MPFR

Defined in mpfr-fix@0.4.0

Provides arbitrary-precision floating-point type MPFR and related functions.

This is a wrapper for the GNU MPFR (Multiple Precision Floating-Point Reliable) Library.

Values

namespace MPFR

c_SIZE_OF_MPFR

Type: Std::FFI::CInt

Size of __mpfr_struct. On 64-bit systems, this is typically 32 bytes.

namespace MPFR::MPFR

abs

Type: MPFR::MPFR -> MPFR::MPFR

Absolute value of an MPFR number (exact operation).

Parameters

x: The number to take absolute value of.

acos

Type: MPFR::MPFR -> MPFR::MPFR

Arccosine function.

Parameters

x: The value (must be in [-1, 1]).

acosh

Type: MPFR::MPFR -> MPFR::MPFR

Inverse hyperbolic cosine function.

Parameters

x: The value (must be >= 1).

add

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Add two MPFR numbers. Uses RNDN rounding and precision is the maximum of the two operands.

Parameters

lhs: The left-hand side operand.
rhs: The right-hand side operand.

agm

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Arithmetic-geometric mean of two MPFR numbers.

Parameters

x: The first number.
y: The second number.

ai

Type: MPFR::MPFR -> MPFR::MPFR

Airy function Ai(x).

Parameters

x: The value.

asin

Type: MPFR::MPFR -> MPFR::MPFR

Arcsine function.

Parameters

x: The value (must be in [-1, 1]).

asinh

Type: MPFR::MPFR -> MPFR::MPFR

Inverse hyperbolic sine function.

Parameters

x: The value.

atan

Type: MPFR::MPFR -> MPFR::MPFR

Arctangent function.

Parameters

x: The value.

atan2

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Two-argument arctangent function (atan2).

Parameters

y: The y coordinate.
x: The x coordinate.

atanh

Type: MPFR::MPFR -> MPFR::MPFR

Inverse hyperbolic tangent function.

Parameters

x: The value (must be in (-1, 1)).

beta

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Beta function: B(x, y) = Γ(x)Γ(y)/Γ(x+y).

Parameters

x: The first parameter.
y: The second parameter.

cbrt

Type: MPFR::MPFR -> MPFR::MPFR

Cube root of an MPFR number.

Parameters

x: The number to take cube root of.

ceil

Type: MPFR::MPFR -> MPFR::MPFR

Round to the next higher integer.

Parameters

x: The number to round up.

cmp

Type: MPFR::MPFR -> MPFR::MPFR -> Std::I64

Compare two MPFR numbers. Returns negative if lhs < rhs, zero if lhs == rhs, positive if lhs > rhs.

Parameters

lhs: The left-hand side number.
rhs: The right-hand side number.

const_catalan

Type: MPFR::Precision -> MPFR::MPFR

Mathematical constant Catalan's constant (0.915...).

Parameters

prec: The precision in bits.

const_euler

Type: MPFR::Precision -> MPFR::MPFR

Mathematical constant Euler's constant (0.577...).

Parameters

prec: The precision in bits.

const_log2

Type: MPFR::Precision -> MPFR::MPFR

Mathematical constant log(2).

Parameters

prec: The precision in bits.

const_pi

Type: MPFR::Precision -> MPFR::MPFR

Mathematical constant Pi.

Parameters

prec: The precision in bits.

copysign

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Copy the sign of y to x.

Parameters

x: The number to copy magnitude from.
y: The number to copy sign from.

cos

Type: MPFR::MPFR -> MPFR::MPFR

Cosine function.

Parameters

x: The angle in radians.

cosh

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic cosine function.

Parameters

x: The value.

cot

Type: MPFR::MPFR -> MPFR::MPFR

Cotangent function: cot(x) = 1/tan(x).

Parameters

x: The angle in radians.

coth

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic cotangent function: coth(x) = 1/tanh(x).

Parameters

x: The value.

csc

Type: MPFR::MPFR -> MPFR::MPFR

Cosecant function: csc(x) = 1/sin(x).

