 @@ -1,418 +1,417 @@
-/*	$NetBSD: fpu_sqrt.c,v 1.8 2020/06/27 04:17:51 rin Exp $ */
+/*	$NetBSD: fpu_sqrt.c,v 1.9 2020/06/27 04:29:27 rin Exp $ */
 /*
  * Copyright (c) 1992, 1993
  *	The Regents of the University of California.  All rights reserved.
+ *
  * This software was developed by the Computer Systems Engineering group
  * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
  * contributed to Berkeley.
+ *
  * All advertising materials mentioning features or use of this software
  * must display the following acknowledgement:
  *	This product includes software developed by the University of
  *	California, Lawrence Berkeley Laboratory.
+ *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
  * are met:
  * 1. Redistributions of source code must retain the above copyright
  *    notice, this list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright
  *    notice, this list of conditions and the following disclaimer in the
  *    documentation and/or other materials provided with the distribution.
  * 3. Neither the name of the University nor the names of its contributors
  *    may be used to endorse or promote products derived from this software
  *    without specific prior written permission.
+ *
  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  * SUCH DAMAGE.
+ *
  *	@(#)fpu_sqrt.c	8.1 (Berkeley) 6/11/93
  */
 /*
  * Perform an FPU square root (return sqrt(x)).
  */
 #include <sys/cdefs.h>
-__KERNEL_RCSID(0, "$NetBSD: fpu_sqrt.c,v 1.8 2020/06/27 04:17:51 rin Exp $");
+__KERNEL_RCSID(0, "$NetBSD: fpu_sqrt.c,v 1.9 2020/06/27 04:29:27 rin Exp $");
 #include <sys/types.h>
 #if defined(DIAGNOSTIC)||defined(DEBUG)
 #include <sys/systm.h>
 #endif
 #include <machine/fpu.h>
 #include <machine/reg.h>
 #include <powerpc/fpu/fpu_arith.h>
 #include <powerpc/fpu/fpu_emu.h>
 /*
  * Our task is to calculate the square root of a floating point number x0.
  * This number x normally has the form:
+ *
  *		    exp
  *	x = mant * 2		(where 1 <= mant < 2 and exp is an integer)
+ *
  * This can be left as it stands, or the mantissa can be doubled and the
  * exponent decremented:
+ *
  *			  exp-1
  *	x = (2 * mant) * 2	(where 2 <= 2 * mant < 4)
+ *
  * If the exponent `exp' is even, the square root of the number is best
  * handled using the first form, and is by definition equal to:
+ *
  *				exp/2
  *	sqrt(x) = sqrt(mant) * 2
+ *
  * If exp is odd, on the other hand, it is convenient to use the second
  * form, giving:
+ *
  *				    (exp-1)/2
  *	sqrt(x) = sqrt(2 * mant) * 2
+ *
  * In the first case, we have
+ *
  *	1 <= mant < 2
+ *
  * and therefore
+ *
  *	sqrt(1) <= sqrt(mant) < sqrt(2)
+ *
  * while in the second case we have
+ *
  *	2 <= 2*mant < 4
+ *
  * and therefore
+ *
  *	sqrt(2) <= sqrt(2*mant) < sqrt(4)
+ *
  * so that in any case, we are sure that
+ *
  *	sqrt(1) <= sqrt(n * mant) < sqrt(4),	n = 1 or 2
+ *
  * or
+ *
  *	1 <= sqrt(n * mant) < 2,		n = 1 or 2.
+ *
  * This root is therefore a properly formed mantissa for a floating
  * point number.  The exponent of sqrt(x) is either exp/2 or (exp-1)/2
  * as above.  This leaves us with the problem of finding the square root
  * of a fixed-point number in the range [1..4).
+ *
  * Though it may not be instantly obvious, the following square root
  * algorithm works for any integer x of an even number of bits, provided
  * that no overflows occur:
+ *
  *	let q = 0
  *	for k = NBITS-1 to 0 step -1 do -- for each digit in the answer...
