PIC Microcontoller Basic Math Multiplication Methods

• 4x4 bit from John Payson, Ray Gardiner, Dmitry Kiryashov (12 cycles/ 12 instructions)
• 8x8 bit from Andrew Warren (10 or 35 instructions, 38 cycles)
• 8x8 bit from unknown author (please step forward) (35 instructions, 37 cycles)
• 8x8 bit from Scott Dattalo with small correction by Dmitry Kiryashov (52 instructions, 24-36 cycles, 34 avg)
• 16x8 bit from Dingbat
• 16x8 bit from Martin Sturm (18 instructions, 84-124 cycles, 104 avg)
• 16x8 bit from Martin Sturm (69 instructions, 69 cycles)
• 10x10 bit from Martin Sturm (73 instructions, 57-73 cycles, 65 avg)
• 14x10 bit from Martin Sturm (83 instructions, 71-83 cycles, 77 avg)
• 12x12 bit from Martin Sturm (92 instructions, 92 cycles)
• 16x16 bit from Martin Sturm (140 instructions, 140 cycles)
• 16x16 bit from Jim Bixby Unsigned, fast (16x16 mpy in 164 instructions ~168 cycles):
• 16x16 bit macro from Bob Fehrenbach, Scott Dattalo (22 instructions, 215 to 295 cycles)
• 16x16 bit From Clyde Smith-Stubbs of HI-TECH software (21 instructions, < 289 cycles)
• 16x16 bit from malin. Unsigned (32 instructions, 128 to 229 cycles)
• 16x16 bit from malin. Signed. (64 instructions, 134 to 248 cycles)
• 16x16 bit from Ravi Pailoor Signed or Unsigned (240 instructions, < 282 cycles)
• 24x8 bit from Byron A Jeff
• 24x24 bit from Nikolai Golovchenko
• 24x24 bit from Fred Maher with Tutorial
• 32x16 bit from anonymous
• 32x16 bit from VegiPete for 18F
• 32-bit signed integer math routines. add, subtract, multiply, divide, round, sqrt, bin2dec, dec2bin. By Peter Hemsley.
• Tutorial1 Logic based
• Tutorial2 Math based
• Russian Peasent Multiplication and Exponentiation
• Novel Methods of Integer Multiplication and Division
• Multiplication and/or Division by a Constant
• (8 bits * 256) / 8 bits by Nikolai Golovchenko
• See also:
  • http://www.iversoft.com/piclist/9802/0021.shtml
  • http://www.myke.com/PICMicro/16bit.htm

Archive:

• PICList post "18 series vs. 16 series" How to multiply two 16 bit values useing only 3 multiplications
• PICList post "multiplication routing 24x8"
• PICList post "Looking for improved integer's math routines"

Interested:

See:

• /techref/piclist/pcbcontest.htm PICList free PCB contest
• /techref/microchip/dttwist.htm Scott Dattalos' Dual Tone Digital Twist for the PIC
• /techref/microchip/seepicsrc/psbpix/multiplication.htm , microchip, seepicsrc, psbpix, multiplication

Code:

See also:

• http://www.reenigne.org/blog/multiplying-faster-with-squares/ (a+b)² = a² + b² + 2ab and (a-b)² = a² + b² - 2ab and subtracting these gives: 4ab = (a+b)² - (a-b)² or ab = (a+b)²/4 - (a-b)²/4. So if we keep in memory a table of x²/4 we can do a multiply with an add, two subtractions and two table lookups. The tables have a+b number of entries rather than a*b, but must hold values as large as a*b if the full range of possible output is to be supported.

Questions: