ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....formalize the xed point arithmetic in higher order logic as a basis for checking the correctness of higher level algorithmic descriptions of DSP designs modeled in oating and xed point representations. Contrary to the oating point arithmetic which is standardized in IEEE 754 [13] and IEEE854 [14], the xed point arithmetic description depends on the tool we use to design the DSP (Digital Signal Processor) chip. In this paper, we consider Cadence SPW [22] xed point arithmetic. Idea Algorithm Floating Point OK OK OK Target System Quantization Code Generation Architectural ....

IEEE, IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....the interval [# 1 , # 2 ) contains a negative number of eigenvalues, namely FloatingCount(# 2 ) FloatingCount(# 1 ) This result is clearly incorrect. In section 4. 1 below, we will see that this can indeed occur using the Eispack routine bisect (using IEEE floating point standard arithmetic [2, 3], and without over underflow) This paper explains how to design correct bracketing algorithms in the face of nonmonotonicity. There are at least four reasons why FloatingCount(x) might not be monotonic: 1. the floating point arithmetic is too inaccurate, 2. over underflow occurs, or is avoided ....

ANSI/IEEE, New York, IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....formalize the xed point arithmetic in higher order logic as a basis for checking the correctness of higher level algorithmic descriptions of DSP designs modeled in oating and xed point representations. Contrary to the oating point arithmetic which is standardized in IEEE 754 [13] and IEEE 854 [14], the xed point arithmetic description depends on the tool we use to design the DSP (Digital Signal Processor) chip. Examples of such tools are SPW (Cadence) 26] Matlab Simulink (Mathworks) 17] CoCentric (Synopsys) 25] DSP Station (Frontier Design) 18] For instance, in SPW (Signal ....

IEEE, IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....respectively. If F 2f , then sorting the s i s more finely by magnitude instead of just the exponents (so that ) does not change the above results. Assumptions 1 through 5 of Theorem 1 are satisfied by the formats of the (proposed revision of the) IEEE binary floating point standard [1, 2, 7]. Assumption 6 depends of course on the data s 1 , s n as well. This theorem completely characterizes the maximum attainable error from Algorithm 1. It is noteworthy that the worst case error deteriorates from nearly perfect (approximately 1.5 ulps) to complete loss of accuracy (computing ....

....work at all, in the case when k n (in which case no progress is made) We discuss these possibilities further in the next section. 5 Comparing Algorithms 1, 2, 3 and 4 We consider various values of f and F arising from computations in the (proposed revision of the) IEEE floating point standard [1, 2, 7]. Recall that the numbers of significant bits (including hidden ones) in single (S) double (D) extended (E) and quad (Q) formats are 24, 53, 64 and 113, respectively. The number of bits in their exponent fields are 8, 11, 15 and 15, respectively. 5.1 Accurate Summation We begin by comparing ....

[Article contains additional citation context not shown here]

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....use #Snir et al. 1996, Section 2.3.3#, so presumably we cannot assumethat #oating pointnumbers will be communicated withoutchange on IEEE machines when using MPI unless wehave additional information aboutthe implementation. 1 It should be noted thatthere is also a radix independentstandard #IEEE, 1987#. 2 It should be noted that it is not clear whether or not this can be assumed for denormalized numbers. 6 Algorithmic Integrity The suggestions wehavemade so far certainly do not solve all the problems. We are still left withmanyofthose problems associated withthemajor concern of varying ....

IEEE #1987#. ANSI#IEEE Standard for Radix Independent Floating Point Arithmetic: Std 854-1987, IEEE Press, New York, NY, USA.

....precision, quadruple (or other language and compilersupported wide precision) may not always be available. Feature 5: Exception handling. IEEE arithmetic defines precise responses to exceptional events like overflow, underflow, division by zero, invalid operations (like # 1) and inexact [3, 4]. In particular, it has rules for arithmetic with NaNs (Not a Number symbols) produced by 7 # 1, 0 0, etc. and # (produced by overflow, 1 0, etc. It also defines flags that the user can reset and later test to see if any exception has occurred since resetting them. This feature can let ....

