FloatingPoint IP Cores User Guide
Version Information
Updated for: 

Intel® Quartus® Prime Design Suite 20.1 
1. About FloatingPoint IP Cores
 ALTERA_FP_MATRIX_INV IP core
 ALTERA_FP_MATRIX_MULT IP core
1.1. List of FloatingPoint IP Cores
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 floatingpoint 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 
IP Core Name  Function Overview  Supported Device 

Floating Point Functions Intel FPGA IP  A collection of floatingpoint functions. This IP core replaces all other floatingpoint 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 installs IP cores in the following locations by default:
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 
1.3. Design Flow
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
 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.
 Rightclick 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 toplevel Intel^{®} Quartus^{®} Prime IP file (.ip) for an IP variation in Intel^{®} Quartus^{®} Prime Pro Edition projects.
The parameter editor generates a toplevel 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.
1.3.1.1. The Parameter Editor
 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 systemlevel 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)
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 doubleclick 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 toplevel 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 devicespecific 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)
File Name  Description 

<your_ip>.ip  Toplevel 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 ipmakesimscript 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 RivieraPRO* 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 subdirectories for each IP submodule directory that Platform Designer generates. 
1.3.3. Generating IP Cores ( Intel Quartus Prime Standard Edition)
 In the IP Catalog (Tools > IP Catalog), locate and doubleclick the name of the IP core to customize. The parameter editor appears.
 Specify a toplevel 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 toplevel
.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
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.
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 endoflife 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 noncritical 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
doubleclick 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
 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, doubleclick 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 reparameterize 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. FloatingPoint IP Cores General Features
 Support for floatingpoint formats.
 Input support for notanumber (NaN), infinity, zero, and normal numbers.
 Optional asynchronous input ports including asynchronous clear (aclr) and clock enable (clk_en).
 Support for roundtonearesteven rounding mode.
 Compute results of any mathematical operations according to the IEEE754 standard compliance with a maximum of 1 unit in the last place (u.l.p.) error. This assumption is applied to all floatingpoint IP cores.
Intel FPGA floatingpoint 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. IEEE754 Standard for FloatingPoint Arithmetic
 Floatingpoint numbers
 Special values (zero, infinity, denormal numbers, and NaN bit combinations)
 Singleprecision, doubleprecision, and singleextended precision formats for floatingpoint numbers
1.6.1. FloatingPoint Formats
For a normal floatingpoint 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.
1.6.1.1. SinglePrecision Format
 The MSB holds the sign bit.
 The next 8 bits hold the exponent bits.
 23 LSBs hold the mantissa.
The total width of a floatingpoint number in the singleprecision format is 32 bits. The bias for the singleprecision format is 127.
1.6.1.2. DoublePrecision Format
 The MSB holds the sign bit.
 The next 11 bits hold the exponent bits.
 52 LSBs hold the mantissa.
The total width of a floatingpoint number in the doubleprecision format is 64 bits. The bias for the doubleprecision format is 1023.
1.6.1.3. SingleExtended Precision Format
 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 singleextended precision format is unspecified in the IEEE754 standard. In these IP cores, a bias of 2 ^{(}WIDTH_EXP–1^{)}–1 is assumed for the singleextended precision format.
1.6.2. Special Case Numbers
Meaning  Sign Field  Exponent Field  Mantissa Field 

Zero  Don’t care  All 0’s  All 0’s 
Positive Denormalized  0  All 0’s  Nonzero 
Negative Denormalized  1  All 0’s  Nonzero 
Positive Infinity  0  All 1’s  All 0’s 
Negative Infinity  1  All 1’s  All 0’s 
NotaNumber (NaN)  Don’t care  All 1’s  Nonzero 
1.6.3. Rounding
 roundtonearesteven
 roundtowardzero
 roundtowardpositiveinfinity
 roundtowardnegativeinfinity
Intel floatingpoint IP cores support only the most commonly used rounding mode, which is the roundtonearesteven mode (TO_NEAREST). With roundtonearesteven, the IP core rounds the result to the nearest floatingpoint number. If the result is exactly halfway between two floatingpoint numbers, the IP core rounds the result so that the LSB becomes a zero, which is even.
1.7. NonIEEE754 Standard Format
The fixedpoint data type is similar to the conventional integer data type, except that the fixedpoint 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 fixedpoint 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 16bit word.
The following figures show the difference between the signedinteger format and the fixedpoint format for a 32bit number.
1.8. FloatingPoints IP Cores Output Latency
For specific details about latency options, refer to the Output Latency section of your selected IP core in this user guide.
1.9. FloatingPoint IP Cores Design Example Files
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.
FloatingPoint IP Cores  Design Files 

