# AN617. Fixed Point Routines FIXED POINT ARITHMETIC INTRODUCTION. Thi d t t d ith F M k Design Consultant

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1 Thi d t t d ith F M k Fixed Point Routines AN617 Author: INTRODUCTION Frank J. Testa Design Consultant This application note presents an implementation of the following fixed point math routines for the PIC16/17 microcontroller families: Multiplication Division Routines for the PIC16/17 families are provided in a variety of fixed point formats, including both unsigned and signed two s complement arithmetic. FIXED POINT ARITHMETIC Unsigned fixed point binary numbers A, can be represented in the form n-1 A = a(k) 2 k-r = 2 -r a(k) 2k k=0 n-1 k=0 where n is the number of bits, a(k) is the kth bit with a(0) = LSb, and r indicates the location of the radix point. For example, in the case where A is an integer, r = 0 and when A is a fraction less than one, r = n. The value of r only affects the interpretation of the numbers in a fixed point calculation, with the actual binary representation of the numbers independent of the value of r. Factoring out of the above sum, it simply locates the radix point of the representation and is analogous to an exponent in a floating point system. Using the notation Qi.j to denote a fixed point binary number with i bits to the left of the radix point and j to the right, the above n-bit format is in Qn-r.r. With care, fixed point calculations can be performed on operands in different Q formats. Although the radix point must be aligned for addition or subtraction, multiplication provides an illustrative example of the simple interpretive nature of r. Consider the unsigned product of a Q20.4 number with a Q8.8. After calling the appropriate unsigned bit multiply for these fixed point arguments, the 40-bit fixed point result is in Q28.12, where the arguments of the Q notation are summed respectively. Similar arguments can be made for two s complement arithmetic, where the negative representation of a positive number is obtained by reversing the value of each bit and incrementing the result by one. Producing a unique representation of zero, and covering the range -2 n-1 to 2 n-1-1, this is more easily applied in addition and subtraction operations and is therefore the most commonly used method of representing positive and negative numbers in fixed point arithmetic. The above analysis in Q notation can be employed to build dedicated fixed point algorithms, leading to improved performance over floating point methods in cases where the size of the arguments required for the range and precision of the calculations is not large enough to destroy gains made by fixed point methods Microchip Technology Inc. DS00617A-page 1

2 FIXED POINT FORMATS The fixed point library routines supports 8-,16-, 24- and 32-bit formats in the following combinations: Division Library Names Format Multiplication Library Names Format PIC16C5X/PIC16CXX Routines FXD0808S, FXD0808U, FXD0807U, FXD0707U FXD1608S, FXD1608U, FXD1607U, FXD1507U FXD1616S, FXD1616U, FXD1515U FXD2416S, FXD2416U, FXD2315U FXD2424S, FXD2424U, FXD2323U FXD3216S, FXD3216U, FXD3115U FXD3224S, FXD3224U, FXD3123U FXD3232S, FXD3232U, FXD3131U PIC17CXX Functions FXD0808S, FXD0808U, FXD0807U, FXD0707U FXD1608S, FXD1608U, FXD1607U, FXD1507U FXD1616S, FXD1616U, FXD1615U, FXD1515U FXD2416S, FXD2416U, FXD2415U, FXD2315U FXD2424S, FXD2424U, FXD2423U, FXD2323U FXD3216S, FXD3216U, FXD3215U, FXD3115U FXD3224S, FXD3224U, FXD3223U, FXD3123U FXD3232S, FXD3232U, FXD3231U, FXD3131U 8/8 FXM0808S, FXM0808U, FXM0807U 16/8 FXM1608S, FXM1608U, FXM1607U, FXM1507U 16/16 FXM1616S, FXM1616U, FXM1515U 24/16 FXM2416S, FXM2416U, FXM2315U 24/24 FXM2424S, FXM2424U, FXM2323U 32/16 FXM3216S, FXM3216U, FXM3115U 32/24 FXM3224S, FXM3224U, FXM3123U 32/32 FXM3232S, FXM3232U, FXM3131U 8/8 FXM0808S, FXM0808U, FXM0807U 16/8 FXM1608S, FXM1608U, FXM1507U 16/16 FXM1616S, FXM1616U, FXM1515U 24/16 FXM2416S, FXM2416U, FXM2315U 24/24 FXM2424S, FXM2424U, FXM2323U 32/16 FXM3216S, FXM3216U, FXM3115U 32/24 FXM3224S, FXM3224U, FXM3123U 32/32 FXM3232S, FXM3232U, FXM3131U Note: U - unsigned math operation, S - signed math operation These general format combinations are implemented in both signed and unsigned versions. Additional unsigned routines are implemented with arguments reduced by one bit to accommodate the case of operations on signed numbers, with arguments known to be nonnegative, thereby, resulting in some performance improvement. DS00617A-page Microchip Technology Inc.

4 is required to align the partial product for the next possible add[1]. Several examples are shown in Example 2. EXAMPLE 2: MULTIPLICATION EXAMPLES FXM2416S(0xC11682,0x608B) = FXM2416S( ,24715) = 0xE84647F896 = FXM1616U(0x0458,0x822C) = FXM1616U(1112,33324) = 0x02356F20 = TABLE 1: PIC17CXX FIXED POINT MULTIPLY PERFORMANCE DATA: APPENDIX E Routine Max Cyc Min Cyc PM DM Page FXM0808S 50/ FXM0808U FXM0707U FXM1608S 74/ FXM1608U FXM1507U FXM1616S 168/ FXM1616U FXM1515U FXM2416S 213/ FXM2416U FXM2315U FXM2424S 334/ FXM2424U FXM2323U FXM3216S 258/ FXM3216U FXM3115U FXM3224S 403/ FXM3224U FXM3123U FXM3232S 556/ FXM3232U FXM3131U Legend: PM - Program memory, DM - Data Memory TABLE 2: PIC16C5X/PIC16CXX FIXED POINT MULTIPLY PERFORMANCE DATA: APPENDIX C Routine Max Cyc Min Cyc PM DM Page FXM0808S 79/ FXM0808U FXM0707U FXM1608S 122/ FXM1608U FXM1507U FXM1616S 260/ FXM1616U FXM1515U FXM2416S 334/ FXM2416U FXM2315U FXM2424S 520/ FXM2424U FXM2323U FXM3216S 408/ FXM3216U FXM3115U FXM3224S 634/ FXM3224U FXM3123U FXM3232S 868/ FXM3232U FXM3131U Legend: PM - Program memory, DM - Data Memory DS00617A-page Microchip Technology Inc.

