#include <mpfr.h>

— Function: void mpfr_init2 (mpfr_t x, mp_prec_t prec)

Initialize x, set its precision to be exactly prec bits and its value to NaN. (Warning: the corresponding mpf functions initialize to zero instead.)

Normally, a variable should be initialized once only or at least be cleared, using mpfr_clear, between initializations. To change the precision of a variable which has already been initialized, use mpfr_set_prec. The precision prec must be an integer between MPFR_PREC_MIN and MPFR_PREC_MAX (otherwise the behavior is undefined).

— Function: void mpfr_clear (mpfr_t x)

Free the space occupied by x. Make sure to call this function for all mpfr_t variables when you are done with them.

— Function: void mpfr_init (mpfr_t x)

Initialize x and set its value to NaN.

Normally, a variable should be initialized once only or at least be cleared, using mpfr_clear, between initializations. The precision of x is the default precision, which can be changed by a call to mpfr_set_default_prec.

— Function: void mpfr_set_default_prec (mp_prec_t prec)

Set the default precision to be exactly prec bits. The precision of a variable means the number of bits used to store its significand. All subsequent calls to mpfr_init will use this precision, but previously initialized variables are unaffected. This default precision is set to 53 bits initially. The precision can be any integer between MPFR_PREC_MIN and MPFR_PREC_MAX.

— Function: mp_prec_t mpfr_get_default_prec (void)

Return the default MPFR precision in bits.

     {
       mpfr_t x, y;
       mpfr_init (x);                /* use default precision */
       mpfr_init2 (y, 256);          /* precision exactly 256 bits */
       ...
       /* When the program is about to exit, do ... */
       mpfr_clear (x);
       mpfr_clear (y);
     }

— Function: void mpfr_set_prec (mpfr_t x, mp_prec_t prec)

Reset the precision of x to be exactly prec bits, and set its value to NaN. The previous value stored in x is lost. It is equivalent to a call to mpfr_clear(x) followed by a call to mpfr_init2(x, prec), but more efficient as no allocation is done in case the current allocated space for the significand of x is enough. The precision prec can be any integer between MPFR_PREC_MIN and MPFR_PREC_MAX.

In case you want to keep the previous value stored in x, use mpfr_prec_round instead.

— Function: mp_prec_t mpfr_get_prec (mpfr_t x)

Return the precision actually used for assignments of x, i.e. the number of bits used to store its significand.

— Function: int mpfr_set (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_set_ui (mpfr_t rop, unsigned long int op, mp_rnd_t rnd)
— Function: int mpfr_set_si (mpfr_t rop, long int op, mp_rnd_t rnd)
— Function: int mpfr_set_uj (mpfr_t rop, uintmax_t op, mp_rnd_t rnd)
— Function: int mpfr_set_sj (mpfr_t rop, intmax_t op, mp_rnd_t rnd)
— Function: int mpfr_set_d (mpfr_t rop, double op, mp_rnd_t rnd)
— Function: int mpfr_set_ld (mpfr_t rop, long double op, mp_rnd_t rnd)
— Function: int mpfr_set_decimal64 (mpfr_t rop, _Decimal64 op, mp_rnd_t rnd)
— Function: int mpfr_set_z (mpfr_t rop, mpz_t op, mp_rnd_t rnd)
— Function: int mpfr_set_q (mpfr_t rop, mpq_t op, mp_rnd_t rnd)
— Function: int mpfr_set_f (mpfr_t rop, mpf_t op, mp_rnd_t rnd)

Set the value of rop from op, rounded toward the given direction rnd. Note that the input 0 is converted to +0 by mpfr_set_ui, mpfr_set_si, mpfr_set_sj, mpfr_set_uj, mpfr_set_z, mpfr_set_q and mpfr_set_f, regardless of the rounding mode. If the system doesn't support the IEEE-754 standard, mpfr_set_d, mpfr_set_ld and mpfr_set_decimal64 might not preserve the signed zeros. The mpfr_set_decimal64 function is built only with the configure option ‘--enable-decimal-float’, which also requires ‘--with-gmp-build’, and when the compiler or system provides the ‘_Decimal64’ data type (GCC version 4.2.0 is known to support this data type, but only when configured with ‘--enable-decimal-float’ too). mpfr_set_q might not be able to work if the numerator (or the denominator) can not be representable as a mpfr_t.

Note: If you want to store a floating-point constant to a mpfr_t, you should use mpfr_set_str (or one of the MPFR constant functions, such as mpfr_const_pi for Pi) instead of mpfr_set_d, mpfr_set_ld or mpfr_set_decimal64. Otherwise the floating-point constant will be first converted into a reduced-precision (e.g., 53-bit) binary number before MPFR can work with it.

— Function: int mpfr_set_ui_2exp (mpfr_t rop, unsigned long int op, mp_exp_t e, mp_rnd_t rnd)
— Function: int mpfr_set_si_2exp (mpfr_t rop, long int op, mp_exp_t e, mp_rnd_t rnd)
— Function: int mpfr_set_uj_2exp (mpfr_t rop, uintmax_t op, intmax_t e, mp_rnd_t rnd)
— Function: int mpfr_set_sj_2exp (mpfr_t rop, intmax_t op, intmax_t e, mp_rnd_t rnd)

Set the value of rop from op multiplied by two to the power e, rounded toward the given direction rnd. Note that the input 0 is converted to +0.

