Abstract:
A method for determining, by means of a circuit, a result s k+2  of an operation of the type  
         s     k   +   2       =       (       s   k              +           ∘              a   k       )              +           ∘              a     k   +   1                               
 
     where s k , a k , and a k+1  are fractional signed operands and symbol  
           +           ∘                             
 
     represents a saturating addition operation, comprising: a step of calculation of three sums representative of a possible value of the result, and a step of selection of one of said three sums according to overflows having occurred in the sum calculation. At least one step of the method uses the positive part and the negative part of at least one of the operands.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention generally relates to the processing of digital signals and more specifically to saturating operators.  
           [0003]    2. Description of the Related Art  
           [0004]    Such operators have an important technical effect. They are used in many signal processing circuits, for example, in mobile phone voice encoding or decoding circuits, where the coding and decoding algorithms use fractional signed numbers.  
           [0005]    Fractional signed numbers are numbers ranging between −1 and +1, generally coded over n bits. These numbers are signed, the bit of rank n (most significant bit) being equal to 1 for negative numbers and to 0 for positive numbers. Precisely, the value assigned to a fractional number of n bits is the value of the corresponding integer in two&#39;s complement, divided by 2 n−1 .  
           [0006]    The fractional representation is a means enabling use of calculation units which operate on integers. This results in circuits easier to form at the hardware level than circuits using floating point arithmetics. These circuits also use less memory and consume less power.  
           [0007]    A so-called “saturating” operator is an operator performing saturating operations, for example, saturating additions and multiplications.  
           [0008]    A saturating operation, which will be designated hereafter with symbol  
             +           ∘         ,                         
 
           [0009]    is an addition of two fractional signed numbers, the result of which is a fractional signed number. This means that if one of the limiting values of the fractional representation is exceeded in the addition, the result is brought to the exceeded limiting value. Thus, if the saturating addition of two signed fractional numbers coded over n bits provides a result greater than 1, said result is brought down to the maximum value that can be taken by a signed fractional number coded over n bits, that is, 1-2 −n+1 . Similarly, if the result of a saturating addition is smaller than −1, the result of the addition is brought up to the minimum number that can be represented by means of n bits in a fractional representation of signed numbers, that is, −1.  
           [0010]    Similarly, a saturating multiplication, here designated with symbol  
         ×   ∘     ,                         
 
           [0011]    is a multiplication the result of which belongs to the field of fractional signed numbers to which the operands belong. If the result of the multiplication exceeds one of the two limiting values of this representation, it is brought to the exceeded limiting value.  
           [0012]    The saturating addition and multiplication are both commutative, but not associative.  
           [0013]    A device such as a mobile phone is comprised of a microcontroller, of digital signal processors DSP, and of dedicated hardware blocks DHB. The digital signal processors and the dedicated hardware blocks are used to form a great number of various functions, for example, encryption, Fourier transform calculations, MPEG coding, etc. Many digital processings must further be accurate to within one bit. This means that the processing of a sequence of reference digital samples in a device must provide the same digital sequence as a reference algorithm for the device to be certified, standards bodies, such as the ITU (International Telecommunication Union) or the ETSI (European Telecommunications Standard Institute) being in charge of providing the reference samples/algorithms and of certifying the devices.  
           [0014]    To provide an exact result to within one bit, a digital signal processor or a dedicated hardware block generally is comprised of many circuits of MAC (Multiply Accumulate Operator) type.  
           [0015]    [0015]FIG. 1A shows a sequence of three operators of MAC type in series, MAC1, MAC2, and MAC3. Operator MAC1 receives on three input terminals three operands x 1 , y 1 , and s 1 . In a known manner, operator MAC1 provides a result:  
         s   2     =       (       x   1              x           ∘              y   1       )              +           ∘                s   1     .                             
 
           [0016]    The second operator, MAC2, receives two operands x 2 , y2, as well as result s 2  of operator MAC1. It provides a result equal to:  
         s   3     =       (       x   2              x           ∘              y   2       )              +           ∘                s   2     .                             
 
