SIST EN 61691-3-2:2007
(Main)Behavioural languages -- Part 3-2: Mathematical operation in VHDL
Behavioural languages -- Part 3-2: Mathematical operation in VHDL
Embodied in the MATH_REAL and MATH_COMPLEX package declarations, and in the semantics of the standard mathematcal definition and the conventional meaning of the functions that are part of this standard.
Verhaltensebenensprache -- Teil 3-2: Mathematische Operationen für VHDL
Langages relatifs au comportement -- Partie 3-2: Exploitation mathématique en VHDL
Disponible uniquement en anglais
Vedenjski jeziki - 3-2. del: Matematično delovanje v VHDL (IEC 61691-3-2:2001)
General Information
Standards Content (Sample)
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EUROPEAN STANDARD EN 61691-3-2
NORME EUROPÉENNE
EUROPÄISCHE NORM December 2001
ICS 35.240.50
English version
Behavioural languages
Part 3-2: Mathematical operation in VHDL
(IEC 61691-3-2:2001)
Langages relatifs au comportement Verhaltensebenensprache
Partie 3-2: Exploitation mathématique Teil 3-2: Mathematische Operationen
en VHDL für VHDL
(CEI 61691-3-2:2001) (IEC 61691-3-2:2001)
This European Standard was approved by CENELEC on 2001-09-01. CENELEC members are bound to
comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and
notified to the Central Secretariat has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Czech Republic,
Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands,
Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels
© 2001 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 61691-3-2:2001 E
---------------------- Page: 2 ----------------------
EN 61691-3-2:2001 - 2 -
Foreword
The text of document 93/131/FDIS, future edition 1 of IEC 61691-3-2, prepared by IEC TC 93, Design
automation, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as
EN 61691-3-2 on 2001-09-01.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2002-06-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2004-09-01
This standard is based on IEEE Std 1076-2:1996, IEEE Standard VHDL mathematical packages.
__________
Endorsement notice
The text of the International Standard IEC 61691-3-2:2001 was approved by CENELEC as a
European Standard without any modification.
__________
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INTERNATIONAL IEC
STANDARD
61691-3-2
First edition
2001-06
Behavioural languages –
Part 3-2:
Mathematical operation in VHDL
IEC 2001 Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Electrotechnical Commission 3, rue de Varembé Geneva, Switzerland
Telefax: +41 22 919 0300 e-mail: inmail@iec.ch IEC web site http://www.iec.ch
Commission Electrotechnique Internationale
PRICE CODE
W
International Electrotechnical Commission
For price, see current catalogue
---------------------- Page: 4 ----------------------
– 2 – 61691-3-2 IEC:2001(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
_________
BEHAVIOURAL LANGUAGES –
Part 3-2: Mathematical operation in VHDL
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, the IEC publishes International Standards. Their preparation is
entrusted to technical committees; any IEC National Committee interested in the subject dealt with may
participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. The IEC collaborates closely with the International
Organization for Standardization (ISO) in accordance with conditions determined by agreement between the
two organizations.
2) The formal decisions or agreements of the IEC on technical matters express, as nearly as possible, an
international consensus of opinion on the relevant subjects since each technical committee has representation
from all interested National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form
of standards, technical specifications, technical reports or guides and they are accepted by the National
Committees in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject
of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61691-3-2 has been prepared by IEC technical committee 93:
Design automation.
This standard is based on IEEE Std 1076-2 (1996): IEEE Standard VHDL mathematical
packages.
The text of this standard is based on the following documents:
FDIS Report on voting
93/131/FDIS 93/141/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This standard does not follow the rules for the structure of international standards given in
Part 3 of the ISO/IEC Directives.
IEC 61691 consists of the following parts, under the general title: Behavioural languages:
1)
IEC 61691-1:1997, VHDL language reference manual
IEC 61691-2:2001, Part 2: VHDL multilogic system for model interoperability
———————
1)
The edition 2 with the title: VHSIC hardware description language VHDL (1076a) (under consideration) will
replace it.
