Variable Precision DSP Blocks User Guide: Agilex™ 5 FPGAs and SoCs

Download PDF
ID 813968
Date 9/20/2024
Public
Document Table of Contents
Document Table of Contents x
1. Agilex™ 5 Variable Precision DSP Blocks Overview 2. Agilex™ 5 Variable Precision DSP Blocks Architecture 3. Agilex™ 5 Variable Precision DSP Blocks Operational Modes 4. Agilex™ 5 Variable Precision DSP Blocks Design Considerations 5. Native Fixed Point DSP Agilex™ FPGA IP Core References 6. Multiply Adder Intel® FPGA IP Core References 7. ALTMULT_COMPLEX Intel® FPGA IP Core References 8. LPM_MULT Intel® FPGA IP Core References 9. LPM_DIVIDE (Divider) Intel FPGA IP Core 10. Native Floating Point DSP Agilex™ FPGA IP References 11. Native AI Optimized DSP Agilex™ FPGA IP References 12. Document Revision History for the Agilex™ 5 Variable Precision DSP Blocks User Guide
1. Agilex™ 5 Variable Precision DSP Blocks Overview x
1.1. Features 1.2. Supported Operational Modes in Agilex™ 5 Devices
1.2. Supported Operational Modes in Agilex™ 5 Devices x
1.2.1. Fixed-point Arithmetic 1.2.2. Floating-point Arithmetic
2. Agilex™ 5 Variable Precision DSP Blocks Architecture x
2.1. Fixed-point Arithmetic 2.2. Floating-point Arithmetic 2.3. Tensor Mode
2.1. Fixed-point Arithmetic x
2.1.1. Input Register Bank for Fixed-point Arithmetic 2.1.2. Pipeline Registers for Fixed-point Arithmetic 2.1.3. Pre-adder for Fixed-point Arithmetic 2.1.4. Internal Coefficient for Fixed-point Arithmetic 2.1.5. Multipliers for Fixed-point Arithmetic 2.1.6. Adder or Subtractor for Fixed-point Arithmetic 2.1.7. Accumulator, Chainout Adder, and Preload Constant for Fixed-point Arithmetic 2.1.8. Systolic Register for Fixed-point Arithmetic 2.1.9. Double Accumulation Register for Fixed-point Arithmetic 2.1.10. Output Register Bank for Fixed-point Arithmetic
2.1.7. Accumulator, Chainout Adder, and Preload Constant for Fixed-point Arithmetic x
2.1.7.1. Dynamic Chainout
2.2. Floating-point Arithmetic x
2.2.1. Input Register Bank for Floating-point Arithmetic 2.2.2. Pipeline Registers for Floating-point Arithmetic 2.2.3. Multipliers for Floating-point Arithmetic 2.2.4. Adder or Subtractor for Floating-point Arithmetic 2.2.5. Output Register Bank for Floating-point Arithmetic 2.2.6. Exception Handling for Floating-point Arithmetic
3. Agilex™ 5 Variable Precision DSP Blocks Operational Modes x
3.1. Operational Modes for Fixed-point Arithmetic 3.2. Operational Modes for Floating-point Arithmetic 3.3. Operational Modes for Tensor Mode
3.1. Operational Modes for Fixed-point Arithmetic x
3.1.1. Independent Multiplier Mode 3.1.2. Multiplier Adder Sum Mode 3.1.3. Independent Complex Multiplier 3.1.4. Systolic FIR Mode
3.1.1. Independent Multiplier Mode x
3.1.1.1. 18 × 18 or 18 × 19 Independent Multiplier 3.1.1.2. 27 × 27 Independent Multiplier
3.1.2. Multiplier Adder Sum Mode x
3.1.2.1. 8 x 8 (Unsigned) or 9 x 9 (Signed) Sum of 6 Mode
3.1.2.1. 8 x 8 (Unsigned) or 9 x 9 (Signed) Sum of 6 Mode x
3.1.2.1.1. 18 × 19 Multiplication Summed with 36-Bit Input Mode
3.1.4. Systolic FIR Mode x
3.1.4.1. Mapping Systolic Mode User View to Variable Precision Block Architecture View 3.1.4.2. 18-bit Systolic FIR Mode 3.1.4.3. 27-Bit Systolic FIR Mode
3.2. Operational Modes for Floating-point Arithmetic x
3.2.1. FP32 Single-precision Floating-point Arithmetic Functions 3.2.2. FP16 Half-precision Floating-point Arithmetic Functions 3.2.3. Multiple Floating-point Variable DSP Blocks Functions
3.2.1. FP32 Single-precision Floating-point Arithmetic Functions x
3.2.1.1. FP32 Multiplication Mode 3.2.1.2. Adder or Subtract Mode 3.2.1.3. Multiply Accumulate Mode 3.2.1.4. FP32 Vector One Mode 3.2.1.5. FP32 Vector Two Mode
