X-Git-Url: https://git.saurik.com/apple/security.git/blobdiff_plain/80e2389990082500d76eb566d4946be3e786c3ef..d8f41ccd20de16f8ebe2ccc84d47bf1cb2b26bbb:/libsecurity_cryptkit/lib/giantFFT.c

diff --git a/libsecurity_cryptkit/lib/giantFFT.c b/libsecurity_cryptkit/lib/giantFFT.c
deleted file mode 100644
index 411a6d19..00000000
--- a/libsecurity_cryptkit/lib/giantFFT.c
+++ /dev/null
@@ -1,520 +0,0 @@
-/* Copyright (c) 1998 Apple Computer, Inc.  All rights reserved.
- *
- * NOTICE: USE OF THE MATERIALS ACCOMPANYING THIS NOTICE IS SUBJECT
- * TO THE TERMS OF THE SIGNED "FAST ELLIPTIC ENCRYPTION (FEE) REFERENCE
- * SOURCE CODE EVALUATION AGREEMENT" BETWEEN APPLE COMPUTER, INC. AND THE
- * ORIGINAL LICENSEE THAT OBTAINED THESE MATERIALS FROM APPLE COMPUTER,
- * INC.  ANY USE OF THESE MATERIALS NOT PERMITTED BY SUCH AGREEMENT WILL
- * EXPOSE YOU TO LIABILITY.
- ***************************************************************************
-
-   giantFFT.c
-   Library for large-integer arithmetic via FFT. Currently unused
-   in CryptKit.
-
-   R. E. Crandall, Scientific Computation Group, NeXT Computer, Inc.
-
- Revision History
- ----------------
- 19 Jan 1998	Doug Mitchell at Apple
- 	Split off from NSGiantIntegers.c.
-
-*/
-
-/*
- * FIXME - make sure platform-specific math lib has floor(), fmod(),
- *         sin(), pow()
- */
-#include <math.h>
-#include "NSGiantIntegers.h"
-
-#define AUTO_MUL 	0
-#define GRAMMAR_MUL 	1
-#define FFT_MUL 	2
-
-#define TWOPI 		(double)(2*3.1415926535897932384626433)
-#define SQRT2 		(double)(1.414213562373095048801688724209)
-#define SQRTHALF 	(double)(0.707106781186547524400844362104)
-#define TWO16 		(double)(65536.0)
-#define TWOM16 		(double)(0.0000152587890625)
-#define BREAK_SHORTS 	400    // Number of shorts at which FFT breaks over.
-
-static int lpt(int n, int *lambda);
-static void mul_hermitian(double *a, double *b, int n) ;
-static void square_hermitian(double *b, int n);
-static void addsignal(giant x, double *zs, int n);
-static void scramble_real(double *x, int n);
-static void fft_real_to_hermitian(double *zs, int n);
-static void fftinv_hermitian_to_real(double *zs, int n);
-static void GiantFFTSquare(giant gx);
-static void GiantFFTMul(giant,giant);
-static void giant_to_double(giant x, int sizex, double *zs, int L);
-
-static int mulmode = AUTO_MUL;
-
-void mulg(giant a, giant b) { /* b becomes a*b. */
-	PROF_START;
-	INCR_MULGS;
-	GiantAuxMul(a,b);
-	#if	FEE_DEBUG
-        (void)bitlen(b); // XXX
-	#endif	FEE_DEBUG
-        PROF_END(mulgTime);
-	PROF_INCR(numMulg);
-}
-
-static void GiantAuxMul(giant a, giant b) {
-/* Optimized general multiply, b becomes a*b. Modes are:
-   AUTO_MUL: switch according to empirical speed criteria.
-   GRAMMAR_MUL: force grammar-school algorithm.
-   FFT_MUL: force floating point FFT method.