Parameters

x: The angle in radians.

csch

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic cosecant function: csch(x) = 1/sinh(x).

Parameters

x: The value.

digamma

Type: MPFR::MPFR -> MPFR::MPFR

Digamma function (psi function): ψ(x) = Γ'(x)/Γ(x).

Parameters

x: The value.

div

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Divide two MPFR numbers. Uses RNDN rounding and precision is the maximum of the two operands.

Parameters

lhs: The left-hand side operand (dividend).
rhs: The right-hand side operand (divisor).

div_2si

Type: Std::I64 -> MPFR::MPFR -> MPFR::MPFR

Divide by 2^n where n can be negative (efficient bit shift).

Parameters

n: The exponent (signed).
x: The number to divide.

div_2ui

Type: Std::U64 -> MPFR::MPFR -> MPFR::MPFR

Divide by 2^n (efficient bit shift).

Parameters

n: The exponent (unsigned).
x: The number to divide.

equal

Type: MPFR::MPFR -> MPFR::MPFR -> Std::Bool

Check if two MPFR numbers are equal.

Parameters

lhs: The left-hand side number.
rhs: The right-hand side number.

erf

Type: MPFR::MPFR -> MPFR::MPFR

Error function.

Parameters

x: The value.

erfc

Type: MPFR::MPFR -> MPFR::MPFR

Complementary error function.

Parameters

x: The value.

exp

Type: MPFR::MPFR -> MPFR::MPFR

Exponential function.

Parameters

x: The number to exponentiate.

exp10

Type: MPFR::MPFR -> MPFR::MPFR

Base-10 exponential function (10^x).

Parameters

x: The exponent.

exp2

Type: MPFR::MPFR -> MPFR::MPFR

Base-2 exponential function (2^x).

Parameters

x: The exponent.

expm1

Type: MPFR::MPFR -> MPFR::MPFR

exp(x) - 1, computed accurately even for small x.

Parameters

x: The number to exponentiate.

fac_ui

Type: Std::U64 -> MPFR::Precision -> MPFR::MPFR

Factorial function: n!

Parameters

n: The non-negative integer to compute factorial of.
prec: The precision in bits.

floor

Type: MPFR::MPFR -> MPFR::MPFR

Round to the next lower integer.

Parameters

x: The number to round down.

fma

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Fused multiply-add: (x * y) + z, computed with a single rounding.

Parameters

x: The first multiplicand.
y: The second multiplicand.
z: The addend.

fmod

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Floating-point remainder: x - n*y where n is the integer quotient x/y rounded toward zero.

Parameters

x: The dividend.
y: The divisor.

gamma

Type: MPFR::MPFR -> MPFR::MPFR

Gamma function.

Parameters

x: The value.

get_f64

Type: MPFR::MPFR -> Std::F64

Convert an MPFR value to F64.

May lose precision if the MPFR value has more precision than F64.

Parameters

x: The MPFR number to convert.

get_prec

Type: MPFR::MPFR -> MPFR::Precision

Get the precision of an MPFR number.

Parameters

x: The number to get precision of.

get_si

Type: MPFR::MPFR -> Std::Option Std::I64

Convert an MPFR value to I64.

Rounds toward zero. Returns none if the value doesn't fit in I64.

Parameters

x: The MPFR number to convert.

get_str

Type: Std::I64 -> Std::I64 -> MPFR::RoundMode -> MPFR::MPFR -> (Std::String, Std::I64)

Convert an MPFR value to a string in a given base with specified number of digits.

Returns a tuple of (mantissa_string, exponent) where the mantissa 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", 1).

If the number is NaN, returns ("@NaN@", 0). If the number is +Inf, returns ("@Inf@", 0). If the number is -Inf, returns ("-@Inf@", 0).

Parameters

base: The base of the string representation (must be in the range [2, 62] or [-36, -2]).
n_digits: Number of significant digits (0 means use get_str_ndigits with the number's precision).
rnd: The rounding mode to use.
num: The MPFR number to convert.

get_str_ndigits

Type: Std::I64 -> MPFR::Precision -> Std::I64

Get the number of digits required to represent an MPFR value in a given base.

