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Introduction to Programmable Active Memories
, 1989
"... We introduce the concept of PAM, Programmable Active Memory and present results obtained with our Perle0 prototype board, featuring: ffl A software silicon foundry for a 50K gate array, with a 50 milliseconds turnaround time. ffl A 3000 one bit processors universal machine with an arbitrary inter ..."
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Cited by 59 (2 self)
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We introduce the concept of PAM, Programmable Active Memory and present results obtained with our Perle0 prototype board, featuring: ffl A software silicon foundry for a 50K gate array, with a 50 milliseconds turnaround time. ffl A 3000 one bit processors universal machine with an arbitrary interconnect structure specified by 400K bits of nanocode. ffl A programmable hardware coprocessor with an initial library including: a long multiplier, an image convolver, a data compressor, etc. Each of these hardware designs speeds up the corresponding software application by at least an order of magnitude.
Hardware Speedups in Long Integer Multiplication
 Computer Architecture News
, 1990
"... We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see [BR ..."
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Cited by 19 (4 self)
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We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see [BRV]) technology which provides us with a 50 millisecond turnaround time silicon foundry for implementing up to 50K gate logic designs fully equipped with fast local RAM and host bus interface. First, we demonstrate how a simple hardware 512 bits integer multiplier coupled with a low end workstation host yields performance on long arithmetic superior to that of the fastest computers for which we could obtain actual benchmark figures. Second, we specialize this hardware in order to speedup one specific application of long integer arithmetic, namely RivestShamir Adleman publickey cryptography [RSA]. We demonstrate how a single host driving 3 differently configured PAM boards delivers RSA enc...
Arbitrary Precision Real Arithmetic: Design and Algorithms
, 1996
"... this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms fo ..."
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Cited by 19 (0 self)
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this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms for rational operations and transcendental functions for this representation. Finally we describe briefly the prototype written in Caml. 2. Computable real numbers
A universal characterization of the closed euclidean interval (Extended Abstract)
 PROC. OF 16TH ANN. IEEE SYMP. ON LOGIC IN COMPUTER SCIENCE, LICS'01
, 2001
"... We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basi ..."
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Cited by 10 (0 self)
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We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basic arithmetic operations and to verify equations between them. We test the notion in categories of interest. In the
Number Computability and Domain Theory
 Information and Computation
, 1996
"... We present the different constructive definitions of real number that can be found in the literature. Using domain theory we analyse the notion of computability that is substantiated by these definitions and we give a definition of computability for real numbers and for functions acting on them. Thi ..."
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Cited by 8 (0 self)
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We present the different constructive definitions of real number that can be found in the literature. Using domain theory we analyse the notion of computability that is substantiated by these definitions and we give a definition of computability for real numbers and for functions acting on them. This definition of computability turns out to be equivalent to other definitions given in the literature using different methods. Domain theory is a useful tool to study higher order computability on real numbers. An interesting connection between Scotttopology and the standard topologies on the real line and on the space of continuous functions on reals is stated. An important result in this paper is the proof that every computable functional on real numbers is continuous w.r.t. the compact open topology on the function space. 1
The constructive reals as a Java Library
 J. Log. Algebr. Program
, 2004
"... We describe an implementation of the computable (or constructive) real numbers as a pure Java library. To the user, the library interface appears very similar to that of some other numeric types provided by the standard Java library. The primary goal of the implementation is simplicity, so that the ..."
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Cited by 4 (0 self)
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We describe an implementation of the computable (or constructive) real numbers as a pure Java library. To the user, the library interface appears very similar to that of some other numeric types provided by the standard Java library. The primary goal of the implementation is simplicity, so that the implementation could be easily understood, and to allow simple informal correctness arguments. We hope to demonstrate that even such a basic implementation of constructive real arithmetic can be useful in a number of contexts, including in a desk calculator utility distributed with the package. A secondary goal was to demonstrate that some secondorder functions on the reals, such as restricted inverse and derivative operations, can be implemented with su#cient performance to be useful.
unknown title
"... We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see [BR ..."
Abstract
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We present various experiments in Hardware/Software design tradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardware designs tested and measured. To implement these designs, we rely on our PAM (for Programmable Active Memory, see [BRV]) technology which provides us with a 50 millisecond turnaround time silicon foundry for implementing up to 50K gate logic designs fully equipped with fast local RAM and host bus interface. First, we demonstrate how a simple hardware 512 bits integer multiplier coupled with a low end workstation host yields performance on long arithmetic superior to that of the fastest computers for which we could obtain actual benchmark figures. Second, we specialize this hardware in order to speedup one specific application of long integer arithmetic, namely RivestShamirAdleman publickey cryptography [RSA]. We demonstrate how a single host driving 3 differently configured PAM boards delivers RSA encryption and decryption faster than 225Kbits/sec for 512 bits keys. This beats the best currently working VLSI specially built for RSA by one order of magnitude.
A golden ratio notation . . .
, 1996
"... Several methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New f ..."
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Several methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New forms of digit notations are necessary. The usual solution to this representation problem consists in adding new digits in the notation, quite often negative digits. In this article we present an alternative solution. It consists in using non natural numbers as "base", that is, in using a positional digit notation where the ratio between the weight of two consecutive digits is not necessarily a natural number, as in the standard case, but it can be a rational or even an irrational number. We discuss in full detail one particular example of this form of notation: namely the one having two digits (0 and 1) and the golden ratio as base. This choice is motivated by the pleasing properties enjoyed...