JPH01183732A - Method and device for conversion between floating point number and integer - Google Patents

Abstract

PURPOSE:To shorten the time required to obtain the value transformed into an integer by making a hidden bit emerge into the mantissa data, setting the mantissa data at a position distant from the exponent data, and taking out only the prescribed number of bits of the lower rank side of the mantissa data. CONSTITUTION:A floating point number holding register 1 holds a normalized floating point number containing the mantissa data showing a part having the prescribed number of bits and less than a decimal point at the lower rank side of the exponent data having the prescribed number of bits. An addition number generating part 2 delivers an addition number where the mantissa data are all equal to 0 and at the same time the higher rank digits of the mantissa data are equal to 1. Then an addition part 3 adds the floating point number to the addition number to obtain the addition result in the form of a floating point number. Thus it is possible to make such a hidden bit that is never shown as it is emerge into the mantissa data and also to set the mantissa data at a position distant from the exponent data. Therefore only the prescribed number of bits can be taken out at the lower rank side of the mantissa data through a conversion data extracting part 4 and the value transformed into an integer can be obtained.

Description

[Detailed Description of the Invention] <Industrial Application Field> The present invention relates to a conversion device and method for converting floating point numbers into integers, and more specifically, the present invention relates to a conversion device and method for converting floating point numbers to integers, and more specifically, to The present invention relates to a conversion device and a conversion method particularly suitable for performing coordinate conversion processing and the like and finally obtaining numerical data converted into integers.

<Prior art and problems to be solved by the invention> Conventionally, when performing calculations that require a wide dynamic range and high precision, floating point calculations are generally preferred to integer calculations. It will be done. That is,
Even when performing integer operations, it is possible to widen the dynamic range and improve precision by increasing the number of bits, but it is not possible to represent integers with a number of bits larger than the bit width of the data bus. For example, there is a problem that the time required for data transfer increases.In contrast, with floating point numbers, the number of bits in the exponent part can be changed by 1 without changing the number of bits in the mantissa part. By increasing the dynamic range, the dynamic range can be doubled, so the dynamic range can be easily expanded without increasing the data transfer time. Since the number of bits in the mantissa can be increased as much as possible, the precision can also be improved. Taking note of these advantages, floating point arithmetic has come into general use in various applications.

This tendency is the same in graphic display devices, and high-precision calculation result data is obtained by performing necessary calculations based on coordinate data expressed in floating point numbers. However, in graphic display devices, it is very inconvenient to use floating point numbers as the final data in terms of display, so the operation result data expressed in floating point numbers is converted to integers. Moreover, since the number of calculation result data to be converted into integers is extremely large, there is a problem that the display speed cannot be increased much. To explain in more detail, in a graphic display device, for example, as shown in FIG. The conversion to integers is performed, and at the stage up to the workstation conversion, modeling coordinate system data, world coordinate data, view reference coordinate system data, and normalized projected coordinate system data expressed in floating point numbers are converted to integers. By applying the necessary arithmetic processing to the image, we ensure a wide dynamic range and high arithmetic accuracy. However, since the final display is on the display plane, Furthermore, since the display plane uses each pixel in the frame memory as the minimum unit, the device coordinate data will ultimately be expressed as an integer. That is, it is necessary to convert device coordinate system data expressed in floating point numbers obtained by workstation conversion into device coordinate system data expressed in integers.

Therefore, not only is it necessary to perform coordinate transformation processing on a significantly large number of coordinate data, but also it is necessary to perform integer processing on floating point numbers after coordinate transformation, and it is necessary to perform integer processing on floating point numbers after coordinate conversion. The time required to obtain device coordinate data becomes significantly longer, and as a result, the display speed becomes slower.

Specifically, in a floating point number, for example, as shown in FIG. The exponent part E indicates the power of , and the residual 23
The bit is the mantissa part F. However, in order to prevent the precision of floating point numbers from decreasing, the most significant bit of the mantissa part F is normalized so that it does not become 0 (for example, I
(See EEE standards). In addition, in the case of floating point numbers according to the IEEE standard, the mantissa part F shows only the part below the decimal point, and the highest value "1°" is a hidden bit that does not appear at all in floating point number representation. It has become.

Therefore, the value of a floating point number based on the above IEEE standard can only be obtained by performing the calculation (-1) 8 (1, F) 2"7 in a processor, etc., and in a graphic display device, The above calculation must be performed for each large number of pixel data, and for each pixel, calculations must be performed for the x and y coordinates for two-dimensional display, and for the X+Y+z coordinates for three-dimensional display. Therefore, it took an extremely long time to obtain device coordinate data converted into integers.