— Function: int mpfr_set_str (mpfr_t rop, const char *s, int base, mp_rnd_t rnd)

Set rop to the value of the whole string s in base base, rounded in the direction rnd. See the documentation of mpfr_strtofr for a detailed description of the valid string formats. This function returns 0 if the entire string up to the final null character is a valid number in base base; otherwise it returns −1, and rop may have changed.

— Function: int mpfr_strtofr (mpfr_t rop, const char *nptr, char **endptr, int base, mp_rnd_t rnd)

Read a floating-point number from a string nptr in base base, rounded in the direction rnd; base must be either 0 (to detect the base, as described below) or a number from 2 to 36 (otherwise the behavior is undefined). If nptr starts with valid data, the result is stored in rop and *endptr points to the character just after the valid data (if endptr is not a null pointer); otherwise rop is set to zero and the value of nptr is stored in the location referenced by endptr (if endptr is not a null pointer). The usual ternary value is returned.

Parsing follows the standard C strtod function with some extensions. Case is ignored. After optional leading whitespace, one has a subject sequence consisting of an optional sign (+ or -), and either numeric data or special data. The subject sequence is defined as the longest initial subsequence of the input string, starting with the first non-whitespace character, that is of the expected form.

The form of numeric data is a non-empty sequence of significand digits with an optional decimal point, and an optional exponent consisting of an exponent prefix followed by an optional sign and a non-empty sequence of decimal digits. A significand digit is either a decimal digit or a Latin letter (62 possible characters), with a = 10, b = 11, ..., z = 36; its value must be strictly less than the base. The decimal point can be either the one defined by the current locale or the period (the first one is accepted for consistency with the C standard and the practice, the second one is accepted to allow the programmer to provide MPFR numbers from strings in a way that does not depend on the current locale). The exponent prefix can be e or E for bases up to 10, or @ in any base; it indicates a multiplication by a power of the base. In bases 2 and 16, the exponent prefix can also be p or P, in which case it introduces a binary exponent: it indicates a multiplication by a power of 2 (there is a difference only for base 16). The value of an exponent is always written in base 10. In base 2, the significand can start with 0b or 0B, and in base 16, it can start with 0x or 0X.

If the argument base is 0, then the base is automatically detected as follows. If the significand starts with 0b or 0B, base 2 is assumed. If the significand starts with 0x or 0X, base 16 is assumed. Otherwise base 10 is assumed.

Note: The exponent must contain at least a digit. Otherwise the possible exponent prefix and sign are not part of the number (which ends with the significand). Similarly, if 0b, 0B, 0x or 0X is not followed by a binary/hexadecimal digit, then the subject sequence stops at the character 0.

Special data (for infinities and NaN) can be @inf@ or @nan@(n-char-sequence), and if base <= 16, it can also be infinity, inf, nan or nan(n-char-sequence), all case insensitive. A n-char-sequence is a non-empty string containing only digits, Latin letters and the underscore (0, 1, 2, ..., 9, a, b, ..., z, A, B, ..., Z, _). Note: one has an optional sign for all data, even NaN.

— Function: void mpfr_set_inf (mpfr_t x, int sign)
— Function: void mpfr_set_nan (mpfr_t x)

Set the variable x to infinity or NaN (Not-a-Number) respectively. In mpfr_set_inf, x is set to plus infinity iff sign is nonnegative.

— Function: void mpfr_swap (mpfr_t x, mpfr_t y)

Swap the values x and y efficiently. Warning: the precisions are exchanged too; in case the precisions are different, mpfr_swap is thus not equivalent to three mpfr_set calls using a third auxiliary variable.

— Macro: int mpfr_init_set (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_ui (mpfr_t rop, unsigned long int op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_si (mpfr_t rop, signed long int op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_d (mpfr_t rop, double op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_ld (mpfr_t rop, long double op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_z (mpfr_t rop, mpz_t op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_q (mpfr_t rop, mpq_t op, mp_rnd_t rnd)
— Macro: int mpfr_init_set_f (mpfr_t rop, mpf_t op, mp_rnd_t rnd)

Initialize rop and set its value from op, rounded in the direction rnd. The precision of rop will be taken from the active default precision, as set by mpfr_set_default_prec.

— Function: int mpfr_init_set_str (mpfr_t x, const char *s, int base, mp_rnd_t rnd)

Initialize x and set its value from the string s in base base, rounded in the direction rnd. See mpfr_set_str.

— Function: double mpfr_get_d (mpfr_t op, mp_rnd_t rnd)
— Function: long double mpfr_get_ld (mpfr_t op, mp_rnd_t rnd)
— Function: _Decimal64 mpfr_get_decimal64 (mpfr_t op, mp_rnd_t rnd)

Convert op to a double (respectively _Decimal64 or long double), using the rounding mode rnd. If op is NaN, some fixed NaN (either quiet or signaling) or the result of 0.0/0.0 is returned. If op is ±Inf, an infinity of the same sign or the result of ±1.0/0.0 is returned. If op is zero, these functions return a zero, trying to preserve its sign, if possible. The mpfr_get_decimal64 function is built only under some conditions: see the documentation of mpfr_set_decimal64.

— Function: double mpfr_get_d_2exp (long *exp, mpfr_t op, mp_rnd_t rnd)
— Function: long double mpfr_get_ld_2exp (long *exp, mpfr_t op, mp_rnd_t rnd)

Return d and set exp such that 0.5<=abs(d)<1 and d times 2 raised to exp equals op rounded to double (resp. long double) precision, using the given rounding mode. If op is zero, then a zero of the same sign (or an unsigned zero, if the implementation does not have signed zeros) is returned, and exp is set to 0. If op is NaN or an infinity, then the corresponding double precision (resp. long-double precision) value is returned, and exp is undefined.