ALTFP_ADD_SUB 

ALTFP_DIV 

ALTFP_MULT 

ALTFP_SQRT 

ALTFP_EXP 

ALTFP_INV 

ALTFP_INV_SQRT 

ALTFP_LOG 

ALTFP_ATAN  Not Available 
ALTFP_SINCOS  Not Available 
ALTFP_ABS 

ALTFP_COMPARE 

ALTFP_CONVERT 

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 LIBRARYUSE 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 floatingpoint 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.
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
 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
2.3. FP_ACC_CUSTOM Intel FPGA IP Resource Utilization and Performance
Device Family  Input Data  Accumulator Size  Target Frequency (MHz)  Latency  ALMs  DSP Blocks  Logic Registers  M10K  M20K  f_{MAX}  

Floating Point Format  MaxMSBX  MSBA  LSBA  Primary  Secondary  
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
Port Name  Required  Description 

clk  Yes  All input signals, otherwise explicitly stated, must be synchronous to this clock 
areset  Yes  Asynchronous activehigh 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. 
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
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. 
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(log_{2}(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(log_{2}(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(log_{2}(365 x 60 x 60 x 24 x 400 x 10^{6}))=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. 
LSBA  —  The weight of
the LSB of the accumulator and the accuracy of the accumulator. Because
an N term accumulation can invalidate the log_{2}(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  log_{2}(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 floatingpoint addition or subtraction between two inputs dynamically.
3.1. ALTFP_ADD_SUB 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
3.3. ALTFP_ADD_SUB Truth Table
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
Device Family  Precision  Optimization  Output latency  Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  f_{MAX} (MHz) 

Stratix IV  single  speed  7  594  376  385  228 
14  674  686  498  495  
area  7  576  345  375  227  
14  596  603  421  484  
double  speed  7  1,198  687  824  187  
14  997  1,607  1,080  398  
area  7  1,106  630  762  189  
14  904  1,518  1,013  265 
3.5. ALTFP_ADD_SUB Design Example: Addition of DoublePrecision Format Numbers
3.5.1. ALTFP_ADD_SUM Design Example: Understanding the Simulation Results
This design example implements a floatingpoint adder for the addition of doubleprecision 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.
Time  Event 

0 ns, startup 
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
Port Name  Required  Description 

aclr  No  Asynchronous clear input for floatingpoint 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 floatingpoint 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 floatingpoint 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 floatingpoint adder or subtractor. This port is configured in the same way as dataa[]. 
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  Floatingpoint 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
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_EXP1) 1 (that is, 127 for singleprecision format and 1023 for doubleprecision format). The WIDTH_EXP parameter must be 8 for the singleprecision mode and 11 for the doubleprecision mode, or a minimum of 11 for the singleextended 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 IEEE754 standard for the singleprecision 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 floatingpoint division operation.
4.1. ALTFP_DIV 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
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
DATAA[]  DATAB[]  SIGN BIT  RESULT[]  Overflow  Underflow  Zero  Divisionbyzero  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
Device family  Precision  Optimization  Output latency  Logic Usage  f_{MAX}(MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18bit DSP  
Stratix IV  Single  Speed  33  3,593  3,351  2,500  —  313 
Area  33  1,646  2,074  1,441  —  308  
Double  Speed  61  13,867  13,143  10,196  —  292  
Area  61  5,125  7,360  4,842  —  267  
Low Latency Option  
Stratix IV  Single  —  6  207  304  212  16  154 
—  14  253  638  385  16  358  
Double  —  10  714  1,077  779  44  151  
—  24  765  2,488  1,397  44  238 
4.5. ALTFP_DIV Design Example: Division of SinglePrecision
4.5.1. ALTFP_DIV Design Example: Understanding the Simulation Results
This design example implements a floatingpoint divider for the division of singleprecision numbers with a low latency option. The output latency is 6, hence every division generates the output result 6 clock cycles later.
Time  Event 