5 DIVISION The fixed point divide routine FXPDxxyy, takes an xx-bit dividend in AARG, a yy-bit divisor in BARG and returns the xx-bit quotient in ACC and yy-bit remainder in REM. Unlike multiplication, division is not deterministic, requiring a trial-and-error sequential shift and subtract process. Binary division is less complicated than decimal division because the possible quotient digits are only zero or one. If the divisor is less than the partial remainder, the corresponding quotient bit is set to one followed by a shift and subtract. Otherwise, the divisor is greater than the partial remainder, the quotient bit is set to zero and only a shift is performed. The intermediate partial remainder may be restored at each stage as in restoring division, or corrected at the end as in nonrestoring division. Implementation dependent trade-offs between worst case versus average performance affect the choice between these two approaches, and therefore, macros for each method are provided. Note: The results of the division process for AARG/BARG, satisfy the relation AARG = BARG QUOTIENT + REMAINDER, where the remainder has the same sign as the quotient, and represents the fraction of the result in units of the denominator BARG. Some simple examples are given in Example 3. EXAMPLE 3: A test for divide by zero exception is not performed and must be explicitly provided by the user. DIVISION EXAMPLES FXD1608S(0xC116,0x60) = 0xFF59, 0xB6 FXD1616U(0x9543,0x4AA1) = 02, Microchip Technology Inc. DS00617A-page 5

6 TABLE 3: PIC17CXX FIXED POINT DIVIDE PERFORMANCE DATA: APPENDIX F TABLE 4: PIC16C5X/PIC16CXX FIXED POINT DIVIDE PERFORMANCE DATA: APPENDIX D Routine Max Cyc Min Cyc PM DM Page FXD0808S 71/77 71/ FXD0808U FXD0807U FXD0707U FXD1608S 135/ / FXD1608U FXD1607U FXD1507U FXD1616S 201/ / FXD1616U FXD1615U FXD1515U FXD2416S 297/ / FXD2416U FXD2415U FXD2315U FXD2424S 371/ / FXD2424U FXD2423U FXD2323U FXD3216S 393/ / FXD3216U FXD3215U FXD3115U FXD3224S 491/ / FXD3224U FXD3223U FXD3123U FXD3232S 589/ / FXD3232U FXD3231U FXD3131U Legend: PM - Program memory, DM - Data Memory Routine Max Cyc Min Cyc PM DM Page FXD0808S 90/96 90/ FXD0808U FXD0807U FXD0707U FXD1608S 176/ / FXD1608U FXD1607U FXD1507U FXD1616S 304/ / FXD1616U FXD1515U FXD2416S 417/ / FXD2416U FXD2315U FXD2424S 541/ / FXD2424U FXD2323U FXD3216S 551/ / FXD3216U FXD3115U FXD3224S 715/ / FXD3224U FXD3123U FXD3232S 879/ / FXD3232U FXD3131U Legend: PM - Program memory, DM - Data Memory REFERENCES 1. Cavanagh, J.J.F., Digital Computer Arithmetic, McGraw-Hill, Hwang, K., Computer Arithmetic, John Wiley & Sons, Scott, N.R., Computer Number Systems & Arithmetic, Prentice Hall, IEEE Standards Board, IEEE Standard for Floating-Point Arithmetic, ANSI/IEEE Std , IEEE, Knuth, D.E., The Art of Computer Programming, Volume 2, Addison-Wesley, F.J.Testa, IEEE 754 Compliant Floating Point Routines, AN575, Embedded Control Handbook, Microchip Technology Inc., DS00617A-page Microchip Technology Inc.

7 APPENDIX A: ALGORITHMS Several algorithms for decimal to binary conversion are given below. The integer and fractional conversion algorithms are useful in both native assembly as well as high level languages. A.1 Integer conversion algorithm[3]: Given an integer I, where d(k) are the bit values of its n bit binary representation with d(0) = LSB, n-1 I = d(k) 2 k k=0 k=0 I(k) = I while I(k) =! 0 d(k) = remainder of I(k)/2 I(k+1) = I(k)/2 k = k + 1 where denotes the greatest integer function (or ceiling function). A.2 Fractional conversion algorithm[3]: Given a fraction F, where d(k) are the bit values of its n bit binary representation with d(1)=msb, k=0 F(k) = F while k <= n d(k) = F(k) 2 n F = d(k) 2 -k k=1 F(k+1) = fractional part of F(k) 2 k = k Microchip Technology Inc. DS00617A-page 7

8 APPENDIX B: FLOWCHARTS FIGURE B-1: MULTIPLICATION FLOWCHART FXPMxxU FXPMxxS i = 0 clear high order partial product i = 0 clear high order partial product multiplier bit i = 1? Yes multiplier < 0? Yes No add multiplicand to high order partial product No negate multiplier and multiplicand save sign of result right shift partial product i = i + 1 multiplier bit i = 1? No Yes add multiplicand to high order partial product Yes i < n? No right shift partial product with sign extension i = i + 1 Return 0 Yes i < n - 1? No Return 0 DS00617A-page Microchip Technology Inc.

9 FIGURE B-2: DIVISION FLOWCHART FXPDxxU FXPDxxS A i = 0 clear remainder partial quotient = dividend compute sign of quotient left shift (remainder, quotient) i < n? No divisor < 0? Yes subtract divisor from partial remainder Yes Return 0 No negate divisor result > 0? Yes left shift (remainder, quotient) subtract division from partial remainder dividend < 0? No Yes negate dividend No restore partial quotient, LSb = 0 partial quotient LSb = 1 result > 0? No Yes restore partial quotient, LSb = 0 i = 0 clear remainder partial quotient = dividend restore partial quotient, LSb = 0 i < n - 1? Yes A No Return Microchip Technology Inc. DS00617A-page 9

10 Thi d t t d ith F M k AN617 Please check the Microchip BBS for the latest version of the source code. For BBS access information, see Section 6, Microchip Bulletin Board Service information, page 6-3. APPENDIX C: MULTIPLY ROUTINES FOR THE PIC16C5X/PIC16CXX Table of Contents for Appendix C C.1 32x32 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.2 32x24 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.3 32x16 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.4 24x24 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.5 24x16 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.6 16x16 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.7 16x8 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.8 8x8 PIC16C5X/PIC16CXX Fixed Point Multiply Routines C.1 32x32 PIC16C5X/PIC16CXX Fixed Point Multiply Routines ; 32x32 PIC16 FIXED POINT MULTIPLY ROUTINES VERSION 1.2 ; Input: fixed point arguments in AARG and BARG ; Output: product AARGxBARG in AARG ; All timings are worst case cycle counts ; It is useful to note that the additional unsigned routines requiring a non-power of two ; argument can be called in a signed multiply application where it is known that the ; respective argument is nonnegative, thereby offering some improvement in performance. ; Routine Clocks Function ; FXM3232S x32 -> 64 bit signed fixed point multiply ; FXM3232U x32 -> 64 bit unsigned fixed point multiply ; FXM3131U x31 -> 62 bit unsigned fixed point multiply ; The above timings are based on the looped macros. If space permits, ; approximately clocks can be saved by using the unrolled macros. list r=dec,x=on,t=off include <PIC16.INC> ; general PIC16 definitions include <MATH16.INC> ; PIC16 math library definitions ; Test suite storage RANDHI equ 0x1A ; random number generator registers RANDLO equ 0x1B DATA equ 0x20 ; beginning of test data ; Test suite for 32x32 bit fixed point multiply algorithms org 05 MAIN MOVLW RAMSTART MEMLOOP MOVLW RAMSTOP,W _Z MEMLOOP MOVLW 0x45 ; seed for random numbers RANDLO MOVLW 0x30 RANDHI MOVLW DATA BCF _RP0 BCF _RP1 BCF _IRP CALL TFXM3232 SELF SELF RANDOM16 RANDHI,W ; random number generator XORWF RANDHI,W B0 SWAPF RANDHI SWAPF RANDLO,W DS00617A-page Microchip Technology Inc.

