From 2340f8210ea8e54b9fafd25b5e164a524b9705d4 Mon Sep 17 00:00:00 2001
From: Brion Vibber <brion@pobox.com>
Date: Thu, 5 Jan 2023 11:32:15 -0800
Subject: [PATCH] update round & sketch out the iter cycle count

---
 mandel.s | 137 ++++++++-----------------------------------------------
 1 file changed, 19 insertions(+), 118 deletions(-)

diff --git a/mandel.s b/mandel.s
index 7701090..b69907c 100644
--- a/mandel.s
+++ b/mandel.s
@@ -176,137 +176,38 @@ next:
 
 .endmacro
 
-.macro round16_addsub arg
-    ; Round top 16 bits of 32-bit fixed-point number in-place
-    .local zero
-    .local one
-    .local positive
-    .local negative
-    .local neg2
-    .local next
-
-    ; no round -  5 cycles
-    ; one, pos - 28 cycles
-    ; one, neg - 31 cycles
-    ; average = 5 / 2 + (28 + 31) / 4
-    ;         = 5/2 + 59 / 4
-    ;         = 2.5 + 14.75
-    ;         = 17.25 cycles average on evenly distributed data
-
-    lda arg + 1  ; 3 cyc
-    bpl zero     ; 2 cyc
-
-one:
-    ; check sign bit
-    lda arg + 3  ; 3 cyc
-    bpl positive ; 2 cyc
-
-negative:
-    sec          ; 2 cyc
-    lda arg + 2  ; 3 cyc
-    sbc #1       ; 2 cyc
-    sta arg + 2  ; 3 cyc
-    lda arg + 3  ; 3 cyc
-    sbc #0       ; 2 cyc
-    sta arg + 3  ; 3 cyc
-    jmp next     ; 3 cyc
-
-positive:
-    clc          ; 2 cyc
-    lda arg + 2  ; 3 cyc
-    adc #1       ; 2 cyc
-    sta arg + 2  ; 3 cyc
-    lda arg + 3  ; 3 cyc
-    adc #0       ; 2 cyc
-    sta arg + 3  ; 3 cyc
-
-zero:
-next:
-
-.endmacro
-
-.macro round16_addsub_copy arg, dest
-    ; Round top 16 bits of 32-bit fixed-point number and copy it
-    .local zero
-    .local one
-    .local positive
-    .local negative
-    .local neg2
-    .local next
-
-    ; no round        - 17 cycles
-    ; round, positive - 31 cycles
-    ; round, negative - 31 cycles
-    ; average = 17 / 2 + (31 + 31) / 4
-    ;         = 17 / 2 + 62 / 4
-    ;         = 24 cycles average
-    ;
-    ; compare with 13.75 cyc in-place plus three copies at 12 cycles
-    ;              13.75 + 36 = 49.75 (41 - 64)
-    ; versus three rounds+copies: 72 (51 - 93)
-
-    lda arg + 1  ; 3 cyc
-    bpl zero     ; 2 cyc
-
-one:
-    ; check sign bit
-    lda arg + 3  ; 3 cyc
-    bpl positive ; 2 cyc
-
-negative:
-    sec          ; 2 cyc
-    lda arg + 2  ; 3 cyc
-    sbc #1       ; 2 cyc
-    sta dest     ; 3 cyc
-    lda arg + 3  ; 3 cyc
-    sbc #0       ; 2 cyc
-    jmp next     ; 3 cyc
-
-positive:
-    clc          ; 2 cyc
-    lda arg + 2  ; 3 cyc
-    adc #1       ; 2 cyc
-    sta dest     ; 3 cyc
-    lda arg + 3  ; 3 cyc
-    adc #0       ; 2 cyc
-    jmp next     ; 3 cyc
-
-zero:
-    lda arg + 2  ; 3 cyc
-    sta dest     ; 3 cyc
-    lda arg + 3  ; 3 cyc
-
-next:
-    sta dest + 2 ; 3 cyc
-
-
-.endmacro
 
 
 .proc iter
-    ; (cx and cy should be pre-scaled to 6.26 fixed point)
+    ; still working on the fixed-point
+    ; should we just use 16-bit adds?
+    ; does that require extra rounding?
+    ; is the integer precision right?
+
+    ; (cx and cy should be pre-scaled to 4.12 fixed point - -8..+7.9)
     ; zx = 0
     ; zy = 0
     ; zx_2 = 0
     ; zy_2 = 0
     ; zx_zy = 0
 
-    ; still working on the fixed-point
 loop:
-    ; iters++
+    ; 1627 - 2603 cyc
 
-    ; 6.26:
-    ; zx = zx_2 + zy_2 + cx
-    ; zy = zx_zy + zx_zy + cy
-    ; round to 6.10.
+    ; iters++ = 2 cyc
 
-    ; 12.20:
-    ; zx_2 = zx * zx
-    ; zy_2 = zy * zy
-    ; dist = zx_2 + zy_2
-    ; if dist >= 4 break, else continue iterating
+    ; 4.12: (-8 .. +7.9)
+    ; zx = zx_2  + zy_2  + cx   = 3 * 20 = 60 cyc
+    ; zy = zx_zy + zx_zy + cy   = 3 * 20 = 60 cyc
 
-    ; round zx_2, zy_2, dist to 6.26
+    ; 8.24:
+    ; zx_2 = zx * zx            = 470 - 780 cyc
+    ; zy_2 = zy * zy            = 470 - 780 cyc
+    ; zx_zy = zx * zy           = 470 - 780 cyc
+    ; dist = zx_2 + zy_2        = 38 cyc
+    ; if dist >= 4 break, else continue iterating = 7 cyc
+
+    ; shift and round zx_2, zy_2, dist up to 4.12 = 2 * (20 + 5) - 2 * (20 + 28) = 50 - 96 cyc
 
     ; if may be in the lake, look for looping output with a small buffer
     ; as an optimization vs running to max iters