/*
*****************************************************
** The AGM itself **
** **
** A[n] = (A[n-1] + B[n-1])/2 **
** B[n] = Sqrt(A[n-1]*B[n-1]) **
** C[n] = (A[n-1]-B[n-1])/2 **
** **
** n **
** PI[n] = 4A[n+1]^2 / (1-(Sum (2^(j+1))*C[j]^2)) **
** j = 1 **
*****************************************************
*/
static int
ComputeSlowAGM(size_t Len, size_t MaxPasses)
{
int Sign;
size_t Pass;
double Pow2;
clock_t LoopTime,StartTime,EndTime;
BigInt AGM_A, AGM_B, AGM_C, AGMWork;
int Done; /* boolean */
if ((Cfg.PiFormulaToUse != 2) && (Cfg.PiFormulaToUse != 3))
FatalError("SlowAGM was somehow called with pi formula %d\n",
Cfg.PiFormulaToUse);
AGM_A = CreateBigInt(Len);
AGM_B = CreateBigInt(Len);
AGM_C = CreateBigInt(Len);
AGMWork = CreateBigInt(Len);
Num1IsCached = Num2IsCached = 0;
StartTime = clock();
Pow2 = 4.0;
Pass = 0;
if (!LoadData(AGM_A,AGM_B,AGM_C,OldRoot,NO_NUM,NO_NUM,
&StartTime,&Pow2,&Pass,Len,Cfg.PiFormulaToUse))
{
LoopTime = clock();
fprintf(stderr, "Init : ");
if (Cfg.PiFormulaToUse==2)
{
SetNum(AGM_A,Len,BI_One,0);
SetNum(AGM_C,Len,BI_One,0);
ClearBigInt(OldRoot,Len);
Sqrt05(AGM_B,Len);
}
else
{
Sqrt20(AGM_A,Len);
Sqrt60(AGM_C,Len);
if (!Cfg.Macintosh) fprintf(stderr,"Square");
Add(AGM_B,AGM_A,AGM_C,Len);
DivBy(AGM_B,AGM_B,4,Len);
if (!Cfg.Macintosh) BackSpace(6);
if (!Cfg.Macintosh) fprintf(stderr,"Setting vars");
ClearBigInt(OldRoot,Len);
SetNum(AGM_A,Len,BI_One,0);
SetNum(AGM_C,Len,BI_One,0);
if (!Cfg.Macintosh) BackSpace(12);
Pass=1;
}
EndTime = clock();
fprintf(stderr,"Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (Cfg.AlwaysSaveData)
SaveData(AGM_A,AGM_B,AGM_C,OldRoot,NO_NUM,NO_NUM,
((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC,Pow2,Pass,Len,Cfg.PiFormulaToUse);
}
/*
DumpBigInt("AGM_A",AGM_A,Len);
DumpBigInt("AGM_B",AGM_B,Len);
DumpBigInt("AGM_C",AGM_C,Len);
*/
Done=0;
MaxPasses+=Pass;
while ((!Done) && (Pass < MaxPasses))
{
fprintf(stderr, "Pass %4s: ", Num2Str(1<<(++Pass)));
LoopTime = clock();
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part1");
/* w = (a-b)/2 */
Sign = Sub(AGMWork, AGM_A, AGM_B, Len);
if (Sign) Negate(AGMWork,Len);
DivBy(AGMWork,AGMWork, 2, Len);
{size_t Nz;
Nz=FindFirstNonZero(AGMWork,Len);
if ((Pass > 4) && (Nz != Len))
if ((1<<(Pass-4)) > Nz)
fprintf(stderr,"AGMCheck1 fails. Predicted: %lu Actual: %lu\a\n",
(unsigned long)1<<(Pass-4),(ULINT)Nz);
}
if (!Cfg.Macintosh) BackSpace(9);
/* m = w*w */
if (!Cfg.Macintosh) fprintf(stderr,"Sqr1");
if (IsZero(AGMWork,Len/2)) Done=1;
if (Done) ClearBigInt(AGMWork,Len);
else FullMul(AGMWork, AGMWork, AGMWork, Len);
if (!Cfg.Macintosh) BackSpace(4);
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part2");
{size_t Nz;
Nz=FindFirstNonZero(AGMWork,Len);
if ((Pass > 3) && (Nz != Len))
if ((1<<(Pass-3)) > Nz)
