CN102135870B - Floating-point number power operation processing method and device and computer system - Google Patents
Floating-point number power operation processing method and device and computer system Download PDFInfo
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- CN102135870B CN102135870B CN 201010104098 CN201010104098A CN102135870B CN 102135870 B CN102135870 B CN 102135870B CN 201010104098 CN201010104098 CN 201010104098 CN 201010104098 A CN201010104098 A CN 201010104098A CN 102135870 B CN102135870 B CN 102135870B
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Abstract
The invention provides a floating-point number power operation processing method, a floating-point number power operation processing device and a computer system. The method comprises the following steps of: setting a floating-point number X into the form of the product of y and 2n according to a binary scientific notation storage structure in a memory of the floating-point number X, wherein the absolute value of the y is a real number which is more than 1 and less than 2, and the n is an integer which is more than -127 and less than 128; acquiring the dereferencing value of ya according to a first preprocessing table created in advance, and acquiring the dereferencing value of 2na according to a second preprocessing table, wherein the dereferencing value of the ya is stored in the first preprocessing table, the dereferencing value of the 2na is stored in the second preprocessing table, and a is a constant; and acquiring a calculated result of the Xa according to the dereferencing value of the ya and the dereferencing value of the 2na. By the processing method, the calculation efficiency of floating-point number power operation processed by a computer can be effectively improved.
Description
Technical field
The embodiment of the invention relates to field of computer technology, relates in particular to a kind of floating number power operation disposal route, device and computer system.
Background technology
In the prior art, computing machine can carry out the power operation of floating number usually, and the power operation of floating number is a class power operation that runs into through regular meeting in the computer processing procedure, and its mathematic(al) representation can be expressed as X
a, wherein, X is the floating number variable, can get different values under different scenes, a is the index of floating number, and a is constant.
In actual applications, computing machine can call built-in function (pow/powf) and calculate when carrying out the floating number power operation, and the function of pow/powf is that to calculate with x be the y power value at the end.When carrying out the power operation of floating number, pow can be expressed as double pow (double x, double y), and powf can be expressed as float powf (float x, float y).
In realizing process of the present invention, the inventor finds that there are the following problems at least in the prior art: calling built-in function, to carry out computing time that the floating number power operation consumes be tens times of common floating number multiplying, if computing machine needs to carry out a large amount of floating number power operations in computation process, just need frequently call the power operation that built-in function calculates floating number, therefore, can cause the treatment effeciency of computing machine low.
Summary of the invention
The embodiment of the invention provides a kind of floating number power operation disposal route, device and computer system, can improve the processing speed of Computer Processing floating number power operation.
The embodiment of the invention provides a kind of floating number power operation disposal route, comprising:
According to the scale-of-two scientific notation storage organization of floating number X in internal memory, described floating number X is set to y and 2
nThe form of product, wherein, the absolute value of y is greater than 1 less than 2 real number, n is less than 128 integer greater than negative 127;
Obtain y according to the first pre-service table that is pre-created
aValue, and obtain 2 according to the second pre-service table
NaValue, wherein, the described first pre-service table stores y
aValue, the described second pre-service table stores 2
NaValue, a is constant;
According to described y
aValue and described 2
NaValue obtain described X
aResult of calculation.
The embodiment of the invention provides a kind of floating number power operation treating apparatus, comprising:
Module is set, is used for according to the scale-of-two scientific notation storage organization of floating number X at internal memory, described floating number X is set to y and 2
nThe form of product, wherein, the absolute value of y is greater than 1 less than 2 real number, n is less than 128 integer greater than negative 127;
Enquiry module is used for according to the first pre-service table inquiry y that is pre-created
aValue, and according to second pre-service table inquiry 2
NaValue, wherein, the described first pre-service table stores y
aValue, the described second pre-service table stores 2
NaValue, a is constant;
Computing module is used for according to described y
aValue and described 2
NaValue obtain described X
aResult of calculation.
The embodiment of the invention provides a kind of computer system, comprises above-mentioned floating number power operation treating apparatus.
Floating number power operation disposal route, device and the computer system of the embodiment of the invention, by setting up the first pre-service table and the second pre-service table, and carry out the floating number power operation by lookup table mode, overcome that computing machine calculates the low defective for the treatment of effeciency that a large amount of floating number power operations cause computing machine by calling built-in function in the prior art, can effectively improve the counting yield of Computer Processing floating number power operation.
