TMS320 is a blanket name for a series of digital signal processors (DSPs) from Texas Instruments . It was introduced on April 8, 1983, through the TMS32010 processor, which was then the fastest DSP on the market.
68-399: The processor is available in many different variants, some with fixed-point arithmetic and some with floating-point arithmetic . The TMS320 processors were fabricated on MOS integrated circuit chips, including both NMOS and CMOS variants. The floating-point DSP TMS320C3x, which exploits delayed branch logic , has as many as three delay slots . This series of processors are used as
136-506: A digital signal processing co-processor and as the main CPU in some applications. Newer implementations support standard IEEE JTAG control for boundary scan and/or in-circuit debugging. The original TMS32010 and its subsequent variants are an example of a CPU with a modified Harvard architecture , which features separate address spaces for instruction and data memory but the ability to read data values from instruction memory. The TMS32010 featured
204-405: A /10 , such as 1/100 or 37/1000, can be exactly represented in fixed point with a power-of-ten scaling factor 1/10 with any n ≥ m . This decimal format can also represent any binary fraction a /2 , such as 1/8 (0.125) or 17/32 (0.53125). More generally, a rational number a / b , with a and b relatively prime and b positive, can be exactly represented in binary fixed point only if b
272-575: A fast multiply-and-accumulate operation useful in both DSP applications as well as transformations used in computer graphics. The graphics controller card for the Apollo Computer DN570 Workstation, released in 1985, was based on the TMS32010 and could transform 20,000 2D vectors per second. The TMS320 architecture has been around for a while so a number of product variants have developed. The product codes used by Texas Instruments after
340-548: A fixed-point representation can have error less than 1.2 × 10 , whereas the standard floating-point representation may have error up to 596 × 10 — because 9 of the bits are wasted with the sign and exponent of the dynamic scaling factor. Specifically, comparing 32-bit fixed-point to floating-point audio, a recording requiring less than 40 dB of headroom has a higher signal-to-noise ratio using 32-bit fixed. Programs using fixed-point computations are usually more portable than those using floating-point since they do not depend on
408-407: A fractional amount of hours may be represented as an integer number of seconds; that is, as a fixed-point number with scale factor of 1/3600. Even with the most careful rounding, fixed-point values represented with a scaling factor S may have an error of up to ±0.5 in the stored integer, that is, ±0.5 S in the value. Therefore, smaller scaling factors generally produce more accurate results. On
476-566: A legal safe and internationally law domains respecting way. The typical freeware use case "share" can be further refined with Creative Commons restriction clauses like non-commerciality ( CC BY-NC ) or no- derivatives ( CC BY-ND ), see description of licenses . There are several usage examples , for instance The White Chamber , Mari0 or Assault Cube , all freeware by being CC BY-NC-SA licensed with only non-commercial sharing allowed. Freeware cannot economically rely on commercial promotion. In May 2015 advertising freeware on Google AdWords
544-468: A license, but displays advertising to either cover development costs or as a means of income. Registerware forces the user to subscribe with the publisher before being able to use the product. While commercial products may require registration to ensure licensed use , registerware do not. Shareware permits redistribution, but the license only allows limited use before paying the license fee. Some features may be disabled prior to payment, in which case it
612-416: A more capable version, as in the freemium and shareware business models . The term freeware was coined in 1982 by Andrew Fluegelman , who wanted to sell PC-Talk , the communications application he had created, outside of commercial distribution channels. Fluegelman distributed the program via the same process as shareware . As software types can change, freeware can change into shareware. In
680-450: A multiply instruction that includes renormalization—the scaling conversion of the product from 2 n −2 to n −1 fraction bits. If the CPU does not provide that feature, the programmer must save the product in a large enough register or temporary variable, and code the renormalization explicitly. Overflow happens when the result of an arithmetic operation is too large to be stored in the designated destination area. In addition and subtraction,
