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	:;

1A74:C
	:#; start of loop.
	:#
	:#;; SWAP-BYTE
1A74 1A         ld a, (de)	:C SWAP_BYTE
	:; each byte of second

1A75:C
1A75 4E         ld c, (hl)	:C
	:; each byte of first

1A76:C
1A76 EB         ex de, hl	:C
	:; swap pointers

1A77:C
1A77 12         ld (de), a	:C
	:; store each byte of first

1A78:C
1A78 71         ld (hl), c	:C
	:; store each byte of second

1A79:C
1A79 23         inc hl	:C
	:; advance both

1A7A:C
1A7A 13         inc de	:C
	:; pointers.

1A7B:C
1A7B 10F7       djnz $1A74	:C
	:; loop back to SWAP-BYTE until all 5 done.
	:;

1A7D:C
1A7D EB         ex de, hl	:C
	:; even up the exchanges
	:; so that DE addresses STKEND.

1A7E:C
1A7E C9         ret	:C
	:; return.
	:;

1A7F:C
	:#; ---------------------------------
	:#; THE 'SERIES GENERATOR' SUBROUTINE
	:#; ---------------------------------
	:#; offset $86: 'series-06'
	:#; offset $88: 'series-08'
	:#; offset $8C: 'series-0C'
	:#; The ZX81 uses Chebyshev polynomials to generate approximations for
	:#; SIN, ATN, LN and EXP. These are named after the Russian mathematician
	:#; Pafnuty Chebyshev, born in 1821, who did much pioneering work on numerical
	:#; series. As far as calculators are concerned, Chebyshev polynomials have an
	:#; advantage over other series, for example the Taylor series, as they can
	:#; reach an approximation in just six iterations for SIN, eight for EXP and
	:#; twelve for LN and ATN. The mechanics of the routine are interesting but
	:#; for full treatment of how these are generated with demonstrations in
	:#; Sinclair BASIC see "The Complete Spectrum ROM Disassembly" by Dr Ian Logan
	:#; and Dr Frank O'Hara, published 1983 by Melbourne House.
	:#
	:#;; series-xx
1A7F 47         ld b, a	:C series_xx
	:; parameter $00 - $1F to B counter

1A80:C
1A80 CDA019     call $19A0	:C
	:; routine GEN-ENT-1 is called.
	:; A recursive call to a special entry point
	:; in the calculator that puts the B register
	:; in the system variable BREG. The return
	:; address is the next location and where
	:; the calculator will expect its first
	:; instruction - now pointed to by HL'.
	:; The previous pointer to the series of
	:; five-byte numbers goes on the machine stack.
	:;

1A83:B
	:#; The initialization phase.
	:#
1A83-1A83 2D	:B
	:;;duplicate       x,x

1A84:B
1A84-1A84 0F	:B
	:;;addition        x+x

1A85:B
1A85-1A85 C0	:B
	:;;st-mem-0        x+x

1A86:B
1A86-1A86 02	:B
	:;;delete          .

1A87:B
1A87-1A87 A0	:B
	:;;stk-zero        0

1A88:B
1A88-1A88 C2	:B
	:;;st-mem-2        0
	:;

1A89:B
	:#; a loop is now entered to perform the algebraic calculation for each of
	:#; the numbers in the series
	:#
	:#;; G-LOOP
1A89-1A89 2D	:B G_LOOP
	:;;duplicate       v,v.

1A8A:B
1A8A-1A8A E0	:B
	:;;get-mem-0       v,v,x+2