Description of drawings
In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art, to do one to the accompanying drawing of required use in embodiment or the description of the Prior Art below introduces simply, apparently, accompanying drawing in describing below is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.
Fig. 1 is the process flow diagram of the floating number power operation disposal route of the embodiment of the invention;
Fig. 2 is the synoptic diagram of the floating number storage organization of the embodiment of the invention;
Fig. 3 is the synoptic diagram of the floating number power operation treating apparatus of the embodiment of the invention.
Embodiment
Further specify the technical scheme of the embodiment of the invention below in conjunction with the drawings and specific embodiments.
According to embodiments of the invention, a kind of floating number power operation disposal route is provided, Fig. 1 is the process flow diagram of the floating number power operation disposal route of the embodiment of the invention, as shown in Figure 1, comprises according to the floating number power operation disposal route of the embodiment of the invention:
Particularly, above-mentioned scale-of-two scientific notation storage organization is ± 1.x and 2
nStorage organization, namely ± 1.x*2
nStorage organization, Fig. 2 is the synoptic diagram of the floating number storage organization of the embodiment of the invention, as shown in Figure 2, in 32 systems, floating number takies the space of 32 bits (bit), and when the storage floating number, the space of 32bit is divided into three parts: sign bit, exponent bits, mantissa position.Wherein, floating number X ± symbol is stored in the sign bit, for example, 0 representative just, 1 be represented as negative; The index n of floating number X is stored in the exponent bits, can adopt the mode of displacement storage to store; The x of mantissa of floating number X is stored in the mantissa position, and wherein, x is less than 1 real number greater than 0.That is to say, utilize the floating number of scale-of-two scientific notation storage, can be expressed as ± 1.x*2
nForm, wherein, n is less than 128 integer greater than-127.Need to prove that above-mentioned floating number is the magnitude range that can express and the floating number in the precision in the 32bit space.Wherein, sign bit can be 1 bit, and exponent bits can be 8 bits, and the mantissa position can be 23 bits.
In step 101, according to floating number ± 1.x*2
nScale-of-two scientific notation storage organization, by simple bit arithmetic arbitrarily floating number be set to the * 2 of following form: X=± (1+x)
n, that is, and according to X=± 1.x*2
n, can floating number X be set to ± (1+x) with 2
nThe form of product, order ± (1+x)=and y, then can be set to and 2 by floating number X
nProduct (y*2
n) form, even X=y*2
n
Particularly, because floating number X is arranged for X=y*2
nForm, therefore, calculating X
aThe time, can be by calculating X
a=y
a* 2
NaDetermine X
aResult of calculation.
In actual applications, because y takies 23bit in internal memory, have 2
23Plant possible value, then y
aAlso can have 2
23Plant possible value; Therefore, at system's pretreatment stage, set up first a pre-service table in advance, be used for depositing y
a2
23Kind possible value, the first pre-service table can calculate the corresponding y of mantissa of 23bit with the mantissa of 23bit among the 32bit as index by pow or powf
aValue.Because n takies 8bit in internal memory, have 256 kinds of possible values, then 2
Na256 kinds of possible values are also arranged, therefore, at system's pretreatment stage, also need to set up again second a pre-service table, be used for depositing 2
Na256 kinds of possible values, the second pre-service table as index, and calculates the index corresponding 2 of 8bit with 8bit index among the 32bit by pow or powf
NaValue.
Particularly, because X
a=y
a* 2
Na, therefore, with y
aValue and 2
NaValue multiply each other, can obtain X
aResult of calculation.
From above-mentioned processing as can be seen, by make up the first pre-service table and the second pre-service table at system's pretreatment stage, in system's operational process, ask X
aComputation process just become and table look-up for twice and process that floating number multiplies each other, can effectively improve the counting yield of Computer Processing floating number power operation.
