mlmpfr 4.2.0 · OCaml Package

OCaml bindings for MPFR.

A mpfr_float is an immutable data structure that contains a mpfr_t number, as well as an optional ternary value, as provided by (and described in) the MPFR library.

A few distinctions are made from the original C library:

the mpfr_ prefix is ommited for all functions;
mpfr_init* and mpfr_set* functions are not provided in order to implement these bindings with respect to the functional paradigm (i.e. immutability). Consequently, mpfr_clear* functions are not provided too, and so, the garbage collector is in charge of memory management;
functions managing the following types are not supported: unsigned long int, uintmax_t, intmax_t, float, long double, __float128, _Decimal64, _Decimal128, mpz_t, mpq_t, and mpf_t. Except for mpfr_sqrt_ui and mpfr_fac_ui which are partially supported on the range of the positive values of an OCaml signed integer. In fact, only the OCaml native types (int, float, and string) are supported, assuming that a float is a double-precision floating-point number and an int is a 64-bits signed integer. Thus, all functions named with *_ui* or *_d* are renamed here with *_int* or *_float*, respectively;
bindings to functions mpfr_*printf, mpfr_*random*, mpfr_get_patches, mpfr_buildopt_*, and, macros MPFR_VERSION*, mpfr_round_nearest_away are not implemented.

In the sequel, if not provided, optional parameters prec and rnd are set to MPFR's defaults precision and rounding mode. Functions which take a precision, or a base as a parameter raise exceptions. See Precision_range and Base_range.

Some of the comments below are derived from the MPFR documentation itself. Nevertheless, please refer to the original documentation for further explanations.

exception Precision_range of int

Raised if precision is not included in [Mlmpfr.mpfr_prec_min; Mlmpfr.mpfr_prec_max].

exception Base_range of int

Raised if base is not included in [2;64], or 0 (automatic base detection).

exception Error of string

Raised if mlmpfr fails to perfom some internal mpfr_t copies.

exception Invalid_integer_input of int

Raised if mlmpfr tries to call a mpfr_*_ui function with a negative integer.

type sign =

| Positive
| Negative

type mpfr_t

Binding to C MPFR mpfr_t type.

type ternary =

| Correct_Rounding
| Greater
| Lower

Associated to an mpfr_t value, a ternary value indicates if it was correctly rounded.

type mpfr_float = mpfr_t * ternary option

type mpfr_rnd_t =

| To_Nearest
| Toward_Zero
| Toward_Plus_Infinity
| Toward_Minus_Infinity
| Away_From_Zero
| Faithful

Rounding modes.

type mpfr_flags_t =

| Underflow
| Overflow
| Nan
| Inexact
| Erange
| Divby0
| All

Flags as described here.

val mpfr_prec_min : int

Minimum allowed precision.

val mpfr_prec_max : int

Maximum allowed precision.

Initialization

val set_default_prec : int -> unit

Mlmpfr.set_default_prec p modifies the default precision to be exactly p bits. The precision of a variable means the number of bits used to store its significand. All subsequent calls to any functions will use this precision by default, but previously initialized variables are unaffected. The default precision is set to 53 bits initially.

val get_default_prec : unit -> int

Return the current default MPFR precision in bits.

val get_prec : mpfr_float -> int

Mlmpfr.get_prec x returns the precision of x. The corresponding Mlmpfr.set_prec x prec function is not allowed, use Mlmpfr.make_from_mpfr ~prec:prec x instead.

Assignment

val make_from_mpfr : ?prec:int -> ?rnd:mpfr_rnd_t -> mpfr_float -> mpfr_float

Return a fresh mpfr_float number of precision ~prec (optional), made from another mpfr_float number, in direction ~rnd (optional).

val make_from_int : ?prec:int -> ?rnd:mpfr_rnd_t -> int -> mpfr_float

Return a fresh mpfr_float number of precision ~prec (optional), made from an int, in direction ~rnd (optional).

val make_from_float : ?prec:int -> ?rnd:mpfr_rnd_t -> float -> mpfr_float

Return a fresh mpfr_float number of precision ~prec (optional), made from a float, in direction ~rnd (optional).