....for finding all the eigenvalues of T by exploiting arithmetic with NaNs and infinities this way ranges from 1.28 times faster on a Sun Ultra 30 to 1. 8 times faster on an IBM RS 6000 590 [43] This does not require the full power of Feature 5: Exception handling, just IEEE default arithmetic [3, 4]. Similarly, ScaLAPACK routine PDLAIECT assumes the availability of arithmetic with # (like 1 # = 0) to remove branches from the inner loop in the computation of eigenvalues, and so go faster. The simplest version of the inner loop in PDLAIECT is as follows: Count the number of eigenvalues less ....

[Article contains additional citation context not shown here]

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....interval [oe 1 ; oe 2 ) contains a negative number of eigenvalues, namely FloatingCount(oe 2 ) Gamma FloatingCount(oe 1 ) This result is clearly incorrect. In section 4. 1 below, we will see that this can indeed occur using the Eispack routine bisect (using IEEE floating point standard arithmetic [2, 3], and without over underflow) This paper explains how to design correct bracketing algorithms in the face of nonmonotonicity. There are at least four reasons why FloatingCount(x) might not be monotonic: 1. the floating point arithmetic is too inaccurate, 2. over underflow occurs, or is avoided ....

ANSI/IEEE, New York, IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....tiny results of the floating point addition or subtraction operation without rounding error, in other words exactly. The underflow exception flag was introduced to signal to the user of a programming environment that (1) is no longer valid and that j 6= 0 has occurred in (2) The IEEE standards [6, 8] relax this condition in the sense that the underflow exception should be signaled at least when j 6= 0. A commentary to the standard however [1] encourages the stricter criterion for setting the underflow flag. That is, it should be set whenever the delivered result is different from what would ....

IEEE Computer Society. IEEE standard for radix-independent floating-point arithmetic. IEEE, New York, 1987.

....continue past exceptions and later permit the program to determine whether an exception occurred, or else support userlevel trap handling. In this paper we will assume the first response to exceptions is available; this corresponds to the default behavior of IEEE standard floating point arithmetic [3, 4]. Our numerical methods will be drawn from the LAPACK library of numerical linear algebra routines for high performance computers [2] In particular, we will consider condition estimation (error bounding) for linear systems as well as computing eigenvectors of general complex matrices. What these ....

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....(Snir et al. 1996, Section 2.3.3) so presumably we cannot assume that floating point numbers will be communicated without change on IEEE machines when using MPI unless we have additional information about the implementation. 1 It should be noted that there is also a radix independent standard (IEEE, 1987). 2 It should be noted that it is not clear whether or not this can be assumed for denormalized numbers. 6 Algorithmic Integrity The suggestions we have made so far certainly do not solve all the problems. We are still left with many of those problems associated with the major concern of ....

IEEE (1987). ANSI/IEEE Standard for Radix Independent Floating Point Arithmetic: Std 854-1987, IEEE Press, New York, NY, USA.

....overflow 5 . To handle this difficulty ScaLAPACK, as LAPACK, restricts the range of representable numbers by a call to routine PDLABAD (in double precision) the equivalent of the LAPACK routine DLABAD, which, if 3 It should be noted that there is also a radix independent standard ([14]) 4 It is not clear whether or not this can be assumed for subnormal (denormalized) numbers. 5 At the time of testing ScaLAPACK version 1.2, the HP9000 exhibited this behavior desired, takes the square root of the smallest and largest representable numbers for the computation to protect ....

IEEE. ANSI/IEEE Standard for Radix Independent Floating Point Arithmetic: Std 854-1987. IEEE Press, New York, NY, USA, 1987.

....specification techniques are sufficiently advanced that it is reasonable to consider their use in the development of future standards. keywords: Floating point arithmetic, Formal Methods, Specification, Verification. 1 Introduction This document describes a definition of the ANSI IEEE 854 [3] Standard for Radix Independent Floating Point Arithmetic in the PVS verification system (developed at SRI International) 4] IEEE 854 is a generalization of the ANSI IEEE 754 [2] Standard for Binary Floating Point Arithmetic. Therefore, this formalization of the IEEE 854 can be instantiated to ....

....result is to be delivered, deliver a quiet NaN as its result. Every operation involving one or two input NaNs, none of them signaling, shall signal no exception, but, if a floating point result is to be delivered, shall deliver as its result a quiet NaN, which should be one of the input NaNs. [3] The following PVS specification captures the various cases for dealing with NaN arguments. Function fp quiet is constrained via the PVS dependent type mechanism to return one of its arguments. Function fp signal tests to see if the invalid trap is enabled; if not, a quiet NaN is returned. ....

