int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t expx;
mpfr_prec_t precy;
int inexact;
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_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x))
{
if (MPFR_IS_POS(x))
MPFR_SET_INF(y);
else
MPFR_SET_ZERO(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
/* First, let's detect most overflow and underflow cases. */
{
mpfr_t e, bound;
/* We must extended the exponent range and save the flags now. */
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (e, sizeof (mpfr_exp_t) * CHAR_BIT);
mpfr_init2 (bound, 32);
inexact = mpfr_set_exp_t (e, expo.saved_emax, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_const_log2 (bound, expo.saved_emax < 0 ? MPFR_RNDD : MPFR_RNDU);
mpfr_mul (bound, bound, e, MPFR_RNDU);
if (MPFR_UNLIKELY (mpfr_cmp (x, bound) >= 0))
{
/* x > log(2^emax), thus exp(x) > 2^emax */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_overflow (y, rnd_mode, 1);
}
inexact = mpfr_set_exp_t (e, expo.saved_emin, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
inexact = mpfr_sub_ui (e, e, 2, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_const_log2 (bound, expo.saved_emin < 0 ? MPFR_RNDU : MPFR_RNDD);
mpfr_mul (bound, bound, e, MPFR_RNDD);
if (MPFR_UNLIKELY (mpfr_cmp (x, bound) <= 0))
{
/* x < log(2^(emin - 2)), thus exp(x) < 2^(emin - 2) */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_underflow (y, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
1);
}
/* Other overflow/underflow cases must be detected
by the generic routines. */
mpfr_clears (e, bound, (mpfr_ptr) 0);
MPFR_SAVE_EXPO_FREE (expo);
}
expx = MPFR_GET_EXP (x);
precy = MPFR_PREC (y);
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
{
mpfr_exp_t emin = __gmpfr_emin;
mpfr_exp_t emax = __gmpfr_emax;
int signx = MPFR_SIGN (x);
MPFR_SET_POS (y);
if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == MPFR_RNDD ||
rnd_mode == MPFR_RNDZ))
{
__gmpfr_emin = 0;
__gmpfr_emax = 0;
mpfr_setmax (y, 0); /* y = 1 - epsilon */
inexact = -1;
}
else
{
__gmpfr_emin = 1;
__gmpfr_emax = 1;
mpfr_setmin (y, 1); /* y = 1 */
if (MPFR_IS_POS_SIGN (signx) && (rnd_mode == MPFR_RNDU ||
rnd_mode == MPFR_RNDA))
{
mp_size_t yn;
int sh;
yn = 1 + (MPFR_PREC(y) - 1) / GMP_NUMB_BITS;
sh = (mpfr_prec_t) yn * GMP_NUMB_BITS - MPFR_PREC(y);
MPFR_MANT(y)[0] += MPFR_LIMB_ONE << sh;
inexact = 1;
}
else
inexact = -MPFR_FROM_SIGN_TO_INT(signx);
}
__gmpfr_emin = emin;
__gmpfr_emax = emax;
}
else /* General case */
{
if (MPFR_UNLIKELY (precy >= MPFR_EXP_THRESHOLD))
/* mpfr_exp_3 saves the exponent range and flags itself, otherwise
the flag changes in mpfr_exp_3 are lost */
inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
{
MPFR_SAVE_EXPO_MARK (expo);
inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
}
}
return mpfr_check_range (y, inexact, rnd_mode);
}
int
mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
{
/****** Declaration ******/
mpfr_t x;
int inexact;
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 value checking */
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))
{
/* tanh(inf) = 1 && tanh(-inf) = -1 */
return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode);
}
else /* tanh (0) = 0 and xt is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO(xt));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, xt);
MPFR_RET (0);
}
}
/* tanh(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, 0,
rnd_mode, {});
MPFR_TMP_INIT_ABS (x, xt);
MPFR_SAVE_EXPO_MARK (expo);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te;
mpfr_exp_t d;
/* Declaration of the size variable */
mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
mpfr_prec_t Nt; /* working precision */
long int err; /* error */
int sign = MPFR_SIGN (xt);
MPFR_ZIV_DECL (loop);
MPFR_GROUP_DECL (group);
/* First check for BIG overflow of exp(2*x):
For x > 0, exp(2*x) > 2^(2*x)
If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */
if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) {