  *		x *= 2			-- multiply by radix, for next digit
  *		if x >= 2q + 2^k then	-- if adding 2^k does not
  *			x -= 2q + 2^k	-- exceed the correct root,
  *			q += 2^k	-- add 2^k and adjust x
  *		fi
  *	done
  *	sqrt = q / 2^(NBITS/2)		-- (and any remainder is in x)
+ *
  * If NBITS is odd (so that k is initially even), we can just add another
  * zero bit at the top of x.  Doing so means that q is not going to acquire
  * a 1 bit in the first trip around the loop (since x0 < 2^NBITS).  If the
  * final value in x is not needed, or can be off by a factor of 2, this is
  * equivalant to moving the `x *= 2' step to the bottom of the loop:
+ *
  *	for k = NBITS-1 to 0 step -1 do if ... fi; x *= 2; done
+ *
  * and the result q will then be sqrt(x0) * 2^floor(NBITS / 2).
  * (Since the algorithm is destructive on x, we will call x's initial
  * value, for which q is some power of two times its square root, x0.)
+ *
  * If we insert a loop invariant y = 2q, we can then rewrite this using
  * C notation as:
+ *
  *	q = y = 0; x = x0;
  *	for (k = NBITS; --k >= 0;) {
  * #if (NBITS is even)
  *		x *= 2;
  * #endif
  *		t = y + (1 << k);
  *		if (x >= t) {
  *			x -= t;
  *			q += 1 << k;
  *			y += 1 << (k + 1);
  *		}
  * #if (NBITS is odd)
  *		x *= 2;
  * #endif
  *	}
+ *
  * If x0 is fixed point, rather than an integer, we can simply alter the
  * scale factor between q and sqrt(x0).  As it happens, we can easily arrange
  * for the scale factor to be 2**0 or 1, so that sqrt(x0) == q.
+ *
  * In our case, however, x0 (and therefore x, y, q, and t) are multiword
  * integers, which adds some complication.  But note that q is built one
  * bit at a time, from the top down, and is not used itself in the loop
  * (we use 2q as held in y instead).  This means we can build our answer
  * in an integer, one word at a time, which saves a bit of work.  Also,
  * since 1 << k is always a `new' bit in q, 1 << k and 1 << (k+1) are
  * `new' bits in y and we can set them with an `or' operation rather than
  * a full-blown multiword add.
+ *
  * We are almost done, except for one snag.  We must prove that none of our
  * intermediate calculations can overflow.  We know that x0 is in [1..4)
  * and therefore the square root in q will be in [1..2), but what about x,
  * y, and t?
+ *
  * We know that y = 2q at the beginning of each loop.  (The relation only
  * fails temporarily while y and q are being updated.)  Since q < 2, y < 4.
  * The sum in t can, in our case, be as much as y+(1<<1) = y+2 < 6, and.
  * Furthermore, we can prove with a bit of work that x never exceeds y by
  * more than 2, so that even after doubling, 0 <= x < 8.  (This is left as
  * an exercise to the reader, mostly because I have become tired of working
  * on this comment.)
+ *
  * If our floating point mantissas (which are of the form 1.frac) occupy
  * B+1 bits, our largest intermediary needs at most B+3 bits, or two extra.
  * In fact, we want even one more bit (for a carry, to avoid compares), or
  * three extra.  There is a comment in fpu_emu.h reminding maintainers of
  * this, so we have some justification in assuming it.
  */
 struct fpn *
 fpu_sqrt(struct fpemu *fe)
+{
 	struct fpn *x = &fe->fe_f1;
 	u_int bit, q, tt;
 	u_int x0, x1, x2, x3;
 	u_int y0, y1, y2, y3;
 	u_int d0, d1, d2, d3;
 	int e;
 	FPU_DECL_CARRY;
 	/*
 	 * Take care of special cases first.  In order:
+	 *
 	 *	sqrt(NaN) = NaN
 	 *	sqrt(+0) = +0
 	 *	sqrt(-0) = -0
 	 *	sqrt(x < 0) = NaN	(including sqrt(-Inf))
 	 *	sqrt(+Inf) = +Inf
+	 *
 	 * Then all that remains are numbers with mantissas in [1..2).