3.2.2. FP16 Half-precision Floating-point Arithmetic Functions x
3.2.2.1. FP16 Supported Precision Formats 3.2.2.2. Sum of Two FP16 Multiplication Mode 3.2.2.3. Sum of Two FP16 Multiplication with FP32 Addition Mode 3.2.2.4. Sum of Two FP16 Multiplication with Accumulation Mode 3.2.2.5. FP16 Vector One Mode 3.2.2.6. FP16 Vector Two Mode 3.2.2.7. FP16 Vector Three Mode
3.2.3. Multiple Floating-point Variable DSP Blocks Functions x
3.2.3.1. Multiply-Add or Multiply-Subtract Mode 3.2.3.2. Direct Vector Dot Product 3.2.3.3. Complex Multiplication
3.3. Operational Modes for Tensor Mode x
3.3.1. Data Input Feed Preloading Method 3.3.2. Side Input Feed Preloading Method 3.3.3. Tensor Floating-point Mode 3.3.4. Tensor Fixed-point Mode 3.3.5. Tensor Accumulation Mode
3.3.3. Tensor Floating-point Mode x
3.3.3.1. Input Register Bank for Tensor Floating-point Mode 3.3.3.2. Pipeline Registers for Tensor Floating-point Mode 3.3.3.3. Cascade Signals for Tensor Floating-point Mode 3.3.3.4. Output Registers for Tensor Floating-point Mode
3.3.4. Tensor Fixed-point Mode x
3.3.4.1. Input Register Bank for Tensor Fixed-point Mode 3.3.4.2. Pipeline Registers for Tensor Fixed-point Mode 3.3.4.3. Cascade Signals for Tensor Fixed-point Mode 3.3.4.4. Output Registers for Tensor Fixed-point Mode
3.3.5. Tensor Accumulation Mode x
3.3.5.1. Input Register Bank for Tensor Accumulation Mode 3.3.5.2. Pipeline Registers for Tensor Accumulation Mode 3.3.5.3. Cascade Signals for Tensor Accumulation Mode 3.3.5.4. Output Registers for Tensor Accumulation Mode
4. Agilex™ 5 Variable Precision DSP Blocks Design Considerations x
4.1. Fixed-point Arithmetic 4.2. Floating-point Arithmetic 4.3. DSP Block Cascade Limit in Agilex™ 5 Devices
4.1. Fixed-point Arithmetic x
4.1.1. Configurations for Input, Pipeline, and Output Registers 4.1.2. Internal Coefficient and Pre-Adder for Fixed-point Arithmetic 4.1.3. Accumulator for Fixed-point Arithmetic 4.1.4. Input Cascade for Fixed-point Arithmetic 4.1.5. Chainout Adder
4.1.1. Configurations for Input, Pipeline, and Output Registers x
4.1.1.1. Restrictions for Input Registers 4.1.1.2. Restrictions for Pipeline Registers 4.1.1.3. Supported Register Configurations per Operation Modes
4.1.4. Input Cascade for Fixed-point Arithmetic x
4.1.4.1. Dynamic Scanin
4.2. Floating-point Arithmetic x
4.2.1. Configurations for Input, Pipeline, and Output Registers 4.2.2. Chainout Adder
4.2.1. Configurations for Input, Pipeline, and Output Registers x
4.2.1.1. FP32 Operation Modes Supported Register Configurations 4.2.1.2. FP16 Operation Mode Supported Register Configurations
5. Native Fixed Point DSP Agilex™ FPGA IP Core References x
5.1. Native Fixed Point DSP Agilex™ FPGA IP Release Information 5.2. Supported Operational Modes 5.3. Maximum Input Data Width for Fixed-point Arithmetic 5.4. Maximum Output Data Width for Fixed-point Arithmetic 5.5. Parameterizing Native Fixed Point DSP IP 5.6. Native Fixed Point DSP Agilex™ FPGA IP Signals 5.7. IP Migration
5.3. Maximum Input Data Width for Fixed-point Arithmetic x
5.3.1. Using Less Than 36-Bit Operand In 18 x 18 Plus 36 Mode Example
5.5. Parameterizing Native Fixed Point DSP IP x
5.5.1. Operation Mode Tab 5.5.2. Input Cascade Tab 5.5.3. Pre-adder Tab 5.5.4. Internal Coefficient Tab 5.5.5. Accumulator/Output Chaining 5.5.6. Pipelining 5.5.7. Clear Signal
5.6. Native Fixed Point DSP Agilex™ FPGA IP Signals x
5.6.1. 9 × 9 Sum of 6 Mode Signals 5.6.2. 16 × 16 Complex Multiplier Mode Signals 5.6.3. 18 × 18 Full Mode Signals 5.6.4. 18 × 18 Sum of Two Mode Signals 5.6.5. 18 × 18 Plus 36 Mode Signals 5.6.6. 18 × 18 Systolic Mode Signals 5.6.7. 27 × 27 Mode Signals
