[PATCH 2/2] Drop dependency on libgcc by importing part of FreeBSD's libquad
Jessica Clarke
jrtc27 at jrtc27.com
Tue Jul 6 08:59:24 PDT 2021
On 6 Jul 2021, at 09:35, Anup Patel <anup at brainfault.org> wrote:
>
> On Sat, Jul 3, 2021 at 11:26 PM Jessica Clarke <jrtc27 at jrtc27.com> wrote:
>>
>> We only need libgcc for 64-bit division on RV32. Whilst GCC toolchains
>> bundle libgcc, Clang toolchains tend not to ship libclang_rt.builtins
>> given every compiler is a cross-compiler for every target and so you
>> would need a silly number of builds of it, with only the native library
>> available; only vendor-provided Clang toolchains specifically for bare
>> metal cross-compiling are likely to provide it.
>>
>> Thus, import part of FreeBSD's implementation of the division support
>> functions needed and stop linking against libgcc.
>>
>> Signed-off-by: Jessica Clarke <jrtc27 at jrtc27.com>
>
> Apart from the query regarding BSD-3-clause compatibility with
> BSD-2-clause, this looks good to me.
The HTIF and SiFive Test device code is already BSD-3-Clause. It does
mean the terms of the 3rd clause (that you can’t use the names of the
university nor any other authors of the file to endorse products using
the code without their permission) apply to binaries built with the
code in it, but that’s already the case given the aforementioned files,
and should not be a restriction anyone cares about. Arm’s TF-A is
BSD-3-Clause, BBL was BSD-3-Clause, FreeBSD is BSD-3-Clause, it’s hard
to find examples of purely BSD-2-Clause software out there as most
BSD-licensed software like this has *something* derived from the
original BSD sources and thus has the 3rd clause.
Jess
> Reviewed-by: Anup Patel <anup.patel at wdc.com>
>
> Regards,
> Anup
>
>> ---
>> Makefile | 2 +-
>> lib/utils/libquad/divdi3.c | 64 ++++++
>> lib/utils/libquad/include/limits.h | 12 ++
>> lib/utils/libquad/include/sys/cdefs.h | 12 ++
>> lib/utils/libquad/include/sys/types.h | 25 +++
>> lib/utils/libquad/moddi3.c | 66 ++++++
>> lib/utils/libquad/objects.mk | 14 ++
>> lib/utils/libquad/qdivrem.c | 278 ++++++++++++++++++++++++++
>> lib/utils/libquad/quad.h | 105 ++++++++++
>> lib/utils/libquad/udivdi3.c | 52 +++++
>> lib/utils/libquad/umoddi3.c | 54 +++++
>> 11 files changed, 683 insertions(+), 1 deletion(-)
>>
>> diff --git a/Makefile b/Makefile
>> index 40bcab6..bc4429a 100644
>> --- a/Makefile
>> +++ b/Makefile
>> @@ -259,7 +259,7 @@ ASFLAGS += $(firmware-asflags-y)
>>
>> ARFLAGS = rcs
>>
>> -ELFFLAGS += -Wl,--build-id=none -Wl,-N -static-libgcc -lgcc
>> +ELFFLAGS += -Wl,--build-id=none -Wl,-N
>> ELFFLAGS += $(platform-ldflags-y)
>> ELFFLAGS += $(firmware-ldflags-y)
>>
>> diff --git a/lib/utils/libquad/divdi3.c b/lib/utils/libquad/divdi3.c
>> new file mode 100644
>> index 0000000..c5b4a37
>> --- /dev/null
>> +++ b/lib/utils/libquad/divdi3.c
>> @@ -0,0 +1,64 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + */
>> +
>> +#if defined(LIBC_SCCS) && !defined(lint)
>> +static char sccsid[] = "@(#)divdi3.c 8.1 (Berkeley) 6/4/93";
>> +#endif /* LIBC_SCCS and not lint */
>> +#include <sys/cdefs.h>
>> +__FBSDID("$FreeBSD$");
>> +
>> +#include "quad.h"
>> +
>> +/*
>> + * Divide two signed quads.