— Function: long mpfr_get_si (mpfr_t op, mp_rnd_t rnd)
— Function: unsigned long mpfr_get_ui (mpfr_t op, mp_rnd_t rnd)
— Function: intmax_t mpfr_get_sj (mpfr_t op, mp_rnd_t rnd)
— Function: uintmax_t mpfr_get_uj (mpfr_t op, mp_rnd_t rnd)

Convert op to a long, an unsigned long, an intmax_t or an uintmax_t (respectively) after rounding it with respect to rnd. If op is NaN, the result is undefined. If op is too big for the return type, it returns the maximum or the minimum of the corresponding C type, depending on the direction of the overflow. The flag erange is set too. See also mpfr_fits_slong_p, mpfr_fits_ulong_p, mpfr_fits_intmax_p and mpfr_fits_uintmax_p.

— Function: mp_exp_t mpfr_get_z_exp (mpz_t rop, mpfr_t op)

Put the scaled significand of op (regarded as an integer, with the precision of op) into rop, and return the exponent exp (which may be outside the current exponent range) such that op exactly equals rop multiplied by two exponent exp. If the exponent is not representable in the mp_exp_t type, the behavior is undefined.

— Function: void mpfr_get_z (mpz_t rop, mpfr_t op, mp_rnd_t rnd)

Convert op to a mpz_t, after rounding it with respect to rnd. If op is NaN or Inf, the result is undefined.

— Function: int mpfr_get_f (mpf_t rop, mpfr_t op, mp_rnd_t rnd)

Convert op to a mpf_t, after rounding it with respect to rnd. Return zero iff no error occurred, in particular a non-zero value is returned if op is NaN or Inf, which do not exist in mpf.

— Function: char * mpfr_get_str (char *str, mp_exp_t *expptr, int b, size_t n, mpfr_t op, mp_rnd_t rnd)

Convert op to a string of digits in base b, with rounding in the direction rnd, where n is either zero (see below) or the number of significant digits; in the latter case, n must be greater or equal to 2. The base may vary from 2 to 36.

The generated string is a fraction, with an implicit radix point immediately to the left of the first digit. For example, the number −3.1416 would be returned as "−31416" in the string and 1 written at expptr. If rnd is to nearest, and op is exactly in the middle of two possible outputs, the one with an even last digit is chosen (for an odd base, this may not correspond to an even significand).

If n is zero, the number of digits of the significand is chosen large enough so that re-reading the printed value with the same precision, assuming both output and input use rounding to nearest, will recover the original value of op. More precisely, in most cases, the chosen precision of str is the minimal precision depending on n and b only that satisfies the above property, i.e., m = 1 + ceil(n*log(2)/log(b)), but in some very rare cases, it might be m+1.

If str is a null pointer, space for the significand is allocated using the current allocation function, and a pointer to the string is returned. To free the returned string, you must use mpfr_free_str.

If str is not a null pointer, it should point to a block of storage large enough for the significand, i.e., at least max(n + 2, 7). The extra two bytes are for a possible minus sign, and for the terminating null character.

If the input number is an ordinary number, the exponent is written through the pointer expptr (the current minimal exponent for 0).

A pointer to the string is returned, unless there is an error, in which case a null pointer is returned.

— Function: void mpfr_free_str (char *str)

Free a string allocated by mpfr_get_str using the current unallocation function (preliminary interface). The block is assumed to be strlen(str)+1 bytes. For more information about how it is done: see Custom Allocation (GNU MP).

— Function: int mpfr_fits_ulong_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_slong_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_uint_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_sint_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_ushort_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_sshort_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_intmax_p (mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_fits_uintmax_p (mpfr_t op, mp_rnd_t rnd)

Return non-zero if op would fit in the respective C data type, when rounded to an integer in the direction rnd.

— Function: int mpfr_add (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_add_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_add_si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)
— Function: int mpfr_add_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd)
— Function: int mpfr_add_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd)

Set rop to op1 + op2 rounded in the direction rnd. For types having no signed zero, it is considered unsigned (i.e. (+0) + 0 = (+0) and (−0) + 0 = (−0)).

— Function: int mpfr_sub (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_ui_sub (mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_sub_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_si_sub (mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_sub_si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)
— Function: int mpfr_sub_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd)
— Function: int mpfr_sub_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd)

Set rop to op1 - op2 rounded in the direction rnd. For types having no signed zero, it is considered unsigned (i.e. (+0) − 0 = (+0), (−0) − 0 = (−0), 0 − (+0) = (−0) and 0 − (−0) = (+0)).

— Function: int mpfr_mul (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_mul_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_mul_si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)
— Function: int mpfr_mul_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd)
— Function: int mpfr_mul_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd)

Set rop to op1 times op2 rounded in the direction rnd. When a result is zero, its sign is the product of the signs of the operands (for types having no signed zero, it is considered positive).

— Function: int mpfr_sqr (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the square of op rounded in the direction rnd.

— Function: int mpfr_div (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_ui_div (mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_div_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_si_div (mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_div_si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)
— Function: int mpfr_div_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd)
— Function: int mpfr_div_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd)

Set rop to op1/op2 rounded in the direction rnd. When a result is zero, its sign is the product of the signs of the operands (for types having no signed zero, it is considered positive).