/* initialise of intermediary variables
since 'set_one' label assumes the variables have been
initialize */
MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te);
goto set_one;
}
/* Compute the precision of intermediary variable */
/* The optimal number of bits: see algorithms.tex */
Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4;
/* if x is small, there will be a cancellation in exp(2x)-1 */
if (MPFR_GET_EXP (x) < 0)
Nt += -MPFR_GET_EXP (x);
/* initialise of intermediary variable */
MPFR_GROUP_INIT_2 (group, Nt, t, te);
MPFR_ZIV_INIT (loop, Nt);
for (;;) {
/* tanh = (exp(2x)-1)/(exp(2x)+1) */
mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */
/* since x > 0, we can only have an overflow */
mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */
if (MPFR_UNLIKELY (MPFR_IS_INF (te))) {
set_one:
inexact = MPFR_FROM_SIGN_TO_INT (sign);
mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign);
if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
{
inexact = -inexact;
mpfr_nexttozero (y);
}
break;
}
d = MPFR_GET_EXP (te); /* For Error calculation */
mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1*/
mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/
d = d - MPFR_GET_EXP (te);
mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
/* Calculation of the error */
d = MAX(3, d + 1);
err = Nt - (d + 1);
if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
{
inexact = mpfr_set4 (y, t, rnd_mode, sign);
break;
}
/* if t=1, we still can round since |sinh(x)| < 1 */
if (MPFR_GET_EXP (t) == 1)
goto set_one;
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
MPFR_GROUP_REPREC_2 (group, Nt, t, te);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
}
MPFR_SAVE_EXPO_FREE (expo);
inexact = mpfr_check_range (y, inexact, rnd_mode);
return inexact;
}
/* 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_ERANGEFLAG ();
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_ERANGEFLAG ();
/* 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] = MPFR_LIMB_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_set_f (mpfr_ptr y, mpf_srcptr x, mpfr_rnd_t rnd_mode)
{
mp_limb_t *my, *mx, *tmp;
unsigned long cnt, sx, sy;
int inexact, carry = 0;
MPFR_TMP_DECL(marker);
sx = ABS(SIZ(x)); /* number of limbs of the mantissa of x */
if (sx == 0) /* x is zero */
{
MPFR_SET_ZERO(y);
MPFR_SET_POS(y);
return 0; /* 0 is exact */
}
if (SIZ(x) * MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(y)) < 0)
MPFR_CHANGE_SIGN (y);
sy = MPFR_LIMB_SIZE (y);
my = MPFR_MANT(y);
mx = PTR(x);
count_leading_zeros(cnt, mx[sx - 1]);
if (sy <= sx) /* we may have to round even when sy = sx */
{
unsigned long xprec = sx * GMP_NUMB_BITS;
MPFR_TMP_MARK(marker);
tmp = MPFR_TMP_LIMBS_ALLOC (sx);
if (cnt)
mpn_lshift (tmp, mx, sx, cnt);
else
/* FIXME: we may avoid the copy here, and directly call mpfr_round_raw
on mx instead of tmp */
MPN_COPY (tmp, mx, sx);
carry = mpfr_round_raw (my, tmp, xprec, (SIZ(x) < 0), MPFR_PREC(y),
rnd_mode, &inexact);
if (MPFR_UNLIKELY(carry)) /* result is a power of two */
my[sy - 1] = MPFR_LIMB_HIGHBIT;
MPFR_TMP_FREE(marker);
}
else
{
if (cnt)
mpn_lshift (my + sy - sx, mx, sx, cnt);
else
MPN_COPY (my + sy - sx, mx, sx);
MPN_ZERO(my, sy - sx);
/* no rounding necessary, since y has a larger mantissa */
inexact = 0;
}
/* warning: EXP(x) * GMP_NUMB_BITS may exceed the maximal exponent */
if (EXP(x) > 1 + (__gmpfr_emax - 1) / GMP_NUMB_BITS)
{
/* EXP(x) >= 2 + floor((__gmpfr_emax-1)/GMP_NUMB_BITS)
EXP(x) >= 2 + (__gmpfr_emax - GMP_NUMB_BITS) / GMP_NUMB_BITS
>= 1 + __gmpfr_emax / GMP_NUMB_BITS
EXP(x) * GMP_NUMB_BITS >= __gmpfr_emax + GMP_NUMB_BITS
Since 0 <= cnt <= GMP_NUMB_BITS-1, and 0 <= carry <= 1,
we have then EXP(x) * GMP_NUMB_BITS - cnt + carry > __gmpfr_emax */
return mpfr_overflow (y, rnd_mode, MPFR_SIGN (y));
}
else
{
/* Do not use MPFR_SET_EXP as the exponent may be out of range. */
MPFR_EXP (y) = EXP (x) * GMP_NUMB_BITS - (mpfr_exp_t) cnt + carry;
}
return mpfr_check_range (y, inexact, rnd_mode);
}