           [0017]    The third operator, MAC3, receives two operands x 3  and y 3 , as well as the result s 3  of operator MAC2. Operator MAC3 provides a result s 4  equal to:  
         s   4     =       (       x   3              x           ∘              y   3       )              +           ∘                s   3     .                             
 
           [0018]    The expressions of results s 2 , s 3 , and S 4  are shown in FIG. 1B.  
           [0019]    The number of calculations requiring operators of MAC type is generally very high. To gain space and processing time, it is known to gather the operators by two as illustrated in relation with FIGS. 2A to  2 C.  
           [0020]    [0020]FIG. 2A shows two operators of MAC type, MAC k  and MAC k+1 , connected one after the other. Operator MAC k  receives operands x k  and y k  and an operand s k  coming from the preceding operator. Operator MAC k  provides a result S k+1  equal to:  
         s     k   +   1       =       (       x   k              x           ∘              y   k       )              +           ∘                s   k     .                             
 
           [0021]    Operator MAC k+1  receives operands x k+1 , y k+1  and s k+1 . It provides a result s k+2  equal to:  
         s     k   +   2       =       (       x     k   +   1                x           ∘              y     k   +   1         )              +           ∘                s     k   +   1       .                             
 
           [0022]    As can be seen in FIG. 2B, which shows the expressions of s k+1  and s k+2 , s k+2  is equal to  
         s     k   +   2       =       (       x     k   +   1                x           ∘              y     k   +   1         )                  +           ∘              [       (       x   k              x           ∘              y   k       )              +           ∘              s   k       ]       .                             
 
           [0023]    Taking  
         a   k     =       x   k              x           ∘              y   k                   and                 a     k   +   1       =       x     k   +   1                x           ∘              y     k   +   1           ,       s     k   +   2       =       a     k   +   1                x           ∘              (       a   k              x           ∘              s   k       )                               
 
           [0024]    is obtained. One also has  
           s     k   +   2       =       (       s   k          +   °          a   k       )                     +   °                     a     k   +   1           ,                  since                 operation                     +   °                             
 
           [0025]    is commutative  
           [0026]    The two operators MAC k  and MAC k+1  can thus be replaced with a circuit 1 shown in FIG. 2C, receiving as an input three operands, a k , a k+1 , and s k . a k  corresponds to the saturating multiplication of operands x k  and y k , a k+1  corresponds to the saturating multiplication of operators x k+1  and y k+1 , and s k  corresponds to the result of the preceding circuit. Circuit  1  provides a result s k+2  equal  
         (       s   k                     +   °                     a   k       )                     +   °                       a     k   +   1       .                           
 
           [0027]    The operations providing operands a k  and a k+1  are executed outside of circuit  1 .  
           [0028]    A problem of known circuits of this type is that they perform complex processing steps and require significant hardware elements.  
           [0029]    Thus, in prior art, one way of calculating sum  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
           [0030]    is the following. The usual non-saturating sum of s k  and a k  is first calculated. Then, it is checked whether a saturation has occurred by means of an overflow circuit. If an upward overflow has occurred, the result of sum s k +a k  is replaced with the maximum fractional number and if a downward overflow has occurred, the result of the sum is replaced with the minimum fractional number. Then, the normal addition of the obtained result with a k+1  is performed. Again, it is checked whether the result of the addition exceeds the limiting values allowed by the fractional representation and, if necessary, the necessary replacements are performed. In addition to the above-mentioned disadvantages, the calculation steps are long and require evaluating twice the upward and downward overflow of the result of an operation.  
         BRIEF SUMMARY OF THE INVENTION  
         [0031]    An embodiment of the present invention provides a method and a circuit for performing operation  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
           [0032]    with a reduced number of hardware elements.  
           [0033]    Another embodiment of the present invention provides a method and a circuit for performing operation  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
           [0034]    in a particularly fast manner.  
           [0035]    Another embodiment of the present invention provides a fast circuit of MAC type comprising a reduced number of hardware elements.  
           [0036]    An embodiment of the present invention provides a method for determining, by means of a circuit, a result s k+2  of an operation of the type  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
           [0037]    where s k , a k , and a k+1  are fractional signed operands and symbol  
       +   ∘                         
 