fprintf(stderr,"AGMCheck2 fails. Predicted: %lu Actual: %lu\a\n",
(unsigned long)1<<(Pass-3),(ULINT)Nz);
}
/* m = m* w^(J+1) */
MulByFloat(AGMWork,Pow2,Len);
Pow2 *= 2.0;
/* c = c - m */
if (Sign) Add(AGM_C, AGM_C, AGMWork, Len);
else Sub(AGM_C, AGM_C, AGMWork, Len);
/* See if it's done */
if (IsZero(AGMWork,Len-(Len/16))) Done=1;
if (!Cfg.Macintosh) BackSpace(9);
/* m = a*b */
if (!Cfg.Macintosh) fprintf(stderr,"Sqr2");
if (Pass==1) Copy(AGMWork,AGM_B,Len); /* first pass, AGM_A = 1.0 */
else if (!Done) /* If last iter, we can skip it. */
FullMul(AGMWork, AGM_A, AGM_B, Len);
if (!Cfg.Macintosh) BackSpace(4);
/* a = (a+b)/2 */
Add(AGM_A, AGM_A, AGM_B, Len);
DivBy(AGM_A,AGM_A, 2, Len);
/* b = sqrt(a*b) */
if (!Done) /* Optimization */
AGMSqrt(AGM_B, AGMWork, Len, (Pass>5) ? (2<<(Pass-5)) : 0 );
EndTime=clock();
/*
DumpBigInt("AGM_A",AGM_A,Len);
DumpBigInt("AGM_B",AGM_B,Len);
DumpBigInt("AGM_C",AGM_C,Len);
*/
DumpDebug("Pass %u took:", Pass);
fprintf(stderr, "Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (TestKeyboard()) break;
if (Cfg.AlwaysSaveData)
SaveData(AGM_A,AGM_B,AGM_C,OldRoot,NO_NUM,NO_NUM,
((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC,Pow2,Pass,Len,Cfg.PiFormulaToUse);
}
LoopTime=clock();
if (Done)
{
fprintf(stderr,"Final : ");
if (!Cfg.Macintosh) fprintf(stderr,"Sqr");
SpecialSquare(AGM_A, AGM_A, Len, AGMWork);
MulBy(AGM_A,AGM_A,4,Len);
if (!Cfg.Macintosh) BackSpace(3);
if (Cfg.PiFormulaToUse==3)
{
Sqrt30(AGM_B,Len);
if (!Cfg.Macintosh) fprintf(stderr,"Part 2");
FullMul(AGM_C,AGM_C,AGM_B,Len);
SubInt(AGM_C, BI_OneHalf);
if (!Cfg.Macintosh) BackSpace(6);
}
AGMDivide(AGM_B, AGM_A, AGM_C, Len, AGMWork);
EndTime=clock();
fprintf(stderr, "Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (Cfg.PiFormulaToUse==2)
PrintFormattedPi("Slow 1/sqrt(2) AGM",((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC, AGM_B, Len);
else
PrintFormattedPi("Slow sqrt(3) AGM",((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC, AGM_B, Len);
DeleteSaveFile();
}
else if (Pass >= FatalPasses)
FatalError("The AGM didn't converge.\n");
else SaveData(AGM_A,AGM_B,AGM_C,OldRoot,NO_NUM,NO_NUM,
((double)clock()-(double)StartTime)
/CLOCKS_PER_SEC,Pow2,Pass,Len,Cfg.PiFormulaToUse);
fprintf(stderr,"\nTotal Execution time: %0.2f seconds.\n\n",((double)clock()-(double)LoopTime)
/CLOCKS_PER_SEC);
if (!Done) DumpTimings(((double)clock()-(double)LoopTime)
/CLOCKS_PER_SEC);
return (Done);
}
void MapLinearIntensities(FourVectors const &intens,uint32 *p1, uint32 *p2, uint32 *p3, uint32 *p4)
{
// convert four pixels worth of sse-style rgb into argb lwords
// NOTE the _mm_empty macro is voodoo. do not mess with this routine casually - simply throwing
// anything that ends up generating a fpu stack references in here would be bad news.