748-556: A promotion for the premium version. The two often share a code base, using a compiler flag to determine which is produced. For example, BBEdit has a BBEdit Lite edition which has fewer features. XnView is available free of charge for personal use but must be licensed for commercial use. The "free" version may be advertising supported, as was the case with the DivX . Ad-supported software and registerware also bear resemblances to freeware. Ad-supported software does not ask for payment for
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#1733086127171816-428: A signed integer in two's complement representation with an implicit scaling factor as above. The sign of the value will always be indicated by the first stored bit (1 = negative, 0 = non-negative), even if the number of fraction bits is greater than or equal to the total number of bits. For example, the 8-bit signed binary integer (11110101) 2 = −11, taken with -3, +5, and +12 implied fraction bits, would represent
884-405: A single entity to be responsible for updating and enhancing the product, which is then given away without charge. Other freeware projects are simply released as one-off programs with no promise or expectation of further development. These may include source code , as does free software, so that users can make any required or desired changes themselves, but this code remains subject to the license of
952-407: A variable or formula may not appear explicitly in the program. Good programming practice then requires that it be provided in the documentation , at least as a comment in the source code . For greater efficiency, scaling factors are often chosen to be powers (positive or negative) of the base b used to represent the integers internally. However, often the best scaling factor is dictated by
1020-423: Is 22×32/100 = 7.04. If the result is not exact, the error introduced by the rounding can be reduced or even eliminated by converting the dividend to a smaller scaling factor. For example, if r = 1.23 is represented as 123 with scaling 1/100, and s = 6.25 is represented as 6250 with scaling 1/1000, then simple division of the integers yields 123÷6250 = 0 (rounded) with scaling factor (1/100)/(1/1000) = 10. If r
1088-488: Is a fixed-point environment having each array (block) of fixed-point data be scaled with a common exponent in a single word. A common use of decimal fixed-point is for storing monetary values, for which the complicated rounding rules of floating-point numbers are often a liability. For example, the open-source money management application GnuCash , written in C, switched from floating-point to fixed-point as of version 1.6, for this reason. Binary fixed-point (binary scaling)
1156-421: Is a power of 2; and in decimal fixed point only if b has no prime factors other than 2 and/or 5. Fixed-point computations can be faster and/or use less hardware than floating-point ones. If the range of the values to be represented is known in advance and is sufficiently limited, fixed point can make better use of the available bits. For example, if 32 bits are available to represent a number between 0 and 1,
1224-437: Is first converted to 1,230,000 with scaling factor 1/1000000, the result will be 1,230,000÷6250 = 197 (rounded) with scale factor 1/1000 (0.197). The exact value 1.23/6.25 is 0.1968. In fixed-point computing it is often necessary to convert a value to a different scaling factor. This operation is necessary, for example: To convert a number from a fixed point type with scaling factor R to another type with scaling factor S ,
1292-466: Is generally easier and safer to select scaling factors and word sizes so as to exclude the possibility of overflow, or to check the operands for excessive values before executing the operation. Freeware Freeware is software , most often proprietary , that is distributed at no monetary cost to the end user . There is no agreed-upon set of rights, license , or EULA that defines freeware unambiguously; every publisher defines its own rules for
1360-406: Is more natural for the problem. Examples of the latter are accounting of dollar amounts, when fractions of cents must be rounded to whole cents in strictly prescribed ways; and the evaluation of functions by table lookup , or any application where rational numbers need to be represented without rounding errors (which fixed-point does but floating-point cannot). Fixed-point representation is still
1428-407: Is possible by adding a 'rounding addend' of half of the scaling factor before shifting; The proof: round(x/y) = floor(x/y + 0.5) = floor((x + y/2)/y) = shift-of-n(x + 2^(n-1)) A similar method is usable in any scaling. To divide two fixed-point numbers, one takes the integer quotient of their underlying integers and assumes that the scaling factor is the quotient of their scaling factors. In general,