           [0038]    represents a saturating addition operation, that is, an addition in which the result is brought, if necessary, to a limiting value allowed by the fractional representation in case this limiting value is exceeded, comprising:  
           [0039]    a step of calculation of three sums representative of a possible value of the result, and  
           [0040]    a step of selection of one of said three sums according to overflows having occurred in the sum calculation.  
           [0041]    At least one step of the method uses the positive part and the negative part of at least one of the operands, the positive part of an operand being defined as being equal to the operand if the operand is a positive number and to zero otherwise, the negative part of an operand being defined as being equal to the operand if the operand is a negative number and to zero otherwise.  
           [0042]    According to an embodiment of the present invention, the step of calculation of said three sums comprises:  
           [0043]    the calculation of a first sum defined by 
           
         s=s 
         k 
         +a 
         k 
         +a 
         k+1 
       
           [0044]    the calculation of a second sum defined by 
             s ′=max  n+a   −   k+1 , and 
           [0045]    the calculation of a third sum defined by 
             s ″=min  n+a   +   k+1   
           [0046]    max n being the value of the maximum fractional signed number, min n being the value of the minimum fractional signed number, a +   k+1  being the positive part of operand a k+1  and a −   k+1  being the negative part of operand a k+1 .  
           [0047]    According to an embodiment of the present invention, the selection step comprises a step of calculation of a first indicator and of a second indicator, the first indicator being equal to a first value if s k +a k +a k+1 &gt;max n+a −   k+1  and equal to a second value otherwise, and the second indicator being equal to a third value if s k +a k +a k+1 &lt;min n+a +   k+1  and equal to a fourth value otherwise.  
           [0048]    According to an embodiment of the present invention, the selection step provides a result s k+2  equal:  
           [0049]    to the second sum if the first indicator is equal to said first value,  
           [0050]    to the third sum if the second indicator is equal to said third value, and  
           [0051]    to the first sum in all other cases.  
           [0052]    According to an embodiment of the present invention, the step of calculation of the sums and the step of calculation of the first and second indicators are performed in parallel.  
           [0053]    One embodiment of the present invention also relates to a circuit for determining a result s k+2  of an operation of the type  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
           [0054]    where s k , a k , and a k+1  respectively are first, second, and third operands represented in the form of signed fractional numbers coded over n bits, comprising:  
           [0055]    a first means for determining the positive and negative parts of the third operand,  
           [0056]    a second means for calculating a first sum equal to the sum of the first, second, and third operands, a second sum equal to the sum of the negative part of the third operand and of the maximum signed fractional number coded over n bits, and a third sum equal to the sum of the positive part of the third operand and of the minimum fractional signed number coded over n bits,  
           [0057]    a third means for calculating a first and a second indicators, the first indicator being equal to a first value if s k +a k +a k+1 &gt;max n+a −   k+1  and equal to a second value otherwise, the second indicator being equal to a third value if s k +a k  +a k+1 &lt;min n+a +   k+1  and equal to a fourth value otherwise, max n being the value of the maximum fractional signed number coded over n bits, min n being the value of the minimum fractional signed number coded over n bits, a +   k+1  being the positive part of the third operand and a −   k+1  being the negative part of the third operand, and  
           [0058]    a fourth means for providing the first sum if the first indicator is equal to said first value, providing the second sum if the second indicator is equal to said third value, and providing the third sum in the other cases.  
           [0059]    According to an embodiment of the present invention, the first means comprises:  
           [0060]    an AND gate supplied by the third operand and the inverse of the sign bit replicated n times of the third operand for providing the positive part of the third operand, and  
           [0061]    an AND gate supplied by the third operand and the inverse of the sign bit replicated n times of the third operand for providing the negative part of the third operand.  
           [0062]    According to an embodiment of the present invention, the second means comprises:  
           [0063]    a first adder receiving the first, second, and third operands and providing said first sum,  
           [0064]    a second adder providing said second sum and receiving the negative part of the third operand and the value of the maximum fractional signed number coded over n bits, and  
           [0065]    a third adder providing said third sum and receiving the positive part of the third operand and the value of the minimum fractional signed number coded over n bits,  
           [0066]    and the fourth means comprises a multiplexer receiving said first, second, and third sums and providing result s k+2  of the operation, the multiplexer being controlled by the first and second indicators.  
           [0067]    According to an embodiment of the present invention, the third means comprises:  
           [0068]    a fourth adder receiving the first operand, the second operand, and the positive part of the third operand,  
           [0069]    a unit for indicating an upward overflow receiving the result of the fourth adder and providing the first indicator,  
           [0070]    a fifth adder receiving the first operand, the second operand, and the negative part of the third operand, and  
           [0071]    a unit for indicating a downward overflow receiving the result of the fifth adder and providing the second indicator.  
           [0072]    An embodiment of the present invention also relates to a unit performing a function of MAC type using an above method or comprising an above circuit.  
           [0073]    The foregoing features of the present invention will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0074]    [0074]FIG. 1A, previously described, shows a series of MAC-type circuits used in a signal processing;  
         [0075]    [0075]FIG. 1B illustrates the functions implemented by the circuits of FIG. 1A;  
         [0076]    [0076]FIG. 2A, previously described, shows two MAC-type circuits in series;  
         [0077]    [0077]FIG. 2B illustrates the functions of the circuits of FIG. 2A;  
         [0078]    [0078]FIG. 2C, previously described, shows a circuit used to replace the two circuits of FIG. 2A; and  
         [0079]    [0079]FIG. 3 shows a circuit according to an embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0080]    Embodiments of a high-efficiency saturating operator are described herein. In the following description, numerous specific details are given to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.  
         [0081]    Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.  
         [0082]    To perform operation  
           s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1           ,                         
 
