--- /dev/null	Sat May 10 12:08:49 2014
+++ new/usr/src/lib/libm/common/C/__rem_pio2m.c	Sat May 10 12:08:49 2014
@@ -0,0 +1,363 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+/*
+ * int __rem_pio2m(x,y,e0,nx,prec,ipio2)
+ * double x[],y[]; int e0,nx,prec; const int ipio2[];
+ *
+ * __rem_pio2m return the last three digits of N with
+ *		y = x - N*pi/2
+ * so that |y| < pi/4.
+ *
+ * The method is to compute the integer (mod 8) and fraction parts of
+ * (2/pi)*x without doing the full multiplication. In general we
+ * skip the part of the product that are known to be a huge integer (
+ * more accurately, = 0 mod 8 ). Thus the number of operations are
+ * independent of the exponent of the input.
+ *
+ * (2/PI) is represented by an array of 24-bit integers in ipio2[].
+ * Here PI could as well be a machine value pi.
+ *
+ * Input parameters:
+ * 	x[]	The input value (must be positive) is broken into nx
+ *		pieces of 24-bit integers in double precision format.
+ *		x[i] will be the i-th 24 bit of x. The scaled exponent
+ *		of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
+ *		match x's up to 24 bits.
+ *
+ *		Example of breaking a double z into x[0]+x[1]+x[2]:
+ *			e0 = ilogb(z)-23
+ *			z  = scalbn(z,-e0)
+ *		for i = 0,1,2
+ *			x[i] =  floor(z)
+ *			z    = (z-x[i])*2**24
+ *
+ *
+ *	y[]	ouput result in an array of double precision numbers.
+ *		The dimension of y[] is:
+ *			24-bit  precision	1
+ *			53-bit  precision	2
+ *			64-bit  precision	2
+ *			113-bit precision	3
+ *		The actual value is the sum of them. Thus for 113-bit
+ *		precsion, one may have to do something like:
+ *
+ *		long double t,w,r_head, r_tail;
+ *		t = (long double)y[2] + (long double)y[1];
+ *		w = (long double)y[0];
+ *		r_head = t+w;
+ *		r_tail = w - (r_head - t);
+ *
+ *	e0	The exponent of x[0]
+ *
+ *	nx	dimension of x[]
+ *
+ *  	prec	an interger indicating the precision:
+ *			0	24  bits (single)
+ *			1	53  bits (double)
+ *			2	64  bits (extended)
+ *			3	113 bits (quad)
+ *
+ *	ipio2[]
+ *		integer array, contains the (24*i)-th to (24*i+23)-th
+ *		bit of 2/pi or 2/PI after binary point. The corresponding
+ *		floating value is
+ *
+ *			ipio2[i] * 2^(-24(i+1)).
+ *
+ * External function:
+ *	double scalbn( ), floor( );
+ *
+ *
+ * Here is the description of some local variables:
+ *
+ * 	jk	jk+1 is the initial number of terms of ipio2[] needed
+ *		in the computation. The recommended value is 3,4,4,
+ *		6 for single, double, extended,and quad.
+ *
+ * 	jz	local integer variable indicating the number of
+ *		terms of ipio2[] used.
+ *
+ *	jx	nx - 1
+ *
+ *	jv	index for pointing to the suitable ipio2[] for the
+ *		computation. In general, we want
+ *			( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
+ *		is an integer. Thus
+ *			e0-3-24*jv >= 0 or (e0-3)/24 >= jv
+ *		Hence jv = max(0,(e0-3)/24).
+ *
+ *	jp	jp+1 is the number of terms in pio2[] needed, jp = jk.
+ *
+ * 	q[]	double array with integral value, representing the
+ *		24-bits chunk of the product of x and 2/pi.
+ *
+ *	q0	the corresponding exponent of q[0]. Note that the
+ *		exponent for q[i] would be q0-24*i.
+ *
+ *	pio2[]	double precision array, obtained by cutting pi/2
+ *		into 24 bits chunks.
+ *
+ *	f[]	ipio2[] in floating point
+ *
+ *	iq[]	integer array by breaking up q[] in 24-bits chunk.
+ *
+ *	fq[]	final product of x*(2/pi) in fq[0],..,fq[jk]
+ *
+ *	ih	integer. If >0 it indicats q[] is >= 0.5, hence
+ *		it also indicates the *sign* of the result.