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61691-3-2 IEC:2001(E) – 3 –
IEC 61691-3-1, Part 3-1: Analog description in VHDL (under consideration)
IEC 61691-3-2:2001, Part 3-2: Mathematical operation in VHDL
IEC 61691-3-3:2001, Part 3-3: Synthesis in VHDL
IEC 61691-3-4, Part 3-4: Timing expressions in VHDL (under consideration)
IEC 61691-3-5, Part 3-5: Library utilities in VHDL (under consideration)
The committee has decided that the contents of this publication will remain unchanged until
2004. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
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– 4 – 61691-3-2 IEC:2001(E)
INTRODUCTION
This set of packages provides a standard for the declaration of most frequently used real and
complex elementary functions required for numerically oriented modeling applications. Use of
these packages with their defined data types, constants, and functions is intended to provide
a mechanism for writing VHDL models (compliant with IEEE Std 1076-1993) that are portable
and interoperable with other VHDL models adhering to this standard. The standard serves a
broad class of applications with reasonable ease of use and requires implementations that are
of high quality.
This standard includes package bodies, as described in annex B, which are available in
electronic format either on a diskette affixed to the back cover, or as a downloadable file from
the IEC Web Store.
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61691-3-2 © IEC:2001(E)
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BEHAVIOURAL LANGUAGES -
Part 3-2: Mathematical operation in VHDL
1. Overview
1.1 Scope
This standard is embodied in the MATH_REAL and MATH_COMPLEX package declarations, and in the
semantics of the standard mathematical definition and the conventional meaning of the functions that are
part of this standard, along with 1.3. The information in annex A is a guide to users and implementors and is
not a normative part of this standard, but suggests ways in which one might use this set of packages. The
information in annex B is provided as a guideline for implementors and is not a normative part of this stan-
dard, but suggests ways in which implementors may implement this standard. The functions in this set of
packages were chosen because of their widespread utility, as well as because they are needed to support gen-
eral floating-point usage and to build other generic packages.
1.2 Constants, types, and functions provided
The following constants of type REAL are provided:
MATH_E MATH_LOG_OF_2 MATH_DEG_TO_RAD
MATH_1_OVER_E MATH_LOG_OF_10 MATH_RAD_TO_DEG
MATH_LOG2_OF_E
MATH_PI MATH_LOG10_OF_E
MATH_2_PI
MATH_1_OVER_PI MATH_SQRT_2
MATH_PI_OVER_2 MATH_1_OVER_SQRT_2
MATH_PI_OVER_3 MATH_SQRT_PI
MATH_PI_OVER_4
MATH_3_PI_OVER_2
The following functions/procedures of type REAL are provided:
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SIGN(X) EXP(X) SINH(X)
CEIL(X) LOG(X) COSH(X)
FLOOR(X) LOG2(X) TANH(X)
ROUND(X) LOG10(X)
TRUNC(X) LOG(X, BASE) ARCSINH(X)
"MOD"(X, Y) ARCCOSH(X)
SIN(X) ARCTANH(X)
REALMAX(X, Y) COS(X)
REALMIN(X, Y) TAN(X)
UNIFORM(SEED1, SEED2, X)
SQRT(X) ARCSIN(X)
CBRT(X) ARCCOS(X)
"**"(X, Y) ARCTAN(Y)
ARCTAN(Y, X)
The following types and subtypes are provided:
COMPLEX POSITIVE_REAL
COMPLEX_POLAR PRINCIPAL_VALUE
The following constants of type COMPLEX are provided:
MATH_CBASE_1 MATH_CBASE_J MATH_CZERO
The following type conversion functions for COMPLEX and COMPLEX_POLAR are provided:
CMPLX(X, Y) POLAR_TO_COMPLEX(Z)
COMPLEX_TO_POLAR(Z) GET_PRINCIPAL_VALUE(X)
The following overloaded relational functions for type COMPLEX_POLAR are provided:
"="(L, R) "/="(L, R)
The following functions for type COMPLEX and COMPLEX_POLAR are provided:
"ABS"(Z) EXP(Z) SIN(Z)
ARG(Z) LOG(Z) COS(Z)
LOG2(Z)
"-"(Z) LOG10(Z) SINH(Z)
CONJ(Z) LOG(Z, BASE) COSH(Z)
SQRT(Z)
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61691-3-2 © IEC:2001(E)
- 7 -
The following arithmetic functions for type COMPLEX and COMPLEX_POLAR are provided:
"+" "*"
"-" "/"
1.3 Conformance with this standard
The following conformance rules shall apply as they pertain to the use and implementation of this standard:
a) The package declarations may be modified to include additional data required by tools, but modifi-
cations shall 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 approved package declaration.
