### 5.5 Basic Arithmetic Functions

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

  Set rop to op1 + op2 rounded in the direction rnd. The IEEE-754 rules are used, in particular for signed zeros. But for types having no signed zeros, 0 is considered unsigned (i.e., (+0) + 0 = (+0) and (−0) + 0 = (−0)). The `mpfr_add_d` function assumes that the radix of the `double` type is a power of 2, with a precision at most that declared by the C implementation (macro `IEEE_DBL_MANT_DIG`, and if not defined 53 bits).

Function: int mpfr_sub (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_ui_sub (mpfr_t rop, unsigned long int op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_sub_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_si_sub (mpfr_t rop, long int op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_sub_si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_rnd_t rnd)
Function: int mpfr_d_sub (mpfr_t rop, double op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_sub_d (mpfr_t rop, mpfr_t op1, double op2, mpfr_rnd_t rnd)
Function: int mpfr_z_sub (mpfr_t rop, mpz_t op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_sub_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mpfr_rnd_t rnd)
Function: int mpfr_sub_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mpfr_rnd_t rnd)

  Set rop to op1 - op2 rounded in the direction rnd. The IEEE-754 rules are used, in particular for signed zeros. But for types having no signed zeros, 0 is considered unsigned (i.e., (+0) − 0 = (+0), (−0) − 0 = (−0), 0 − (+0) = (−0) and 0 − (−0) = (+0)). The same restrictions than for `mpfr_add_d` apply to `mpfr_d_sub` and `mpfr_sub_d`.

Function: int mpfr_mul (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_d (mpfr_t rop, mpfr_t op1, double op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mpfr_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 zeros, 0 is considered positive). The same restrictions than for `mpfr_add_d` apply to `mpfr_mul_d`.

Function: int mpfr_sqr (mpfr_t rop, mpfr_t op, mpfr_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, mpfr_rnd_t rnd)
Function: int mpfr_ui_div (mpfr_t rop, unsigned long int op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_div_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_si_div (mpfr_t rop, long int op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_div_si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_rnd_t rnd)
Function: int mpfr_d_div (mpfr_t rop, double op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_div_d (mpfr_t rop, mpfr_t op1, double op2, mpfr_rnd_t rnd)
Function: int mpfr_div_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mpfr_rnd_t rnd)
Function: int mpfr_div_q (mpfr_t rop, mpfr_t op1, mpq_t op2, mpfr_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 zeros, 0 is considered positive). The same restrictions than for `mpfr_add_d` apply to `mpfr_d_div` and `mpfr_div_d`.

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

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

Function: int mpfr_rec_sqrt (mpfr_t rop, mpfr_t op, mpfr_rnd_t rnd)

  Set rop to the reciprocal square root of op rounded in the direction rnd. Set rop to +Inf if op is ±0, +0 if op is +Inf, and NaN if op is negative. Warning! Therefore the result on −0 is different from the one of the rSqrt function recommended by the IEEE 754-2008 standard (Section 9.2.1), which is −Inf instead of +Inf.

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

  Set rop to the cubic root (resp. the kth root) of op rounded in the direction rnd. For k odd (resp. even) and op negative (including −Inf), set rop to 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, mpfr_rnd_t rnd)
Function: int mpfr_pow_ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_pow_si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_rnd_t rnd)
Function: int mpfr_pow_z (mpfr_t rop, mpfr_t op1, mpz_t op2, mpfr_rnd_t rnd)
Function: int mpfr_ui_pow_ui (mpfr_t rop, unsigned long int op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_ui_pow (mpfr_t rop, unsigned long int op1, mpfr_t op2, mpfr_rnd_t rnd)

  Set rop to op1 raised to op2, rounded in the direction rnd. Special values are handled as described in the ISO C99 and IEEE 754-2008 standards for the `pow` function:

  - `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, ±0)` returns 1 for any x, 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, mpfr_rnd_t rnd)
Function: int mpfr_abs (mpfr_t rop, mpfr_t op, mpfr_rnd_t rnd)

  Set rop to -op and the absolute value of op respectively, rounded in the direction rnd. Just changes or adjusts the sign if rop and op are the same variable, otherwise a rounding might occur if the precision of rop is less than that of op.

Function: int mpfr_dim (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_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, +0 if op1 <= op2, and NaN if op1 or op2 is NaN.

Function: int mpfr_mul_2ui (mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
Function: int mpfr_mul_2si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_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, mpfr_rnd_t rnd)
Function: int mpfr_div_2si (mpfr_t rop, mpfr_t op1, long int op2, mpfr_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.