Floating-Point IP Cores User Guide

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UG-01058 | 2020.06.22

Version Information

Updated for:
Intel® Quartus® Prime Design Suite 20.1

1. About Floating-Point IP Cores

Attention: Intel has discontinued the support for the following IPs:

ALTERA_FP_MATRIX_INV IP core
ALTERA_FP_MATRIX_MULT IP core

Therefore, Intel does not recommend use of these IPs in new designs. For more information about Intel’s current IP offering, refer to Intel’s Intellectual Property website.

The Intel floating-point IP cores enable you to perform floating-point arithmetic in FPGAs through optimized parameterizable functions for Intel device architectures. You can customize the IP cores by configuring various parameters to accommodate your needs.

1.1. List of Floating-Point IP Cores

This table lists the floating-point IP cores.

Table 1. IP Cores Available in Intel^® Quartus^® Prime Standard Edition Software
IP Core Name	Function Overview	Supported Device
Operator Functions
ALTFP_ADD_SUB	Adder/Subtractor	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_DIV	Divider	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_MULT	Multiplier	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_SQRT	Square Root	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
Algebraic and Transcendental Functions
ALTFP_EXP	Exponential	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_INV	Inverse	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_INV_SQRT	Inverse Square Root	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_LOG	Natural Logarithm	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
Trigonometric Functions
ALTFP_ATAN	Arctangent	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_SINCOS	Trigonometric Sine/Cosine	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
Other Functions
ALTFP_ABS	Absolute value	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_COMPARE	Comparator	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
ALTFP_CONVERT	Converter	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, and Stratix IV
FP_ACC_CUSTOM Intel FPGA IP	An application specific accumulator	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria 10, Arria II GX, Cyclone IV GX, Stratix V, Stratix IV, and Intel Max 10
FP_FUNCTIONS Intel FPGA IP	A collection of floating-point functions.	Arria II GZ, Arria V, Arria V GZ, Intel Cyclone 10 LP, Cyclone IV E, Cyclone V, Arria II GX, Cyclone IV GX, Stratix V, Stratix IV, and Intel Max 10

Table 2. IP Cores Available in Intel^® Quartus^® Prime Pro Edition Software
IP Core Name	Function Overview	Supported Device
Floating Point Functions Intel FPGA IP	A collection of floating-point functions. This IP core replaces all other floating-point IP cores listed in the Quartus Prime Standard Edition table for devices available in Quartus Prime Pro Edition software.	Intel Stratix 10, Intel Arria 10, Intel Cyclone 10 GX, and Intel Agilex
Floating Point Custom Accumulator Intel FPGA IP	An application specific accumulator	Intel Cyclone 10 GX and Intel Arria 10

1.2. Installing and Licensing Intel FPGA IP Cores

The Intel^® Quartus^® Prime software installation includes the Intel^® FPGA IP library. This library provides many useful IP cores for your production use without the need for an additional license. Some Intel^® FPGA IP cores require purchase of a separate license for production use. The Intel^® FPGA IP Evaluation Mode allows you to evaluate these licensed Intel^® FPGA IP cores in simulation and hardware, before deciding to purchase a full production IP core license. You only need to purchase a full production license for licensed Intel^® IP cores after you complete hardware testing and are ready to use the IP in production.

The Intel^® Quartus^® Prime software installs IP cores in the following locations by default:

Figure 1. IP Core Installation Path

Table 3. IP Core Installation Locations
Location	Software	Platform
`<drive>`:\intelFPGA_pro\quartus\ip\altera	Intel^® Quartus^® Prime Pro Edition	Windows*
`<drive>`:\intelFPGA\quartus\ip\altera	Intel^® Quartus^® Prime Standard Edition	Windows
`<home directory>`:/intelFPGA_pro/quartus/ip/altera	Intel^® Quartus^® Prime Pro Edition	Linux*
`<home directory>`:/intelFPGA/quartus/ip/altera	Intel^® Quartus^® Prime Standard Edition	Linux

Note: The Intel^® Quartus^® Prime software does not support spaces in the installation path.

1.3. Design Flow

Use the IP Catalog and parameter editor to define and instantiate complex IP cores. Using the GUI ensures that you set all IP core ports and parameters properly.

If you are an expert user, and choose to configure the IP core directly through parameterized instantiation in your design, refer to the port and parameter details. The details of these ports and parameters are hidden in the parameter editor.

1.3.1. IP Catalog and Parameter Editor

The IP Catalog displays the IP cores available for your project, including Intel^® FPGA IP and other IP that you add to the IP Catalog search path.. Use the following features of the IP Catalog to locate and customize an IP core:

Filter IP Catalog to Show IP for active device family or Show IP for all device families. If you have no project open, select the Device Family in IP Catalog.
Type in the Search field to locate any full or partial IP core name in IP Catalog.
Right-click an IP core name in IP Catalog to display details about supported devices, to open the IP core's installation folder, and for links to IP documentation.
Click Search for Partner IP to access partner IP information on the web.

The parameter editor prompts you to specify an IP variation name, optional ports, and output file generation options. The parameter editor generates a top-level Intel^® Quartus^® Prime IP file (.ip) for an IP variation in Intel^® Quartus^® Prime Pro Edition projects.

The parameter editor generates a top-level Quartus IP file (.qip) for an IP variation in Intel^® Quartus^® Prime Standard Edition projects. These files represent the IP variation in the project, and store parameterization information.

Figure 2. IP Parameter Editor ( Intel^® Quartus^® Prime Standard Edition)

1.3.1.1. The Parameter Editor

The parameter editor helps you to configure IP core ports, parameters, and output file generation options. The basic parameter editor controls include the following:

Use the Presets window to apply preset parameter values for specific applications (for select cores).
Use the Details window to view port and parameter descriptions, and click links to documentation.
Click Generate > Generate Testbench System to generate a testbench system (for select cores).
Click Generate > Generate Example Design to generate an example design (for select cores).
Click Validate System Integrity to validate a system's generic components against companion files. (Platform Designer systems only)
Click Sync All System Info to validate a system's generic components against companion files. (Platform Designer systems only)

The IP Catalog is also available in Platform Designer (View > IP Catalog). The Platform Designer IP Catalog includes exclusive system interconnect, video and image processing, and other system-level IP that are not available in the Intel^® Quartus^® Prime IP Catalog. Refer to Creating a System with Platform Designer or Creating a System with Platform Designer (Standard) for information on use of IP in Platform Designer (Standard) and Platform Designer, respectively.

1.3.2. Generating IP Cores ( Intel Quartus Prime Pro Edition)

Quickly configure Intel^® FPGA IP cores in the Intel^® Quartus^® Prime parameter editor. Double-click any component in the IP Catalog to launch the parameter editor. The parameter editor allows you to define a custom variation of the IP core. The parameter editor generates the IP variation synthesis and optional simulation files, and adds the .ip file representing the variation to your project automatically.

Follow these steps to locate, instantiate, and customize an IP core in the parameter editor:

Create or open an Intel^® Quartus^® Prime project (.qpf) to contain the instantiated IP variation.
In the IP Catalog (Tools > IP Catalog), locate and double-click the name of the IP core to customize. To locate a specific component, type some or all of the component’s name in the IP Catalog search box. The New IP Variation window appears.
Specify a top-level name for your custom IP variation. Do not include spaces in IP variation names or paths. The parameter editor saves the IP variation settings in a file named <your_ip> .ip. Click OK. The parameter editor appears.

Figure 3. IP Parameter Editor ( Intel^® Quartus^® Prime Pro Edition)
Set the parameter values in the parameter editor and view the block diagram for the component. The Parameterization Messages tab at the bottom displays any errors in IP parameters:
- Optionally, select preset parameter values if provided for your IP core. Presets specify initial parameter values for specific applications.
- Specify parameters defining the IP core functionality, port configurations, and device-specific features.
- Specify options for processing the IP core files in other EDA tools.
Note: Refer to your IP core user guide for information about specific IP core parameters.
Click Generate HDL. The Generation dialog box appears.
Specify output file generation options, and then click Generate. The synthesis and simulation files generate according to your specifications.
To generate a simulation testbench, click Generate > Generate Testbench System. Specify testbench generation options, and then click Generate.
To generate an HDL instantiation template that you can copy and paste into your text editor, click Generate > Show Instantiation Template.
Click Finish. Click Yes if prompted to add files representing the IP variation to your project.
After generating and instantiating your IP variation, make appropriate pin assignments to connect ports.

Note: Some IP cores generate different HDL implementations according to the IP core parameters. The underlying RTL of these IP cores contains a unique hash code that prevents module name collisions between different variations of the IP core. This unique code remains consistent, given the same IP settings and software version during IP generation. This unique code can change if you edit the IP core's parameters or upgrade the IP core version. To avoid dependency on these unique codes in your simulation environment, refer to Generating a Combined Simulator Setup Script.

1.3.2.1. IP Core Generation Output ( Intel Quartus Prime Pro Edition)

The Intel^® Quartus^® Prime software generates the following output file structure for individual IP cores that are not part of a Platform Designer system.

Figure 4. Individual IP Core Generation Output ( Intel^® Quartus^® Prime Pro Edition)

Table 4. Output Files of Intel^® FPGA IP Generation
File Name	Description
<`your_ip`>.ip	Top-level IP variation file that contains the parameterization of an IP core in your project. If the IP variation is part of a Platform Designer system, the parameter editor also generates a .qsys file.
<`your_ip`>.cmp	The VHDL Component Declaration (.cmp) file is a text file that contains local generic and port definitions that you use in VHDL design files.
<`your_ip`>_generation.rpt	IP or Platform Designer generation log file. Displays a summary of the messages during IP generation.
<`your_ip`>.qgsimc (Platform Designer systems only)	Simulation caching file that compares the .qsys and .ip files with the current parameterization of the Platform Designer system and IP core. This comparison determines if Platform Designer can skip regeneration of the HDL.
<`your_ip`>.qgsynth (Platform Designer systems only)	Synthesis caching file that compares the .qsys and .ip files with the current parameterization of the Platform Designer system and IP core. This comparison determines if Platform Designer can skip regeneration of the HDL.
<`your_ip`>.qip	Contains all information to integrate and compile the IP component.
<`your_ip`>.csv	Contains information about the upgrade status of the IP component.
`<your_ip>`.bsf	A symbol representation of the IP variation for use in Block Diagram Files (.bdf).
<`your_ip`>.spd	Input file that `ip-make-simscript` requires to generate simulation scripts. The .spd file contains a list of files you generate for simulation, along with information about memories that you initialize.
<`your_ip`>.ppf	The Pin Planner File (.ppf) stores the port and node assignments for IP components you create for use with the Pin Planner.
<`your_ip`>_bb.v	Use the Verilog blackbox (_bb.v) file as an empty module declaration for use as a blackbox.
<`your_ip`>_inst.v or _inst.vhd	HDL example instantiation template. Copy and paste the contents of this file into your HDL file to instantiate the IP variation.
<`your_ip`>.regmap	If the IP contains register information, the Intel^® Quartus^® Prime software generates the .regmap file. The .regmap file describes the register map information of master and slave interfaces. This file complements the .sopcinfo file by providing more detailed register information about the system. This file enables register display views and user customizable statistics in System Console.
<`your_ip`>.svd	Allows HPS System Debug tools to view the register maps of peripherals that connect to HPS within a Platform Designer system. During synthesis, the Intel^® Quartus^® Prime software stores the .svd files for slave interface visible to the System Console masters in the .sof file in the debug session. System Console reads this section, which Platform Designer queries for register map information. For system slaves, Platform Designer accesses the registers by name.
<`your_ip`>.v <`your_ip`>.vhd	HDL files that instantiate each submodule or child IP core for synthesis or simulation.
mentor/	Contains a msim_setup.tcl script to set up and run a ModelSim* simulation.
aldec/	Contains a Riviera-PRO* script rivierapro_setup.tcl to setup and run a simulation.
/synopsys/vcs /synopsys/vcsmx	Contains a shell script vcs_setup.sh to set up and run a VCS* simulation. Contains a shell script vcsmx_setup.sh and synopsys_sim.setup file to set up and run a VCS* MX simulation.
/cadence	Contains a shell script ncsim_setup.sh and other setup files to set up and run an NCSim simulation.
/xcelium	Contains an Xcelium* Parallel simulator shell script xcelium_setup.sh and other setup files to set up and run a simulation.
/submodules	Contains HDL files for the IP core submodule.
<`IP submodule`>/	Platform Designer generates /synth and /sim sub-directories for each IP submodule directory that Platform Designer generates.

1.3.3. Generating IP Cores ( Intel Quartus Prime Standard Edition)

This topic describes parameterizing and generating an IP variation using a legacy parameter editor in the Intel^® Quartus^® Prime Standard Edition software.

Figure 5. Legacy Parameter Editors

Note: The legacy parameter editor generates a different output file structure than the Intel^® Quartus^® Prime Pro Edition software.

In the IP Catalog (Tools > IP Catalog), locate and double-click the name of the IP core to customize. The parameter editor appears.
Specify a top-level name and output HDL file type for your IP variation. This name identifies the IP core variation files in your project. Click OK. Do not include spaces in IP variation names or paths.
Specify the parameters and options for your IP variation in the parameter editor. Refer to your IP core user guide for information about specific IP core parameters.
Click Finish or Generate (depending on the parameter editor version). The parameter editor generates the files for your IP variation according to your specifications. Click Exit if prompted when generation is complete. The parameter editor adds the top-level .qip file to the current project automatically.

Note: For devices released prior to Intel^® Arria^® 10 devices, the generated .qip and .sip files must be added to your project to represent IP and Platform Designer systems. To manually add an IP variation generated with legacy parameter editor to a project, click Project > Add/Remove Files in Project and add the IP variation .qip file.

1.4. Upgrading IP Cores

Any Intel^® FPGA IP variations that you generate from a previous version or different edition of the Intel^® Quartus^® Prime software, may require upgrade before compilation in the current software edition or version. The Project Navigator displays a banner indicating the IP upgrade status. Click Launch IP Upgrade Tool or Project > Upgrade IP Components to upgrade outdated IP cores.

Figure 6. IP Upgrade Alert in Project Navigator

Icons in the Upgrade IP Components dialog box indicate when IP upgrade is required, optional, or unsupported for an IP variation in the project. Upgrade IP variations that require upgrade before compilation in the current version of the Intel^® Quartus^® Prime software.

Note: Upgrading IP cores may append a unique identifier to the original IP core entity names, without similarly modifying the IP instance name. There is no requirement to update these entity references in any supporting Intel^® Quartus^® Prime file, such as the Intel^® Quartus^® Prime Settings File (.qsf), Synopsys* Design Constraints File (.sdc), or Signal Tap File (.stp), if these files contain instance names. The Intel^® Quartus^® Prime software reads only the instance name and ignores the entity name in paths that specify both names. Use only instance names in assignments.

Table 5. IP Core Upgrade Status
IP Core Status	Description
IP Upgraded	Indicates that your IP variation uses the latest version of the Intel^® FPGA IP core.
IP Component Outdated	Indicates that your IP variation uses an outdated version of the IP core.
IP Upgrade Optional	Indicates that upgrade is optional for this IP variation in the current version of the Intel^® Quartus^® Prime software. You can upgrade this IP variation to take advantage of the latest development of this IP core. Alternatively, you can retain previous IP core characteristics by declining to upgrade. Refer to the Description for details about IP core version differences. If you do not upgrade the IP, the IP variation synthesis and simulation files are unchanged and you cannot modify parameters until upgrading.
IP Upgrade Required	Indicates that you must upgrade the IP variation before compiling in the current version of the Intel^® Quartus^® Prime software. Refer to the Description for details about IP core version differences.
IP Upgrade Unsupported	Indicates that upgrade of the IP variation is not supported in the current version of the Intel^® Quartus^® Prime software due to incompatibility with the current version of the Intel^® Quartus^® Prime software. The Intel^® Quartus^® Prime software prompts you to replace the unsupported IP core with a supported equivalent IP core from the IP Catalog. Refer to the Description for details about IP core version differences and links to Release Notes.
IP End of Life	Indicates that Intel designates the IP core as end-of-life status. You may or may not be able to edit the IP core in the parameter editor. Support for this IP core discontinues in future releases of the Intel^® Quartus^® Prime software.
IP Upgrade Mismatch Warning	Provides warning of non-critical IP core differences in migrating IP to another device family.
IP has incompatible subcores	Indicates that the current version of the Intel^® Quartus^® Prime software does not support compilation of your IP variation, because the IP has incompatible subcores
Compilation of IP Not Supported	Indicates that the current version of the Intel^® Quartus^® Prime software does not support compilation of your IP variation. This can occur if another edition of the Intel^® Quartus^® Prime software, such as the Intel^® Quartus^® Prime Standard Edition, generated this IP. Replace this IP component with a compatible component in the current edition.

