path: root/libraries/ieee/math_real.vhdl

-- -----------------------------------------------------------------
-- 
-- Copyright 2019 IEEE P1076 WG Authors
-- 
-- See the LICENSE file distributed with this work for copyright and
-- licensing information and the AUTHORS file.
-- 
-- This file to you under the Apache License, Version 2.0 (the "License").
-- You may obtain a copy of the License at
-- 
--     http://www.apache.org/licenses/LICENSE-2.0
-- 
-- Unless required by applicable law or agreed to in writing, software
-- distributed under the License is distributed on an "AS IS" BASIS,
-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
-- implied.  See the License for the specific language governing
-- permissions and limitations under the License.
--
--   Title     :  Standard VHDL Mathematical Packages
--             :  (MATH_REAL package declaration)
--             :
--   Library   :  This package shall be compiled into a library
--             :  symbolically named IEEE.
--             :
--   Developers:  IEEE DASC VHDL Mathematical Packages Working Group
--             :
--   Purpose   :  This package defines a standard for designers to use in
--             :  describing VHDL models that make use of common REAL
--             :  constants and common REAL elementary mathematical
--             :  functions.
--             :
--   Limitation:  The values generated by the functions in this package
--             :  may vary from platform to platform, and the precision
--             :  of results is only guaranteed to be the minimum required
--             :  by IEEE Std 1076-2008.
--             :
--   Note      :  This package may be modified to include additional data
--             :  required by tools, but it must in no way change the
--             :  external interfaces or simulation behavior of the
--             :  description. It is permissible to add comments and/or
--             :  attributes to the package declarations, but not to change
--             :  or delete any original lines of the package declaration.
--             :  The package body may be changed only in accordance with
--             :  the terms of Clause 16 of this standard.
--             :
-- --------------------------------------------------------------------
-- $Revision: 1220 $
-- $Date: 2008-04-10 17:16:09 +0930 (Thu, 10 Apr 2008) $
-- --------------------------------------------------------------------

package MATH_REAL is
  constant CopyRightNotice : STRING
    := "Copyright IEEE P1076 WG. Licensed Apache 2.0";

  --
  -- Constant Definitions
  --
  constant MATH_E             : REAL := 2.71828_18284_59045_23536;
                                        -- Value of e
  constant MATH_1_OVER_E      : REAL := 0.36787_94411_71442_32160;
                                        -- Value of 1/e
  constant MATH_PI            : REAL := 3.14159_26535_89793_23846;
                                        -- Value of pi
  constant MATH_2_PI          : REAL := 6.28318_53071_79586_47693;
                                        -- Value of 2*pi
  constant MATH_1_OVER_PI     : REAL := 0.31830_98861_83790_67154;
                                        -- Value of 1/pi
  constant MATH_PI_OVER_2     : REAL := 1.57079_63267_94896_61923;
                                        -- Value of pi/2
  constant MATH_PI_OVER_3     : REAL := 1.04719_75511_96597_74615;
                                        -- Value of pi/3
  constant MATH_PI_OVER_4     : REAL := 0.78539_81633_97448_30962;
                                        -- Value of pi/4
  constant MATH_3_PI_OVER_2   : REAL := 4.71238_89803_84689_85769;
                                        -- Value 3*pi/2
  constant MATH_LOG_OF_2      : REAL := 0.69314_71805_59945_30942;
                                        -- Natural log of 2
  constant MATH_LOG_OF_10     : REAL := 2.30258_50929_94045_68402;
                                        -- Natural log of 10
  constant MATH_LOG2_OF_E     : REAL := 1.44269_50408_88963_4074;
                                        -- Log base 2 of e
  constant MATH_LOG10_OF_E    : REAL := 0.43429_44819_03251_82765;
                                        -- Log base 10 of e
  constant MATH_SQRT_2        : REAL := 1.41421_35623_73095_04880;
                                        -- square root of 2
  constant MATH_1_OVER_SQRT_2 : REAL := 0.70710_67811_86547_52440;
                                        -- square root of 1/2
  constant MATH_SQRT_PI       : REAL := 1.77245_38509_05516_02730;
                                        -- square root of pi
  constant MATH_DEG_TO_RAD    : REAL := 0.01745_32925_19943_29577;
  -- Conversion factor from degree to radian
  constant MATH_RAD_TO_DEG    : REAL := 57.29577_95130_82320_87680;
  -- Conversion factor from radian to degree