— Function: int mpfr_sqrt (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_sqrt_ui (mpfr_t rop, unsigned long int op, mp_rnd_t rnd)

Set rop to the square root of op rounded in the direction rnd. Return −0 if op is −0 (to be consistent with the IEEE 754-1985 standard). Set rop to NaN if op is negative.

— Function: int mpfr_cbrt (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_root (mpfr_t rop, mpfr_t op, unsigned long int k, mp_rnd_t rnd)

Set rop to the cubic root (resp. the kth root) of op rounded in the direction rnd. An odd (resp. even) root of a negative number (including −Inf) returns a negative number (resp. NaN). The kth root of −0 is defined to be −0, whatever the parity of k.

— Function: int mpfr_pow (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)
— Function: int mpfr_pow_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_pow_si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)
— Function: int mpfr_pow_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd)
— Function: int mpfr_ui_pow_ui (mpfr_t rop, unsigned long int op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_ui_pow (mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd)

Set rop to op1 raised to op2, rounded in the direction rnd. Special values are currently handled as described in the ISO C99 standard for the pow function (note this may change in future versions):

• pow(±0, y) returns plus or minus infinity for y a negative odd integer.
• pow(±0, y) returns plus infinity for y negative and not an odd integer.
• pow(±0, y) returns plus or minus zero for y a positive odd integer.
• pow(±0, y) returns plus zero for y positive and not an odd integer.
• pow(-1, ±Inf) returns 1.
• pow(+1, y) returns 1 for any y, even a NaN.
• pow(x, y) returns NaN for finite negative x and finite non-integer y.
• pow(x, -Inf) returns plus infinity for 0 < abs(x) < 1, and plus zero for abs(x) > 1.
• pow(x, +Inf) returns plus zero for 0 < abs(x) < 1, and plus infinity for abs(x) > 1.
• pow(-Inf, y) returns minus zero for y a negative odd integer.
• pow(-Inf, y) returns plus zero for y negative and not an odd integer.
• pow(-Inf, y) returns minus infinity for y a positive odd integer.
• pow(-Inf, y) returns plus infinity for y positive and not an odd integer.
• pow(+Inf, y) returns plus zero for y negative, and plus infinity for y positive.

— Function: int mpfr_neg (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to -op rounded in the direction rnd. Just changes the sign if rop and op are the same variable.

— Function: int mpfr_abs (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the absolute value of op, rounded in the direction rnd. Just changes the sign if rop and op are the same variable.

— Function: int mpfr_dim (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)

Set rop to the positive difference of op1 and op2, i.e., op1 - op2 rounded in the direction rnd if op1 > op2, and +0 otherwise. Returns NaN when op1 or op2 is NaN.

— Function: int mpfr_mul_2ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_mul_2si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)

Set rop to op1 times 2 raised to op2 rounded in the direction rnd. Just increases the exponent by op2 when rop and op1 are identical.

— Function: int mpfr_div_2ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd)
— Function: int mpfr_div_2si (mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd)

Set rop to op1 divided by 2 raised to op2 rounded in the direction rnd. Just decreases the exponent by op2 when rop and op1 are identical.

— Function: int mpfr_cmp (mpfr_t op1, mpfr_t op2)
— Function: int mpfr_cmp_ui (mpfr_t op1, unsigned long int op2)
— Function: int mpfr_cmp_si (mpfr_t op1, signed long int op2)
— Function: int mpfr_cmp_d (mpfr_t op1, double op2)
— Function: int mpfr_cmp_ld (mpfr_t op1, long double op2)
— Function: int mpfr_cmp_z (mpfr_t op1, mpz_t op2)
— Function: int mpfr_cmp_q (mpfr_t op1, mpq_t op2)
— Function: int mpfr_cmp_f (mpfr_t op1, mpf_t op2)

Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, and a negative value if op1 < op2. Both op1 and op2 are considered to their full own precision, which may differ. If one of the operands is NaN, set the erange flag and return zero.

Note: These functions may be useful to distinguish the three possible cases. If you need to distinguish two cases only, it is recommended to use the predicate functions (e.g., mpfr_equal_p for the equality) described below; they behave like the IEEE-754 comparisons, in particular when one or both arguments are NaN. But only floating-point numbers can be compared (you may need to do a conversion first).

— Function: int mpfr_cmp_ui_2exp (mpfr_t op1, unsigned long int op2, mp_exp_t e)
— Function: int mpfr_cmp_si_2exp (mpfr_t op1, long int op2, mp_exp_t e)

Compare op1 and op2 multiplied by two to the power e. Similar as above.

— Function: int mpfr_cmpabs (mpfr_t op1, mpfr_t op2)

Compare |op1| and |op2|. Return a positive value if |op1| > |op2|, zero if |op1| = |op2|, and a negative value if |op1| < |op2|. If one of the operands is NaN, set the erange flag and return zero.

— Function: int mpfr_nan_p (mpfr_t op)
— Function: int mpfr_inf_p (mpfr_t op)
— Function: int mpfr_number_p (mpfr_t op)
— Function: int mpfr_zero_p (mpfr_t op)

Return non-zero if op is respectively NaN, an infinity, an ordinary number (i.e. neither NaN nor an infinity) or zero. Return zero otherwise.

— Macro: int mpfr_sgn (mpfr_t op)

Return a positive value if op > 0, zero if op = 0, and a negative value if op < 0. If the operand is NaN, set the erange flag and return zero.

— Function: int mpfr_greater_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 > op2, zero otherwise.

— Function: int mpfr_greaterequal_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 >= op2, zero otherwise.