>> + * ??? if -1/2 should produce -1 on this machine, this code is wrong
>> + */
>> +quad_t
>> +__divdi3(quad_t a, quad_t b)
>> +{
>> + u_quad_t ua, ub, uq;
>> + int neg;
>> +
>> + if (a < 0)
>> + ua = -(u_quad_t)a, neg = 1;
>> + else
>> + ua = a, neg = 0;
>> + if (b < 0)
>> + ub = -(u_quad_t)b, neg ^= 1;
>> + else
>> + ub = b;
>> + uq = __qdivrem(ua, ub, (u_quad_t *)0);
>> + return (neg ? -uq : uq);
>> +}
>> diff --git a/lib/utils/libquad/include/limits.h b/lib/utils/libquad/include/limits.h
>> new file mode 100644
>> index 0000000..9c69d27
>> --- /dev/null
>> +++ b/lib/utils/libquad/include/limits.h
>> @@ -0,0 +1,12 @@
>> +/*
>> + * SPDX-License-Identifier: BSD-2-Clause
>> + *
>> + * Copyright (c) 2021 Jessica Clarke <jrtc27 at jrtc27.com>
>> + */
>> +
>> +#ifndef __LIMITS_H__
>> +#define __LIMITS_H__
>> +
>> +#define CHAR_BIT 8
>> +
>> +#endif
>> diff --git a/lib/utils/libquad/include/sys/cdefs.h b/lib/utils/libquad/include/sys/cdefs.h
>> new file mode 100644
>> index 0000000..e8d6faa
>> --- /dev/null
>> +++ b/lib/utils/libquad/include/sys/cdefs.h
>> @@ -0,0 +1,12 @@
>> +/*
>> + * SPDX-License-Identifier: BSD-2-Clause
>> + *
>> + * Copyright (c) 2021 Jessica Clarke <jrtc27 at jrtc27.com>
>> + */
>> +
>> +#ifndef __SYS_CDEFS_H__
>> +#define __SYS_CDEFS_H__
>> +
>> +#define __FBSDID(s) struct __hack
>> +
>> +#endif
>> diff --git a/lib/utils/libquad/include/sys/types.h b/lib/utils/libquad/include/sys/types.h
>> new file mode 100644
>> index 0000000..e372437
>> --- /dev/null
>> +++ b/lib/utils/libquad/include/sys/types.h
>> @@ -0,0 +1,25 @@
>> +/*
>> + * SPDX-License-Identifier: BSD-2-Clause
>> + *
>> + * Copyright (c) 2021 Jessica Clarke <jrtc27 at jrtc27.com>
>> + */
>> +
>> +#ifndef __SYS_TYPES_H__
>> +#define __SYS_TYPES_H__
>> +
>> +#include <sbi/sbi_types.h>
>> +
>> +typedef unsigned long u_long;
>> +
>> +typedef int64_t quad_t;
>> +typedef uint64_t u_quad_t;
>> +
>> +#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
>> +#define _QUAD_LOWWORD 1
>> +#define _QUAD_HIGHWORD 0
>> +#else
>> +#define _QUAD_LOWWORD 0
>> +#define _QUAD_HIGHWORD 1
>> +#endif
>> +
>> +#endif
>> diff --git a/lib/utils/libquad/moddi3.c b/lib/utils/libquad/moddi3.c
>> new file mode 100644
>> index 0000000..fc13b4d
>> --- /dev/null
>> +++ b/lib/utils/libquad/moddi3.c
>> @@ -0,0 +1,66 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + */
>> +
>> +#if defined(LIBC_SCCS) && !defined(lint)
>> +static char sccsid[] = "@(#)moddi3.c 8.1 (Berkeley) 6/4/93";
>> +#endif /* LIBC_SCCS and not lint */
>> +#include <sys/cdefs.h>
>> +__FBSDID("$FreeBSD$");
>> +
>> +#include "quad.h"
>> +
>> +/*
>> + * Return remainder after dividing two signed quads.
