### 5.13 Exception Related Functions

Function: mpfr_exp_t mpfr_get_emin (void)
Function: mpfr_exp_t mpfr_get_emax (void)

  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.

Function: int mpfr_set_emin (mpfr_exp_t exp)
Function: int mpfr_set_emax (mpfr_exp_t exp)

  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. If the user changes the exponent range, it is her/his responsibility to check that all current floating-point variables are in the new allowed range (for example using `mpfr_check_range`), otherwise the subsequent behavior will be undefined, in the sense of the ISO C standard.

Function: mpfr_exp_t mpfr_get_emin_min (void)
Function: mpfr_exp_t mpfr_get_emin_max (void)
Function: mpfr_exp_t mpfr_get_emax_min (void)
Function: mpfr_exp_t mpfr_get_emax_max (void)

  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.

Function: int mpfr_check_range (mpfr_t x, int t, mpfr_rnd_t rnd)

  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.

Function: int mpfr_subnormalize (mpfr_t x, int t, mpfr_rnd_t rnd)

  This function rounds x emulating subnormal number arithmetic: if x is outside the subnormal exponent range, it just propagates the ternary value t; otherwise, 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.

  `PREC(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 (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.

This is an example of how to emulate binary double IEEE 754 arithmetic (binary64 in IEEE 754-2008) 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);
    }

Warning: this emulates a double IEEE 754 arithmetic with correct rounding in the subnormal range, which may not be the case for your hardware.

Function: void mpfr_clear_underflow (void)
Function: void mpfr_clear_overflow (void)
Function: void mpfr_clear_divby0 (void)
Function: void mpfr_clear_nanflag (void)
Function: void mpfr_clear_inexflag (void)
Function: void mpfr_clear_erangeflag (void)

  Clear the underflow, overflow, divide-by-zero, invalid, inexact and erange flags.

Function: void mpfr_set_underflow (void)
Function: void mpfr_set_overflow (void)
Function: void mpfr_set_divby0 (void)
Function: void mpfr_set_nanflag (void)
Function: void mpfr_set_inexflag (void)
Function: void mpfr_set_erangeflag (void)

  Set the underflow, overflow, divide-by-zero, invalid, inexact and erange flags.

Function: void mpfr_clear_flags (void)

  Clear all global flags (underflow, overflow, divide-by-zero, invalid, inexact, erange).

Function: int mpfr_underflow_p (void)
Function: int mpfr_overflow_p (void)
Function: int mpfr_divby0_p (void)
Function: int mpfr_nanflag_p (void)
Function: int mpfr_inexflag_p (void)
Function: int mpfr_erangeflag_p (void)

  Return the corresponding (underflow, overflow, divide-by-zero, invalid, inexact, erange) flag, which is non-zero iff the flag is set.