  --
  -- Function Declarations
  --
  function SIGN (X : in REAL) return REAL;
  -- Purpose:
  --         Returns 1.0 if X > 0.0; 0.0 if X = 0.0; -1.0 if X < 0.0
  -- Special values:
  --         None
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ABS(SIGN(X)) <= 1.0
  -- Notes:
  --         None

  function CEIL (X : in REAL) return REAL;
  -- Purpose:
  --         Returns smallest INTEGER value (as REAL) not less than X
  -- Special values:
  --         None
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         CEIL(X) is mathematically unbounded
  -- Notes:
  --         a) Implementations have to support at least the domain
  --                ABS(X) < REAL(INTEGER'HIGH)

  function FLOOR (X : in REAL) return REAL;
  -- Purpose:
  --         Returns largest INTEGER value (as REAL) not greater than X
  -- Special values:
  --         FLOOR(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         FLOOR(X) is mathematically unbounded
  -- Notes:
  --         a) Implementations have to support at least the domain
  --                ABS(X) < REAL(INTEGER'HIGH)

  function ROUND (X : in REAL) return REAL;
  -- Purpose:
  --         Rounds X to the nearest integer value (as real). If X is
  --         halfway between two integers, rounding is away from 0.0
  -- Special values:
  --         ROUND(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ROUND(X) is mathematically unbounded
  -- Notes:
  --         a) Implementations have to support at least the domain
  --                ABS(X) < REAL(INTEGER'HIGH)

  function TRUNC (X : in REAL) return REAL;
  -- Purpose:
  --         Truncates X towards 0.0 and returns truncated value
  -- Special values:
  --         TRUNC(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         TRUNC(X) is mathematically unbounded
  -- Notes:
  --         a) Implementations have to support at least the domain
  --                ABS(X) < REAL(INTEGER'HIGH)

  function "MOD" (X, Y : in REAL) return REAL;
  -- Purpose:
  --         Returns floating point modulus of X/Y, with the same sign as
  --         Y, and absolute value less than the absolute value of Y, and
  --         for some INTEGER value N the result satisfies the relation
  --         X = Y*N + MOD(X,Y)
  -- Special values:
  --         None
  -- Domain:
  --         X in REAL; Y in REAL and Y /= 0.0
  -- Error conditions:
  --         Error if Y = 0.0
  -- Range:
  --         ABS(MOD(X,Y)) < ABS(Y)
  -- Notes:
  --         None

  function REALMAX (X, Y : in REAL) return REAL;
  -- Purpose:
  --         Returns the algebraically larger of X and Y
  -- Special values:
  --         REALMAX(X,Y) = X when X = Y
  -- Domain:
  --         X in REAL; Y in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         REALMAX(X,Y) is mathematically unbounded
  -- Notes:
  --         None

  function REALMIN (X, Y : in REAL) return REAL;
  -- Purpose:
  --         Returns the algebraically smaller of X and Y
  -- Special values:
  --         REALMIN(X,Y) = X when X = Y
  -- Domain:
  --         X in REAL; Y in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         REALMIN(X,Y) is mathematically unbounded
  -- Notes:
  --         None

  procedure UNIFORM(variable SEED1, SEED2 : inout POSITIVE; variable X : out REAL);
  -- Purpose:
  --         Returns, in X, a pseudo-random number with uniform
  --         distribution in the open interval (0.0, 1.0).
  -- Special values:
  --         None
  -- Domain:
  --         1 <= SEED1 <= 2147483562; 1 <= SEED2 <= 2147483398
  -- Error conditions:
  --         Error if SEED1 or SEED2 outside of valid domain
  -- Range:
  --         0.0 < X < 1.0
  -- Notes:
  --         a) The semantics for this function are described by the
  --            algorithm published by Pierre L'Ecuyer in "Communications
  --            of the ACM," vol. 31, no. 6, June 1988, pp. 742-774.
  --            The algorithm is based on the combination of two
  --            multiplicative linear congruential generators for 32-bit
  --            platforms.
  --
  --         b) Before the first call to UNIFORM, the seed values
  --            (SEED1, SEED2) have to be initialized to values in the range
  --            [1, 2147483562] and [1, 2147483398] respectively.  The
  --            seed values are modified after each call to UNIFORM.
  --
  --         c) This random number generator is portable for 32-bit
  --            computers, and it has a period of ~2.30584*(10**18) for each
  --            set of seed values.
  --
  --         d) For information on spectral tests for the algorithm, refer
  --            to the L'Ecuyer article.

