shave some cycles off 16-bit squaring with shift instead of add

also fix the comments about how many cycles shift takes

mandel.s

@@ -129,11 +129,8 @@ KEY_0     = 50
     mantissa .byte 5
 .endstruct
 
-.import mul_lobyte256
-.import mul_hibyte256
-.import mul_hibyte512
-.import sqr_lobyte
-.import sqr_hibyte
+.import mul_lobyte
+.import mul_hibyte
 
 .data
 
@@ -351,7 +348,7 @@ viewport_oy:
     sub 4, dest, arg1, arg2
 .endmacro
 
-; 3 + 5 * bytes cycles
+; 3 + 5 * (bytes - 1) cycles
 .macro shl bytes, arg
     asl arg              ; 3 cyc
     .repeat bytes-1, i
@@ -359,17 +356,17 @@ viewport_oy:
     .endrepeat
 .endmacro
 
-; 13 cycles
+; 8 cycles
 .macro shl16 arg
     shl 2, arg
 .endmacro
 
-; 18 cycles
+; 13 cycles
 .macro shl24 arg
     shl 3, arg
 .endmacro
 
-; 23 cycles
+; 18 cycles
 .macro shl32 arg
     shl 4, arg
 .endmacro
@@ -445,21 +442,13 @@ viewport_oy:
 ; clobbers a, x
 .macro sqr8 dest, arg
     ldx arg
-    lda sqr_lobyte,x
+    txa
+    lsr
+    lda mul_lobyte,x
+    rol
     sta dest
-    lda sqr_hibyte,x
-    sta dest + 1
-.endmacro
-
-; clobbers a, x
-.macro sqr8_add16 dest, arg
-    ldx arg
-    clc
-    lda sqr_lobyte,x
-    adc dest
-    sta dest
-    lda sqr_hibyte,x
-    adc dest + 1
+    lda mul_hibyte,x
+    rol
     sta dest + 1
 .endmacro
 
@@ -548,22 +537,25 @@ bank_switch_table:
             clc                   ; 2 cyc         
             adc mul_factor_x      ; 3 cyc
             tax                   ; 2 cyc
-            bcc under256          ; 2 cyc
-            lda mul_hibyte512,x   ; 4 cyc
-            bcs next              ; 2 cyc
-        under256:
-            lda mul_hibyte256,x   ; 4 cyc
-            sec                   ; 2 cyc
+            lda mul_hibyte,x      ; 4 cyc
+            bcc next              ; 2 cyc
+            ; carry is set so we get to add 1 for free, but need to add 0x80
+            adc #$7f              ; 2 cyc
+            clc                   ; 2 cyc
+            ; stash the sum temporarily so we can use it as an operand to add
+            stx mul_product_lo    ; 3 cyc
+            adc mul_product_lo    ; 3 cyc
         next:
+            sec                   ; 2 cyc
             sta mul_product_hi    ; 3 cyc
-            lda mul_lobyte256,x   ; 4 cyc
+            lda mul_lobyte,x      ; 4 cyc
 
             ; - a^2/2
             ldx mul_factor_a      ; 3 cyc
-            sbc mul_lobyte256,x   ; 4 cyc
+            sbc mul_lobyte,x      ; 4 cyc
             sta mul_product_lo    ; 3 cyc
             lda mul_product_hi    ; 3 cyc
-            sbc mul_hibyte256,x   ; 4 cyc
+            sbc mul_hibyte,x      ; 4 cyc
             sta mul_product_hi    ; 3 cyc
 
             ; + x & a & 1:
@@ -582,10 +574,10 @@ bank_switch_table:
             ; - x^2/2
         small_product:
             sec                   ; 2 cyc
-            sbc mul_lobyte256,x   ; 4 cyc
+            sbc mul_lobyte,x      ; 4 cyc
             sta mul_product_lo    ; 3 cyc
             lda mul_product_hi    ; 3 cyc
-            sbc mul_hibyte256,x   ; 4 cyc
+            sbc mul_hibyte,x      ; 4 cyc
             sta mul_product_hi    ; 3 cyc
         .endscope
     .endif
@@ -792,18 +784,14 @@ arg2_pos:
         ; h*h*256*256 + h*l*256 + h*l*256 + l*l
 
         sqr8 result, arg
-        lda #0
-        sta result + 2
-        sta result + 3
+        sqr8 result + 2, arg + 1
 
         imul8 inter, arg + 1, arg, xe
-        add16 result + 1, result + 1, inter
+        shl16 inter
         add_carry result + 3
         add16 result + 1, result + 1, inter
         add_carry result + 3
 
-        sqr8_add16 result + 2, arg + 1
-
         rts ; 6 cyc
     .endscope
 .endmacro

tables.js

@@ -11,40 +11,19 @@ function db(func) {
     return lines.join('\n');
 }
 
-let squares = [];
-for (let i = 0; i < 512; i++) {
-    squares.push(Math.trunc((i * i + 1) / 2));
-}
-
 console.log(
 `.segment "TABLES"
 
-.export mul_lobyte256
-.export mul_hibyte256
-.export mul_hibyte512
-.export sqr_lobyte
-.export sqr_hibyte
+.export mul_lobyte
+.export mul_hibyte
 
-; (i * i + 1) / 2 for the multiplier
+; (i * i) / 2 for the multiplier
 .align 256
-mul_lobyte256:
-${db((i) => squares[i] & 0xff)}
+mul_lobyte:
+${db((i) => ((i * i) >> 1) & 0xff)}
 
 .align 256
-mul_hibyte256:
-${db((i) => (squares[i] >> 8) & 0xff)}
-
-.align 256
-mul_hibyte512:
-${db((i) => (squares[i + 256] >> 8) & 0xff)}
-
-; (i * i) for the plain squares
-.align 256
-sqr_lobyte:
-${db((i) => (i * i) & 0xff)}
-
-.align 256
-sqr_hibyte:
-${db((i) => ((i * i) >> 8) & 0xff)}
+mul_hibyte:
+${db((i) => ((i * i) >> 9) & 0xff)}
 
 `);