This function returns the minimal integer m such that any number of p bits, when output in base b with m digits, can be recovered exactly when read back in base b.

Parameters

base: The base (must be in the range [2, 62]).
prec: The precision in bits.

get_ui

Type: MPFR::MPFR -> Std::Option Std::U64

Convert an MPFR value to U64.

Rounds toward zero. Returns none if the value doesn't fit in U64.

Parameters

x: The MPFR number to convert.

hypot

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Euclidean norm: sqrt(x^2 + y^2), computed without intermediate overflow or underflow.

Parameters

x: The first component.
y: The second component.

inf

Type: MPFR::Precision -> MPFR::MPFR

Create an MPFR value representing positive infinity.

Parameters

prec: The precision in bits.

is_inf

Type: MPFR::MPFR -> Std::Bool

Check if the value is infinite.

Parameters

x: The number to check.

is_nan

Type: MPFR::MPFR -> Std::Bool

Check if the value is NaN.

Parameters

x: The number to check.

is_number

Type: MPFR::MPFR -> Std::Bool

Check if the value is a regular number (not NaN, not Inf).

Parameters

x: The number to check.

is_zero

Type: MPFR::MPFR -> Std::Bool

Check if the value is zero.

Parameters

x: The number to check.

j0

Type: MPFR::MPFR -> MPFR::MPFR

Bessel function of the first kind of order 0.

Parameters

x: The value.

j1

Type: MPFR::MPFR -> MPFR::MPFR

Bessel function of the first kind of order 1.

Parameters

x: The value.

jn

Type: Std::I64 -> MPFR::MPFR -> MPFR::MPFR

Bessel function of the first kind of order n.

Parameters

n: The order.
x: The value.

less

Type: MPFR::MPFR -> MPFR::MPFR -> Std::Bool

Check if lhs < rhs.

Parameters

lhs: The left-hand side number.
rhs: The right-hand side number.

lesseq

Type: MPFR::MPFR -> MPFR::MPFR -> Std::Bool

Check if lhs <= rhs.

Parameters

lhs: The left-hand side number.
rhs: The right-hand side number.

lngamma

Type: MPFR::MPFR -> MPFR::MPFR

Natural logarithm of the absolute value of the Gamma function.

Parameters

x: The value.

log

Type: MPFR::MPFR -> MPFR::MPFR

Natural logarithm.

Parameters

x: The number to take logarithm of.

log10

Type: MPFR::MPFR -> MPFR::MPFR

Base-10 logarithm.

Parameters

x: The number to take logarithm of.

log1p

Type: MPFR::MPFR -> MPFR::MPFR

log(1 + x), computed accurately even for small x.

Parameters

x: The number to add to 1 before taking logarithm.

log2

Type: MPFR::MPFR -> MPFR::MPFR

Base-2 logarithm.

Parameters

x: The number to take logarithm of.

max

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Return the maximum of two MPFR numbers.

Parameters

x: The first number.
y: The second number.

min

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Return the minimum of two MPFR numbers.

Parameters

x: The first number.
y: The second number.

mpfr

Type: MPFR::Precision -> Std::F64 -> MPFR::MPFR

Create an MPFR value from an F64 with specified precision.

Parameters

prec: The precision in bits.
val: The F64 value to convert.

mpfr_i

Type: MPFR::Precision -> Std::I64 -> MPFR::MPFR

Create an MPFR value from an I64 with specified precision.

Parameters

prec: The precision in bits.
val: The I64 value to convert.

mpfr_str

Type: MPFR::Precision -> Std::String -> Std::I64 -> Std::Option MPFR::MPFR

Create an MPFR value from a string with specified precision and base.

Parameters

prec: The precision in bits.
str: The string representation of the number.
base: The base of the string representation (2 to 62, or 0 for auto-detection).

mpfr_ui

Type: MPFR::Precision -> Std::U64 -> MPFR::MPFR

Create an MPFR value from a U64 with specified precision.

Parameters

prec: The precision in bits.
val: The U64 value to convert.

mul

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Multiply two MPFR numbers. Uses RNDN rounding and precision is the maximum of the two operands.