-*/
-    int square = (a==b);
-
-    if (isZero(b)) return;
-    if (isZero(a)) {
-        gtog(a, b);
-        return;
-    }
-    switch(mulmode) {
-    case GRAMMAR_MUL:
-        GiantGrammarMul(a,b);
-        break;
-    case FFT_MUL:
-        if (square) {
-            GiantFFTSquare(b);
-        }
-        else {
-            GiantFFTMul(a,b);
-        }
-        break;
-    case AUTO_MUL: {
-        int sizea, sizeb;
-        float grammartime;
-        sizea = abs(a->sign);
-        sizeb = abs(b->sign);
-        grammartime = sizea; grammartime *= sizeb;
-        if(grammartime < BREAK_SHORTS*BREAK_SHORTS) {
-                GiantGrammarMul(a,b);
-        }
-        else {
-            if (square) GiantFFTSquare(b);
-            else GiantFFTMul(a,b);
-        }
-        break;
-      }
-   }
-}
-
-/***************** Commence FFT multiply routines ****************/
-
-static int CurrentRun = 0;
-double *sincos = NULL;
-static void init_sincos(int n) {
-    int j;
-    double e = TWOPI/n;
-
-    if (n <= CurrentRun) return;
-    CurrentRun = n;
-    if (sincos) free(sincos);
-    sincos = (double *)malloc(sizeof(double)*(1+(n>>2)));
-    for(j=0;j<=(n>>2);j++) {
-        sincos[j] = sin(e*j);
-    }
-}
-
-static double s_sin(int n) {
-    int seg = n/(CurrentRun>>2);
-
-    switch(seg) {
-    case 0: return(sincos[n]);
-    case 1: return(sincos[(CurrentRun>>1)-n]);
-    case 2: return(-sincos[n-(CurrentRun>>1)]);
-    case 3:
-    default: return(-sincos[CurrentRun-n]);
-    }
-}
-
-static double s_cos(int n) {
-    int quart = (CurrentRun>>2);
-
-    if (n < quart) return(s_sin(n+quart));
-    return(-s_sin(n-quart));
-}
-
-
-static int lpt(int n, int *lambda) {
-/* returns least power of two greater than n */
-    register int i = 1;
-
-    *lambda = 0;
-    while(i<n) {
-        i<<=1;
-        ++(*lambda);
-    }
-    return(i);
-}
-
-static void addsignal(giant x, double *zs, int n) {
-   register int j, k, m, car;
-   register double f, g;
-   /*double  err,  maxerr = 0.0;*/
-
-   for(j=0;j<n;j++) {
-   	f = floor(zs[j]+0.5);
-
-	/* err = fabs(zs[j]-f);
-	if(err>maxerr) maxerr = err;
-	*/
-
-	zs[j] =0;
-	k = 0;
-	do{
-           g = floor(f*TWOM16);
-	   zs[j+k] += f-g*TWO16;
-	   ++k;
-	   f=g;
-	} while(f != 0.0);
-   }
-   car = 0;
-   for(j=0;j<n;j++) {
-   	m = zs[j]+car;
-	x->n[j] = m & 0xffff;
-	car = (m>>16);
-   }
-   if(car) x->n[j] = car;
-      else --j;
-   while(!(x->n[j])) --j;
-   x->sign = j+1;
-   if (abs(x->sign) > x->capacity) NSGiantRaise("addsignal overflow");
-}
-
-static void GiantFFTSquare(giant gx) {
-    int j,size = abs(gx->sign);
-    register int L;
-
-    if(size<4) { GiantGrammarMul(gx,gx); return; }
-    L = lpt(size+size, &j);
-    {
-        //was...double doubles[L];
-	//is...
-	double *doubles = malloc(sizeof(double) * L);
-	// end
-        giant_to_double(gx, size, doubles, L);
-        fft_real_to_hermitian(doubles, L);
-        square_hermitian(doubles, L);
-        fftinv_hermitian_to_real(doubles, L);
-        addsignal(gx, doubles, L);
-	// new
-	free(doubles);
-    }
-    gx->sign = abs(gx->sign);
-    bitlen(gx); // XXX
-    if (abs(gx->sign) > gx->capacity) NSGiantRaise("GiantFFTSquare overflow");
-}
-
-static void GiantFFTMul(giant y, giant x) { /* x becomes y*x. */
-    int lambda, size, sizex = abs(x->sign), sizey = abs(y->sign);
-    int finalsign = gsign(x)*gsign(y);
-    register int L;
-
-    if((sizex<=4)||(sizey<=4)) { GiantGrammarMul(y,x); return; }
-    size = sizex; if(size<sizey) size=sizey;
-    L = lpt(size+size, &lambda);
-    {
-        //double doubles1[L];
-        //double doubles2[L];
-       	double *doubles1 = malloc(sizeof(double) * L);
-	double *doubles2 = malloc(sizeof(double) * L);
-
-        giant_to_double(x, sizex, doubles1, L);
-        giant_to_double(y, sizey, doubles2, L);
-        fft_real_to_hermitian(doubles1, L);
-        fft_real_to_hermitian(doubles2, L);
-        mul_hermitian(doubles2, doubles1, L);
-        fftinv_hermitian_to_real(doubles1, L);
-        addsignal(x, doubles1, L);
-
-	free(doubles1);
-	free(doubles2);
-    }
-    x->sign = finalsign*abs(x->sign);
-    bitlen(x); // XXX
-    if (abs(x->sign) > x->capacity) NSGiantRaise("GiantFFTMul overflow");
-}
-
-static void scramble_real(double *x, int n) {
-    register int i,j,k;
-    register double tmp;
-
-    for(i=0,j=0;i<n-1;i++) {
-        if(i<j) {
-            tmp = x[j];
-            x[j]=x[i];
-            x[i]=tmp;
-        }
-        k = n/2;
-        while(k<=j) {
-            j -= k;
-            k>>=1;
-        }
-        j += k;
-    }
-}
-
-static void fft_real_to_hermitian(double *zs, int n) {
-/* Output is {Re(z^[0]),...,Re(z^[n/2),Im(z^[n/2-1]),...,Im(z^[1]).