 	 */
 	DPRINTF(FPE_REG, ("fpu_sqrt:\n"));
 	DUMPFPN(FPE_REG, x);
 	DPRINTF(FPE_REG, ("=>\n"));
 	if (ISNAN(x)) {
 		fe->fe_cx |= FPSCR_VXSNAN;
 		DUMPFPN(FPE_REG, x);
 		return (x);
+	}
 	if (ISZERO(x)) {
 		fe->fe_cx |= FPSCR_ZX;
 		x->fp_class = FPC_INF;
 		DUMPFPN(FPE_REG, x);
 		return (x);
+	}
 	if (x->fp_sign) {
 		fe->fe_cx |= FPSCR_VXSQRT;
 		return (fpu_newnan(fe));
+	}
 	if (ISINF(x)) {
-		fe->fe_cx |= FPSCR_VXSQRT;
+		DUMPFPN(FPE_REG, x);
-		DUMPFPN(FPE_REG, 0);
+		return (x);
 		return (0);
+	}
 	/*
 	 * Calculate result exponent.  As noted above, this may involve
 	 * doubling the mantissa.  We will also need to double x each
 	 * time around the loop, so we define a macro for this here, and
 	 * we break out the multiword mantissa.
 	 */
 #ifdef FPU_SHL1_BY_ADD
 #define	DOUBLE_X { \
 	FPU_ADDS(x3, x3, x3); FPU_ADDCS(x2, x2, x2); \
 	FPU_ADDCS(x1, x1, x1); FPU_ADDC(x0, x0, x0); \
+}
 #else
 #define	DOUBLE_X { \
 	x0 = (x0 << 1) | (x1 >> 31); x1 = (x1 << 1) | (x2 >> 31); \
 	x2 = (x2 << 1) | (x3 >> 31); x3 <<= 1; \
+}
 #endif
 #if (FP_NMANT & 1) != 0
 # define ODD_DOUBLE	DOUBLE_X
 # define EVEN_DOUBLE	/* nothing */
 #else
 # define ODD_DOUBLE	/* nothing */
 # define EVEN_DOUBLE	DOUBLE_X
 #endif
 	x0 = x->fp_mant[0];
 	x1 = x->fp_mant[1];
 	x2 = x->fp_mant[2];
 	x3 = x->fp_mant[3];
 	e = x->fp_exp;
 	if (e & 1)		/* exponent is odd; use sqrt(2mant) */
 		DOUBLE_X;
 	/* THE FOLLOWING ASSUMES THAT RIGHT SHIFT DOES SIGN EXTENSION */
 	x->fp_exp = e >> 1;	/* calculates (e&1 ? (e-1)/2 : e/2 */
 	/*
 	 * Now calculate the mantissa root.  Since x is now in [1..4),
 	 * we know that the first trip around the loop will definitely
 	 * set the top bit in q, so we can do that manually and start
 	 * the loop at the next bit down instead.  We must be sure to
 	 * double x correctly while doing the `known q=1.0'.
+	 *
 	 * We do this one mantissa-word at a time, as noted above, to
 	 * save work.  To avoid `(1 << 31) << 1', we also do the top bit
 	 * outside of each per-word loop.
+	 *
 	 * The calculation `t = y + bit' breaks down into `t0 = y0, ...,
 	 * t3 = y3, t? |= bit' for the appropriate word.  Since the bit
 	 * is always a `new' one, this means that three of the `t?'s are
 	 * just the corresponding `y?'; we use `#define's here for this.
 	 * The variable `tt' holds the actual `t?' variable.