0 ns, startup 
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 startup 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 forcedzero values, therefore, attempts to divide a normal value with a zero result in an infinity value. 
4.6. ALTFP_DIV Signals
Port Name  Required  Description 

aclr  No  Asynchronous clear input for the floatingpoint 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 floatingpoint 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. 
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 2WIDTH_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  Divisionbyzero 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
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 floatingpoint
format is the singleprecision 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 floatingpoint 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 singleprecision format, the
latency options are
33,
14 or
6. For the
doubleprecision format, the latency options are
61,
24 or
10.
For the singleextended precision format, the value ranges from a minimum of 41 to a maximum of 61. For the lowlatency 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 floatingpoint multiplication operation.
5.1. ALTFP_MULT IP Core 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
Precision  Mantissa Width  Latency (in clock cycles) 

Single  23  5, 6, 10,11 
Double  52  5, 6, 10,11 
SingleExtended  31–52  5, 6, 10,11 
5.3. ALTFP_MULT Truth Table
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
Device Family  Precision  Output latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18bit DSP  
Stratix IV  Single  5  138  148  100  4  274 
11  185  301  190  4  445  
Double  5  306  367  272  10  255  
11  419  523  348  10  395 
5.5. ALTFP_MULT Design Example: Multiplication of DoublePrecision Format Numbers
5.5.1. ALTFP_MULT Design Example: Understanding the Simulation Waveform
This design example implements a floatingpoint multiplier for the multiplication of doubleprecision 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.
Time  Event 

0 ns, startup 
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 startup 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 nonzero 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
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 singleprecision format and 1023 for the doubleprecision format). WIDTH_EXP must be 8 for the singleprecision format or a minimum of 11 for the doubleprecision format and the singleextended 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 floatingpoint format is singleprecision, 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
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  Floatingpoint 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  Floatingpoint 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. 
Port Name  Required  Description 

result[]  Yes  Output port for the multiplier. The floatingpoint 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
 Square root functions.
 Optional exception handling output ports such as zero, overflow, and nan.
6.2. Output Latency
Precision  Mantissa Width  Latency (in clock cycles) 

Single  23  16, 28 
Double  52  30, 57 
Singleextended  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
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
Device Family  Precision  Output latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Login Registers (DLRs)  Adaptive Logic Modules (ALMs)  
Stratix IV  Single  28  502  932  528  472 
Double  57  2,177  3,725  2,202  366 
6.5. ALTFP_SQRT Design Example: Square Root of SinglePrecision Format Numbers
6.5.1. ALTFP_SQRT Design Example: Understanding the Simulation Results
These figures show the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floatingpoint square root function for singleprecision 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.
Time  Event 

0 ns, startup  Output value: All values seen on the output port before the 28th clock cycle are merely due to the behavior of the system during startup 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
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  Floatingpoint 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. 
Port Name  Required  Description 

result[]  Yes  Square root output port for the floatingpoint 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
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 singleprecision format and 1023 for the doubleprecision format. The value of the WIDTH_EXP parameter must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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
 Exponential value of a given input.
 Optional exception handling output ports such as zero, overflow, underflow, and nan.
7.2. Output Latency
Precision  Mantissa Width  Latency (in clock cycles) 

Single  23  17 
Double  52  25 
Singleextended  31 – 38  22 
39 – 52  25 
7.3. ALTFP_EXP Truth Table
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 
7.4. ALTFP_EXP Resource Utilization and Performance
Device Family  Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18bit DSP  
Stratix IV  Single  17  631  521  448  19  284 
Double  25  4,104  2,007  2,939  46  279 
7.5. ALTFP_EXP Design Example: Exponential of SinglePrecision Format Numbers
7.5.1. ALTFP_EXP Design Example: Understanding the Simulation Results
These figures show the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floatingpoint exponential for the singleprecision 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 singleprecision format numbers, the latency is fixed at 17 clock cycles. Therefore, every exponential operation outputs the results 17 clock cycles later.
Time  Event 

0 ns, startup 
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 startup 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
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  Floatingpoint 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. 
Port Name  Required  Description 

result[]  Yes  The floatingpoint 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
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 singleprecision format and 1023 for the doubleprecision format. The value of the WIDTH_EXP parameter must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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 PlugIn 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
 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 
40 – 52  27 
8.3. ALTFP_INV Truth Table
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 
8.4. ALTFP_INV Resource Utilization and Performance
Device Family  Precision  Output Latency  Logic usage  f_{MAX }(MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18Bit DSP  
Stratix IV  Single  20  401  616  373  16  412 
Double  27  939  1,386  912  48  203 
8.5. ALTFP_INV Design Example: Inverse of SinglePrecision Format Numbers
This design example uses the ALTFP_INV IP core to compute the inverse of singleprecision 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
These figures show the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floatingpoint inverse for singleprecision 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.
Time  Event 