11 1995 Microchip Technology Inc. DS00617A-page 11 AN617 B1 B1,W B1 B1,W XORWF RANDHI,W SWAPF RANDHI ANDLW 0x01 B0 RANDLO XORWF RANDLO RANDHI RETEW 0 ; Test suite for FXM3232 TFXM3232 CALL RANDOM16 RANDHI,W BARGB0 BCF BARGB0,MSB RANDLO,W BARGB1 CALL RANDOM16 RANDHI,W BARGB2 RANDLO,W BARGB3 CALL RANDOM16 RANDHI,W AARGB0 BCF AARGB0,MSB AARGB0,W RANDLO,W AARGB1 CALL RANDOM16 RANDHI,W AARGB2 RANDLO,W AARGB3 CALL FXM3131U AARGB0,W AARGB1,W AARGB2,W AARGB4,W

12 AARGB5,W AARGB6,W AARGB7,W ; 32x32 Bit Multiplication Macros SMUL3232L macro ; Max Timing: * * * * = 851 clks ; Min Timing: 2+7* * * *6+5+6 = 192 clks ; PM: = 152 DM: 17 MOVLW 0x8 LOOPSM3232A BARGB3 ALSM3232NA LOOPSM3232A LOOPSM3232B BARGB2 BLSM3232NA LOOPSM3232B LOOPSM3232C BARGB1 CLSM3232NA LOOPSM3232C MOVLW 0x7 LOOPSM3232D BARGB0 DLSM3232NA LOOPSM3232D AARGB0 AARGB1 AARGB2 AARGB3 ALOOPSM3232 BARGB3 ALSM3232NA B3,W B2,W B2,W B1,W B1,W DS00617A-page Microchip Technology Inc.

13 1995 Microchip Technology Inc. DS00617A-page 13 AN617 B0,W B0,W ALSM3232NA B0,W ACCB4 ALOOPSM3232 MOVLW 0x8 BLOOPSM3232 BARGB2 BLSM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLSM3232NA B0,W ACCB4 ACCB5 BLOOPSM3232 MOVLW 0x8 CLOOPSM3232 BARGB1 CLSM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W CLSM3232NA B0,W

14 ACCB4 ACCB5 ACCB6 CLOOPSM3232 MOVLW 0x7 DLOOPSM3232 BARGB0 DLSM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W DLSM3232NA B0,W ACCB4 ACCB5 ACCB6 ACCB7 DLOOPSM3232 B0,W ACCB4 ACCB5 ACCB6 ACCB7 endm UMUL3232L macro ; Max Timing: * * * *28+27 = 842 clks ; Min Timing: 2+7* * * *6+5+6 = 197 clks ; PM: = 155 DM: 17 MOVLW 0x08 LOOPUM3232A BARGB3 ALUM3232NAP LOOPUM3232A LOOPUM3232B BARGB2 BLUM3232NAP LOOPUM3232B DS00617A-page Microchip Technology Inc.

15 LOOPUM3232C BARGB1 CLUM3232NAP LOOPUM3232C LOOPUM3232D BARGB0 DLUM3232NAP LOOPUM3232D AARGB0 AARGB1 AARGB2 AARGB3 ALUM3232NAP BCF ALUM3232NA BLUM3232NAP BCF BLUM3232NA CLUM3232NAP BCF CLUM3232NA DLUM3232NAP BCF DLUM3232NA ALOOPUM3232 BARGB3 ALUM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALUM3232NA ACCB4 ALOOPUM3232 MOVLW 0x08 BLOOPUM3232 BARGB2 BLUM3232NA B3,W B2,W B2,W B1,W 1995 Microchip Technology Inc. DS00617A-page 15

16 DS00617A-page Microchip Technology Inc. B1,W B0,W B0,W BLUM3232NA ACCB4 ACCB5 BLOOPUM3232 MOVLW 0x08 CLOOPUM3232 BARGB1 CLUM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W CLUM3232NA ACCB4 ACCB5 ACCB6 CLOOPUM3232 MOVLW 0x08 DLOOPUM3232 BARGB0 DLUM3232NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W

17 DLUM3232NA ACCB4 ACCB5 ACCB6 ACCB7 DLOOPUM3232 endm UMUL3131L macro ; Max Timing: * * * * = 822 clks ; Min Timing: 2+7* * * *6+5+6 = 192 clks ; PM: = 155 DM: 17 MOVLW 0x8 LOOPUM3131A BARGB3 ALUM3131NAP LOOPUM3131A LOOPUM3131B BARGB2 BLUM3131NAP LOOPUM3131B LOOPUM3131C BARGB1 CLUM3131NAP LOOPUM3131C MOVLW 0x7 LOOPUM3131D BARGB0 DLUM3131NAP LOOPUM3131D AARGB0 AARGB1 AARGB2 AARGB3 ALUM3131NAP BCF ALUM3131NA BLUM3131NAP BCF BLUM3131NA CLUM3131NAP BCF CLUM3131NA DLUM3131NAP BCF DLUM3131NA ALOOPUM3131 BARGB Microchip Technology Inc. DS00617A-page 17

18 DS00617A-page Microchip Technology Inc. ALUM3131NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALUM3131NA ACCB4 ALOOPUM3131 MOVLW 0x08 BLOOPUM3131 BARGB2 BLUM3131NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLUM3131NA ACCB4 ACCB5 BLOOPUM3131 MOVLW 0x08 CLOOPUM3131 BARGB1 CLUM3131NA B3,W B2,W B2,W B1,W

19 CLUM3131NA DLOOPUM3131 DLUM3131NA MOVLW endm B1,W B0,W B0,W ACCB4 ACCB5 ACCB6 CLOOPUM3131 0x07 BARGB0 DLUM3131NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ACCB4 ACCB5 ACCB6 ACCB7 DLOOPUM3131 ACCB4 ACCB5 ACCB6 ACCB7 SMUL3232 macro ; Max Timing: 9+7*22+8*23+8*24+7*25+9 = 723 clks ; Min Timing: 62+6 = 68 clks ; PM: *22+8*23+8*24+7*25+9 = 788 DM: 16 variable i i = 0 while i < Microchip Technology Inc. DS00617A-page 19

20 i = i + 1 i = 8 BARGB3,i SM3232NA#v(i) while i < 16 i = i + 1 i = 16 BARGB2,i-8 SM3232NA#v(i) while i < 24 i = i + 1 i = 24 BARGB1,i-16 SM3232NA#v(i) while i < 31 BARGB0,i-24 SM3232NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 SM3232NA0 B0,W ACCB4 i = 1 while i < 8 BARGB3,i SM3232NA#v(i) SM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3232NA#v(i) B0,W ACCB4 i = i + 1 i = 8 DS00617A-page Microchip Technology Inc.

21 while i < 16 BARGB2,i-8 SM3232NA#v(i) SM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3232NA#v(i) B0,W ACCB4 ACCB5 i = i + 1 i = 16 while i < 24 BARGB1,i-16 SM3232NA#v(i) SM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3232NA#v(i) B0,W ACCB4 ACCB5 ACCB6 i = i + 1 i = 24 while i < 31 BARGB0,i-24 SM3232NA#v(i) SM3232A#v(i) B3,W B2,W B2,W B1,W 1995 Microchip Technology Inc. DS00617A-page 21

22 B1,W B0,W B0,W SM3232NA#v(i) B0,W ACCB4 ACCB5 ACCB6 ACCB7 i = i + 1 B0,W ACCB4 ACCB5 ACCB6 ACCB7 endm UMUL3232 macro ; Max Timing: 9+8*21+8*22+8*23+8*24 = 729 clks ; Min Timing: 63+6 = 69 clks ; PM: *21+8*22+8*23+8*24 = 795 DM: 16 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 BARGB3,i UM3232NA#v(i) while i < 16 i = i + 1 i = 16 BARGB2,i-8 UM3232NA#v(i) while i < 24 i = i + 1 i = 24 BARGB1,i-16 UM3232NA#v(i) while i < 32 BARGB0,i-24 UM3232NA#v(i) i = i + 1 ; if we get here, BARG = 0 DS00617A-page Microchip Technology Inc.