-   This is a decimation-in-time, split-radix algorithm.
- */
-	register double cc1, ss1, cc3, ss3;
-	register int is, iD, i0, i1, i2, i3, i4, i5, i6, i7, i8,
-		     a, a3, b, b3, nminus = n-1, dil, expand;
-	register double *x, e;
-	int nn = n>>1;
-	double t1, t2, t3, t4, t5, t6;
-	register int n2, n4, n8, i, j;
-
-        init_sincos(n);
-	expand = CurrentRun/n;
-	scramble_real(zs, n);
-	x = zs-1;  /* FORTRAN compatibility. */
-	is = 1;
-	iD = 4;
-	do{
-	   for(i0=is;i0<=n;i0+=iD) {
-		i1 = i0+1;
-		e = x[i0];
-		x[i0] = e + x[i1];
-		x[i1] = e - x[i1];
-	   }
-	   is = (iD<<1)-1;
-	   iD <<= 2;
-	} while(is<n);
-	n2 = 2;
-	while(nn>>=1) {
-		n2 <<= 1;
-		n4 = n2>>2;
-		n8 = n2>>3;
-		is = 0;
-		iD = n2<<1;
-		do {
-			for(i=is;i<n;i+=iD) {
-				i1 = i+1;
-				i2 = i1 + n4;
-				i3 = i2 + n4;
-				i4 = i3 + n4;
-				t1 = x[i4]+x[i3];
-				x[i4] -= x[i3];
-				x[i3] = x[i1] - t1;
-				x[i1] += t1;
-				if(n4==1) continue;
-				i1 += n8;
-				i2 += n8;
-				i3 += n8;
-				i4 += n8;
-				t1 = (x[i3]+x[i4])*SQRTHALF;
-				t2 = (x[i3]-x[i4])*SQRTHALF;
-				x[i4] = x[i2] - t1;
-				x[i3] = -x[i2] - t1;
-				x[i2] = x[i1] - t2;
-				x[i1] += t2;
-			}
-			is = (iD<<1) - n2;
-			iD <<= 2;
-		} while(is<n);
-		dil = n/n2;
-		a = dil;
-		for(j=2;j<=n8;j++) {
-		    	a3 = (a+(a<<1))&nminus;
-			b = a*expand;
-			b3 = a3*expand;
-			cc1 = s_cos(b);
-			ss1 = s_sin(b);
-			cc3 = s_cos(b3);
-			ss3 = s_sin(b3);
-			a = (a+dil)&nminus;
-			is = 0;
-			iD = n2<<1;
-		        do {
-				for(i=is;i<n;i+=iD) {
-					i1 = i+j;
-					i2 = i1 + n4;
-					i3 = i2 + n4;
-					i4 = i3 + n4;
-					i5 = i + n4 - j + 2;
-					i6 = i5 + n4;
-					i7 = i6 + n4;
-					i8 = i7 + n4;
-					t1 = x[i3]*cc1 + x[i7]*ss1;
-					t2 = x[i7]*cc1 - x[i3]*ss1;
-					t3 = x[i4]*cc3 + x[i8]*ss3;
-					t4 = x[i8]*cc3 - x[i4]*ss3;
-					t5 = t1 + t3;
-					t6 = t2 + t4;
-					t3 = t1 - t3;
-					t4 = t2 - t4;
-					t2 = x[i6] + t6;
-					x[i3] = t6 - x[i6];
-					x[i8] = t2;
-					t2 = x[i2] - t3;
-					x[i7] = -x[i2] - t3;
-					x[i4] = t2;
-					t1 = x[i1] + t5;
-					x[i6] = x[i1] - t5;
-					x[i1] = t1;
-					t1 = x[i5] + t4;
-					x[i5] -= t4;
-					x[i2] = t1;
-				}
-			        is = (iD<<1) - n2;
-				iD <<= 2;
-			} while(is<n);
-		}
-	}
-}
-
-static void fftinv_hermitian_to_real(double *zs, int n) {
-/* Input is {Re(z^[0]),...,Re(z^[n/2),Im(z^[n/2-1]),...,Im(z^[1]).
-   This is a decimation-in-frequency, split-radix algorithm.
