TW579482B - Exponent operation device and method for floating point number - Google Patents

Abstract

The present invention is an exponent operation device and method for floating point number for obtaining an exponent operation result of a floating point number with 2 as the base, which comprises: a conversion device for receiving the input of floating point number to convert the floating point number into an integer portion and a fraction portion for output; K exponent index tables, wherein the fraction portion includes N bits, and dividing the N bits into K portions, and each portion has N1, N2, ..., Nk bits, and N=N1+N2+...+NK, and each exponent table receives an input within the N portions and looks up the table to generate an output result; and, a multiplier for receiving the output result from each exponent index table as input to generate an odd amount; wherein, the integer portion is an exponent, and the result of exponent operation is represented with an odd amount, an exponent, and an output symbol number with value as zero. The representation of result from exponent operation is (-1)<Sy>.2<Ey>.my, wherein Sy is the symbol number, Ey is the exponent, my is the odd amount, 1 <= mx < 2, and the above-mentioned N, K, K1, K2, ..., KN are natural numbers.

Description

579482 V. Description of the invention (1) The present invention relates to a method and device for exponential operation, and particularly relates to a method and device for exponential operation of floating point numbers. In the target computer, the most commonly used representation of the floating-point number F is: the number F = MX ySE where M is the mantissa (mantissa is the index, cold is the index of the Institute of Electrical and Electronic Engineers (ΙΕΕΕ) established four standard formats for the representation of floating-point numbers. The first two formats are single-precision 32-bit format and double-bit precise 64-bit format (d〇). Uble-precisi〇n 64 one-bit f0rmat), the other two are extended formats used to represent intermediate results in operations. For a single precise 32-bit format representation, the most important purpose is to represent floating-point numbers Accuracy, and only in order to get more significant digits, the double-bit precise 64-bit format notation is used to store the floating-point receiver in double-length (DuoMe Ungth) storage space. See section 1 Figure 1. Figure 1 shows a schematic representation of the single precision 32-bit format representation above. In this notation, a floating point number s · 2E · Μ is used as the base number 2, where M is the mantissa of the floating point number (mantissa ), It is represented by 23 bits, E is the exponent of the floating-point number, it is represented by 8 bits, and the number of symbols of the points is represented by 1 bit. In the current electronic computers, almost all operations are performed. Use floating-point page 0702-7516TW; 90P130; Ellen.ptd 579482 V. Description of the invention (2) The efficiency of the computer determines the establishment of a comparison table for the computer, and uses 2 to check the method when calculating , Calculate the result in advance, and use this side to proud ... the second table to find the exponent of the net points: = Q: an 8-bit comparison table is quite pang i the accuracy of the result is still about From the "number of counties", the number of calculations is 23 bits. "Because a floating-point number usually has the part here." The main purpose of the present invention is an index calculation device and method for obtaining The point with the most points refers to the arithmetic operation result. To achieve the above purpose, the floating point number with the same accuracy and accuracy is achieved by the present invention. The expression of the number of points in the present invention is (-1) Sx · 2Eχ. The expression is (-1) sy. 2Ey mHe Γχ s sii index calculation results table ,; 'In F, the symbol number of the * point number, sy is the heart number of the Shanghai child fm of the exponential calculation social fruit, Ey is the number, Xi 筲 = tx is the mantissa of the western point number, and m is the parenthesis :-Conversion device for receiving the exponent of the above-mentioned floating-point number and the package point exponent and the mantissa input of the floating-point number, and replacing ^ yang with an -integer part and a fractional part for output; κ fingers Back: 矣 The number of digits in the fractional part has N bits, and the N bits, two, and money have N, N2, ..., NK bits, and N = Νι + Ν2Ϊ = Ν, the mother: part of the index table Receive a part of the input from the above K part, 1 Page 5 0702-7516BfF; 90Pl30; Ellen.ptd V. Description of the invention (3) f gives the result;-a multiplier, which is used to connect the 'output result input' and generate The integer part rounded out by the conversion device of the above-mentioned several index comparison tables is the mantissa of the upper fruit. Among them, the above exponential operation &amp; I # f #mentioned the result of the operation of the digit number refers to H,…, “from: the number of the fruit number has a value of zero 'and above”] On the other hand, the present invention also provides a Method for obtaining ―floating point number with 2 as the base—the exponent operation of the sub-point number is represented by (_ 丨) Sx · 2Ex · /, and the result of 1 θ is different from the floating-point number, I is the exponent of the floating-point number, = is &amp; tSx is the sign of the floating-point number% &lt; 2. The exponential operation method includes "steps :: two's mantissa and the sign of the 1 $ number, the above floating-point The exponent of the number and the above-mentioned floating point into the conversion device. Then, the mantissa input of the points is converted into an integer part and a fraction part into the above floating point parts. The above fraction part has N divisions, and the fraction part is divided into K Nl,... And M1 + N2 + ... + N 'mothers: ~' parts 4 each have a part of the input mother-in-the-exponential table to receive the results of the part. Then 1 each of the above exponents + ^ lookup table produces an output knot which produces a mantissa. Finally, # use the above-mentioned tail-out-multiplier and a number of zero symbols to represent the above-mentioned exponent ^ integer part, and the representation of the result is (−1) Sy · 2Ey, luck ... fruit, edge exponential operation above Integer part, my is the above output; number, m sign number, Ey is K, Ki, K2, ..., natural number. Gross number ^ 〆2 ′ and the above N, embodiment FIG. 2 shows a schematic diagram of the structure of a floating-point number arithmetic operation device according to the present invention.