0 ns, startup 
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 startup 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 forcedzero values, therefore, the inverse of a zero results in infinity. 
8.6. 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  Floatingpoint 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. 
Port Name  Required  Description 

result[]  Yes  The floatingpoint 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  Divisionbyzero 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
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 singleprecision format and 1023 for the doubleprecision format. The value of the WIDTH_EXP parameter must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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
 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
Precision  Mantissa Width  Latency (in clock cycles) 

Single  23  26 
Double  52  36 
SingleExtended  31– 39  26 
40 – 52  36 
9.3. ALTFP_INV_SQRT Truth Table
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 
9.4. ALTFP_INV_SQRT Resource Utilization and Performance
Device Family  Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive Lookup Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18Bit DSP  
Stratix IV  Single  26  502  658  430  22  413 
Double  36  1,324  1,855  1,209  78  209 
9.5. ALTFP_INV_SQRT Design Example: Inverse Square Root of SinglePrecision Format Numbers
9.5.1. ALTFP_INV_SQRT Design Example: Understanding the Simulation Results
These figures show the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floatingpoint inverse square root for singleprecision 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.
Time  Event 

0 ns, startup 
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 startup 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 forcedzero 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
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  Floatingpoint 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 floatingpoint 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  Divisionbyzero 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
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 singleprecision format and 1023 for the doubleprecision format. The value of the WIDTH_EXP parameter must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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
 Natural logarithm functions.
 Optional exception handling output ports such as zero and nan.
10.2. Output Latency
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
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.
Device Family  Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18Bit DSP  
Stratix IV  Single  21  1,950  1,864  1,378  8  385 
Double  34  5,451  6,031  4,151  64  211 
10.5. ALTFP_LOG Design Example: Natural Logarithm of SinglePrecision Format Numbers
10.5.1. ALTFP_LOG Design Example: Understanding the Simulation Results
These figures show the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
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.
Time  Event 

0 ns, startup 
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 startup 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
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 
Floatingpoint 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. 
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 floatingpoint 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 nonzero, respectively. This occurs when the input is a negative number or NaN. 
10.7. 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 singleprecision format and 1023 for the doubleprecision format. The value of the WIDTH_EXP parameter must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 singleprecision format, and 52 for the doubleprecision format. For the singleextended 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
Trigonometric Function  Precision  Mantissa Width  Latency (in clock cycles) 

Arctangent  Single  23  34 
11.2. ALTFP_ATAN Features
 Arctangent value of a given angle, θ in unit radian.
 Support for singleprecision 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
Device Family  Function  Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18Bit DSP  
Stratix V  ArcTangent  Single  36  2,454  1,010  1,303  27  255.49 
11.4. 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  Floatingpoint 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 floatingpoint format. The widths of the result[] output port and data[] input port are the same. 
11.5. 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_EXP1) 1 (that is, 127 for singleprecision format). The value of WIDTH_EXP must be 8 for singleprecision 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
 Implements sine and cosine calculations.
 Support for singleprecision floating point format.
 Support for optional input ports such as asynchronous clear (aclr) and clock enable (clk_en) ports.
12.2. Output Latency
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
Device Family  Function  Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  18Bit DSP  
Stratix IV  Sine  Single  36  2,859  2,190  1,830  16  292.96 
Cosine  Single  35  2,753  2,041  1,745  16  258.26 
12.4. ALTFP_SINCOS 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  Floatingpoint 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 trigonemetric of the data[] input port in floatingpoint format. The widths of the result[] output port and data[] input port are the same. 
12.5. ALTFP_SINCOS 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_EXP1)} 1 (that is, 127 for singleprecision format). The value of WIDTH_EXP must be 8 for singleprecision 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
 Absolute value of a given input.
 Optional exception handling output ports such as zero, division_by_zero, overflow, underflow, and nan.
 Carrythrough exception ports from other floatingpoint modules that act as inputs to the ALTFP_ABS IP core.
13.2. ALTFP_ABS Output Latency
13.3. ALTFP_ABS Resource Utilization and Performance
Precision  Output Latency  Logic usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  18Bit DSP  Memory  
Single  0  0  0  0  0  The f _{MAX} of this IP core depends on the speed of the selected device 
1  0  36  0  0  
Double  0  0  0  0  0  
1  0  68  0  0 
13.4. ALTFP_ABS Design Example: Absolute Value of Multiplication Results
13.4.1. ALTFP_ABS Design Example: Understanding the Simulation Results
This design example produces a floatingpoint absolute value function for the multiplication results of singleprecision 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.
Time  Event 

