Error in mpfr_zeta, prec=34, MPFR_RNDD\n");
mpfr_dump (z);
exit (1);
}
/* bug found by nightly tests on June 7, 2007 */
mpfr_set_prec (s, 23);
mpfr_set_prec (z, 25);
mpfr_set_str_binary (s, "-1.0110110110001000000000e-27");
mpfr_zeta (z, s, MPFR_RNDN);
mpfr_set_prec (s, 25);
mpfr_set_str_binary (s, "-1.111111111111111111111111e-2");
if (mpfr_cmp (s, z))
{
printf ("Error in mpfr_zeta, prec=25, MPFR_RNDN\n");
printf ("expected "); mpfr_dump (s);
printf ("got "); mpfr_dump (z);
exit (1);
}
/* bug reported by Kevin Rauch on 26 Oct 2007 */
mpfr_set_prec (s, 128);
mpfr_set_prec (z, 128);
mpfr_set_str_binary (s, "-0.1000000000000000000000000000000000000000000000000000000000000001E64");
inex = mpfr_zeta (z, s, MPFR_RNDN);
MPFR_ASSERTN (mpfr_inf_p (z) && MPFR_SIGN (z) < 0 && inex < 0);
inex = mpfr_zeta (z, s, MPFR_RNDU);
mpfr_set_inf (s, -1);
mpfr_nextabove (s);
MPFR_ASSERTN (mpfr_equal_p (z, s) && inex > 0);
mpfr_clear (s);
mpfr_clear (y);
mpfr_clear (z);
test_generic (2, 70, 5);
test2 ();
tests_end_mpfr ();
return 0;
}
static void
particular_cases (void)
{
mpfr_t t[11], r;
static const char *name[11] = {
"NaN", "+inf", "-inf", "+0", "-0", "+1", "-1", "+2", "-2", "+0.5", "-0.5"
};
int i, j;
int error = 0;
for (i = 0; i < 11; i++)
mpfr_init2 (t[i], 2);
mpfr_init2 (r, 6);
mpfr_set_nan (t[0]);
mpfr_set_inf (t[1], 1);
mpfr_set_ui (t[3], 0, GMP_RNDN);
mpfr_set_ui (t[5], 1, GMP_RNDN);
mpfr_set_ui (t[7], 2, GMP_RNDN);
mpfr_div_2ui (t[9], t[5], 1, GMP_RNDN);
for (i = 1; i < 11; i += 2)
mpfr_neg (t[i+1], t[i], GMP_RNDN);
for (i = 0; i < 11; i++)
for (j = 0; j < 11; j++)
{
double d;
int p;
static int q[11][11] = {
/* NaN +inf -inf +0 -0 +1 -1 +2 -2 +0.5 -0.5 */
/* NaN */ { 0, 0, 0, 128, 128, 0, 0, 0, 0, 0, 0 },
/* +inf */ { 0, 1, 2, 128, 128, 1, 2, 1, 2, 1, 2 },
/* -inf */ { 0, 1, 2, 128, 128, -1, -2, 1, 2, 1, 2 },
/* +0 */ { 0, 2, 1, 128, 128, 2, 1, 2, 1, 2, 1 },
/* -0 */ { 0, 2, 1, 128, 128, -2, -1, 2, 1, 2, 1 },
/* +1 */ {128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128 },
/* -1 */ { 0, 128, 128, 128, 128,-128,-128, 128, 128, 0, 0 },
/* +2 */ { 0, 1, 2, 128, 128, 256, 64, 512, 32, 180, 90 },
/* -2 */ { 0, 1, 2, 128, 128,-256, -64, 512, 32, 0, 0 },
/* +0.5 */ { 0, 2, 1, 128, 128, 64, 256, 32, 512, 90, 180 },
/* -0.5 */ { 0, 2, 1, 128, 128, -64,-256, 32, 512, 0, 0 }
};
test_pow (r, t[i], t[j], GMP_RNDN);
p = mpfr_nan_p (r) ? 0 : mpfr_inf_p (r) ? 1 :
mpfr_cmp_ui (r, 0) == 0 ? 2 :
(d = mpfr_get_d (r, GMP_RNDN), (int) (ABS(d) * 128.0));
if (p != 0 && MPFR_SIGN(r) < 0)
p = -p;
if (p != q[i][j])
{
printf ("Error in mpfr_pow for particular case (%s)^(%s) (%d,%d):\n"
"got %d instead of %d\n", name[i], name[j], i,j,p, q[i][j]);
mpfr_dump (r);
error = 1;
}
}
for (i = 0; i < 11; i++)
mpfr_clear (t[i]);
mpfr_clear (r);
if (error)
exit (1);
}
int
mpfr_copysign (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd_mode)
{
return mpfr_set4 (z, x, rnd_mode, MPFR_SIGN (y));
}
static void
check_pow_ui (void)
{
mpfr_t a, b;
int res;
mpfr_init2 (a, 53);