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#17330861271711496-431: Is sometimes known as crippleware. Both freeware and shareware sometimes have a limited evaluation period, after which the software is automatically disabled or starts displaying a request to pay a registration fee. In the latter case it is colloquially known as nagware. The Creative Commons offer licenses , applicable to all by copyright governed works including software, which allow a developer to define "freeware" in
1564-643: Is typically proprietary and distributed without source code. By contrast, the "free" in "free software" refers to freedoms granted users under the software license (for example, to run the program for any purpose, modify and redistribute the program to others), and such software may be sold at a price. According to the Free Software Foundation (FSF), "freeware" is a loosely defined category and it has no clear accepted definition, although FSF asks that free software (libre; unrestricted and with source code available) should not be called freeware. In contrast
1632-647: The TDA4VM , which features a C71x DSP. General Instrument manufactured the TMS32010 as a second source . Around 1991, a CMOS-version of the TMS32020 was manufactured by ZMD under the designation U320C20FC. A number of devices from the TMS320 series are in production at NIIET Voronezh as the 1867 series, including a radiation-hardened version of the TMS320C25 under the designation 1867VM7T ( Russian : 1867ВМ7Т ). Clones of
1700-406: The cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation . In the fixed-point representation,
1768-545: The discrete cosine transform algorithms used to compress JPEG images. Electronic instruments such as electricity meters and digital clocks often use polynomials to compensate for introduced errors, e.g. from temperature or power supply voltage. The coefficients are produced by polynomial regression . Binary fixed-point polynomials can utilize more bits of precision than floating-point and do so in fast code using inexpensive CPUs. Accuracy, crucial for instruments, compares well to equivalent-bit floating-point calculations, if
1836-411: The 1980s and 1990s, the term freeware was often applied to software released without source code . Freeware software is available for use without charge and typically has limited functionality with a more capable version available commercially or as shareware. It is typically fully functional for an unlimited period of time. In contrast to what the Free Software Foundation calls free software ,
1904-603: The C6x series in GCC, as part of their effort to port the Linux kernel to C6x. This culminated in C6x being a supported architecture in GCC release 4.7 on March 22, 2012. Fixed-point arithmetic In computing , fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing
1972-476: The Oxford English Dictionary simply characterizes freeware as being "available free of charge (sometimes with the suggestion that users should make a donation to the provider)". Some freeware products are released alongside paid versions that either have more features or less restrictive licensing terms. This approach is known as freemium ("free" + "premium"), since the "free" version is intended as
2040-652: The TMS320 processors is done using Texas Instruments proprietary toolchain and their integrated development environment Code Composer Studio , which includes a mini operating system called DSP/BIOS . Additionally, a department at the Chemnitz University of Technology has developed preliminary support for the TMS320C6x series in the GNU Compiler Collection . In November 2007, TI released part of its toolchain as freeware for non-commercial users, offering
2108-462: The TMS320C546 went into production at PKK Milandr Moscow in 2009 under the designation 1967VC1T ( Russian : 1967ВЦ1Т ) and in 2016 at MVC Nizhny Novgorod as 1910VM1T ( Russian : 1910ВМ1Т ). PKK Milandr also manufactures a TMS320C54x with an additional ARM core as the 1901VC1T ( Russian : 1901ВЦ1Т ). The TMS320 series can be programmed using C , C++ , and/or assembly language . Most work on
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2176-449: The accuracy δ = S /2 of values that could be represented in 16-bit signed binary fixed point format, depending on the number f of implied fraction bits. Fixed-point formats with scaling factors of the form 2 -1 (namely 1, 3, 7, 15, 31, etc.) have been said to be appropriate for image processing and other digital signal processing tasks. They are supposed to provide more consistent conversions between fixed- and floating-point values than
2244-488: The application. Thus one often uses scaling factors that are powers of 10 (e.g. 1/100 for dollar values), for human convenience, even when the integers are represented internally in binary. Decimal scaling factors also mesh well with the metric (SI) system , since the choice of the fixed-point scaling factor is often equivalent to the choice of a unit of measure (like centimeters or microns instead of meters ). However, other scaling factors may be used occasionally, e.g.
