TL:DR: this is normal and you can't reasonably change it.
The 32-bit library may be using 80-bit FP values in x87 registers for its temporaries, avoiding rounding off to 64-bit
double after every operation. (Unless there's a whole separate library, compiling your own code to use SSE doesn't change what's inside the library, or even the calling convention for passing data to the library. But since 32-bit passes
float in memory on the stack, a library is free to load it with SSE2 or with x87. Still, you don't get the performance advantage of passing FP values in xmm registers unless it's impossible for non-SSE code to use the library.)
It's also possible that they're different simply because they use a different order of operations, producing different temporaries along the way. That's less plausible, unless they're separately hand-written in asm. If they're built from the same C source (without "unsafe" FP optimizations), then the compiler isn't allowed to reorder things, because of this non-associative behaviour of FP math.
glibc's libm (used on Linux) typically favours precision over speed, so its giving you the correctly-rounded result out to the last bit of the mantissa for both 32 and 64-bit. The IEEE FP standard only requires the basic operations (+ - * / FMA and FP remainder) to be "correctly rounded" out to the last bit of the mantissa. (i.e. rounding error of at most 0.5 ulp). (The exact result, according to
1.047304076386807714.... Keep in mind that
double (on x86 with normal compilers) is IEEE754 binary64, so internally the mantissa and exponent are in base2. If you print enough extra decimal digits, though, you can tell that
...7714 should round up to
...78, although really you should print more digits in case they're not zero beyond that. I'm just assuming it's
So Microsoft's 64-bit library implementation produces
1.0473040763868076 and there's pretty much nothing you can do about it, other than not use it. (e.g. find your own
acos() implementation and use it.) But FP determinism is hard, even if you limit yourself to just x86 with SSE. See Does any floating point-intensive code produce bit-exact results in any x86-based architecture?. If you limit yourself to a single compiler, it can be possible if you avoid complicated library functions like
You might be able to get the 32-bit library version to produce the same value as the 64-bit version, if it uses x87 and changing the x87 precision setting affects it. But the other way around is not possible: SSE2 has separate instructions for 64-bit
double and 32-bit
float, and always rounds after every instruction, so you can't change any setting that will increase precision result. (You could change the SSE rounding mode, and that will change the result, but not in a good way!)
The linked article describes how some versions of VC++'s CRT runtime startup set the x87 FP register precision to 53-bit mantissa instead of 80-bit full precision. Also that D3D9 will set it to 24, so even
double only has the precision of
float if done with x87.