diff options
Diffstat (limited to 'libraries/ieee/math_real.vhdl')
| -rw-r--r-- | libraries/ieee/math_real.vhdl | 1247 |
1 files changed, 622 insertions, 625 deletions
diff --git a/libraries/ieee/math_real.vhdl b/libraries/ieee/math_real.vhdl index ca1cec3fe..37d9a35df 100644 --- a/libraries/ieee/math_real.vhdl +++ b/libraries/ieee/math_real.vhdl @@ -1,628 +1,625 @@ ------------------------------------------------------------------------- +-- ----------------------------------------------------------------- +-- +-- 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. -- --- Copyright 1996 by IEEE. All rights reserved. --- --- This source file is an essential part of IEEE Std 1076.2-1996, IEEE Standard --- VHDL Mathematical Packages. This source file may not be copied, sold, or --- included with software that is sold without written permission from the IEEE --- Standards Department. This source file may be used to implement this standard --- and may be distributed in compiled form in any manner so long as the --- compiled form does not allow direct decompilation of the original source file. --- This source file may be copied for individual use between licensed users. --- This source file is provided on an AS IS basis. The IEEE disclaims ANY --- WARRANTY EXPRESS OR IMPLIED INCLUDING ANY WARRANTY OF MERCHANTABILITY --- AND FITNESS FOR USE FOR A PARTICULAR PURPOSE. The user of the source --- file shall indemnify and hold IEEE harmless from any damages or liability --- arising out of the use thereof. --- --- Title: Standard VHDL Mathematical Packages (IEEE Std 1076.2-1996, --- MATH_REAL) --- --- 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- --- 1993. --- --- Notes: --- No declarations or definitions shall be included in, or --- excluded from, this package. --- The "package declaration" defines the types, subtypes, and --- declarations of MATH_REAL. --- The standard mathematical definition and conventional meaning --- of the mathematical functions that are part of this standard --- represent the formal semantics of the implementation of the --- MATH_REAL package declaration. The purpose of the MATH_REAL --- package body is to provide a guideline for implementations to --- verify their implementation of MATH_REAL. Tool developers may --- choose to implement the package body in the most efficient --- manner available to them. --- --- ----------------------------------------------------------------------------- --- Version : 1.5 --- Date : 24 July 1996 --- ----------------------------------------------------------------------------- +-- 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 1996 IEEE. All rights reserved."; - - -- - -- 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 MATH_REAL; + 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; |