2312-474: The author of freeware usually restricts the rights of the user to use, copy, distribute, modify, make derivative works, or reverse engineer the software. The software license may impose additional usage restrictions; for instance, the license may be "free for private, non-commercial use" only, or usage over a network, on a server, or in combination with certain other software packages may be prohibited. Restrictions may be required by license or enforced by
2380-627: The availability of an FPU. This advantage was particularly strong before the IEEE Floating Point Standard was widely adopted when floating-point computations with the same data would yield different results depending on the manufacturer, and often on the computer model. Many embedded processors lack an FPU, because integer arithmetic units require substantially fewer logic gates and consume much smaller chip area than an FPU; and software emulation of floating-point on low-speed devices would be too slow for most applications. CPU chips for
2448-510: The bare compiler, assembler, optimizer and linker under a proprietary license. However, neither the IDE nor a debugger were included, so for debugging and JTAG access to the DSPs, users still need to purchase the complete toolchain. In 2010, Texas Instruments contracted CodeSourcery (the assignment later transferred to Mentor Graphics as part of their acquisition) to provide deep integration and support for
2516-426: The base b ; whereas their absolute resolution varies by many orders of magnitude, like the values themselves. In many cases, the rounding and truncation errors of fixed-point computations are easier to analyze than those of the equivalent floating-point computations. Applying linearization techniques to truncation, such as dithering and/or noise shaping is more straightforward within fixed-point arithmetic. On
2584-586: The distinction between the two groups of digits is defined only by the programs that handle such numbers. Fixed-point representation was the norm in mechanical calculators . Since most modern processors have fast floating-point unit (FPU), fixed-point representations in processor-based implementations are now used only in special situations, such as in low-cost embedded microprocessors and microcontrollers ; in applications that demand high speed or low power consumption or small chip area, like image , video , and digital signal processing ; or when their use
2652-455: The earlier personal computers and game consoles , like the Intel 386 and 486SX , also lacked an FPU. The absolute resolution (difference between successive values) of any fixed-point format is constant over the whole range, namely the scaling factor S . In contrast, the relative resolution of a floating-point format is approximately constant over their whole range, varying within a factor of
2720-438: The first TMS32010 processor have involved a series of processor named "TMS320Cabcd", where a is the main series, b the generation and cd is some custom number for a minor sub-variant. For this reason, those working with DSPs often abbreviate a processor as "C5x" when the actual name is, for example, TMS320C5510, since all products have the name "TMS320", and all processors with "C5" in the name are code compatible and share
2788-477: The first division requires rounding and therefore the result is not exact. For example, division of 3456 scaled by 1/100 (34.56) and 1234 scaled by 1/1000 (1.234) yields the integer 3456÷1234 = 3 (rounded) with scale factor (1/100)/(1/1000) = 10, that is, 30. As another example, the division of the first number by 155 implicitly scaled by 1/32 (155/32 = 4.84375) yields the integer 3456÷155 = 22 (rounded) with implicit scaling factor (1/100)/(1/32) = 32/100 = 8/25, that
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2856-407: The first number by 155 implicitly scaled by 1/32 (155/32 = 4.84375) yields the integer 123×155 = 19065 with implicit scaling factor (1/1000)×(1/32) = 1/32000, that is 19065/32000 = 0.59578125. In binary, it is common to use a scaling factor that is a power of two. After the multiplication, the scaling factor can be divided away by shifting right. Shifting is simple and fast in most computers. Rounding
2924-443: The fixed-point polynomials are evaluated using Horner's method (e.g. y = (( ax + b ) x + c ) x + d ) to reduce the number of times that rounding occurs, and the fixed-point multiplications utilize rounding addends. To add or subtract two values with the same implicit scaling factor, it is sufficient to add or subtract the underlying integers; the result will have their common implicit scaling factor and can thus be stored in
2992-402: The fraction is often expressed in the same number base as the integer part, but using negative powers of the base b . The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling . Thus, if n fraction digits are stored, the value will always be an integer multiple of b . Fixed-point representation can also be used to omit
3060-425: The freeware it offers. For instance, modification , redistribution by third parties, and reverse engineering are permitted by some publishers but prohibited by others. Unlike with free and open-source software , which are also often distributed free of charge, the source code for freeware is typically not made available. Freeware may be intended to benefit its producer by, for example, encouraging sales of