Follow these steps to upgrade IP cores:

In the latest version of the Intel^® Quartus^® Prime software, open the Intel^® Quartus^® Prime project containing an outdated IP core variation. The Upgrade IP Components dialog box automatically displays the status of IP cores in your project, along with instructions for upgrading each core. To access this dialog box manually, click Project > Upgrade IP Components.
To upgrade one or more IP cores that support automatic upgrade, ensure that you turn on the Auto Upgrade option for the IP cores, and click Auto Upgrade. The Status and Version columns update when upgrade is complete. Example designs that any Intel^® FPGA IP core provides regenerate automatically whenever you upgrade an IP core.
To manually upgrade an individual IP core, select the IP core and click Upgrade in Editor (or simply double-click the IP core name). The parameter editor opens, allowing you to adjust parameters and regenerate the latest version of the IP core.

Figure 7. Upgrading IP Cores

Note: Intel^® FPGA IP cores older than Intel^® Quartus^® Prime software version 12.0 do not support upgrade. Intel verifies that the current version of the Intel^® Quartus^® Prime software compiles the previous two versions of each IP core. The Intel^® FPGA IP Core Release Notes reports any verification exceptions for Intel^® FPGA IP cores. Intel does not verify compilation for IP cores older than the previous two releases.

1.4.1. Migrating IP Cores to a Different Device

Migrate an Intel^® FPGA IP variation when you want to target a different (often newer) device. Most Intel^® FPGA IP cores support automatic migration. Some IP cores require manual IP regeneration for migration. A few IP cores do not support device migration, requiring you to replace them in the project. The Upgrade IP Components dialog box identifies the migration support level for each IP core in the design.

To display the IP cores that require migration, click Project > Upgrade IP Components. The Description field provides migration instructions and version differences.
To migrate one or more IP cores that support automatic upgrade, ensure that the Auto Upgrade option is turned on for the IP cores, and click Perform Automatic Upgrade. The Status and Version columns update when upgrade is complete.
To migrate an IP core that does not support automatic upgrade, double-click the IP core name, and click OK. The parameter editor appears. If the parameter editor specifies a Currently selected device family, turn off Match project/default, and then select the new target device family.
Click Generate HDL, and confirm the Synthesis and Simulation file options. Verilog HDL is the default output file format. If you specify VHDL as the output format, select VHDL to retain the original output format.
Click Finish to complete migration of the IP core. Click OK if the software prompts you to overwrite IP core files. The Device Family column displays the new target device name when migration is complete.
To ensure correctness, review the latest parameters in the parameter editor or generated HDL.

Note: IP migration may change ports, parameters, or functionality of the IP variation. These changes may require you to modify your design or to re-parameterize your IP variant. During migration, the IP variation's HDL generates into a library that is different from the original output location of the IP core. Update any assignments that reference outdated locations. If a symbol in a supporting Block Design File schematic represents your upgraded IP core, replace the symbol with the newly generated <my_ip> .bsf. Migration of some IP cores requires installed support for the original and migration device families.

1.5. Floating-Point IP Cores General Features

All Intel FPGA floating-point IP cores offer the following features:

Support for floating-point formats.
Input support for not-a-number (NaN), infinity, zero, and normal numbers.
Optional asynchronous input ports including asynchronous clear (aclr) and clock enable (clk_en).
Support for round-to-nearest-even rounding mode.
Compute results of any mathematical operations according to the IEEE-754 standard compliance with a maximum of 1 unit in the last place (u.l.p.) error. This assumption is applied to all floating-point IP cores.

Intel FPGA floating-point IP cores do not support denormal number inputs. If the input is a denormal value, the IP core forces the value to zero and treats the value as a zero before going through any operation.

1.6. IEEE-754 Standard for Floating-Point Arithmetic

The floating-point IP cores implement the following representations in the IEEE-754 standard:

Floating-point numbers
Special values (zero, infinity, denormal numbers, and NaN bit combinations)
Single-precision, double-precision, and single-extended precision formats for floating-point numbers

1.6.1. Floating-Point Formats

All floating-point formats have binary patterns. In the following figure, S represents a sign bit, E represents an exponent field, and M is the mantissa (part of a logarithm, or fraction) field.

For a normal floating-point number, a leading 1 is always implied, for example, binary 1.0011 or decimal 1.1875 is stored as 0011 in the mantissa field. This format saves the mantissa field from using an extra bit to represent the leading 1. However, the leading bit for a denormal number can be either 0 or 1. For zero, infinity, and NaN, the mantissa field does not have an implied leading 1 nor any explicit leading bit.

Figure 8. IEEE-754 Floating-Point FormatThis figure shows a floating-point format.

1.6.1.1. Single-Precision Format

The single-precision format contains the following binary patterns:

The MSB holds the sign bit.
The next 8 bits hold the exponent bits.
23 LSBs hold the mantissa.

The total width of a floating-point number in the single-precision format is 32 bits. The bias for the single-precision format is 127.

Figure 9. Single-Precision RepresentationThis figure shows a single-precision representation.

1.6.1.2. Double-Precision Format

The double-precision format contains the following binary patterns:

The MSB holds the sign bit.
The next 11 bits hold the exponent bits.
52 LSBs hold the mantissa.

The total width of a floating-point number in the double-precision format is 64 bits. The bias for the double-precision format is 1023.

Figure 10. Double-Precision RepresentationThis figure shows a double-precision representation.

1.6.1.3. Single-Extended Precision Format

The single-extended precision format contains the following binary patterns:

The MSB holds the sign bit.
The exponent and mantissa fields do not have fixed widths.
The minimum exponent field width is 11 bits and must be less than the width of the mantissa field.
The width of the mantissa field must be a minimum of 31 bits.

The sum of the widths of the sign bit, exponent field, and mantissa field must be a minimum of 43 bits and a maximum of 64 bits. The bias for the single-extended precision format is unspecified in the IEEE-754 standard. In these IP cores, a bias of 2 ⁽WIDTH_EXP–1⁾–1 is assumed for the single-extended precision format.

1.6.2. Special Case Numbers

The following table lists the special case numbers defined by the IEEE-754 standard and the data bit representations.

Table 6. Special Case Numbers in IEEE-754 Representation
Meaning	Sign Field	Exponent Field	Mantissa Field
Zero	Don’t care	All 0’s	All 0’s
Positive Denormalized	0	All 0’s	Non-zero
Negative Denormalized	1	All 0’s	Non-zero
Positive Infinity	0	All 1’s	All 0’s
Negative Infinity	1	All 1’s	All 0’s
Not-a-Number (NaN)	Don’t care	All 1’s	Non-zero

1.6.3. Rounding

The IEEE-754 standard defines four types of rounding modes, which are:

round-to-nearest-even
round-toward-zero
round-toward-positive-infinity
round-toward-negative-infinity

Intel floating-point IP cores support only the most commonly used rounding mode, which is the round-to-nearest-even mode (TO_NEAREST). With round-to-nearest-even, the IP core rounds the result to the nearest floating-point number. If the result is exactly halfway between two floating-point numbers, the IP core rounds the result so that the LSB becomes a zero, which is even.

1.7. Non-IEEE-754 Standard Format

Only the ALTFP_CONVERT and FP_FUNCTIONS Intel FPGA IP (when the convert function is selected) support the fixed point format.

The fixed-point data type is similar to the conventional integer data type, except that the fixed-point data carries a predetermined number of fractional bits. If the width of the fraction is 0, the data becomes a normal signed integer.

The notation for fixed-point format numbers in this user guide is Qm.f, where Q designates that the number is in Q format notation, m is the number of bits used to indicate the integer portion of the number, and f is the number of bits used to indicate the fractional portion of the number.

For example, Q4.12 describes a number with 4 integer bits and 12 fractional bits in a 16-bit word.

The following figures show the difference between the signed-integer format and the fixed-point format for a 32-bit number.

Figure 11. Signed-Integer Format

Figure 12. Fixed-Point Format

1.8. Floating-Points IP Cores Output Latency

The IP cores measure the output latency in clock cycles and is different for each IP core. In some IP cores, the precision modes determine the number of clock cycles between the input and output result. When you select a mode, the options for latency are fixed for that mode.

For specific details about latency options, refer to the Output Latency section of your selected IP core in this user guide.

1.9. Floating-Point IP Cores Design Example Files

The design examples for each IP core in this user guide use the IP Catalog and parameter editor to define custom IP variations.

Simulate the designs in the ModelSim* - Intel^® FPGA Edition software to generate a waveform display of the device behavior. You must be familiar with the ModelSim* - Intel^® FPGA Edition software before trying out the design examples.

Table 7. Design Files for Floating-Point IP Cores
Floating-Point IP Cores	Design Files
ALTFP_ADD_SUB	altfp_add_sub_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_add_sub_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_DIV	altfp_div_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_div_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_MULT	altfp_mult_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_mult_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_SQRT	altfp_sqrt_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_sqrt_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_EXP	altfp_exp_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_exp_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_INV	altfp_inv_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_inv_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_INV_SQRT	altfp_inv_sqrt_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_inv_sqrt_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_LOG	altfp_log_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_log_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_ATAN	Not Available
ALTFP_SINCOS	Not Available
ALTFP_ABS	altfp_mult_abs_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_mult_abs_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_COMPARE	altfp_compare_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_compare_ex_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
ALTFP_CONVERT	altfp_convert_DesignExample.zip ( Intel^® Quartus^® Prime design files) altfp_convert_float2int_msim.zip ( ModelSim* - Intel^® FPGA Edition files)
FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP	Not Available
FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP	Not Available

1.10. VHDL Component Declaration

The VHDL component declaration is located in the < Intel^® Quartus^® Prime installation directory>\libraries\vhdl\altera_mf\altera_mf_components.vhd

1.11. VHDL LIBRARY-USE Declaration

The VHDL LIBRARY-USE declaration is not required if you use the VHDL Component Declaration.

LIBRARY altera_mf;

USE altera_mf.altera_mf_components.all;

2. FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP Core

This IP core performs floating-point accumulation and allows you to restrict the range of inputs and maximum accumulated value to save resources. The core uses device latency models to generate RTL to meet a target FMax at the cost of latency.

Table 8. Floating Point Custom Accumulator Intel^® FPGA IP Release Information
Item	Description
Version	19.1
Intel^® Quartus^® Prime Version	20.1
Release Date	2020.04.13

2.1. FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP Features

The FPACC_CUSTOM Intel^® FPGA IP or Floating Point Custom Accumulator Intel^® FPGA IP core offers the following features:

Supports frequency driven cores.
Supports VHDL RTL generation.
Supports customization of the required range of the input and output values.

2.2. FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP Output Latency

The amount of latency is driven by the target frequency and the selected device family. You must set the desired frequency and the target device before generating the IP core. The IP core reports the latency when you set the parameters and when you generate the IP core. Then, use the reported latency to incorporate the IP core into your design.

2.3. FP_ACC_CUSTOM Intel FPGA IP Resource Utilization and Performance

Table 9. FP_ACC_CUSTOM Intel^® FPGA IP Resource Utilization and PerformanceThis table lists the resource utilization and performance information for the FP_ACC_CUSTOM Intel^® FPGA IP core. The information was derived using the Intel^® Quartus^® Prime software version 13.1.
Device Family	Input Data		Accumulator Size		Target Frequency (MHz)	Latency	ALMs	DSP Blocks	Logic Registers		M10K	M20K	f_MAX
Device Family	Floating Point Format	MaxMSBX	MSBA	LSBA	Target Frequency (MHz)	Latency	ALMs	DSP Blocks	Primary	Secondary	M10K	M20K	f_MAX
Arria V (5AGXFB3H4F40C5)	Double	24	40	-52	270	15	866	0	1,166	106	0	--	265
Cyclone V (5CGXFC7D6F31C7)	Double	24	40	-52	230	15	830	0	1,102	32	0	--	198
Stratix V (5SGXEA7K2F40C2)	Double	24	40	-52	400	15	968	0	1,655	27	--	0	426
Arria V (5AGXFB3H4F40C5)	Single	12	20	-26	270	12	337	0	588	52	0	--	309
Cyclone V (5CGXFC7D6F31C7)	Single	12	20	-26	230	12	383	0	494	28	0	--	225
Stratix V (5SGXEA7K2F40C2)	Single	12	20	-26	400	13	475	0	903	20	--	0	450

2.4. FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP Signals

Figure 13. FP_ACC_CUSTOM Intel^® FPGA IP or Floating Point Custom Accumulator Intel^® FPGA IP

Table 10. FP_ACC_CUSTOM Intel^® FPGA IP or Floating Point Custom Accumulator Intel^® FPGA IP Input Ports
Port Name	Required	Description
`clk`	Yes	All input signals, otherwise explicitly stated, must be synchronous to this clock
`areset`	Yes	Asynchronous active-high reset. Deassert this signal synchronously to the input clock to avoid metastability issues.
`en`	No	Global enable signal. This port is optional.
`x`	Yes	Data input port.
`n`	Yes	Boolean port which signals the beginning of a new data set to be accumulated. This should go high together with the first element in the new data set and should go low the next cycle. The data sets may be of variable length and a new data set may be started at any time. The accumulation result for an input is available after the reported latency.

Table 11. FP_ACC_CUSTOM Intel^® FPGA IP or Floating Point Custom Accumulator Intel^® FPGA IP Output Ports
Port Name	Required	Description
`r`	Yes	The running value of the accumulation.
`xo`	Yes	The overflow flag for port `x`. The signal goes high when the exponent of the input `x` is larger than maxMSBX. The signal remains high for the entire data set. This flag invalidates port `r`. You should consider increasing maxMSBX. This flag also indicate infinity and NaN.
`xu`	Yes	The underflow flag for port `x`. The signal goes high when the exponent of the input `x` is smaller than LSBA. The signal remains high for the entire data set. This flag does not invalidate port `r`. You should consider lowering LSBA.
`ao`	Yes	The overflow flag for Accumulator. The signal goes high when the exponent of the accumulated value is larger than MSBA. The signal remains high for the entire data set. This flag invalidates port `r`. You should consider increasing MSBA.

2.5. FP_ACC_CUSTOM Intel FPGA IP or Floating Point Custom Accumulator Intel FPGA IP Parameters

Table 12. FP_ACC_CUSTOM Intel^® FPGA IP or Floating Point Custom Accumulator Intel^® FPGA IP Parameters
Category	Parameter	Values	Description
Input Data	Floating point format	single, double	Choose the floating point format of the input data values. The output data values of the accumulator is in the same format. The default is single.
Input Data	maxMSBX	—	The maximum weight of the MSB of an input. For example, when adding probabilities in the 0 to 1 range set this weight to ceil(log₂(1))=0. The `xo` output signal goes high when the MSB of an input value has a weight larger than maxMSBX. The result of the accumulation is then invalid. If you are unsure about the range of the inputs, then set the maxMSBX parameter to MSBA, at the possible expense of increased resource usage. The default value is 12.
Accumulator Size	MSBA	—	The weight of the MSB of the accumulator. For example, in a financial simulation, if the value of a stock cannot exceed 100,000 dollars, use a value of ceil(log₂(100000))=17. In a circuit simulation where the circuit adds numbers in the 0 to 1 range, for one year, at 400 MHz, use a value of ceil(log₂(365 x 60 x 60 x 24 x 400 x 10⁶))=54. The `ao` output signal goes high when the MSB of the accumulated value has a weight larger than MSBA. The result of the accumulation is then invalid. Intel recommends adding a few guard bits to avoid possible accumulator overflow. A few guard bits have little impact on the accumulator size. The default value is 20.
Accumulator Size	LSBA	—	The weight of the LSB of the accumulator and the accuracy of the accumulator. Because an N term accumulation can invalidate the log₂(N) LSBs of the accumulator, you must consider the length of the accumulation and the range of the inputs when setting this parameter. For example, if a 2^-30 accuracy is required over an accumulation of 1024 numbers, then set the LSBA to: (-30 - log₂(1024)) = -40. Any input 2^e×1.F, where F is the mantissa and e is less than the LSBA will be shifted out of the accumulator. The `au` output signal goes high to indicate this situation. The default value is -26.
Required Performance	Target frequency	Any positive integer value.	Choose the frequency in MHz at which this core is expected to run. This together with the target device family determines the amount of pipelining in the core. The default value is 200 MHz.
Optional	Generate an enable port	—	Choose if the accumulator should have an enable signal. This parameter is disabled by default.
Report	—	—	Reports the latency of the device, which is the number of cycles it takes for an accumulation to propagate through the block from input to output.

