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

diff --git a/Security/libsecurity_cryptkit/lib/giantFFT.c b/Security/libsecurity_cryptkit/lib/giantFFT.c
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+/* Copyright (c) 1998,2011,2014 Apple 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, INC. AND THE
+ * ORIGINAL LICENSEE THAT OBTAINED THESE MATERIALS FROM APPLE,
+ * 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.
+
+
+ Revision History
+ ----------------
+ 19 Jan 1998 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];
+	}
+}