3128-406: The integer 3075 then must be multiplied by 1/100, that is, divided by 100, to yield either 31 (0.31) or 30 (0.30), depending on the rounding policy used. Similarly, the operation r ← r / s will require dividing the integers and explicitly multiplying the quotient by S . Rounding and/or overflow may occur here too. To convert a number from floating point to fixed point, one may multiply it by
3196-461: The integer, or appending zero digits. However, this operation must preserve the sign of the number. In two's complement representation, that means extending the sign bit as in arithmetic shift operations. If S does not divide R (in particular, if the new scaling factor S is greater than the original R ), the new integer may have to be rounded . In particular, if r and s are fixed-point variables with implicit scaling factors R and S ,
3264-464: The last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented as 1230 with an implicit scaling factor of 1000 (with "minus 3" implied decimal fraction digits, that is, with 3 implicit zero digits at right). This representation allows standard integer arithmetic logic units to perform rational number calculations. Negative values are usually represented in binary fixed-point format as
3332-449: The low-order digits of integer values, e.g. when representing large dollar values as multiples of $ 1000. When decimal fixed-point numbers are displayed for human reading, the fraction digits are usually separated from those of the integer part by a radix character (usually '.' in English, but ',' or some other symbol in many other languages). Internally, however, there is no separation, and
3400-451: The norm for field-programmable gate array (FPGA) implementations, as floating-point support in an FPGA requires significantly more resources than fixed-point support. A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that
3468-404: The operation r ← r × s requires multiplying the respective integers and explicitly dividing the result by S . The result may have to be rounded, and overflow may occur. For example, if the common scaling factor is 1/100, multiplying 1.23 by 0.25 entails multiplying 123 by 25 to yield 3075 with an intermediate scaling factor of 1/10000. In order to return to the original scaling factor 1/100,
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#17330861271713536-462: The other hand, a smaller scaling factor means a smaller range of the values that can be stored in a given program variable. The maximum fixed-point value that can be stored into a variable is the largest integer value that can be stored into it, multiplied by the scaling factor; and similarly for the minimum value. For example, the table below gives the implied scaling factor S , the minimum and maximum representable values V min and V max , and
3604-432: The other hand, the use of fixed point requires greater care by the programmer. Avoidance of overflow requires much tighter estimates for the ranges of variables and all intermediate values in the computation, and often also extra code to adjust their scaling factors. Fixed-point programming normally requires the use of integer types of different widths . Fixed-point applications can make use of block floating point , which
3672-401: The result may require one bit more than the operands. In multiplication of two unsigned integers with m and n bits, the result may have m + n bits. In case of overflow, the high-order bits are usually lost, as the un-scaled integer gets reduced modulo 2 where n is the size of the storage area. The sign bit, in particular, is lost, which may radically change the sign and the magnitude of
3740-444: The same basic features. Similarly, a subgrouping may be referred to as, for example, C55x, as processors in the same series and generation are even more similar. TMS320 processors are fabricated on MOS integrated circuit chips, including both NMOS and CMOS variants. The C7000 series was released in early 2020, but cores are not available individually. As of August 2023, they are only available bundled inside other SOCs, such as
3808-411: The same program variables as the operands. These operations yield the exact mathematical result, as long as no overflow occurs—that is, as long as the resulting integer can be stored in the receiving program variable . If the operands have different scaling factors, then they must be converted to a common scaling factor before the operation. To multiply two fixed-point numbers, it suffices to multiply
3876-409: The scaling factor S , then round the result to the nearest integer. Care must be taken to ensure that the result fits in the destination variable or register. Depending on the scaling factor and storage size, and on the range input numbers, the conversion may not entail any rounding. To convert a fixed-point number to floating-point, one may convert the integer to floating-point and then divide it by
