$(DDOC $(DDOC_BLANKLINE ) $(DDOC_BLANKLINE ) $(SPEC_S Floating-Point, $(DDOC_BLANKLINE ) $(HEADERNAV_TOC $(HEADERNAV_ITEM fp_intermediate_values, Floating-Point Intermediate Values) $(HEADERNAV_ITEM fp_const_folding, Floating-Point Constant Folding) $(HEADERNAV_ITEM rounding_control, Rounding Control) $(HEADERNAV_ITEM exception_flags, Exception Flags) $(HEADERNAV_ITEM floating-point-transformations, Floating-Point Transformations) ) $(DDOC_BLANKLINE )

$(LNAME2 fp_intermediate_values, Floating-Point Intermediate Values)

$(DDOC_BLANKLINE ) $(P For floating-point operations and expression intermediate values, a greater precision can be used than the type of the expression. Only the minimum precision is set by the types of the operands, not the maximum. $(B Implementation Note:) On Intel x86 machines, for example, it is expected (but not required) that the intermediate calculations be done to the full 80 bits of precision implemented by the hardware. ) $(DDOC_BLANKLINE ) $(P Execution of floating-point expressions may yield a result of greater precision than dictated by the source.) $(DDOC_BLANKLINE )

$(LNAME2 fp_const_folding, Floating-Point Constant Folding)

$(DDOC_BLANKLINE ) $(P Regardless of the type of the operands, floating-point constant folding is done in $(D real) or greater precision. It is always done following $(LINK2 https://standards.ieee.org/standard/754-2019.html, IEEE-754) rules and round-to-nearest is used.) $(DDOC_BLANKLINE ) $(P Floating-point constants are internally represented in the implementation in at least $(D real) precision, regardless of the constant's type. The extra precision is available for constant folding. Committing to the precision of the result is done as late as possible in the compilation process. For example:) $(DDOC_BLANKLINE ) $(D_CODE $(D_KEYWORD const) $(D_KEYWORD float) f = 0.2f; writeln(f - 0.2); ) $(P will print 0. A non-const static variable's value cannot be propagated at compile time, so:) $(DDOC_BLANKLINE ) $(D_CODE $(D_KEYWORD static) $(D_KEYWORD float) f = 0.2f; writeln(f - 0.2); ) $(P will print 2.98023e-09. Hex floating-point constants can also be used when specific floating-point bit patterns are needed that are unaffected by rounding. To find the hex value of 0.2f:) $(DDOC_BLANKLINE ) $(D_CODE $(D_KEYWORD import) std.stdio; $(D_KEYWORD void) main() { writefln($(D_STRING "%a"), 0.2f); } ) $(P which is 0x1.99999ap-3. Using the hex constant:) $(DDOC_BLANKLINE ) $(D_CODE $(D_KEYWORD const) $(D_KEYWORD float) f = 0x1.99999ap-3f; writeln(f - 0.2); ) $(DDOC_BLANKLINE ) $(P prints 2.98023e-09.) $(DDOC_BLANKLINE ) $(P Different compiler settings, optimization settings, and inlining settings can affect opportunities for constant folding, therefore the results of floating-point calculations may differ depending on those settings.) $(DDOC_BLANKLINE )

$(LNAME2 rounding_control, Rounding Control)

$(DDOC_BLANKLINE ) $(P IEEE 754 floating-point arithmetic includes the ability to set 4 different rounding modes. These are accessible via the functions in $(D core.stdc.fenv). ) $(DDOC_BLANKLINE ) $(P If the floating-point rounding mode is changed within a function, it must be restored before the function exits. If this rule is violated (for example, by the use of inline asm), the rounding mode used for subsequent calculations is undefined. ) $(DDOC_BLANKLINE ) $(DDOC_BLANKLINE )

$(LNAME2 exception_flags, Exception Flags)

$(DDOC_BLANKLINE ) $(P IEEE 754 floating-point arithmetic can set several flags based on what happened with a computation:) $(DDOC_BLANKLINE ) $(TABLE $(TR $(TD $(D FE_INVALID))) $(TR $(TD $(D FE_DENORMAL))) $(TR $(TD $(D FE_DIVBYZERO))) $(TR $(TD $(D FE_OVERFLOW))) $(TR $(TD $(D FE_UNDERFLOW))) $(TR $(TD $(D FE_INEXACT))) ) $(DDOC_BLANKLINE ) $(P These flags can be set/reset via the functions in $(D core.stdc.fenv).) $(DDOC_BLANKLINE )

$(LNAME2 floating-point-transformations, Floating-Point Transformations)

$(DDOC_BLANKLINE ) $(P An implementation may perform transformations on floating-point computations in order to reduce their strength. ) $(DDOC_BLANKLINE ) $(P Not all transformations are valid: The following transformations of floating-point expressions are not allowed because under IEEE rules they could produce different results. ) $(DDOC_BLANKLINE ) $(TABLE2 Disallowed Floating-Point Transformations, transformation, comments $(TROW $(ARGS $(I x) + 0 $(RARR ) $(I x)) , $(ARGS not valid if $(I x) is -0) ) $(TROW $(ARGS $(I x) - 0 $(RARR ) $(I x)) , $(ARGS not valid if $(I x) is $(PLUSMN )0 and rounding is towards -$(INFIN )) ) $(TROW $(ARGS -$(I x) $(HARR ) 0 - $(I x)) , $(ARGS not valid if $(I x) is +0) ) $(TROW $(ARGS $(I x) - $(I x) $(RARR ) 0) , $(ARGS not valid if $(I x) is NaN or $(PLUSMN )$(INFIN )) ) $(TROW $(ARGS $(I x) - $(I y) $(HARR ) -($(I y) - $(I x))) , $(ARGS not valid because (1-1=+0) whereas -(1-1)=-0) ) $(TROW $(ARGS $(I x) * 0 $(RARR ) 0) , $(ARGS not valid if $(I x) is NaN or $(PLUSMN )$(INFIN )) ) $(COMMENT $(TROW $(ARGS $(I x) * 1 $(RARR ) $(I x)) , $(ARGS not valid if $(I x) is a signaling NaN) ) ) $(TROW $(ARGS $(I x) / $(I c) $(HARR ) $(I x) * (1/$(I c))) , $(ARGS valid if (1/$(I c)) yields an e$(I x)act result) ) $(TROW $(ARGS $(I x) != $(I x) $(RARR ) false) , $(ARGS not valid if $(I x) is a NaN) ) $(TROW $(ARGS $(I x) == $(I x) $(RARR ) true) , $(ARGS not valid if $(I x) is a NaN) ) $(TROW $(ARGS $(I x) !$(I op) $(I y) $(HARR ) !($(I x) $(I op) $(I y))) , $(ARGS not valid if $(I x) or $(I y) is a NaN) ) ) $(DDOC_BLANKLINE ) $(P Of course, transformations that would alter side effects are also invalid.) $(DDOC_BLANKLINE ) $(SPEC_SUBNAV_PREV_NEXT garbage, Garbage Collection, iasm, D x86 Inline Assembler) ) )