mpfr_init2 (b, 53);
/* check in-place operations */
mpfr_set_str (b, "0.6926773", 10, GMP_RNDN);
mpfr_pow_ui (a, b, 10, GMP_RNDN);
mpfr_pow_ui (b, b, 10, GMP_RNDN);
if (mpfr_cmp (a, b))
{
printf ("Error for mpfr_pow_ui (b, b, ...)\n");
exit (1);
}
/* check large exponents */
mpfr_set_ui (b, 1, GMP_RNDN);
mpfr_pow_ui (a, b, 4294967295UL, GMP_RNDN);
mpfr_set_inf (a, -1);
mpfr_pow_ui (a, a, 4049053855UL, GMP_RNDN);
if (!mpfr_inf_p (a) || (mpfr_sgn (a) >= 0))
{
printf ("Error for (-Inf)^4049053855\n");
exit (1);
}
mpfr_set_inf (a, -1);
mpfr_pow_ui (a, a, (unsigned long) 30002752, GMP_RNDN);
if (!mpfr_inf_p (a) || (mpfr_sgn (a) <= 0))
{
printf ("Error for (-Inf)^30002752\n");
exit (1);
}
/* Check underflow */
mpfr_set_str_binary (a, "1E-1");
res = mpfr_pow_ui (a, a, -mpfr_get_emin (), GMP_RNDN);
if (MPFR_GET_EXP (a) != mpfr_get_emin () + 1)
{
printf ("Error for (1e-1)^MPFR_EMAX_MAX\n");
mpfr_dump (a);
exit (1);
}
mpfr_set_str_binary (a, "1E-10");
res = mpfr_pow_ui (a, a, -mpfr_get_emin (), GMP_RNDZ);
if (!MPFR_IS_ZERO (a))
{
printf ("Error for (1e-10)^MPFR_EMAX_MAX\n");
mpfr_dump (a);
exit (1);
}
/* Check overflow */
mpfr_set_str_binary (a, "1E10");
res = mpfr_pow_ui (a, a, ULONG_MAX, GMP_RNDN);
if (!MPFR_IS_INF (a) || MPFR_SIGN (a) < 0)
{
printf ("Error for (1e10)^ULONG_MAX\n");
exit (1);
}
/* Check 0 */
MPFR_SET_ZERO (a);
MPFR_SET_POS (a);
mpfr_set_si (b, -1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 1, GMP_RNDN);
if (res != 0 || MPFR_IS_NEG (b))
{
printf ("Error for (0+)^1\n");
exit (1);
}
MPFR_SET_ZERO (a);
MPFR_SET_NEG (a);
mpfr_set_ui (b, 1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 5, GMP_RNDN);
if (res != 0 || MPFR_IS_POS (b))
{
printf ("Error for (0-)^5\n");
exit (1);
}
MPFR_SET_ZERO (a);
MPFR_SET_NEG (a);
mpfr_set_si (b, -1, GMP_RNDN);
res = mpfr_pow_ui (b, a, 6, GMP_RNDN);
if (res != 0 || MPFR_IS_NEG (b))
{
printf ("Error for (0-)^6\n");
exit (1);
}
mpfr_set_prec (a, 122);
mpfr_set_prec (b, 122);
mpfr_set_str_binary (a, "0.10000010010000111101001110100101101010011110011100001111000001001101000110011001001001001011001011010110110110101000111011E1");
mpfr_set_str_binary (b, "0.11111111100101001001000001000001100011100000001110111111100011111000111011100111111111110100011000111011000100100011001011E51290375");
mpfr_pow_ui (a, a, 2026876995UL, GMP_RNDU);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error for x^2026876995\n");
exit (1);
}
mpfr_set_prec (a, 29);
mpfr_set_prec (b, 29);
mpfr_set_str_binary (a, "1.0000000000000000000000001111");
mpfr_set_str_binary (b, "1.1001101111001100111001010111e165");
mpfr_pow_ui (a, a, 2055225053, GMP_RNDZ);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error for x^2055225053\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
/* worst case found by Vincent Lefevre, 25 Nov 2006 */
mpfr_set_prec (a, 53);
mpfr_set_prec (b, 53);
mpfr_set_str_binary (a, "1.0000010110000100001000101101101001011101101011010111");
mpfr_set_str_binary (b, "1.0000110111101111011010110100001100010000001010110100E1");
