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--- base:fastest_multiplication [2017-04-19 09:47] – repose
+++ base:fastest_multiplication [2023-08-21 02:45] – repose
@@ Line 9: / Line 9: @@
 Mine: 196 zp variation: 192 \\
 Times above need to add 12 for jsr/rts \\
+Note: updated 2023; corrected typos and timings \\
 <code>
@@ Line 15: / Line 16: @@
 ;and being less elegant and harder to follow.
 ;by Repose 2017
+;table generator by Graham
+;addition improvement suggested by JackAsser
+;data: 2044 bytes
+;zero page ram required: minimum 8 bytes, ideally 14
+;do_add: 30 bytes in zp, if used
+;time: 196 cycles, option for 192 if you use 30 more zp bytes for do_add
+;measurement method: average timings over all input combinations
+;How to use:
+;put numbers in x/y and result is Y reg, X reg, z1, z0
 ;tables of squares
@@ Line 35: / Line 47: @@
 y0=$fd;multiplicand, 2 bytes
 y1=$fe
-z0=$80;product, 4 bytes
+z0=$80;product, 2 bytes
 z1=$81
-z2=$82
+z2=$82 ;returned in X reg
-z3=$83
+z3=$83 ;returned in Y reg
 ;Example showing use
@@ Line 46: / Line 58: @@
 sta y0
 sta y1
-jsr maketables
+jsr makesqrtables
 jsr umult16
+stx z2
+sty z3
 ;result should be $fffe0001, e.g. as viewed with a typical m 0080 monitor command:
 ;0080 01 00 fe ff
@@ Line 110: / Line 124: @@
 sta p_invsqr_hi;17
-ldy y0
 sec
+ldy y0
 lda (p_sqr_lo),y
-sbc (p_invsqr_lo),y;note these two lines taken as 11 total
+sbc (p_invsqr_lo),y;note these two lines taken as 10.996 total or 10+65280/65536
 sta z0;x0*y0l
 lda (p_sqr_hi),y
 sbc (p_invsqr_hi),y
-sta c1a+1;x0*y0h;31
+sta c1a+1;x0*y0h; 2+3+10.996+3+10.996+4=33.992
 ;c1a means column 1, row a (partial product to be added later)
 ldy y1
-;sec  ;notice that the high byte of sub above is always +ve
+;sec  ;notice that the high byte of subtraction above is always positive, leaving Carry set
 lda (p_sqr_lo),y
 sbc (p_invsqr_lo),y
@@ Line 127: / Line 141: @@
 lda (p_sqr_hi),y
 sbc (p_invsqr_hi),y
-sta c2a+1;x0*y1h;31
+sta c2a+1;x0*y1h; 3+10.996+4+10.996+4=32.992
 ;set multiplier as x1
@@ Line 144: / Line 158: @@
 lda (p_sqr_hi),y
 sbc (p_invsqr_hi),y
-sta c2b+1;x1*y1h;31
+sta c2b+1;x1*y1h;32.992
 ldy y1
@@ Line 153: / Line 167: @@
 lda (p_sqr_hi),y
 sbc (p_invsqr_hi),y
-tay;x1*y1h;Y=z3, 30 cycles
+tay;x1*y1h;Y=z3, 30.992 cycles
-;17+33+31+17+31+30=159
+;17+34+33+17+33+31=164.97 cycles for main multiply part (minimum=157, maximum=173)
+;jmp do_adds; can put do_adds in zp for a slight speed increase
 do_adds:
 ;-add the first two numbers of column 1
@@ Line 188: / Line 203: @@
 Diagram of the additions
-                  y1  y0
+                y1    y0
-               x  x1  x0
+             x  x1    x0
-               ---------
+                --------
              x0y0h x0y0l
 +      x0y1h x0y1l