mag.h

Initialise x to zero, respectively to a copy of y.

Frees the memory used by x. Only an exponent too large for an inline fmpz uses heap memory.

Swaps x and y without copying.

Allocate a vector of n entries initialised to zero, and free such a vector.

Returns the number of bytes allocated on the heap by x, excluding sizeof(mag_struct).

Set res to 0, 1 and +\infty respectively.

Return whether x is zero or infinite, zero, infinite, and finite respectively. Since there is no NaN, mag_is_finite is the negation of mag_is_inf.

Sets res to x. Exact.

Set res to an upper bound for |x|. The result can be larger than |x| even when |x| is representable: mag_set_d always adds one unit in the 30th bit. A NaN double gives +\infty.

Set res to a lower bound for |x|. A NaN double gives 0.

Set res to an upper bound for |x| \cdot 2^y.

Set res to a lower bound for |x| \cdot 2^y.

Returns a double upper bound for x. The result is exact when the exponent of x lies in [-1000, 1000]; outside this range it is 2^{-1000} for small x and +\infty for large x.

Returns an approximation of \log_2 x, clamped to [\mathrm{COEFF\_MIN}, \mathrm{COEFF\_MAX}], for estimating magnitudes. It is not a rigorous bound.

Set res to the exact value of x, to \lceil x \rceil, and to \lfloor x \rfloor respectively.

Returns whether x and y are equal.

Return a negative number, zero or a positive number according as x is less than, equal to or greater than y, respectively 2^e. Both comparisons are exact and handle infinity.

Set res to the smaller, respectively the larger, of x and y. Exact.

Set res to an upper bound for x + y.

Set res to a lower bound for x + y.

Set res to an upper bound for x + 2^e, respectively x + y 2^e.

Set res to an upper, respectively lower, bound for \max(x - y, 0).

Set res to x \cdot 2^y. Exact.

Set res to an upper bound for xy (with |y| for the integer versions). 0 \cdot \infty gives +\infty.

Set res to a lower bound for xy. 0 \cdot \infty gives 0.

Sets z to an upper bound for z + xy.

Set res to an upper bound for x / y. Division by zero, and \infty/\infty, give +\infty.

Sets res to a lower bound for x / y. Division by zero, and \infty/\infty, give 0.

Set res to an upper, respectively lower, bound for 1 / x. The upper bound for 1/0 is +\infty; the lower bound for 1/0 is 0, which is valid but weak.

Set res to an upper bound for x^e. A negative exponent in mag_pow_fmpz is handled as (1/x)^{-e}.

Set res to a lower bound for x^e.

Set res to an upper, respectively lower, bound for \sqrt{x}.

Set res to an upper, respectively lower, bound for 1/\sqrt{x}, with 1/\sqrt{0} = +\infty.

Sets res to an upper bound for \sqrt{x^2 + y^2}.

Sets res to an upper bound for x^{1/n}. For n = 0 the result is +\infty.

Set res to an upper, respectively lower, bound for \log(\max(1, x)).

Set res to an upper, respectively lower, bound for -\log(\min(1, x)), which is |\log x| for x \le 1. The value for x = 0 is +\infty.

Sets res to an upper bound for \log n. For n = 0 the result is +\infty.

Sets res to an upper bound for \log(1 + x), with small relative error also when x is small.

Set res to an upper, respectively lower, bound for e^x.

Set res to an upper, respectively lower, bound for e^{-x}.

Sets res to an upper bound for e^x - 1, with small relative error also when x is small.

Set res to an upper or lower bound for \cosh x or \sinh x.

Set res to an upper, respectively lower, bound for \operatorname{atan} x.

Set res to an upper, respectively lower, bound for \pi.

Return an upper, respectively lower, bound for \log x as a double, for x > 0 (with \log 0 = -\infty).

Set res to an upper bound for n!, respectively 1/n!.

Sets res to an upper bound for the binomial coefficient \binom{n}{k}.

Sets res to an upper bound for (1 + 1/m)^n.

Sets res to an upper bound for |B_n| / n!, where B_n is a Bernoulli number.

Sets res to an upper bound for \sum_{k=N}^{\infty} x^k = x^N / (1 - x), which is +\infty if x \ge 1.

Sets res to an upper bound for \sum_{k=N}^{\infty} x^k / k!.

Sets res to an upper bound for

Sets res to an upper bound for \zeta(s, a) = \sum_{k=0}^{\infty} (k+a)^{-s}.

Print the exact value of x as (man * 2^exp), with the mantissa as an integer, to standard output or to file. Zero and infinity are printed as (0) and (inf).

Print x in decimal with d significant digits, to standard output or to file. The decimal conversion is not rigorous.

mag_dump_str returns a string, to be freed with flint_free, holding a binary representation of x that mag_load_str reads back exactly. mag_load_str returns nonzero if str is not in this format.

Write x to stream in the format of mag_dump_str, and read it back. Both return nonzero on failure. The data is delimited by whitespace or end of file, so several values written in sequence must be separated by whitespace.

Set res to a random finite value with an exponent of up to expbits bits. mag_randtest_special also produces 0 and +\infty sometimes.

Initialise x to a copy of y, set res to zero, and test whether x is zero.

Set res to an upper bound for xy, z to an upper bound for z + xy, and res to an upper bound for x + 2^e.

Sets res to x \cdot 2^e. Exact.