6. Multiply Adder Intel® FPGA IP Core References x
6.1. Multiply Adder Intel® FPGA IP Release Information 6.2. Features 6.3. Parameters 6.4. Signals
6.2. Features x
6.2.1. Pre-adder 6.2.2. Systolic Delay Register 6.2.3. Pre-load Constant 6.2.4. Double Accumulator
6.2.1. Pre-adder x
6.2.1.1. Pre-adder Simple Mode 6.2.1.2. Pre-adder Coefficient Mode 6.2.1.3. Pre-adder Input Mode 6.2.1.4. Pre-adder Square Mode 6.2.1.5. Pre-adder Constant Mode
6.3. Parameters x
6.3.1. General Tab 6.3.2. Extra Modes 6.3.3. Multipliers Tab 6.3.4. Preadder Tab 6.3.5. Accumulator Tab 6.3.6. Systolic/Chainout Tab 6.3.7. Pipelining Tab
7. ALTMULT_COMPLEX Intel® FPGA IP Core References x
7.1. ALTMULT_COMPLEX Intel® FPGA IP Release Information 7.2. Features 7.3. Parameters 7.4. Signals
8. LPM_MULT Intel® FPGA IP Core References x
8.1. LPM_MULT Intel® FPGA IP Release Information 8.2. Features 8.3. Parameters 8.4. Signals
8.3. Parameters x
8.3.1. General Tab 8.3.2. General 2 Tab 8.3.3. Pipelining Tab
9. LPM_DIVIDE (Divider) Intel FPGA IP Core x
9.1. LPM_DIVIDE Intel® FPGA IP Release Information 9.2. Features 9.3. Verilog HDL Prototype 9.4. VHDL Component Declaration 9.5. VHDL LIBRARY_USE Declaration 9.6. Ports 9.7. Parameters
9.7. Parameters x
9.7.1. General Tab 9.7.2. General1 Tab
10. Native Floating Point DSP Agilex™ FPGA IP References x
10.1. Native Floating Point DSP Agilex™ FPGA IP Release Information 10.2. Native Floating Point DSP Agilex™ FPGA IP Core Supported Operational Modes 10.3. Parameterizing the Native Floating Point DSP Agilex™ FPGA IP 10.4. Native Floating Point DSP Agilex™ FPGA IP Core Signals 10.5. IP Migration
10.3. Parameterizing the Native Floating Point DSP Agilex™ FPGA IP x
10.3.1. General Tab 10.3.2. Registers Tab
10.4. Native Floating Point DSP Agilex™ FPGA IP Core Signals x
10.4.1. FP32 Multiplication Mode Signals 10.4.2. FP32 Addition or Subtraction Mode Signals 10.4.3. FP32 Multiplication with Addition or Subtraction Mode Signals 10.4.4. FP32 Multiplication with Accumulation Mode Signals 10.4.5. FP32 Vector One and Vector Two Modes Signals 10.4.6. Sum of Two FP16 Multiplication Mode Signals 10.4.7. Sum of Two FP16 Multiplication with FP32 Addition Mode Signals 10.4.8. Sum of Two FP16 Multiplication with Accumulation Mode Signals 10.4.9. FP16 Vector One and Vector Two Modes Signals 10.4.10. FP16 Vector Three Mode Signals
11. Native AI Optimized DSP Agilex™ FPGA IP References x
11.1. Native AI Optimized DSP Agilex™ FPGA IP Release Information 11.2. Native AI Optimized DSP Agilex™ FPGA IP Core Supported Operational Modes 11.3. Parameterizing the Native AI Optimized DSP Agilex™ FPGA IP 11.4. Native AI Optimized DSP Agilex™ FPGA IP Core Signals 11.5. IP Migration
11.3. Parameterizing the Native AI Optimized DSP Agilex™ FPGA IP x
11.3.1. Operation Mode Tab 11.3.2. Clock Source Enable/Clear Tab
11.4. Native AI Optimized DSP Agilex™ FPGA IP Core Signals x
11.4.1. Tensor Floating-point Mode Signals 11.4.2. Tensor Fixed-point Mode Signals 11.4.3. Tensor Accumulation Mode Signals
1. Agilex™ 5 Variable Precision DSP Blocks Overview
2. Agilex™ 5 Variable Precision DSP Blocks Architecture
3. Agilex™ 5 Variable Precision DSP Blocks Operational Modes
4. Agilex™ 5 Variable Precision DSP Blocks Design Considerations
5. Native Fixed Point DSP Agilex™ FPGA IP Core References
6. Multiply Adder Intel® FPGA IP Core References
7. ALTMULT_COMPLEX Intel® FPGA IP Core References
8. LPM_MULT Intel® FPGA IP Core References
9. LPM_DIVIDE (Divider) Intel FPGA IP Core
10. Native Floating Point DSP Agilex™ FPGA IP References
11. Native AI Optimized DSP Agilex™ FPGA IP References
12. Document Revision History for the Agilex™ 5 Variable Precision DSP Blocks User Guide