Furthermore, the above-mentioned inconvenience is particularly noticeable in graphic display devices, but even in devices other than graphic display devices that contain many floating point numbers and need to be converted into integers,
Similar inconveniences will occur.

<Object of the invention> This invention was made in view of the above problems,
An object of the present invention is to provide a conversion device and method for converting floating point numbers into integers that can significantly reduce the overall time required to convert floating point numbers into integers when there are many floating point numbers to be converted into integers. It is said that

Means for Solving the Problems> In order to achieve the above object, the floating point number to integer conversion device of the present invention has a predetermined number of bits and a decimal point on the lower side of exponent data of a predetermined number of bits. There are 0 floating -point retention methods that hold regular floating -point numbers, which have a fascal data indicating only the following parts
, and the addition number output means outputs an addition number in which the high-order digit of the mantissa data is 1, and the floating point number held in the floating point number holding means and the addition number output from the addition number output means are added together. and conversion data extraction means for extracting only lower predetermined bits of mantissa data constituting the addition result expressed as a floating point number as conversion data. ing.

However, the above floating point numbers and conversion data are as follows:
Both may be n-ary numbers, but preferably both are binary numbers.

Also, the floating point number above is the data before coordinate conversion,
It is preferable that the above-mentioned integer is the data after coordinate transformation, and that the operation of outputting the addition number by the addition number output means and the operation of generating the addition result by the addition means are performed simultaneously with the coordinate transformation operation.

Furthermore, the method of converting a floating point number into an integer according to the present invention is a method for converting a floating point number into an integer using a normalized floating point number, which has mantissa data of a predetermined number of bits and indicating only the part below the decimal point on the lower side of exponent data of a predetermined number of bits. Add a number whose mantissa data is all 0 and the upper digit of the mantissa data is 1 to a number, and use only the lower predetermined bits of the mantissa data that constitute the addition result expressed as a floating point number as conversion data. This is how to take it out.

The above floating-point number to integer converter converts normalized data that has a predetermined number of bits of mantissa data on the lower side of the exponent data that has a predetermined number of bits and shows only the part below the decimal point. The floating point number is held in the floating point number holding means, and the mantissa data is all 0 from the addition output means.
, and outputs an addition number in which the upper digit of the mantissa data is 1. Then, the addition means adds the floating point number and the addition number to generate an addition result expressed as a floating point number, so hidden bits that would not otherwise appear at all can appear in the mantissa data. At the same time, the mantissa data can be located away from the exponent data. Therefore, by extracting only a predetermined number of lower bits of this mantissa data by the conversion data extracting means, for example, (-1)8 (1,F)2B-
An integer value can be obtained without performing 127 operations.

When the floating point number and the conversion data are both binary numbers, the present invention can be suitably applied to binary operations widely used in digital computers and the like.

Also, the floating point number above is the data before coordinate conversion,
If the above integer is the data after coordinate transformation, and the addition output means outputs the addition number and the addition means generates the addition result at the same time as the coordinate transformation,
By performing the coordinate transformation, it is possible to obtain data that has been subjected to the coordinate transformation and has been converted into an integer.

Furthermore, with the above conversion method from a floating point number to an integer, a normalized floating point number that has mantissa data of a predetermined number of bits and indicating only the part below the decimal point on the lower side of the exponent data of a predetermined number of bits. If you add a number whose mantissa data is all 0 and the high-order digit of the mantissa data is 1 to a decimal point number, the value of the floating point number expressed as a whole will not be an accurate addition result. However, if we focus only on the lower predetermined bits of the mantissa data, it is equal to the value converted from a floating point number to an integer, so by extracting only this part of the data, we can obtain the integer data. can.

To explain in more detail, if we consider the case where the sign bit of a floating point number expressed in binary is 1 bit, the exponent part is a bit, and the mantissa part is b bits, the number is padded to the exponent part. If the value of the mantissa is F, the value of the floating point number is (1, F
) is multiplied by 2 to the power of E-(2b-1), and the integer value cannot be extracted as it is (see FIG. 1A). However, according to the new knowledge of the inventor of the present invention, by adding numbers whose mantissa data are all 0 and whose high-order digit is 1, that is, 2b, the mantissa data of the addition result can be changed to the above 1. ．． It turns out that the bit array corresponding to F is packed to the side away from the exponent part.

Therefore, in this state, the hidden bits are also exposed and the lower bits of the mantissa data directly indicate the integer data, so the upper bits of the exponent and mantissa parts are ignored and only the relevant part is extracted. By doing this, it is possible to easily convert floating point numbers to integers.

<Example> Hereinafter, embodiments will be described in detail with reference to the accompanying drawings showing examples.