         [0083]    an embodiment of the present invention uses the positive and negative parts of one at least of the operands.  
         [0084]    It should be reminded that, by definition, the positive part of number a k , designated as a +   k , is equal to a k  if a k  is positive or zero and equal to zero if a k  is negative or zero. The negative part of a k , designated as a −   k , is equal to a k  if a k  is negative or zero and equal to zero if a k  is positive or zero. A property of the positive and negative parts of a number a k  is that a +   k +a −   k =a k .  
         [0085]    The positive and negative parts are calculated in a very simple way from the number and its sign bit, as described hereafter. The use of the positive and negative parts of an operand will remarkably simplify the circuit performing the operation. Further, in an embodiment of the present invention, conventional overflow circuits are not used.  
         [0086]    In one embodiment of the present invention, three sums are calculated in parallel, each sum being representative of a possible value of result s k+2 . Simultaneously to the calculation of the three sums, two indicators S′ and S″, the calculation of which is much simpler than a limiting value overflow calculation, are determined. The choice of the final result is obtained by selecting one of the three calculated sums according to the value of indicators S′ and S″. The calculation of the indicators is performed in parallel with the sum calculation. The obtaining of the result is very fast, shorter than one clock cycle.  
         [0087]    [0087]FIG. 3 shows a circuit for providing the result of an operation of the type  
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                       a     k   +   1       .                             
 
