BBC BASIC Programmers' Reference

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