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Floating-Point Multiplication
5-30
Example 5–9. Floating-Point Multiply (Both Mantissas = 1.5)
Let:
α = 1.5 × 2
α
(
exp
)
= 01.0000000000000000000000 × 2
α
(
exp
)
b
= 1.5 × 2
b
(
exp
)
= 01.0000000000000000000000 × 2
b
(
exp
)
Where:
a
and
b
are both represented in binary form according to the single-preci-
sion floating-point format.
Then:
10.00000000000000000000000 × 2
α
(
exp
)
x 10.00000000000000000000000 × 2
b
(
exp
)
01.0000000000000000000000000000000000000000000000 × 2
(
α
(
exp
)
+
b
(
exp
)
+
2)
To place this number in the proper normalized format, it is necessary to shift
the mantissa one place to the right and add 1 to the exponent. This yields:
01.0000000000000000000000 × 2
α
(
exp
)
× 01.0000000000000000000000 × 2
b
(
exp
)
01. 00100000000000000000000000000000000000000000000 × 2
(
α
(
exp
)
+
b
(
exp
)
+
1)
Example 5–10. Floating-Point Multiply (Both Mantissas = 1.0)
Let:
α = 1.0 × 2
α
(
exp
)
= 01.00000000000000000000000 × 2
α
(
exp
)
b
= 1.0 × 2
b
(
exp
)
= 01.00000000000000000000000 × 2
b
(
exp
)
Where:
a
and
b
are both represented in binary form according to the single-preci-
sion floating-point format.
Then:
01.00000000000000000000000 × 2
α
(
exp
)
× 01.00000000000000000000000 × 2
b
(
exp
)
0001.0000000000000000000000000000000000000000000000 y 2
(
a
(
exp
)
+
b
(
exp
))
This number is in the proper normalized format. Therefore, no shift of the
mantissa or modification of the exponent is necessary.
The previous examples show cases where the product of two normalized
numbers can be normalized with a shift of 0, 1, or 2. The floating-point format
of the ‘C3x makes this possible.
- TMS320C3x 1
- User’s Guide 1
- Read This First 3
- Notational Conventions 4
- Information About Cautions 5
- References 6
- References 7
- Read This First 7
- Array Signal 9
- Processing 9
- Adaptive Array Principles 9
- If You Need Assistance . . 10
- Trademarks 11
- Contents 12
- Contents 14
- Contents 14
- Figures 20
- Examples 27
- Examples 28
- Introduction 30
- 1.1 TMS320C3x Devices 31
- 1.1.2 TMS320C30 32
- 1.1.4 TMS320C32 33
- TMS320C3x Devices 34
- 1.2 Typical Applications 36
- Architectural Overview 37
- 2.1 Overview 38
- Overview 39
- Central Processing Unit (CPU) 42
- Operation 44
- Addressing 44
- 2.3 CPU Primary Register File 45
- Data Formats and 46
- Floating-Point Operation 46
- CPU Primary Register File 47
- 2.4 Other Registers 48
- 2.5 Memory Organization 49
- Memory Organization 50
- 2.5.2 Memory Addressing Modes 53
- 2.6 Internal Bus Operation 54
- 2.7 External Memory Interface 55
- External Memory Interface 56
- 2.8 Interrupts 57
- 2.9 Peripherals 58
- 2.9.1 Timers 59
- 2.9.2 Serial Ports 59
- Figure 2–10. DMA Controller 61
- CPU Registers 64
- Table 3–1. CPU Registers 65
- 3.1.3 Data-Page Pointer (DP) 67
- 3.1.7 Status (ST) Register 68
- CPU Multiport Register File 69
- (TMS320C30 and TMS320C31) 72
- 3.2 Other Registers 81
- Chapter 4 83
- 4.1 Memory 84
- Peripheral Bus Memory Map 85
- 4.1.1.2 TMS320C31 Memory Map 87
- Reset/Interrupt/ 87
- Trap Vector Map 87
- Data-Page Pointer (DP) 88
- 4.1.1.3 TMS320C32 Memory Map 89