23 RETEW 0 UM3232NA0 ACCB4 i = 1 while i < 8 BARGB3,i UM3232NA#v(i) UM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3232NA#v(i) ACCB4 i = i + 1 i = 8 while i < 16 BARGB2,i-8 UM3232NA#v(i) UM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3232NA#v(i) ACCB4 ACCB5 i = i + 1 i = 16 while i < 24 BARGB1,i-16 UM3232NA#v(i) UM3232A#v(i) B3,W 1995 Microchip Technology Inc. DS00617A-page 23

24 B2,W B2,W B1,W B1,W B0,W B0,W UM3232NA#v(i) ACCB4 ACCB5 ACCB6 i = i + 1 i = 24 while i < 32 BARGB0,i-24 UM3232NA#v(i) UM3232A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3232NA#v(i) ACCB4 ACCB5 ACCB6 ACCB7 i = i + 1 endm UMUL3131 macro ; Max Timing: 9+7*21+8*22+8*23+7*24+9 = 693 clks ; Min Timing: 62+6 = 68 clks ; PM: *22+8*23+8*24+7*25+9 = 788 DM: 16 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 while i < 16 BARGB3,i UM3131NA#v(i) DS00617A-page Microchip Technology Inc.

25 i = i + 1 i = 16 while i < 24 i = i + 1 i = 24 while i < 31 BARGB2,i-8 UM3131NA#v(i) BARGB1,i-16 UM3131NA#v(i) BARGB0,i-24 UM3131NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM3131NA0 ACCB4 i = 1 while i < 8 BARGB3,i UM3131NA#v(i) UM3131A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3131NA#v(i) ACCB4 i = i + 1 i = 8 while i < 16 BARGB2,i-8 UM3131NA#v(i) UM3131A#v(i) B3,W B2,W B2,W B1,W B1,W 1995 Microchip Technology Inc. DS00617A-page 25

26 B0,W B0,W UM3131NA#v(i) ACCB4 ACCB5 i = i + 1 i = 16 while i < 24 BARGB1,i-16 UM3131NA#v(i) UM3131A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3131NA#v(i) ACCB4 ACCB5 ACCB6 i = i + 1 i = 24 while i < 31 BARGB0,i-24 UM3131NA#v(i) UM3131A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3131NA#v(i) ACCB4 ACCB5 ACCB6 ACCB7 DS00617A-page Microchip Technology Inc.

27 i = i + 1 endm ACCB4 ACCB5 ACCB6 ACCB7 ; 32x32 Bit Signed Fixed Point Multiply 32x32 -> 64 ; Input: 32 bit signed fixed point multiplicand in AARGB0 ; 32 bit signed fixed point multiplier in BARGB0 ; Use: CALL FXM3232S ; Output: 64 bit signed fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 868 clks B > 0 ; = 889 clks B < 0 ; Min Timing: = 207 clks ; PM: = 189 DM: 17 FXM3232S BARGB0,MSB M3232SOK BARGB3 ; make multiplier BARG > 0 BARGB3 _Z DECF BARGB2 BARGB2 _Z DECF BARGB1 BARGB1 _Z DECF BARGB0 BARGB0 AARGB3 AARGB3 _Z DECF AARGB2 AARGB2 _Z DECF AARGB1 AARGB1 _Z DECF AARGB0 AARGB0 M3232SOK ACCB4 ; clear partial product ACCB5 ACCB7 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 SMUL3232L ; 32x32 Bit Unsigned Fixed Point Multiply 32x32 -> 64 ; Input: 32 bit unsigned fixed point multiplicand in AARGB Microchip Technology Inc. DS00617A-page 27

28 ; 32 bit unsigned fixed point multiplier in BARGB0 ; Use: CALL FXM3232U ; Output: 64 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 856 clks ; Min Timing: = 209 clks ; PM: = 168 DM: 17 FXM3232U ACCB4 ; clear partial product ACCB5 ACCB7 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 UMUL3232L ; 31x31 Bit Unsigned Fixed Point Divide 31x31 -> 62 ; Input: 31 bit unsigned fixed point multiplicand in AARGB0 ; 31 bit unsigned fixed point multiplier in BARGB0 ; Use: CALL FXM3131U ; Output: 62 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 836 clks ; Min Timing: = 204 clks ; PM: = 168 DM: 17 FXM3131U ACCB4 ; clear partial product ACCB5 ACCB7 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 UMUL3131L END C.2 32x24 PIC16C5X/PIC16CXX Fixed Point Multiply Routines ; 32x24 PIC16 FIXED POINT MULTIPLY ROUTINES VERSION 1.2 ; Input: fixed point arguments in AARG and BARG ; Output: product AARGxBARG in AARG ; All timings are worst case cycle counts ; It is useful to note that the additional unsigned routines requiring a non-power of two ; argument can be called in a signed multiply application where it is known that the ; respective argument is nonnegative, thereby offering some improvement in ; performance. ; Routine Clocks Function ; FXM3224S x24 -> 56 bit signed fixed point multiply ; FXM3224U x24 -> 56 bit unsigned fixed point multiply ; FXM3123U x23 -> 54 bit unsigned fixed point multiply DS00617A-page Microchip Technology Inc.

29 ; The above timings are based on the looped macros. If space permits, ; approximately clocks can be saved by using the unrolled macros. list r=dec,x=on,t=off include <PIC16.INC> ; general PIC16 definitions include <MATH16.INC> ; PIC16 math library definitions ; Test suite storage RANDHI equ 0x1A ; random number generator registers RANDLO equ 0x1B DATA equ 0x20 ; beginning of test data ; Test suite for 32x24 bit fixed point multiply algorithms org 05 MAIN MOVLW RAMSTART MEMLOOP MOVLW RAMSTOP,W _Z MEMLOOP MOVLW 0x45 ; seed for random numbers RANDLO MOVLW 0x30 RANDHI MOVLW DATA BCF _RP0 BCF _RP1 BCF _IRP CALL TFXM3224 SELF SELF RANDOM16 RANDHI,W ; random number generator XORWF RANDHI,W B0 SWAPF RANDHI SWAPF RANDLO,W B1 B1,W B1 B1,W XORWF RANDHI,W SWAPF RANDHI ANDLW 0x01 B0 RANDLO XORWF RANDLO RANDHI RETEW 0 ; Test suite for FXM3224 TFXM3224 CALL RANDOM16 RANDHI,W BARGB0 ; BCF BARGB0,MSB ; RANDLO,W BARGB1 CALL RANDOM Microchip Technology Inc. DS00617A-page 29

30 RANDHI,W BARGB2 CALL RANDOM16 RANDHI,W AARGB0 ; BCF AARGB0,MSB ; AARGB0,W RANDLO,W AARGB1 CALL RANDOM16 RANDHI,W AARGB2 RANDLO,W AARGB3 CALL FXM3224S AARGB0,W AARGB1,W AARGB2,W AARGB3,W AARGB4,W AARGB5,W AARGB6,W ; 32x24 Bit Multiplication Macros SMUL3224L macro ; Max Timing: * * * = 618 clks ; Min Timing: 2+7* * *6+5+6 = 146 clks ; PM: = 115 DM: 15 MOVLW 0x8 LOOPSM3224A BARGB2 ALSM3224NA LOOPSM3224A LOOPSM3224B BARGB1 DS00617A-page Microchip Technology Inc.