mpfr_pow_ui (a, a, 35, GMP_RNDN);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (1)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
/* worst cases found on 2006-11-26 */
mpfr_set_str_binary (a, "1.0110100111010001101001010111001110010100111111000011");
mpfr_set_str_binary (b, "1.1111010011101110001111010110000101110000110110101100E17");
mpfr_pow_ui (a, a, 36, GMP_RNDD);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (2)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_str_binary (a, "1.1001010100001110000110111111100011011101110011000100");
mpfr_set_str_binary (b, "1.1100011101101101100010110001000001110001111110010001E23");
mpfr_pow_ui (a, a, 36, GMP_RNDU);
if (mpfr_cmp (a, b) != 0)
{
printf ("Error in mpfr_pow_ui for worst case (3)\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, b, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, a, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_clear (a);
mpfr_clear (b);
}
int
mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
{
int inexact;
mpfr_t x, t, te;
mpfr_prec_t Nx, Ny, Nt;
mpfr_exp_t err;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (y), mpfr_log_prec, y, inexact));
/* Special cases */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
{
/* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
between -1 and 1 */
if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else /* necessarily xt is 0 */
{
MPFR_ASSERTD (MPFR_IS_ZERO (xt));
MPFR_SET_ZERO (y); /* atanh(0) = 0 */
MPFR_SET_SAME_SIGN (y,xt);
MPFR_RET (0);
}
}
/* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
if (MPFR_UNLIKELY (MPFR_GET_EXP (xt) > 0))
{
if (MPFR_GET_EXP (xt) == 1 && mpfr_powerof2_raw (xt))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, xt);
mpfr_set_divby0 ();
MPFR_RET (0);
}
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
/* atanh(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 1,
rnd_mode, {});
MPFR_SAVE_EXPO_MARK (expo);
/* Compute initial precision */
Nx = MPFR_PREC (xt);
MPFR_TMP_INIT_ABS (x, xt);
Ny = MPFR_PREC (y);
Nt = MAX (Nx, Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
mpfr_init2 (te, Nt);
/* First computation of cosh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute atanh */
mpfr_ui_sub (te, 1, x, MPFR_RNDU); /* (1-xt)*/
mpfr_add_ui (t, x, 1, MPFR_RNDD); /* (xt+1)*/
mpfr_div (t, t, te, MPFR_RNDN); /* (1+xt)/(1-xt)*/
mpfr_log (t, t, MPFR_RNDN); /* ln((1+xt)/(1-xt))*/
mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
/* error estimate: see algorithms.tex */
/* FIXME: this does not correspond to the value in algorithms.tex!!! */
/* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
if (MPFR_LIKELY (MPFR_IS_ZERO (t)
|| MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* reactualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
mpfr_clear(t);
mpfr_clear(te);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
/* Since MPFR-3.0, return the usual inexact value.