- ’C31, and ’C32 91
- Interrupt-Trap Table 96
- Pointer (ITTP) 96
- Microprocessor Mode 97
- Microcomputer Mode 99
- Note: Traps 28–31 100
- 4.3 Instruction Cache 101
- Instruction Cache 102
- 4.3.3 Cache Control Bits 104
- Chapter 5 106
- 5.1 Integer Formats 107
- 5.2 Unsigned-Integer Formats 108
- 5.3 Floating-Point Formats 109
- Floating-Point Formats 110
- Example 5–1. Positive Number 115
- Example 5–2. Negative Number 116
- Floating-Point Format 117
- (the actual expo 119
- ±1,R0 ; Add the positive sign 128
- Floating-Point Multiplication 132
- 0–α =–α (α ≠ 0) 141
- Rounding (RND Instruction) 144
- Mantissa 150
- 5.11.2 Points to Consider 152
- Addressing Modes 154
- 6.1 Addressing Types 155
- 6.2 Register Addressing 156
- 6.3 Direct Addressing 157
- 6.4 Indirect Addressing 158
- Indirect Addressing 159
- 6.5 Immediate Addressing 171
- 6.6 PC-Relative Addressing 172
- PC-Relative Addressing 173
- (c) RPTB: repeat block 173
- 6.7 Circular Addressing 174
- Circular Addressing 176
- 6.8 Bit-Reversed Addressing 179
- Bit-Reversed Addressing 180
- Language Tools 181
- 6.10.1 System-Stack Pointer 182
- 6.10.2 Stacks 183
- 6.10.3 Queues 184
- Program Flow Control 185
- 7.1 Repeat Modes 186
- 7.1.2 Repeat-Mode Operation 187
- Example 7–2. RPTB Operation 188
- 7.1.4 RPTS Instruction 189
- Repeat Modes 190
- 7.1.7 Nested Block Repeats 192
- 7.2 Delayed Branches 193
- Delayed Branches 194
- 7.3 Calls, Traps, and Returns 195
- Calls, Traps, and Returns 196
- 7.4 Interlocked Operations 197
- Interlocked Operations 198
- I/O Flag Register (IOF) 203
- (see Example 7–14) 204
- 7.5 Reset Operation 205
- Reset Operation 206
- Peripherals 209
- ’C30 and ’C31 External-Memory 209
- Interface 209
- 7.6 Interrupts 210
- TMS320C31 Microprocessor Mode 211
- Microcomputer Boot Mode 212
- Interrupts 213
- 7.6.6 Interrupt Processing 217
- Note: CPU and DMA Interrupts 218
- 7.6.7 CPU Interrupt Latency 219
- Table 7–8. Interrupt Latency 220
- 7.7 DMA Interrupts 222
- DMA Interrupts 223
- 7.7.3 CPU/DMA Interaction 224
- ... ; GIE = 1 226
- LDI 02000h, ST ; GIE = 0 226
- ADD *AR0, R1 226
- 7.8 Traps 231
- 7.9 Power Management Modes 233
- Figure 7–11.IDLE2 Timing 234
- 7.9.2 LOPOWER 235
- Figure 7–13. LOPOWER Timing 236
- Figure 7–14. MAXSPEED Timing 236
- Pipeline Operation 237
- 8.1 Pipeline Structure 238
- Pipeline Structure 239
- 8.2 Pipeline Conflicts 240
- Example 8–1. Standard Branch 241
- Example 8–2. Delayed Branch 242
- LDI 7,AR2 ; 7 → AR2 243
- 8.2.3 Memory Conflicts 244
- 8.2.3.1 Program Wait 245
- ADDF3 *AR0,*AR1,R0 246
- MPY ; code in internal memory 247
- 8.2.3.3 Execute Only 248
- → R1 in parallel with 249
- LDF *AR3,R2 ; *AR3 → R2 249
- STF R2,*AR1 ; R2 → *AR1 250
- ADDF @SUM,R1 ; R1 + @SUM → R1 250
- 8.2.3.4 Hold Everything 251
- STF R0,@DMA1 252
- LDF @DMA2,R0 252
- LDF @DMA,R0 253
- Generation 255
- Pipeline Conflict 256
- Resolving Register Conflicts 257
- 8.5 Clocking Memory Accesses 260
- Clocking Memory Accesses 261
- Example 8–17. Dummy sr2 Read 263
- ; AR1 points to MSTRB space ( 264
- TMS320C30 and TMS320C31 267
- External-Memory Interface 267
- 9.1 Overview 268