  function SQRT (X : in REAL) return REAL;
  -- Purpose:
  --         Returns square root of X
  -- Special values:
  --         SQRT(0.0) = 0.0
  --         SQRT(1.0) = 1.0
  -- Domain:
  --         X >= 0.0
  -- Error conditions:
  --         Error if X < 0.0
  -- Range:
  --         SQRT(X) >= 0.0
  -- Notes:
  --         a) The upper bound of the reachable range of SQRT is
  --            approximately given by:
  --                SQRT(X) <= SQRT(REAL'HIGH)

  function CBRT (X : in REAL) return REAL;
  -- Purpose:
  --         Returns cube root of X
  -- Special values:
  --         CBRT(0.0) = 0.0
  --         CBRT(1.0) = 1.0
  --         CBRT(-1.0) = -1.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         CBRT(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of CBRT is approximately given by:
  --                ABS(CBRT(X)) <= CBRT(REAL'HIGH)

  function "**" (X : in INTEGER; Y : in REAL) return REAL;
  -- Purpose:
  --         Returns Y power of X ==>  X**Y
  -- Special values:
  --         X**0.0 = 1.0; X /= 0
  --         0**Y = 0.0; Y > 0.0
  --         X**1.0 = REAL(X); X >= 0
  --         1**Y = 1.0
  -- Domain:
  --         X > 0
  --         X = 0 for Y > 0.0
  --         X < 0 for Y = 0.0
  -- Error conditions:
  --         Error if X < 0 and Y /= 0.0
  --         Error if X = 0 and Y <= 0.0
  -- Range:
  --         X**Y >= 0.0
  -- Notes:
  --         a) The upper bound of the reachable range for "**" is
  --            approximately given by:
  --                X**Y <= REAL'HIGH

  function "**" (X : in REAL; Y : in REAL) return REAL;
  -- Purpose:
  --         Returns Y power of X ==>  X**Y
  -- Special values:
  --         X**0.0 = 1.0; X /= 0.0
  --         0.0**Y = 0.0; Y > 0.0
  --         X**1.0 = X; X >= 0.0
  --         1.0**Y = 1.0
  -- Domain:
  --         X > 0.0
  --         X = 0.0 for Y > 0.0
  --         X < 0.0 for Y = 0.0
  -- Error conditions:
  --         Error if X < 0.0 and Y /= 0.0
  --         Error if X = 0.0 and Y <= 0.0
  -- Range:
  --         X**Y >= 0.0
  -- Notes:
  --         a) The upper bound of the reachable range for "**" is
  --            approximately given by:
  --                X**Y <= REAL'HIGH

  function EXP (X : in REAL) return REAL;
  -- Purpose:
  --         Returns e**X; where e = MATH_E
  -- Special values:
  --         EXP(0.0) = 1.0
  --         EXP(1.0) = MATH_E
  --         EXP(-1.0) = MATH_1_OVER_E
  --         EXP(X) = 0.0 for X <= -LOG(REAL'HIGH)
  -- Domain:
  --         X in REAL such that EXP(X) <= REAL'HIGH
  -- Error conditions:
  --         Error if X > LOG(REAL'HIGH)
  -- Range:
  --         EXP(X) >= 0.0
  -- Notes:
  --         a) The usable domain of EXP is approximately given by:
  --                X <= LOG(REAL'HIGH)

  function LOG (X : in REAL) return REAL;
  -- Purpose:
  --         Returns natural logarithm of X
  -- Special values:
  --         LOG(1.0) = 0.0
  --         LOG(MATH_E) = 1.0
  -- Domain:
  --         X > 0.0
  -- Error conditions:
  --         Error if X <= 0.0
  -- Range:
  --         LOG(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of LOG is approximately given by:
  --                LOG(0+) <= LOG(X) <= LOG(REAL'HIGH)

