Why are there different casts in the generated code for signed and unsigned values in the Fixed-Point Toolbox 2.1 (R2007b)?

I generate code for the attached model. The data conversion code for an unsigned value (line 41) uses an intermediate cast to uint32, where for the signed value this intermediate cast is not inserted (line 47) (code see below)

Can you please explain the difference or explain why the cast is needed or done in the unsigned case and ignored for the signed case. (when changing the hardware configurations to a 16-bit processor, the cast appears in both cases.)

The code is generated using R2007b

     35   /* Output and update for atomic system: '<Root>/input scaling' */ 

     36   void casting_question_M_inputscaling(void) 

     37   { 

     38     /* DataTypeConversion: '<S2>/Data Type Conversion' incorporates: 

     39      *  Constant: '<Root>/Constant' 

     40      */ 

     41     casting_question_MPS_B.DataTypeConversion = (uint16_T)((uint32_T) 

     42       casting_question_MPS_P.Constant_Value * 16777U >> 11); 

     43   

     44     /* DataTypeConversion: '<S2>/Data Type Conversion1' incorporates: 

     45      *  Constant: '<Root>/Constant1' 

     46      */ 

     47     casting_question_MPS_B.DataTypeConversion1 = (int16_T) 

     48       (casting_question_MPS_P.Constant1_Value * 16777 >> 12); 

     49   }When

Answer 1

[MathWorks Support Team]

The missing cast is due to different scaling factors, see the explaination:

For cast, ideal real world behavior is

V1 = V2;

Replace with scaling equations, assuming zero bias

 S1 * Q1 = S2*Q2

Solve for output stored integer

 Q1 = (S2/S1) * Q2

For UNSiGNED CAST, substitute actual scaling

    Q1 = (0.001/2^-13) * Q2

    Q1 = 8.192 * Q2

The generated code is

    Q1 = Q2 * 16777U >> 11

Assuming ideal math with no overflows, etc, this is mathematically equivalent to

    Q1 = Q2 * 8.19189453125

So * 16777 >> 11 is a fixed point approximation of 8.192

For the SIGNED CAST, the output scaling is different by a factor of two

    Q1 = (0.001/2^-12) * Q2

    Q1 = 4.096 * Q2

The generated codes * 16777 >> 12 is a fixed point approximation of 4.096.