I'm trying to profile the time it takes to compute a sqrt using the following simple C code, where readTSC() is a function to read the CPU's cycle counter.
double sum = 0.0;
int i;
tm = readTSC();
for ( i = 0; i < n; i++ )
sum += sqrt((double) i);
tm = readTSC() - tm;
printf("%lld clocks in total\n",tm);
printf("%15.6e\n",sum);
However, as I printed out the assembly code using
gcc -S timing.c -o timing.s
on an Intel machine, the result (shown below) was surprising?
Why there are two sqrts in the assembly code with one using the sqrtsd
instruction and the other using a function call? Is it related to loop unrolling and trying to execute two sqrts in one iteration?
And how to understand the line
ucomisd %xmm0, %xmm0
Why does it compare %xmm0
to itself?
//----------------start of for loop----------------
call readTSC
movq %rax, -32(%rbp)
movl $0, -4(%rbp)
jmp .L4
.L6:
cvtsi2sd -4(%rbp), %xmm1
// 1. use sqrtsd instruction
sqrtsd %xmm1, %xmm0
ucomisd %xmm0, %xmm0
jp .L8
je .L5
.L8:
movapd %xmm1, %xmm0
// 2. use C funciton call
call sqrt
.L5:
movsd -16(%rbp), %xmm1
addsd %xmm1, %xmm0
movsd %xmm0, -16(%rbp)
addl $1, -4(%rbp)
.L4:
movl -4(%rbp), %eax
cmpl -36(%rbp), %eax
jl .L6
//----------------end of for loop----------------
call readTSC
It's using the library sqrt
function for error handling. See glibc's documentation: 20.5.4 Error Reporting by Mathematical Functions: math functions set errno
for compatibility with systems that don't have IEEE754 exception flags. Related: glibc's math_error(7)
man page.
As an optimization, it first tries to perform the square root by the inlined sqrtsd
instruction, then checks the result against itself using the ucomisd
instruction which sets the flags as follows:
CASE (RESULT) OF UNORDERED: ZF,PF,CF 111; GREATER_THAN: ZF,PF,CF 000; LESS_THAN: ZF,PF,CF 001; EQUAL: ZF,PF,CF 100; ESAC;
In particular, comparing a QNaN
to itself will return UNORDERED
, which is what you will get if you try to take the square root of a negative number. This is covered by the jp
branch. The je
check is just paranoia, checking for exact equality.
Also note that gcc has a -fno-math-errno
option which will sacrifice this error handling for speed. This option is part of -ffast-math
, but can be used on its own without enabling any result-changing optimizations.
sqrtsd
on its own correctly produces NaN for negative and NaN inputs, and sets the IEEE754 Invalid flag. The check and branch is only to preserve the errno
-setting semantics which most code doesn't rely on.
-fno-math-errno
is the default on Darwin (OS X), where the math library never sets errno
, so functions can be inlined without this check.
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