The erange flag is set if an error occurred in the conversion
(y is NaN, +Inf, or -Inf that have no equivalent in mpf)
*/
int
mpfr_get_f (mpf_ptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode)
{
int inex;
mp_size_t sx, sy;
mpfr_prec_t precx, precy;
mp_limb_t *xp;
int sh;
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(y)))
{
if (MPFR_IS_ZERO(y))
{
mpf_set_ui (x, 0);
return 0;
}
else if (MPFR_IS_NAN (y))
{
MPFR_SET_ERANGE ();
return 0;
}
else /* y is plus infinity (resp. minus infinity), set x to the maximum
value (resp. the minimum value) in precision PREC(x) */
{
int i;
mp_limb_t *xp;
MPFR_SET_ERANGE ();
/* To this day, [mp_exp_t] and mp_size_t are #defined as the same
type */
EXP (x) = MP_SIZE_T_MAX;
sx = PREC (x);
SIZ (x) = sx;
xp = PTR (x);
for (i = 0; i < sx; i++)
xp[i] = MP_LIMB_T_MAX;
if (MPFR_IS_POS (y))
return -1;
else
{
mpf_neg (x, x);
return +1;
}
}
}
sx = PREC(x); /* number of limbs of the mantissa of x */
precy = MPFR_PREC(y);
precx = (mpfr_prec_t) sx * GMP_NUMB_BITS;
sy = MPFR_LIMB_SIZE (y);
xp = PTR (x);
/* since mpf numbers are represented in base 2^GMP_NUMB_BITS,
we loose -EXP(y) % GMP_NUMB_BITS bits in the most significant limb */
sh = MPFR_GET_EXP(y) % GMP_NUMB_BITS;
sh = sh <= 0 ? - sh : GMP_NUMB_BITS - sh;
MPFR_ASSERTD (sh >= 0);
if (precy + sh <= precx) /* we can copy directly */
{
mp_size_t ds;
MPFR_ASSERTN (sx >= sy);
ds = sx - sy;
if (sh != 0)
{
mp_limb_t out;
out = mpn_rshift (xp + ds, MPFR_MANT(y), sy, sh);
MPFR_ASSERTN (ds > 0 || out == 0);
if (ds > 0)
xp[--ds] = out;
}
else
MPN_COPY (xp + ds, MPFR_MANT (y), sy);
if (ds > 0)
MPN_ZERO (xp, ds);
EXP(x) = (MPFR_GET_EXP(y) + sh) / GMP_NUMB_BITS;
inex = 0;
}
else /* we have to round to precx - sh bits */
{
mpfr_t z;
mp_size_t sz;
/* Recall that precx = (mpfr_prec_t) sx * GMP_NUMB_BITS, thus removing
sh bits (sh < GMP_NUMB_BITSS) won't reduce the number of limbs. */
mpfr_init2 (z, precx - sh);
sz = MPFR_LIMB_SIZE (z);
MPFR_ASSERTN (sx == sz);
inex = mpfr_set (z, y, rnd_mode);
/* warning, sh may change due to rounding, but then z is a power of two,
thus we can safely ignore its last bit which is 0 */
sh = MPFR_GET_EXP(z) % GMP_NUMB_BITS;
sh = sh <= 0 ? - sh : GMP_NUMB_BITS - sh;
MPFR_ASSERTD (sh >= 0);
if (sh != 0)
{
mp_limb_t out;
out = mpn_rshift (xp, MPFR_MANT(z), sz, sh);
/* If sh hasn't changed, it is the number of the non-significant
bits in the lowest limb of z. Therefore out == 0. */
MPFR_ASSERTD (out == 0); (void) out; /* avoid a warning */
}
else
MPN_COPY (xp, MPFR_MANT(z), sz);
EXP(x) = (MPFR_GET_EXP(z) + sh) / GMP_NUMB_BITS;
mpfr_clear (z);
}
/* set size and sign */
SIZ(x) = (MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(y)) < 0) ? -sx : sx;
return inex;
}
int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
{
mpfr_t x;
int inexact;
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (y), mpfr_log_prec, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
{
if (MPFR_IS_NAN (xt))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (xt))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, xt);
MPFR_RET (0);
}
else /* xt is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (xt));
MPFR_SET_ZERO (y); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN (y, xt);
MPFR_RET (0);
}
}
/* sinh(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP(xt), 2, 1,
rnd_mode, {});
MPFR_TMP_INIT_ABS (x, xt);
{
mpfr_t t, ti;
mpfr_exp_t d;