2.2.6. Exception Handling for Floating-point Arithmetic

The Agilex™ 5 floating-point arithmetic supports exception handling for the multiplier and adder blocks.

Table 9.  Supported Exception Flags
Floating-point Format Exception Flags Width Description
Single precision Multiplication
fp32_mult_overflow 1

This signal indicates if the multiplier result is a larger value than the maximum presentable value.

1: If the multiplier result is a larger value than the maximum representable value and the result is cast to infinity.

0: If the multiplier result is not larger than the maximum presentable value.

This signal is not available in Adder or Subtract Mode.

fp32_mult_underflow 1

This signal indicates if the multiplier result is a smaller value than the minimum presentable value.

1: If the multiplier result is a smaller value than the minimum representable non-zero absolute value and the result is flushed to zero.

0: If the multiplier result is a larger than the minimum representable value.

This signal is not available in Adder or Subtract Mode.

fp32_mult_inexact 1

This signal indicates if the multiplier result is not accurately represented.

1: If the multiplier result is:
  • a rounded value
  • a smaller value than the minimum representable value or
  • a larger value than the maximum representable value.

0: If the multiplier result does not meet any of the criteria above.

This signal is not available in Adder or Subtract Mode.

fp32_mult_invalid 1

This signal indicates if the multiplier operation is ill-defined and produces an invalid result.

1: If the multiplier result is invalid and cast to qNaN.

0: If the multiplier result is not an invalid number.

This signal is not available in Adder or Subtract Mode.

Addition
fp32_adder_overflow 1

This signal indicates if the adder result is a larger value than the maximum representable value.

1: If the adder result is a larger value than the maximum presentable value and the result is cast to infinity.

0: If the adder result is not larger than the maximum presentable value.

This signal is not available in Multiplication Mode.

fp32_adder_underflow 1

This signal indicates if the adder result is a smaller value than the minimum presentable value.

1: If the adder result is a smaller value than the minimum representable non-zero absolute value and the result is flushed to zero.

0: If the adder result is a larger than the minimum representable value.

This signal is not available in Multiplication Mode.

fp32_adder_inexact 1

This signal indicates if the adder result is not accurately represented.

1: If the adder result is:
  • a rounded value
  • a smaller value than the minimum representable value or
  • a larger value than the maximum representable value.

0: If the adder result does not meet any of the criteria above.

This signal is not available in Multiplication Mode.

fp32_adder_invalid 1

This signal indicates if the adder operation is ill-defined and produces an invalid result.

1: If the adder result is invalid and cast to qNaN.

0: If the adder result is not an invalid number.

This signal is not available in Multiplication Mode.

Half precision Multiplication

fp16_mult_top_overflow

fp16_mult_bot_overflow

1

This signal indicates if the top or bottom multiplier result is a larger value than the maximum presentable value.

1: If the multiplier result is a larger value than the maximum representable value and the result is cast to infinity.

0: If the multiplier result is smaller than the maximum presentable value.

This signal is not available in Adder or Subtract Mode and Extended format.

fp16_mult_top_underflow

fp16_mult_bot_underflow

1

This signal indicates if the top or bottom multiplier result is a smaller value than the minimum presentable value.