         [0088]    The circuit has three inputs E 1 , E 2 , E 3 , respectively receiving three operands s k , a k , and a k+1 . The circuit has an output S, providing result s k+2  of the operation. Operands s k , a k , and a k+1 , as well as result s k+2 , are signed fractional numbers coded over n bits.  
         [0089]    The circuit comprises three adders  4 ,  6 , and  8 . Adder  4  is a three-input adder, each of the inputs receiving one of the three operands a k , a k+1 , and s k . It provides a sum s equal to s k +a k +a k+1 . Adder  6  is a two-input adder. On one of its inputs, it receives the maximum limiting value, max n, which corresponds to the maximum signed fractional number that can be represented over n bits. The other input of adder  6  receives negative part a −   k+1  of the third operand. Adder  6  provides sum s′ equal to max n+a −   k+1 . Adder  8  is a two-input adder. On one of its inputs, it receives the minimum limiting value of the used fractional representation, min n. On the other input, it receives positive part a +   k+1  of third operand a k+1 . Adder  8  outputs a sum s″ equal to min n+a −   k+1 . In practice, the circuit providing an output over n bits, only the n least significant bits of sums s, s′, and s″ can be used hereafter. The n least significant bits of sums s, s′, and s″ can be obtained by simple truncating at the level of adders  4 ,  6 , and  8 , or subsequently.  
         [0090]    Values min n and max n, respectively provided to adders  8  and  6 , can be stored or determined internally to the circuit. They can also be provided to the circuit, especially in the case where the circuit is parameterizable and provided to operate with operands coded over different numbers of bits according to the applications.  
         [0091]    Positive part a +   k+1  of operator a k+1  is determined by a unit  10 . Unit  10  is formed of a sign extraction unit  12  and of an AND-type gate  11  over n bits, one input of which is inverting. The non-inverting input of gate  11  receives third operand a k+1 . On its inverting input, gate  11  receives the sign bit replicated n times of operand a k+1 . This bit is provided by unit  12 , which receives operand a k+1  and replicates n times the most significant bit thereof, of rank n. The output of gate  11  provides positive part a +   k+1  of operand a k+1 .  
         [0092]    Negative part a −   k+1  of operand a k+1  is determined by a unit  14 . Unit  14  comprises an AND-type gate  15  and a sign extraction unit  16 . Unit  16  receives third operand a k+1  and replicates its most significant bit, representing the sign of the operand, n times. Gate  15  receives on one input the sign bit replicated n times of operand a k+1 , provided by unit  16 , and on the other input operand a k+1 . The output of gate  15  provide negative part a −   k+1  of the third operand.  
         [0093]    At the same time as sums s, s′, and s″ are determined, the circuit calculates two indicators S′ and S″, the value of which enables selection of the sum corresponding to the result.  
         [0094]    The calculation of indicator S′ is performed as follows. A three-input adder  20  receives first operand s k , second operand a k , and the positive part of third operand a +   k+1 . It provides sum R′ of the three operands. Since each of the operands is coded over n bits, result R′ is provided over n+2 bits. Result R′ is provided to three bit extraction units  21 ,  22 , and  23 . Unit  21  provides the n-th bit of result R′. Unit  22  provides the bit of rank n+1 of result R′. Unit  23  provides the bit of rank n+2 of result R′. The outputs of units  21  and  22  supply an OR-type gate  25 . The output of gate  25  supplies a non-inverting input of an AND-type gate  26 . Gate  26  comprises two inputs, a non-inverting and an inverting input. The inverting input of gate  26  receives the bit of rank n+2 of result R′ provided by unit  23 . The output of gate  26  provides indicator S′, which is equal to 1 only if the bit of rank n+2 of result R′ is equal to 0 and one of the two bits of rank n or n+1 of result R′ is equal to 1. It is demonstrated that indicator S′ is equal to 1 if s k +a k +a k+1 &gt;max n+a −   k+1 , which is equivalent to s k +a k +a +   k+1 &gt;max n. Indicator S′ is equal to 0 otherwise. The assembly of units  21 ,  22 ,  23  and of gates  25  and  26  forms a unit  28  indicating an upward overflow only and is particularly simple to form.  