mpfr_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_MARK (expo);
/* compute the precision of intermediary variable */
Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
/* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */
if (MPFR_GET_EXP (x) < 0)
Nt -= 2*MPFR_GET_EXP (x);
/* initialise of intermediary variables */
MPFR_GROUP_INIT_2 (group, Nt, t, ti);
/* First computation of sinh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute sinh */
MPFR_BLOCK (flags, mpfr_exp (t, x, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* exp(x) does overflow */
{
/* sinh(x) = 2 * sinh(x/2) * cosh(x/2) */
mpfr_div_2ui (ti, x, 1, MPFR_RNDD); /* exact */
/* t <- cosh(x/2): error(t) <= 1 ulp(t) */
MPFR_BLOCK (flags, mpfr_cosh (t, ti, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* when x>1 we have |sinh(x)| >= cosh(x/2), so sinh(x)
overflows too */
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* ti <- sinh(x/2): , error(ti) <= 1 ulp(ti)
cannot overflow because 0 < sinh(x) < cosh(x) when x > 0 */
mpfr_sinh (ti, ti, MPFR_RNDD);
/* multiplication below, error(t) <= 5 ulp(t) */
MPFR_BLOCK (flags, mpfr_mul (t, t, ti, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* doubling below, exact */
MPFR_BLOCK (flags, mpfr_mul_2ui (t, t, 1, MPFR_RNDN));
if (MPFR_OVERFLOW (flags))
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* we have lost at most 3 bits of precision */
err = Nt - 3;
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
rnd_mode)))
{
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
break;
}
err = Nt; /* double the precision */
}
else
{
d = MPFR_GET_EXP (t);
mpfr_ui_div (ti, 1, t, MPFR_RNDU); /* 1/exp(x) */
mpfr_sub (t, t, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */
mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
/* it may be that t is zero (in fact, it can only occur when te=1,
and thus ti=1 too) */
if (MPFR_IS_ZERO (t))
err = Nt; /* double the precision */
else
{
/* calculation of the error */
d = d - MPFR_GET_EXP (t) + 2;
/* error estimate: err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/
err = Nt - (MAX (d, 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
rnd_mode)))
{
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
break;
}
}
}
/* actualisation of the precision */
Nt += err;
MPFR_ZIV_NEXT (loop, Nt);
MPFR_GROUP_REPREC_2 (group, Nt, t, ti);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
MPFR_SAVE_EXPO_FREE (expo);
}
return mpfr_check_range (y, inexact, rnd_mode);
}
int
mpc_sqr (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
int ok;
mpfr_t u, v;
mpfr_t x;
/* temporary variable to hold the real part of op,
needed in the case rop==op */
mpfr_prec_t prec;
int inex_re, inex_im, inexact;
mpfr_exp_t emin;
int saved_underflow;
/* special values: NaN and infinities */
if (!mpc_fin_p (op)) {
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op))) {
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
else if (mpfr_inf_p (mpc_realref (op))) {
if (mpfr_inf_p (mpc_imagref (op))) {
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_nan (mpc_realref (rop));
}
else {
if (mpfr_zero_p (mpc_imagref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), +1);
}
}
else /* IM(op) is infinity, RE(op) is not */ {
if (mpfr_zero_p (mpc_realref (op)))
mpfr_set_nan (mpc_imagref (rop));
else
mpfr_set_inf (mpc_imagref (rop),
MPFR_SIGN (mpc_realref (op)) * MPFR_SIGN (mpc_imagref (op)));
mpfr_set_inf (mpc_realref (rop), -1);