— Function: int mpfr_less_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 < op2, zero otherwise.

— Function: int mpfr_lessequal_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 <= op2, zero otherwise.

— Function: int mpfr_lessgreater_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 < op2 or op1 > op2 (i.e. neither op1, nor op2 is NaN, and op1 <> op2), zero otherwise (i.e. op1 and/or op2 are NaN, or op1 = op2).

— Function: int mpfr_equal_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 = op2, zero otherwise (i.e. op1 and/or op2 are NaN, or op1 <> op2).

— Function: int mpfr_unordered_p (mpfr_t op1, mpfr_t op2)

Return non-zero if op1 or op2 is a NaN (i.e. they cannot be compared), zero otherwise.

— Function: int mpfr_log (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_log2 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_log10 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the natural logarithm of op, log2(op) or log10(op), respectively, rounded in the direction rnd. Return −Inf if op is −0 (i.e. the sign of the zero has no influence on the result).

— Function: int mpfr_exp (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_exp2 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_exp10 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the exponential of op, to 2 power of op or to 10 power of op, respectively, rounded in the direction rnd.

— Function: int mpfr_cos (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_sin (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_tan (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the cosine of op, sine of op, tangent of op, rounded in the direction rnd.

— Function: int mpfr_sec (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_csc (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_cot (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the secant of op, cosecant of op, cotangent of op, rounded in the direction rnd.

— Function: int mpfr_sin_cos (mpfr_t sop, mpfr_t cop, mpfr_t op, mp_rnd_t rnd)

Set simultaneously sop to the sine of op and cop to the cosine of op, rounded in the direction rnd with the corresponding precisions of sop and cop, which must be different variables. Return 0 iff both results are exact.

— Function: int mpfr_acos (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_asin (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_atan (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the arc-cosine, arc-sine or arc-tangent of op, rounded in the direction rnd. Note that since acos(-1) returns the floating-point number closest to Pi according to the given rounding mode, this number might not be in the output range 0 <= rop < \pi of the arc-cosine function; still, the result lies in the image of the output range by the rounding function. The same holds for asin(-1), asin(1), atan(-Inf), atan(+Inf).

— Function: int mpfr_atan2 (mpfr_t rop, mpfr_t y, mpfr_t x, mp_rnd_t rnd)

Set rop to the arc-tangent2 of y and x, rounded in the direction rnd: if x > 0, atan2(y, x) = atan (y/x); if x < 0, atan2(y, x) = sign(y)*(Pi - atan (abs(y/x))). As for atan, in case the exact mathematical result is +Pi or -Pi, its rounded result might be outside the function output range.

atan2(y, 0) does not raise any floating-point exception. Special values are currently handled as described in the ISO C99 standard for the atan2 function (note this may change in future versions):

• atan2(+0, -0) returns +Pi.
• atan2(-0, -0) returns -Pi.
• atan2(+0, +0) returns +0.
• atan2(-0, +0) returns −0.
• atan2(+0, x) returns +Pi for x < 0.
• atan2(-0, x) returns -Pi for x < 0.
• atan2(+0, x) returns +0 for x > 0.
• atan2(-0, x) returns −0 for x > 0.
• atan2(y, 0) returns -Pi/2 for y < 0.
• atan2(y, 0) returns +Pi/2 for y > 0.
• atan2(+Inf, -Inf) returns +3*Pi/4.
• atan2(-Inf, -Inf) returns -3*Pi/4.
• atan2(+Inf, +Inf) returns +Pi/4.
• atan2(-Inf, +Inf) returns -Pi/4.
• atan2(+Inf, x) returns +Pi/2 for finite x.
• atan2(-Inf, x) returns -Pi/2 for finite x.
• atan2(y, -Inf) returns +Pi for finite y > 0.
• atan2(y, -Inf) returns -Pi for finite y < 0.
• atan2(y, +Inf) returns +0 for finite y > 0.
• atan2(y, +Inf) returns −0 for finite y < 0.

— Function: int mpfr_cosh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_sinh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_tanh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the hyperbolic cosine, sine or tangent of op, rounded in the direction rnd.

— Function: int mpfr_sech (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_csch (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_coth (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the hyperbolic secant of op, cosecant of op, cotangent of op, rounded in the direction rnd.

— Function: int mpfr_acosh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_asinh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_atanh (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the inverse hyperbolic cosine, sine or tangent of op, rounded in the direction rnd.

— Function: int mpfr_fac_ui (mpfr_t rop, unsigned long int op, mp_rnd_t rnd)

Set rop to the factorial of the unsigned long int op, rounded in the direction rnd.

— Function: int mpfr_log1p (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the logarithm of one plus op, rounded in the direction rnd.

— Function: int mpfr_expm1 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the exponential of op minus one, rounded in the direction rnd.

— Function: int mpfr_eint (mpfr_t y, mpfr_t x, mp_rnd_t rnd)

Set y to the exponential integral of x, rounded in the direction rnd. For positive x, the exponential integral is the sum of Euler's constant, of the logarithm of x, and of the sum for k from 1 to infinity of x to the power k, divided by k and factorial(k). For negative x, the returned value is NaN.

— Function: int mpfr_gamma (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the Gamma function on op, rounded in the direction rnd. When op is a negative integer, NaN is returned.

— Function: int mpfr_lngamma (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the logarithm of the Gamma function on op, rounded in the direction rnd. When −2k−1 <= x <= −2k, k being a non-negative integer, NaN is returned. See also mpfr_lgamma.