31 1995 Microchip Technology Inc. DS00617A-page 31 AN617 BLSM3224NA LOOPSM3224B MOVLW 0x7 LOOPSM3224C BARGB0 CLSM3224NA LOOPSM3224C AARGB0 AARGB1 AARGB2 AARGB3 ALOOPSM3224 BARGB2 ALSM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALSM3224NA B0,W ACCB4 ALOOPSM3224 MOVLW 0x8 BLOOPSM3224 BARGB1 BLSM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLSM3224NA B0,W

32 ACCB4 ACCB5 BLOOPSM3224 MOVLW 0x7 CLOOPSM3224 BARGB0 CLSM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W CLSM3224NA B0,W ACCB4 ACCB5 ACCB6 CLOOPSM3224 B0,W ACCB4 ACCB5 ACCB6 endm UMUL3224L macro ; Max Timing: * * *27+26 = 617 clks ; Min Timing: 2+7* * *6+5+6 = 151 clks ; PM: = 139 DM: 15 MOVLW 0x08 LOOPUM3224A BARGB2 ALUM3224NAP LOOPUM3224A LOOPUM3224B BARGB1 BLUM3224NAP LOOPUM3224B LOOPUM3224C BARGB0 DS00617A-page Microchip Technology Inc.

33 1995 Microchip Technology Inc. DS00617A-page 33 AN617 CLUM3224NAP LOOPUM3224C AARGB0 AARGB1 AARGB2 AARGB3 ALUM3224NAP BCF ALUM3224NA BLUM3224NAP BCF BLUM3224NA CLUM3224NAP BCF CLUM3224NA ALOOPUM3224 BARGB2 ALUM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALUM3224NA ACCB4 ALOOPUM3224 MOVLW 0x08 BLOOPUM3224 BARGB1 BLUM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLUM3224NA

34 ACCB4 ACCB5 BLOOPUM3224 MOVLW 0x08 CLOOPUM3224 BARGB0 CLUM3224NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W CLUM3224NA ACCB4 ACCB5 ACCB6 CLOOPUM3224 endm UMUL3123L macro ; Max Timing: * * * = 597 clks ; Min Timing: 2+7* * *6+5+6 = 146 clks ; PM: = 117 DM: 15 MOVLW 0x8 LOOPUM3123A BARGB2 ALUM3123NAP LOOPUM3123A LOOPUM3123B BARGB1 BLUM3123NAP LOOPUM3123B MOVLW 0x7 LOOPUM3123C BARGB0 CLUM3123NAP LOOPUM3123C AARGB0 DS00617A-page Microchip Technology Inc.

35 1995 Microchip Technology Inc. DS00617A-page 35 AN617 AARGB1 AARGB2 AARGB3 ALUM3123NAP BCF ALUM3123NA BLUM3123NAP BCF BLUM3123NA CLUM3123NAP BCF CLUM3123NA ALOOPUM3123 BARGB2 ALUM3123NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALUM3123NA ACCB4 ALOOPUM3123 MOVLW 0x08 BLOOPUM3123 BARGB1 BLUM3123NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLUM3123NA ACCB4 ACCB5

36 CLOOPUM3123 CLUM3123NA MOVLW endm BLOOPUM3123 0x07 BARGB0 CLUM3123NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ACCB4 ACCB5 ACCB6 CLOOPUM3123 ACCB4 ACCB5 ACCB6 SMUL3224 macro ; Max Timing: 9+7*22+8*23+7*24+8 = 523 clks ; Min Timing: 40+6 = 46 clks ; PM: *22+8*23+7*24+8 = 566 DM: 14 variable i i = 0 while i < 8 i = i + 1 i = 8 BARGB2,i SM3224NA#v(i) while i < 16 i = i + 1 i = 16 BARGB1,i-8 SM3224NA#v(i) while i < 23 DS00617A-page Microchip Technology Inc.

37 BARGB0,i-16 SM3224NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 SM3224NA0 B0,W ACCB4 i = 1 while i < 8 BARGB2,i SM3224NA#v(i) SM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3224NA#v(i) B0,W ACCB4 i = i + 1 i = 8 while i < 16 BARGB1,i-8 SM3224NA#v(i) SM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3224NA#v(i) B0,W ACCB4 ACCB Microchip Technology Inc. DS00617A-page 37

38 i = i + 1 i = 16 while i < 23 BARGB0,i-16 SM3224NA#v(i) SM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3224NA#v(i) B0,W ACCB4 ACCB5 ACCB6 i = i + 1 B0,W ACCB4 ACCB5 ACCB6 endm UMUL3224 macro ; Max Timing: 9+8*21+8*22+8*23 = 537 clks ; Min Timing: 41+6 = 47 clks ; PM: *21+8*22+8*23 = 581 DM: 14 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 BARGB2,i UM3224NA#v(i) while i < 16 i = i + 1 i = 16 BARGB1,i-8 UM3224NA#v(i) while i < 24 BARGB0,i-16 DS00617A-page Microchip Technology Inc.

39 UM3224NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM3224NA0 ACCB4 i = 1 while i < 8 BARGB2,i UM3224NA#v(i) UM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3224NA#v(i) ACCB4 i = i + 1 i = 8 while i < 16 BARGB1,i-8 UM3224NA#v(i) UM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3224NA#v(i) ACCB4 ACCB5 i = i + 1 i = 16 while i < Microchip Technology Inc. DS00617A-page 39

40 BARGB0,i-16 UM3224NA#v(i) UM3224A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3224NA#v(i) ACCB4 ACCB5 ACCB6 i = i + 1 endm UMUL3123 macro ; Max Timing: 9+7*21+8*22+7*23+7 = 500 clks ; Min Timing: 41+6 = 47 clks ; PM: *22+8*23+7*24+7 = 565 DM: 14 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 while i < 16 i = i + 1 i = 16 while i < 23 BARGB2,i UM3123NA#v(i) BARGB1,i-8 UM3123NA#v(i) BARGB0,i-16 UM3123NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM3123NA0 ACCB4 i = 1 while i < 8 BARGB2,i DS00617A-page Microchip Technology Inc.

41 UM3123NA#v(i) UM3123A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3123NA#v(i) ACCB4 i = i + 1 i = 8 while i < 16 BARGB1,i-8 UM3123NA#v(i) UM3123A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3123NA#v(i) ACCB4 ACCB5 i = i + 1 i = 16 while i < 23 BARGB0,i-16 UM3123NA#v(i) UM3123A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W 1995 Microchip Technology Inc. DS00617A-page 41

42 UM3123NA#v(i) ACCB4 ACCB5 ACCB6 i = i + 1 ACCB4 ACCB5 ACCB6 endm ; 32x24 Bit Signed Fixed Point Multiply 32x24 -> 56 ; Input: 32 bit signed fixed point multiplicand in AARGB0, AARGB1, ; AARGB2, AARGB3 ; 24 bit signed fixed point multiplier in BARGB0, BARGB1, ; BARGB2 ; Use: CALL FXM3224S ; Output: 56 bit signed fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 634 clks B > 0 ; = 652 clks B < 0 ; Min Timing: = 160 clks ; PM: = 152 DM: 15 FXM3224S BARGB0,MSB M3224SOK BARGB2 ; make multiplier BARG > 0 BARGB2 _Z DECF BARGB1 BARGB1 _Z DECF BARGB0 BARGB0 AARGB3 AARGB3 _Z DECF AARGB2 AARGB2 _Z DECF AARGB1 AARGB1 _Z DECF AARGB0 AARGB0 M3224SOK ACCB4 ; clear partial product ACCB5 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 SMUL3224L DS00617A-page Microchip Technology Inc.