val make_from_str : 
  ?prec:int ->
  ?rnd:mpfr_rnd_t ->
  ?base:int ->
  string ->
  mpfr_float

Mlmpfr.make_from_str s ~base:b ~prec:p ~rnd:r returns a fresh mpfr_float of precision p from the string value s in base b, rounded in direction r (p, b, and r are optional).

val make_nan : ?prec:int -> unit -> mpfr_float

Return a NaN with precision ~prec if provided, otherwise default precision is used.

val make_inf : ?prec:int -> sign -> mpfr_float

Return a infinity with precision ~prec if provided, otherwise default precision is used.

val make_zero : ?prec:int -> sign -> mpfr_float

Return a zero with precision ~prec if provided, otherwise default precision is used.

Conversion

If not provided, default values for rnd and prec are the defaults MPFR precision and rounding mode internal settings (use Mlmpfr.set_default_rounding_mode or Mlmpfr.set_default_prec to modify them).

val get_float : ?rnd:mpfr_rnd_t -> mpfr_float -> float

Conversion to a float.

val get_int : ?rnd:mpfr_rnd_t -> mpfr_float -> int

Conversion to an int.

val get_float_2exp : ?rnd:mpfr_rnd_t -> mpfr_float -> float * int

Mlmpfr.get_float_2exp x returns (n, exp) such that 0.5 <= |n| < 1 and n times 2 raised to exp equals x rounded to float precision.

val get_mpfr_2exp : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float * int

Mlmpfr.get_mpfr_2exp x returns (n, exp) such that 0.5 <= |n| < 1 and n times 2 raised to exp equals x rounded to ~prec precision.

val get_str : 
  ?rnd:mpfr_rnd_t ->
  ?base:int ->
  ?size:int ->
  mpfr_float ->
  string * string

Mlmpfr.get_str ~rnd:r ~base:b ~size:s x converts x to a tuple (frac, exp), where frac is a fraction (a string of digits in base b) with rounding to direction r, and exp is an exponent. s is the number of significand digits output in frac. If s 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 x. Decimal is the default base and default size is zero.

val get_str_ndigits : int -> int -> int

Mlmpfr.get_str_ndigits b p returns the minimal integer m such that any number of p bits, when output with m digits in radix b with rounding to nearest, can be recovered exactly when read again, still with rounding to nearest.

val get_formatted_str : 
  ?rnd:mpfr_rnd_t ->
  ?base:int ->
  ?size:int ->
  ?ktz:bool ->
  mpfr_float ->
  string

Mlmpfr.get_formatted_str is identical to Mlmpfr.get_str except that it returns a full-formatted string (equivalent to mpfr_printf("%Re", x)). Set ktz to false to remove trailing zeroes.

val fits_int_p : ?rnd:mpfr_rnd_t -> mpfr_float -> bool

Return true if the mpfr_float would fit in a int, when rounded to an integer in the direction ~rnd.

Arithmetic

val add : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Addition of two mpfr_float.

val add_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Addition of a mpfr_float and an int.

val add_float : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  float ->
  mpfr_float

Addition of a mpfr_float and a float.

val sub : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Subtraction of two mpfr_float.

val sub_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Subtraction of a mpfr_float and an int.

val int_sub : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float -> mpfr_float

Subtraction of an int and a mpfr_float.

val sub_float : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  float ->
  mpfr_float

Addition of a mpfr_float and a float.

val float_sub : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  float ->
  mpfr_float ->
  mpfr_float

Subtraction of a float and an mpfr_float.

val mul : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Multiplication of two mpfr_float.

val mul_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Multiplication of a mpfr_float and an int.

val mul_float : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  float ->
  mpfr_float

Multiplication of an int and a mpfr_float.

val div : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Division of two mpfr_float.

val div_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Division of a mpfr_float by an int.

val int_div : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float -> mpfr_float

Division of an int by a mpfr_float.

val div_float : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  float ->
  mpfr_float

Division of an int by a mpfr_float.

val float_div : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  float ->
  mpfr_float ->
  mpfr_float

Division of a float by a mpfr_float.

val sqrt : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the square root of a mpfr_float number.

