8-bit Sine Approximation using bit twiddling

sine-approx.py

#!/usr/bin/python3

# This is ported from:
#    https://www.omnimaga.org/asm-language/sine-approximation-(z80)/
# (Xeda112358  a.k.a.  Zeda  a.k.a.  ZedaZ80)
#

from math import sin

def sineb(x):
    """Approximates 128*sin(x*2*pi/256)"""

    a1 = int(x)
    a0 = a1 << 1
    a2 = a1 >> 1

    # iteration 1
    if a1 & 64:
        l = ~a0 & 127
    else:
        l =  a0 & 127

    # iteration 2
    if a1 & 32:
        l += ~a1 & 31   # 30 will have better overall accuracy, but a more jagged curve
    else:
        l +=  a1 & 31   # 30

    # iteration 3
    if a1 & 16:
        l += ~a2 & 7    # 6 will have better overall accuracy, but a more jagged curve
    else:
        l +=  a2 & 7    # 6

    # check if it needs to be negated
    if a1 & 128:
        return -l
    else:
        return l

# Plot a graph of the approximation vs the actual
for x in range(0, 256, 2):
    y = sineb(x)
    z = int(sin(x*3.1415926535/128)*128)

    # translate and scale for "graphing"
    y += 128
    z += 128
    y >>= 1
    z >>= 1

    # "graph"
    #    X - Approximation
    #    O - Actual
    #    8 - used when the graphs overlap
    if y == z:
        print(" "*y + "8")
    elif y > z:
        print(" "*z + "O" + " "*(y-z-1) + "X")
    else:
        print(" "*y + "X" + " "*(z-y-1) + "O")

sine-approx.z80

cosine:
; same inputs/outputs as sine
    add a,64  ; cos(x) = sin(x + pi/2)

sine:
;Approximates 128*sin(A*2*pi/256)
;Input:
;    A is the input, [0, 256) map to [0, 2pi)
;Output:
;    A is the result
;    C is a copy of the input
;Destroys:
;    B, L
;
;Speed: 137cc or 149cc (if the input is >= 128)
;Size: 37 bytes
;
    ld c,a      ; a1
    add a,a
    add a,a
    ld b,a      ; a2
    sbc a,a
    xor b
    rra
    ld l,a

    ld a,c
    and 32
    add a,-32
    sbc a,a
    xor c
    and 31          ; Change to `30` for a jagged curve, but better average performance
    add a,l
    ld l,a

    ld a,c
    rra
    ld b,a
    and 8
    add a,-8
    sbc a,a
    xor b
    and 7           ; Change to `6` for a jagged curve, but better average performance
    add a,l

    bit 7,c
    ret z
    neg
    ret