43 ; 32x24 Bit Unsigned Fixed Point Multiply 32x24 -> 56 ; Input: 32 bit unsigned fixed point multiplicand in AARGB0, AARGB1, ; AARGB2, AARGB3 ; 24 bit unsigned fixed point multiplier in BARGB0, BARGB1, ; BARGB2 ; Use: CALL FXM3224U ; Output: 56 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 630 clks ; Min Timing: = 162 clks ; PM: = 151 DM: 15 FXM3224U ACCB4 ; clear partial product ACCB5 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 UMUL3224L ; 31x23 Bit Unsigned Fixed Point Divide 31x23 -> 54 ; Input: 31 bit unsigned fixed point multiplicand in AARGB0, AARGB1, ; AARGB2, AARGB3 ; 23 bit unsigned fixed point multiplier in BARGB0, BARGB1, ; BARGB2 ; Use: CALL FXM3123U ; Output: 54 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 610 clks ; Min Timing: = 157 clks ; PM: = 129 DM: 15 FXM3123U ACCB4 ; clear partial product ACCB5 ACCB6 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 UMUL3123L END C.3 32x16 PIC16C5X/PIC16CXX Fixed Point Multiply Routines ; 32x16 PIC16 FIXED POINT MULTIPLY ROUTINES VERSION 1.2 ; Input: fixed point arguments in AARG and BARG ; Output: product AARGxBARG in AARG ; All timings are worst case cycle counts 1995 Microchip Technology Inc. DS00617A-page 43

44 ; It is useful to note that the additional unsigned routines requiring a non-power of two ; argument can be called in a signed multiply application where it is known that the ; respective argument is nonnegative, thereby offering some improvement in ; performance. ; Routine Clocks Function ; FXM3216S x16 -> 48 bit signed fixed point multiply ; FXM3216U x16 -> 48 bit unsigned fixed point multiply ; FXM3115U x15 -> 46 bit unsigned fixed point multiply ; The above timings are based on the looped macros. If space permits, ; approximately clocks can be saved by using the unrolled macros. list r=dec,x=on,t=off include <PIC16.INC> ; general PIC16 definitions include <MATH16.INC> ; PIC16 math library definitions ; Test suite storage RANDHI equ 0x1A ; random number generator registers RANDLO equ 0x1B TESTCOUNT equ 0x20 ; counter DATA equ 0x21 ; beginning of test data ; Test suite for 32x16 bit fixed point multiply algorithms org 05 MAIN MOVLW RAMSTART MEMLOOP MOVLW RAMSTOP,W _Z MEMLOOP MOVLW 0x45 ; seed for random numbers RANDLO MOVLW 0x30 RANDHI MOVLW DATA BCF _RP0 BCF _RP1 BCF _IRP CALL TFXM3216 SELF SELF RANDOM16 RANDHI,W ; random number generator XORWF RANDHI,W B0 SWAPF RANDHI SWAPF RANDLO,W B1 B1,W B1 B1,W XORWF RANDHI,W SWAPF RANDHI ANDLW 0x01 B0 RANDLO XORWF RANDLO RANDHI RETEW 0 ; Test suite for FXM3216 TFXM3216 MOVLW 1 TESTCOUNT M3216LOOP CALL RANDOM16 DS00617A-page Microchip Technology Inc.

45 RANDHI,W BARGB0 BCF BARGB0,MSB RANDLO,W BARGB1 CALL RANDOM16 RANDHI,W AARGB0 BCF AARGB0,MSB AARGB0,W RANDLO,W AARGB1 CALL RANDOM16 RANDHI,W AARGB2 RANDLO,W AARGB3 CALL FXM3115U AARGB0,W AARGB1,W AARGB2,W AARGB3,W AARGB4,W AARGB5,W TESTCOUNT M3216LOOP ; 32x16 Bit Multiplication Macros SMUL3216L macro ; Max Timing: * * = 393 clks ; Min Timing: 2+7* *6+5+6 = 98 clks ; PM: = 79 DM: 11 MOVLW 0x8 LOOPSM3216A BARGB1 ALSM3216NA 1995 Microchip Technology Inc. DS00617A-page 45

46 DS00617A-page Microchip Technology Inc. LOOPSM3216A MOVLW 0x7 LOOPSM3216B BARGB0 BLSM3216NA LOOPSM3216B AARGB0 AARGB1 AARGB2 AARGB3 ALOOPSM3216 BARGB1 ALSM3216NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALSM3216NA B0,W ACCB4 ALOOPSM3216 MOVLW 0x7 BLOOPSM3216 BARGB0 BLSM3216NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLSM3216NA B0,W ACCB4

47 ACCB5 BLOOPSM3216 B0,W ACCB4 ACCB5 endm UMUL3216L macro ; Max Timing: * *26+25 = 400 clks ; Min Timing: 2+7* *6+5+6 = 103 clks ; PM: 73 DM: 11 MOVLW 0x08 LOOPUM3216A BARGB1 ALUM3216NAP LOOPUM3216A LOOPUM3216B BARGB0 BLUM3216NAP LOOPUM3216B AARGB0 AARGB1 AARGB2 AARGB3 BLUM3216NAP BCF BLUM3216NA ALUM3216NAP BCF ALUM3216NA ALOOPUM3216 BARGB1 ALUM3216NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ALUM3216NA ACCB Microchip Technology Inc. DS00617A-page 47

48 ALOOPUM3216 MOVLW 0x08 BLOOPUM3216 BARGB0 BLUM3216NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W BLUM3216NA ACCB4 ACCB5 BLOOPUM3216 endm UMUL3115L macro ; Max Timing: * * = 380 clks ; Min Timing: 2+7* *6+5+6 = 96 clks ; PM: 80 DM: 11 MOVLW 0x8 LOOPUM3115A BARGB1 ALUM3115NAP LOOPUM3115A MOVLW 0x7 LOOPUM3115B BARGB0 BLUM3115NAP LOOPUM3115B AARGB0 AARGB1 AARGB2 AARGB3 BLUM3115NAP BCF BLUM3115NA ALUM3115NAP BCF ALUM3115NA ALOOPUM3115 BARGB1 ALUM3115NA DS00617A-page Microchip Technology Inc.

49 ALUM3115NA BLOOPUM3115 BLUM3115NA MOVLW endm B3,W B2,W B2,W B1,W B1,W B0,W B0,W ACCB4 ALOOPUM3115 0x07 BARGB0 BLUM3115NA B3,W B2,W B2,W B1,W B1,W B0,W B0,W ACCB4 ACCB5 BLOOPUM3115 ACCB4 ACCB5 SMUL3216 macro ; Max Timing: 5+8+7*20+7*21+5 = 305 clks ; Min Timing: = 57 clks ; PM: *20+7*21+5 = 353 DM: 10 variable i i = 0 AARGB0,MSB 1995 Microchip Technology Inc. DS00617A-page 49

50 ACCB4 ACCB4,W ACCB5,W while i < 8 BCF i = i + 1 i = 8 BARGB1,i SM3216NA#v(i) ACCB4,7-i while i < 15 BARGB0,i-8 SM3216NA#v(i) BCF ACCB5,15-i i = i + 1 ; if we get here, BARG = 0 ACCB5 RETEW 0 SM3216NA0 ACCB4 i = 1 while i < 8 BARGB1,i SM3216NA#v(i) SM3216A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W SM3216NA#v(i) ACCB4 i = i + 1 i = 8 while i < 15 BARGB0,i-8 SM3216NA#v(i) SM3216A#v(i) B3,W B2,W DS00617A-page Microchip Technology Inc.