0 ns, startup 
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 startup 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
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  Floatingpoint 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. Carrythrough exception input port from other floatingpoint modules. 
nan_in  No  NaN exception input. Carrythrough exception input port from other floatingpoint modules. 
overflow_in  No  Overflow exception input. Carrythrough exception input port from other floatingpoint modules. 
underflow_in  No  Underflow exception input. Carrythrough exception input port from other floatingpoint modules. 
division_by_zero_in  No  Divisionbyzero exception input. Carrythrough exception input port from other floatingpoint modules. 
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 carrythrough port from the input is asserted. 
nan  No  NaN output carried from the input. Asserted if the corresponding carrythrough port from the input is asserted. 
overflow  No  Overflow exception output carried from the input. Asserted if the corresponding carrythrough port from the input is asserted. 
underflow  No  Underflow exception output carried from the input. Asserted if the corresponding carrythrough port from the input is asserted. 
division_by_zero  No  Divisionbyzero exception output carried from the input. Asserted if the corresponding carrythrough port from the input is asserted. 
13.6. 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 singleprecision format and 1023 for the doubleprecision format. The value of WIDTH_EXP must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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
 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
14.3. ALTFP_COMPARE Resource Utilization and Performance
Device Family  Precision  Output Latency  Logic Usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive LookUp Modules (ALMs)  
Stratix IV  single  3  68  33  47  794 
double  3  121  47  87  680 
14.4. ALTFP_COMPARE Design Example: Comparison of SinglePrecision Format Numbers
14.4.1. ALTFP_COMPARE Design Example: Understanding the Simulation Results
This figure shows the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floatingpoint comparator for singleprecision 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.
Time  Event 

0 ns, startup 
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 startup 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
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. 
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
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 singleprecision format and 1023 for the doubleprecision format. The value of WIDTH_EXP must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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
 Conversion functions for the following formats:
 IntegertoFloat
 FloattoInteger
 FloattoFloat
 FixedtoFloat
 FloattoFixed
 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 IntegertoFloat Not supported FloattoInteger overflow, underflow, and nan FloattoFloat overflow, underflow, and nan FixedtoFloat Not supported FloattoFixed overflow, underflow, and nan
15.2. ALTFP_CONVERT Conversion Operations
Operation  Features 

IntegertoFloat Conversion 

FloattoInteger Conversion 

FloattoFloat Conversion 

FixedtoFloat Conversion 

FloattoFixed Conversion 

15.3. ALTFP_CONVERT Output Latency
Operation  Conversion From  Latency (in clock cycles) 

IntegertoFloat  N/A  6 
FloattoInteger  N/A  6 
FloattoFloat  Singleprecision format  2 
Doubleprecision format  3  
Singleextended precision format  3  
FixedtoFloat  N/A  6 
FloattoFixed  N/A  6 
15.4. ALTFP_CONVERT Resource Utilization and Performance
Operation  Format  Pipeline  Logic Usage  f_{MAX} (MHz)  

