Routines
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14211: THE 'REDUCE ARGUMENT' SUBROUTINE (offset 57)
The address of this routine is found in the table of addresses. It is called via the calculator literal 57 by the routines at cos and sin.
This subroutine transforms the argument X of SIN X or COS X into a value V.
The subroutine first finds the value Y=X/2π-INT(X/2π+0.5), where -0.5<=Y<0.5.
The subroutine returns with:
  • V=4*Y if -1<=4*Y<=1 (case i)
  • or V=2-4*Y if 1<4*Y<2 (case ii)
  • or V=-4*Y-2 if -2<=4*Y<-1 (case iii)
In each case, -1<=V<=1 and SIN (πV/2)=SIN X.
get_argt 14211 RST 40 X
14212 DEFB 61 re_stack: X (in full floating-point form)
14213 DEFB 52 stk_data: X, 1/2π
14214 DEFB 238,34,249,131,110
14219 DEFB 4 multiply: X/2π
14220 DEFB 49 duplicate: X/2π, X/2π
14221 DEFB 162 stk_half: X/2π, X/2π, 0.5
14222 DEFB 15 addition: X/2π, X/2π+0.5
14223 DEFB 39 int: X/2π, INT (X/2π+0.5)
14224 DEFB 3 subtract: X/2π-INT (X/2π+0.5)=Y
Note: adding 0.5 and taking INT rounds the result to the nearest integer.
14225 DEFB 49 duplicate: Y, Y
14226 DEFB 15 addition: 2*Y
14227 DEFB 49 duplicate: 2*Y, 2*Y
14228 DEFB 15 addition: 4*Y
14229 DEFB 49 duplicate: 4*Y, 4*Y
14230 DEFB 42 abs: 4*Y, ABS (4*Y)
14231 DEFB 161 stk_one: 4*Y, ABS (4*Y), 1
14232 DEFB 3 subtract: 4*Y, ABS (4*Y)-1=Z
14233 DEFB 49 duplicate: 4*Y, Z, Z
14234 DEFB 55 greater_0: 4*Y, Z, (1/0)
14235 DEFB 192 st_mem_0: (mem-0 holds the result of the test)
14236 DEFB 0 jump_true to ZPLUS: 4*Y, Z
14237 DEFB 4
14238 DEFB 2 delete: 4*Y
14239 DEFB 56 end_calc: 4*Y=V (case i)
14240 RET Finished.
If the jump was made then continue.
ZPLUS 14241 DEFB 161 stk_one: 4*Y, Z, 1
14242 DEFB 3 subtract: 4*Y, Z-1
14243 DEFB 1 exchange: Z-1, 4*Y
14244 DEFB 54 less_0: Z-1, (1/0)
14245 DEFB 0 jump_true to YNEG: Z-1
14246 DEFB 2
14247 DEFB 27 negate: 1-Z
YNEG 14248 DEFB 56 end_calc: 1-Z=V (case ii) or Z-1=V (case iii)
14249 RET Finished.
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