— Function: int mpfr_lgamma (mpfr_t rop, int *signp, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the logarithm of the absolute value of the Gamma function on op, rounded in the direction rnd. The sign (1 or −1) of Gamma(op) is returned in the object pointed to by signp. When op is an infinity or a non-positive integer, +Inf is returned. When op is NaN, −Inf or a negative integer, *signp is undefined, and when op is ±0, *signp is the sign of the zero.

— Function: int mpfr_zeta (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_zeta_ui (mpfr_t rop, unsigned long op, mp_rnd_t rnd)

Set rop to the value of the Riemann Zeta function on op, rounded in the direction rnd.

— Function: int mpfr_erf (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the error function on op, rounded in the direction rnd.

— Function: int mpfr_erfc (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the complementary error function on op, rounded in the direction rnd.

— Function: int mpfr_j0 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_j1 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_jn (mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the first order Bessel function of order 0, 1 and n on op, rounded in the direction rnd. When op is NaN, rop is always set to NaN. When op is plus or minus Infinity, rop is set to +0. When op is zero, and n is not zero, rop is +0 or −0 depending on the parity and sign of n, and the sign of op.

— Function: int mpfr_y0 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_y1 (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_yn (mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd)

Set rop to the value of the second order Bessel function of order 0, 1 and n on op, rounded in the direction rnd. When op is NaN or negative, rop is always set to NaN. When op is +Inf, rop is +0. When op is zero, rop is +Inf or −Inf depending on the parity and sign of n.

— Function: int mpfr_fma (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd)

Set rop to op1 times op2 + op3, rounded in the direction rnd.

— Function: int mpfr_fms (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd)

Set rop to op1 times op2 - op3, rounded in the direction rnd.

— Function: int mpfr_agm (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)

Set rop to the arithmetic-geometric mean of op1 and op2, rounded in the direction rnd. The arithmetic-geometric mean is the common limit of the sequences u[n] and v[n], where u[0]=op1, v[0]=op2, u[n+1] is the arithmetic mean of u[n] and v[n], and v[n+1] is the geometric mean of u[n] and v[n]. If any operand is negative, the return value is NaN.

— Function: int mpfr_hypot (mpfr_t rop, mpfr_t x, mpfr_t y, mp_rnd_t rnd)

Set rop to the Euclidean norm of x and y, i.e. the square root of the sum of the squares of x and y, rounded in the direction rnd. Special values are currently handled as described in Section F.9.4.3 of the ISO C99 standard, for the hypot function (note this may change in future versions): If x or y is an infinity, then plus infinity is returned in rop, even if the other number is NaN.

— Function: int mpfr_const_log2 (mpfr_t rop, mp_rnd_t rnd)
— Function: int mpfr_const_pi (mpfr_t rop, mp_rnd_t rnd)
— Function: int mpfr_const_euler (mpfr_t rop, mp_rnd_t rnd)
— Function: int mpfr_const_catalan (mpfr_t rop, mp_rnd_t rnd)

Set rop to the logarithm of 2, the value of Pi, of Euler's constant 0.577..., of Catalan's constant 0.915..., respectively, rounded in the direction rnd. These functions cache the computed values to avoid other calculations if a lower or equal precision is requested. To free these caches, use mpfr_free_cache.

— Function: void mpfr_free_cache (void)

Free various caches used by MPFR internally, in particular the caches used by the functions computing constants (currently mpfr_const_log2, mpfr_const_pi, mpfr_const_euler and mpfr_const_catalan). You should call this function when terminating a thread.

— Function: int mpfr_sum (mpfr_t rop, mpfr_ptr const tab[], unsigned long n, mp_rnd_t rnd)

Set ret to the sum of all elements of tab whose size is n, rounded in the direction rnd. Warning, tab is a table of pointers to mpfr_t, not a table of mpfr_t (preliminary interface). The returned int value is zero when the computed value is the exact value, and non-zero when this cannot be guaranteed, without giving the direction of the error as the other functions do.

— Function: size_t mpfr_out_str (FILE *stream, int base, size_t n, mpfr_t op, mp_rnd_t rnd)

Output op on stream stream, as a string of digits in base base, rounded in the direction rnd. The base may vary from 2 to 36. Print n significant digits exactly, or if n is 0, enough digits so that op can be read back exactly (see mpfr_get_str).

In addition to the significant digits, a decimal point (defined by the current locale) at the right of the first digit and a trailing exponent in base 10, in the form ‘eNNN’, are printed. If base is greater than 10, ‘@’ will be used instead of ‘e’ as exponent delimiter.

Return the number of bytes written, or if an error occurred, return 0.

— Function: size_t mpfr_inp_str (mpfr_t rop, FILE *stream, int base, mp_rnd_t rnd)

Input a string in base base from stream stream, rounded in the direction rnd, and put the read float in rop.

This function reads a word (defined as a sequence of characters between whitespace) and parses it using mpfr_set_str (it may change). See the documentation of mpfr_strtofr for a detailed description of the valid string formats.

Return the number of bytes read, or if an error occurred, return 0.

— Function: int mpfr_rint (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_ceil (mpfr_t rop, mpfr_t op)
— Function: int mpfr_floor (mpfr_t rop, mpfr_t op)
— Function: int mpfr_round (mpfr_t rop, mpfr_t op)
— Function: int mpfr_trunc (mpfr_t rop, mpfr_t op)

Set rop to op rounded to an integer. mpfr_rint rounds to the nearest representable integer in the given rounding mode, mpfr_ceil rounds to the next higher or equal representable integer, mpfr_floor to the next lower or equal representable integer, mpfr_round to the nearest representable integer, rounding halfway cases away from zero, and mpfr_trunc to the next representable integer toward zero.