579482 V. Description of the invention (4) Figure. As shown in the figure, the floating-point number exponential operation device includes K sets of conversion units, a number comparison table 2 to 2 κκ, and a multiplier 3 〇. The conversion device 丨 〇 uses the sign of the number of convergent points X, the exponent of the floating point number χ, and the mantissa of the number X to input, converts the floating point number to an integer part, and rotates the part. An error message Err is output when the floating-point number is represented as an integer part x ° or two. Fractional part F: and please divide the bits into K parts, each-part has (, a wide place / cloth general, and ν = Μν2 + ... + Nκ, κ index comparison table ^ index table receives the above One input in the K part, and one input * θ: Use the output result of the index table to receive the result of the index operation outside the input integer part; Refer to: E: The index operation result γ of the device is positive, so y and because it is zero, the symbol number sy of the fruit ¥ The above floating-point number X is expressed as: X = (-1) Sx · 2Ex · mx ⑴ where Sx is the sign number of the floating-point number, float The sign of the number of points is 0. When the floating point appears to be a negative number, the number sx is 1; Ex is the sign of the exponent two subpoints of the floating point number 1 Smx <2. X 4 5 Mantissa and exponential operation device of western points of the present invention, X exponential operation result γ · 2 as the base; obtain the floating point number Y-2 ^ (^ l) Sy. 2Ey. Ffly (2) where sy is The sign number U of the exponential operation result is' numerical operation result page 70702-7516TW; 90P130; Ellen.ptd 579482 V. Description of the invention (5) __ If Y is a positive number, the result of the exponential operation The sign of the number of days is 1 ?, and the number Sy is zero; Ey is $ my &lt; 2. y is the mantissa of the result of the number operation of σ, and 1 part is to find 仵 Υ Divided into integer parts and fractions X = (~ 1) S: ,, = IX + FX (3)-, where Ix is the number part, Fx is the fraction Pχ = Φ2-ν = (Σα 「2,2_ν ⑷ X &lt; 1 where q is an N-bit number and ^ is a digit number. Y = = 2Ιχ Π2Α / · (5) Therefore, the exponent Ey of the exponential operation result, the number of the exponential operation result my, and the sign number of the exponential operation result γ. , Respectively: 毛 Ε'Ιχ (6) my-2Fx = Π2Αί2 ^ N = Πτίi; (7) (8) where TiL .... and 1, K is the number of the index comparison table, and because 〇 $ FX &lt; 1, so 20, that is, 1 $ 2Fx &lt; 2, ra shi, Ganzu 1- &lt; 2. Using the exponential arithmetic device of the floating-point number of the present invention can obtain the exponent of the floating-point number X as a base 2. The calculation result γ, first, the ^ number of the floating-point number χ, χ, the exponent Εχ of the floating-point number X, and the mantissa χ of the floating-point number X are input and set.