static fltx4 pixscale={255.0,255.0,255.0,255.0};
fltx4 r,g,b;
r=MinSIMD(pixscale,MulSIMD(pixscale,PowSIMD(intens.x,IGAMMA)));
g=MinSIMD(pixscale,MulSIMD(pixscale,PowSIMD(intens.y,IGAMMA)));
b=MinSIMD(pixscale,MulSIMD(pixscale,PowSIMD(intens.z,IGAMMA)));
// now, convert to integer
r=AndSIMD( AddSIMD( r, Four_MagicNumbers ), PIXMASK );
g=AndSIMD( AddSIMD( g, Four_MagicNumbers ), PIXMASK );
b=AndSIMD( AddSIMD( b, Four_MagicNumbers ), PIXMASK );
*(p1)=(SubInt(r, 0))|(SubInt(g, 0)<<8)|(SubInt(b, 0)<<16);
*(p2)=(SubInt(r, 1))|(SubInt(g, 1)<<8)|(SubInt(b, 1)<<16);
*(p3)=(SubInt(r, 2))|(SubInt(g, 2)<<8)|(SubInt(b, 2)<<16);
*(p4)=(SubInt(r, 3))|(SubInt(g, 3)<<8)|(SubInt(b, 3)<<16);
}
/*
** The AGM itself
**
** A[0]=1 B[0]=1/sqrt(2) Sum=1
**
** n=1..inf
** A[n] = (A[n-1] + B[n-1])/2
** B[n] = Sqrt(A[n-1]*B[n-1])
** C[n] = (A[n-1]-B[n-1])/2 or:
** C[n]^2 = A[n]^2 - B[n]^2 or:
** C[n]^2 = 4A[n+1]*C[n+1]
** Sum = Sum - C[n]^2*(2^(n+1))
** PI[n] = 4A[n+1]^2 / Sum
**
** However, it's not implemented that way. We can save a full
** sized multiplication (with two numbers) by rearranging it,
** and keeping the squares of the A and B. Also, we can do the
** first pass a little differently since A and A^2 will both be 1.
**
** A[0]=1 A[0]^2=1
** B[0]=1/sqrt(2) B[0]^2=0.5
**
** First pass:
**
** A[1] = (A[0] + B[0])/2
** B[1]^2 = A[0]*B[0] ; Since A[0]==1, B[1]^2=B[0]
** C[1]^2 = ((A[0]^2+B[0]^2)/2-B[1]^2)/2
**
** Remainging passes:
**
** C[n] = (A[n-1]-B[n-1])/2; C[n] is actually temp usage of C[n]^2
** A[n] = A[n-1] - C[n]
** C[n]^2 = C[n]*C[n]
** B[n]^2 = (A[n-1]^2+B[n-1]^2-4C[n]^2)/2
**
** Then the rest of the formula is done the same:
**
** A[n]^2 = C[n]^2 + B[n]^2
** B[n] = sqrt(B[n]^2)
** Sum = Sum - C[n]^2*(2^(n+1))
**
** It is an unusual arrangment, but they are all derived directly
** from the standard AGM formulas as given by Salamin.
**
*/
static int
ComputeFastAGM(size_t Len, size_t MaxPasses)
{
int Sign;
size_t Pass;
double Pow2;
clock_t LoopTime,EndTime,StartTime;
BigInt AGM_A, AGM_B, AGM_Sum, AGM_C2;
BigInt AGM_A2, AGM_B2; /* Squares */
int Done; /* boolean */
if ((Cfg.PiFormulaToUse != 2) && (Cfg.PiFormulaToUse != 3))
FatalError("FastAGM was somehow called with pi formula %d\n",
Cfg.PiFormulaToUse);
if (!Cfg.Macintosh) fprintf(stderr,"Creating vars");
AGM_A = CreateBigInt(Len);
