Why does the amplitude have halved by using arm_rfft_q15 ?

[LLily.1]

I was trying to use arm_rfft_q15 .In the CMSIS documentation for arm_rfft_q15, it says the output format is Q7.9 and 6 bits should be upscaled when the input RFFT size is 128 .

Why does the amplitude have halved by using arm_rfft_q15 ?

 uint16_t i;

 float32_t testout[128],testoutf[128],amplitude;

arm_rfft_instance_q15 SS;

 static q15_t testInput_q15[128];

static q15_t testOutput[256];

arm_rfft_init_q15(&SS,128,0,1);

 for(i=0;i<128;i++)

{

 testInput_q15[i]= arm_sin_q15(256*i);

}

 arm_rfft_q15(&SS, testInput_q15, testOutput);

for(i=0;i<128;i++)

 {

testoutf[i]= (float32_t)testOutput[i]/512;

}

arm_cmplx_mag_f32(testoutf,testout,64);

 amplitude=testout[1]/64;

[RMcCa]

Read up on the meaning of the q data type & fixed point dsp. Scaling inputs and outputs is common and is used to get maximum resolution while preventing overflows​.

Also, what do 512 and 64 mean in your code? You need to be careful about data types and constants to prevent the compiler ​from doing things you might not expect. Hint: 512 is not the same number as 512.0f.