0702-7516TW; 90P130; Ellen.ptd j / 舛 82 V. Description of the invention (6) The floating object is represented by the integer part κ in "two two by two" (the third formula of the above eight 2). Then, Divide the above fraction into &amp; ten ... N? "Several parts receive the n + ... code from the above, each index table will then each index j, 'and look up the table to produce an output result, different results The mantissa ray of γ (refer to the 4th, 5th, ^; m 'to generate the exponential operation my, the integer part I, and a dry or capital formula). Finally, using the mantissa result Y, the exponent X calculates the symbol number sy of the table of the last name Y to indicate that the exponent operation considers formula 6) 'my is the mantissa magic (= 8 / Ey is the integer part U parameter, == Table 2 Schematic diagram of the conversion device of the present invention. As shown in the figure, if ^ includes the shifting device 12, the detection device 14, and the decision to install ru, set 1 2 to receive the exponent of the floating-point number £}; 'According to the floating-point number, the mantissa of the floating-point number; the number of mm ρ: the heart's number of the number χ integer, then the positive integer ^ the mantissa of the point number mx to the left'. For example: the exponent of the floating-point number Ex Is 5, = the mantissa of the ordinal number is shifted 5 bits to the left, when χ /, .., ^, = E is -bu, the tail of the floating-point number is shifted to the right by i bits, and == 2 is generated A shifted fraction &amp; and a shifted integer portion are output. The detection device 14 is used to detect the shifted device 12 and sends an error message Err when the device is shifted. The determination device 16 is used to receive the shifted integer portion Isc And the sign of the floating point number Sx input, and according to the sign of the floating point number ^ I · »0702-7516TW; 90P130; Ellen.ptd page 9 579482 V. Description of the invention (7) Shift section Share the sign of 1sc to produce an integer part (X outputs this = change device 10, when Sx is 1, Ix = -Isc 'when \ is 0, i. 〃. The middle shift fraction part Fsc outputs the conversion Pei After setting it to 10, it is 5 fractional fractions Γ X ° The fourth figure shows the second tolerance chart of the exponential arithmetic device for floating-point numbers in the embodiment of the present invention. As shown in the figure, the exponential arithmetic device for floating-point numbers includes shift Device 12 γ detection device 14, decision device 16, three index comparison tables 2 〇 2 〇 3 and multiplier 3 〇 The floating point exponent computing device of this embodiment is used to obtain the floating point number X by 2 The result of the exponential operation based on γ is γ = x, and the representation of ί mx is x = (-i) sx · 2Εχ · ~ 'where ~ is the number of symbols of the floating point?' Floating point when the number of points is positive

Number = sign number \ is 0, when t floating point number X is negative, the sign number of floating point number \ is 1; Ex is the exponent of the floating point number, expressed in 8 bits;% is the floating point number Mantissa, expressed in 24 bits, and i $ 牝 &lt; 2. In order to find Y, X needs to be divided into an integer part represented by 8 bits, and a fraction part represented by 23 bits. Among them, • The shift device x is set to 12 to receive the floating-point exponent Εχ and The mantissa% of the floating-point number is input, and the mantissa of the floating-point number is shifted according to the exponent of the floating-point number χ. For example, when the exponent of the floating-point number is a positive integer, the mantissa of the floating-point number is based on the positive integer. ^ Shift to the left, for example: if the exponent Εχ of the floating-point number is 5, the tail of the floating-point number is shifted to the left by 5 bits. When the exponent EF of the floating-point number is a negative integer, the f The mantissa mx is shifted to the right 'for example: the exponent of the floating-point number &amp; is ", then the mantissa mx of the western point is shifted to the right by 1 bit, and the shifting device 2 generates a shifting knife number 4 Fsc and a shift Bit integer part Isc output. Detection device 1 4

579482 V. Description of the invention (8) Measure shift dream W 1 9+ The error message Err includes shift benefit: the device sends ^ 4 ^ ^ including overflow message and downward overflow message from 12 / benefit position. When the floating point number is I i /, the mantissa% of the western point is shifted to the left by more than 7 bits. The mantissa of this number is m ':: Mingbao. When the exponent 仏 of the floating-point number is less than _23, the floating-point mantissa "nx is shifted to the right by more than 23-bit ΐ, and is fixed into the device 16 and used to: receive the shifted integer part 12 and: 22 : I: fr,, r /;: ^^ ^ change,-exponent Ey of the result Y of the number operation (refer to formula 6 ^. And the integer part is the next, then the fraction part Fx is divided into 3 bits And 7 digits, successively _ each part H = 8 bits, 8 and 24, and in each index comparison table, the private number comparison table 20, 22 output results of each index table In turn, the output result of the __ is generated, and then the mantissa of the fruit Y is entered into [3] to generate the exponential operation knot according to the seventh formula: my = 2Fx = n2Ai2NiN = nTi ii In this embodiment, 1 $ ig 3, h1 I Lu Yi:. ,,, 9, the number of comparison table, so X 2α3 · 2 ^