51 B2,W B1,W B1,W B0,W B0,W SM3216NA#v(i) ACCB4 ACCB5 i = i + 1 ACCB4 ACCB5 endm UMUL3216 macro ; Max Timing: 1+8+7*21+8*22 = 332 clks ; Min Timing: 1+2*8+2*8+6 = 39 clks ; PM: 1+2*8+2*8+6+7*21+8*22 = 362 DM: 10 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 BARGB1,i UM3216NA#v(i) while i < 16 BARGB0,i-8 UM3216NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM3216NA0 ACCB4 i = 1 while i < 8 BARGB1,i UM3216NA#v(i) UM3216A#v(i) B3,W B2,W 1995 Microchip Technology Inc. DS00617A-page 51

52 B2,W B1,W B1,W B0,W B0,W UM3216NA#v(i) ACCB4 i = i + 1 i = 8 while i < 16 BARGB0,i-8 UM3216NA#v(i) UM3216A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3216NA#v(i) ACCB4 ACCB5 i = i + 1 endm UMUL3115 macro ; Max Timing: 9+7*21+7*22+6 = 316 clks ; Min Timing: = 37 clks ; PM: *21+7*22+6 = 348 DM: 10 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 while i < 15 BARGB1,i UM3115NA#v(i) BARGB0,i-8 UM3115NA#v(i) i = i + 1 ; if we get here, BARG = 0 DS00617A-page Microchip Technology Inc.

53 RETEW 0 UM3115NA0 ACCB4 i = 1 while i < 8 BARGB1,i UM3115NA#v(i) UM3115A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3115NA#v(i) ACCB4 i = i + 1 i = 8 while i < 15 BARGB0,i-8 UM3115NA#v(i) UM3115A#v(i) B3,W B2,W B2,W B1,W B1,W B0,W B0,W UM3115NA#v(i) ACCB4 ACCB5 i = i + 1 ACCB4 ACCB5 endm 1995 Microchip Technology Inc. DS00617A-page 53

54 ; 32x16 Bit Signed Fixed Point Multiply 32x16 -> 32 ; Input: 16 bit signed fixed point multiplicand in AARGB0 ; 16 bit signed fixed point multiplier in BARGB0 ; Use: CALL FXM3216S ; Output: 32 bit signed fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 408 clks B > 0 ; = 423 clks B < 0 ; Min Timing: = 111 clks ; PM: = 98 DM: 9 FXM3216S BARGB0,MSB M3216SOK BARGB1 ; make multiplier BARG > 0 BARGB1 _Z DECF BARGB0 BARGB0 AARGB3 AARGB3 _Z DECF AARGB2 AARGB2 _Z DECF AARGB1 AARGB1 _Z DECF AARGB0 AARGB0 M3216SOK ACCB4 ; clear partial product ACCB5 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 SMUL3216L ; 32x16 Bit Unsigned Fixed Point Multiply 32x16 -> 32 ; Input: 16 bit unsigned fixed point multiplicand in AARGB0 ; 16 bit unsigned fixed point multiplier in BARGB0 ; Use: CALL FXM3216U ; Output: 32 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 412 clks ; Min Timing: = 114 clks ; PM: = 84 DM: 9 FXM3216U ACCB4 ; clear partial product ACCB5 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 DS00617A-page Microchip Technology Inc.

55 AARGB3,W B3 UMUL3216L ; 31x15 Bit Unsigned Fixed Point Divide 31x15 -> 30 ; Input: 15 bit unsigned fixed point multiplicand in AARGB0 ; 15 bit unsigned fixed point multiplier in BARGB0 ; Use: CALL FXM3115U ; Output: 30 bit unsigned fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 392 clks ; Min Timing: = 106 clks ; PM: = 91 DM: 9 FXM3115U ACCB4 ; clear partial product ACCB5 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 AARGB3,W B3 UMUL3115L END C.4 24x24 PIC16C5X/PIC16CXX Fixed Point Multiply Routines ; 24x24 PIC16 FIXED POINT MULTIPLY ROUTINES VERSION 1.2 ; Input: fixed point arguments in AARG and BARG ; Output: product AARGxBARG in AARG ; All timings are worst case cycle counts ; It is useful to note that the additional unsigned routines requiring a non-power of two ; argument can be called in a signed multiply application where it is known that the ; respective argument is nonnegative, thereby offering some improvement in ; performance. ; Routine Clocks Function ; FXM2424S x24 -> 48 bit signed fixed point multiply ; FXM2424U x24 -> 48 bit unsigned fixed point multiply ; FXM2323U x23 -> 46 bit unsigned fixed point multiply ; The above timings are based on the looped macros. If space permits, ; approximately clocks can be saved by using the unrolled macros. list r=dec,x=on,t=off include <PIC16.INC> ; general PIC16 definitions include <MATH16.INC> ; PIC16 math library definitions ; Test suite storage RANDHI equ 0x1A ; random number generator registers RANDLO equ 0x1B DATA equ 0x20 ; beginning of test data ; Test suite for 24x24 bit fixed point multiply algorithms org 05 MAIN MOVLW RAMSTART MEMLOOP MOVLW RAMSTOP 1995 Microchip Technology Inc. DS00617A-page 55

56 ,W _Z MEMLOOP MOVLW 0x45 ; seed for random numbers RANDLO MOVLW 0x30 RANDHI MOVLW DATA BCF _RP0 BCF _RP1 BCF _IRP CALL TFXM2424 SELF SELF RANDOM16 RANDHI,W ; random number generator XORWF RANDHI,W B0 SWAPF RANDHI SWAPF RANDLO,W B1 B1,W B1 B1,W XORWF RANDHI,W SWAPF RANDHI ANDLW 0x01 B0 RANDLO XORWF RANDLO RANDHI RETEW 0 ; Test suite for FXM2424 TFXM2424 CALL RANDOM16 RANDHI,W BARGB0 BCF BARGB0,MSB RANDLO,W BARGB1 CALL RANDOM16 RANDHI,W BARGB2 CALL RANDOM16 RANDHI,W AARGB0 BCF AARGB0,MSB AARGB0,W RANDLO,W AARGB1 CALL RANDOM16 RANDHI,W AARGB2 DS00617A-page Microchip Technology Inc.

57 CALL FXM2323U AARGB0,W AARGB1,W AARGB2,W AARGB3,W AARGB4,W AARGB5,W ; 24x24 Bit Multiplication Macros SMUL2424L macro ; Max Timing: * * * = 506 clks ; Min Timing: 2+7* * *6+5+5 = 145 clks ; PM: = 98 DM: 13 MOVLW 0x8 LOOPSM2424A BARGB2 ALSM2424NA LOOPSM2424A LOOPSM2424B BARGB1 BLSM2424NA LOOPSM2424B MOVLW 0x7 LOOPSM2424C BARGB0 CLSM2424NA LOOPSM2424C AARGB0 AARGB1 AARGB2 ALOOPSM2424 BARGB2 ALSM2424NA B2,W B1,W B1,W B0,W 1995 Microchip Technology Inc. DS00617A-page 57

58 DS00617A-page Microchip Technology Inc. B0,W ALSM2424NA B0,W ALOOPSM2424 MOVLW 0x8 BLOOPSM2424 BARGB1 BLSM2424NA B2,W B1,W B1,W B0,W B0,W BLSM2424NA B0,W ACCB4 BLOOPSM2424 MOVLW 0x7 CLOOPSM2424 BARGB0 CLSM2424NA B2,W B1,W B1,W B0,W B0,W CLSM2424NA B0,W ACCB4 ACCB5 CLOOPSM2424 B0,W ACCB4 ACCB5 endm