>> + *
>> + * XXX
>> + * If -1/2 should produce -1 on this machine, this code is wrong.
>> + */
>> +quad_t
>> +__moddi3(quad_t a, quad_t b)
>> +{
>> + u_quad_t ua, ub, ur;
>> + int neg;
>> +
>> + if (a < 0)
>> + ua = -(u_quad_t)a, neg = 1;
>> + else
>> + ua = a, neg = 0;
>> + if (b < 0)
>> + ub = -(u_quad_t)b;
>> + else
>> + ub = b;
>> + (void)__qdivrem(ua, ub, &ur);
>> + return (neg ? -ur : ur);
>> +}
>> diff --git a/lib/utils/libquad/objects.mk b/lib/utils/libquad/objects.mk
>> new file mode 100644
>> index 0000000..5e53cd0
>> --- /dev/null
>> +++ b/lib/utils/libquad/objects.mk
>> @@ -0,0 +1,14 @@
>> +#
>> +# SPDX-License-Identifier: BSD-2-Clause
>> +#
>> +# Copyright (c) 2021 Jessica Clarke <jrtc27 at jrtc27.com>
>> +#
>> +
>> +ifeq ($(PLATFORM_RISCV_XLEN),32)
>> +libsbiutils-objs-y += libquad/divdi3.o
>> +libsbiutils-objs-y += libquad/moddi3.o
>> +libsbiutils-objs-y += libquad/qdivrem.o
>> +libsbiutils-objs-y += libquad/udivdi3.o
>> +libsbiutils-objs-y += libquad/umoddi3.o
>> +libsbiutils-genflags-y += -I$(libsbiutils_dir)/libquad/include
>> +endif
>> diff --git a/lib/utils/libquad/qdivrem.c b/lib/utils/libquad/qdivrem.c
>> new file mode 100644
>> index 0000000..ea09e7f
>> --- /dev/null
>> +++ b/lib/utils/libquad/qdivrem.c
>> @@ -0,0 +1,278 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + */
>> +
>> +#if defined(LIBC_SCCS) && !defined(lint)
>> +static char sccsid[] = "@(#)qdivrem.c 8.1 (Berkeley) 6/4/93";
>> +#endif /* LIBC_SCCS and not lint */
>> +#include <sys/cdefs.h>
>> +__FBSDID("$FreeBSD$");
>> +
>> +/*
>> + * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
>> + * section 4.3.1, pp. 257--259.
>> + */
>> +
>> +#include "quad.h"
>> +
>> +#define B (1L << HALF_BITS) /* digit base */
>> +
>> +/* Combine two `digits' to make a single two-digit number. */
>> +#define COMBINE(a, b) (((u_long)(a) << HALF_BITS) | (b))
>> +
>> +/* select a type for digits in base B: use unsigned short if they fit */
>> +#if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
>> +typedef unsigned short digit;
>> +#else
>> +typedef u_long digit;
>> +#endif
>> +
>> +/*
>> + * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
>> + * `fall out' the left (there never will be any such anyway).
>> + * We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
>> + */
>> +static void
>> +shl(digit *p, int len, int sh)
>> +{
>> + int i;
>> +
>> + for (i = 0; i < len; i++)
>> + p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
>> + p[i] = LHALF(p[i] << sh);
>> +}
>> +
>> +/*
>> + * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
>> + *
>> + * We do this in base 2-sup-HALF_BITS, so that all intermediate products
>> + * fit within u_long. As a consequence, the maximum length dividend and
>> + * divisor are 4 `digits' in this base (they are shorter if they have
>> + * leading zeros).
>> + */
>> +u_quad_t
>> +__qdivrem(u_quad_t uq, u_quad_t vq, u_quad_t *arq)
>> +{
>> + union uu tmp;
>> + digit *u, *v, *q;
>> + digit v1, v2;
>> + u_long qhat, rhat, t;
>> + int m, n, d, j, i;
>> + digit uspace[5], vspace[5], qspace[5];
>> +
>> + /*
>> + * Take care of special cases: divide by zero, and u < v.