Wly == I ~ [Ti = Τι x Τ2 x Τ3 = 2 ^ 1 ^ X 2 ^ 2 2 ~ 16 mi 0702-7516TWF; 90P130; Ellen.ptd $ 11 pages (9) 579482 V. Description of the invention (9) a Where Tl 2 'and Αι are fL-r in the three parts divided by the fractional part Fx, an 8-bit number' · T2 =, and the heart is in the 3 parts formed by the fractional part χ. The second part is an 8-bit number T3 = 2 ^ * 2 &quot; 23, and the last of the 3 parts divided by the fractional part Fx is still 'a 7-bit number . Because the results of the exponential operation γ are all positive numbers, the sign number Sy is zero (refer to Equation 8). After counting the number of different results of the dry car Y of V, W uses ~, Ιχ ', and Sy to represent the exponential operation of the fruit Y, which is incorrectly Y = (-i) Sy. 2Ey.m, ,,,,,,,,, If Y, the number of the table number and Ey are the mantissa of the exponent, the mantissa of the result of the β-Hyde number calculation result, and 1 "y &lt; 2. The heart number and% are the results of the index calculation. Although the present invention p LV &amp; / 4_ _ t Limits the invention, • Ho I: 2: Open the road as above, but it is not used within the scope, when it can be done: Xu Zhi Li does not depart from the spirit of the invention, as the attached patent Scope; Definer = Protection of the invention

0702-7516TW; 90P130; Ellen.ptd 579482 ----- Simple and clear explanation of the drawings: To make the above and other purposes of the present invention, the detailed description of Γ ^ is as follows: · The accompanying figure is shown in Figure 1. Knowing a single master ^ Working master-Accurate 32 bits and several masters-Figure 2 shows a schematic diagram of the exponential operation of the floating-point number of the present invention, and the schematic diagram of the device structure Figure 3 shows the conversion device of the present invention FIG. 4 shows an embodiment of the present invention. Schematic diagram. Symbol description of the exponential operation device of the number: Μ, A ~ the mantissa of the floating point number; E, Ex ~ the exponent of the floating point number; S, Sx ~ the sign number of the sign; Ix ~ the integer part;

Fx ~ fraction part; 10 ~ conversion device; 12 ~ shift device; 14 ~ detection device; 16 ~ decision device; 20ι-20κ ~ index comparison table; 30 ~ multiplier;

Fsc ~ shift fraction part;

Isc ~ shifted integer part output; Err ~ error message;

579482

0702-7516TWF; 90P130; Ellen.ptd p. 14

Claims (1)

