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Return the (current) smallest and largest exponents allowed for a floating-point variable. The smallest positive value of a floating-point variable is one half times 2 raised to the smallest exponent and the largest value has the form (1 − epsilon) times 2 raised to the largest exponent, where epsilon depends on the precision of the considered variable.
Set the smallest and largest exponents allowed for a floating-point variable. Return a non-zero value when exp is not in the range accepted by the implementation (in that case the smallest or largest exponent is not changed), and zero otherwise.
For the subsequent operations, it is the user’s responsibility to check
that any floating-point value used as an input is in the new exponent range
(for example using mpfr_check_range). If a floating-point value
outside the new exponent range is used as an input, the default behavior
is undefined, in the sense of the ISO C standard; the behavior may also be
explicitly documented, such as for mpfr_check_range.
Note: Caches may still have values outside the current exponent range. This is not an issue as the user cannot use these caches directly via the API (MPFR extends the exponent range internally when need be).
If emin > emax and a floating-point value needs to
be produced as output, the behavior is undefined (mpfr_set_emin
and mpfr_set_emax do not check this condition as it might occur
between successive calls to these two functions).
Return the minimum and maximum of the exponents
allowed for mpfr_set_emin and mpfr_set_emax respectively.
These values are implementation dependent, thus a program using
mpfr_set_emax(mpfr_get_emax_max())
or mpfr_set_emin(mpfr_get_emin_min()) may not be portable.
This function assumes that x is the correctly rounded value of some
real value y in the direction rnd and some extended exponent
range, and that t is the corresponding ternary value.
For example, one performed t = mpfr_log (x, u, rnd), and y is the
exact logarithm of u.
Thus t is negative if x is smaller than y,
positive if x is larger than y, and zero if x equals y.
This function modifies x if needed
to be in the current range of acceptable values: It
generates an underflow or an overflow if the exponent of x is
outside the current allowed range; the value of t may be used
to avoid a double rounding. This function returns zero if the new value of
x equals the exact one y, a positive value if that new value
is larger than y, and a negative value if it is smaller than y.
Note that unlike most functions,
the new result x is compared to the (unknown) exact one y,
not the input value x, i.e., the ternary value is propagated.
Note: If x is an infinity and t is different from zero (i.e.,
if the rounded result is an inexact infinity), then the overflow flag is
set. This is useful because mpfr_check_range is typically called
(at least in MPFR functions) after restoring the flags that could have
been set due to internal computations.
This function rounds x emulating subnormal number arithmetic: if x is outside the subnormal exponent range of the emulated floating-point system, this function just propagates the ternary value t; otherwise, if EXP(x) denotes the exponent of x, it rounds x to precision EXP(x)−emin+1 according to rounding mode rnd and previous ternary value t, avoiding double rounding problems. More precisely in the subnormal domain, denoting by e the value of emin, x is rounded in fixed-point arithmetic to an integer multiple of two to the power e − 1; as a consequence, 1.5 multiplied by two to the power e − 1 when t is zero is rounded to two to the power e with rounding to nearest.
The precision PREC(x) of x is not modified by
this function. rnd and t must be the rounding mode
and the returned ternary value used when computing x
(as in mpfr_check_range). The subnormal exponent range is
from emin to emin+PREC(x)−1.
If the result cannot be represented in the current exponent range of MPFR
(due to a too small emax), the behavior is undefined.
Note that unlike most functions, the result is compared to the exact one,
not the input value x, i.e., the ternary value is propagated.
As usual, if the returned ternary value is non zero, the inexact flag is set. Moreover, if a second rounding occurred (because the input x was in the subnormal range), the underflow flag is set.
Warning! If you change emin (with mpfr_set_emin) just before
calling mpfr_subnormalize, you need to make sure that the value is
in the current exponent range of MPFR. But it is better to change
emin before any computation, if possible.
This is an example of how to emulate binary64 IEEE 754 arithmetic (a.k.a. double precision) using MPFR:
{
mpfr_t xa, xb; int i; volatile double a, b;
mpfr_set_default_prec (53);
mpfr_set_emin (-1073); mpfr_set_emax (1024);
mpfr_init (xa); mpfr_init (xb);
b = 34.3; mpfr_set_d (xb, b, MPFR_RNDN);
a = 0x1.1235P-1021; mpfr_set_d (xa, a, MPFR_RNDN);
a /= b;
i = mpfr_div (xa, xa, xb, MPFR_RNDN);
i = mpfr_subnormalize (xa, i, MPFR_RNDN); /* new ternary value */
mpfr_clear (xa); mpfr_clear (xb);
}
Note that mpfr_set_emin and mpfr_set_emax are called early
enough in order to make sure that all computed values are in the current
exponent range.
Warning! This emulates a double IEEE 754 arithmetic with correct rounding
in the subnormal range, which may not be the case for your hardware.
Below is another example showing how to emulate fixed-point arithmetic in a specific case. Here we compute the sine of the integers 1 to 17 with a result in a fixed-point arithmetic rounded at two to the power −42 (using the fact that the result is at most 1 in absolute value):
{
mpfr_t x; int i, inex;
mpfr_set_emin (-41);
mpfr_init2 (x, 42);
for (i = 1; i <= 17; i++)
{
mpfr_set_ui (x, i, MPFR_RNDN);
inex = mpfr_sin (x, x, MPFR_RNDZ);
mpfr_subnormalize (x, inex, MPFR_RNDZ);
mpfr_dump (x);
}
mpfr_clear (x);
}
Clear (lower) the underflow, overflow, divide-by-zero, invalid, inexact and erange flags.
Clear (lower) all global flags (underflow, overflow, divide-by-zero, invalid,
inexact, erange). Note: a group of flags can be cleared by using
mpfr_flags_clear.
Set (raise) the underflow, overflow, divide-by-zero, invalid, inexact and erange flags.
Return the corresponding (underflow, overflow, divide-by-zero, invalid, inexact, erange) flag, which is non-zero iff the flag is set.
The mpfr_flags_ functions below that take an argument mask
can operate on any subset of the exception flags: a flag is part of this
subset (or group) if and only if the corresponding bit of the argument
mask is set. The MPFR_FLAGS_ macros will normally be used
to build this argument. See Exceptions.
Clear (lower) the group of flags specified by mask.
Set (raise) the group of flags specified by mask.
Return the flags specified by mask. To test whether any flag from
mask is set, compare the return value to 0. You can also test
individual flags by AND’ing the result with MPFR_FLAGS_ macros.
Example:
mpfr_flags_t t = mpfr_flags_test (MPFR_FLAGS_UNDERFLOW|
MPFR_FLAGS_OVERFLOW)
…
if (t) /* underflow and/or overflow (unlikely) */
{
if (t & MPFR_FLAGS_UNDERFLOW) { /* handle underflow */ }
if (t & MPFR_FLAGS_OVERFLOW) { /* handle overflow */ }
}
Return all the flags. It is equivalent to
mpfr_flags_test(MPFR_FLAGS_ALL).
Restore the flags specified by mask to their state represented in flags.
Next: Memory Handling Functions, Previous: Miscellaneous Functions, Up: MPFR Interface [Index]