From aee587388de88e35e8f3b345898bd4abc9acf3ed Mon Sep 17 00:00:00 2001
From: Jamey Sharp <jamey@minilop.net>
Date: Tue, 31 Dec 2024 02:01:45 -0800
Subject: [PATCH] eliminate mul_hibyte512 table

This costs an extra half cycle on average, assuming uniform distribution
of multiplication inputs. I don't think a half cycle is worth an extra
256-byte table.
---
 mandel.s  | 30 ++++++++++++++++--------------
 tables.js | 24 +++++++-----------------
 2 files changed, 23 insertions(+), 31 deletions(-)

diff --git a/mandel.s b/mandel.s
index fc30532..ec1b086 100644
--- a/mandel.s
+++ b/mandel.s
@@ -129,9 +129,8 @@ KEY_0     = 50
     mantissa .byte 5
 .endstruct
 
-.import mul_lobyte256
-.import mul_hibyte256
-.import mul_hibyte512
+.import mul_lobyte
+.import mul_hibyte
 .import sqr_lobyte
 .import sqr_hibyte
 
@@ -548,22 +547,25 @@ 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 +584,10 @@ 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
diff --git a/tables.js b/tables.js
index 50cbef9..f4802ce 100644
--- a/tables.js
+++ b/tables.js
@@ -11,32 +11,22 @@ 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 mul_lobyte
+.export mul_hibyte
 .export sqr_lobyte
 .export sqr_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)}
+mul_hibyte:
+${db((i) => ((i * i) >> 9) & 0xff)}
 
 ; (i * i) for the plain squares
 .align 256