Fast float to int conversion (truncate)

Question

I'm looking for a way to truncate a float into an int in a fast and portable (IEEE 754) way. The reason is because in this function 50% of the time is spent in the cast:

float fm_sinf(float x) {
    const float a =  0.00735246819687011731341356165096815f;
    const float b = -0.16528911397014738207016302002888890f;
    const float c =  0.99969198629596757779830113868360584f;

    float r, x2;
    int k;

    /* bring x in range */
    k = (int) (F_1_PI * x + copysignf(0.5f, x)); /* <-- 50% of time is spent in cast */

    x -= k * F_PI;

    /* if x is in an odd pi count we must flip */
    r = 1 - 2 * (k & 1); /* trick for r = (k % 2) == 0 ? 1 : -1; */

    x2 = x * x;

    return r * x*(c + x2*(b + a*x2));
}

Answer 1

The slowness of float->int casts mainly occurs when using x87 FPU instructions on x86. To do the truncation, the rounding mode in the FPU control word needs to be changed to round-to-zero and back, which tends to be very slow.

When using SSE instead of x87 instructions, a truncation is available without control word changes. You can do this using compiler options (like -mfpmath=sse -msse -msse2 in GCC) or by compiling the code as 64-bit.

The SSE3 instruction set has the FISTTP instruction to convert to integer with truncation without changing the control word. A compiler may generate this instruction if instructed to assume SSE3.

Alternatively, the C99 lrint() function will convert to integer with the current rounding mode (round-to-nearest unless you changed it). You can use this if you remove the copysignf term. Unfortunately, this function is still not ubiquitous after more than ten years.

Answer 2

to be portable you would have to add some directives and learn a couple assembler languages but you could theoretically could use some inline assembly to move portions of the floating point register into eax/rax ebx/rbx and convert what you would need by hand, floating point specification though is a pain in the butt, but I am pretty certain that if you do it with assembly you will be way faster, as your needs are very specific and the system method is probably more generic and less efficient for your purpose

Answer 3

I found a fast truncate method by Sree Kotay which provides exactly the optimization that I needed.

Answer 4

You could skip the conversion to int altogether by using frexpf to get the mantissa and exponent, and inspect the raw mantissa (use a union) at the appropriate bit position (calculated using the exponent) to determine (the quadrant dependent) r.