- 9.2 Memory Interface Signals 269
- Memory Interface Signals 270
- 9.4 Programmable Wait States 276
- Programmable Wait States 277
- Figure 9–4. BNKCMP Example 278
- Programmable Bank Switching 279
- 9.6.1 Primary-Bus Cycles 281
- changes 284
- is sampled, it is 0 285
- The next time (X)RDY 286
- 9.6.3 Hold Cycles 303
- TMS320C32 Memory Features 305
- TMS320C32 Memory Overview 306
- 10.2.2 Program Memory Access 307
- Figure 10–2. Status Register 308
- External 16-Bit Data 309
- 10.3 Configuration 310
- Configuration 311
- 10.4 Programmable Wait States 318
- Figure 10–8. BNKCMP Example 320
- 32-Bit-Wide Memory Interface 323
- 16-Bit-Wide Memory Interface 329
- 8-Bit-Wide Memory Interface 335
- 10.10 Bus Timing 342
- Bus Timing 343
- 10.10.2 IOSTRB Bus Cycles 345
- 10.10.3 Inactive Bus States 354
- Using the TMS320C31 and 356
- TMS320C32 Boot Loaders 356
- 11.1 TMS320C31 Boot Loader 357
- TMS320C31 Boot Loader 358
- 11.1.4.2 Serial-Port Loading 366
- 11.2 TMS320C32 Boot Loader 369
- TMS320C32 Boot Loader 370
- SSSSSS6x 377
- 12.1 Timers 381
- 12.1.1 Timer Pins 382
- Timer Operation Modes 384
- 12.1.5 Timer Pulse Generation 386
- Figure 12–4. Timer Timing 387
- = 0 (pulse mode) 388
- 12.1.6 Timer Operation Modes 389
- 12.1.8 Timer Interrupts 392
- 12.2 Serial Ports 394
- Serial Ports 395
- It is also set to 0 at reset 406
- 12.2.7 Data-Transmit Register 407
- 12.2.8 Data-Receive Register 407
- 12.2.10 Serial-Port Timing 410
- 12.2.10.2 Handshake Mode 412
- 12.3 DMA Controller 427
- DMA Controller 428
- 12.3.2 DMA Basic Operation 429
- 12.3.3 DMA Registers 430
- Interrupt-Enable Register 439
- Clocking Memory Access 442
- 12.3.7 DMA and Interrupts 443
- Chapter 13 459
- 13.1 Instruction Set 460
- 13.1.2 2-Operand Instructions 461
- 13.1.3 3-Operand Instructions 462
- Instruction Set 464
- 13.1.8 Illegal Instructions 467
- 13.2 Instruction Set Summary 468
- General Addressing Modes 478
- field. Refer to 479
- B 0 0 0 485
- Condition Codes and Flags 486
- Figure 13–6. Status Register 487
- (a) Unconditional compares 488
- (b) Unsigned compares 488
- (c) Signed compares 488
- (d) Compare to zero 489
- 13.6 Individual Instructions 490
- Individual Instructions 492
- Note the alternate notation R 494
- Example Instruction 496
- Example Instruction 497
- ABSF 500
- Absolute Value of Integer 502
- Example 1 ABSI R0,R0 503
- Example 2 ABSI *AR1,R3 503
- ABSI 504
- Add Integer With Carry 506
- 31 2423 16 8 7 015 507
- 00100 0 T 507
- Data Loads and Stores 508
- Add Floating-Point Values 509
- Example ADDF *AR4++(IR1),R5 510
- ADDF3 513
- Add Integer 515
- Add Integer, 3-Operand 516
- ADDI3 518
- ADDl3 519
- Bitwise-Logical AND 520
- 31 24 23 16 8 7 015 521
- AND3 523
- Example ANDN @980Ch,R2 526
- Arithmetic Shift 529
- Arithmetic Shift 530
- Arithmetic Shift, 3-Operand 531
- Arithmetic Shift, 3-Operand 532
- ASH3 534
- 01101 00 537
- B0 Register or displacement00 537
- Example BZ R0 538
- B0 Register or displacement01 539
- Call Subroutine 543
- CALLcond 544
- Compare Floating-Point Value 546
- Example CMPF *+AR4,R6 547
- 0010 0110 548
- Compare Integer 550
- Compare Integer, 3-Operand 551
- Register or displacementAR 553