AGM_A2 = CreateBigInt(Len);
AGM_B = CreateBigInt(Len);
AGM_B2 = CreateBigInt(Len);
AGM_C2 = CreateBigInt(Len);
AGM_Sum = CreateBigInt(Len);
if (!Cfg.Macintosh) BackSpace(13);
Num1IsCached = Num2IsCached = 0;
StartTime = clock();
Pow2 = 4.0;
Pass = 0;
if (!LoadData(AGM_A,AGM_A2,AGM_B,AGM_B2,AGM_Sum,OldRoot,
&StartTime,&Pow2,&Pass,Len,Cfg.PiFormulaToUse))
{
fprintf(stderr, "Init : ");
LoopTime = clock();
Pow2 = 4.0;
Pass = 0;
if (Cfg.PiFormulaToUse==2)
{
if (!Cfg.Macintosh) fprintf(stderr,"Setting vars");
SetNum(AGM_A,Len, BI_One,0);
SetNum(AGM_A2,Len, BI_One,0);
SetNum(AGM_B2,Len, BI_OneHalf,0);
SetNum(AGM_Sum,Len,BI_One,0);
ClearBigInt(OldRoot,Len);
if (!Cfg.Macintosh) BackSpace(12);
Sqrt05(AGM_B,Len);
if ((Cfg.AGMSelfCheck == 3) || (Cfg.AGMSelfCheck == 4))
{
/* We can use OldRoot and DSWork as scratch. */
if (!Cfg.Macintosh) fprintf(stderr,"Self Check");
SpecialSquare(OldRoot,AGM_B,Len,DSWork);
DoCheck(OldRoot,AGM_B2,0,Len);
ClearBigInt(OldRoot,Len);
if (!Cfg.Macintosh) BackSpace(10);
}
}
else
{
Sqrt20(AGM_A,Len);
Sqrt60(AGM_A2,Len);
if (!Cfg.Macintosh) fprintf(stderr,"Square");
Add(AGM_B,AGM_A,AGM_A2,Len);
DivBy(AGM_B,AGM_B,4,Len);
SpecialSquare(AGM_B2,AGM_B,Len,AGM_A);
if (!Cfg.Macintosh) BackSpace(6);
if (!Cfg.Macintosh) fprintf(stderr,"Setting vars");
ClearBigInt(OldRoot,Len);
SetNum(AGM_A,Len, BI_One,0);
SetNum(AGM_A2,Len, BI_One,0);
SetNum(AGM_Sum,Len,BI_One,0);
if (!Cfg.Macintosh) BackSpace(12);
Pass=1;
}
EndTime = clock();
fprintf(stderr, "Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (Cfg.AlwaysSaveData)
SaveData(AGM_A,AGM_A2,AGM_B,AGM_B2,AGM_Sum,OldRoot,
((double)EndTime-(double)StartTime)/CLOCKS_PER_SEC,
Pow2,Pass,Len,Cfg.PiFormulaToUse);
}
/*
DumpBigInt("AGM_A ",AGM_A,Len);
DumpBigInt("AGM_A2 ",AGM_A2,Len);
DumpBigInt("AGM_B ",AGM_B,Len);
DumpBigInt("AGM_B2 ",AGM_B2,Len);
DumpBigInt("AGM_C2 ",AGM_C2,Len);
DumpBigInt("AGM_Sum",AGM_Sum,Len);
*/
Done=0;
MaxPasses+=Pass;
while ((!Done) && (Pass < MaxPasses))
{size_t FNZ;
int Key=0;
/* DJGPP stuff to test the self checking.
** Comment out the keyboard break statement at the end of the loop.
extern int getkey(void);
if (TestKeyboard()) {Key=getkey();srand((unsigned int)time(NULL));}
*/
fprintf(stderr, "Pass %4s: ", Num2Str(2<<(++Pass)));
LoopTime = clock();
if ((Pass==1) &&
(strcmp(GetCheckStr(AGM_A),"1000000000000000")==0))