3. ALTFP_ADD_SUB IP Core

This IP core allows you to perform floating-point addition or subtraction between two inputs dynamically.

3.1. ALTFP_ADD_SUB Features

The ALTFP_ADD_SUB IP core offers the following features:

Dynamically configurable adder and subtracter functions.
Optional exception handling output ports such as zero, overflow, underflow, and nan.
Optimization of speed and area.

3.2. ALTFP_ADD_SUB Output Latency

The output latency options for the ALTFP_ADD_SUB IP core are the same for all three precision formats—single, double, and single-extended. The options available are 7, 8, 9, 10, 11, 12, 13, and 14 clock cycles.

3.3. ALTFP_ADD_SUB Truth Table

Table 13. Truth Table for Addition/Subtraction Operations
DATAA[]	DATAB[]	SIGN BIT	RESULT[]	Overflow	Underflow	Zero	NaN
Normal	Normal	0	Zero	0	0	1	0
Normal	Normal	0/1	Normal	0	0	0	0
Normal	Normal	0/1	Denormal	0	1	1	0
Normal	Normal	0/1	Infinity	1	0	0	0
Normal	Denormal	0/1	Normal	0	0	0	0
Normal	Zero	0/1	Normal	0	0	0	0
Normal	Infinity	0/1	Infinity	1	0	0	0
Normal	NaN	X	NaN	0	0	0	1
Denormal	Normal	0/1	Normal	0	0	0	0
Denormal	Denormal	0/1	Normal	0	0	0	0
Denormal	Zero	0/1	Zero	0	0	1	0
Denormal	Infinity	0/1	Infinity	1	0	0	0
Denormal	NaN	X	NaN	0	0	0	1
Zero	Normal	0/1	Normal	0	0	0	0
Zero	Denormal	0/1	Zero	0	0	1	0
Zero	Zero	0/1	Zero	0	0	1	0
Zero	Infinity	0/1	Infinity	1	0	0	0
Zero	NaN	X	NaN	0	0	0	1
Infinity	Normal	0/1	Infinity	1	0	0	0
Infinity	Denormal	0/1	Infinity	1	0	0	0
Infinity	Zero	0/1	Infinity	1	0	0	0
Infinity	Infinity	0/1	Infinity	1	0	0	0
Infinity	NaN	X	NaN	0	0	0	1
NaN	Normal	X	NaN	0	0	0	1
NaN	Denormal	X	NaN	0	0	0	1
NaN	Zero	X	NaN	0	0	0	1
NaN	Infinity	X	NaN	0	0	0	1
NaN	NaN	X	NaN	0	0	0	1

3.4. ALTFP_ADD_SUB Resource Utilization and Performance

The following lists the resource utilization and performance information for the ALTFP_ADD_SUB IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 14. ALTFP_ADD_SUB Resource Utilization and Performance for the Stratix Series of Devices
Device Family	Precision	Optimization	Output latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	f_MAX (MHz)
Stratix IV	single	speed	7	594	376	385	228
		speed	14	674	686	498	495
		area	7	576	345	375	227
		area	14	596	603	421	484
	double	speed	7	1,198	687	824	187
		speed	14	997	1,607	1,080	398
		area	7	1,106	630	762	189
		area	14	904	1,518	1,013	265

3.5. ALTFP_ADD_SUB Design Example: Addition of Double-Precision Format Numbers

This design example uses the ALTFP_ADD_SUB IP core to perform the addition of double-precision format numbers using the parameter editor in the Intel^® Quartus^® Prime software.

3.5.1. ALTFP_ADD_SUM Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

Figure 14. ALTFP_ADD_SUB Simulation Waveform

This design example implements a floating-point adder for the addition of double-precision format numbers. All the optional input ports (clk_en and aclr) and optional output ports (overflow, underflow, zero, and nan) are enabled.

In this example, the output latency of the multiplier is set to 7 clock cycles. Every addition result appears at the result[] port 7 clock cycles after the input values are captured on the dataa[] and datab[] ports.

The following lists the inputs and corresponding outputs obtained from the simulation waveform.

Table 15. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`dataa[]` value: 0000 0000 0000 0000h `datab[]` value: 7FF0 0000 0000 0000h Output value: All values seen on the output port before the 7th clock cycle are merely due to the behavior of the system during startup and should be disregarded.
4250 ns	Output value: 7FF0 0000 0000 0000h Exception handling ports: `overflow` asserts The addition of zero at the input port `dataa[]`, and infinity value at the input port `datab[]` results in infinity value.
40,511 ns	`dataa[]` value: 0000 0000 0000 0000h `datab[]` value: 0000 0000 1000 0123h The is the addition of a zero and a denormal value.
43,750 ns	Output value: 0000 0000 0000 0000h Exception handling ports: `zero` remains asserted. Denormal inputs are not supported and are forced to zero before addition takes place.This results in a zero.

3.6. ALTFP_ADD_SUB Signals

Figure 15. ALTFP_ADD_SUB

Table 16. ALTFP_ADD_SUB Input Ports
Port Name	Required	Description
`aclr`	No	Asynchronous clear input for floating-point adder or subtractor. The source is asynchronously reset when the `aclr` signal is asserted high.
`add_sub`	No	Optional input port to enable dynamic switching between the adder and subtractor functions. The `add_sub` port must be used when the `DIRECTION` parameter is set to `VARIABLE`. When the `add_sub` port is high, `result[] = dataa[] + datab[]`, otherwise, `result[] = dataa[] - datab[]`.
`clk_en`	No	Clock enable to the floating-point adder or subtractor. This port allows addition or subtraction to occur when asserted high. When asserted low, no operations occur and the outputs are unchanged.
`clock`	Yes	Clock input to the IP core.
`dataa[]`	Yes	Data input to the floating-point adder or subtractor. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa bits. The size of this port is the total width of the sign bit, the exponent bits, and the mantissa bits.
`datab[]`	Yes	Data input to the floating-point adder or subtractor. This port is configured in the same way as `dataa[]`.

Table 17. ALTFP_ADD_SUB Output Ports
Port Name	Required	Description
`nan`	Yes	NaN exception output. Asserted when an illegal addition or subtraction occurs, such as infinity minus infinity. When an invalid addition or subtraction occurs, a NaN value is output to the `result[]` port. Any adding or subtracting involving NaN values also produces a NaN value.
`overflow`	Yes	Overflow exception port. Asserted when the result of the addition or subtraction, after rounding, exceeds or reaches infinity. Infinity is defined as a number in which the exponent exceeds `2` ^WIDTH_EXP -1.
`result[]`	Yes	Floating-point output result. Like the input values, the MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`underflow`	Yes	Underflow port for the adder or subtractor. Asserted when the result of the addition or subtraction, after rounding, the value is zero and the inputs are not equal. The `underflow` port is also asserted when the result is a denormalized number.
`zero`	No	Zero port for the adder or subtractor. Asserted when the `result[]` port is zero.

3.7. ALTFP_ADD_SUB Parameters

Table 18. ALTFP_ADD_SUB Parameters
Parameter Name	Type	Required	Description
`DIRECTION`	String	Yes	Specifies addition or subtraction operations. Values are `ADD`, `SUB`, or `VARIABLE`. If this parameter is not specified, the default is `ADD`. When the value is `VARIABLE`, the `add_sub` port determines whether the operation is addition or subtraction. The `add_sub` port must be connected if the `DIRECTION` parameter is set to `VARIABLE`. If the value is `ADD` or `SUB`, the `add_sub` port is ignored.
`PIPELINE`	Integer	No	Specifies the latency in clock cycles used in the ALTFP_ADD_SUB IP core. The `PIPELINE` parameter supports values of `7` through `14`. If this parameter is not specified, the default value is `11`. In general, a higher pipeline value produces better f_MAX performance.
`ROUNDING`	String	Yes	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are currently not supported.
`OPTIMIZE`	String	No	Defines the design preference, whether the design is optimized for speed (faster f_MAX), or optimized for area (lower resource count). Values are `SPEED` and `AREA`. If this parameter is not specified, the default is `SPEED`.
`WIDTH_EXP`	Integer	No	Specifies the precision of the exponent. The bias of the exponent is always set to `2` (WIDTH_EXP-1) -`1` (that is, `127` for single-precision format and `1023` for double-precision format). The `WIDTH_EXP` parameter must be `8` for the single-precision mode and `11` for the double-precision mode, or a minimum of `11` for the single-extended precision mode. The `WIDTH_EXP` parameter must be less than the `WIDTH_MAN` parameter. The sum of `WIDTH_EXP` and the `WIDTH_MAN` parameters must be less than `64`. If this parameter is not specified, the default is `8`.
`WIDTH_MAN`	Integer	No	Specifies the precision of the mantissa. The `WIDTH_MAN` parameter must be `23` (to comply with the IEEE-754 standard for the single-precision mode) when the `WIDTH_EXP` parameter is `8`. Otherwise, the `WIDTH_MAN` parameter must have a value that is greater than or equal to `31`. The `WIDTH_MAN` parameter must be greater than the `WIDTH_EXP` parameter. The sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`. If this parameter is not specified, the default is `23`.

4. ALTFP_DIV IP Core

This IP core performs floating-point division operation.

4.1. ALTFP_DIV Features

The ALTFP_DIV IP core offers the following features:

Division functions.
Optional exception handling output ports such as zero, division_by_zero, overflow, underflow, and nan.
Optimization of speed and area.
Low latency option.

4.2. ALTFP_DIV Output Latency

The output latency options for the ALTFP_DIV IP core differs depending on the precision selected, the width of the mantissa, or both. You have the choice of selecting the smaller figures of clock cycles delay in your design if the low latency option is desired.

Table 19. Latency Options for Each Operation
Precision	Mantissa Width	Latency (in clock cycles)
Single	23	6, 14, 33
Double	52	10, 24, 61
Single Extended	31 – 32	8, 18, 41
	33 – 34	8, 18, 43
	35 – 36	8, 18, 45
	37 – 38	8, 18, 47
	39 – 40	8, 18, 49
	41	10, 24, 41
	42	10, 24, 51
	43 – 44	10, 24, 53
	45 – 46	10, 24, 55
	47 – 48	10, 24, 57
	49 – 50	10, 24, 59
	51 – 52	10, 24, 61

4.3. ALTFP_DIV Truth Table

Table 20. Truth Table for Division Operations
DATAA[]	DATAB[]	SIGN BIT	RESULT[]	Overflow	Underflow	Zero	Division-by-zero	NaN
Normal	Normal	0/1	Normal	0	0	0	0	0
Normal	Normal	0/1	Denormal	0	0	1	0	0
Normal	Normal	0/1	Infinity	1	0	0	0	0
Normal	Normal	0/1	Zero	0	1	1	0	0
Normal	Denormal	0/1	Infinity	0	0	0	1	0
Normal	Zero	0/1	Infinity	0	0	0	1	0
Normal	Infinity	0/1	Zero	0	0	1	0	0
Normal	NaN	X	NaN	0	0	0	0	1
Denormal	Normal	0/1	Zero	0	0	1	0	0
Denormal	Denormal	0/1	NaN	0	0	0	0	1
Denormal	Zero	0/1	NaN	0	0	0	0	1
Denormal	Infinity	0/1	Zero	0	0	1	0	0
Denormal	NaN	X	NaN	0	0	0	0	1
Zero	Normal	0/1	Zero	0	0	1	0	0
Zero	Denormal	0/1	NaN	0	0	0	0	1
Zero	Zero	0/1	NaN	0	0	0	0	1
Zero	Infinity	0/1	Zero	0	0	1	0	0
Zero	NaN	X	NaN	0	0	0	0	1
Infinity	Normal	0/1	Infinity	0	0	0	0	0
Infinity	Denormal	0/1	Infinity	0	0	0	0	0
Infinity	Zero	0/1	Infinity	0	0	0	0	0
Infinity	Infinity	0/1	NaN	0	0	0	0	1
Infinity	NaN	X	NaN	0	0	0	0	1
NaN	Normal	X	NaN	0	0	0	0	1
NaN	Denormal	X	NaN	0	0	0	1	1
NaN	Zero	X	NaN	0	0	0	1	1
NaN	Infinity	X	NaN	0	0	0	0	1
NaN	NaN	X	NaN	0	0	0	0	1

4.4. ALTFP_DIV Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_DIV IP core. The information was derived using the Quartus II software version 10.0.

Table 21. ALTFP_DIV Resource Utilization and Performance for Stratix IV Devices
Device family	Precision	Optimization	Output latency	Logic Usage				f_MAX(MHz)
Device family	Precision	Optimization	Output latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-bit DSP	f_MAX(MHz)
Stratix IV	Single	Speed	33	3,593	3,351	2,500	—	313
	Single	Area	33	1,646	2,074	1,441	—	308
	Double	Speed	61	13,867	13,143	10,196	—	292
	Double	Area	61	5,125	7,360	4,842	—	267
Low Latency Option
Stratix IV	Single	—	6	207	304	212	16	154
	Single	—	14	253	638	385	16	358
	Double	—	10	714	1,077	779	44	151
	Double	—	24	765	2,488	1,397	44	238

4.5. ALTFP_DIV Design Example: Division of Single-Precision

This design example uses the ALTFP_DIV IP core to implement a floating-point divider for the division of single-precision format numbers with low latency. This example uses the parameter editor to define the core.

4.5.1. ALTFP_DIV Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

Figure 16. ALTFP_DIV Simulation WaveformThis figure shows the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

This design example implements a floating-point divider for the division of single-precision numbers with a low latency option. The output latency is 6, hence every division generates the output result 6 clock cycles later.

Table 22. Summary of Input Values and Corresponding Outputs This table lists the inputs and corresponding outputs obtained from the simulation in the waveform.
Time	Event
0 ns, start-up	`dataa[]` value: 0000 0000h `datab[]` value: 0000 0000h Output value: The undefined value is seen on the `result[]` port, which is ignored. All values seen on the output port before the 6th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
17600 ns	Output value: 7FC0 0000h Exception handling ports: `nan` asserts The division of zeros result in a NaN.
2000 ns	`dataa[]` value: 2D0B 496Ah `datab[]` value: 3A5A FC26h Both inputs hold normal values.
20800 ns	Output result: 321F 6EC6h Exception output ports: `nan` deasserts The division of two normal value results in a normal value.
11000 ns	`dataa[]` value: 046E 78BCh `datab[]` value: 6798 698Bh Both inputs hold normal values.
27200 ns	Output value: 0h Exception handling ports: `underflow` and `zero` asserts The division of the two normal values results in a denormal value. As denormal values are not supported, the result is zero and the `underflow` port asserts. The `zero` port is also asserted to indicate that the result is zero.
2600 ns	`dataa[]` value: 0D72 54A8h `datab[]` value: 0070 0000h The input port `dataa[]` holds a normal value while the input port `datab[]` holds a denormal value.
36800 ns	Output value: 7F80 0000h Exception handling ports: `division_by_zero` asserts Denormal numbers are forced-zero values, therefore, attempts to divide a normal value with a zero result in an infinity value.

4.6. ALTFP_DIV Signals

Figure 17. ALTFP_DIV Signals

Table 23. ALTFP_DIV Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear input for the floating-point divider. The source is asynchronously reset when the `aclr` signal is asserted high.
`clock`	Yes	Clock input to the IP core.
`clk_en`	No	Clock enable to the floating-point divider. This port enables division. This signal is active high. When this signal is low, no division takes place and the outputs remain the same.
`dataa[]`	Yes	Numerator data input. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits and mantissa bits.
`datab[]`	Yes	Denominator data input.The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits and mantissa bits.

Table 24. ALTFP_DIV Output Signals
Port Name	Required	Description
`result[]`	Yes	Divider output port. The division result (after rounding). As with the input values, the MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`overflow`	No	Overflow port for the divider. Asserted when the result of the division (after rounding) exceeds or reaches infinity. Infinity is defined as a number in which the exponent exceeds `2`WIDTH_EXP–1.
`underflow`	No	Underflow port for the divider. Asserted when the result of the division (after rounding) is zero even though neither of the inputs to the divider is zero, or when the result is a denormalized number.
`zero`	No	Zero port for the divider. Asserted when the value of `result[]` is zero.
`division_by_zero`	No	Division-by-zero output port for the divider. Asserted when the value of `datab[] is a zero.`
`nan`	No	NaN port. Asserted when an invalid division occurs, such as infinity dividing infinity or zero dividing zero. A NaN value appears as output at the `result[]` port. Any division of a NaN value causes the `nan` output port to be asserted.