The returned value is zero when the result is exact, positive when it is greater than the original value of op, and negative when it is smaller. More precisely, the returned value is 0 when op is an integer representable in rop, 1 or −1 when op is an integer that is not representable in rop, 2 or −2 when op is not an integer.

Note that mpfr_round is different from mpfr_rint called with the rounding to nearest mode (where halfway cases are rounded to an even integer or significand). Note also that no double rounding is performed; for instance, 4.5 (100.1 in binary) is rounded by mpfr_round to 4 (100 in binary) in 2-bit precision, though round(4.5) is equal to 5 and 5 (101 in binary) is rounded to 6 (110 in binary) in 2-bit precision.

— Function: int mpfr_rint_ceil (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_rint_floor (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_rint_round (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)
— Function: int mpfr_rint_trunc (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to op rounded to an integer. mpfr_rint_ceil rounds to the next higher or equal integer, mpfr_rint_floor to the next lower or equal integer, mpfr_rint_round to the nearest integer, rounding halfway cases away from zero, and mpfr_rint_trunc to the next integer toward zero. If the result is not representable, it is rounded in the direction rnd. The returned value is the ternary value associated with the considered round-to-integer function (regarded in the same way as any other mathematical function).

— Function: int mpfr_frac (mpfr_t rop, mpfr_t op, mp_rnd_t rnd)

Set rop to the fractional part of op, having the same sign as op, rounded in the direction rnd (unlike in mpfr_rint, rnd affects only how the exact fractional part is rounded, not how the fractional part is generated).

— Function: int mpfr_remainder (mpfr_t r, mpfr_t x, mpfr_t y, mp_rnd_t rnd)
— Function: int mpfr_remquo (mpfr_t r, long* q, mpfr_t x, mpfr_t y, mp_rnd_t rnd)

Set r to the remainder of the division of x by y, with quotient rounded to the nearest integer (ties rounded to even), and r rounded according to the direction rnd. If r is zero, it has the sign of x. The return value is the inexact flag corresponding to r. Additionally, mpfr_remquo stores the low significant bits from the quotient in *q (more precisely the number of bits in a long minus one), with the sign of x divided by y (except if those low bits are all zero, in which case zero is returned). Note that x may be so large in magnitude relative to y that an exact representation of the quotient is not practical. These functions are useful for additive argument reduction.

— Function: int mpfr_integer_p (mpfr_t op)

Return non-zero iff op is an integer.

— Function: void mpfr_nexttoward (mpfr_t x, mpfr_t y)

If x or y is NaN, set x to NaN. Otherwise, if x is different from y, replace x by the next floating-point number (with the precision of x and the current exponent range) in the direction of y, if there is one (the infinite values are seen as the smallest and largest floating-point numbers). If the result is zero, it keeps the same sign. No underflow or overflow is generated.

— Function: void mpfr_nextabove (mpfr_t x)

Equivalent to mpfr_nexttoward where y is plus infinity.

— Function: void mpfr_nextbelow (mpfr_t x)

Equivalent to mpfr_nexttoward where y is minus infinity.

— Function: int mpfr_min (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)

Set rop to the minimum of op1 and op2. If op1 and op2 are both NaN, then rop is set to NaN. If op1 or op2 is NaN, then rop is set to the numeric value. If op1 and op2 are zeros of different signs, then rop is set to −0.

— Function: int mpfr_max (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)

Set rop to the maximum of op1 and op2. If op1 and op2 are both NaN, then rop is set to NaN. If op1 or op2 is NaN, then rop is set to the numeric value. If op1 and op2 are zeros of different signs, then rop is set to +0.

— Function: int mpfr_urandomb (mpfr_t rop, gmp_randstate_t state)

Generate a uniformly distributed random float in the interval 0 <= rop < 1. Return 0, unless the exponent is not in the current exponent range, in which case rop is set to NaN and a non-zero value is returned. The second argument is a gmp_randstate_t structure which should be created using the GMP gmp_randinit function, see the GMP manual.

— Function: void mpfr_random (mpfr_t rop)

Generate a uniformly distributed random float in the interval 0 <= rop < 1. This function is deprecated; mpfr_urandomb should be used instead.

— Function: void mpfr_random2 (mpfr_t rop, mp_size_t size, mp_exp_t exp)

Generate a random float of at most size limbs, with long strings of zeros and ones in the binary representation. The exponent of the number is in the interval −exp to exp. This function is useful for testing functions and algorithms, since this kind of random numbers have proven to be more likely to trigger corner-case bugs. Negative random numbers are generated when size is negative. Put +0 in rop when size if zero. The internal state of the default pseudorandom number generator is modified by a call to this function (the same one as GMP if MPFR was built using ‘--with-gmp-build’).

— Function: mp_exp_t mpfr_get_exp (mpfr_t x)

Get the exponent of x, assuming that x is a non-zero ordinary number and the significand is chosen in [1/2,1). The behavior for NaN, infinity or zero is undefined.

— Function: int mpfr_set_exp (mpfr_t x, mp_exp_t e)

Set the exponent of x if e is in the current exponent range, and return 0 (even if x is not a non-zero ordinary number); otherwise, return a non-zero value. The significand is assumed to be in [1/2,1).