1: If the multiplier result is a smaller value than the minimum representable value and the result is flushed to zero.

0: If the multiplier result is a larger than the minimum representable value.

This signal is not available in Adder or Subtract Mode and Extended format.

fp16_mult_top_inexact

fp16_mult_bot_inexact

1

This signal indicates if the top or bottom multiplier result is an exact representation.

1: If the multiplier result is:
  • a rounded value
  • a smaller value than the minimum representable value or
  • a larger value than the maximum representable value.

0: If the multiplier result does not meet any of the criteria above.

This signal is not available in Adder or Subtract Mode.

fp16_mult_top_invalid

fp16_mult_bot_invalid

1

This signal indicates if the multiplier operation is ill-defined and produces an invalid result.

1: If the multiplier result is invalid and cast to qNaN.

0: If the multiplier result is not an invalid number.

This signal is not available in Adder or Subtract Mode.

fp16_mult_top_infinite

fp16_mult_bot_infinite

1

This signal indicates if the top or bottom multiplier result is a positive or negative infinity.

1: If the result is infinite

0: If the result is normalized float or in the appropriate infinity range

This signal is only available for Extended format.

fp16_mult_top_zero

fp16_mult_bot_zero

1

This signal indicates if the top or bottom multiplier result is a positive or negative zero.

1: If the result is zero

0: If the result is not a zero

This signal is only available for Extended format.

Addition
fp16_adder_overflow 1

This signal indicates if the adder result is a larger value than the maximum representable value.

1: If the adder result is a larger value than the maximum presentable value and the result is cast to infinity.

0: If the adder result is not larger than the maximum presentable value.

This signal is not available in Multiplication Mode Extended format.

fp16_adder_underflow 1

This signal indicates if the adder result is a smaller value than the minimum presentable value.

1: If the adder result is a smaller value than the minimum representable value and the result is flushed to zero.

0: If the adder result is a larger than the minimum representable value.

This signal is not available in Multiplication Mode Extended format.

fp16_adder_inexact 1

This signal indicates if the adder result is an exact representation.

1: If the adder result is:
  • a rounded value
  • a smaller value than the minimum representable value or
  • a larger value than the maximum representable value.

0: If the adder result does not meet any of the criteria above.

This signal is not available in Multiplication Mode.

fp16_adder_invalid 1

This signal indicates if the adder operation is ill-defined and produces an invalid result.

1: If the adder result is invalid and cast to qNaN.

0: If the adder result is not an invalid number.

This signal is not available in Multiplication Mode.

fp16_adder_infinite 1

This signal indicates if the adder result is a positive or negative infinity.

1: If the result is infinite

0: If the result is normalized float or in the appropriate infinity range

This signal is only available for Extended format.

fp16_adder_zero 1

This signal indicates if the adder result is a positive or negative zero.

1: If the result is zero

0: If the result is not a zero

This signal is only available for Extended format.

Table 10.  Multiplier Exception Handling Possible Results for FP32 Multiplication, FP16 Flushed, and FP16 Bfloat16 Modes
Input A Input B Result 4

Flags

Overflow/Underflow/Inexact/Invalid
Normalized Normalized Normalized value 0/0/0/0
Normalized (rounded) value 0/0/1/0
Positive/negative infinity value 1/0/1/0
Subnormal (denormal) value 0/1/1/0
0 or Subnormal (denormal) Normalized 0 value 0/0/0/0
Positive/negative infinity Normalized Positive/negative infinity value 0/0/0/0
Quiet Not A Number (qNaN) Normalized qNaN value 0/0/0/0
0 or Subnormal (denormal) 0 or Subnormal (denormal) 0 value 0/0/0/0
Positive/negative infinity 0 or Subnormal (denormal) qNaN value 0/0/0/1
Quiet Not A Number (qNaN) 0 or Subnormal (denormal) qNaN value 0/0/0/0
Positive/negative infinity Positive/negative Infinity Positive/negative infinity value 0/0/0/0
Quiet Not A Number (qNaN) Positive/negative Infinity qNaN value 0/0/0/0
Quiet Not A Number (qNaN) Quiet Not A Number (qNaN) qNaN value 0/0/0/0
Table 11.  Adder Exception Handling Possible Results for FP32 Addition/Subtraction, FP16 Flushed, and FP16 Bfloat16 Modes
Input A Input B Result : 4