- Example FIX R1,R2 558
- FIX 559
- Example FLOAT *++AR2(2),R5 562
- FLOAT 563
- Interrupt Acknowledge 565
- Example IACK *AR5 566
- Idle Until Interrupt 567
- Low-Power Idle 568
- Low-Power Idle 569
- Load Floating-Point Exponent 570
- Example LDE R0,R5 571
- Load Floating-Point Value 572
- Example LDFZ R3,R5 574
- 000 00 1 575
- Example LDFI *+AR2,R7 576
- LDF 577
- LDF 579
- Load Integer 581
- Example LDI *–AR1(IR0),R5 582
- Load Integer Conditionally 583
- Example LDIZ *ARO++,R6 584
- Load Integer, Interlocked 585
- Example LDII @985Fh,R3 586
- LDI 587
- LDI 589
- Load Floating-Point Mantissa 591
- Load Data-Page Pointer 592
- Divide Clock by 16 593
- Logical Shift 594
- Logical Shift 595
- Logical Shift, 3-Operand 596
- Logical Shift, 3-Operand 597
- LSH3 599
- MAXSPEED 603
- Multiply Floating-Point Value 604
- MPYF3 607
- MPYF3 611
- MPYF3 613
- Multiply Integer 617
- Example MPYI R1,R5 618
- Multiply Integer, 3-Operand 619
- MPYI3 621
- MPYl3 624
- MPYI3 625
- MPYI3 627
- Negative Integer With Borrow 631
- Negate Floating-Point Value 632
- Example NEGF *++AR3(2),R1 633
- NEGF 634
- Negate Integer 636
- NEGI 637
- No Operation 639
- Normalize 640
- Example NORM R1,R2 641
- Bitwise-Logical Complement 642
- Example NOT @982Ch,R4 643
- NOT 644
- Bitwise-Logical OR 646
- Example OR *++AR1(IR1),R2 647
- Bitwise-Logical OR, 3-Operand 648
- OR3 650
- Pop Integer 652
- Pop Floating-Point Value 653
- PUSH Integer 654
- PUSH Floating-Point Value 655
- RETIcond 656
- RETScond 658
- Round Floating-Point Value 660
- Round Floating-Point Value 661
- Rotate Left 662
- Rotate Left Through Carry 663
- Example 2 ROLC R3 664
- Rotate Right 665
- Rotate Right Through Carry 666
- Repeat Block 667
- Repeat Block 668
- Repeat Single Instruction 669
- Repeat Single Instruction 670
- Store Floating-Point Value 672
- STF 675
- Store Integer 677
- Store Integer, Interlocked 678
- STI 679
- Subtract Integer With Borrow 681
- 00 0 10 1 684
- Example 1 SUBC @98C5h,R1 685
- Subtract Floating-Point Value 686
- Example SUBF *AR0––(IR0),R5 687
- SUBF3 690
- Subtract Integer 692
- Subtract Integer, 3-Operand 693
- SUBI3 695
- Subtract Reverse Integer 699
- Software Interrupt 700
- TRAPcond 701
- Test Bit Fields 703
- Example TSTB *–AR4(1),R5 704
- Test Bit Fields, 3-Operand 705
- Bitwise-Exclusive OR 707
- XOR3 710
- Instruction Opcodes 712
- Instruction Opcodes 714
- Instruction Opcodes 714
- Appendix A 718
- Appendix B 718
- Appendix C 724
- Glossary 734
- Block-size register 735
- Central processing unit 735
- See also LD0–LD31 735
- First-in, first-out buffer 736
- Interrupt acknowledge signal 737
- Interrupt service routine 737
- Least significant bit 737
- CPU cycle 738
- MP/MC pin 738
- Most significant bit 738
- Nonmaskable interrupt 738
- Program counte 739
- See read/write pin 739
- Glossary 740
- Glossary 740
- See also A0–A23 741
- See also 741
- 3-operand instruction 13-58 742
- 3-operand instruction 13-49 742
- TMS320C32 2-16 749
- (LDF) 13-114 750
- TMS320C30 4-9 751
- TMS320C31 4-11 751
- TMS320C32 4-12 751
- (SUBRI) 13-241 756
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