/* $NetBSD: umul.S,v 1.1 2005/12/20 19:28:50 christos 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. * * 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. * * from: Header: umul.s,v 1.4 92/06/25 13:24:05 torek Exp */ #include <machine/asm.h> #if defined(LIBC_SCCS) && !defined(lint) #if 0 .asciz "@(#)umul.s 8.1 (Berkeley) 6/4/93" #else RCSID("$NetBSD: umul.S,v 1.1 2005/12/20 19:28:50 christos Exp $") #endif #endif /* LIBC_SCCS and not lint */ /* * Unsigned multiply. Returns %o0 * %o1 in %o1%o0 (i.e., %o1 holds the * upper 32 bits of the 64-bit product). * * This code optimizes short (less than 13-bit) multiplies. Short * multiplies require 25 instruction cycles, and long ones require * 45 instruction cycles. * * On return, overflow has occurred (%o1 is not zero) if and only if * the Z condition code is clear, allowing, e.g., the following: * * call .umul * nop * bnz overflow (or tnz) */ FUNC(.umul) or %o0, %o1, %o4 mov %o0, %y ! multiplier -> Y andncc %o4, 0xfff, %g0 ! test bits 12..31 of *both* args be Lmul_shortway ! if zero, can do it the short way andcc %g0, %g0, %o4 ! zero the partial product and clear N and V /* * Long multiply. 32 steps, followed by a final shift step. */ mulscc %o4, %o1, %o4 ! 1 mulscc %o4, %o1, %o4 ! 2 mulscc %o4, %o1, %o4 ! 3 mulscc %o4, %o1, %o4 ! 4 mulscc %o4, %o1, %o4 ! 5 mulscc %o4, %o1, %o4 ! 6 mulscc %o4, %o1, %o4 ! 7 mulscc %o4, %o1, %o4 ! 8 mulscc %o4, %o1, %o4 ! 9 mulscc %o4, %o1, %o4 ! 10 mulscc %o4, %o1, %o4 ! 11 mulscc %o4, %o1, %o4 ! 12 mulscc %o4, %o1, %o4 ! 13 mulscc %o4, %o1, %o4 ! 14 mulscc %o4, %o1, %o4 ! 15 mulscc %o4, %o1, %o4 ! 16 mulscc %o4, %o1, %o4 ! 17 mulscc %o4, %o1, %o4 ! 18 mulscc %o4, %o1, %o4 ! 19 mulscc %o4, %o1, %o4 ! 20 mulscc %o4, %o1, %o4 ! 21 mulscc %o4, %o1, %o4 ! 22 mulscc %o4, %o1, %o4 ! 23 mulscc %o4, %o1, %o4 ! 24 mulscc %o4, %o1, %o4 ! 25 mulscc %o4, %o1, %o4 ! 26 mulscc %o4, %o1, %o4 ! 27 mulscc %o4, %o1, %o4 ! 28 mulscc %o4, %o1, %o4 ! 29 mulscc %o4, %o1, %o4 ! 30 mulscc %o4, %o1, %o4 ! 31 mulscc %o4, %o1, %o4 ! 32 mulscc %o4, %g0, %o4 ! final shift /* * Normally, with the shift-and-add approach, if both numbers are * positive you get the correct result. WIth 32-bit two's-complement * numbers, -x is represented as * * x 32 * ( 2 - ------ ) mod 2 * 2 * 32 * 2 * * (the `mod 2' subtracts 1 from 1.bbbb). To avoid lots of 2^32s, * we can treat this as if the radix point were just to the left * of the sign bit (multiply by 2^32), and get * * -x = (2 - x) mod 2 * * Then, ignoring the `mod 2's for convenience: * * x * y = xy * -x * y = 2y - xy * x * -y = 2x - xy * -x * -y = 4 - 2x - 2y + xy * * For signed multiplies, we subtract (x << 32) from the partial * product to fix this problem for negative multipliers (see mul.s). * Because of the way the shift into the partial product is calculated * (N xor V), this term is automatically removed for the multiplicand, * so we don't have to adjust. * * But for unsigned multiplies, the high order bit wasn't a sign bit, * and the correction is wrong. So for unsigned multiplies where the * high order bit is one, we end up with xy - (y << 32). To fix it * we add y << 32. */ tst %o1 bl,a 1f ! if %o1 < 0 (high order bit = 1), add %o4, %o0, %o4 ! %o4 += %o0 (add y to upper half) 1: rd %y, %o0 ! get lower half of product retl addcc %o4, %g0, %o1 ! put upper half in place and set Z for %o1==0 Lmul_shortway: /* * Short multiply. 12 steps, followed by a final shift step. * The resulting bits are off by 12 and (32-12) = 20 bit positions, * but there is no problem with %o0 being negative (unlike above), * and overflow is impossible (the answer is at most 24 bits long). */ mulscc %o4, %o1, %o4 ! 1 mulscc %o4, %o1, %o4 ! 2 mulscc %o4, %o1, %o4 ! 3 mulscc %o4, %o1, %o4 ! 4 mulscc %o4, %o1, %o4 ! 5 mulscc %o4, %o1, %o4 ! 6 mulscc %o4, %o1, %o4 ! 7 mulscc %o4, %o1, %o4 ! 8 mulscc %o4, %o1, %o4 ! 9 mulscc %o4, %o1, %o4 ! 10 mulscc %o4, %o1, %o4 ! 11 mulscc %o4, %o1, %o4 ! 12 mulscc %o4, %g0, %o4 ! final shift /* * %o4 has 20 of the bits that should be in the result; %y has * the bottom 12 (as %y's top 12). That is: * * %o4 %y * +----------------+----------------+ * | -12- | -20- | -12- | -20- | * +------(---------+------)---------+ * -----result----- * * The 12 bits of %o4 left of the `result' area are all zero; * in fact, all top 20 bits of %o4 are zero. */ rd %y, %o5 sll %o4, 12, %o0 ! shift middle bits left 12 srl %o5, 20, %o5 ! shift low bits right 20 or %o5, %o0, %o0 retl addcc %g0, %g0, %o1 ! %o1 = zero, and set Z
