by Tony Tooth, January 2016. Edited by Tony Tooth April 2018
Randall Hyde's book “The Art of Assembly Language” omits to cover or even mention the fscale instruction in the main text or in the index, although it is in his Table B-2: Floating Point Instruction Set.
fscale (I discovered only late in 2015 - after more than 10 years experience programming in assembly language) is a fast and efficient way to implement the exponential function in assembly language. The way I did this hitherto was incredibly cumbersome. I have written a simple sub-routine in assembly language to illustrate the use of fscale. Note that my illustrative routine does not check for out-of-bounds numbers.
DEF FN_fractpower(num, pow) LOCAL pass&, res PRIVATE Fract%, P% num = 1.0*num : pow = 1.0*pow IF Fract% = 0 THEN DIM P% 1000 FOR pass& = 0 TO 2 STEP 2 [opt pass& .Fract% finit fld tbyte [^num] fld1 fxch st1 fyl2x ;Calculates st1 = st1*lg2(st0) where st = 1.0 & pops st0 fld tbyte [^pow] fmulp st1,st0 ;Calculates N = pow*lg2(num) fld st0 ;Make a copy 0f what's at st0, so st1 & st0 are the same number frndint ;Round st0 t0 the nearest Integer fsub st1,st0 ;Calculates Ans = N - Int(N) where Ans will be between -1.0 & +1.0 fxch st1 ;Exchange st1 with st0 f2xm1 ;Calculate 2^Ans - 1 fld1 faddp st1,st0 ;Add 1 t0 the above so we have left 2^Ans fscale ;Automatically calculates st0 = (2^st1)*st0 which is 2^N = num^pow fstp st1 ;Throw away st1 fstp tbyte [^res] ;Answer is at st0 ret ] NEXT pass& ENDIF CALL Fract% = res
Edit by Richard Russell, January 2016:
An alternative way of computing the exponential function in BB4W v6 assembly language is to call the internal EXP routine, which is exposed via the @fn%() jump table, as follows (it uses fscale internally):
@% = &1415 REPEAT INPUT '"Enter a value: " x PRINT "BBC version of EXP(x) = "; EXP(x) PRINT "ASM version of EXP(x) = "; FNexp(x) UNTIL FALSE END DEF FNexp(x) LOCAL P%, y PRIVATE X% IF X% = 0 THEN DIM P% 50 [OPT 2 .X% mov edx,[^x] mov ecx,[^x+4] mov bx,[^x+8] call @fn%(16) ; xexp mov [^y],edx mov [^y+4],ecx mov [^y+8],bx ret ] ENDIF x *= 1.0 CALL X% = y