Adaptive LookUp Tables (ALUTs)  Dedicated Logic Registers (DLRs)  Adaptive Logic Modules (ALMs)  
Integer toFloat  32bit integer to singleprecision  6  182  238  157  515 
32bit integer to doubleprecision  6  150  139  123  510  
64bit integer to singleprecision  6  385  371  296  336  
64bit integer to singleprecision  6  393  461  344  336  
FloattoInteger  Singleprecision to 32bit integer  6  256  255  176  455 
Singleprecision to 64bit integer  6  417  361  257  311  
Doubleprecision to 32bit integer  6  406  387  273  409  
Doubleprecision to 64bit integer  6  535  480  362  309  
FloattoFloat  Singleprecision to doubleprecision  2  44  73  40  868 
Doubleprecision to singleprecision  3  103  140  89  520  
FixedtoFloat  16.16 fixedpoint to doubleprecision  6  182  238  155  519 
16.16 fixedpoint to doubleprecision  6  150  139  122  513  
32.32 fixedpoint to singleprecision  6  384  371  296  334  
32.32 fixedpoint to singleprecision  6  393  461  336  333  
FloattoFixed  Singleprecision to 16.16 fixedpoint  6  319  261  210  438 
Singleprecision to 32.32 fixedpoint  6  469  367  288  315  
Doubleprecision to 16.16 fixedpoint  6  579  393  402  365  
Doubleprecision to 32.32 fixedpoint  6  695  486  474  306 
15.5. ALTFP_CONVERT Design Example: Convert DoublePrecision FloatingPoint Format Numbers
15.5.1. ALTFP_CONVERT Design Example: Understanding the Simulation Results
This figure shows the expected simulation results in the ModelSim*  Intel^{®} FPGA Edition software.
This design example implements a floattointeger converter for converting doubleprecision floatingpoint format numbers to 64bit integers. In this operation, the optional exception ports of overflow, underflow, and nan are available apart from the result[] port.
The latency for the floattointeger 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.
Time  Event 

0 ns, startup 
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 startup 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
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 floatingpoint representation. In the singleprecision format, the input bus width value is 32. In the doubleprecision format, the input bus width value is 64. In the singleextended 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 floatingpoint representation. In the singleprecision format, the input bus width value is 32. In the doubleprecision format, the input bus width value is 64. In the singleextended precision format, the input bus range is from 43 to 64. 
Port Name  Required  Description 

result[]  Yes  Output for the
floatingpoint 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 floatingpoint representation. If the operation mode is FLOAT2INT, the output bus is an integer representation. If the selected precision is the singleprecision format, the output bus width value is 32. If the selected precision is the doubleprecision format, the output bus width value is 64. If the selected precision is the singleextended precision format, the input bus range is from 43 to 64. If the operation mode value is FLOAT2FLOAT, the output bus is an IEEE floatingpoint representation. If the selected precision is the singleprecision format, the output bus is in the 64bit doubleprecision format. If the selected precision is the doubleprecision format, the output bus is in the 32bit singleprecision format. If the selected precision is the singleextended 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 floatingpoint input is smaller than the exponent bias. In FLOAT2FLOAT operations, this port is asserted when the floatingpoint input has a value smaller than the lowest exponent limit of the target floatingpoint 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
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 singleprecision format and 1023 for the doubleprecision format. The value of WIDTH_EXP_INPUT must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 floatingpoint format is singleprecision, 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 singleprecision format and 1023 for the doubleprecision format. The value of WIDTH_EXP_OUTPUT must be 8 for the singleprecision format, 11 for the doubleprecision format, and a minimum of 11 for the singleextended 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 singleprecision, 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 floatingpoint representation output takes place. When set to FLOAT2INT, the conversion of an IEEE floatingpoint representation input to an integer output takes place. When set to FLOAT2FLOAT, the conversion between IEEE floatingpoint representations input and output takes place. When set to FIXED2FLOAT, the conversion of a fixed point input to an IEEE floatingpoint representation output takes place. When set to FLOAT2FIXED, the IEEE floatingpoint input conversion to fixed point representation output takes place. 
16. FP_FUNCTIONS Intel FPGA IP or Floating Point Functions Intel FPGA IP Core
Item  Description 

Version  19.1 
Intel^{®} Quartus^{®} Prime Version  20.1 
Release Date  2020.04.13 
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 
MultiplyAccumulate  Two input multiplication followed by a single cycle accumulation 
Accumulate  Perform single input accumulation in a single cycle 
MultiplyAdd  Performs two input multiplication followed by addition 
ComplexMultiply  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  
FixedtoFloating Point  Converts a fixed point input to floating point representation 
Floating PointtoFixed  Converts a floatingpoint input to fixed point representation 
Floating to Floating Point  Converts a floatingpoint input to floatingpoint 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 
Log_{2}  Performs the function of log_{2}(a) where a is the input 
Log_{10}  Performs the function of log_{10}(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 floatingpoint 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
 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
 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
 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
 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
Family  Function  Precision  Latency  f_{MAX }  ALMs  M10K  M20K  DSP Blocks  Logic Registers  

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