>> + */
>> + if (vq == 0) {
>> + /* divide by zero. */
>> + static volatile const unsigned int zero = 0;
>> +
>> + tmp.ul[H] = tmp.ul[L] = 1 / zero;
>> + if (arq)
>> + *arq = uq;
>> + return (tmp.q);
>> + }
>> + if (uq < vq) {
>> + if (arq)
>> + *arq = uq;
>> + return (0);
>> + }
>> + u = &uspace[0];
>> + v = &vspace[0];
>> + q = &qspace[0];
>> +
>> + /*
>> + * Break dividend and divisor into digits in base B, then
>> + * count leading zeros to determine m and n. When done, we
>> + * will have:
>> + * u = (u[1]u[2]...u[m+n]) sub B
>> + * v = (v[1]v[2]...v[n]) sub B
>> + * v[1] != 0
>> + * 1 < n <= 4 (if n = 1, we use a different division algorithm)
>> + * m >= 0 (otherwise u < v, which we already checked)
>> + * m + n = 4
>> + * and thus
>> + * m = 4 - n <= 2
>> + */
>> + tmp.uq = uq;
>> + u[0] = 0;
>> + u[1] = HHALF(tmp.ul[H]);
>> + u[2] = LHALF(tmp.ul[H]);
>> + u[3] = HHALF(tmp.ul[L]);
>> + u[4] = LHALF(tmp.ul[L]);
>> + tmp.uq = vq;
>> + v[1] = HHALF(tmp.ul[H]);
>> + v[2] = LHALF(tmp.ul[H]);
>> + v[3] = HHALF(tmp.ul[L]);
>> + v[4] = LHALF(tmp.ul[L]);
>> + for (n = 4; v[1] == 0; v++) {
>> + if (--n == 1) {
>> + u_long rbj; /* r*B+u[j] (not root boy jim) */
>> + digit q1, q2, q3, q4;
>> +
>> + /*
>> + * Change of plan, per exercise 16.
>> + * r = 0;
>> + * for j = 1..4:
>> + * q[j] = floor((r*B + u[j]) / v),
>> + * r = (r*B + u[j]) % v;
>> + * We unroll this completely here.
>> + */
>> + t = v[2]; /* nonzero, by definition */
>> + q1 = u[1] / t;
>> + rbj = COMBINE(u[1] % t, u[2]);
>> + q2 = rbj / t;
>> + rbj = COMBINE(rbj % t, u[3]);
>> + q3 = rbj / t;
>> + rbj = COMBINE(rbj % t, u[4]);
>> + q4 = rbj / t;
>> + if (arq)
>> + *arq = rbj % t;
>> + tmp.ul[H] = COMBINE(q1, q2);
>> + tmp.ul[L] = COMBINE(q3, q4);
>> + return (tmp.q);
>> + }
>> + }
>> +
>> + /*
>> + * By adjusting q once we determine m, we can guarantee that
>> + * there is a complete four-digit quotient at &qspace[1] when
>> + * we finally stop.
>> + */
>> + for (m = 4 - n; u[1] == 0; u++)
>> + m--;
>> + for (i = 4 - m; --i >= 0;)
>> + q[i] = 0;
>> + q += 4 - m;
>> +
>> + /*
>> + * Here we run Program D, translated from MIX to C and acquiring
>> + * a few minor changes.
>> + *
>> + * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
>> + */
>> + d = 0;
>> + for (t = v[1]; t < B / 2; t <<= 1)
>> + d++;
>> + if (d > 0) {
>> + shl(&u[0], m + n, d); /* u <<= d */
>> + shl(&v[1], n - 1, d); /* v <<= d */
>> + }
>> + /*
>> + * D2: j = 0.
>> + */
>> + j = 0;
>> + v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
>> + v2 = v[2]; /* for D3 */
>> + do {
>> + digit uj0, uj1, uj2;
>> +
>> + /*
>> + * D3: Calculate qhat (\^q, in TeX notation).
>> + * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
>> + * let rhat = (u[j]*B + u[j+1]) mod v[1].
>> + * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
>> + * decrement qhat and increase rhat correspondingly.
