How to perform uint32/float conversion with SSE?

Question

In SSE there is a function _mm_cvtepi32_ps(__m128i input) which takes input vector of 32 bits wide signed integers (int32_t) and converts them into floats.

Now, I want to interpret input integers as not signed. But there is no function _mm_cvtepu32_ps and I could not find an implementation of one. Do you know where I can find such a function or at least give a hint on the implementation? To illustrate the the difference in results:

unsigned int a = 2480160505; // 10010011 11010100 00111110 11111001   
float a1 = a; // 01001111 00010011 11010100 00111111;  
float a2 = (signed int)a; // 11001110 11011000 01010111 10000010

Answer 1

I think Paul's answer is nice, but it fails for v=4294967295U (=2^32-1). In that case v2=2^31-1 and v1=2^31. Intrinsic _mm_cvtepi32_ps converts 2^31 to -2.14748365E9 . v2=2^31-1 is converted to 2.14748365E9 and consequently _mm_add_ps returns 0 (due to rounding v1f and v2f are the exact opposite of each other).

The idea of the solution below is to copy the most significant bit of v to v_high. The other bits of v are copied to v_low. v_high is converted to 0 or 2.14748365E9 .

inline __m128 _mm_cvtepu32_v3_ps(const __m128i v)
{
__m128i msk0=_mm_set1_epi32(0x7FFFFFFF);
__m128i zero=_mm_xor_si128(msk0,msk0);
__m128i cnst2_31=_mm_set1_epi32(0x4F000000); /* IEEE representation of float 2^31 */

__m128i v_high=_mm_andnot_si128(msk0,v);
__m128i v_low=_mm_and_si128(msk0,v);
__m128  v_lowf=_mm_cvtepi32_ps(v_low);
__m128i msk1=_mm_cmpeq_epi32(v_high,zero);
__m128  v_highf=_mm_castsi128_ps(_mm_andnot_si128(msk1,cnst2_31));  
__m128  v_sum=_mm_add_ps(v_lowf,v_highf);
return v_sum;

}

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Update

It was possible to reduce the number of instructions:

inline __m128 _mm_cvtepu32_v4_ps(const __m128i v)
{
__m128i msk0=_mm_set1_epi32(0x7FFFFFFF);
__m128i cnst2_31=_mm_set1_epi32(0x4F000000);

__m128i msk1=_mm_srai_epi32(v,31);
__m128i v_low=_mm_and_si128(msk0,v);
__m128  v_lowf=_mm_cvtepi32_ps(v_low);
__m128  v_highf=_mm_castsi128_ps(_mm_and_si128(msk1,cnst2_31));  
__m128  v_sum=_mm_add_ps(v_lowf,v_highf);
return v_sum;
}

Intrinsic _mm_srai_epi32 shifts the most significant bit of v to the right, while shifting in sign bits, which turns out to be quite useful here.

Answer 2

This functionality exists in AVX-512, but if you can't wait until then the only thing I can suggest is to convert the unsigned int input values into pairs of smaller values, convert these, and then add them together again, e.g.

inline __m128 _mm_cvtepu32_ps(const __m128i v)
{
    __m128i v2 = _mm_srli_epi32(v, 1);     // v2 = v / 2
    __m128i v1 = _mm_sub_epi32(v, v2);     // v1 = v - (v / 2)
    __m128 v2f = _mm_cvtepi32_ps(v2);
    __m128 v1f = _mm_cvtepi32_ps(v1);
    return _mm_add_ps(v2f, v1f); 
}

---

UPDATE

As noted by @wim in his answer, the above solution fails for an input value of UINT_MAX. Here is a more robust, but slightly less efficient solution, which should work for the full uint32_t input range:

inline __m128 _mm_cvtepu32_ps(const __m128i v)
{
    __m128i v2 = _mm_srli_epi32(v, 1);                 // v2 = v / 2
    __m128i v1 = _mm_and_si128(v, _mm_set1_epi32(1));  // v1 = v & 1
    __m128 v2f = _mm_cvtepi32_ps(v2);
    __m128 v1f = _mm_cvtepi32_ps(v1);
    return _mm_add_ps(_mm_add_ps(v2f, v2f), v1f);      // return 2 * v2 + v1
}