28-byte BASIC sine generator

table   = $0400     ;; The output is a set of negated (phase-shifted by 180°)
            ;; sines between -128 and +127.
            ;; Preferably a low page. Must be paged aligned!

loop    lda #<index ;; Load 5-byte float at 'index' into FAC, the fraction of
    ldy #>index ;; which is stepped between -0/256..-255/256.
    jsr $bba2   ;; However an integer bias is also added in order to fix
            ;; the exponent and make hence it possible to increment the
            ;; fraction as a normal binary byte, e.g. a version of the
            ;; classic x86 float-to-int conversion trick.

    jsr $e277   ;; Now calculate sine of FAC. Except skip the initial part
            ;; of the BASIC function which divides by 2*PI to get
            ;; a fraction out of radians since we've already got one.
            ;; The integer bias is taken care by BASIC since sin()
            ;; is supposed to be periodic.

    lda #<bias  ;; Convert the output in FAC from a float in -1..+1 to a
    ldy #>bias  ;; fixed-point value in -128..+127 at the LSB of the
    jsr $b867   ;; mantissa by employing the same trick as before of
    lda $65     ;; adding a high integer bias.

index   .byte $88   ;; This is both a float *and* a piece of code. The exponent
    sta table   ;; ($88 corresponds to 2^8) fixes our 8-bit fraction as the
            ;; second byte of the mantissa and the STA address' LSB
            ;; (don't forget that BASIC floats are big-endian!). And $88
            ;; when interpreted as code corresponds to a harmless DEY.
            ;; Note that the STA's opcode is an integer part which only
            ;; has the effect of negating the index (the sign bit is set).
            ;; However the table address' high byte and the subsequent
            ;; INC opcode *do* serve as a small offset, shifting the
            ;; result by up to one index value. Some might even argue
            ;; that placing the table at $8000 would produce the 'proper'
            ;; rounding.
    inc *-2
    bne loop

bias    = $befa     ;; A float with an exponent of $99 (2^25) and an LSB of
;;  .byte $99   ;; zero is used to convert the output to binary. Such byte
;;  .byte $02   ;; sequences can be found in six places in the BASIC/Kernal
;;  .byte $01   ;; ROMs, at $befa/$bf04/$bf09/$fd53/$fd56/$ff38.
;;  .byte $a9   ;; A version with an LSB of $80 would have been useful to
;;  .byte $00   ;; create unsigned output (e.g. between $00 and $ff with the
            ;; origin at $80) but unfortunately doesn't seem to exist.
            ;; Values with different exponents and offsets might be found
            ;; to better suit your particular application.