59 UMUL2424L macro ; Max Timing: * * *22+21 = 501 clks ; Min Timing: 2+7* * *6+5+5 = 150 clks ; PM: = 88 DM: 13 MOVLW 0x08 LOOPUM2424A BARGB2 ALUM2424NAP LOOPUM2424A LOOPUM2424B BARGB1 BLUM2424NAP LOOPUM2424B LOOPUM2424C BARGB0 CLUM2424NAP LOOPUM2424C AARGB0 AARGB1 AARGB2 CLUM2424NAP BCF CLUM2424NA BLUM2424NAP BCF BLUM2424NA ALUM2424NAP BCF ALUM2424NA ALOOPUM2424 BARGB2 ALUM2424NA B2,W B1,W B1,W B0,W B0,W ALUM2424NA ALOOPUM2424 MOVLW 0x08 BLOOPUM2424 BARGB1 BLUM2424NA 1995 Microchip Technology Inc. DS00617A-page 59

60 B2,W B1,W B1,W B0,W B0,W BLUM2424NA ACCB4 BLOOPUM2424 MOVLW 0x08 CLOOPUM2424 BARGB0 CLUM2424NA B2,W B1,W B1,W B0,W B0,W CLUM2424NA ACCB4 ACCB5 CLOOPUM2424 endm UMUL2323L macro ; Max Timing: * * * = 486 clks ; Min Timing: 2+7* * *6+5+5 = 145 clks ; PM: = 97 DM: 13 MOVLW 0x8 LOOPUM2323A BARGB2 ALUM2323NAP LOOPUM2323A LOOPUM2323B BARGB1 BLUM2323NAP LOOPUM2323B MOVLW 0x7 LOOPUM2323C DS00617A-page Microchip Technology Inc.

61 1995 Microchip Technology Inc. DS00617A-page 61 AN617 BARGB0 CLUM2323NAP LOOPUM2323C AARGB0 AARGB1 AARGB2 CLUM2323NAP BCF CLUM2323NA BLUM2323NAP BCF BLUM2323NA ALUM2323NAP BCF ALUM2323NA ALOOPUM2323 BARGB2 ALUM2323NA B2,W B1,W B1,W B0,W B0,W ALUM2323NA ALOOPUM2323 MOVLW 0x08 BLOOPUM2323 BARGB1 BLUM2323NA B2,W B1,W B1,W B0,W B0,W BLUM2323NA ACCB4 BLOOPUM2323 MOVLW 0x07 CLOOPUM2323

62 CLUM2323NA endm BARGB0 CLUM2323NA B2,W B1,W B1,W B0,W B0,W ACCB4 ACCB5 CLOOPUM2323 ACCB4 ACCB5 SMUL2424 macro ; Max Timing: 8+7*17+8*18+7*19+7 = 411 clks ; Min Timing: 46+5 = 51 clks ; PM: *17+8*18+7*19+7 = 466 DM: 12 variable i i = 0 while i < 8 i = i + 1 i = 8 BARGB2,i SM2424NA#v(i) while i < 16 i = i + 1 i = 16 BARGB1,i-8 SM2424NA#v(i) while i < 23 BARGB0,i-16 SM2424NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 SM2424NA0 B0,W DS00617A-page Microchip Technology Inc.

63 i = 1 while i < 8 BARGB2,i SM2424NA#v(i) SM2424A#v(i) B2,W B1,W B1,W B0,W B0,W SM2424NA#v(i) B0,W i = i + 1 i = 8 while i < 16 BARGB1,i-8 SM2424NA#v(i) SM2424A#v(i) B2,W B1,W B1,W B0,W B0,W SM2424NA#v(i) B0,W ACCB4 i = i + 1 i = 16 while i < 23 BARGB0,i-16 SM2424NA#v(i) SM2424A#v(i) B2,W B1,W B1,W B0,W B0,W SM2424NA#v(i) B0,W ACCB4 ACCB Microchip Technology Inc. DS00617A-page 63

64 i = i + 1 B0,W ACCB4 ACCB5 endm UMUL2424 macro ; Max Timing: 8+8*17+8*18+8*19 = 440 clks ; Min Timing: 49+5 = 54 clks ; PM: *17+8*18+8*19 = 490 DM: 12 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 BARGB2,i UM2424NA#v(i) while i < 16 i = i + 1 i = 16 BARGB1,i-8 UM2424NA#v(i) while i < 24 BARGB0,i-16 UM2424NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM2424NA0 i = 1 while i < 8 BARGB2,i UM2424NA#v(i) UM2424A#v(i) B2,W B1,W B1,W B0,W B0,W UM2424NA#v(i) DS00617A-page Microchip Technology Inc.

65 i = i + 1 i = 8 while i < 16 BARGB1,i-8 UM2424NA#v(i) UM2424A#v(i) B2,W B1,W B1,W B0,W B0,W UM2424NA#v(i) ACCB4 i = i + 1 i = 16 while i < 24 BARGB0,i-16 UM2424NA#v(i) UM2424A#v(i) B2,W B1,W B1,W B0,W B0,W UM2424NA#v(i) ACCB4 ACCB5 i = i + 1 endm UMUL2323 macro ; Max Timing: 8+7*17+8*18+7*19+7 = 411 clks ; Min Timing: 46+5 = 51 clks ; PM: *17+8*18+7*19+7 = 466 DM: 12 variable i i = 0 BCF ; clear carry for first right shift while i < 8 i = i + 1 i = 8 while i < 16 i = i + 1 BARGB2,i UM2323NA#v(i) BARGB1,i-8 UM2323NA#v(i) 1995 Microchip Technology Inc. DS00617A-page 65

66 i = 16 while i < 23 BARGB0,i-16 UM2323NA#v(i) i = i + 1 ; if we get here, BARG = 0 RETEW 0 UM2323NA0 i = 1 while i < 8 BARGB2,i UM2323NA#v(i) UM2323A#v(i) B2,W B1,W B1,W B0,W B0,W UM2323NA#v(i) i = i + 1 i = 8 while i < 16 BARGB1,i-8 UM2323NA#v(i) UM2323A#v(i) B2,W B1,W B1,W B0,W B0,W UM2323NA#v(i) ACCB4 i = i + 1 i = 16 while i < 23 BARGB0,i-16 UM2323NA#v(i) UM2323A#v(i) B2,W B1,W B1,W DS00617A-page Microchip Technology Inc.

67 B0,W B0,W UM2323NA#v(i) ACCB4 ACCB5 i = i + 1 ACCB4 ACCB5 endm ; 24x24 Bit Signed Fixed Point Multiply 24x24 -> 48 ; Input: 24 bit signed fixed point multiplicand in AARGB0 ; 24 bit signed fixed point multiplier in BARGB0 ; Use: CALL FXM2424S ; Output: 48 bit signed fixed point product in AARGB0 ; Result: AARG <-- AARG x BARG ; Max Timing: = 520 clks B > 0 ; = 535 clks B < 0 ; Min Timing: = 157 clks ; PM: = 126 DM: 13 FXM2424S BARGB0,MSB M2424SOK BARGB2 ; make multiplier BARG > 0 BARGB2 _Z DECF BARGB1 BARGB1 _Z DECF BARGB0 BARGB0 AARGB2 AARGB2 _Z DECF AARGB1 AARGB1 _Z DECF AARGB0 AARGB0 M2424SOK ; clear partial product ACCB4 ACCB5 AARGB0,W B0 AARGB1,W B1 AARGB2,W B2 SMUL2424L 1995 Microchip Technology Inc. DS00617A-page 67

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