  function LOG2 (X : in REAL) return REAL;
  -- Purpose:
  --         Returns logarithm base 2 of X
  -- Special values:
  --         LOG2(1.0) = 0.0
  --         LOG2(2.0) = 1.0
  -- Domain:
  --         X > 0.0
  -- Error conditions:
  --         Error if X <= 0.0
  -- Range:
  --         LOG2(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of LOG2 is approximately given by:
  --                LOG2(0+) <= LOG2(X) <= LOG2(REAL'HIGH)

  function LOG10 (X : in REAL) return REAL;
  -- Purpose:
  --         Returns logarithm base 10 of X
  -- Special values:
  --         LOG10(1.0) = 0.0
  --         LOG10(10.0) = 1.0
  -- Domain:
  --         X > 0.0
  -- Error conditions:
  --         Error if X <= 0.0
  -- Range:
  --         LOG10(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of LOG10 is approximately given by:
  --                LOG10(0+) <= LOG10(X) <= LOG10(REAL'HIGH)

  function LOG (X : in REAL; BASE : in REAL) return REAL;
  -- Purpose:
  --         Returns logarithm base BASE of X
  -- Special values:
  --         LOG(1.0, BASE) = 0.0
  --         LOG(BASE, BASE) = 1.0
  -- Domain:
  --         X > 0.0
  --         BASE > 0.0
  --         BASE /= 1.0
  -- Error conditions:
  --         Error if X <= 0.0
  --         Error if BASE <= 0.0
  --         Error if BASE = 1.0
  -- Range:
  --         LOG(X, BASE) is mathematically unbounded
  -- Notes:
  --         a) When BASE > 1.0, the reachable range of LOG is
  --            approximately given by:
  --                LOG(0+, BASE) <= LOG(X, BASE) <= LOG(REAL'HIGH, BASE)
  --         b) When 0.0 < BASE < 1.0, the reachable range of LOG is
  --            approximately given by:
  --                LOG(REAL'HIGH, BASE) <= LOG(X, BASE) <= LOG(0+, BASE)

  function SIN (X : in REAL) return REAL;
  -- Purpose:
  --         Returns sine of X; X in radians
  -- Special values:
  --         SIN(X) = 0.0 for X = k*MATH_PI, where k is an INTEGER
  --         SIN(X) = 1.0 for X = (4*k+1)*MATH_PI_OVER_2, where k is an
  --                                                           INTEGER
  --         SIN(X) = -1.0 for X = (4*k+3)*MATH_PI_OVER_2, where k is an
  --                                                           INTEGER
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ABS(SIN(X)) <= 1.0
  -- Notes:
  --         a) For larger values of ABS(X), degraded accuracy is allowed.

  function COS (X : in REAL) return REAL;
  -- Purpose:
  --         Returns cosine of X; X in radians
  -- Special values:
  --         COS(X) = 0.0 for X = (2*k+1)*MATH_PI_OVER_2, where k is an
  --                                                            INTEGER
  --         COS(X) = 1.0 for X = (2*k)*MATH_PI, where k is an INTEGER
  --         COS(X) = -1.0 for X = (2*k+1)*MATH_PI, where k is an INTEGER
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ABS(COS(X)) <= 1.0
  -- Notes:
  --         a) For larger values of ABS(X), degraded accuracy is allowed.

  function TAN (X : in REAL) return REAL;
  -- Purpose:
  --         Returns tangent of X; X in radians
  -- Special values:
  --         TAN(X) = 0.0 for X = k*MATH_PI, where k is an INTEGER
  -- Domain:
  --         X in REAL and
  --         X /= (2*k+1)*MATH_PI_OVER_2, where k is an INTEGER
  -- Error conditions:
  --         Error if X = ((2*k+1) * MATH_PI_OVER_2), where k is an
  --                                                           INTEGER
  -- Range:
  --         TAN(X) is mathematically unbounded
  -- Notes:
  --         a) For larger values of ABS(X), degraded accuracy is allowed.