{
/*
** Since AGM_A==1, we can do the first pass a little differently
** and avoide the multiplication completely.
*/
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part1");
/* Compute a=(a+b)/2 */
if (Key=='1') CorruptVar(AGM_A,Len);
Add(AGM_A, AGM_A, AGM_B, Len);DivBy(AGM_A,AGM_A, 2, Len);
if (Cfg.AGMSelfCheck >= 1)
{
DivBy(DSWork,AGM_B,2,Len);AddInt(DSWork,BI_OneHalf);
DoCheck(DSWork,AGM_A,1,Len);
}
/* Compute C^2 and B^2 */
Add(AGM_C2,AGM_A2,AGM_B2,Len);DivBy(AGM_C2,AGM_C2,2,Len);
if (Cfg.AGMSelfCheck >= 1) Add(DSWork,AGM_A2,AGM_B2,Len);
Copy(AGM_B2,AGM_B,Len); /* AGM_A == 1.0, so we can copy */
Sign=Sub(AGM_C2,AGM_C2,AGM_B2,Len);DivBy(AGM_C2,AGM_C2,2,Len);
if (Key=='4') CorruptVar(AGM_B2,Len);
if (Key=='5') CorruptVar(AGM_C2,Len);
if (Sign) FatalError("AGM_C2 should never be negative.\n");
if (!Cfg.Macintosh) BackSpace(9);
}
else
{
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part1");
/* Compute C */
/*
Sign=Sub(AGM_C2, AGM_A, AGM_B, Len);DivBy(AGM_C2,AGM_C2,2,Len);
*/
Sign=HalfDiff(AGM_C2,AGM_A,AGM_B,Len);
if (Sign) FatalError("AGM_C2 should never be negative.\n");
/* Compute A. AGM_C2 is still only C at the moment. */
if (Cfg.AGMSelfCheck >= 1)
{Add(DSWork,AGM_A,AGM_B,Len);DivBy(DSWork,DSWork,2,Len);}
if (Sub(AGM_A,AGM_A,AGM_C2,Len))
FatalError("AGM_A should never be negative.\n");
if (Key=='1') CorruptVar(AGM_A,Len);
if (Cfg.AGMSelfCheck >= 1) DoCheck(DSWork,AGM_A,2,Len);
if (!Cfg.Macintosh) BackSpace(9);
if (!Cfg.Macintosh) fprintf(stderr,"Sqr");
/* Compute C^2 */
SpecialSquare(AGM_C2,AGM_C2,Len,AGM_B);
if (Key=='5') CorruptVar(AGM_C2,Len);
if (!Cfg.Macintosh) BackSpace(3);
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part2");
if (Cfg.AGMSelfCheck >= 1) Add(DSWork,AGM_A2,AGM_B2,Len);
/* Compute B^2 */
Sign=SpecialAGMFunc1(AGM_B2,AGM_A2,AGM_C2,Len);
if (Key=='4') CorruptVar(AGM_B2,Len);
/*
Add(AGM_B2,AGM_B2,AGM_A2,Len);
MulBy(AGM_A2,AGM_C2,4,Len);
Sign=Sub(AGM_B2,AGM_B2,AGM_A2,Len);
DivBy(AGM_B2,AGM_B2,2,Len);
*/
if (Sign) FatalError("AGM_B2 should never be negative.\n");
if (!Cfg.Macintosh) BackSpace(9);
}
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part3");
/* Compute A^2 */
if (Cfg.AGMSelfCheck >= 1)
{
Add(DSWork,DSWork,AGM_B2,Len);
Add(DSWork,DSWork,AGM_B2,Len);
DivBy(DSWork,DSWork,4,Len);
}
Add(AGM_A2,AGM_C2,AGM_B2,Len);
if (Key=='2') CorruptVar(AGM_A2,Len);
if (Cfg.AGMSelfCheck >= 1) DoCheck(DSWork,AGM_A2,3,Len);
if (!Cfg.Macintosh) BackSpace(9);
/*
** Do some self checking. The estimate formula predicts the number of
** leading zeros. It's based on the regular AGM accuracy formula. It
** predicts just a couple of digits less than what is actually there,
** so if anything happens, this should fail. But, since it is so
** close, it just might fail for the wrong reason.
*/
if (!Cfg.Macintosh) fprintf(stderr,"Self Check");
FNZ=FindFirstNonZero(AGM_C2,Len);
if ((Pass > 3) && (FNZ != Len))
{size_t P=Pass-2;size_t Est;
/* formula based on the AGM 'number of digits right' formula */
if (Cfg.PiFormulaToUse==2)
Est=(1.364376354*(1<<(P))-P*.301029995-2.342434419)/2;
else /* other agm does 1 less pass, so pass is one higher, so div by 4 */
Est=(sqrt(3.0)*1.364376354*(1<<(P))-P*.301029995-2.690531961)/4;
if (Est >= FNZ)
{
fprintf(stderr,"\aAGM self check fails. Predicted: %lu Actual: %lu\n",