Need to prove that in actual applications, the length of the first pre-service table can be 2
23=8M, the length of the second pre-service table can be 256, if each list item takies 4 bytes in two pre-service tables, then first pre-service and the shared space of the second pre-service table are respectively 8M*4=32M byte and 1K byte.Obviously, the first pre-service table has taken bigger memory headroom.Therefore, in actual applications, the embodiment of the invention can be saved the space by reducing precision.Particularly, the bit stealing 23bit of mantissa, if give up the last 3bit of mantissa position, then the first pre-service table occupation space is down to 4*2
20=4M, corresponding, the precision of the x of mantissa of mantissa's bit representation then is down to 2
-20≈ 0.00000095.And the like, if system can only provide the memory headroom of 1M for the first pre-service table, then the mantissa position must be cut to 18, the precision of the x of mantissa of mantissa's bit representation also can only reach 2
-18≈ 0.0000038.That is to say that the first pre-service table can store 2
zIndividual y
aValue, wherein, z is for greater than 0 and be less than or equal to 23 integer, in actual applications, the value of z can be between precision and memory source trade-off.By above-mentioned processing, can reduce the space of the shared internal memory of the first pre-service table, and the resource of the system of saving.
Need to prove that the technical scheme of the embodiment of the invention is according to the storage rule of floating number in computing machine, and improved the counting yield of floating number power operation by the mode of tabling look-up.The embodiment of the invention can be applied to computing machine and need handle under the various situations of floating number power operation.Particularly computing machine is frequently being handled under the situation of floating number power operation in large quantities, for example, computing machine is when handling statistical data analysis, if need to carry out continually the power operation of floating number in this statistical data analysis, then can use the technical scheme of the embodiment of the invention and carry out the processing of the power operation of floating number, can improve the efficient of these data of Computer Processing significantly.
According to embodiments of the invention, a kind of floating number power operation treating apparatus is provided, Fig. 3 is the synoptic diagram of the floating number power operation treating apparatus of the embodiment of the invention, as shown in Figure 3, the floating number power operation treating apparatus according to the embodiment of the invention comprises: module 30, enquiry module 32, computing module 34 are set.Below, the above-mentioned module of the embodiment of the invention is elaborated.
Particularly, above-mentioned scale-of-two scientific notation storage organization is ± 1.x*2
nStorage organization, in 32 systems, floating number takies the space of 32bit, during floating number, the space of 32bit is divided into three parts: sign bit, exponent bits, mantissa position in storage.Wherein, floating number X ± symbol is stored in the sign bit, for example, 0 representative just, 1 be represented as negative; The index n of floating number X is stored in the exponent bits, can adopt the mode of displacement storage to store; The x of mantissa of floating number X is stored in the mantissa position, and wherein, x is less than 1 real number greater than 0.That is to say, utilize the floating number of scale-of-two scientific notation storage, can be expressed as ± form of 1.x*2n, wherein, n be greater than bearing 127 less than 128 integer.Need to prove that above-mentioned floating number is the magnitude range that can express and the floating number in the precision in the 32bit space.The floating number storage organization can be understood with reference to Fig. 2.Wherein, sign bit can be 1 bit, and exponent bits can be 8 bits, and the mantissa position can be 23 bits.
Concrete, module 30 is set can comprises that first arranges submodule 301 and second submodule 302 is set, wherein:
First arranges submodule 301, is used for according to floating number ± 1.x*2
nScale-of-two scientific notation storage organization, be set to the * 2 of following form: X=± (1+x) by simple bit arithmetic floating number X
nThat is to say that first arranges submodule is used for according to X=± 1.x*2
n, floating number X is set to the * 2 of X=± (1+x)
nForm.
Particularly, owing to module 30 is set floating number X is arranged for X=y*2
nForm, therefore, calculating X
aThe time, can be by calculating X
a=y
a* 2
NaDetermine X
aResult of calculation.
In actual applications, y takies 23bit in internal memory, have 2
23Plant possible value, then y
aAlso can have 2
23Plant possible value; At system's pretreatment stage, can set up first a pre-service table in advance, be used for depositing y
a2
23Kind possible value, the first pre-service table can calculate the corresponding y of mantissa of 23bit with the mantissa of 23bit among the 32bit as index by pow or powf
aValue.N takies 8bit in internal memory, have 256 kinds of possible values, 2
Na256 kinds of possible values are also arranged, at system's pretreatment stage, also need to set up again second a pre-service table, be used for depositing 2
Na256 kinds of possible values, the second pre-service table as index, and calculates the index corresponding 2 of 8bit with 8bit index among the 32bit by pow or powf
NaValue.
From above-mentioned processing as can be seen, the embodiment of the invention in system's operational process, is asked X by make up the first pre-service table and the second pre-service table at system's pretreatment stage
aComputation process just become and table look-up for twice and process that floating number multiplies each other, can effectively improve the counting yield of Computer Processing floating number power operation.