FIG. 4 is a flowchart showing the coordinate transformation process of a graphic display device incorporating the device of the present invention. Obtain world coordinate system data expressed as a decimal point number, perform view transformation in step ■ to obtain view reference coordinate system data expressed as a floating point number, and perform projection transformation in step ■ to convert the floating point By obtaining normalized projected coordinate system data expressed in numbers and applying workstation transformation in step
I am trying to obtain device coordinate system data expressed as integers.

FIG. 3 is a flowchart showing the details of the workstation conversion section, showing the case where workstation conversion is performed based on normalized projected coordinate system data in which the exponent data is 7 bits and the mantissa data is 23 bits. .

In step (2), a predetermined coordinate transformation matrix is read from a matrix stack memory (not shown), and the parallel movement element d of the coordinate transformation matrix is read out.1. d2. A new coordinate transformation matrix is obtained by performing a transformation equivalent to adding 223 to d3 (specifically, by adding 223 to the constant part of the coordinate transformation matrix), and the coordinate transformation is performed in step (■). Read the three-dimensional coordinate data x, y, z corresponding to the point to be applied, and proceed to step ■
In ■■, respectively, X −a l x + b 1 y + c 1 z
+ (d l+223), Y = a 2 x + b
2 y + c 2 z + (d 2 + 223),
Z −a 3 x + b 3 y + c 3 z
+ (d3+223) is performed to calculate the three-dimensional coordinate data x, y, z corresponding to the corresponding point, and in step (2) it is determined whether coordinate transformation has been performed for all the points. If it is determined that there are points for which coordinate transformation has not been performed, the process from step ① is repeated, and conversely, if it is determined that coordinate transformation has been performed for all points, The series of processing ends immediately.

Then, if the coordinate transformation processing using the above coordinate transformation matrix is performed, integer processing is also performed at the same time as conversion to device coordinate system data, so it is necessary to perform special integer processing for each data. Since the process is eliminated, the overall process can be simplified and the time required for the process can be shortened.

FIG. 2 is a block diagram showing an embodiment of a floating point number to integer conversion device, which includes a register (1) for temporarily holding a floating point number according to the IEEE standard, a register (1) whose mantissa data is all 0, and an addition part (3) which adds the addition number to the contents of the register (1), and an addition part (
Conversion data extraction unit (4) that extracts only a predetermined number of low-order bits of the floating point number obtained by 3) as conversion data.
It has

FIG. 1 is a diagram illustrating the operation of the conversion device in detail.

Figure 1A shows the device coordinate system data “1” expressed as a floating point number according to the IEEE standard, and
Figure 1B shows device coordinate system data “1023”
It shows the state expressed as a floating point number according to the EE standard.

That is, in FIG. 1A, the sign bit S is "0" in binary, and the exponent data E is "01111111" in binary.
(“127” in decimal), the mantissa data F is a binary number in which all bits are “0°”, and in FIG. 1B, the sign bit S is “01” in binary and the exponent data E is 2
"10001000" in decimal number ("127+ in decimal number"
9°), the mantissa data F is all 11m in the above 9 bits.
In addition, it is a binary number in which the lower bits are all "0".

Figure 1C shows 223 expressed as a floating point number according to the IEEE standard, where the sign bit S is "0" in binary and the exponent data E is "1001011" in binary.
0” (decimal number “127+23”), mantissa data F
is a binary number in which all bits are "0".

Then, the floating point number in Figure 1 A1 or Figure 1 B and the first
When performing addition with the floating point number in Figure C, first,
Since the exponent data E is aligned to the larger one, the exponent data E for both floating point numbers A and B in FIG. 1 is forcibly set to "127+23" in decimal notation. Therefore, in the case of FIG. 1A, the exponent data E is forcibly increased by "23" in decimal notation, and the mantissa data F is increased by 23 bits.
The hidden bit "1" is revealed at the least significant bit position (see the first diagram). Also,
In the case of Figure 1B, as the exponent data E is forcibly increased by "14" in decimal notation, the mantissa data F is shifted away from the exponent data E by 14 bits. , the hidden bit "1" is revealed at the lower 10th bit position (see FIG. 1E).

That is, in both the first diagram and H, for example,
By extracting only the contents of the lower 16 digits, data corresponding to the integer state can be obtained.

As is clear from the above explanation, when converting a workstation, it is necessary to add 223 to the workstation conversion matrix to generate a new conversion matrix. However, when the number of data to be converted to workstations increases, in the past, each While it is necessary to perform integer processing for each data, in the case of the above example,
It is only necessary to generate a new transformation matrix once, and there is no need to perform special integer processing after that, so overall, the processing load can be significantly reduced and processing efficiency can be significantly improved. .