4.7. ALTFP_DIV Parameters

Table 25. ALTFP_DIV Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to (2 ^ (`WIDTH_EXP` - 1)) - 1, that is, 127 for single precision and 1023 for double precision. The value of `WIDTH_EXP` must be `8` for single precision, `11` for double precision, and a minimum of 11 for single extended precision. The value of `WIDTH_EXP` must be less than the value of `WIDTH_MAN`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP` is `8` and the floating-point format is the single-precision format, the `WIDTH_MAN` value must be `23`. Otherwise, the value of `WIDTH_MAN` must be a minimum of `31`. The value of `WIDTH_MAN` must be greater than the value of `WIDTH_EXP`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`ROUNDING`	String	Yes	Specifies the rounding mode. The default value is `TO_NEAREST`. The floating-point divider does not support other rounding modes.
`OPTIMIZE`	String	No	Specifies whether to optimize for area or for speed. Values are `AREA` and `SPEED`. A value of `AREA` optimizes the design using less total logic utilization or resources. A value of `SPEED` optimizes the design for better performance. If this parameter is not specified, the default value is `SPEED`.
`PIPELINE`	Integer	No	Specifies the number of clock cycles needed to produce the result. For the single-precision format, the latency options are `33`, `14` or `6`. For the double-precision format, the latency options are `61`, `24` or `10`. For the single-extended precision format, the value ranges from a minimum of `41` to a maximum of `61`. For the low-latency option, the latency is determined from the mantissa width. For a mantissa width of `31` to `40` bits, the value is `8` or `18`. For a mantissa width of `41` bits or more, the value is `10` or `24`.

5. ALTFP_MULT IP Core

This IP core performs floating-point multiplication operation.

5.1. ALTFP_MULT IP Core Features

The ALTFP_MULT IP core offers the following features:

Multiplication functions.
Optional exception handling output ports such as zero, overflow, underflow, and nan.
Optional dedicated multiplier circuitries in Cyclone and Stratix series.

5.2. ALTFP_MULT Output Latency

The output latency options for the ALTFP_MULT IP core are similar for all precisions.

Table 26. Latency Options for Each Precision Format
Precision	Mantissa Width	Latency (in clock cycles)
Single	23	5, 6, 10,11
Double	52	5, 6, 10,11
Single-Extended	31–52	5, 6, 10,11

5.3. ALTFP_MULT Truth Table

Table 27. Truth Table for Multiplier Operations
DATAA[]	DATAB[]	RESULT[]	Overflow	Underflow	Zero	NaN
Normal	Normal	Normal	0	0	0	0
Normal	Normal	Denormal	0	1	1	0
Normal	Normal	Infinity	1	0	0	0
Normal	Normal	Zero	0	1	1	0
Normal	Denormal	Zero	0	0	1	0
Normal	Zero	Zero	0	0	1	0
Normal	Infinity	Infinity	1	0	0	0
Normal	NaN	NaN	0	0	0	1
Denormal	Normal	Zero	0	0	1	0
Denormal	Denormal	Zero	0	0	1	0
Denormal	Zero	Zero	0	0	1	0
Denormal	Infinity	NaN	0	0	0	1
Denormal	NaN	NaN	0	0	0	1
Zero	Normal	Zero	0	0	1	0
Zero	Denormal	Zero	0	0	1	0
Zero	Zero	Zero	0	0	1	0
Zero	Infinity	NaN	0	0	0	1
Zero	NaN	NaN	0	0	0	1
Infinity	Normal	Infinity	1	0	0	0
Infinity	Denormal	NaN	0	0	0	1
Infinity	Zero	NaN	0	0	0	1
Infinity	Infinity	Infinity	1	0	0	0
Infinity	NaN	NaN	0	0	0	1
NaN	Normal	NaN	0	0	0	1
NaN	Denormal	NaN	0	0	0	1
NaN	Zero	NaN	0	0	0	1
NaN	Infinity	NaN	0	0	0	1
NaN	NaN	NaN	0	0	0	1

5.4. ALTFP_MULT Resource Utilization and Performance

The following tables list the resource utilization and performance information for the ALTFP_MULT IP core. The information was derived using the Quartus II software version 10.0.

Table 28. ALTFP_MULT Resource Utilization and Performance for Stratix IV Devices with Dedicated Multiplier Circuitry
Device Family	Precision	Output latency	Logic usage				f_MAX (MHz)
Device Family	Precision	Output latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-bit DSP	f_MAX (MHz)
Stratix IV	Single	5	138	148	100	4	274
	Single	11	185	301	190	4	445
	Double	5	306	367	272	10	255
	Double	11	419	523	348	10	395

5.5. ALTFP_MULT Design Example: Multiplication of Double-Precision Format Numbers

This design example uses the ALTFP_MULT IP core to compute the multiplication results of two double-precision format numbers. This example uses the parameter editor GUI to define the core.

5.5.1. ALTFP_MULT Design Example: Understanding the Simulation Waveform

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

Figure 18. ALTFP_MULT Simulation WaveformThis figure shows the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

This design example implements a floating-point multiplier for the multiplication of double-precision format numbers. All the optional input ports (clk_en and aclr) and output ports (overflow, underflow, zero, and nan) are enabled.

In this example, the latency is set to 6 clock cycles. Therefore, every multiplication result appears at the result port 6 clock cycles later.

Table 29. Summary of Input Values and Corresponding OutputsThis table lists the inputs and corresponding outputs obtained from the simulation in the waveform.
Time	Event
0 ns, start-up	`dataa[]` value: 0000 0000 0000 0000h `datab[]` value: 4037 742C 3C9E ECC0h Output value: All values seen on the output port before the 6th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
110 ns	Output value: 0000 0000 0000 0000h Exception handling ports: `zero` asserts The multiplication of zero at the input port `dataa[]`, and a non-zero value at the input port`datab[]` results in a zero.
600 ns	`dataa[]` value: 7FF0 0000 0000 0000h `datab[]` value: 4037 742C 3C9E ECC0h This is the multiplication of an infinity value and a normal value.
710 ns	Output value: 7FF0 0000 0000 0000h Exception handling ports: `overflow` asserts The multiplication of an infinity value and a normal value results in infinity. All multiplications with an infinity value results in infinity except when infinity is multiplied with a zero.

5.6. Parameters

Table 30. ALTFP_MULT Intel^® FPGA IP core Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	No	Specifies the value of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always `2^{(WIDTH_EXP - 1)}-1` (that is, `127` for the single-precision format and `1023` for the double-precision format). `WIDTH_EXP` must be `8` for the single-precision format or a minimum of `11` for the double-precision format and the single-extended precision format. `WIDTH_EXP` must less than `WIDTH_MAN`. The sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`WIDTH_MAN`	Integer	No	Specifies the value of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP` is `8` and the floating-point format is single-precision, the `WIDTH_MAN` value must be `23`; otherwise, the value of `WIDTH_MAN` must be a minimum of `31`. The `WIDTH_MAN` value must always be greater than the `WIDTH_EXP` value. The sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`DEDICATED_MULTIPLIER_ CIRCUITRY`	String	No	Specifies whether to use dedicated multiplier circuitry. Values are `AUTO`, `YES`, or `NO`. If this parameter is not specified, the default is `AUTO`. If a device does not have dedicated multiplier circuitry, the `DEDICATED_MULTIPLIER_CIRCUITRY` parameter has no effect and defaults to `NO`.
`PIPELINE`	Integer	No	Specifies the number of clock cycles needed to produce the multiplied result. Values are `5`, `6`, `10`, and `11`. If this parameter is not specified, the default is `5`.

5.7. ALTFP_MULT Signals

Table 31. ALTFP_MULT IP Core Input Signals
Port Name	Required	Description
`clock`	Yes	Clock input to the IP core.
`clk_en`	No	Clock enable. Allows multiplication to take place when asserted high. When signal is asserted low, no multiplication occurs and the outputs remain unchanged.
`aclr`	No	Synchronous clear. Source is asynchronously reset when asserted high.
`dataa[]`	Yes	Floating-point input data input to the multiplier. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.
`datab[]`	Yes	Floating-point input data to the multiplier. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.

Table 32. ALTFP_MULT IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	Output port for the multiplier. The floating-point result after rounding. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa.
`overflow`	No	Overflow port for the multiplier. Asserted when the result of the multiplication, after rounding, exceeds or reaches infinity. Infinity is defined as a number in which the exponent exceeds `2^WIDTH_EXP-1`.
`underflow`	No	Underflow port for the multiplier. Asserted when the result of the multiplication (after rounding) is `0` while none of the inputs to the multiplication is `0`, or asserted when the result is a denormalized number.
`zero`	No	Zero port for the multiplier. Asserted when the value of `result[]` is `0`.
`nan`	No	NaN port for the multiplier. This port is asserted when an invalid multiplication occurs, such as the multiplication of infinity and zero. In this case, a NaN value is the output generated at the `result[]` port. The multiplication of any value and NaN produces NaN.

6. ALTFP_SQRT

This IP core performs square root calculation based on the input provided. You can use the ports and parameters available to customize the ALTFP_SQRT IP core according to your application.

6.1. ALTFP_SQRT Features

The ALTFP_SQRT IP core offers the following features:

Square root functions.
Optional exception handling output ports such as zero, overflow, and nan.

6.2. Output Latency

The output latency options for the ALTFP_SQRT IP core differs depending on the precision selected, the width of the mantissa, or both.

Table 33. Latency Options for Each Precision Format
Precision	Mantissa Width	Latency (in clock cycles)
Single	23	16, 28
Double	52	30, 57
Single-extended	31	20, 36
	32	20, 37
	33	21, 38
	34	21, 39
	35	22, 40
	36	22, 41
	37	23, 42
	38	23, 43
	39	24, 44
	40	24, 45
	41	25, 46
	42	25, 47
	43	26, 48
	44	26, 49
	45	27, 50
	46	27, 51
	47	28, 52
	48	28, 53
	49	29, 54
	50	29, 55
	51	30, 56

6.3. ALTFP_SQRT Truth Table

Truth Table for Square Root Operations

DATA[]	SIGN BIT	RESULT[]	NaN	Overflow	Zero
Normal	0	Normal	0	0	0
Denormal	0/1	Zero	0	0	1
Positive Infinity	0	Infinity	0	1	0
Negative Infinity	1	All 1’s	1	0	0
Positive NaN	0	All 1’s	1	0	0
Negative NaN	1	All 1’s	1	0	0
Zero	0/1	Zero	0	0	1
Normal	1	All 1’s	1	0	0

6.4. ALTFP_SQRT Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_SQRT IP core. The information was derived using the Quartus II software version 10.0.

Table 34. ALTFP_SQRT Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output latency	Logic usage			f_MAX (MHz)
Device Family	Precision	Output latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Login Registers (DLRs)	Adaptive Logic Modules (ALMs)	f_MAX (MHz)
Stratix IV	Single	28	502	932	528	472
Stratix IV	Double	57	2,177	3,725	2,202	366

6.5. ALTFP_SQRT Design Example: Square Root of Single-Precision Format Numbers

This design example uses the ALTFP_SQRT IP core to compute the square root of single-precision format numbers. This example uses the parameter editor in the Intel^® Quartus^® Prime software.

6.5.1. ALTFP_SQRT Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

These figures show the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 19. ALTFP_SQRT Simulation Waveform (Input Data)

Figure 20. ALTFP_SQRT Simulation Waveform (Output Data)

This design example implements a floating-point square root function for single-precision format numbers with all the exception output ports instantiated. The output ports include overflow, zero, and nan.

The output latency is 28 clock cycles. Every square root computation generates the output result 28 clock cycles later.

Table 35. Summary of Input Values and Corresponding OutputsThis table lists the inputs and corresponding outputs obtained from the simulation in the waveforms.
Time	Event
0 ns, start-up	Output value: All values seen on the output port before the 28th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
2 000 ns	`data[]` value: 2D0B 496Ah The data input is a normal number.
84 000 ns	Output value: 363C D4EBh The square root computation of a normal input results in a normal output.
14 000 ns	`data[]` value: 0000 0000h
96 000 ns	Output value: 0000 0000h Exception handling ports: `zero` asserts The square root computation of zero results in a zero.
23 000 ns	`data[]` value: 7F80 0000h The input is infinity.
105 000 ns	Output value: 7F80 0000h Exception handling ports: `overflow` asserts

6.6. ALTFP_SQRT Signals

Figure 21. ALTFP_SQRT Signals

Table 36. ALTFP_SQRT IP Core Input Signals
Port Name	Required	Description
`clock`	Yes	Clock input to the IP core.
`clk_en`	No	Clock enable that allows square root operations when the port is asserted high. When the port is asserted low, no operation occurs and the outputs remain unchanged.
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously reset.
	Yes	Floating-point input data. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.

Table 37. ALTFP_SQRT IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	Square root output port for the floating-point result. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`overflow`	Yes	Overflow port. Asserted when the result of the square root (after rounding) exceeds or reaches infinity. Infinity is defined as a number in which the exponent exceeds `2^WIDTH_EXP -1`.
`zero`	Yes	Zero port. Asserted when the value of the `result[]` port is `0`.
`nan`	Yes	NaN port. Asserted when an invalid square root occurs, such as negative numbers or NaN inputs.

6.7. ALTFP_SQRT Parameters

Table 38. ALTFP_SQRT Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2` (`WIDTH_EXP` -1) -`1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of the `WIDTH_EXP` parameter must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of the `WIDTH_EXP` parameter must be less than the value of the `WIDTH_MAN` parameter, and the sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the value of the mantissa. If this parameter is not specified, the default is `23`. When the `WIDTH_EXP` parameter is `8` and the floating-point format is single-precision, the `WIDTH_MAN` parameter value must be `23`. Otherwise, the value of the `WIDTH_MAN` parameter must be a minimum of `31`. The value of the `WIDTH_MAN` parameter must be greater than the value of the `WIDTH_EXP` parameter. The sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`ROUNDING`	String	Yes	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are not supported.
`PIPELINE`	Integer	Yes	Specifies the number of clock cycles for the square root results of the `result[]` port. Values are `WIDTH_MAN` + `5` and ((`WIDTH_MAN` + `5/2`)+`2`) as specified by truncating the radix point.

7. ALTFP_EXP IP Core

This IP core performs exponential calculation based on the input provided.

7.1. ALTFP_EXP Features

The ALTFP_EXP IP core offers the following features:

Exponential value of a given input.
Optional exception handling output ports such as zero, overflow, underflow, and nan.

7.2. Output Latency

The output latency options for the ALTFP_EXP IP core differs depending on the precision selected, the width of the mantissa, or both.

Precision	Mantissa Width	Latency (in clock cycles)
Single	23	17
Double	52	25
Single-extended	31 – 38	22
Single-extended	39 – 52	25

7.3. ALTFP_EXP Truth Table

Table 39. Truth Table for Exponential Operations
DATAA[]	Calculation	RESULT[]	NaN	Overflow	Underflow	Zero
Normal	edata	Normal	0	0	0	0
Normal	edata	Infinity	0	1	0	0
Normal (numbers of small magnitude)	edata	1	0	0	1	0
Normal (negative numbers of large magnitude)	edata	0	0	0	1	0
Denormal	e0	1	0	0	0	0
Zero	e0	1	0	0	0	0
Infinity (+)	e+	Infinity	0	0	0	0
Infinity (-)	e-	0	0	0	0	1
NaN	—	NaN	1	0	0	0

¹ Any denormal input is treated as a zero before going through the exponential process.

7.4. ALTFP_EXP Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_EXP IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 40. ALTFP_EXP Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output Latency	Logic usage				f_MAX (MHz)
Device Family	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-bit DSP	f_MAX (MHz)
Stratix IV	Single	17	631	521	448	19	284
Stratix IV	Double	25	4,104	2,007	2,939	46	279

7.5. ALTFP_EXP Design Example: Exponential of Single-Precision Format Numbers

This design example uses the ALTFP_EXP IP core to compute the exponential value of single-precision format numbers. This example uses the parameter editor in the Intel^® Quartus^® Prime software.

7.5.1. ALTFP_EXP Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

These figures show the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 22. ALTFP_EXP Simulation Waveform (Input Data)

Figure 23. ALTFP_EXP Simulation Waveform (Output Data)

This design example implements a floating-point exponential for the single-precision format numbers. The optional input ports (clk_en and aclr) and all four exception handling output ports (nan, overflow, underflow, and zero) are enabled.

For single-precision format numbers, the latency is fixed at 17 clock cycles. Therefore, every exponential operation outputs the results 17 clock cycles later.

