Re: [boost] Math constants for naive and gurus? - which constants do you want?

From: Greg Colvin (gcolvin_at_[hidden])
Date: 2001-10-23 11:43:53

For what it is worth, appendedis a very simple test program and
the 80x86 assembly language output from MSVC.  I had to add the
call to f(double&,double&,double&,double&,double&) to prevent the
optimizer removing almost all the code.  The operations for each
way of assigning pi to a local are a bit scrambled up, I assume
for optimal scheduling.  When I unscamble them they look like:

    ; double pi_template = constant<pi_tag,double>();
        mov     DWORD PTR _pi_template$[esp+60], 1413754136 ; 54442d18H
        mov     DWORD PTR _pi_template$[esp+64], 1074340347 ; 400921fbH

    ; double pi_function = pi();

        mov     DWORD PTR _pi_function$[esp+60], 1413754136 ; 54442d18H
        mov     DWORD PTR _pi_function$[esp+64], 1074340347 ; 400921fbH

    ; double pi_constant = Pi;
        mov     eax, DWORD PTR _Pi$S188
        mov     DWORD PTR _pi_constant$[esp+40], eax
        mov     ecx, DWORD PTR _Pi$S188+4
        mov     DWORD PTR _pi_constant$[esp+52], ecx

    ; double pi_defined = PI;
        mov     DWORD PTR _pi_defined$[esp+60], 1413754136 ; 54442d18H
        mov     DWORD PTR _pi_defined$[esp+64], 1074340347 ; 400921fbH

    ; double pi_literal =  3.141592653589793238462643383279502884197;
        mov     DWORD PTR _pi_literal$[esp+60], 1413754136 ; 54442d18H
        mov     DWORD PTR _pi_literal$[esp+64], 1074340347 ; 400921fbH

    ; return f(pi_template,pi_function,pi_constant,pi_defined,pi_literal);
        lea     edx, DWORD PTR _pi_literal$[esp+40]
        push    edx
        lea     eax, DWORD PTR _pi_defined$[esp+44]
        push    eax
        lea     ecx, DWORD PTR _pi_constant$[esp+48]
        push    ecx
        lea     edx, DWORD PTR _pi_function$[esp+52]
        push    edx
        lea     eax, DWORD PTR _pi_template$[esp+56]
        push    eax
        call    ?f@@YAHAAN0000_at_Z                        ; f

Make of it all what you will.

//////////////////////////////////////////////////////////////////
// pi_test.cpp

template <typename Tag, typename Rep> struct constant {
   constant() {}
   operator Rep() const;
};

struct pi_tag {};

template<> inline constant<pi_tag, double>::operator double() const {
   return 3.141592653589793238462643383279502884197;
}

inline double pi() {
   return 3.141592653589793238462643383279502884197;
}

const double Pi = 3.141592653589793238462643383279502884197;

#define PI 3.141592653589793238462643383279502884197

extern int f(double&,double&,double&,double&,double&);

int pi_test() {

   double pi_template = constant<pi_tag,double>();

   double pi_function = pi();

   double pi_constant = Pi;

   double pi_defined = PI;

   double pi_literal =  3.141592653589793238462643383279502884197;

   return f(pi_template,pi_function,pi_constant,pi_defined,pi_literal);
}

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 TITLE pi_test.cpp
 .386P
include listing.inc
if @Version gt 510
.model FLAT
else
_TEXT SEGMENT PARA USE32 PUBLIC 'CODE'
_TEXT ENDS
_DATA SEGMENT DWORD USE32 PUBLIC 'DATA'
_DATA ENDS
CONST SEGMENT DWORD USE32 PUBLIC 'CONST'
CONST ENDS
_BSS SEGMENT DWORD USE32 PUBLIC 'BSS'
_BSS ENDS
_TLS SEGMENT DWORD USE32 PUBLIC 'TLS'
_TLS ENDS
; COMDAT ??B?$constant_at_Upi_tag@@N@@QBENXZ
_TEXT SEGMENT PARA USE32 PUBLIC 'CODE'
_TEXT ENDS
; COMDAT ?pi@@YANXZ
_TEXT SEGMENT PARA USE32 PUBLIC 'CODE'
_TEXT ENDS
; COMDAT ??0?$constant_at_Upi_tag@@N@@QAE_at_XZ
_TEXT SEGMENT PARA USE32 PUBLIC 'CODE'
_TEXT ENDS
FLAT GROUP _DATA, CONST, _BSS
 ASSUME CS: FLAT, DS: FLAT, SS: FLAT
endif
CONST SEGMENT
_Pi$S188 DQ 0400921fb54442d18r  ; 3.14159
CONST ENDS
PUBLIC ?pi_test@@YAHXZ     ; pi_test
EXTRN ?f@@YAHAAN0000_at_Z:NEAR    ; f
EXTRN __fltused:NEAR
CONST SEGMENT
$T214 DQ 0400921fb54442d18r  ; 3.14159
CONST ENDS
_TEXT SEGMENT
_pi_template$ = -8
_pi_function$ = -16
_pi_constant$ = -24
_pi_defined$ = -32
_pi_literal$ = -40
?pi_test@@YAHXZ PROC NEAR    ; pi_test

; 25   : int pi_test() {

 sub esp, 40     ; 00000028H

; 26   : 
; 27   :    double pi_template = constant<pi_tag,double>();
; 28   : 
; 29   :    double pi_function = pi();
; 30   : 
; 31   :    double pi_constant = Pi;

 mov eax, DWORD PTR _Pi$S188
 mov ecx, DWORD PTR _Pi$S188+4
 mov DWORD PTR _pi_constant$[esp+40], eax

; 32   : 
; 33   :    double pi_defined = PI;
; 34   : 
; 35   :    double pi_literal =  3.141592653589793238462643383279502884197;
; 36   : 
; 37   :    return f(pi_template,pi_function,pi_constant,pi_defined,pi_literal);

 lea edx, DWORD PTR _pi_literal$[esp+40]
 mov DWORD PTR _pi_constant$[esp+44], ecx
 lea eax, DWORD PTR _pi_defined$[esp+40]
 push edx
 lea ecx, DWORD PTR _pi_constant$[esp+44]
 push eax
 lea edx, DWORD PTR _pi_function$[esp+48]
 push ecx
 lea eax, DWORD PTR _pi_template$[esp+52]
 push edx
 push eax
 mov DWORD PTR _pi_template$[esp+60], 1413754136 ; 54442d18H
 mov DWORD PTR _pi_template$[esp+64], 1074340347 ; 400921fbH
 mov DWORD PTR _pi_function$[esp+60], 1413754136 ; 54442d18H
 mov DWORD PTR _pi_function$[esp+64], 1074340347 ; 400921fbH
 mov DWORD PTR _pi_defined$[esp+60], 1413754136 ; 54442d18H
 mov DWORD PTR _pi_defined$[esp+64], 1074340347 ; 400921fbH
 mov DWORD PTR _pi_literal$[esp+60], 1413754136 ; 54442d18H
 mov DWORD PTR _pi_literal$[esp+64], 1074340347 ; 400921fbH
 call ?f@@YAHAAN0000_at_Z   ; f
 add esp, 20     ; 00000014H

; 38   : } 

 add esp, 40     ; 00000028H
 ret 0
?pi_test@@YAHXZ ENDP     ; pi_test
_TEXT ENDS
END