}
return MPC_INEX (0, 0); /* exact */
}
prec = MPC_MAX_PREC(rop);
/* Check for real resp. purely imaginary number */
if (mpfr_zero_p (mpc_imagref(op))) {
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = mpfr_sqr (mpc_realref(rop), mpc_realref(op), MPC_RND_RE(rnd));
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, MPFR_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
if (mpfr_zero_p (mpc_realref(op))) {
int same_sign = mpfr_signbit (mpc_realref (op)) == mpfr_signbit (mpc_imagref (op));
inex_re = -mpfr_sqr (mpc_realref(rop), mpc_imagref(op), INV_RND (MPC_RND_RE(rnd)));
mpfr_neg (mpc_realref(rop), mpc_realref(rop), MPFR_RNDN);
inex_im = mpfr_set_ui (mpc_imagref(rop), 0ul, MPFR_RNDN);
if (!same_sign)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX(inex_re, inex_im);
}
if (rop == op)
{
mpfr_init2 (x, MPC_PREC_RE (op));
mpfr_set (x, op->re, MPFR_RNDN);
}
else
x [0] = op->re [0];
/* From here on, use x instead of op->re and safely overwrite rop->re. */
/* Compute real part of result. */
if (SAFE_ABS (mpfr_exp_t,
mpfr_get_exp (mpc_realref (op)) - mpfr_get_exp (mpc_imagref (op)))
> (mpfr_exp_t) MPC_MAX_PREC (op) / 2) {
/* If the real and imaginary parts of the argument have very different
exponents, it is not reasonable to use Karatsuba squaring; compute
exactly with the standard formulae instead, even if this means an
additional multiplication. Using the approach copied from mul, over-
and underflows are also handled correctly. */
inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
}
else {
/* Karatsuba squaring: we compute the real part as (x+y)*(x-y) and the
imaginary part as 2*x*y, with a total of 2M instead of 2S+1M for the
naive algorithm, which computes x^2-y^2 and 2*y*y */
mpfr_init (u);
mpfr_init (v);
emin = mpfr_get_emin ();
do
{
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (u, prec);
mpfr_set_prec (v, prec);
/* Let op = x + iy. We need u = x+y and v = x-y, rounded away. */
/* The error is bounded above by 1 ulp. */
/* We first let inexact be 1 if the real part is not computed */
/* exactly and determine the sign later. */
inexact = mpfr_add (u, x, mpc_imagref (op), MPFR_RNDA)
| mpfr_sub (v, x, mpc_imagref (op), MPFR_RNDA);
/* compute the real part as u*v, rounded away */
/* determine also the sign of inex_re */
if (mpfr_sgn (u) == 0 || mpfr_sgn (v) == 0) {
/* as we have rounded away, the result is exact */
mpfr_set_ui (mpc_realref (rop), 0, MPFR_RNDN);
inex_re = 0;
ok = 1;
}
else {
inexact |= mpfr_mul (u, u, v, MPFR_RNDA); /* error 5 */
if (mpfr_get_exp (u) == emin || mpfr_inf_p (u)) {
/* under- or overflow */
inex_re = mpfr_fsss (rop->re, x, op->im, MPC_RND_RE (rnd));
ok = 1;
}
else {
ok = (!inexact) | mpfr_can_round (u, prec - 3,
MPFR_RNDA, MPFR_RNDZ,
MPC_PREC_RE (rop) + (MPC_RND_RE (rnd) == MPFR_RNDN));
if (ok) {
inex_re = mpfr_set (mpc_realref (rop), u, MPC_RND_RE (rnd));
if (inex_re == 0)
/* remember that u was already rounded */
inex_re = inexact;
}
}
}
}
while (!ok);
mpfr_clear (u);
mpfr_clear (v);
}
saved_underflow = mpfr_underflow_p ();
mpfr_clear_underflow ();
inex_im = mpfr_mul (rop->im, x, op->im, MPC_RND_IM (rnd));
if (!mpfr_underflow_p ())
inex_im |= mpfr_mul_2ui (rop->im, rop->im, 1, MPC_RND_IM (rnd));
/* We must not multiply by 2 if rop->im has been set to the smallest
representable number. */
if (saved_underflow)
mpfr_set_underflow ();
if (rop == op)
mpfr_clear (x);
return MPC_INEX (inex_re, inex_im);