579482 VI. Scope of patent application? Angstrom "· An exponential calculation method of exponential calculation of net points ... The result of an exponential calculation based on: used to get paid-the number of foreign points is 2x ·%. The index operates The expression of the 钍 jun from the number 1 ′ is〗) & It is assumed that the expression of the operation result is (η χ is the symbol number of 亥 stain number, s s 2 my,: number, Ex is the floating number The exponent of the points, the sign% of the two-digit operation result is the exponent of the floating-point number, the exponent of the 5 operation result, $ mx &lt; 2, 1 幺 m &lt;?, Makeup And 1-to-1 conversion: y; s Hai index calculation device includes: exponent of points: and above] the number of symbols of floating-point numbers described above, the above floating-to-integer part and ϊ: =: = input, the above floating-point Points are converted to Nπ, and each 乂 V number is received, \, 『; two into ^ and the look-up table is produced-the output result is connected to one of the rounds in μ, multiplied by 2 to receive each of the above index comparisons. The output # of the table is input, and the mantissa of the above-mentioned exponential operation result is generated; the integer part of the output of the conversion device is the above-mentioned exponential operation μ Λ: The number of the sign of the exponential operation result is zero, and N, K, K2 ... KN is a natural number, and the exponent of the floating-point number described in the first straight patent range The operation f is set, wherein the conversion device includes: a disagreement-shifting device for receiving the exponent of the floating-point number and inputting the mantissa of the point, shifting according to the floating-point number J = mantissa, and generating a shift Fractional part and a shift _ 0702-7516TW; 90P130; Ellen.ptd page 15 579482 VI. Patent application scope; and a determining device for receiving the shifted integer part and the number of symbols of the floating point number Input and determine the sign of the shifted integer part according to the sign of the floating-point number to generate the integer part. 3. The exponential arithmetic device for floating-point numbers as described in item 2 of the scope of patent application, further includes A detection device for detecting the above-mentioned shifting device, and an error message is issued when "the above-mentioned shifting device overflows." The digit fraction part is the above Fractional part., Set 5. The exponential operation of the floating-point number as described in item 2 of the scope of patent application, where the value of the shifted fractional part is greater than or equal to zero, and less than 丨. ^ 6 · As the item of scope of patent application The exponential operation of the floating-point number is set in which the value of the fractional part is greater than or equal to zero and less than 1. 7. The exponential operation of the floating-point number according to item 1 of the scope of patent application, wherein the above-mentioned index comparison table is established in advance The exponent pair with a base of 2 is set as the exponent of the floating-point number described in item 丨 of the scope of the patent application. The first index of A is included in the above-mentioned index. The table receives the i part of the above fraction, For the input of Ai, the above fraction has N bits and Aι has 乂 bits. The result is: Ti = 2A'N, where soil is a natural number. Set Λ ί :: The exponential operation of the floating-point number described in item 1 of the profit range is 0. When the above %% / point is positive, the sign of the floating-point number is a negative number. , The sign number of the above floating-point number is 0, 0, 0, 70, 7516TWF; 90P130; Ellen.ptd 579482 1 〇 If item 1 of the scope of patent application is set to ′, the number of symbols and signs in the result of the exponential operation is zero. The exponential operation of the floating-point number is presumed to be a positive number, so the above-mentioned exponent 11 · An exponential operation method of a floating-point number base 2 is an exponential operation result, the floating-point 2Eχ · mx, where sx is the floating-point number The sign of the point number, mx is the mantissa of the floating point number and 1 The following steps: X 'The expression used to obtain a floating point number is (-l) Sx ·' Ex is the floating point number means the The exponential operation method includes inputting the sign of the floating-point number and the mantissa of the floating-point number into a conversion device, and converting the floating-point fraction in the conversion device; ^ the exponent of the number of points and converting the point to an integer portion And one divides the above fractional part into 1 (partial bits, each part has ~, N2,… + NK, each index table receives the above-mentioned reverse lookup table to produce an output result; An exponential table with a mantissa; and 'The fractional part above has N ..., Nκ bits, and N = Ni + N2 + one of the damages, and the result is grounded in a multiplier. Mantissa, the integer part of the fan, ΐ number table is not the above As a result of the number operation, the exponent (~ 1) Sy · 2Ey · m, the complex middle helmet is too high. 4 y Eight middle Sy is the number of 5 Hai symbols, e% is the above output mantissa, 1 SmY <2, and the upper KN is Natural numbers. The expression of the symbolic fruit with a value of N is zero is the above integer part, ,, K2, ..., 12. The exponential operation of floating point numbers as described in item 1 i of the scope of patent application. 579482 /, claiming that the patent scope $ goes' where the above-mentioned floating-point number is represented by an integer 4 and a fractional part in the above conversion device includes the following sub-steps; f uses a shift device to receive the above-mentioned floating-point number The exponent of the floating-point number and the mantissa input of the number, shift the number of the floating-point number according to the exponent of the floating-point number, and generate a shifted fraction part and a shifted integer part output; and Lee 2 — The determining device receives the input of the shifted integer part and the sign number of the floating point number, and determines the sign of the shifted integer part according to the sign of the floating point number to generate the integer part. 1, 3 · The exponential operation of the floating-point number as described in Item 12 of the patent application range ft ', wherein the step of representing the floating-point number as an integer ^ and a fraction in the conversion device further includes sub-steps ; Use the detection device 'to send the above error message when the shift device overflows. Charge 1 4 · The exponential operation method for floating point numbers as described in item 12 of the scope of the patent application, wherein the shift fraction part is the above fraction part. 1, 15 · The exponential arithmetic method for floating-point numbers as described in Item 12 of the scope of patent application, wherein the value of the shift fraction is greater than or equal to zero and less than 1. 1, 16 · The exponential arithmetic method for floating-point numbers as described in item 11 of the scope of patent application, wherein the value of the fractional part is greater than or equal to zero and less than 1. 17. The method of exponential operation of a floating point number as described in item 11 of the scope of the patent application, wherein the index comparison table above is to first establish a base 2 index = photo. I to 1 8 · Exponential operation of floating point numbers as described in item 11 of the scope of patent application 6. The method of applying for a patent scope, in which the i-th index mentioned above is part of the input of Ai, the i-th score in the above-mentioned fraction 1 is above /, there are N bits, and Ai has ^ divisors, and the output result is It is: Ti == 2 绛 2Ni-N ^ · '1 9 As Shen Guzhu 衮 丨 i is a natural number. Method, in a: the exponent operation of the floating-point number described in item 11 of the upper, the upper and the lower ranges is 0, and when the round and sub-point numbers are positive, the sign of the above floating-point number '9η * 1' is a negative number In this case, the sign of the floating-point number is one. The exponent operation I of the floating-point numbers described in the patent application, u method I, is described later. Because the above exponential operation result is always a positive number, the sign number of the above index operation result is zero. 0702-7516TWF; 90P130; Ellen.ptd page 19