Table 41. Summary of Input Values and Corresponding OutputsThis table lists the inputs and corresponding outputs obtained from the simulation in the waveforms.
Time	Event
0 ns, start-up	`data[]` value: 1A03 568Ch Output value: An undefined value is seen on the `result[]` port, which is ignored. All values seen on the output port before the 17th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
82.5 ns	Output value: 3F80 0000h As the input value of 1A03568Ch is a very small number, it is seen as a value that is approaching zero, and the result approaches 1 (which is represented by 3F800000). Exponential operations carried out on numbers of very small magnitudes result in a 1 and assert the `underflow` flag. Exception handling ports: `underflow` asserts
30 ns	`data[]` value: F3FC DEFFh This is a normal negative value of a very large magnitude.
112.5 ns	Output value: 0000 0000h The outcome of exponential operations on negative numbers of very large magnitudes approaches zero. Exception handling ports: `underflow` remains asserted
60 ns	`data[]` value: 7F80 0000h This is a positive infinite value.
142.5 ns	Output value: 7F80 0000h The operation on positive infinite values results in infinity. Exception handling ports: `underflow` deasserts, `overflow` asserts
90 ns	`data[]` value: 7FC0 0000h This is a NaN.
172.5 ns	Output value: 7FC0 0000h The exponential of a NaN results in a NaN. Exception handling ports: `nan` asserts
120 ns	`data[]` value: C1D4 49BAh This is a normal value.
202.5 ns	Output value: 2C52 5981h The result is a normal value. Exception handling ports: `nan` deasserts

7.6. ALTFP_EXP Signals

Figure 24. ALTFP_EXP Signals

Table 42. ALTFP_EXP IP Core Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high the function is asynchronously reset.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, an exponential value operation takes place. When this signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits.

Table 43. ALTFP_EXP IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	The floating-point exponential result of the value at `data[]`. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`overflow`	No	Overflow exception output. Asserted when the result of the operation (after rounding) is infinite.
`underflow`	No	Underflow exception output. Asserted when the result of the exponential approaches `1` (from numbers of very small magnitude), or when the result approaches `0` (from negative numbers of very large magnitudes).
`zero`	No	Zero exception output. Asserted when the value in the `result[]` port is zero.
`nan`	No	NaN exception output. Asserted when an invalid operation occurs. Any operation involving NaN also asserts the `nan` port.

7.7. ALTFP_EXP Parameters

Table 44. ALTFP_EXP IP Core Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is 8. The bias of the exponent is always set to `2 ^{(WIDTH_EXP -1)} -1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of the `WIDTH_EXP` parameter must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of the `WIDTH_EXP` parameter must be less than the value of the `WIDTH_MAN` parameter, and the sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the value of the mantissa. If this parameter is not specified, the default is `23`. When the `WIDTH_EXP` parameter is `8` and the floating-point format is single-precision, the `WIDTH_MAN` parameter value must be `23`. Otherwise, the value of the `WIDTH_MAN` parameter must be a minimum of `31`. The value of the `WIDTH_MAN` parameter must be greater than the value of the `WIDTH_EXP` parameter. The sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`PIPELINE`	Integer	Yes	Specifies the amount of latency, expressed in clock cycles, used in the ALTFP_EXP IP core. Acceptable pipeline values are `17`, `22`, and `25` cycles of latency. Create the ALTFP_EXP IP core with the MegaWizard Plug-In Manager to calculate the value for this parameter.
`ROUNDING`	String	Yes	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are not supported.

8. ALTFP_INV IP Core

This IP core performs the function of 1/a where a is the given input.

8.1. ALTFP_INV Features

The ALTFP_INV IP core offers the following features:

Inverse value of a given input.
Optional exception handling output ports such as zero, division_by_zero, underflow, and nan.

8.2. Output Latency

The output latency options for the ALTFP_INVIP core differs depending on the precision selected, the width of the mantissa, or both.

Precision	Mantissa Width	Latency (in clock cycles)
Single	23	20
Double	52	27
Single Extended	31 – 39	20
Single Extended	40 – 52	27

8.3. ALTFP_INV Truth Table

Table 45. Truth Table for Inverse Operations
DATA[]	SIGN BIT	RESULT[]	Underflow	Zero	Division_by_zero	NaN
Normal	0/1	Normal	0	0	0	0
Normal	0/1	Denormal	1	1	0	0
Normal	0/1	Infinity	0	0	0	0
Normal	0/1	Zero	1	1	0	0
Denormal	0/1	Infinity	0	0	1	0
Zero	0/1	Infinity	0	0	1	0
Infinity	0/1	Zero	0	1	0	0
NaN	X	NaN	0	0	0	1

² Any calculated or computed denormal output is replaced by a zero and asserts the zero and underflow flags.

³ Any denormal input is treated as a zero before going through the inverse process.

8.4. ALTFP_INV Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_INV IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 46. ALTFP_INV Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output Latency	Logic usage				f_MAX(MHz)
Device Family	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-Bit DSP	f_MAX(MHz)
Stratix IV	Single	20	401	616	373	16	412
Stratix IV	Double	27	939	1,386	912	48	203

8.5. ALTFP_INV Design Example: Inverse of Single-Precision Format Numbers

This design example uses the ALTFP_INV IP core to compute the inverse of single-precision format numbers. This example uses the parameter editor in the Intel^® Quartus^® Prime software.

8.5.1. ALTFP_INV Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

These figures show the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 25. ALTFP_INV Simulation Waveform (Input Data)

Figure 26. ALTFP_INV Simulation Waveform (Output Data)

This design example implements a floating-point inverse for single-precision format numbers. The optional input ports (clk_en and aclr) and all four exception handling output ports (division_by_zero, nan, zero, and underflow) are enabled.

The latency is fixed at 20 clock cycles; therefore, every inverse operation outputs results 20 clock cycles later.

This table lists the inputs and corresponding outputs obtained from the simulation in the waveforms.

Table 47. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`data[]` value: 34A2 E42Fh Output value: An undefined value is seen on the `result[]` port, which is ignored. All values seen on the output port before the 20th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
97.5 ns	Output value: 4A49 2A2Fh Exception handling ports: `division_by_zero` deasserts The inverse of a normal number results in a normal value.
10 ns	`data[]` value: 7F80 0000h This is an infinity value.
107.5 ns	Output value: 0000 0000h Exception handling ports: `zero` asserts The inverse of an infinity value produces a zero.
60 ns	`data[]` value: 7FC0 0000h This is a NaN.
157.5 ns	Output value: 7FC0 0000h Exception handling ports: `nan` asserts The inverse of a NaN results in a NaN
70 ns	`data[]` value: 0000 1000h This is a denormal number.
167.5 ns	Output value: 7F80 0000h Exception handling ports: `nan` deasserts, `division_by_zero` asserts Denormal numbers are forced-zero values, therefore, the inverse of a zero results in infinity.

8.6. Ports

Table 48. ALTFP_INV IP core Input Ports
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, an inversion value operation takes place. When signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits.

Table 49. ALTFP_INV IP core Output Ports
Port Name	Required	Description
`result[]`	Yes	The floating-point inverse result of the value at the `data[]`input port. The MSB is the sign, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`underflow`	No	Underflow exception output. Asserted when the result of the inversion (after rounding) is a denormalized number.
`zero`	No	Zero exception output. Asserted when the value at the `result[]` port is a zero.
`division_by_zero`	No	Division-by-zero exception output. Asserted when the denominator input is a zero.
`nan`	No	NaN exception output. Asserted when an invalid inversion occurs, such as the inversion of NaN. In this case, a NaN value is output to the `result[]` port. Any operation involving NaN also asserts the `nan` port.

8.7. Parameters

Table 50. ALTFP_INV IP core Parameters
Parameter Name	Type	Required	Description
WIDTH_EXP	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is 8. The bias of the exponent is always set to `2 ^{(WIDTH_EXP -1)} -1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of the `WIDTH_EXP` parameter must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of the `WIDTH_EXP` parameter must be less than the value of the `WIDTH_MAN` parameter, and the sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
WIDTH_MAN	Integer	Yes	Specifies the value of the mantissa. If this parameter is not specified, the default is `23`. When the `WIDTH_EXP` parameter is `8` and the floating-point format is single-precision, the `WIDTH_MAN` parameter value must be `23`. Otherwise, the value of the `WIDTH_MAN` parameter must be a minimum of `31`. The value of the `WIDTH_MAN` parameter must be greater than the value of the `WIDTH_EXP` parameter. The sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
PIPELINE	Integer	Yes	Specifies the amount of latency in clock cycles used in the ALTFP_INV IP core. Create the ALTFP_INV IP core to calculate the value for this parameter.
ROUNDING	String	No	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are not supported.

9. ALTFP_INV_SQRT IP Core

This IP core performs inverse square root value of a given input.

9.1. ALTFP_INV_SQRT Features

The ALTFP_INV_SQRT IP core offers the following features:

Inverse square root value of a given input.
Optional exception handling output ports such as zero, division_by_zero, and nan.

9.2. Output Latency

The output latency options for the ALTFP_INV_SQRT IP core differs depending on the precision selected, the width of the mantissa, or both.

Table 51. Latency Options for Each Precision Format
Precision	Mantissa Width	Latency (in clock cycles)
Single	23	26
Double	52	36
Single-Extended	31– 39	26
Single-Extended	40 – 52	36

9.3. ALTFP_INV_SQRT Truth Table

Table 52. Truth Table for Inverse Square Root Operations
DATA[]	SIGN BIT	RESULT[]	Zero	Division_by_zero	NaN
Normal	0	Normal	0	0	0
Normal	1	NaN	0	0	1
Denormal	0/1	Infinity	0	1	0
Zero	0/1	Infinity	0	1	0
Infinity	0/1	Zero	1	0	0
NaN	X	NaN	0	0	1

⁴ Any denormal input is treated as a zero before going through the inverse process.

9.4. ALTFP_INV_SQRT Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_INV_SQRT IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 53. ALTFP_INV_SQRT Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output Latency	Logic usage				f_MAX (MHz)
Device Family	Precision	Output Latency	Adaptive Look-up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-Bit DSP	f_MAX (MHz)
Stratix IV	Single	26	502	658	430	22	413
Stratix IV	Double	36	1,324	1,855	1,209	78	209

9.5. ALTFP_INV_SQRT Design Example: Inverse Square Root of Single-Precision Format Numbers

This design example uses the ALTFP_INV_SQRT IP core to compute the inverse square root of single-precision format numbers. This example uses the parameter editor GUI to define the core.

9.5.1. ALTFP_INV_SQRT Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

These figures show the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 27. ALTFP_INV_SQRT Simulation Waveform (Input Data)

Figure 28. ALTFP_INV_SQRT Simulation Waveform (Output Data)

This design example implements a floating-point inverse square root for single-precision format numbers. The optional input ports (clk_en and aclr) and all three exception handling output ports (division_by_zero, nan, and zero) are enabled.

The latency is fixed at 26 clock cycles. Therefore, every inverse square root operation outputs the results 26 clock cycles later.

This table lists the inputs and corresponding outputs obtained from the simulation in the waveforms.

Table 54. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`data[]` value: 05AE 470Bh Output value: An undefined value is seen on the `result[]` port, which can be ignored. All values seen on the output port before the 26th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
127.5 ns	Output value: 5C5B 64CEh The inverse square root of a normal number results in a normal value.
10 ns	`data[]` value: E8A7 E93Dh This is a negative normal value.
137.5 ns	Output value: FFC0 0000h Exception handling ports: `nan` asserts The inverse square root of a negative value produces a NaN.
20 ns	`data[]` value: 0000 0004h The is a denormal value.
147.5 ns	Output value: 7F80 0000h Denormal numbers are forced-zero values, therefore the inverse square root of zero results in infinity. Exception handling ports: `nan` deasserts, `division_by_zero` asserts
50 ns	`data[]` value: 7F80 0000h This is an infinity value.
177.5 ns	Output value: 0000 0000h The inverse square root of an infinity value produces a zero. Exception handling ports: `zero` asserts

9.6. Ports

Figure 29. ALTFP_INV_SQRT Signals

Table 55. ALTFP_INV_SQRT IP Core Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, an inversion value operation takes place. When signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits.

Table 56. ALTFP_INV_SQRT IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	The floating-point inverse result of the value at the `data[]` input port. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. The size of this port is the total width of the sign bit, exponent bits, and mantissa bits.
`zero`	No	Zero exception output. Asserted when the value at the `result[]` port is a zero.
`division_by_zero`	No	Division-by-zero exception output. Asserted when the denominator input is a zero.
`nan`	No	NaN exception output. Asserted when an invalid inversion of square root occurs, such as the square root of a negative number. In this case, a NaN value is output to the `result[]` output port. Any operation involving a NaN produces a NaN.

9.7. Parameters

Table 57. ALTFP_INV_SQRT IP core Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2 ^{(WIDTH_EXP -1)} -1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of the `WIDTH_EXP` parameter must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of the `WIDTH_EXP` parameter must be less than the value of the `WIDTH_MAN` parameter, and the sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the value of the mantissa. If this parameter is not specified, the default is `23`. When the `WIDTH_EXP` parameter is `8` and the floating-point format is single-precision, the `WIDTH_MAN` parameter value must be `23`. Otherwise, the value of the `WIDTH_MAN` parameter must be a minimum of `31`. The value of the `WIDTH_MAN` parameter must be greater than the value of the `WIDTH_EXP` parameter. The sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
`PIPELINE`	Integer	Yes	Specifies the amount of latency, expressed in clock cycles, used in the ALTFP_INV_SQRT IP core. Create the ALTFP_INV_SQRT IP core to calculate the value for this parameter.
`ROUNDING`	String	No	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are not supported.

10. ALTFP_LOG

This IP core performs natural logarithm function. You can use the ports and parameters available to customize the ALTFP_LOG IP core according to your application.

10.1. ALTFP_LOG Features

The ALTFP_LOG IP core offers the following features:

Natural logarithm functions.
Optional exception handling output ports such as zero and nan.

10.2. Output Latency

The output latency options for the ALTFP_LOG IP core differs depending on the precision selected, the width of the mantissa, or both.

Table 58. Latency Options for Each Precision Format
Precision	Mantissa Width	Latency (in clock cycles)
Single	23	21
Double	52	34
Single Extended	31–36	25
	37–42	28
	43–48	31
	49–52	34

10.3. ALTFP_LOG Truth Table

This table lists the truth table for the natural logarithm operation.

Table 59. Truth Table for Natural Logarithm Operations
DATA[]	SIGN BIT	RESULT[]	Zero	NaN
Normal	0	Normal	0	0
Normal	1	NaN ⁵	0	1
1 ⁶	0	Zero	1	0
Denormal ⁷	0	Negative Infinity	0	0
Zero ⁸	0/1	Negative Infinity	0	0
Infinity	0	Positive Infinity	1	0
NaN	X	NaN	0	1

⁵ The natural logarithm of a negative value is invalid. Therefore, the output produced is a NaN.

⁶ The “1” in this case is equivalent to In 1.

⁷ The value of positive denormalized numbers is a value that approximates zero, and the output produced is a negative infinity number.

⁸ The zero in this case represents zero special case of the IEEE standard. It is not equivalent to In 0, but instead approximates to it.

10.4. ALTFP_LOG Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_LOG IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 60. ALTFP_LOG Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output Latency	Logic usage				f_MAX (MHz)
Device Family	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-Bit DSP	f_MAX (MHz)
Stratix IV	Single	21	1,950	1,864	1,378	8	385
Stratix IV	Double	34	5,451	6,031	4,151	64	211

10.5. ALTFP_LOG Design Example: Natural Logarithm of Single-Precision Format Numbers

This design example uses the ALTFP_LOG IP core to compute the natural logarithm of single-precision format numbers. This example uses the parameter editor GUI to define the core.

10.5.1. ALTFP_LOG Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

These figures show the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 30. ALTFP_LOG Simulation Waveform (Input Data)

Figure 31. ALTFP_LOG Simulation Waveform (Output Data)

This design example includes the input of special cases to show the exception handling of the IP core, such as the smallest valid input and the input value of “1”.

In this example, the output delay is set to 21 clock cycles. Therefore, the result is only shown at the output port after the 21st clock cycle at 102.5 ns.