}
static void
compute_l2b (int output)
{
mpfr_ptr p;
mpfr_srcptr t;
int beta, i;
int error = 0;
char buffer[30];
if (output)
printf ("#ifndef UINT64_C\n# define UINT64_C(c) c\n#endif\n\n");
for (beta = 2; beta <= BASE_MAX; beta++)
{
for (i = 0; i < 2; i++)
{
p = &l2b[beta-2][i];
/* Compute the value */
if (i == 0)
{
/* 23-bit upper approximation to log(b)/log(2) */
mpfr_init2 (p, 23);
mpfr_set_ui (p, beta, MPFR_RNDU);
mpfr_log2 (p, p, MPFR_RNDU);
}
else
{
/* 77-bit upper approximation to log(2)/log(b) */
mpfr_init2 (p, 77);
mpfr_set_ui (p, beta, MPFR_RNDD);
mpfr_log2 (p, p, MPFR_RNDD);
mpfr_ui_div (p, 1, p, MPFR_RNDU);
}
sprintf (buffer, "mpfr_l2b_%d_%d", beta, i);
if (output)
print_mpfr (p, buffer);
/* Check the value */
t = &__gmpfr_l2b[beta-2][i];
if (t == NULL || MPFR_PREC (t) == 0 || !mpfr_equal_p (p, t))
{
if (!output)
{
error = 1;
printf ("Error for constant %s\n", buffer);
}
}
if (!output)
mpfr_clear (p);
}
}
if (output)
{
if (printf ("const __mpfr_struct __gmpfr_l2b[BASE_MAX-1][2] = {\n")
< 0)
{ fprintf (stderr, "Error in printf\n"); exit (1); }
for (beta = 2; beta <= BASE_MAX; beta++)
{
for (i = 0; i < 2; i++)
{
p = &l2b[beta-2][i];
if (printf (" %c {%3d,%2d,%3ld, (mp_limb_t *) "
"mpfr_l2b_%d_%d__tab }%s\n", i == 0 ? '{' : ' ',
(int) MPFR_PREC (p), MPFR_SIGN (p),
(long) MPFR_GET_EXP (p), beta, i,
i == 0 ? "," : beta < BASE_MAX ? " }," : " } };")
< 0)
{ fprintf (stderr, "Error in printf\n"); exit (1); }
mpfr_clear (p);
}
}
}
/* If there was an error, the test fails. */
if (error)
exit (1);
}
/* compute sign(b) * (|b| + |c|)
Returns 0 iff result is exact,
a negative value when the result is less than the exact value,
a positive value otherwise. */
int
mpfr_add1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_uexp_t d;
mpfr_prec_t p;
unsigned int sh;
mp_size_t n;
mp_limb_t *ap, *cp;
mpfr_exp_t bx;
mp_limb_t limb;
int inexact;
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));
MPFR_ASSERTD(MPFR_GET_EXP(b) >= MPFR_GET_EXP(c));
/* Read prec and num of limbs */
p = MPFR_PREC(b);
n = MPFR_PREC2LIMBS (p);
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
bx = MPFR_GET_EXP(b);
d = (mpfr_uexp_t) (bx - MPFR_GET_EXP(c));
DEBUG (printf ("New add1sp with diff=%lu\n", (unsigned long) d));
if (MPFR_UNLIKELY(d == 0))
{
/* d==0 */
DEBUG( mpfr_print_mant_binary("C= ", MPFR_MANT(c), p) );
DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) );
bx++; /* exp + 1 */
ap = MPFR_MANT(a);
limb = mpn_add_n(ap, MPFR_MANT(b), MPFR_MANT(c), n);
DEBUG( mpfr_print_mant_binary("A= ", ap, p) );
MPFR_ASSERTD(limb != 0); /* There must be a carry */
limb = ap[0]; /* Get LSB (In fact, LSW) */
mpn_rshift(ap, ap, n, 1); /* Shift mantissa A */
ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */
ap[0] &= ~MPFR_LIMB_MASK(sh); /* Clear LSB bit */
if (MPFR_LIKELY((limb&(MPFR_LIMB_ONE<<sh)) == 0)) /* Check exact case */
{ inexact = 0; goto set_exponent; }
/* Zero: Truncate
Nearest: Even Rule => truncate or add 1
Away: Add 1 */
if (MPFR_LIKELY(rnd_mode==MPFR_RNDN))
{
if (MPFR_LIKELY((ap[0]&(MPFR_LIMB_ONE<<sh))==0))
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b));
if (rnd_mode==MPFR_RNDZ)
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
else if (MPFR_UNLIKELY (d >= p))
{
if (MPFR_LIKELY (d > p))
{
/* d > p : Copy B in A */
/* Away: Add 1
Nearest: Trunc
Zero: Trunc */
if (MPFR_LIKELY (rnd_mode==MPFR_RNDN
|| MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b))))
