Was macht -ffast-math eigentlich und was bringt es für Vorteile?
Aus der Dokumentation:
This option is not turned on by any -O option besides -Ofast since it can result in incorrect output for programs that depend on an exact implementation of IEEE or ISO rules/specifications for math functions. It may, however, yield faster code for programs that do not require the guarantees of these specifications.
-ffast-math
Sets the options -fno-math-errno, -funsafe-math-optimizations, -ffinite-math-only, -fno-rounding-math, -fno-signaling-nans, -fcx-limited-range and -fexcess-precision=fast.This option causes the preprocessor macro __FAST_MATH__ to be defined.
-fno-math-errno
Do not set errno after calling math functions that are executed with a single instruction, e.g., sqrt. A program that relies on IEEE exceptions for math error handling may want to use this flag for speed while maintaining IEEE arithmetic compatibility.The default is -fmath-errno.
-funsafe-math-optimizations
Allow optimizations for floating-point arithmetic that (a) assume that arguments and results are valid and (b) may violate IEEE or ANSI standards. When used at link time, it may include libraries or startup files that change the default FPU control word or other similar optimizations.
Enables -fno-signed-zeros, -fno-trapping-math, -fassociative-math and -freciprocal-math.
-fno-signed-zeros
Allow optimizations for floating-point arithmetic that ignore the signedness of zero. IEEE arithmetic specifies the behavior of distinct +0.0 and -0.0 values, which then prohibits simplification of expressions such as x+0.0 or 0.0*x (even with -ffinite-math-only). This option implies that the sign of a zero result isn’t significant.
-fno-trapping-math
Compile code assuming that floating-point operations cannot generate user-visible traps. These traps include division by zero, overflow, underflow, inexact result and invalid operation. This option requires that -fno-signaling-nans be in effect. Setting this option may allow faster code if one relies on “non-stop” IEEE arithmetic, for example.
-fassociative-math
Allow re-association of operands in series of floating-point operations. This violates the ISO C and C++ language standard by possibly changing computation result.
NOTE: re-ordering may change the sign of zero as well as ignore NaNs and inhibit or create underflow or overflow (and thus cannot be used on code that relies on rounding behavior like (x + 2**52) - 2**52. May also reorder floating-point comparisons and thus may not be used when ordered comparisons are required. This option requires that both -fno-signed-zeros and -fno-trapping-math be in effect. Moreover, it doesn’t make much sense with -frounding-math.
-freciprocal-math
Allow the reciprocal of a value to be used instead of dividing by the value if this enables optimizations. For example x / y can be replaced with x * (1/y), which is useful if (1/y) is subject to common subexpression elimination. Note that this loses precision and increases the number of flops operating on the value.
-ffinite-math-only
Allow optimizations for floating-point arithmetic that assume that arguments and results are not NaNs or +-Infs.
-frounding-math
Disable transformations and optimizations that assume default floating-point rounding behavior. This is round-to-zero for all floating point to integer conversions, and round-to-nearest for all other arithmetic truncations. This option should be specified for programs that change the FP rounding mode dynamically, or that may be executed with a non-default rounding mode. This option disables constant folding of floating-point expressions at compile time (which may be affected by rounding mode) and arithmetic transformations that are unsafe in the presence of sign-dependent rounding modes.
-f-signaling-nans
Compile code assuming that IEEE signaling NaNs may generate user-visible traps during floating-point operations. Setting this option disables optimizations that may change the number of exceptions visible with signaling NaNs. This option implies -ftrapping-math.
This option causes the preprocessor macro __SUPPORT_SNAN__ to be defined.
-fcx-limited-range
When enabled, this option states that a range reduction step is not needed when performing complex division. Also, there is no checking whether the result of a complex multiplication or division is NaN + I*NaN, with an attempt to rescue the situation in that case. The default is -fno-cx-limited-range, but is enabled by -ffast-math.
This option controls the default setting of the ISO C99 CX_LIMITED_RANGE pragma. Nevertheless, the option applies to all languages.
-fexcess-precision=style
This option allows further control over excess precision on machines where floating-point operations occur in a format with more precision or range than the IEEE standard and interchange floating-point types. By default, -fexcess-precision=fast is in effect; this means that operations may be carried out in a wider precision than the types specified in the source if that would result in faster code, and it is unpredictable when rounding to the types specified in the source code takes place. When compiling C, if -fexcess-precision=standard is specified then excess precision follows the rules specified in ISO C99; in particular, both casts and assignments cause values to be rounded to their semantic types (whereas -ffloat-store only affects assignments). This option is enabled by default for C if a strict conformance option such as -std=c99 is used. -ffast-math enables -fexcess-precision=fast by default regardless of whether a strict conformance option is used.
-fexcess-precision=standard is not implemented for languages other than C. On the x86, it has no effect if -mfpmath=sse or -mfpmath=sse+387 is specified; in the former case, IEEE semantics apply without excess precision, and in the latter, rounding is unpredictable.
Das ist eine ganze Menge. Viele Sachen klingen für mich, als wenn einfach jede Menge if/else Zweige raus genommen werden. Und ich denke diese Optimierungen wirken für double wie für float. Das erklärt noch nicht den Geschwindigkeitsunterschied im letzten Post. Da muss ich wohl mal in den Assembler Code schaun.
https://gcc.gnu.org/onlinedocs/gcc/Optimize-Options.html#Optimize-Options
https://gcc.gnu.org/wiki/FloatingPointMath