Table 61. Summary of Input Values and Corresponding OutputsThis table lists the inputs and corresponding outputs obtained from the simulation in the waveforms.
Time	Event
0 ns, start-up	`data[]` value: 0000 0000h Output value: An undefined value is seen on the `result[]` port, which is ignored. All values seen on the output port before the 21st clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
102.5 ns	Output value: FF80 0000h The natural logarithm of zero is negative infinity.
5 ns	`data[]` value: 8000 0000h This is a negative number.
107.5 ns	Output value: FFC0 0000h Exception handling ports: `nan` asserts The natural logarithm of a negative value is invalid. Therefore, the output produced is a NaN.
30 ns	`data[]` value: 0040 0000h The is a denormal value.
132.5 ns	Output value: FF80 0000h As denormal numbers are not supported, the input is forced to zero before going through the logarithm function. The natural logarithm of zero is negative infinity.
45 ns	`data[]` value: 0080 0000h This is the smallest valid input. All the input bits are 0 except the LSB of the exponent field.
147.5 ns	Output value: C2AE AC50h
60 ns	`data[]` value: 3F80 0000h The input value 3F80 0000h is equivalent to the actual value,  1.0 × 20 = 1.
152.5 ns	Output value: 0000 0000h Exception handling ports: `zero` asserts Since In 1 results in zero, it produces an output of zero.

10.6. Signals

Figure 32. ALTFP_LOG Signals

Table 62. ALTFP_LOG IP Core Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, a natural logarithm operation takes place. When signal is asserted low, no operation occurs and the outputs remain unchanged. Deasserting `clk_en` halts operation until it is asserted again. Assert the `clk_en` signal for the number of clock cycles equivalent to the required output latency (`PIPELINE` parameter value) for the results to be shown at the output.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits. For single precision, the width is fixed to 32 bits. For double precision, the width is fixed to 64 bits. For single extended precision, you can choose a width in the range from 43 to 64 bits.

Table 63. ALTFP_LOG IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	The natural logarithm of the value on input data. The natural logarithm of the `data[]` input port, shown in floating-point format. The widths of the `result[]` output port and `data[]` input port are the same.
`zero`	No	Zero exception output. Asserted when the exponent and mantissa of the output port are zero. This occurs when the actual input value is `1` because ln `1 = 0`.
`nan`	No	NaN exception output. Asserted when the exponent and mantissa of the output port are all 1’s and non-zero, respectively. This occurs when the input is a negative number or NaN.

10.7. Parameters

Table 64. ALTFP_LOG IP core Parameters
Parameter Name	Type	Required	Description
WIDTH_EXP	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2 ^{(WIDTH_EXP -1)} -1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of the `WIDTH_EXP` parameter must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of the `WIDTH_EXP` parameter must be less than the value of the `WIDTH_MAN` parameter, and the sum of the `WIDTH_EXP` and `WIDTH_MAN` parameters must be less than `64`.
WIDTH_MAN	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. The value of `WIDTH_MAN` must be `23` for the single-precision format, and `52` for the double-precision format. For the single-extended precision format, the valid value ranges from `31` to `52`. The value of `WIDTH_MAN` must be greater than the value of `WIDTH_EXP`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
PIPELINE	Integer	Yes	Specifies the amount of latency in clock cycles used in the ALTFP_LOG IP core. Create the ALTFP_LOG IP core to calculate the value for this parameter.

11. ALTFP_ATAN IP Core

This IP core performs arctangent calculation. You can use the ports and parameters available to customize the ALTFP_ATAN IP core according to your application.

11.1. Output Latency

The output latency option for the ALTFP_ATAN Intel FPGA IP core have a fixed latency level for single-precision format.

Table 65. Latency Option
Trigonometric Function	Precision	Mantissa Width	Latency (in clock cycles)
Arctangent	Single	23	34

11.2. ALTFP_ATAN Features

The ALTFP_ATAN IP core offers the following features:

Arctangent value of a given angle, θ in unit radian.
Support for single-precision floating point format.
Support for optional input ports such as asynchronous clear (aclr) and clock enable (clk_en) ports.

11.3. ALTFP_ATAN Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_ATAN IP core. The information was derived using the Intel^® Quartus^® Prime software version 11.0.

Table 66. ALTFP_ATAN Resource Utilization and Performance
Device Family	Function	Precision	Output Latency	Logic usage				f_MAX (MHz)
Device Family	Function	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-Bit DSP	f_MAX (MHz)
Stratix V	ArcTangent	Single	36	2,454	1,010	1,303	27	255.49

11.4. Ports

Table 67. ALTFP_ATAN IP core Input Ports
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, division takes place. When the signal is deasserted, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits.

Port Name	Required	Description
`result[]`	Yes	The result of the trigonometric function in floating-point format. The widths of the `result[]` output port and `data[]` input port are the same.

11.5. ALTFP_ATAN Parameters

Table 68. ALTFP_ATAN Parameters
Parameter Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. The bias of the exponent is always set to `2`(`WIDTH_EXP`-1) -1 (that is, `127` for single-precision format). The value of `WIDTH_EXP` must be `8` for single-precision format. The default value for `WIDTH_EXP` is `8`.
`WIDTH_MAN`	Integer	Yes	Specifies the precision of the mantissa. The value of `WIDTH_MAN` must be `23` when `WIDTH_EXP` is `8`. The default value for `WIDTH_MAN` is `23`.
`PIPELINE`	Integer	Yes	The number of pipeline is fixed for the mantissa width and some internal parameter. For the correct settings, refer to Table 12–1 on page 12–2.
`ROUNDING`	Integer	No	Specifies the rounding mode. The default value is `TO_NEAREST`. Other rounding modes are not supported.

12. ALTFP_SINCOS IP Core

This IP core perform trigonometric Sine/Cosine functions. You can use the ports and parameters available to customize the ALTFP_SINCOS IP core according to your application.

12.1. ALTFP_SINCOS Features

The ALTFP_SINCOS IP core offers the following features:

Implements sine and cosine calculations.
Support for single-precision floating point format.
Support for optional input ports such as asynchronous clear (aclr) and clock enable (clk_en) ports.

12.2. Output Latency

The output latency options for the ALTFP_SINCOS IP core have a fixed latency level for sine and cosine functions.

Trigonometric Function	Precision	Mantissa Width	Latency (in clock cycles)
Sine	Single	23	36
Cosine	Single	23	36

12.3. ALTFP_SINCOS Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_SINCOS IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.1.

Table 69. ALTFP_SINCOS Resource Utilization and Performance
Device Family	Function	Precision	Output Latency	Logic usage				f_MAX (MHz)
Device Family	Function	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	18-Bit DSP	f_MAX (MHz)
Stratix IV	Sine	Single	36	2,859	2,190	1,830	16	292.96
Stratix IV	Cosine	Single	35	2,753	2,041	1,745	16	258.26

12.4. ALTFP_SINCOS Signals

Figure 33. ALTFP_SINCOS Signals

Table 70. ALTFP_SINCOS IP Core Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, sine or cosine operation takes place. When the signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the Intel^® FPGA IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of the sign bit, exponent bits, and mantissa bits.

Table 71. ALTFP_SINCOS IP Core Output Signals
Port Name	Required	Description
`result[]`	Yes	The trigonemetric of the `data[]` input port in floating-point format. The widths of the `result[]` output port and `data[]` input port are the same.

12.5. ALTFP_SINCOS Parameters

Table 72. ALTFP_SINCOS IP Core Parameters
Parameter Name	Type	Required	Description
WIDTH_EXP	Integer	Yes	Specifies the precision of the exponent. The bias of the exponent is always set to `2^{(WIDTH_EXP-1)} -1` (that is, `127` for single-precision format). The value of `WIDTH_EXP` must be `8` for single-precision format and must be less than `WIDTH_MAN`. The available value for `WIDTH_EXP` is `8`.
WIDTH_MAN	Integer	Yes	Specifies the precision of the mantissa. The value of `WIDTH_MAN` must be `23` when `WIDTH_EXP` is `8`. Otherwise, `WIDTH_MAN` must be a minimum of `31`. The value of `WIDTH_MAN` must be greater than `WIDTH_EXP`. The available value for `WIDTH_MAN` is `23`.
PIPELINE	Integer	Yes	The number of pipeline is fixed for the mantissa width and some internal parameter. For the correct settings, refer to Output Latency.

13. ALTFP_ABS IP Core

This IP core performs absolute value calculation for the given input.

13.1. ALTFP_ABS Features

The ALTFP_ABS IP core offers the following features:

Absolute value of a given input.
Optional exception handling output ports such as zero, division_by_zero, overflow, underflow, and nan.
Carry-through exception ports from other floating-point modules that act as inputs to the ALTFP_ABS IP core.

13.2. ALTFP_ABS Output Latency

The output latency options for the ALTFP_ABS IP core are the same for all three precision formats—single, double, and single-extended. The options available are zero without pipeline, and 1 clock cycle.

13.3. ALTFP_ABS Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_ABS IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 73. ALTFP_ABS Resource Utilization and Performance for the Stratix III Device Family
Precision	Output Latency	Logic usage				f_MAX (MHz)
Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	18-Bit DSP	Memory	f_MAX (MHz)
Single	0	0	0	0	0	The f _MAX of this IP core depends on the speed of the selected device
Single	1	0	36	0	0
Double	0	0	0	0	0
Double	1	0	68	0	0

13.4. ALTFP_ABS Design Example: Absolute Value of Multiplication Results

This design example uses the ALTFP_ABS IP core to compute the absolute value of the multiplication result of single-precision format numbers. This example incorporates the ALTFP_MULT IP core and uses the parameter editor in the Intel^® Quartus^® Prime software.

13.4.1. ALTFP_ABS Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

Figure 34. ALTFP_ABS Simulation Waveform

This design example produces a floating-point absolute value function for the multiplication results of single-precision format numbers. All the optional input ports (clk_en and aclr) and optional output ports (overflow, underflow, zero, division_by_zero, and nan) are enabled.

In this example, the latency of the multiplier is set to five clock cycles, while none is being set for the absolute value function. Thus, the absolute value result only appears at the result[] port five cycles after the input values are captured on the input ports.

The dataa[] and datab[] values in the simulation waveform above portray the two input values that are being fed to the multiplier. The value in the result[] port depicts the multiplication result that has gone through the absolute value operation.

This table lists the inputs and corresponding outputs obtained from the simulation.

Table 74. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`dataa[]` value: C080 0000h `datab[]` value: 4000 0000h Output value: All values seen on the output port before the 5th clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
22.5 ns	Output value: 4100 0000h The multiplication of a negative number with a positive number results in a negative number. The absolute value of the result is reflected on the `result[]` port.
20 ns	`dataa[]` value: 579D F479h `datab[]` value: 7F80 0000h The value of `dataa[]` is normal while the value of `datab[]` is infinity.
42.5 ns	Output value: 7F80 0000h Exception handling ports: `overflow` asserts The multiplication of a normal value with infinity results in infinity and sets the `overflow` port in the multiplier. The absolute value of the output is infinity and the `overflow` port is also set as this assertion of the port is being carried through from the corresponding `overflow` port in the multiplier.

13.5. ALTFP_ABS Signals

Figure 35. ALTFP_ABS Signals

Table 75. ALTFP_ABS Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. When the `aclr` port is asserted high, the function is asynchronously cleared.
`clk_en`	No	Clock enable. When the `clk_en` port is asserted high, an absolute value operation takes place. When the signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`data[]`	Yes	Floating-point input data. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.
`zero_in`	No	Zero exception input. Carry-through exception input port from other floating-point modules.
`nan_in`	No	NaN exception input. Carry-through exception input port from other floating-point modules.
`overflow_in`	No	Overflow exception input. Carry-through exception input port from other floating-point modules.
`underflow_in`	No	Underflow exception input. Carry-through exception input port from other floating-point modules.
`division_by_zero_in`	No	Division-by-zero exception input. Carry-through exception input port from other floating-point modules.

Table 76. ALTFP_ABS Output Signals
Port Name	Required	Description
`result[]`	Yes	The absolute value result of the input data. The size of this port corresponds to the size of the input `data[]` port.
`zero`	No	Zero exception output carried from the input. Asserted if the corresponding carry-through port from the input is asserted.
`nan`	No	NaN output carried from the input. Asserted if the corresponding carry-through port from the input is asserted.
`overflow`	No	Overflow exception output carried from the input. Asserted if the corresponding carry-through port from the input is asserted.
`underflow`	No	Underflow exception output carried from the input. Asserted if the corresponding carry-through port from the input is asserted.
`division_by_zero`	No	Division-by-zero exception output carried from the input. Asserted if the corresponding carry-through port from the input is asserted.

13.6. ALTFP_ABS Parameters

Table 77. ALTFP_ABS Parameters
Port Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2` (WIDTH_EXP - 1) - `1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of `WIDTH_EXP` must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of `WIDTH_EXP` must be less than the value of `WIDTH_MAN`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP` is `8` and the floating-point format is single-precision, the `WIDTH_MAN` value must be `23`. Otherwise, the value of `WIDTH_MAN` must be a minimum of `31`. The value of `WIDTH_MAN` must be greater than the value of `WIDTH_EXP`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`PIPELINE`	Integer	Yes	Specifies the amount of latency, expressed in clock cycles, used in the ALTFP_ABS IP core. Create the ALTFP_ABS IP core with the parameter editor to calculate the value for this parameter.

14. ALTFP_COMPARE IP Core

This IP core performs comparison functions between two inputs.

14.1. ALTFP_COMPARE Features

The ALTFP_COMPARE IP core offers the following features:

Comparison functions between two inputs.
Seven status output ports:
- aeb (input A is equal to input B).
- aneb (input A is not equal to input B).
- agb (input A is greater than input B).
- ageb (input A is greater than or equal to input B).
- alb (input A is less than input B).
- aleb (input A is less than or equal to input B).
- unordered (used as an output to flag if one or both input ports are NaN).

14.2. ALTFP_COMPARE Output Latency

The output latency options for the ALTFP_COMPARE IP core are the same for all three precision formats—single, double, and single-extended. The options available are 1, 2, and 3 clock cycles.

14.3. ALTFP_COMPARE Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_COMPARE IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 78. ALTFP_COMPARE Resource Utilization and Performance for Stratix IV Devices
Device Family	Precision	Output Latency	Logic Usage			f_MAX (MHz)
Device Family	Precision	Output Latency	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Look-Up Modules (ALMs)	f_MAX (MHz)
Stratix IV	single	3	68	33	47	794
Stratix IV	double	3	121	47	87	680

14.4. ALTFP_COMPARE Design Example: Comparison of Single-Precision Format Numbers

This design example uses the ALTFP_COMPARE IP core to implement the comparison of single-precision format numbers using the parameter editor in the Intel^® Quartus^® Prime software.

14.4.1. ALTFP_COMPARE Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

This figure shows the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 36. ALTFP_COMPARE Simulation Waveform

This design example implements a floating-point comparator for single-precision numbers. Both optional input ports (clk_en and aclr) and all seven output ports (ageb, aeb, agb, aneb, alb, aleb, and unordered) are enabled.

The chosen output latency is 3. Therefore, the comparison operation generates the output result 3 clock cycles later.

This table lists the inputs and corresponding outputs obtained from the simulation in the waveform.

Table 79. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`dataa[]` value: 619B CE11h `datab[]` value: 9106 CA22h Output value: An undefined value is seen on the `result[]` port, which is ignored. All values seen on the output port before the 3rd clock cycle are merely due to the behavior of the system during start-up and should be disregarded.
25 ns	Output ports: `ageb`, `aneb`, and `agb` assert
350 ns	`dataa[]` value: 0060 0000h `datab[]` value: 0070 0000h Both input values are denormal numbers.
375 ns	Output ports: `aeb`, `ageb`, and `aleb` assert Denormal inputs are not supported and are forced to zero before comparison takes place, which results in the `dataa[]` value being equal to `datab[]`.
460 ns	The `aclr` signal is set for 1 clock cycle.
495.5 ns	The comparisons of subsequent data inputs are performed 3 clock cycles after the `aclr` signal deasserts.

14.5. ALTFP_COMPARE Signals

Figure 37. ALTFP_COMPARE Signals

Table 80. ALTFP_COMPARE Input Signals
Port Name	Required	Description
`aclr`	No	Asynchronous clear. The source is asynchronously reset when asserted high.
`clk_en`	No	Clock enable. When this port is asserted high, a compare operation takes place. When signal is asserted low, no operation occurs and the outputs remain unchanged.
`clock`	Yes	Clock input to the IP core.
`dataa[]`	Yes	Data input. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.
`datab[]`	Yes	Data input. The MSB is the sign bit, the next MSBs are the exponent, and the LSBs are the mantissa. This input port size is the total width of sign bit, exponent bits, and mantissa bits.