{
copy_set_exponent:
ap = MPFR_MANT (a);
MPN_COPY (ap, MPFR_MANT(b), n);
inexact = -1;
goto set_exponent;
}
else
{
copy_add_one_ulp:
ap = MPFR_MANT(a);
MPN_COPY (ap, MPFR_MANT(b), n);
goto add_one_ulp;
}
}
else
{
/* d==p : Copy B in A */
/* Away: Add 1
Nearest: Even Rule if C is a power of 2, else Add 1
Zero: Trunc */
if (MPFR_LIKELY(rnd_mode==MPFR_RNDN))
{
/* Check if C was a power of 2 */
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);
if (MPFR_UNLIKELY(k<0))
/* Power of 2: Even rule */
if ((MPFR_MANT (b)[0]&(MPFR_LIMB_ONE<<sh))==0)
goto copy_set_exponent;
}
/* Not a Power of 2 */
goto copy_add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b)))
goto copy_set_exponent;
else
goto copy_add_one_ulp;
}
}
else
{
mp_limb_t mask;
mp_limb_t bcp, bcp1; /* Cp and C'p+1 */
/* General case: 1 <= d < p */
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift c in temporary allocated place */
{
mpfr_uexp_t dm;
mp_size_t m;
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 >=1 and m == 0: just shift */
MPFR_ASSERTD(dm >= 1);
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 > 0))
{
/* Try to compute them from C' rather than C */
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 /* sh == 0 */
{
/* 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
{
do {
kx--;
} while (kx>=0 && tp[kx]==0);
bcp1 = (kx>=0);
}
}
DEBUG (printf("sh=%u Cp=%lu C'p+1=%lu\n", sh,
(unsigned long) bcp, (unsigned long) bcp1));
/* Clean shifted C' */
mask = ~MPFR_LIMB_MASK(sh);
cp[0] &= mask;
/* Add the mantissa c from b in a */
ap = MPFR_MANT(a);
limb = mpn_add_n (ap, MPFR_MANT(b), cp, n);
DEBUG( mpfr_print_mant_binary("Add= ", ap, p) );
/* Check for overflow */
if (MPFR_UNLIKELY (limb))
{
limb = ap[0] & (MPFR_LIMB_ONE<<sh); /* Get LSB */
mpn_rshift (ap, ap, n, 1); /* Shift mantissa*/
bx++; /* Fix exponent */
ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */
ap[0] &= mask; /* Clear LSB bit */
bcp1 |= bcp; /* Recompute C'p+1 */
bcp = limb; /* Recompute Cp */
DEBUG (printf ("(Overflow) Cp=%lu C'p+1=%lu\n",
(unsigned long) bcp, (unsigned long) bcp1));
DEBUG (mpfr_print_mant_binary ("Add= ", ap, p));
}
/* Round:
Zero: Truncate but could be exact.
Away: Add 1 if Cp or C'p+1 !=0
Nearest: Truncate but could be exact if Cp==0
Add 1 if C'p+1 !=0,
Even rule else */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_LIKELY(bcp == 0))
{ inexact = MPFR_LIKELY(bcp1) ? -1 : 0; goto set_exponent; }
else if (MPFR_UNLIKELY(bcp1==0) && (ap[0]&(MPFR_LIMB_ONE<<sh))==0)
{ inexact = -1; goto set_exponent; }
else
goto add_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b));
if (rnd_mode == MPFR_RNDZ)
{
inexact = MPFR_LIKELY(bcp || bcp1) ? -1 : 0;
goto set_exponent;
}
else
{
if (MPFR_UNLIKELY(bcp==0 && bcp1==0))
{ inexact = 0; goto set_exponent; }
else
goto add_one_ulp;
}
}
MPFR_ASSERTN(0);
add_one_ulp:
/* add one unit in last place to a */
DEBUG( printf("AddOneUlp\n") );
if (MPFR_UNLIKELY( mpn_add_1(ap, ap, n, MPFR_LIMB_ONE<<sh) ))
{
/* Case 100000x0 = 0x1111x1 + 1*/
DEBUG( printf("Pow of 2\n") );
bx++;
ap[n-1] = MPFR_LIMB_HIGHBIT;
}
inexact = 1;
set_exponent:
if (MPFR_UNLIKELY(bx > __gmpfr_emax)) /* Check for overflow */
{
DEBUG( printf("Overflow\n") );
MPFR_TMP_FREE(marker);
MPFR_SET_SAME_SIGN(a,b);
return mpfr_overflow(a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
MPFR_SET_SAME_SIGN(a,b);
MPFR_TMP_FREE(marker);
MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