>> + * Note that if rhat >= B, v[2]*qhat < rhat*B.
>> + */
>> + uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
>> + uj1 = u[j + 1]; /* for D3 only */
>> + uj2 = u[j + 2]; /* for D3 only */
>> + if (uj0 == v1) {
>> + qhat = B;
>> + rhat = uj1;
>> + goto qhat_too_big;
>> + } else {
>> + u_long n = COMBINE(uj0, uj1);
>> + qhat = n / v1;
>> + rhat = n % v1;
>> + }
>> + while (v2 * qhat > COMBINE(rhat, uj2)) {
>> + qhat_too_big:
>> + qhat--;
>> + if ((rhat += v1) >= B)
>> + break;
>> + }
>> + /*
>> + * D4: Multiply and subtract.
>> + * The variable `t' holds any borrows across the loop.
>> + * We split this up so that we do not require v[0] = 0,
>> + * and to eliminate a final special case.
>> + */
>> + for (t = 0, i = n; i > 0; i--) {
>> + t = u[i + j] - v[i] * qhat - t;
>> + u[i + j] = LHALF(t);
>> + t = (B - HHALF(t)) & (B - 1);
>> + }
>> + t = u[j] - t;
>> + u[j] = LHALF(t);
>> + /*
>> + * D5: test remainder.
>> + * There is a borrow if and only if HHALF(t) is nonzero;
>> + * in that (rare) case, qhat was too large (by exactly 1).
>> + * Fix it by adding v[1..n] to u[j..j+n].
>> + */
>> + if (HHALF(t)) {
>> + qhat--;
>> + for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
>> + t += u[i + j] + v[i];
>> + u[i + j] = LHALF(t);
>> + t = HHALF(t);
>> + }
>> + u[j] = LHALF(u[j] + t);
>> + }
>> + q[j] = qhat;
>> + } while (++j <= m); /* D7: loop on j. */
>> +
>> + /*
>> + * If caller wants the remainder, we have to calculate it as
>> + * u[m..m+n] >> d (this is at most n digits and thus fits in
>> + * u[m+1..m+n], but we may need more source digits).
>> + */
>> + if (arq) {
>> + if (d) {
>> + for (i = m + n; i > m; --i)
>> + u[i] = (u[i] >> d) |
>> + LHALF(u[i - 1] << (HALF_BITS - d));
>> + u[i] = 0;
>> + }
>> + tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
>> + tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
>> + *arq = tmp.q;
>> + }
>> +
>> + tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
>> + tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
>> + return (tmp.q);
>> +}
>> diff --git a/lib/utils/libquad/quad.h b/lib/utils/libquad/quad.h
>> new file mode 100644
>> index 0000000..a9f8447
>> --- /dev/null
>> +++ b/lib/utils/libquad/quad.h
>> @@ -0,0 +1,105 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + *
>> + * @(#)quad.h 8.1 (Berkeley) 6/4/93
>> + * $FreeBSD$
>> + */
>> +
>> +/*
>> + * Quad arithmetic.
>> + *
>> + * This library makes the following assumptions:
>> + *
>> + * - The type long long (aka quad_t) exists.
>> + *
>> + * - A quad variable is exactly twice as long as `long'.
>> + *
>> + * - The machine's arithmetic is two's complement.
>> + *
>> + * This library can provide 128-bit arithmetic on a machine with 128-bit
>> + * quads and 64-bit longs, for instance, or 96-bit arithmetic on machines
>> + * with 48-bit longs.
>> + */
>> +
>> +#include <sys/types.h>
>> +#include <limits.h>
>> +
>> +/*
>> + * Depending on the desired operation, we view a `long long' (aka quad_t) in
>> + * one or more of the following formats.
>> + */
>> +union uu {
>> + quad_t q; /* as a (signed) quad */
>> + quad_t uq; /* as an unsigned quad */
>> + long sl[2]; /* as two signed longs */
>> + u_long ul[2]; /* as two unsigned longs */
>> +};
>> +
>> +/*
>> + * Define high and low longwords.