Parameters

lhs: The left-hand side operand.
rhs: The right-hand side operand.

mul_2si

Type: Std::I64 -> MPFR::MPFR -> MPFR::MPFR

Multiply by 2^n where n can be negative (efficient bit shift).

Parameters

n: The exponent (signed).
x: The number to multiply.

mul_2ui

Type: Std::U64 -> MPFR::MPFR -> MPFR::MPFR

Multiply by 2^n (efficient bit shift).

Parameters

n: The exponent (unsigned).
x: The number to multiply.

nan

Type: MPFR::Precision -> MPFR::MPFR

Create an MPFR value representing NaN (Not a Number).

Parameters

prec: The precision in bits.

neg

Type: MPFR::MPFR -> MPFR::MPFR

Negate an MPFR number (exact operation).

Parameters

x: The number to negate.

neg_inf

Type: MPFR::Precision -> MPFR::MPFR

Create an MPFR value representing negative infinity.

Parameters

prec: The precision in bits.

nextabove

Type: MPFR::MPFR -> MPFR::MPFR

Return the next floating-point number toward +infinity.

Parameters

x: The starting number.

nextbelow

Type: MPFR::MPFR -> MPFR::MPFR

Return the next floating-point number toward -infinity.

Parameters

x: The starting number.

nexttoward

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Return the next floating-point number in the direction of y.

Parameters

x: The starting number.
direction: The direction to move toward.

pow

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Power function: base^exponent.

Parameters

base: The base.
exponent: The exponent.

pow_si

Type: Std::I64 -> MPFR::MPFR -> MPFR::MPFR

Power function with signed integer exponent.

Parameters

exponent: The signed integer exponent.
base: The base.

pow_ui

Type: Std::U64 -> MPFR::MPFR -> MPFR::MPFR

Power function with unsigned integer exponent.

Parameters

exponent: The unsigned integer exponent.
base: The base.

rec_sqrt

Type: MPFR::MPFR -> MPFR::MPFR

Reciprocal square root of an MPFR number.

Parameters

x: The number to take reciprocal square root of (1/sqrt(x)).

remainder

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

IEEE remainder: x - n*y where n is the integer quotient x/y rounded to nearest.

Parameters

x: The dividend.
y: The divisor.

rootn_ui

Type: Std::U64 -> MPFR::MPFR -> MPFR::MPFR

N-th root of an MPFR number.

Parameters

n: The degree of the root (must be > 0).
x: The number to take n-th root of.

round

Type: MPFR::MPFR -> MPFR::MPFR

Round to the nearest integer, rounding halfway cases away from zero.

Parameters

x: The number to round.

sec

Type: MPFR::MPFR -> MPFR::MPFR

Secant function: sec(x) = 1/cos(x).

Parameters

x: The angle in radians.

sech

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic secant function: sech(x) = 1/cosh(x).

Parameters

x: The value.

setsign

Type: Std::Bool -> MPFR::MPFR -> MPFR::MPFR

Set the sign of x according to the boolean s (false = positive, true = negative).

Parameters

sign: The sign to set (false for positive, true for negative).
x: The number to set sign of.

sgn

Type: MPFR::MPFR -> Std::I64

Get the sign of a number. Returns negative if num < 0, zero if num == 0, positive if num > 0.

Parameters

x: The number to get sign of.

signbit

Type: MPFR::MPFR -> Std::Bool

Test if the sign bit is set (even for NaN and zero).

Parameters

x: The number to check sign bit of.

sin

Type: MPFR::MPFR -> MPFR::MPFR

Sine function.

Parameters

x: The angle in radians.

sinh

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic sine function.

Parameters

x: The value.

sqr

Type: MPFR::MPFR -> MPFR::MPFR

Square an MPFR number.

Parameters

x: The number to square.

sqrt

Type: MPFR::MPFR -> MPFR::MPFR

Square root of an MPFR number.