b) The standard mathematical definition and conventional meaning of the mathematical functions that
are part of this standard, together with the MATH_REAL and MATH_COMPLEX package declara-
tions, represent the formal semantics of the implementation of the MATH_REAL and
MATH_COMPLEX packages. An implementation is provided as a guideline in annex B. Imple-
mentors of these packages may choose to simply compile the package bodies provided in annex B,
or they may choose to implement the package bodies in the most efficient form available to them.
Implementations should conform to the semantics and minimum precision required by this standard.
c) The MATH_REAL package shall be built on top of the standard data type and precision require-
ments for floating point operations defined in IEEE Std 1076-1993 (STD.STANDARD).
d) The minimum precision required is that of IEEE Std 1076-1993. Because of this reason and the fact
that the functions are implemented on digital computers with only finite precision, the functions and
constants in this set of packages can, at best, only approximate the corresponding mathematically
defined functions and constants. An implementation is allowed to provide a higher precision than
the minimum required.
e) For some functions, the implementation shall deliver “prescribed results” for certain special argu-
ments, as defined in the comments for the functions in the function declaration. The purpose is to
strengthen the accuracy requirements at special argument values. Prescribed results take precedence
over maximum relative error requirements.
f) The semantics of the standard require that all the functions in the packages detect and report invalid
parameters (out of valid domain) through an assert statement. The domain of valid values is indi-
cated in the MATH_REAL and MATH_COMPLEX package declarations. The default value of the
severity level shall be Error.
g) The semantics of the standard do not require detection of overflow or underflow. Therefore, detec-
tion of underflow/overflow is optional and implementation dependent.
h) If an implementation chooses to provide any extensions beyond the minimum requirements of this
standard (e.g., precision, overflow handling), then it shall document its behavior accordingly.
i) The MATH_REAL and MATH_COMPLEX packages shall be compiled into a library symbolically
named IEEE.
2. References
This standard shall be used in conjunction with the following publications:
1
IEEE Std 754-1985 (Reaff 1990), IEEE Standard for Binary Floating-Point Arithmetic (ANSI).
IEEE Std 1076-1993, IEEE Standard VHDL Language Reference Manual (ANSI).
1
IEEE publications are available from the Institute of Electrical and Electronics Engineers, 445 Hoes Lane, P. O. Box 1331, Piscataway,
NJ 08855-1331, USA.
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3. Package declarations
The declaration of each function includes the following information: description of the mathematical defini-
tion of the function; values to be returned by the function for special arguments; valid domain of values for
the input arguments; error conditions; range of values into which the function maps the values in its domain;
and notes on special accuracy situations, reachable values, usable domains, or algorithms to be used by an
implementation.
3.1 MATH_REAL
------------------------------------------------------------------------
--
-- 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.
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61691-3-2 © IEC:2001(E)
- 9 -
--
-- -----------------------------------------------------------------------------
-- Version : 1.5
-- Date : 24 July 1996
-- -----------------------------------------------------------------------------
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:
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-- 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
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61691-3-2 © IEC:2001(E)
- 11 -
-- 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).
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-- 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:
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61691-3-2 © IEC:2001(E)
- 13 -
-- 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
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-- Error conditions:
-- Error if X > LOG(REAL’HIGH)
-- Range:
-- EXP(X) >= 0.0
-- Notes:
-- a) The usable domain of EXP
...
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