  function ARCSIN (X : in REAL) return REAL;
  -- Purpose:
  --         Returns inverse sine of X
  -- Special values:
  --         ARCSIN(0.0) = 0.0
  --         ARCSIN(1.0) = MATH_PI_OVER_2
  --         ARCSIN(-1.0) = -MATH_PI_OVER_2
  -- Domain:
  --         ABS(X) <= 1.0
  -- Error conditions:
  --         Error if ABS(X) > 1.0
  -- Range:
  --         ABS(ARCSIN(X) <= MATH_PI_OVER_2
  -- Notes:
  --         None

  function ARCCOS (X : in REAL) return REAL;
  -- Purpose:
  --         Returns inverse cosine of X
  -- Special values:
  --         ARCCOS(1.0) = 0.0
  --         ARCCOS(0.0) = MATH_PI_OVER_2
  --         ARCCOS(-1.0) = MATH_PI
  -- Domain:
  --         ABS(X) <= 1.0
  -- Error conditions:
  --         Error if ABS(X) > 1.0
  -- Range:
  --         0.0 <= ARCCOS(X) <= MATH_PI
  -- Notes:
  --         None

  function ARCTAN (Y : in REAL) return REAL;
  -- Purpose:
  --         Returns the value of the angle in radians of the point
  --        (1.0, Y), which is in rectangular coordinates
  -- Special values:
  --         ARCTAN(0.0) = 0.0
  -- Domain:
  --         Y in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ABS(ARCTAN(Y)) <= MATH_PI_OVER_2
  -- Notes:
  --         None

  function ARCTAN (Y : in REAL; X : in REAL) return REAL;
  -- Purpose:
  --         Returns the principal value of the angle in radians of
  --         the point (X, Y), which is in rectangular coordinates
  -- Special values:
  --         ARCTAN(0.0, X) = 0.0 if X > 0.0
  --         ARCTAN(0.0, X) = MATH_PI if X < 0.0
  --         ARCTAN(Y, 0.0) = MATH_PI_OVER_2 if Y > 0.0
  --         ARCTAN(Y, 0.0) = -MATH_PI_OVER_2 if Y < 0.0
  -- Domain:
  --         Y in REAL
  --         X in REAL, X /= 0.0 when Y = 0.0
  -- Error conditions:
  --         Error if X = 0.0 and Y = 0.0
  -- Range:
  --         -MATH_PI < ARCTAN(Y,X) <= MATH_PI
  -- Notes:
  --         None

  function SINH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns hyperbolic sine of X
  -- Special values:
  --         SINH(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         SINH(X) is mathematically unbounded
  -- Notes:
  --         a) The usable domain of SINH is approximately given by:
  --                ABS(X) <= LOG(REAL'HIGH)


  function COSH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns hyperbolic cosine of X
  -- Special values:
  --         COSH(0.0) = 1.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         COSH(X) >= 1.0
  -- Notes:
  --         a) The usable domain of COSH is approximately given by:
  --                ABS(X) <= LOG(REAL'HIGH)

  function TANH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns hyperbolic tangent of X
  -- Special values:
  --         TANH(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ABS(TANH(X)) <= 1.0
  -- Notes:
  --         None

  function ARCSINH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns inverse hyperbolic sine of X
  -- Special values:
  --         ARCSINH(0.0) = 0.0
  -- Domain:
  --         X in REAL
  -- Error conditions:
  --         None
  -- Range:
  --         ARCSINH(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of ARCSINH is approximately given by:
  --                ABS(ARCSINH(X)) <= LOG(REAL'HIGH)

  function ARCCOSH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns inverse hyperbolic cosine of X
  -- Special values:
  --         ARCCOSH(1.0) = 0.0
  -- Domain:
  --         X >= 1.0
  -- Error conditions:
  --         Error if X < 1.0
  -- Range:
  --         ARCCOSH(X) >= 0.0
  -- Notes:
  --         a) The upper bound of the reachable range of ARCCOSH is
  --            approximately given by:   ARCCOSH(X) <= LOG(REAL'HIGH)

  function ARCTANH (X : in REAL) return REAL;
  -- Purpose:
  --         Returns inverse hyperbolic tangent of X
  -- Special values:
  --         ARCTANH(0.0) = 0.0
  -- Domain:
  --         ABS(X) < 1.0
  -- Error conditions:
  --         Error if ABS(X) >= 1.0
  -- Range:
  --         ARCTANH(X) is mathematically unbounded
  -- Notes:
  --         a) The reachable range of ARCTANH is approximately given by:
  --                ABS(ARCTANH(X)) < LOG(REAL'HIGH)

end package MATH_REAL;