 	 */
 	/* calculate q0 */
 #define	t0 tt
 	bit = FP_1;
 	EVEN_DOUBLE;
 	/* if (x >= (t0 = y0 | bit)) { */	/* always true */
 		q = bit;
 		x0 -= bit;
 		y0 = bit << 1;
 	/* } */
 	ODD_DOUBLE;
 	while ((bit >>= 1) != 0) {	/* for remaining bits in q0 */
 		EVEN_DOUBLE;
 		t0 = y0 | bit;		/* t = y + bit */
 		if (x0 >= t0) {		/* if x >= t then */
 			x0 -= t0;	/*	x -= t */
 			q |= bit;	/*	q += bit */
 			y0 |= bit << 1;	/*	y += bit << 1 */
+		}
 		ODD_DOUBLE;
+	}
 	x->fp_mant[0] = q;
 #undef t0
 	/* calculate q1.  note (y0&1)==0. */
 #define t0 y0
 #define t1 tt
 	q = 0;
 	y1 = 0;
 	bit = 1 << 31;
 	EVEN_DOUBLE;
 	t1 = bit;
 	FPU_SUBS(d1, x1, t1);
 	FPU_SUBC(d0, x0, t0);		/* d = x - t */
 	if ((int)d0 >= 0) {		/* if d >= 0 (i.e., x >= t) then */
 		x0 = d0, x1 = d1;	/*	x -= t */
 		q = bit;		/*	q += bit */
 		y0 |= 1;		/*	y += bit << 1 */
+	}
 	ODD_DOUBLE;
 	while ((bit >>= 1) != 0) {	/* for remaining bits in q1 */
 		EVEN_DOUBLE;		/* as before */
 		t1 = y1 | bit;
 		FPU_SUBS(d1, x1, t1);
 		FPU_SUBC(d0, x0, t0);
 		if ((int)d0 >= 0) {
 			x0 = d0, x1 = d1;
 			q |= bit;
 			y1 |= bit << 1;
+		}
 		ODD_DOUBLE;
+	}
 	x->fp_mant[1] = q;
 #undef t1
 	/* calculate q2.  note (y1&1)==0; y0 (aka t0) is fixed. */
 #define t1 y1
 #define t2 tt
 	q = 0;
 	y2 = 0;
 	bit = 1 << 31;
 	EVEN_DOUBLE;
 	t2 = bit;
 	FPU_SUBS(d2, x2, t2);
 	FPU_SUBCS(d1, x1, t1);
 	FPU_SUBC(d0, x0, t0);
 	if ((int)d0 >= 0) {
 		x0 = d0, x1 = d1, x2 = d2;
 		q |= bit;
 		y1 |= 1;		/* now t1, y1 are set in concrete */
+	}
 	ODD_DOUBLE;
 	while ((bit >>= 1) != 0) {
 		EVEN_DOUBLE;
 		t2 = y2 | bit;
 		FPU_SUBS(d2, x2, t2);
 		FPU_SUBCS(d1, x1, t1);
 		FPU_SUBC(d0, x0, t0);
 		if ((int)d0 >= 0) {
 			x0 = d0, x1 = d1, x2 = d2;
 			q |= bit;
 			y2 |= bit << 1;
+		}
 		ODD_DOUBLE;
+	}
 	x->fp_mant[2] = q;
 #undef t2
 	/* calculate q3.  y0, t0, y1, t1 all fixed; y2, t2, almost done. */
 #define t2 y2
 #define t3 tt
 	q = 0;
 	y3 = 0;
 	bit = 1 << 31;
 	EVEN_DOUBLE;
 	t3 = bit;
 	FPU_SUBS(d3, x3, t3); __USE(d3);
 	FPU_SUBCS(d2, x2, t2);
 	FPU_SUBCS(d1, x1, t1);
 	FPU_SUBC(d0, x0, t0);
 	ODD_DOUBLE;
 	if ((int)d0 >= 0) {
 		x0 = d0, x1 = d1, x2 = d2;
 		q |= bit;
 		y2 |= 1;
+	}
 	while ((bit >>= 1) != 0) {
 		EVEN_DOUBLE;
 		t3 = y3 | bit;
 		FPU_SUBS(d3, x3, t3);
 		FPU_SUBCS(d2, x2, t2);
 		FPU_SUBCS(d1, x1, t1);
 		FPU_SUBC(d0, x0, t0);
 		if ((int)d0 >= 0) {
 			x0 = d0, x1 = d1, x2 = d2;
 			q |= bit;
 			y3 |= bit << 1;
+		}
 		ODD_DOUBLE;
+	}
 	x->fp_mant[3] = q;
 	/*
 	 * The result, which includes guard and round bits, is exact iff
 	 * x is now zero; any nonzero bits in x represent sticky bits.
 	 */
 	x->fp_sticky = x0 | x1 | x2 | x3;
 	DUMPFPN(FPE_REG, x);
 	return (x);
+}