val sqrt_int : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float

Return the square root of an int. Return nan if negative.

val rec_sqrt : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the reciprocal square root of an mpfr_float number.

val cbrt : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Returns the cubic root of an mpfr_float number.

val rootn_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.rootn_int x k returns the k-th root of x.

val neg : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Compute the negation of an mpfr_float number.

val abs : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Compute the absolute value of an mpfr_float number.

val dim : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.dim x y returs the positive difference of x and y, i.e., x - y if x > y, +0 if x <= y, and NaN if x or y is NaN.

val mul_2int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.mul_2int x y returns x times 2 raised to y.

val div_2int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.div_2int x y returns x divided by 2 raised to y.

val fac_int : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float

Return the factorial of an int. Return NaN if input is negative.

val fma : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the fused multiply and add of mpfr_float numbers. Mlmpfr.fma x y z retuns xy+z.

val fms : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the fused multiply and sub of mpfr_float numbers. Mlmpfr.fms x y z retuns xy-z.

val fmma : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.fmma x y z t retuns xy+zt. In case the computation of xy overflows or underflows (or that of zt), the result is computed as if the two intermediate products were computed with rounding toward zero.

val fmms : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.fmms x y z t retuns xy-zt. See Mlmpfr.fmma for further comments

val hypot : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the Euclidean norm of a mpfr_float number.

val sum : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float list -> mpfr_float

Return the sum of all the elements of the list.

val dot : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float list ->
  mpfr_float list ->
  mpfr_float

Return the dot product of the lists (commun size of the list is determined by the size of the smallest one).

Comparison

Operators =, <>, >, <, >=, and <= are supported. They are based on mpfr_cmp.

val cmp : mpfr_float -> mpfr_float -> int

Mlmpfr.cmp a b returns a positive value if a > b, zero if a = b, and a negative value if a < b. If one of the operands is NaN, set the Erange flag and return zero.

val cmp_int : mpfr_float -> int -> int

Mlmpfr.cmp_int a b compares a and b. Similar as above.

val cmp_float : mpfr_float -> float -> int

Mlmpfr.cmp_float a b compares a and b. Similar as above.

val cmp_int_2exp : mpfr_float -> int -> int -> int

Mlmpfr.cmp_int_2exp a b e compares a and b multiplied by two to the power e. Similar as above.

val cmpabs : mpfr_float -> mpfr_float -> int

Mlmpfr.cmpabs a b returns a positive value if |a| > |b|, zero if |a| = |b|, and a negative value if |a| < |b|.

val cmpabs_int : mpfr_float -> int -> int

Mlmpfr.cmpabs_int a b compares a and b. Similar as above.

val nan_p : mpfr_float -> bool

Its a NaN.

val inf_p : mpfr_float -> bool

Its an infinity.

val number_p : mpfr_float -> bool

Its a ordinary number (i.e., neither NaN nor an infinity).

val zero_p : mpfr_float -> bool

It's a zero.

val regular_p : mpfr_float -> bool

Its a regular number (i.e., neither NaN, nor an infinity nor zero).

val sgn : mpfr_float -> sign

Return the sign of a mpfr_float number.

val greater_p : mpfr_float -> mpfr_float -> bool

Operator > in MPFR syntax style.

val greaterequal_p : mpfr_float -> mpfr_float -> bool

Operator >=in MPFR syntax style.

val less_p : mpfr_float -> mpfr_float -> bool

Operator < in MPFR syntax style.

val lessequal_p : mpfr_float -> mpfr_float -> bool

Operator <= in MPFR syntax style.

val equal_p : mpfr_float -> mpfr_float -> bool

Operator = in MPFR syntax style.

val lessgreater_p : mpfr_float -> mpfr_float -> bool

Operator <> in MPFR syntax style.

val unordered_p : mpfr_float -> mpfr_float -> bool

Return true if the operands are comparable (i.e. one of them is a NaN), false otherwise.

val total_order_p : mpfr_float -> mpfr_float -> bool

This function implements the totalOrder predicate from IEEE 754-2008.