[Article contains additional citation context not shown here]

IEEE. IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....past exceptions and later permit the program to determine whether an exception occurred, or else support user level trap handling. In this paper we will assume the first response to exceptions is available; this corresponds to the default behavior of IEEE standard floating point arithmetic [3, 4]. Our numerical methods will be drawn from the LAPACK library of numerical linear algebra routines for high performance computers [2] In particular, we will consider condition estimation (error bounding) for linear systems, computing eigenvectors of general complex matrices, the symmetric ....

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....MiniCayuga micro processors [131, 7] The Mini Cayuga is a small but formally verified microprocessor developed by ORA. It was a research prototype and was not fabricated. 4.3 Other Fundamental Research 4.3. 1 Specification of Floating point Arithmetic Significant portions of the ANSI IEEE 854 [62] standard have been defined using the PVS [86] and HOL [21] systems. IEEE 854 is a standard for radix independent floating point arithmetic. The main motivating factors for the formalization of the standard are 1) The creation of a formal specification against which an implementation (such as the ....

IEEE. IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....[oe 1 ; oe 2 ) contains a negative number of eigenvalues, namely FloatingCount(oe 2 ) Gamma FloatingCount(oe 1 ) This result is clearly incorrect. In section 4 below, we will see that this can indeed occur using the the Eispack routine bisect (using IEEE floating point standard arithmetic [2, 3], and without over underflows or other exceptions) The goal of this paper is to explore the impact of nonmonotonicity on the bisection algorithm. There are at least three reasons why FloatingCount(x) might not be monotonic: 1. the floating point arithmetic is too inaccurate, 2. over underflow ....

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

....Inc. 4 Current In House Research In addition to supporting the technology transfer projects discussed in the previous section, the NASA Langley local staff are performing research in a number of areas. 4. 1 Specification of Floating point Arithmetic Significant portions of the ANSI IEEE 854 [52] standard have been defined using the PVS [76] and HOL [19] systems. IEEE 854 is a standard for radix independent floating point arithmetic. The main motivating factors for the formalization of the standard are 1) The creation of a formal specification against which an implementation (such as the ....

IEEE. IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....systems on the specification. 1 Introduction The HOL [3] and PVS [7] systems are general purpose mechanical verification systems whose specification languages are based on higher order logic. We have partially defined the ANSI IEEE 854 standard for radix independent floating point arithmetic [5] in both of these verification systems [2, 6] This effort to formalize IEEE 854 has given the opportunity to compare the styles imposed by the two verification systems on the specification. This is not the first formalization of floating point arithmetic. Geoff Barrett [1] describes the Z ....

....smaller sub types of the reals. For example, the rationals are defined as a sub type of the reals that does not satisfy the Completeness Axiom. Similarly, the integers are defined as a sub type of the rationals that is not closed under division. In PVS, the parameters required by IEEE 854 [5] can be defined as parameters to the formal theory. Within a theory, the parameters are treated as constants of the appropriate type. By instantiating the following theory multiple times with different values for the parameters, we can readily define the different precisions allowed by the ....

IEEE. IEEE Standard for Radix-Independent Floating-Point Arithmetic, 1987. ANSI/IEEE Std 854-1987.

....of algorithms leads to the essential concepts of forward and backward error analysis, numerical stability and ill conditioning. These are discussed and illustrated in great detail in Section 6. To top off the build up in the previous sections, Section 7 discusses the IEEE standard [2] [3] for floating point arithmetic. This standard embodies all of the details encountered when effectively implementing floating point arithmetic on a binary machine. Several important but very detailistic concepts such as denormals, special representations, exception flags and so on come about. For ....

ANSI/IEEE Std 854-1987, "IEEE standard for radixindependent floating-point arithmetic," New York, 1987.

No context found.

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

No context found.

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

No context found.

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

No context found.

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

No context found.

IEEE (1987) IEEE Standard for Radix-Independent FloatingPoint Arithmetic. IEEE 854.

No context found.

ANSI/IEEE, New York. IEEE Standard for Radix Independent Floating Point Arithmetic, Std 854-1987 edition, 1987.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC