In the Tasking tool chain, the parameter transforms of the first four arguments of the function will be in R12 to R16. Using C166SV2 instruction set, the micro rotations according to Equation (8) is given below as reference implementation. A fixed point number representation is used for the implementation. The registers R1, R2, R13 are assigned with X, Y, shift value respectively.

Label3: MOV R12,#0h MOV R3,R1 MOV R5,R2 ASHR R5,#0fh CMP R5,#0 JMPA cc_NZ, Label1 ; Micro rotation 1 ;I=I+(Q>>K) MOV R7,R2 ASHR R7,R13 MOV MAH,R1 CoADD R12,R7 CoSTORE R1,MAS ;Q=Q-(I_tmp>>K) ASHR R3,R13 MOV MAH,R2 CoSUB R12,R3 CoSTORE R2,MAS JMPA cc_NZ,Label 2 ; Micro rotation 2 Label1: ;I=I-(Q>>K) MOV R7, R2 ASHR R7,R13 MOV MAH,R1 CoSUB R12,R7 CoSTORE R1,MAS ; Q=Q+ (I_tmp>>K) ASHR R3, R13 MOV MAH, R2 CoADD R12, R3 CoSTORE R2,MAS Label2: ADD R13, #1h CMPD1 R6,#0h JMPR cc_NZ, Label3

The number of iterations is fixed to 15 and the direction of rotation is depended on Y, therefore there is no need to record the degree of rotation (i.e. the value of Z). This reduces the latency from n + 25 to n + 19 cycles, where 'n' is the number of iterations. In Figure 2 (in the attached PDF file ), the program flowchart of the full assembler program of the complex magnitude is shown.

Table 2 Output |

Table 3 Cycle count |

Table 4 Code Size (Bytes) |

**Computation of Sine and Cosine for an input angle**

Sine and cosine of the input angles is calculated using CORDIC. If the initial Y component of rotation transform is set to zero the rotation mode reduces to:

Where, K is the CORDIC Gain. By setting initial X component to 0.60725 the rotation process produces an unscaled version of sine and cosine term. Since the rotational angle is limited to "90^{o} and +90^{o} additional rotation is required. This is done by exploiting the symmetry property of the sine wave.

The values in other Quadrants are computed by using the relations, Sine (-Z) = -Sine (Z) and Sine (180-Z) = Sine (Z). The absolute value of the input is calculated. If the input is negative (III/IV Quadrant), then sign=1. If absolute value of the input is greater than 1/2 (II/III Quadrant), it is subtracted from 1. If sign=1, the result is negated to give the final sine result.

**Implementation.**

The input vector Z contains the angle in radians between [-,] which is normalized between (-1, 1) in 1Q15 format (Z=Z rad/). For example, 45^{o}=/4 is equivalent to Z =1/4 =0.25 (8192 in 1Q15 format. Denormalisation is done in the algorithm.

The algorithm is presented in a 'C' like pseudo code. Note that the Cos Θ constant for this algorithm is 0.60725. We also assume that the 12 values of tan-1 (1/2i) are stored as a look up table in 4Q12 format.

Using C166SV2 instruction set, the micro rotations according to Equation (7) is given below as reference implementation. A fixed point number representation is used for the implementation. The registers R1, R2, R11 and R13 are assigned with X, Y, Z, shift value respectively.

Label3: MOV R12,#0h MOV R3,R1 MOV R5,R2 ASHR R5,#0fh CMP R5,#0 JMPA cc_NZ, Label1 ; Micro rotation 1 ;I=I+(Q>>K) MOV R7,R2 ASHR R7,R13 MOV MAH,R1 CoADD R12,R7 CoSTORE R1,MAS ;Q=Q-(I_tmp>>K) ASHR R3,R13 MOV MAH,R2 CoSUB R12,R3 CoSTORE R2,MAS ;Z=Z+atan(K[L]) MOV MAH,R11 CoADD R12,[R4+] CoSTORE R11,MAS JMPA cc_NZ,Label 2 ; Micro rotation 2 Label1: ;I=I-(Q>>K) MOV R7, R2 ASHR R7,R13 MOV MAH,R1 CoSUB R12,R7 CoSTORE R1,MAS ; Q=Q+ (I_tmp>>K) ASHR R3, R13 MOV MAH, R2 CoADD R12, R3 CoSTORE R2,MAS ;Z=Z-atan(K[L]) MOV MAH,R11 CoSUB R12,[R4+] CoSTORE R11,MAS Label2: ADD R13, #1h CMPD1 R6,#0h JMPR cc_NZ, Label3

We cannot neglect the angle information as in complex magnitude, since the direction of rotation is dependent on Z Parameter. To denormalize, the input is multiplied by 4DBAh (4Q12 format). Therefore the lookup table value (tan-1 (1/2i)) has to be in 4Q12 format. Due to this the number of iterations is reduced to 12.