Transcendental

val log : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the natural logarithm of a mpfr_float.

val log_int : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float

Return the natural logarithm of an int.

val log2 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the log2 of a mpfr_float.

val log10 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the log10 of a mpfr_float.

val log1p : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the logarithm of one plus a mpfr_float.

val exp : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the exponential of a mpfr_float.

val exp2 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the 2 power of a mpfr_float.

val exp10 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the 10 power of a mpfr_float.

val expm1 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the exponential of a mpfr_float followed by a subtraction by one.

val pow : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.pow x y returns x raised to y.

val pow_int : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.pow_int x y returns x raised to y.

TODO: int_pow_int

TODO: int_pow

val cos : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the cosine of a mpfr_float.

val sin : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the sine of a mpfr_float.

val tan : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the tangent of a mpfr_float.

val cosu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.cosu x u returns the cosine of a x multiplied by Pi and divided by u.

val sinu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.sinu x u returns the cosine of a x multiplied by Pi and divided by u.

val tanu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.tanu x u returns the cosine of a x multiplied by Pi and divided by u.

val cospi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the cosine of a mpfr_float multiplied by Pi.

val sinpi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the sine of a mpfr_float multiplied by Pi.

val tanpi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the tangent of a mpfr_float multiplied by Pi.

val sin_cos : 
  ?rnd:mpfr_rnd_t ->
  ?sprec:int ->
  ?cprec:int ->
  mpfr_float ->
  mpfr_float * mpfr_float

Return simultaneously the sine and cosine of an mpfr_float number.

val sec : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the secant of a mpfr_float.

val csc : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the cosecant of a mpfr_float.

val cot : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the cotangent of a mpfr_float.

val acos : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-cosine of a mpfr_float.

val asin : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-sine of a mpfr_float.

val atan : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-tangent of a mpfr_float.

val acosu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.acosu x u returns a mpfr_float set to a multiplied by u and divided by 2 Pi, where a is the arc-cosine of x

val asinu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.acosu x u returns a mpfr_float set to a multiplied by u and divided by 2 Pi, where a is the arc-sine of x

val atanu : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> int -> mpfr_float

Mlmpfr.acosu x u returns a mpfr_float set to a multiplied by u and divided by 2 Pi, where a is the arc-tangent of x

val acospi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-cosine of a mpfr_float divided by Pi.

val asinpi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-sine of a mpfr_float divided by Pi.

val atanpi : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the arc-tangent of a mpfr_float divided by Pi.

val atan2 : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.atan2 x y returns the arc-tangent2 of x and y.

val atan2u : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  int ->
  mpfr_float

Mlmpfr.atan2u x y u returns the arc-tangent2 of x and y, multiplied by u and divided by 2 Pi.

val atan2pi : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.atan2pi x y is the same as Mlmpfr.atan2u x y u with u = 2.

val cosh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperbolic cosine of a mpfr_float.

val sinh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperbolic sine of a mpfr_float.

val tanh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperbolic tangent of a mpfr_float.

val sinh_cosh : 
  ?rnd:mpfr_rnd_t ->
  ?sprec:int ->
  ?cprec:int ->
  mpfr_float ->
  mpfr_float * mpfr_float

Return simultaneously the sine and cosine of an mpfr_float number.

val sech : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperbolic secant of a mpfr_float.

val csch : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperboloc cosecant of a mpfr_float.

val coth : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the hyperbolic cotangent of a mpfr_float.

val acosh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the inverse hyperbolic cosine of a mpfr_float.

val asinh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the inverse hyperbolic sine of a mpfr_float.

val atanh : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the inverse hyperbolic tangent of a mpfr_float.

val eint : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the exponential integral of a mpfr_float.

val li2 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the real part of the dilogarithm of a mpfr_float.

val gamma : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the Gamma function on a mpfr_float.

val gamma_inc : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.gamma_inc x y returns the incomplete Gamma function on x and y.

val lngamma : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the logarithm of the Gamma function on a mpfr_float.

val lgamma : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float * sign

Return the logarithm of the absolute value of the Gamma function and the sign of the Gamma function on a mpfr_float.

val digamma : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the Digamma (sometimes also called Psi) function on a mpfr_float.

val beta : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.beta op1 op2 returns the Beta function at arguments op1 and op2.