Further, this device can also comprise:
Concrete, at system's pretreatment stage, can set up the first pre-service table and the second pre-service table in advance by presetting module 36, wherein, the first pre-service table is used for depositing y
a2
23Plant possible value; The first pre-service table can calculate the corresponding y of mantissa of 23bit with the mantissa of 23bit among the 32bit as index by pow or powf
aValue.
Because n takies 8bit in internal memory, have 256 kinds of possible values, then 2
Na256 kinds of possible values are also arranged, therefore, can set up the second pre-service table in advance by presetting module 36 and be used for depositing 2
Na256 kinds of possible values, the second pre-service table can be with 8bit index among the 32bit as index, and calculates the index corresponding 2 of 8bit by pow or powf
NaValue.
Need to prove that in actual applications, the length of the first pre-service table is 2
23=8M, the length of the second pre-service table is 256, if each list item takies 4 bytes in two pre-service tables, then first pre-service and the shared space of the second pre-service table are respectively 8M*4=32M byte and 1K byte.Obviously, the first pre-service table has taken bigger memory headroom.
In order to address the above problem, in actual applications, the embodiment of the invention is saved the space by reducing precision.Particularly, the bit stealing 23bit of mantissa, if give up the last 3bit of mantissa position, then the first pre-service table occupation space is down to 4*2
20=4M, corresponding, the precision of the x of mantissa of mantissa's bit representation then is down to 2
-20≈ 0.00000095.And the like, if system can only provide the memory headroom of 1M for the first pre-service table, then the mantissa position must be cut to 18, the precision of the x of mantissa of mantissa's bit representation also can only reach 2
-18≈ 0.0000038.That is to say that the first pre-service table can store 2
zIndividual y
aValue, wherein, z is for greater than 0 and be less than or equal to 23 integer, in actual applications, the value of z can be between precision and memory source trade-off.
By above-mentioned processing, can reduce the space of the shared internal memory of the first pre-service table, and the resource of the system of saving.
Need to prove that the embodiment of the invention can be applied to computing machine and need handle under the various situations of floating number power operation.Particularly computing machine is frequently being handled under the situation of floating number power operation in large quantities, for example, computing machine is when handling statistical data analysis, if need to carry out continually the power operation of floating number in this statistical data analysis, then can use the technical scheme of the embodiment of the invention and carry out the processing of the power operation of floating number, can improve the efficient of these data of Computer Processing significantly.
According to embodiments of the invention, a kind of computer system is provided, this computer system comprises floating number power operation treating apparatus, this floating number power operation treating apparatus can adopt the floating number power operation treating apparatus among the embodiment of above-mentioned Fig. 3, specifically can repeat no more referring to the embodiment of said apparatus herein.
As described in above-mentioned embodiment, by setting up the first pre-service table and the second pre-service table, and carry out the floating number power operation by lookup table mode, overcome in the existing computer system and calculated the low defective for the treatment of effeciency that a large amount of floating number power operations cause computing machine by calling built-in function, can effectively improve the counting yield of computer system processor floating number power operation.
Device embodiment described above only is schematic, wherein said unit as the separating component explanation can or can not be physically to separate also, the parts that show as the unit can be or can not be physical locations also, namely can be positioned at a place, perhaps also can be distributed on a plurality of network element.Can select wherein some or all of module to realize the purpose of present embodiment scheme according to the actual needs.Those of ordinary skills namely can understand and implement under the situation of not paying performing creative labour.
The method of describing in conjunction with embodiment disclosed herein or the step of algorithm can use the software module of hardware, processor execution, and perhaps the combination of the two is implemented.Software module can place random access memory (RAM), internal memory, ROM (read-only memory) (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM or the storage medium of other form arbitrarily.
It should be noted that at last: above embodiment only in order to technical scheme of the present invention to be described, is not intended to limit; Although with reference to previous embodiment the present invention is had been described in detail, those of ordinary skill in the art is to be understood that: it still can be made amendment to the technical scheme that aforementioned each embodiment puts down in writing, and perhaps part technical characterictic wherein is equal to replacement; And these modifications or replacement do not make the essence of appropriate technical solution break away from the spirit and scope of various embodiments of the present invention technical scheme.