Parameters

x: The number to take square root of.

sub

Type: MPFR::MPFR -> MPFR::MPFR -> MPFR::MPFR

Subtract two MPFR numbers. Uses RNDN rounding and precision is the maximum of the two operands.

Parameters

lhs: The left-hand side operand.
rhs: The right-hand side operand.

tan

Type: MPFR::MPFR -> MPFR::MPFR

Tangent function.

Parameters

x: The angle in radians.

tanh

Type: MPFR::MPFR -> MPFR::MPFR

Hyperbolic tangent function.

Parameters

x: The value.

to_string_digits

Type: Std::I64 -> MPFR::MPFR -> Std::String

Convert an MPFR value to string with specified significant digits.

The output format is standard decimal notation with exactly digits significant digits (e.g., "3.14", "-0.0012346").

Parameters

digits: The number of significant digits.
num: The MPFR number to convert.

to_string_exp

Type: MPFR::MPFR -> Std::String

Convert an MPFR value to exponential form string.

The output format is "d.dddd...e±exp" (e.g., "3.14159e+0", "-1.23456e-10"). The number of significant digits is determined by the number's precision.

Parameters

num: The MPFR number to convert.

to_string_exp_digits

Type: Std::I64 -> MPFR::MPFR -> Std::String

Convert an MPFR value to exponential form string with specified significant digits.

The output format is "d.ddd...e±exp" with exactly digits significant digits (e.g., "3.14e+0", "-1.23e+2").

Parameters

digits: The number of significant digits.
num: The MPFR number to convert.

to_string_exp_precision

Type: Std::I64 -> MPFR::MPFR -> Std::String

Convert an MPFR value to exponential form string with specified precision.

The output format is "d.{prec digits}e±exp" where the number of digits after the decimal point is exactly prec.

Parameters

prec: The number of digits after the decimal point.
num: The MPFR number to convert.

to_string_precision

Type: Std::I64 -> MPFR::MPFR -> Std::String

Convert an MPFR value to string with specified precision (digits after decimal point).

The output format is standard decimal notation with exactly prec digits after the decimal point (e.g., "3.14", "-123.456").

Parameters

prec: The number of digits after the decimal point.
num: The MPFR number to convert.

trunc

Type: MPFR::MPFR -> MPFR::MPFR

Round to the next integer toward zero.

Parameters

x: The number to truncate.

y0

Type: MPFR::MPFR -> MPFR::MPFR

Bessel function of the second kind of order 0.

Parameters

x: The value.

y1

Type: MPFR::MPFR -> MPFR::MPFR

Bessel function of the second kind of order 1.

Parameters

x: The value.

yn

Type: Std::I64 -> MPFR::MPFR -> MPFR::MPFR

Bessel function of the second kind of order n.

Parameters

n: The order.
x: The value.

zero

Type: MPFR::Precision -> MPFR::MPFR

Create an MPFR value representing zero.

Parameters

prec: The precision in bits.

zeta

Type: MPFR::MPFR -> MPFR::MPFR

Riemann zeta function.

Parameters

x: The value.

zeta_ui

Type: Std::U64 -> MPFR::Precision -> MPFR::MPFR

Riemann zeta function for unsigned integer argument.

Parameters

n: The unsigned integer argument.
prec: The precision in bits.

namespace MPFR::RoundMode

to_c_rnd

Type: MPFR::RoundMode -> Std::FFI::CInt

Convert RoundMode to C integer constant.

Types and aliases

namespace MPFR

MPFR

Defined as: type MPFR = unbox struct { ...fields... }

Arbitrary-precision floating-point number type.

field `_0`

Type: Std::FFI::Destructor MPFR::MPFRHandle

MPFRHandle

Defined as: type MPFRHandle = Std::Ptr

A pointer to struct __mpfr_struct.

Precision

Defined as: type Precision = Std::I64

Precision type for MPFR numbers (in bits).

RoundMode

Defined as: type RoundMode = unbox union { ...variants... }

Rounding mode for MPFR operations.

variant `rndn`

Type: ()

variant `rndz`

Type: ()

variant `rndu`

Type: ()

variant `rndd`

Type: ()

variant `rnda`

Type: ()