val zeta : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the Riemann Zeta function on a mpfr_float.

val erf : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the error function on a mpfr_float.

val erfc : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the complementary error function on a mpfr_float.

val j0 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the value of the first kind Bessel function of order 0 on a mpfr_float.

val j1 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the value of the first kind Bessel function of order 1 on a mpfr_float.

val jn : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float -> mpfr_float

Mlmpfr.jn n x returns the value of the first kind Bessel function of order n on x. Return NaN if n is negative.

val y0 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the value of the second kind Bessel function of order 0 on a mpfr_float.

val y1 : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the value of the second kind Bessel function of order 1 on a mpfr_float.

val yn : ?rnd:mpfr_rnd_t -> ?prec:int -> int -> mpfr_float -> mpfr_float

Mlmpfr.jn n x returns the value of the second kind Bessel function of order n on x. Return NaN if n is negative.

val agm : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the arithmetic-geometric mean of a mpfr_float number.

val ai : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the value of the Airy function Ai on a mpfr_float number.

val const_log2 : ?rnd:mpfr_rnd_t -> int -> mpfr_float

Return the logarithm of 2.

val const_pi : ?rnd:mpfr_rnd_t -> int -> mpfr_float

Return the value of Pi.

val const_euler : ?rnd:mpfr_rnd_t -> int -> mpfr_float

Return the value of Euler's constant 0.577...

val const_catalan : ?rnd:mpfr_rnd_t -> int -> mpfr_float

Return the value of Catalan's constant 0.915...

Input and Output

The two following functions are deprecated. Use Mlmpfr.get_formatted_str and Mlmpfr.make_from_str.

val out_str : out_channel -> int -> int -> mpfr_float -> mpfr_rnd_t -> unit

Mlmpfr.out_str stdout b s x Mlmpfr.To_Nearest outputs x, in base b, to stdout, in the direction Mlmpfr.To_Nearest. The size of the printed output is s digits long. It uses Printf.fprintf and Mlmpfr.get_formatted_string.

val inp_str : in_channel -> int -> int -> mpfr_rnd_t -> mpfr_float

Mlmpfr.inp_str stdin b p Mlmpfr.To_Nearest returns a mpfr_float number of precision p from a string in base b read on stdin. It uses Pervasives.input_line and Mlmpfr.make_from_str.

val fpif_export : out_channel -> mpfr_float -> unit

Mlmpfr.fpif_export chan op exports the number op to the stream chan in a floating-point interchange format. In particular one can export on a 32-bit computer and import on a 64-bit computer, or export on a little-endian computer and import on a big-endian computer. The precision of op and the sign bit of a NaN are stored too.

val fpif_import : in_channel -> mpfr_float

Mlmpfr.fpif_import chan imports a mpfr_float number from the stream chan in a floating-point interchange format (see Mlmpfr.mpfr_fpif_export). Note that the precision of op is set to the one read from the stream, and the sign bit is always retrieved (even for NaN). If the stored precision is zero or greater than Mlmpfr.mpfr_prec_max, the function fails (its ternary value is non-zero) and op is undefined. If the function fails for another reason, op is set to NaN. Ternary value is 0 iff the import was successful.

val rint : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer in the direction ~rnd.

val ceil : ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the next higher or equal representable integer.

val floor : ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the next lower or equal representable integer.

val round : ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer (rounding halfway cases away from zero as in the roundTiesToAway mode of IEEE 754-2008).

val roundeven : ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer (rounding halfway cases athe even-rounding rule).

val trunc : ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer toward zero.

val rint_ceil : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the next higher or equal representable integer. If the result is not representable, it is rounded in the direction ~rnd

val rint_floor : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the next lower or equal representable integer. If the result is not representable, it is rounded in the direction ~rnd

val rint_round : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer (rounding halfway cases away from zero). If the result is not representable, it is rounded in the direction ~rnd

val rint_roundeven : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the nearest representable integer (rounding halfway cases to the nearest even integer). If the result is not representable, it is rounded in the direction ~rnd

val rint_trunc : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Retrun the input rounded to an integer, i.e. the next integer toward zero. If the result is not representable, it is rounded in the direction ~rnd

val frac : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> mpfr_float

Return the fractional part of an mpfr_float (with the same sign).