- */
-	register double cc1, ss1, cc3, ss3;
-	register int is, iD, i0, i1, i2, i3, i4, i5, i6, i7, i8,
-		 a, a3, b, b3, nminus = n-1, dil, expand;
-	register double *x, e;
-	int nn = n>>1;
-	double t1, t2, t3, t4, t5;
-	int n2, n4, n8, i, j;
-
-        init_sincos(n);
-	expand = CurrentRun/n;
-	x = zs-1;
-	n2 = n<<1;
-	while(nn >>= 1) {
-		is = 0;
-		iD = n2;
-		n2 >>= 1;
-		n4 = n2>>2;
-		n8 = n4>>1;
-		do {
-			for(i=is;i<n;i+=iD) {
-				i1 = i+1;
-				i2 = i1 + n4;
-				i3 = i2 + n4;
-				i4 = i3 + n4;
-				t1 = x[i1] - x[i3];
-				x[i1] += x[i3];
-				x[i2] += x[i2];
-				x[i3] = t1 - 2.0*x[i4];
-				x[i4] = t1 + 2.0*x[i4];
-				if(n4==1) continue;
-				i1 += n8;
-				i2 += n8;
-				i3 += n8;
-				i4 += n8;
-				t1 = (x[i2]-x[i1])*SQRTHALF;
-				t2 = (x[i4]+x[i3])*SQRTHALF;
-				x[i1] += x[i2];
-				x[i2] = x[i4]-x[i3];
-				x[i3] = -2.0*(t2+t1);
-				x[i4] = 2.0*(t1-t2);
-			}
-			is = (iD<<1) - n2;
-			iD <<= 2;
-		} while(is<n-1);
-		dil = n/n2;
-		a = dil;
-		for(j=2;j<=n8;j++) {
-		    	a3 = (a+(a<<1))&nminus;
-			b = a*expand;
-			b3 = a3*expand;
-			cc1 = s_cos(b);
-			ss1 = s_sin(b);
-			cc3 = s_cos(b3);
-			ss3 = s_sin(b3);
-			a = (a+dil)&nminus;
-			is = 0;
-			iD = n2<<1;
-			do {
-			   for(i=is;i<n;i+=iD) {
-				i1 = i+j;
-				i2 = i1+n4;
-				i3 = i2+n4;
-				i4 = i3+n4;
-				i5 = i+n4-j+2;
-				i6 = i5+n4;
-				i7 = i6+n4;
-				i8 = i7+n4;
-				t1 = x[i1] - x[i6];
-				x[i1] += x[i6];
-				t2 = x[i5] - x[i2];
-				x[i5] += x[i2];
-				t3 = x[i8] + x[i3];
-				x[i6] = x[i8] - x[i3];
-				t4 = x[i4] + x[i7];
-				x[i2] = x[i4] - x[i7];
-				t5 = t1 - t4;
-				t1 += t4;
-				t4 = t2 - t3;
-				t2 += t3;
-				x[i3] = t5*cc1 + t4*ss1;
-				x[i7] = -t4*cc1 + t5*ss1;
-				x[i4] = t1*cc3 - t2*ss3;
-				x[i8] = t2*cc3 + t1*ss3;
-			   }
-			   is = (iD<<1) - n2;
-			   iD <<= 2;
-			} while(is<n-1);
-		}
-	}
-	is = 1;
-	iD = 4;
-	do {
-	  for(i0=is;i0<=n;i0+=iD){
-		i1 = i0+1;
-		e = x[i0];
-		x[i0] = e + x[i1];
-		x[i1] = e - x[i1];
-	  }
-	  is = (iD<<1) - 1;
-	  iD <<= 2;
-	} while(is<n);
-	scramble_real(zs, n);
-	e = 1/(double)n;
-	for(i=0;i<n;i++) zs[i] *= e;
-}
-
-
-static void mul_hermitian(double *a, double *b, int n) {
-	register int k, half = n>>1;
-	register double aa, bb, am, bm;
-
-	b[0] *= a[0];
-	b[half] *= a[half];
-	for(k=1;k<half;k++) {
-	        aa = a[k]; bb = b[k];
-		am = a[n-k]; bm = b[n-k];
-		b[k] = aa*bb - am*bm;
-		b[n-k] = aa*bm + am*bb;
-	}
-}
-
-static void square_hermitian(double *b, int n) {
-	register int k, half = n>>1;
-	register double c, d;
-
-	b[0] *= b[0];
-	b[half] *= b[half];
-	for(k=1;k<half;k++) {
-	        c = b[k]; d = b[n-k];
-		b[n-k] = 2.0*c*d;
-		b[k] = (c+d)*(c-d);
-	}
-}
-
-static void giant_to_double(giant x, int sizex, double *zs, int L) {
-	register int j;
-	for(j=sizex;j<L;j++) zs[j]=0.0;
-	for(j=0;j<sizex;j++) {
-		 zs[j] = x->n[j];
-	}
-}