Claims (7)
1. a floating number power operation disposal route is characterized in that, comprising:
According to the scale-of-two scientific notation storage organization of floating number X in internal memory, described floating number X is set to y and 2
nThe form of product, wherein, the absolute value of y is greater than 1 less than 2 real number, n is less than 128 integer greater than negative 127;
Obtain y according to the first pre-service table that is pre-created
aValue, and obtain 2 according to the second pre-service table
NaValue, wherein, the described first pre-service table stores y
aValue, the described second pre-service table stores 2
NaValue, a is constant;
According to described y
aValue and described 2
NaValue obtain X
aResult of calculation;
Wherein, described scale-of-two scientific notation storage organization comprises: ± 1.x and 2
nThe storage organization of product, then the scale-of-two scientific notation storage organization of described X in internal memory comprises: X equals ± 1.x and 2
nProduct, wherein, described floating number X ± symbol is stored in the sign bit, and the index n of described floating number X is stored in the exponent bits, the x of mantissa of described floating number X is stored in the mantissa position, and wherein, x is less than 1 real number greater than 0.
2. method according to claim 1 is characterized in that, described according to the scale-of-two scientific notation storage organization of floating number X in internal memory, described floating number X is set to data y and 2
nThe form of product comprises:
Equal ± 1.x and 2 according to X
nProduct, described floating number X is set to ± (1+x) with 2
nThe form of product;
Make ± (1+x) equal y, described floating number X is set to y and 2
nThe form of product.
3. method according to claim 2 is characterized in that, according to described y
aValue and described 2
NaValue obtain X
aResult of calculation comprise:
With described y
aValue and described 2
NaValue multiply each other, obtain X
aResult of calculation.
4. a floating number power operation treating apparatus is characterized in that, comprising:
Module is set, is used for according to the scale-of-two scientific notation storage organization of floating number X at internal memory, described floating number X is set to y and 2
nThe form of product, wherein, the absolute value of y is greater than 1 less than 2 real number, n is less than 128 integer greater than-127;
Enquiry module is used for according to the first pre-service table inquiry y that is pre-created
aValue, and according to second pre-service table inquiry 2
NaValue, wherein, the described first pre-service table stores y
aValue, the described second pre-service table stores 2
NaValue, a is constant;
Computing module is used for according to described y
aValue and described 2
NaValue obtain X
aResult of calculation;
Wherein, described scale-of-two scientific notation storage organization comprises: ± 1.x and 2
nThe storage organization of product, then the scale-of-two scientific notation storage organization of described X in internal memory comprises: X equals ± 1.x and 2
nProduct, wherein, described floating number X ± symbol is stored in the sign bit, and the index n of described floating number X is stored in the exponent bits, the x of mantissa of described floating number X is stored in the mantissa position, and wherein, x is less than 1 real number greater than 0.
5. device according to claim 4 is characterized in that, the described module that arranges comprises:
First arranges submodule, is used for equaling ± 1.x and 2 according to X
nProduct, described floating number X is set to ± (1+x) with 2
nThe form of product;
Second arranges submodule, is used for making ± (1+x) equal y, and described floating number X is set to y and 2
nThe form of product.
6. device according to claim 5 is characterized in that, described computing module specifically is used for: with described y
aValue and described 2
NaValue multiply each other, obtain X
aResult of calculation.
7. according to any described device of claim 4-6, it is characterized in that, also comprise:
Presetting module is used for setting in advance the first pre-service table and the second pre-service table, and wherein, the described first pre-service table stores y
aValue, the described second pre-service table stores 2
NaValue, a is constant.
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| US9792087B2 (en) * | 2012-04-20 | 2017-10-17 | Futurewei Technologies, Inc. | System and method for a floating-point format for digital signal processors |
| CN113296732B (en) * | 2020-06-16 | 2024-03-01 | 阿里巴巴集团控股有限公司 | Data processing method and device, processor and data searching method and device |
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| CN1979411A (en) * | 2005-11-30 | 2007-06-13 | 北京中电华大电子设计有限责任公司 | Method for realizing high-speed divider and apparatus therefor |
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| Title |
|---|
| DSP数字信号处理器的浮点数正弦的实现;赵俊奇等;《仪表技术》;20020531;第29-30,33页 * |
| 赵俊奇等.DSP数字信号处理器的浮点数正弦的实现.《仪表技术》.2002,第29-30,33页. |
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