val modf : 
  ?rnd:mpfr_rnd_t ->
  ?iprec:int ->
  ?fprec:int ->
  mpfr_float ->
  mpfr_float * mpfr_float

Return simultaneously the integral part and the fractional part of an mpfr_float.

val fmod : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.fmod x y returns the value x - ny, where n is the integer quotient of x / y (rounded toward zero).

val fmodquo : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float * int

Mlmpfr.fmodquo x y returns the tuple (x - ny, q). See Mlmpfr.remquo for the meanings of n and q.

val remainder : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.remainder x y returns the value x - ny, where n is the integer quotient of x / y (rounded to the nearest integer, ties rounded to even).

val remquo : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float * int

Mlmpfr.remquo x y returns the tuple (x - ny, q), where n is the integer quotient of x / y (rounded to the nearest integer, ties rounded to even), and q are the low significant bits from the quotient n with the sign of x divided by y (except if those low bits are all zero, in which case zero is returned).

val integer_p : mpfr_float -> bool

Return true iff the input mpfr_float is an integer.

val set_default_rounding_mode : mpfr_rnd_t -> unit

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

val get_default_rounding_mode : unit -> mpfr_rnd_t

Get the default rounding mode.

val prec_round : ?rnd:mpfr_rnd_t -> mpfr_float -> int -> mpfr_float

Mlmpfr.prec_round ~rnd:r x p rounds x according to r with precision p.

val can_round : mpfr_float -> int -> mpfr_rnd_t -> mpfr_rnd_t -> int -> bool

Assuming b is an approximation of an unknown mpfr_number x in the direction r1 with error at most two to the power E(b)-err where E(b) is the exponent of b, return true if Mlmpfr.can_round x err r1 r2 p is able to round correctly x to precision p with the direction r2, and false otherwise (including for NaN and Inf).

val min_prec : mpfr_float -> int

Return the minimal number of bits required to store the significand of an mpfr_float, and 0 for special values, including 0.

val print_rnd_mode : mpfr_rnd_t -> string

Return a MPFR-like string ("MPFR_RNDD", "MPFR_RNDU", "MPFR_RNDN", "MPFR_RNDZ", "MPFR_RNDA") corresponding to the (Toward_Minus_Infinity, Toward_Plus_Infinity, To_Nearest, Toward_Zero, Away_From_Zero) rounding modes.

val print_ternary : ternary -> string

Return ternary value as a string ("Correct", "Lower", and "Greater" for Correct_Rounding, Lower, and Greater, respectively).

Miscellaneous

val nexttoward : mpfr_float -> mpfr_float -> mpfr_float

Mlmpfr.nexttoward x y returns NaN if x or y is NaN, returns a copy of x if x and y are equal. Otherwise, if x is different from y, return the next floating-point number of x (with the precision of x and the current exponent range) in the direction of y (the infinite values are seen as the smallest and largest floating-point numbers). If the result is zero, it keeps the sign of x. No underflow or overflow is generated.

val nextabove : mpfr_float -> mpfr_float

Equivalent to Mlmpfr.nexttoward where y is plus infinity.

val nextbelow : mpfr_float -> mpfr_float

Equivalent to Mlmpfr.nexttoward where y is minus infinity.

val min : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the minimum of two mpfr_float. If operands are both NaN, then return NaN. If one operand is NaN, then return the other value. If operands are zeros of different signs, then return -0.

val max : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Return the maximum of two mpfr_float. If operands are both NaN, then return NaN. If one operand is NaN, then return the other value. If operands are zeros of different signs, then return +0.

val get_exp : mpfr_float -> int

Return the exponent of a mpfr_float.

val set_exp : mpfr_float -> int -> mpfr_float

Return a fresh mpfr_float from input with new precision.

val signbit : mpfr_float -> sign

Return the sign of a mpfr_float.

val setsign : ?rnd:mpfr_rnd_t -> ?prec:int -> mpfr_float -> sign -> mpfr_float

Mlmpfr.setsign x s ~rnd:r returns a fresh copy of x with the sign s, with precision p in direction r.