         [0095]    The calculation of indicator S″ is performed as follows. A three-input adder  30  receives first operand s k , second operand a k , and the negative part of the third operand, a −   k+1 . Adder  30  provides, over n+2 bits, a result R″ equal to the sum of the three signals present on its inputs. The adder output drives three bit-extracting units  31 ,  32 , and  33 . Unit  31  provides a bit of rank n of result R″. Unit  32  provides the bit of rank n+1 of result R″ and unit  33  provides the bit of rank n+2 of result R″. The outputs of units  31  and  32  drive a NAND gate  35 . The output of gate  35  drives an input of a two-input AND-type gate  36  receiving, on its other input, the bit of rank n+2 of result R″, provided by unit  33 . The output of gate  36  provides second indicator S″, which is equal to 1 only if the bit of rank n+2 of result R″ is equal to 1 and one of the two bits of rank n or n+1 is equal to zero. It is demonstrated that indicator S″ is equal to 1 if s k +a k +a k+1 &lt;min n+a +   k+1 , which is equivalent to s k +a k +a −   k+1 &lt;min n. Indicator S″ is equal to 0 otherwise. The assembly of units  31 ,  32 ,  33  and of gates  35  and  36  forms a unit  38  indicating a downward overflow only and is particularly simple to form.  
         [0096]    The output of gate  26  is connected to a first control input of a multiplexer  40  and the output of gate  36  is connected to a second control input of multiplexer  40 . Multiplexer  40  comprises three inputs, respectively receiving sums s, s′ and s″, possibly the n least significant bits of these sums. Indicators S′ and S″ control multiplexer  40  so that the multiplexer selects sum s′ and provides the n least significant bits of this sum if indicator S′ is equal to 1. Multiplexer  40  selects sum s″ and provides the n least significant bits of this sum if indicator S″ is equal to 1. In the other cases, the multiplexer provides the n least significant bits of sum s. The multiplexer output is connected to output S of the circuit. It should be noted that indicators S′ and S″ cannot be equal to 1 at the same time.  
         [0097]    The circuit of FIG. 3 is particularly advantageous since it uses few elements. For example, it uses a single multiplexer  40 . Further, one of the prior art problems solved by the present invention relates to overflow circuits. Indeed, in the present invention, not only is the use of conventional overflow units, calculating both an upward and a downward overflow, avoided, but also is the calculation of indicators S′ and S″, indicating either an upward overflow or a downward overflow, performed simultaneously to the sum calculation, without having to wait for the result of the sums. The circuit simplification and the time gain are significant. In embodiments using CMOS electronic circuits, it is possible to significantly decrease the electric consumption by lowering the supply voltage, at the cost of an increase in propagation delays. The time gain introduced by the circuit can thus be exploited to decrease the electric consumption.  
         [0098]    It should also be noted that the elements used in the circuit are extremely fast. All the calculations can be provided in less than one clock cycle. The insertion of such a circuit in a digital signal processor or a dedicated hardware block enables significant improvement of the performances in many applications, especially applications where the processing must be performed with a precision to within one bit. Indeed, the use of this circuit enables adding with saturation twice as many operands per cycle than in the case where conventional saturating adders are used. n, namely the number of bits on which the operands are coded, may have any value. For example, n may be equal to 32.  
         [0099]    Of course, the present invention is likely to have various alterations, modifications, and improvements which will readily occur to those skilled in the art. For example, one or several elements forming the described circuit may be replaced with other elements generally performing the same function.  
         [0100]    It should further be noted that the field of the present invention extends to any circuit or method comprising an operator performing operation s k+2   
         s     k   +   2       =       (       s   k                     +   °                     a   k       )                     +   °                     a     k   +   1                               
 
         [0101]    according to the present invention. For example, the circuit of an embodiment of the present invention may be easily completed to implement the function of a MAC-type circuit, the calculation of operands a k  and a k+1  being integrated to the circuit.  
         [0102]    Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present invention. Accordingly, the foregoing description is by way of example only and is not intended to be limiting. The present invention is limited only as defined in the following claims and the equivalents thereto.  
         [0103]    All of the above U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet, are incorporated herein by reference, in their entirety.