— Function: int mpfr_signbit (mpfr_t op)

Return a non-zero value iff op has its sign bit set (i.e. if it is negative, −0, or a NaN whose representation has its sign bit set).

— Function: int mpfr_setsign (mpfr_t rop, mpfr_t op, int s, mp_rnd_t rnd)

Set the value of rop from op, rounded toward the given direction rnd, then set (resp. clear) its sign bit if s is non-zero (resp. zero), even when op is a NaN.

— Function: int mpfr_copysign (mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd)

Set the value of rop from op1, rounded toward the given direction rnd, then set its sign bit to that of op2 (even when op1 or op2 is a NaN). This function is equivalent to mpfr_setsign (rop, op1, mpfr_signbit (op2), rnd).

— Function: const char * mpfr_get_version (void)

Return the MPFR version, as a null-terminated string.

— Macro: MPFR_VERSION
— Macro: MPFR_VERSION_MAJOR
— Macro: MPFR_VERSION_MINOR
— Macro: MPFR_VERSION_PATCHLEVEL
— Macro: MPFR_VERSION_STRING

MPFR_VERSION is the version of MPFR as a preprocessing constant. MPFR_VERSION_MAJOR, MPFR_VERSION_MINOR and MPFR_VERSION_PATCHLEVEL are respectively the major, minor and patch level of MPFR version, as preprocessing constants. MPFR_VERSION_STRING is the version (with an optional suffix, used in development and pre-release versions) as a string constant, which can be compared to the result of mpfr_get_version to check at run time the header file and library used match:

          if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING))
            fprintf (stderr, "Warning: header and library do not match\n");

Note: Obtaining different strings is not necessarily an error, as in general, a program compiled with some old MPFR version can be dynamically linked with a newer MPFR library version (if allowed by the library versioning system).

— Macro: long MPFR_VERSION_NUM (major, minor, patchlevel)

Create an integer in the same format as used by MPFR_VERSION from the given major, minor and patchlevel. Here is an example of how to check the MPFR version at compile time:

          #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0)))
          # error "Wrong MPFR version."
          #endif

— Function: const char * mpfr_get_patches (void)

Return a null-terminated string containing the ids of the patches applied to the MPFR library (contents of the PATCHES file), separated by spaces. Note: If the program has been compiled with an older MPFR version and is dynamically linked with a new MPFR library version, the ids of the patches applied to the old (compile-time) MPFR version are not available (however this information should not have much interest in general).

— Function: void mpfr_set_default_rounding_mode (mp_rnd_t rnd)

Set the default rounding mode to rnd. The default rounding mode is to nearest initially.

— Function: mp_rnd_t mpfr_get_default_rounding_mode (void)

Get the default rounding mode.

— Function: int mpfr_prec_round (mpfr_t x, mp_prec_t prec, mp_rnd_t rnd)

Round x according to rnd with precision prec, which must be an integer between MPFR_PREC_MIN and MPFR_PREC_MAX (otherwise the behavior is undefined). If prec is greater or equal to the precision of x, then new space is allocated for the significand, and it is filled with zeros. Otherwise, the significand is rounded to precision prec with the given direction. In both cases, the precision of x is changed to prec.

— Function: int mpfr_round_prec (mpfr_t x, mp_rnd_t rnd, mp_prec_t prec)

[This function is obsolete. Please use mpfr_prec_round instead.]

— Function: const char * mpfr_print_rnd_mode (mp_rnd_t rnd)

Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ) corresponding to the rounding mode rnd or a null pointer if rnd is an invalid rounding mode.

— Function: mp_exp_t mpfr_get_emin (void)
— Function: mp_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.

— Function: int mpfr_set_emin (mp_exp_t exp)
— Function: int mpfr_set_emax (mp_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: mp_exp_t mpfr_get_emin_min (void)
— Function: mp_exp_t mpfr_get_emin_max (void)
— Function: mp_exp_t mpfr_get_emax_min (void)
— Function: mp_exp_t mpfr_get_emax_max (void)

Return the minimum and maximum of the smallest and largest exponents allowed for mpfr_set_emin and mpfr_set_emax. These values are implementation dependent; it is possible to create a non portable program by writing mpfr_set_emax(mpfr_get_emax_max()) and mpfr_set_emin(mpfr_get_emin_min()) since the values of the smallest and largest exponents become implementation dependent.

— Function: int mpfr_check_range (mpfr_t x, int t, mp_rnd_t rnd)

This function forces x to be in the current range of acceptable values, t being the current ternary value: negative if x is smaller than the exact value, positive if x is larger than the exact value and zero if x is exact (before the call). 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 rounded result is equal to the exact one, a positive value if the rounded result is larger than the exact one, a negative value if the rounded result is smaller than the exact one. 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.

— Function: int mpfr_subnormalize (mpfr_t x, int t, mp_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 used rounding mode for computing x and the returned ternary value when computing x. 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. This is a preliminary interface.

     {
       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, GMP_RNDN);
       a = 0x1.1235P-1021; mpfr_set_d (xa, a, GMP_RNDN);
     
       a /= b;
       i = mpfr_div (xa, xa, xb, GMP_RNDN);
       i = mpfr_subnormalize (xa, i, GMP_RNDN);
     
       mpfr_clear (xa); mpfr_clear (xb);
     }

— Function: void mpfr_clear_underflow (void)
— Function: void mpfr_clear_overflow (void)
— Function: void mpfr_clear_nanflag (void)
— Function: void mpfr_clear_inexflag