val copysign : 
  ?rnd:mpfr_rnd_t ->
  ?prec:int ->
  mpfr_float ->
  mpfr_float ->
  mpfr_float

Mlmpfr.copysign x y ~rnd:r returns a fresh copy of x with the sign of y, with precision p in direction r.

val get_version : unit -> string

Return the MPFR version.

val get_emin : unit -> int

Return the (current) smallest exponent allowed for a mpfr_float.

val get_emax : unit -> int

Return the (current) largest exponent allowed for a mpfr_float.

val set_emin : int -> unit

Set the smallest exponent allowed for a mpfr_float.

val set_emax : int -> unit

Set the largest exponent allowed for a mpfr_float.

val get_emin_min : unit -> int

Return the minimum of the exponents allowed for Mlmpfr.set_emin.

val get_emin_max : unit -> int

Return the maximum of the exponents allowed for Mlmpfr.set_emin.

val get_emax_min : unit -> int

Return the minimum of the exponents allowed for Mlmpfr.set_emax.

val get_emax_max : unit -> int

Return the maximum of the exponents allowed for Mlmpfr.set_emax.

val check_range : ?rnd:mpfr_rnd_t -> mpfr_float -> mpfr_float

Mlmpfr.check_range ~rnd:r x assumes that x is the correctly-rounded value of some real value y in the direction r and some extended exponent range. Note that this function doesn't modify x as mpfr does (it returns a copy, or fails with Error).

val subnormalize : ?rnd:mpfr_rnd_t -> mpfr_float -> mpfr_float

Mlmpfr.subnormalize ~rnd:r x rounds x emulating subnormal number arithmetic: if x is outside the subnormal exponent range, it just return a copy of x; otherwise, it returns a roudning of x to precision EXP(x)-emin+1 according to rounding mode r. Note that this function doesn't modify x as mpfr does (it returns a copy, or fails with Error).

val clear_underflow : unit -> unit

Clear the underflow flag.

val clear_overflow : unit -> unit

Clear the overflow flag.

val clear_divby0 : unit -> unit

Clear the divide-by-zero flag.

val clear_nanflag : unit -> unit

Clear the invalid flag.

val clear_inexflag : unit -> unit

Clear the inexact flag.

val clear_erangeflag : unit -> unit

Clear the erange flag.

val clear_flags : unit -> unit

Clear all global flags.

val set_underflow : unit -> unit

Set the underflow flag.

val set_overflow : unit -> unit

Set the overflow flag.

val set_divby0 : unit -> unit

Set the divide-by-zero flag.

val set_nanflag : unit -> unit

Set the invalid flag.

val set_inexflag : unit -> unit

Set the inexact flag.

val set_erangeflag : unit -> unit

Set the erange flag.

val underflow_p : unit -> bool

Is underflow flag set?

val overflow_p : unit -> bool

Is overflow flag set?

val divby0_p : unit -> bool

Is divide-by-zero flag set?

val nanflag_p : unit -> bool

Is invalid flag set?

val inexflag_p : unit -> bool

Is inexact flag set?

val erangeflag_p : unit -> bool

Is erange flag set?

The Mlmpfr.flags_* functions below that take or return an argument mask (i.e., a list of mpfr_flags_t flags) can operate on any subset of the exception flags.

val flags_clear : mpfr_flags_t list -> unit

Mlmpfr.flags_clear f clears (lowers) the group of flags specified by mask f.

val flags_set : mpfr_flags_t list -> unit

Mlmpfr.flags_clear f sets (raises) the group of flags specified by mask f.

val flags_test : mpfr_flags_t list -> mpfr_flags_t list

Return the flags specified by mask.

val flags_save : unit -> mpfr_flags_t list

Return all the flags. It is equivalent to Mlmpfr.flags_test [Mlmpfr.All].

val flags_restore : mpfr_flags_t list -> mpfr_flags_t list -> unit

Mlmpfr.flags_restore f1 f2 restores the flags specified by mask f2 to their state represented in flags f1.

Memory Handling

val free_cache : unit -> unit

Free all caches and pools used by MPFR internally.

package mlmpfr