Table 81. ALTFP_COMPARE Output Signals
Port Name	Required	Description
`aeb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port equals the value of the `datab[]` port.
`agb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port is greater than the value of the `datab[]` port.
`ageb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port is greater than or equal to the value of the `datab[]` port`.`
`alb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port is less than the value of the `datab[]` port.
`aleb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port is less than or equal to the value of the `datab[]` port.
`aneb`	Yes	Output port for the comparator. Asserted if the value of the `dataa[]` port is not equal to the value of the `datab[]` port.
`unordered`	Yes	Output port for the comparator. Asserted when either the `dataa[]` port and the `datab[]` port is set to NaN, or if both the `dataa[]` port and the `datab[]` port are set to NaN.

14.6. ALTFP_COMPARE Parameters

Table 82. ALTFP_COMPARE Parameters
Port Name	Type	Required	Description
`WIDTH_EXP`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2` (WIDTH_EXP - 1) - `1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of `WIDTH_EXP` must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of `WIDTH_EXP` must be less than the value of `WIDTH_MAN`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`WIDTH_MAN`	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP` is `8` and the floating-point format is single-precision, the `WIDTH_MAN` value must be `23`. Otherwise, the value of `WIDTH_MAN` must be a minimum of `31`. The value of `WIDTH_MAN` must be greater than the value of `WIDTH_EXP`, and the sum of `WIDTH_EXP` and `WIDTH_MAN` must be less than `64`.
`PIPELINE`	Integer	Yes	Specifies the latency in clock cycles used in the ALTFP_COMPARE IP core. The pipeline values are `1`, `2`, and `3` latency in clock cycles.

15. ALTFP_CONVERT IP Core

This IP core performs conversion functions for various formats.

15.1. ALTFP_CONVERT Features

The ALTFP_CONVERT IP core offers the following features:

Conversion functions for the following formats:
- Integer-to-Float
- Float-to-Integer
- Float-to-Float
- Fixed-to-Float
- Float-to-Fixed
Support for signed and unsigned integer

Optional exception handling output ports such as overflow, underflow, and nan

Table 83. Supported Operations and Exception Ports
Operation	Supported Exception Ports
Integer-to-Float	Not supported
Float-to-Integer	`overflow`, `underflow`, and `nan`
Float-to-Float	`overflow`, `underflow`, and `nan`
Fixed-to-Float	Not supported
Float-to-Fixed	`overflow`, `underflow`, and `nan`

15.2. ALTFP_CONVERT Conversion Operations

This table lists the features of each conversion operation.

Table 84. ALTFP_CONVERT Conversion Operations
Operation	Features
Integer-to-Float Conversion	Converts integers to the IEEE-754 standard floating-point representation. Supports conversions of signed integers to floating-point numbers in single, double, and single-extended precision formats.
Float-to-Integer Conversion	Converts IEEE-754 standard floating-point representations to the integer-bit format. Supports conversions of single, double, and single-extended precision formats to signed integers.
Float-to-Float Conversion	Converts between IEEE-754 standard floating-point representations. Supports conversions of between single double, and single-extended precision formats. This operation offers the following modes: Single-precision format to single-extended precision format or double-precision format. Double-precision format to single-precision format or single-extended precision format. Single-extended precision format to single-precision or double-precision format.
Fixed-to-Float Conversion	Converts fixed-point format data to the IEEE-754 standard floating-point representation. Supports conversions of fixed-point format data to floating-point numbers in single, double, and single-extended precision formats.
Float-to-Fixed Conversion	Converts IEEE-754 standard floating-point representations to the fixed-point format. Supports conversion of floating-point numbers in single, double, and single-extended precision formats.

15.3. ALTFP_CONVERT Output Latency

The output latency options for the all the conversion operations in the ALTFP_CONVERT IP core are fixed, except for the Float-to-Float operation.

Table 85. Latency Options for Each Operation
Operation	Conversion From	Latency (in clock cycles)
Integer-to-Float	N/A	6
Float-to-Integer	N/A	6
Float-to-Float	Single-precision format	2
	Double-precision format	3
	Single-extended precision format	3
Fixed-to-Float	N/A	6
Float-to-Fixed	N/A	6

15.4. ALTFP_CONVERT Resource Utilization and Performance

This table lists the resource utilization and performance information for the ALTFP_CONVERT IP core. The information was derived using the Intel^® Quartus^® Prime software version 10.0.

Table 86. ALTFP_CONVERT Resource Utilization and Performance for Stratix III Devices
Operation	Format	Pipeline	Logic Usage			f_MAX (MHz)
Operation	Format	Pipeline	Adaptive Look-Up Tables (ALUTs)	Dedicated Logic Registers (DLRs)	Adaptive Logic Modules (ALMs)	f_MAX (MHz)
Integer to-Float	32-bit integer to single-precision	6	182	238	157	515
	32-bit integer to double-precision	6	150	139	123	510
	64-bit integer to single-precision	6	385	371	296	336
	64-bit integer to single-precision	6	393	461	344	336
Float-to-Integer	Single-precision to 32-bit integer	6	256	255	176	455
	Single-precision to 64-bit integer	6	417	361	257	311
	Double-precision to 32-bit integer	6	406	387	273	409
	Double-precision to 64-bit integer	6	535	480	362	309
Float-to-Float	Single-precision to double-precision	2	44	73	40	868
Float-to-Float	Double-precision to single-precision	3	103	140	89	520
Fixed-to-Float	16.16 fixed-point to double-precision	6	182	238	155	519
	16.16 fixed-point to double-precision	6	150	139	122	513
	32.32 fixed-point to single-precision	6	384	371	296	334
	32.32 fixed-point to single-precision	6	393	461	336	333
Float-to-Fixed	Single-precision to 16.16 fixed-point	6	319	261	210	438
	Single-precision to 32.32 fixed-point	6	469	367	288	315
	Double-precision to 16.16 fixed-point	6	579	393	402	365
	Double-precision to 32.32 fixed-point	6	695	486	474	306

15.5. ALTFP_CONVERT Design Example: Convert Double-Precision Floating-Point Format Numbers

This design example uses the ALTFP_CONVERT IP core to convert double-precision floating-point format numbers to 64-bit integers. This design example uses the parameter editor in the Intel^® Quartus^® Prime software.

15.5.1. ALTFP_CONVERT Design Example: Understanding the Simulation Results

The simulation waveform in this design example is not shown in its entirety. Run the design example files in the ModelSim* - Intel^® FPGA Edition software to see the complete simulation waveforms.

This figure shows the expected simulation results in the ModelSim* - Intel^® FPGA Edition software.

Figure 38. ALTFP_CONVERT Simulation Waveform

This design example implements a float-to-integer converter for converting double-precision floating-point format numbers to 64-bit integers. In this operation, the optional exception ports of overflow, underflow, and nan are available apart from the result[] port.

The latency for the float-to-integer operation is six clock cycles. Therefore, each conversion generates the output result six clock cycles after receiving the input value.

This table lists the inputs and corresponding outputs obtained from the simulation in the waveform.

Table 87. Summary of Input Values and Corresponding Outputs
Time	Event
0 ns, start-up	`dataa[]` value: C394 AD22 761B 9EE5h Output value: The `result[]` port displays 0 regardless of what the input value is. This value seen on the output port before the 6th clock cycle is merely due to the behavior of the system during start-up and should be disregarded.
55 ns	Output value: FAD4 B762 7918 46C0h
150 ns	`dataa[]` value: 000F 0000 5555 1111h This value is a denormal number.
205 ns	Denormal inputs are not supported and are forced to zero before conversion takes place.
300 ns	`dataa[]` value: 5706 40CF OEC6 1176h
355 ns	Output value: 7FFF FFFF FFFF FFFFh Exception handling ports: `overflow` asserts. The `overflow` flag is triggered because the width of the resulting integer is more than the maximum width allowed, and the value seen on the `result[]` port is the standard value used to represent a positive overflow number.
350 ns	`dataa[]` value: C728 3147 8444 1F75h
405 ns	Output value: 8000 0000 0000 0000h Exception handling ports: `overflow` remains asserted. This is a standard value to represent a negative overflow number.
400 ns	`dataa[]` value: 145A 257C 895A B309h
455 ns	Output value: 0000 0000h Exception handling ports: `underflow` asserts. The input value triggers the `underflow` port because the exponent of the input value is less than the exponent bias of 1023.
500 ns	`dataa[]` value: FFFF 0000 DDDD 5555h This value is a NaN.
555 ns	Output value: 0000 0000h Exception handling ports: `nan` asserts.

15.6. ALTFP_CONVERT Signals

Figure 39. ALTFP_CONVERT Signals

Table 88. ALTFP_CONVERT Input Signals
Port Name	Required	Description
`clock`	Yes	The clock input to the ALTFP_CONVERT IP core.
`clk_en`	No	Clock enable that allows conversions to take place when asserted high. When asserted low, no operation occurs and the outputs are unchanged.
`aclr`	No	Asynchronous clear. The source is asynchronously reset when the `aclr` signal is asserted high.
`dataa[]`	Yes	Data input. The size of this input port depends on the `WIDTH_DATA` parameter value. If the operation mode value is `INT2FLOAT` or `FIXED2FLOAT`, the data on the input bus is an integer. If the operation mode value is `FLOAT2INT` or `FLOAT2FIXED`, the input bus is the IEEE floating-point representation. In the single-precision format, the input bus width value is `32`. In the double-precision format, the input bus width value is `64`. In the single-extended precision format, the input bus range is from `43` to `64`. If the operation mode value is `FLOAT2FLOAT`, the input bus value is the IEEE floating-point representation. In the single-precision format, the input bus width value is `32`. In the double-precision format, the input bus width value is `64`. In the single-extended precision format, the input bus range is from `43` to `64`.

Table 89. ALTFP_CONVERT Output Signals
Port Name	Required	Description
`result[]`	Yes	Output for the floating-point converter. The size of this output port depends on the `WIDTH_RESULT` parameter value. If the operation mode value is `FLOAT2INT` or `FLOAT2FIXED`, the output bus is an IEEE floating-point representation. If the operation mode is `FLOAT2INT`, the output bus is an integer representation. If the selected precision is the single-precision format, the output bus width value is `32`. If the selected precision is the double-precision format, the output bus width value is `64`. If the selected precision is the single-extended precision format, the input bus range is from `43` to `64`. If the operation mode value is `FLOAT2FLOAT`, the output bus is an IEEE floating-point representation. If the selected precision is the single-precision format, the output bus is in the 64-bit double-precision format. If the selected precision is the double-precision format, the output bus is in the 32-bit single-precision format. If the selected precision is the single-extended precision format, the output bus ranges from `43` to `64`.
`overflow`	No	Optional overflow exception output. This port is available only when the operation mode values are `FLOAT2FIXED`, `FLOAT2INT`, or `FLOAT2FLOAT`. Asserted when the result of the conversion (after rounding), exceeds the maximum width of the `result[]` port, or when the `dataa[]` input is infinity.
`underflow`	No	Optional underflow exception output. This port is available only when the operation mode values are `FLOAT2FIXED`, `FLOAT2INT`, or `FLOAT2FLOAT`. Asserted when the result of the conversion, after rounding, is fractional. In `FLOAT2INT` operations, this port is asserted when the exponent value of the floating-point input is smaller than the exponent bias. In `FLOAT2FLOAT` operations, this port is asserted when the floating-point input has a value smaller than the lowest exponent limit of the target floating-point format.
`nan`	No	Optional NaN exception output. This port is available only when the operation mode values are `FLOAT2INT`, `FLOAT2FLOAT`, or `FLOAT2FIXED`. Asserted when the input port is a NaN representation. If the operation mode value is `FLOAT2INT` or `FLOAT2FIXED`, the `result[]` port is set to zero. If the operation mode value is `FLOAT2FLOAT`, the `result[]` port is set to a NaN representation.

15.7. ALTFP_CONVERT Parameters

Table 90. ALTFP_CONVERT Parameters
Port Name	Type	Required	Description
`WIDTH_EXP_INPUT`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2` (WIDTH_EXP - 1) - `1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of `WIDTH_EXP_INPUT` must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of `WIDTH_EXP_INPUT` must be less than the value of `WIDTH_MAN_INPUT`, and the sum of `WIDTH_EXP_INPUT` and `WIDTH_MAN_INPUT` must be less than `64`. These settings apply only to the `FLOAT2FIXED`, `FLOAT2INT`, and `FLOAT2FLOAT` operation modes.
`WIDTH_MAN_INPUT`	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP_INPUT` is `8` and the floating-point format is single-precision, the `WIDTH_MAN_INPUT` value must be `23`. Otherwise, the value of `WIDTH_MAN_INPUT` must be a minimum of `31`. The value of `WIDTH_MAN_INPUT` must be greater than the value of `WIDTH_EXP_INPUT`, and the sum of `WIDTH_EXP_INPUT` and `WIDTH_MAN_INPUT` must be less than `64`. These settings apply only to the `FLOAT2FIXED`, `FLOAT2INT`, and `FLOAT2FLOAT` operation modes.
`WIDTH_INT`	Integer	Yes	Specifies the integer width. If the operation is `FIXED2FLOAT` or `INT2FLOAT`, this parameter defines the integer width on the input side. If the operation is `FLOAT2INT` or `FLOAT2FIXED`, this parameter defines the result width on the output side. The available settings are `32` bits, `64` bits or n bits. For n bits settings, the range is from `4` bits to `64` bits. If unspecified, the default setting for `WIDTH_INT` is `32` bits.
`WIDTH_DATA`	Integer	Yes	Specifies the input data width. If the operation is `INT2FLOAT`, the `WIDTH_DATA` is also `WIDTH_INT`. If the operation is `FIXED2FLOAT`, the data width value is `WIDTH_INT` + fractional width. If the operation is `FLOAT2FIXED`, `FLOAT2INT` or `FLOAT2FLOAT`, the data width value is `WIDTH_EXP_INPUT` + `WIDTH_MAN_INPUT` + `1`. The available settings are `32` bits, `64` bits or n bits. For n bits settings, the range is from `4` bits to `64` bits. If unspecified, the default setting for `WIDTH_DATA` is `32` bits.
`WIDTH_EXP_OUTPUT`	Integer	Yes	Specifies the precision of the exponent. If this parameter is not specified, the default is `8`. The bias of the exponent is always set to `2` (WIDTH_EXP - 1) - `1`, that is, `127` for the single-precision format and `1023` for the double-precision format. The value of `WIDTH_EXP_OUTPUT` must be `8` for the single-precision format, `11` for the double-precision format, and a minimum of `11` for the single-extended precision format. The value of `WIDTH_EXP_OUTPUT` must be less than the value of `WIDTH_MAN_OUTPUT`, and the sum of `WIDTH_EXP_OUTPUT` and `WIDTH_MAN_OUTPUT` must be less than `64`. These settings apply only to the `FLOAT2FIXED`, `FLOAT2INT`, and `FLOAT2FLOAT` operation modes.
`WIDTH_MAN_OUTPUT`	Integer	Yes	Specifies the precision of the mantissa. If this parameter is not specified, the default is `23`. When `WIDTH_EXP_OUTPUT` is `8` and the floating point format is single-precision, the `WIDTH_MAN_OUTPUT` value must be `23`. Otherwise, the value of `WIDTH_MAN_OUTPUT` must be a minimum of `31`. The value of `WIDTH_MAN_OUTPUT` must be greater than the value of `WIDTH_EXP_OUTPUT`, and the sum of `WIDTH_EXP_OUTPUT` and `WIDTH_MAN_OUTPUT` must be less than `64`. These settings apply only to the `FLOAT2FIXED`, `FLOAT2INT`, and `FLOAT2FLOAT` operation modes.
`WIDTH_RESULT`	Integer	Yes	Specifies the width of the output result. In an `INT2FLOAT`, `FLOAT2FLOAT`, or `FIXED2FLOAT` operation, the result width is `WIDTH_EXP_OUTPUT` + `WIDTH_MAN_OUTPUT` + `1`. In a `FLOAT2INT` operation, the result width is the value of the `WIDTH_INT` parameter. In a `FLOAT2FIXED` operation, this parameter is the result width. The available settings are `32` bits, `64` bits or n bits. For n bits settings, the range is from `4` bits to `64` bits.
`ROUNDING`	Integer	Yes	Specifies the rounding mode. The default value is `TO_NEAREST`. Other modes are not supported.
`OPERATION`	Integer	Yes	Specifies the operating mode. Values are `INT2FLOAT`, `FLOAT2INT`, `FLOAT2FLOAT`, `FLOAT2FIXED`, and `FIXED2FLOAT`. If this parameter is not specified, the default value is `INT2FLOAT`. When set to `INT2FLOAT`, the conversion of an integer input to an IEEE floating-point representation output takes place. When set to `FLOAT2INT`, the conversion of an IEEE floating-point representation input to an integer output takes place. When set to `FLOAT2FLOAT`, the conversion between IEEE floating-point representations input and output takes place. When set to `FIXED2FLOAT`, the conversion of a fixed point input to an IEEE floating-point representation output takes place. When set to `FLOAT2FIXED`, the IEEE floating-point input conversion to fixed point representation output takes place.

16. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Core

This IP core replaces all the functions supported by the existing floating point IP cores shown in the previous chapters in this document for devices in the Intel^® Quartus^® Prime Pro Edition software.

Table 91. Floating Point Functions Intel^® FPGA IP Release Information
Item	Description
Version	19.1
Intel^® Quartus^® Prime Version	20.1
Release Date	2020.04.13

Table 92. List of Functions Supported by FP_FUNCTIONS Intel^® FPGA IP or Floating Point Functions Intel^® FPGA IP
Function	Description
Arithmetic
Add	Two input addition
Sub	Two input subtraction
Add/Sub	Two input addition and subtraction. The IP core provides both addition and subtraction outputs and an option to generate a `select` signal to dynamically select the desired operation.
Multiply	Two input multiplication
Divide	Two input division
Reciprocal	Performs the function of 1/a where a is the input. Note: This function replaces the ALTFP_INV IP core in Intel^® Arria^® 10 devices.
Absolute	Generates absolute value of the input
Scalar Product	Performs addition of an arbitrary number if inputs
Multiply-Accumulate	Two input multiplication followed by a single cycle accumulation
Accumulate	Perform single input accumulation in a single cycle
Multiply-Add	Performs two input multiplication followed by addition
Complex-Multiply	Performs multiplication of two complex value
Roots
Square Root	Performs square root to the input value
Reciprocal Square Root	Performs the function of 1/√a where a is the input Note: This function replaces the ALTFP_INV_SQRT IP core in Intel^® Arria^® 10 devices.
Cube Root	Performs cube root to the input value
3D Hypotenuse	Performs the function of Q=√(a^2+b^2+c^2)
Conversions
Fixed-to-Floating Point	Converts a fixed point input to floating point representation
Floating Point-to-Fixed	Converts a floating-point input to fixed point representation
Floating to Floating Point	Converts a floating-point input to floating-point representation of a different precision
Comparisons
Minimum	Compares and output the smallest value of two input
Maximum	Compares and output the biggest value of two input
Less Than	Compares and returns true if input a is less than input b
Less Than or Equal	Compares and returns true if input a is less than or equal to input b
Equal	Compares and returns true if input a is equal to input b
Greater Than	Compares and returns true if input a is greater than input b
Greater Than or Equal	Compares and returns true if input a is greater than or equal to input b
Not Equal	Compares and returns true if input a is not equal to input b
Exp/Log/Pow
Exponent	Performs the function of e^a where a is the input
Exponent base 2	Performs the function of 2^a where a is the input
Exponent base 10	Performs the function of 10^a where a is the input
Log	Performs the function of log_e(a) where a is the input
Log₂	Performs the function of log₂(a) where a is the input
Log₁₀	Performs the function of log₁₀(a) where a is the input
Log(1+x)	Performs the function of log_e(1+a) where a is the input
Power
LdExp	Sets the exponential value of a floating-point input
Trigonometry
Sin	Performs sine function of a single input
Cos	Performs cosine function of a single input
Tan	Performs tangent function of a single input
Arcsin	Performs arc sine function of a single input
Arccos	Performs arc cosine function of a single input
Arctan	Performs arc tangent function of a single input
Arctan2	Performs the function of arctan (a/b) where a and b are the inputs

16.1. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Features

The FP_FUNCTIONS Intel^® FPGA IP or Floating Point Functions Intel^® FPGA IP core offers the following features:

Supports both latency and frequency driven cores.
Supports VHDL code generation.

16.2. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Output Latency

If you require a specific latency, follow these steps:

In the FP_FUNCTIONS Intel^® FPGA IP or Floating Point Functions Intel^® FPGA IP parameter editor, click the Basic tab.
Under the Performance category, in the Goal option, select latency.
In the Target field, set your desired latency (cycles).
Then, click Check Performance.

16.3. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Target Frequency

If you require a specific frequency, follow these steps:

In the FP_FUNCTIONS Intel^® FPGA IP or Floating Point Functions Intel^® FPGA IP parameter editor, click Basic tab.
Under the Performance category, in the Goal option, select frequency.
In the Target field, set your desired frequency (MHz).
The IP core reports the latency for the instance that it generates in the Report category.

Note: You must verify the frequency by running the Timing Analyzer.

16.4. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Combined Target

If you require a combined target of latency and frequency, follow these steps:

In the FP_FUNCTIONS Intel^® FPGA IP or Floating Point Functions Intel^® FPGA IP parameter editor, click the Basic tab.
Under the Performance category, in the Goal option, select Combined.
In the Target field, set your desired frequency (MHz).
In the Target field, set your desired latency (cycles).
Then, click Finish.

16.5. FP_FUNCTIONS Intel FPGA IP Resource Utilization and Performance

These tables list the resource utilization and performance information for the FP_Functions Intel^® FPGA IP core. The information was derived using the Intel^® Quartus^® Prime software version 14.1. The frequency target was set to 200 MHz.

Table 93. Arithmetic
Family	Function	Precision	Latency	f_MAX	ALMs	M10K	M20K	DSP Blocks	Logic Registers
Family	Function	Precision	Latency	f_MAX	ALMs	M10K	M20K	DSP Blocks	Primary	Secondary
Arria V (5AGXFB3H4F40C5)	Abs	Single	0	—	33	0	—	0	0	0
	Abs	Double	0	—	65	0	—	0	0	0
	Add	Single	9	233.1	360	0	—	0	507	29
	Add	Double	12	251.95	886	0	—	0	1064	61
	AddSubtract	Single	9	249.31	477	0	0	0	651	63
	AddSubtract	Double	12	252.46	1161	0	0	0	1713	91
	Cube Root	Single	9	275.18	132	6	—	2	132	20
	Cube Root	Double	24	185.77	634	17	—	10	1297	58
	Divide	Single	18	249	456	5	—	4	771	100
	Divide	Double	35	185.29	1409	39	—	15	3035	138
	Exp base 10	Single	16	212.72	547	3	—	2	675	18
	Exp base 10	Double	31	185.77	2194	0	—	10	2626	56
Arria V (5AGXFB3H4F40C5)	Exp base 2	Single	7	236.41	345	0	—	2	214	19
	Exp base 2	Double	21	185.84	932	0	—	10	1324	51
	Exp base e	Single	14	217.96	718	0	—	2	597	46
	Exp base e	Double	28	185.87	2134	0	—	10	2398	46
	Reciprocal	Single	12	253.16	210	4	—	3	294	26
	Reciprocal	Double	30	185.29	877	9	—	14	1764	105
	Reciprocal Square Root	Single	7	267.52	118	4	—	2	141	14
	Reciprocal Square Root	Double	20	185.74	539	13	—	9	1210	52
	LDExp	Single	2	367.92	69	0	—	0	85	0
	LDExp	Double	2	359.32	100	0	—	0	146	0
Arria V (5AGXFB3H4F40C5)	Log base 10	Single	16	250	379	4	--	3	622	65
Arria V (5AGXFB3H4F40C5)	Log base 10	Double	34	186.12	1,380	40	--	11	3,025	143
Arria V (5AGXFB3H4F40C5)	Log(1+x)	Single	21	222.77	766	4	--	3	1,171	82
	Log(1+x)	Double	43	185.94	2,361	40	--	14	4,702	183
	Log base 2	Single	16	232.29	350	4	--	3	584	64
	Log base 2	Double	37	185.32	1,342	13	--	17	3,156	121
	Log base e	Single	16	248.57	379	4	--	3	616	57
	Log base e	Double	35	185.84	1,422	40	--	13	3,066	147
	Multiply	Single	5	281.14	156	0	--	1	152	6
	Multiply	Double	7	186.01	339	0	--	4	549	13
Arria V (5AGXFB3H4F40C5)	Power	Single	45	201.82	1,347	11	--	14	2,410	165
	Power	Double	82	185.43	4,195	20	--	38	8,149	266
	Square Root	Single	8	261.92	119	3	--	2	174	13
	Square Root	Double	21	185.94	548	8	--	9	1,225	44
	Subtract	Single	9	232.67	363	0	--	0	505	32
	Subtract	Double	12	257.07	884	0	--	0	1,064	61
Cyclone V (5CGXFC7D6F31C7)	Abs	Single	0	--	33	0	--	0	0	0
	Abs	Double	0	--	65	0	--	0	0	0
	Add	Single	12	225.94	403	0	--	0	562	35
	Add	Double	20	208.99	932	0	--	0	1,813	72
	AddSubtract	Single	12	224.67	509	0	--	0	805	65
	AddSubtract	Double	20	211.55	1,197	0	--	0	2,647	120
	Cube Root	Single	10	230.47	131	6	--	2	213	11
	Cube Root	Double	34	212.49	890	17	--	10	1,991	54
	Divide	Single	20	232.61	466	5	--	4	991	62
	Divide	Double	51	201.01	1,782	41	--	15	4,317	165
Cyclone V (5CGXFC7D6F31C7)	Exp base 10	Single	20	217.58	552	3	--	2	905	32
	Exp base 10	Double	52	212.77	2,317	0	--	10	4,287	122
	Exp base 2	Single	9	211.33	352	0	--	2	314	13
	Exp base 2	Double	36	219.3	1,128	0	--	10	2,364	87
	Exp base e	Single	17	207.68	698	0	--	2	860	31
	Exp base e	Double	50	198.85	2,309	0	--	10	4,300	126
	Reciprocal	Single	14	230.95	245	4	--	3	378	26
	Reciprocal	Double	44	207.43	1,201	9	--	14	2,694	94
	Reciprocal Square Root	Single	9	233.37	137	4	--	2	223	25
	Reciprocal Square Root	Double	30	250	782	13	--	9	1,932	46
Cyclone V (5CGXFC7D6F31C7)	LDExp	Single	2	346.02	69	0	--	0	87	1
	LDExp	Double	3	357.91	104	0	--	0	215	0
	Log base 10	Single	22	203.33	486	4	--	3	1,066	47
	Log base 10	Double	49	196.97	1,888	40	--	11	4,483	153
	Log(1+x)	Single	29	191.5	944	4	--	3	1,844	105
	Log(1+x)	Double	62	168.27	3,012	40	--	14	6,899	210
	Log base 2	Single	20	202.1	413	4	--	3	918	50
	Log base 2	Double	54	194.21	1,898	13	--	17	4,732	151
Cyclone V (5CGXFC7D6F31C7)	Log base e	Single	22	181.42	482	4	--	3	1,058	45
	Log base e	Double	50	196.27	1,941	40	--	13	4,611	197
	Multiply	Single	6	268.6	159	0	--	1	223	2
	Multiply	Double	11	205.17	431	0	--	4	970	18
	Power	Single	62	181.19	1,778	11	--	14	3,562	154
	Power	Double	127	186.53	5,411	22	--	38	12,361	325
	Square Root	Single	8	219.15	126	3	--	2	205	12
	Square Root	Double	31	250	822	8	--	9	2,056	55
	Subtract	Single	12	232.07	399	0	--	0	566	42
	Subtract	Double	20	204.25	918	0	--	0	1,839	60
Stratix V (5SGXEA7K2F40C2)	Abs	Single	0	--	33	--	0	0	0	0
	Abs	Double	0	--	65	--	0	0	0	0
	Add	Single	5	364.83	366	--	0	0	299	19
	Add	Double	7	329.49	834	--	0	0	801	53
	AddSubtract	Single	5	354.74	489	--	0	0	411	29
	AddSubtract	Double	7	338.41	1,106	--	0	0	1,039	134
	Cube Root	Single	8	420.17	114	--	5	2	124	11
	Cube Root	Double	20	277.7	520	--	11	10	997	17
	Divide	Single	13	363.5	377	--	3	4	591	71
	Divide	Double	23	270.86	1,091	--	20	15	2,274	120
	Exp base 10	Single	11	292.4	486	--	3	2	417	12
	Exp base 10	Double	22	271.74	2,033	--	0	10	1,761	48
Stratix V (5SGXEA7K2F40C2)	Exp base 2	Single	5	387.3	351	--	0	2	160	1
	Exp base 2	Double	17	279.56	897	--	0	10	995	27
	Exp base e	Single	8	284.09	653	--	0	2	350	18
	Exp base e	Double	23	268.38	2,043	--	0	10	1,710	44
	Reciprocal	Single	9	279.33	199	--	3	3	211	13
	Reciprocal	Double	22	241.31	764	--	9	14	1,391	49
	Reciprocal Square Root	Single	6	420.52	105	--	3	2	129	9
	Reciprocal Square Root	Double	17	271.37	449	--	8	9	1,009	47
	LDExp	Single	0	--	67	--	0	0	0	0
	LDExp	Double	0	717.36	99	--	0	0	66	0
	Log base 10	Single	11	359.58	358	--	3	3	443	29
	Log base 10	Double	23	271.96	1,077	--	20	11	2,252	101
Stratix V (5SGXEA7K2F40C2)	Log(1+x)	Single	15	338.64	748	--	3	3	905	55
	Log(1+x)	Double	27	280.98	1,911	--	20	13	3,301	122
	Log base 2	Single	11	340.37	304	--	3	3	392	15
	Log base 2	Double	27	258.33	1,053	--	8	16	2,241	110
	Log base e	Single	11	351.86	359	--	3	3	439	35
	Log base e	Double	23	270.49	1,071	--	20	13	2,210	94
	Multiply	Single	3	399.52	136	--	0	1	72	1
	Multiply	Double	4	250.75	312	--	0	4	237	5
	Power	Single	31	261.23	1,171	--	8	12	1,492	83
	Power	Double	60	267.81	3,555	--	13	37	5,347	244
	Square Root	Single	6	393.7	112	--	3	2	129	7
	Square Root	Double	17	274.12	458	--	8	9	1,019	41
	Subtract	Single	5	320.41	360	--	0	0	299	14
	Subtract	Double	7	338.52	835	--	0	0	801	51
Arria 10 (10AX115H4F34I3SP)	Abs	Single	0	--	33	--	0	0	0	0
	Abs	Double	0	--	65	--	0	0	0	0
	Add	Single	4	296.4	49	--	0	1	0	0
	Add	Double	7	296.3	840	--	0	0	779	67
	AddSubtract	Single	5	319.39	483	--	0	0	408	37
	AddSubtract	Double	7	289.77	1,106	--	0	0	1,006	156
	Cube Root	Single	10	432.9	126	--	5	2	121	0
	Cube Root	Double	24	282.09	594	--	11	10	1,155	29
	Divide	Single	16	347.34	394	--	3	4	561	66
	Divide	Double	30	258.26	1,208	--	20	15	2,175	136
	Exp base 10	Single	14	271.37	502	--	3	2	432	40
	Exp base 10	Double	29	242.42	2,185	--	0	10	1,683	90
Arria 10 (10AX115H4F34I3SP)	Exp base 2	Single	7	317.86	370	--	0	2	124	9
	Exp base 2	Double	22	251.45	906	--	0	10	1,172	47
	Exp base e	Single	26	365.36	298	--	3	6	137	11
	Exp base e	Double	28	260.42	2,156	--	0	10	1,724	93
	Reciprocal	Single	12	278.94	225	--	3	3	172	3
	Reciprocal	Double	27	260.89	824	--	9	14	1,448	100
	Reciprocal Square Root	Single	8	418.94	117	--	3	2	130	1
	Reciprocal Square Root	Double	22	243.43	523	--	8	9	950	37
	LDExp	Single	0	--	68	--	0	0	0	0
	LDExp	Double	0	--	99	--	0	0	66	0
	Log base 10	Single	15	293.69	364	--	3	3	441	42
	Log base 10	Double	28	272.03	1,158	--	20	11	2,095	214
	Log(1+x)	Single	18	301.3	747	--	3	3	882	79
	Log(1+x)	Double	32	251.95	2,018	--	20	13	3,019	248
Arria 10 (10AX115H4F34I3SP)	Log base 2	Single	14	275.79	316	--	3	3	402	3
	Log base 2	Double	32	271.96	1,173	--	8	16	2,372	132
	Log base e	Single	29	378.07	297	--	3	9	315	6
	Log base e	Double	29	256.54	1,219	--	20	13	2,338	152
	Multiply	Single	3	288.4	49	--	0	1	0	0
	Multiply	Double	5	288.35	312	--	0	4	236	26
	Power	Single	40	262.12	1,335	--	8	14	1,523	127
	Power	Double	73	237.7	3,957	--	13	37 <