+ *
+ */
+
+#include "libm.h"
+
+#if defined(__i386) && !defined(__amd64)
+extern int __swapRP(int);
+#endif
+
+static const int init_jk[] = { 3, 4, 4, 6 }; /* initial value for jk */
+
+static const double pio2[] = {
+	1.57079625129699707031e+00,
+	7.54978941586159635335e-08,
+	5.39030252995776476554e-15,
+	3.28200341580791294123e-22,
+	1.27065575308067607349e-29,
+	1.22933308981111328932e-36,
+	2.73370053816464559624e-44,
+	2.16741683877804819444e-51,
+};
+
+static const double
+	zero	= 0.0,
+	one	= 1.0,
+	half	= 0.5,
+	eight	= 8.0,
+	eighth	= 0.125,
+	two24	= 16777216.0,
+	twon24	= 5.960464477539062500E-8;
+
+int
+__rem_pio2m(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
+{
+	int	jz, jx, jv, jp, jk, carry, n, iq[20];
+	int	i, j, k, m, q0, ih;
+	double	z, fw, f[20], fq[20], q[20];
+#if defined(__i386) && !defined(__amd64)
+	int	rp;
+
+	rp = __swapRP(fp_extended);
+#endif
+
+	/* initialize jk */
+	jp = jk = init_jk[prec];
+
+	/* determine jx,jv,q0, note that 3>q0 */
+	jx = nx - 1;
+	jv = (e0 - 3) / 24;
+	if (jv < 0)
+		jv = 0;
+	q0 = e0 - 24 * (jv + 1);
+
+	/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+	j = jv - jx;
+	m = jx + jk;
+	for (i = 0; i <= m; i++, j++)
+		f[i] = (j < 0)? zero : (double)ipio2[j];
+
+	/* compute q[0],q[1],...q[jk] */
+	for (i = 0; i <= jk; i++) {
+		for (j = 0, fw = zero; j <= jx; j++)
+			fw += x[j] * f[jx+i-j];
+		q[i] = fw;
+	}
+
+	jz = jk;
+recompute:
+	/* distill q[] into iq[] reversingly */
+	for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) {
+		fw = (double)((int)(twon24 * z));
+		iq[i] = (int)(z - two24 * fw);
+		z = q[j-1] + fw;
+	}
+
+	/* compute n */
+	z = scalbn(z, q0);		/* actual value of z */
+	z -= eight * floor(z * eighth);	/* trim off integer >= 8 */
+	n = (int)z;
+	z -= (double)n;
+	ih = 0;
+	if (q0 > 0) {			/* need iq[jz-1] to determine n */
+		i = (iq[jz-1] >> (24 - q0));
+		n += i;
+		iq[jz-1] -= i << (24 - q0);
+		ih = iq[jz-1] >> (23 - q0);
+	} else if (q0 == 0) {
+		ih = iq[jz-1] >> 23;
+	} else if (z >= half) {
+		ih = 2;
+	}
+
+	if (ih > 0) {	/* q > 0.5 */
+		n += 1;
+		carry = 0;
+		for (i = 0; i < jz; i++) {	/* compute 1-q */
+			j = iq[i];
+			if (carry == 0) {
+				if (j != 0) {
+					carry = 1;
+					iq[i] = 0x1000000 - j;
+				}
+			} else {
+				iq[i] = 0xffffff - j;
+			}
+		}
+		if (q0 > 0) {		/* rare case: chance is 1 in 12 */
+			switch (q0) {
+			case 1:
+				iq[jz-1] &= 0x7fffff;
+				break;
+			case 2:
+				iq[jz-1] &= 0x3fffff;
+				break;
+			}
+		}
+		if (ih == 2) {
+			z = one - z;
+			if (carry != 0)
+				z -= scalbn(one, q0);
+		}
+	}
+
+	/* check if recomputation is needed */
+	if (z == zero) {
+		j = 0;
+		for (i = jz - 1; i >= jk; i--)
+			j |= iq[i];
+		if (j == 0) {	/* need recomputation */
+			/* set k to no. of terms needed */
+			for (k = 1; iq[jk-k] == 0; k++)
+				;
+
+			/* add q[jz+1] to q[jz+k] */
+			for (i = jz + 1; i <= jz + k; i++) {
+				f[jx+i] = (double)ipio2[jv+i];
+				for (j = 0, fw = zero; j <= jx; j++)
+					fw += x[j] * f[jx+i-j];
+				q[i] = fw;
+			}
+			jz += k;
+			goto recompute;
+		}
+	}
+
+	/* cut out zero terms */
+	if (z == zero) {
+		jz -= 1;
+		q0 -= 24;
+		while (iq[jz] == 0) {
+			jz--;
+			q0 -= 24;
+		}
+	} else {		/* break z into 24-bit if neccessary */
+		z = scalbn(z, -q0);
+		if (z >= two24) {
+			fw = (double)((int)(twon24 * z));
+			iq[jz] = (int)(z - two24 * fw);
+			jz += 1;
+			q0 += 24;
+			iq[jz] = (int)fw;
+		} else {
+			iq[jz] = (int)z;
+		}
+	}
+
+	/* convert integer "bit" chunk to floating-point value */
+	fw = scalbn(one, q0);
+	for (i = jz; i >= 0; i--) {
+		q[i] = fw * (double)iq[i];
+		fw *= twon24;
+	}
+
+	/* compute pio2[0,...,jp]*q[jz,...,0] */
+	for (i = jz; i >= 0; i--) {
+		for (fw = zero, k = 0; k <= jp && k <= jz - i; k++)
+			fw += pio2[k] * q[i+k];
+		fq[jz-i] = fw;
+	}
+
+	/* compress fq[] into y[] */
+	switch (prec) {
+	case 0:
+		fw = zero;
+		for (i = jz; i >= 0; i--)
+			fw += fq[i];
+		y[0] = (ih == 0)? fw : -fw;
+		break;
+
+	case 1:
+	case 2:
+		fw = zero;
+		for (i = jz; i >= 0; i--)
+			fw += fq[i];
+		y[0] = (ih == 0)? fw : -fw;
+		fw = fq[0] - fw;
+		for (i = 1; i <= jz; i++)
+			fw += fq[i];
+		y[1] = (ih == 0)? fw : -fw;
+		break;
+
+	default:
+		for (i = jz; i > 0; i--) {
+			fw = fq[i-1] + fq[i];
+			fq[i] += fq[i-1] - fw;
+			fq[i-1] = fw;
+		}
+		for (i = jz; i > 1; i--) {
+			fw = fq[i-1] + fq[i];
+			fq[i] += fq[i-1] - fw;
+			fq[i-1] = fw;
+		}
+		for (fw = zero, i = jz; i >= 2; i--)
+			fw += fq[i];
+		if (ih == 0) {
+			y[0] = fq[0];
+			y[1] = fq[1];
+			y[2] = fw;
+		} else {
+			y[0] = -fq[0];
+			y[1] = -fq[1];
+			y[2] = -fw;
+		}
+	}
+
+#if defined(__i386) && !defined(__amd64)
+	(void) __swapRP(rp);
+#endif
+	return (n & 7);
+}