>> + */
>> +#define H _QUAD_HIGHWORD
>> +#define L _QUAD_LOWWORD
>> +
>> +/*
>> + * Total number of bits in a quad_t and in the pieces that make it up.
>> + * These are used for shifting, and also below for halfword extraction
>> + * and assembly.
>> + */
>> +#define QUAD_BITS (sizeof(quad_t) * CHAR_BIT)
>> +#define LONG_BITS (sizeof(long) * CHAR_BIT)
>> +#define HALF_BITS (sizeof(long) * CHAR_BIT / 2)
>> +
>> +/*
>> + * Extract high and low shortwords from longword, and move low shortword of
>> + * longword to upper half of long, i.e., produce the upper longword of
>> + * ((quad_t)(x) << (number_of_bits_in_long/2)). (`x' must actually be u_long.)
>> + *
>> + * These are used in the multiply code, to split a longword into upper
>> + * and lower halves, and to reassemble a product as a quad_t, shifted left
>> + * (sizeof(long)*CHAR_BIT/2).
>> + */
>> +#define HHALF(x) ((x) >> HALF_BITS)
>> +#define LHALF(x) ((x) & ((1L << HALF_BITS) - 1))
>> +#define LHUP(x) ((x) << HALF_BITS)
>> +
>> +int __cmpdi2(quad_t a, quad_t b);
>> +quad_t __divdi3(quad_t a, quad_t b);
>> +quad_t __moddi3(quad_t a, quad_t b);
>> +u_quad_t __qdivrem(u_quad_t u, u_quad_t v, u_quad_t *rem);
>> +int __ucmpdi2(u_quad_t a, u_quad_t b);
>> +u_quad_t __udivdi3(u_quad_t a, u_quad_t b);
>> +u_quad_t __umoddi3(u_quad_t a, u_quad_t b);
>> +
>> +typedef unsigned int qshift_t;
>> diff --git a/lib/utils/libquad/udivdi3.c b/lib/utils/libquad/udivdi3.c
>> new file mode 100644
>> index 0000000..0e6f27e
>> --- /dev/null
>> +++ b/lib/utils/libquad/udivdi3.c
>> @@ -0,0 +1,52 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + */
>> +
>> +#if defined(LIBC_SCCS) && !defined(lint)
>> +static char sccsid[] = "@(#)udivdi3.c 8.1 (Berkeley) 6/4/93";
>> +#endif /* LIBC_SCCS and not lint */
>> +#include <sys/cdefs.h>
>> +__FBSDID("$FreeBSD$");
>> +
>> +#include "quad.h"
>> +
>> +/*
>> + * Divide two unsigned quads.
>> + */
>> +u_quad_t
>> +__udivdi3(u_quad_t a, u_quad_t b)
>> +{
>> +
>> + return (__qdivrem(a, b, (u_quad_t *)0));
>> +}
>> diff --git a/lib/utils/libquad/umoddi3.c b/lib/utils/libquad/umoddi3.c
>> new file mode 100644
>> index 0000000..7f45134
>> --- /dev/null
>> +++ b/lib/utils/libquad/umoddi3.c
>> @@ -0,0 +1,54 @@
>> +/*-
>> + * SPDX-License-Identifier: BSD-3-Clause
>> + *
>> + * 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.
>> + */
>> +
>> +#if defined(LIBC_SCCS) && !defined(lint)
>> +static char sccsid[] = "@(#)umoddi3.c 8.1 (Berkeley) 6/4/93";
>> +#endif /* LIBC_SCCS and not lint */
>> +#include <sys/cdefs.h>
>> +__FBSDID("$FreeBSD$");
>> +
>> +#include "quad.h"
>> +
>> +/*
>> + * Return remainder after dividing two unsigned quads.
>> + */
>> +u_quad_t
>> +__umoddi3(u_quad_t a, u_quad_t b)
>> +{
>> + u_quad_t r;
>> +
>> + (void)__qdivrem(a, b, &r);
>> + return (r);
>> +}
>> --
>> 2.31.0
>>
>>
>> --
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