From 7ac0df034356ef0b186f56591b8eff4737adcc44 Mon Sep 17 00:00:00 2001
From: Brion Vibber <brion@pobox.com>
Date: Thu, 5 Jan 2023 09:06:07 -0800
Subject: [PATCH] Added two version of 16-bit rounding

round16_incdec uses inc and dec
round16_addsub uses adc and sbc

the incdec version is the same when no rounding is needed
but saves about 8 cycles on the rounding cases, for an
average savings of 4.5 cycles for randomly distributed inputs

untested so far
---
 mandel.s | 98 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 98 insertions(+)

diff --git a/mandel.s b/mandel.s
index 2b55f78..665ea70 100644
--- a/mandel.s
+++ b/mandel.s
@@ -128,6 +128,104 @@ positive_result:
     rts ; 6 cyc
 .endproc
 
+.macro round16_incdec 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
+    ; round pos, no carry - 17
+    ; round pos, carry    - 22
+    ; round neg, no carry - 23
+    ; round neg, carry    - 28
+    ; average = 5 / 2 + (17 + 22 + 23 + 28) / 8
+    ;         = 5 / 2 + 90 / 8
+    ;         = 2.5 + 11.25 = 13.75 cycles average on evenly distributed input
+
+    lda arg + 1  ; 3 cyc
+    bpl zero     ; 2 cyc
+
+one:
+    ; check sign bit
+    lda arg + 3  ; 3 cyc
+    bpl positive ; 2 cyc
+
+negative:
+    lda arg + 2  ; 3 cyc
+    beq neg2     ; 2 cyc
+
+    dec arg + 2  ; 5 cyc
+    jmp next     ; 3 cyc
+
+neg2:
+    dec arg + 2  ; 5 cyc
+    dec arg + 3  ; 5 cyc
+    jmp next     ; 3 cyc
+
+positive:
+    inc arg + 2  ; 5 cyc
+    beq next     ; 2 cyc
+    inc arg + 3  ; 5 cyc
+
+zero:
+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
+    lda 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
+
+
 .proc iter
     ; (cx and cy should be pre-scaled to 6.26 fixed point)
     ; zx = 0