Flags

Overflow/Underflow/Inexact/Invalid
Normalized Normalized Normalized value 0/0/0/0
Normalized (rounded) value 0/0/1/0
Positive/negative infinity value 1/0/1/0
0 value

Sign bit = 0

 0/0/0/0
Subnormal (denormal) value

The sign is preserved

 0/1/1/0
0 or Subnormal (denormal) Normalized Input b 0/0/0/0
Positive/negative infinity Normalized Positive/negative infinity value 0/0/0/0
Quiet Not A Number (qNaN) Normalized qNaN value 0/0/0/0
0 or Subnormal (denormal) 0 or Subnormal (denormal) 0 value

For (-0 + (-0)) equation, sign bit = 1. For any other equation, sign bit = 0.

 0/0/0/0
Positive/negative infinity 0 or Subnormal (denormal) Positive/negative infinity value 0/0/0/0
Quiet Not A Number (qNaN) 0 or Subnormal (denormal) qNaN value 0/0/0/0
Positive/negative infinity Positive/negative infinity

qNaN value for invalid cases

Positive/negative infinity value for valid cases

 0/0/0/1 for invalid cases

0/0/0/0 for valid cases

Valid cases are:
  • Positive infinity value + positive infinity value
  • Negative infinity value + negative infinity value
  • Negative infinity value - positive infinity value
  • Positive infinity value - negative infinity value
Quiet Not A Number (qNaN) Positive/negative infinity qNaN value 0/0/0/0
Quiet Not A Number (qNaN) Quiet Not A Number (qNaN) qNaN value 0/0/0/0
Table 12.  Multiplication Exception Handling Possible Results for FP16 Extended Modes
Input A Input B Result: 4

Flags

Infinite/Zero/Inexact/Invalid
Normalized/Subnormalized Normalized/Subnormalized Normalized/Subnormalized 0/0/x/0
0 value Normalized/Subnormalized 0 value 0/1/0/0
Positive/negative infinity Normalized/Subnormalized Positive/negative infinity value 1/0/0/0
Quiet Not A Number (qNaN) Normalized/Subnormalized qNaN value 0/0/0/1

Mantissa = {100...00}
0 value 0 value 0 value 0/1/0/0
Positive/negative infinity 0 value qNaN value 0/0/0/1

Mantissa = {100...00}
Quiet Not A Number (qNaN) 0 value qNaN value 0/0/0/1

Mantissa = {100...00}
Positive/negative infinity Positive/negative infinity Positive/negative infinity value 1/0/0/0
Quiet Not A Number (qNaN) Positive/negative infinity qNaN value 0/0/0/1

Mantissa = {100...00}
Quiet Not A Number (qNaN) Quiet Not A Number (qNaN) qNaN value 0/0/0/1

Mantissa = {100...00}
Table 13.  Addition Exception Handling Possible Results for FP16 Extended Modes
Input A Input B Result: 4

Flags

Infinite/Zero/Inexact/Invalid
Normalized/Subnormalized Normalized/Subnormalized Normalized/Subnormalized 0/0/x/0
0 value

Sign bit = 0

 0/0/0/0
0 value Normalized/Subnormalized Input b 0/0/0/0
Positive/negative infinity Normalized/Subnormalized Positive/negative infinity value 1/0/0/0
Quiet Not A Number (qNaN) Normalized/Subnormalized qNaN value 0/0/0/1

Mantissa = {100...00}
0 value 0 value 0 value

For (-0 + (-0)) equation, sign bit = 1. For any other equation, sign bit = 0.

0/0/0/0
Positive/negative infinity 0 value Positive/negative infinity value 1/0/0/0
Quiet Not A Number (qNaN) 0 value qNaN value 0/0/0/1

Mantissa = {100...00}
Positive/negative infinity Positive/negative infinity

qNaN value for invalid cases

Positive/negative infinity value for valid cases

 0/0/0/1 for invalid cases

Mantissa = {100...00}

1/0/0/0 for valid cases

Valid cases are:
  • Positive infinity value + positive infinity value
  • Negative infinity value + negative infinity value
  • Negative infinity value - positive infinity value
  • Positive infinity value - negative infinity value
Quiet Not A Number (qNaN) Positive/negative infinity qNaN value 0/0/0/1

Mantissa = {100...00}
Quiet Not A Number (qNaN) Quiet Not A Number (qNaN) qNaN value 0/0/0/1

Mantissa = {100...00}
4 Output exception flags. These flags do not change if exceptions are at input value.
Level Two Title