3944-657: The scaling factor S . This conversion may entail rounding if the integer's absolute value is greater than 2 (for binary single-precision IEEE floating point) or of 2 (for double-precision). Overflow or underflow may occur if | S | is very large or very small, respectively. Typical processors do not have specific support for fixed-point arithmetic. However, most computers with binary arithmetic have fast bit shift instructions that can multiply or divide an integer by any power of 2; in particular, an arithmetic shift instruction. These instructions can be used to quickly change scaling factors that are powers of 2, while preserving
4012-737: The sign of the number. Early computers like the IBM 1620 and the Burroughs B3500 used a binary-coded decimal (BCD) representation for integers, namely base 10 where each decimal digit was independently encoded with 4 bits. Some processors, such as microcontrollers, may still use it. In such machines, conversion of decimal scaling factors can be performed by bit shifts and/or by memory address manipulation. Some DSP architectures offer native support for specific fixed-point formats, for example, signed n -bit numbers with n −1 fraction bits (whose values may range between −1 and almost +1). The support may include
4080-458: The software itself; e.g., the package may fail to function over a network. The U.S. Department of Defense (DoD) defines "open source software" (i.e., free software or free and open-source software), as distinct from "freeware" or "shareware"; it is software where "the Government does not have access to the original source code". The "free" in "freeware" refers to the price of the software, which
4148-450: The two underlying integers, and assume that the scaling factor of the result is the product of their scaling factors. The result will be exact, with no rounding, provided that it does not overflow the receiving variable. For example, multiplying the numbers 123 scaled by 1/1000 (0.123) and 25 scaled by 1/10 (2.5) yields the integer 123×25 = 3075 scaled by (1/1000)×(1/10) = 1/10000, that is 3075/10000 = 0.3075. As another example, multiplying
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#17330861271714216-448: The underlying integer must be multiplied by the ratio R / S . Thus, for example, to convert the value 1.23 = 123/100 from scaling factor R =1/100 to one with scaling factor S =1/1000, the integer 123 must be multiplied by (1/100)/(1/1000) = 10, yielding the representation 1230/1000. If the scaling factor is a power of the base used internally to represent the integer, changing the scaling factor requires only dropping low-order digits of
4284-410: The usual 2 scaling. The Julia programming language implements both versions. Any binary fraction a /2 , such as 1/16 or 17/32, can be exactly represented in fixed-point, with a power-of-two scaling factor 1/2 with any n ≥ m . However, most decimal fractions like 0.1 or 0.123 are infinite repeating fractions in base 2. and hence cannot be represented that way. Similarly, any decimal fraction
4352-433: The value. Some processors can set a hardware overflow flag and/or generate an exception on the occurrence of an overflow. Some processors may instead provide saturation arithmetic : if the result of an addition or subtraction were to overflow, they store instead the value with the largest magnitude that can fit in the receiving area and has the correct sign. However, these features are not very useful in practice; it
4420-501: The values −11/2 = −88, −11/2 = −0. 343 75 , and −11/2 = −0. 002 685 546 875 , respectively. Alternatively, negative values can be represented by an integer in the sign-magnitude format, in which case the sign is never included in the number of implied fraction bits. This variant is more commonly used in decimal fixed-point arithmetic. Thus the signed 5-digit decimal integer (−00025) 10 , taken with -3, +5, and +12 implied decimal fraction digits, would represent
4488-449: The values −25/10 = −25000, −25/10 = −0.00025, and −25/10 = −0. 000 000 000 025 , respectively. A program will usually assume that all fixed-point values that will be stored into a given variable, or will be produced by a given instruction , will have the same scaling factor. This parameter can usually be chosen by the programmer depending on the precision needed and range of values to be stored. The scaling factor of
4556-509: Was restricted to "authoritative source"[s]. Thus web sites and blogs are the primary resource for information on which freeware is available, useful, and is not malware . However, there are also many computer magazines or newspapers that provide ratings for freeware and include compact discs or other storage media containing freeware. Freeware is also often bundled with other products such as digital cameras or scanners . Freeware has been criticized as "unsustainable" because it requires
4624-463: Was widely used from the late 1960s to the 1980s for real-time computing that was mathematically intensive, such as flight simulation and in nuclear power plant control algorithms. It is still used in many DSP applications and custom-made microprocessors. Computations involving angles would use binary angular measurement . Binary fixed point is used in the STM32G4 series CORDIC co-processors and in
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