Note that the present invention is not limited to the above-described embodiments, and can be applied, for example, to converting floating point numbers into integers based on any base other than binary numbers. It can be similarly applied to cases where the number is other than 32 bits, and the addition number generation unit (to) may be an addition number calculation unit, or it may hold the addition number obtained in advance. It may also be possible to output the addition number at the necessary timing, and it is also possible to apply it to devices other than two-dimensional graphic display devices and graphic display devices. In addition, it is possible to make various design changes without changing the gist of the invention.

<Effects of the Invention> As described above, the first invention provides a number in which the mantissa data is all 0 and the upper digit of the mantissa data is 1 for a floating point number having only data below the decimal point as mantissa data. , and only the lower predetermined bits of the mantissa data that make up the addition result expressed as a floating point number are extracted as conversion data. Especially when there is a large amount of data to be converted into integers, the processing load can be greatly reduced and the processing efficiency can be greatly improved.

The second invention also has the unique effect that it can be suitably applied to binary operations widely used in digital computers and the like.

The third invention is that by performing coordinate transformation, it is possible to obtain data that has been subjected to coordinate transformation and has been converted into an integer,
As a result, a unique effect is achieved in that the time required for coordinate transformation can be significantly shortened.

In the fourth invention as well, it is possible to convert a floating point number into an integer without performing any special operation for converting it into an integer, and the processing load can be greatly reduced, especially when there is a large amount of data to be converted into an integer. This has the unique effect of greatly improving processing efficiency.

[Brief explanation of the drawing]

Figure 1 is a diagram explaining the conversion operation from a floating point number to an integer, Figure 2 is a block diagram showing an example of a device for converting a floating point number to an integer, and Figure 3 is a diagram explaining the operation of converting a floating point number to an integer. FIG. 4 is a flowchart explaining the coordinate conversion process in a graphic display device to which the integer conversion method of the present invention is applied. FIG. FIG. 6 is a flowchart illustrating coordinate conversion processing in a conventional graphic display device. (1)...Register, ■...Addition number calculation unit, (3)
... Addition section, (4) ... Conversion data extraction section, E.
... Index data, F... Mantissa data Patent applicant: Daikin Industries, Ltd. Agent Patent attorney: Tomo Tsugawa Amendment (voluntary) December 29, 1988 Patent Application No. 8987 2. Name of the invention Apparatus and method for converting floating point numbers to integers 3.
Relationship with the case of the person making the amendment Patent applicant address Umeda Center Building, 2-4-12 Nakazaki Nishi, Kita-ku, Osaka Name (285) Daikin Industries, Ltd. Representative Yama 1) Minoru 4, Agent 5, Amendment meeting Date of (voluntary) 6. In the specification to be amended, the Detailed Description of the Invention column and Drawing 7. Contents of the amendment (1) In the specification, between lines 7 and 8 on page 10, "
In addition, for numbers where the mantissa data is all 0 and the high-order digit of the mantissa data is 1, the mantissa data is regarded as an integer value, and the number has a force feeling [Yes].

Claims (1)

[Claims] 1. A normalized floating point number having mantissa data (F) of a predetermined number of bits and indicating only the part below the decimal point on the lower side of exponent data (E) of a predetermined number of bits. Floating point number holding means (1) for holding, addition number output means (2) for outputting an added number in which the mantissa data is all 0 and the high-order digit of the mantissa data is 1, and the floating point number holding means holds an addition means (3) for generating an addition result expressed as a floating point number by adding the floating point number output from the addition number output means and the addition number outputted from the addition number output means; and an addition result expressed as a floating point number. 1. A converting device for converting a floating point number into an integer, comprising: converting data extracting means (4) for extracting only lower predetermined bits of mantissa data (F) constituting the mantissa data (F) as converted data. 2. The floating point number to integer conversion device according to claim 1, wherein both the floating point number and the conversion data are binary numbers. 3. The floating point number is the data before the coordinate transformation, and the integer is the data after the coordinate transformation. Simultaneously with the coordinate transformation operation, the addition number output means (2) outputs the addition number, and the addition means (3) A converting device from a floating point number to an integer according to claim 1 or 2, which performs an addition result generation operation according to the above claim 1 or 2. 4. For a normalized floating point number that has mantissa data (F) of a predetermined number of bits and indicating only the part below the decimal point on the lower side of exponent data (E) of a predetermined number of bits,
Adding numbers whose mantissa data are all 0 and where the high-order digit of the mantissa data is 1, and extracting only the lower predetermined bits of the mantissa data (F) that constitute the addition result expressed as a floating point number as conversion data. A method of converting floating point numbers to integers featuring the following.