(ULINT)Est,(ULINT)FNZ);
fprintf(stderr,"Beyond what I've tested, this may not be an actual failure\n");
fprintf(stderr,"but an inaccuracy in the self check formula itself.\n");
}
}
/* See if it's done. (ie: more than half zeros) */
if (FNZ > Len/2+4) Done=1;
if ((Cfg.AGMSelfCheck == 2) || (Cfg.AGMSelfCheck == 4))
{
/* We can use AGM_B and DSWork as scratch. */
SpecialSquare(AGM_B,AGM_A,Len,DSWork);
DoCheck(AGM_B,AGM_A2,4,Len);
}
if (!Cfg.Macintosh) BackSpace(10);
/* Compute B=sqrt(B^2) */
if (!Done)
AGMSqrt(AGM_B, AGM_B2, Len, (Pass>5) ? (2<<(Pass-5)) : 0);
if (Key=='3') CorruptVar(AGM_B,Len);
if (!Cfg.Macintosh) fprintf(stderr,"AGM Part4");
/* Sum = Sum - C2 * 2^(J+1) */
MulByFloat(AGM_C2,Pow2,Len);Pow2 *= 2.0;
if (Sub(AGM_Sum,AGM_Sum,AGM_C2,Len))
FatalError("AGM_Sum should never be negative.\n");
EndTime=clock();
/*
DumpBigInt("AGM_A ",AGM_A,Len);
DumpBigInt("AGM_A2 ",AGM_A2,Len);
DumpBigInt("AGM_B ",AGM_B,Len);
DumpBigInt("AGM_B2 ",AGM_B2,Len);
DumpBigInt("AGM_C2 ",AGM_C2,Len);
DumpBigInt("AGM_Sum",AGM_Sum,Len);
*/
if (!Cfg.Macintosh) BackSpace(9);
if (!Done && ((Cfg.AGMSelfCheck == 3) || (Cfg.AGMSelfCheck == 4)))
{
/* We can use AGM_C2 and DSWork as scratch. */
if (!Cfg.Macintosh) fprintf(stderr,"Self Check");
SpecialSquare(AGM_C2,AGM_B,Len,DSWork);
DoCheck(AGM_C2,AGM_B2,5,Len);
if (!Cfg.Macintosh) BackSpace(10);
}
DumpDebug("Pass %u took:", Pass);
fprintf(stderr,"Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (Cfg.AlwaysSaveData)
SaveData(AGM_A,AGM_A2,AGM_B,AGM_B2,AGM_Sum,OldRoot,
((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC,Pow2,Pass,Len,Cfg.PiFormulaToUse);
if (TestKeyboard()) break;
}
/* We've done the AGM part, now do the final calculation. */
LoopTime=clock();
if (Done)
{
fprintf(stderr, "Final : ");
/*
** Since AGM_A and AGM_B have converged, I can compute the AGM_A2
** by calculating AGM_B2. That can be done like up above, except
** we don't need the 4*AGM_C2 because that will be zero.
*/
if (!Cfg.Macintosh) fprintf(stderr,"Part 1");
Add(AGM_B2,AGM_B2,AGM_A2,Len);
MulBy(AGM_B2,AGM_B2,2,Len);
if (!Cfg.Macintosh) BackSpace(6);
if (Cfg.PiFormulaToUse==3)
{
if (!Cfg.Macintosh) fprintf(stderr,"Part 2");
if (!Cfg.Macintosh) BackSpace(6);
Sqrt30(AGM_A2,Len);
if (!Cfg.Macintosh) fprintf(stderr,"Part 3");
SpecialFullMul(AGM_A,AGM_Sum,AGM_A2,Len,AGM_B);
SubInt(AGM_A, BI_OneHalf);
Copy(AGM_Sum,AGM_A,Len);
if (!Cfg.Macintosh) BackSpace(6);
}
AGMDivide(AGM_B, AGM_B2, AGM_Sum, Len, AGM_A2);
EndTime=clock();
fprintf(stderr, "Time= %0.2f\n", ((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
DumpTimings(((double)EndTime-(double)LoopTime)
/CLOCKS_PER_SEC);
if (Cfg.PiFormulaToUse==2)
PrintFormattedPi("Fast 1/sqrt(2) AGM",((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC, AGM_B, Len);
else
PrintFormattedPi("Fast sqrt(3) AGM",((double)EndTime-(double)StartTime)
/CLOCKS_PER_SEC, AGM_B, Len);
DeleteSaveFile();
}
else if (Pass >= FatalPasses)
FatalError("The AGM didn't converge.\n");
else SaveData(AGM_A,AGM_A2,AGM_B,AGM_B2,AGM_Sum,OldRoot,
((double)clock()-(double)StartTime)
/CLOCKS_PER_SEC,Pow2,Pass,Len,Cfg.PiFormulaToUse);
fprintf(stderr,"\nTotal Execution time: %0.2f\n\n",((double)clock()-(double)StartTime)
/CLOCKS_PER_SEC);
if (!Done) DumpTimings(((double)clock()-(double)StartTime)
/CLOCKS_PER_SEC);
return (Done);
}
