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[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] [xen master] lib: move 64-bit div/mod compiler helpers
commit 849db4945b8b166085751681ac8b4f5b7cefece0
Author: Jan Beulich <jbeulich@xxxxxxxx>
AuthorDate: Fri Apr 16 14:43:10 2021 +0200
Commit: Jan Beulich <jbeulich@xxxxxxxx>
CommitDate: Fri Apr 16 14:43:10 2021 +0200
lib: move 64-bit div/mod compiler helpers
These were built for 32-bit architectures only (the same code could,
with some tweaking, sensibly be used to provide TI-mode helpers on
64-bit arch-es) - retain this property, while still avoiding to have
a CU without any contents at all. For this, Arm's CONFIG_64BIT gets
generalized.
Note that we imply "32-bit arch" to be the same as BITS_PER_LONG == 32,
i.e. we aren't (not just here) prepared to have a 64-bit arch with
BITS_PER_LONG == 32. Yet even if we supported such, likely the compiler
would get away there without invoking these helpers, so the code would
remain unused in practice.
Signed-off-by: Jan Beulich <jbeulich@xxxxxxxx>
Acked-by: Julien Grall <jgrall@xxxxxxxxxx>
---
xen/arch/Kconfig | 2 +
xen/arch/arm/Kconfig | 12 +-
xen/arch/x86/Kconfig | 1 +
xen/common/Makefile | 1 -
xen/common/lib.c | 404 ---------------------------------------------------
xen/lib/Makefile | 4 +
xen/lib/divmod.c | 402 ++++++++++++++++++++++++++++++++++++++++++++++++++
7 files changed, 412 insertions(+), 414 deletions(-)
diff --git a/xen/arch/Kconfig b/xen/arch/Kconfig
index d144d4c8d3..f16eb0df43 100644
--- a/xen/arch/Kconfig
+++ b/xen/arch/Kconfig
@@ -1,3 +1,5 @@
+config 64BIT
+ bool
config NR_CPUS
int "Maximum number of CPUs"
diff --git a/xen/arch/arm/Kconfig b/xen/arch/arm/Kconfig
index 330bbf6232..ecfa6822e4 100644
--- a/xen/arch/arm/Kconfig
+++ b/xen/arch/arm/Kconfig
@@ -1,17 +1,11 @@
-config 64BIT
- bool
- default "$(ARCH)" != "arm32"
- help
- Say yes to build a 64-bit Xen
- Say no to build a 32-bit Xen
-
config ARM_32
def_bool y
- depends on !64BIT
+ depends on "$(ARCH)" = "arm32"
config ARM_64
def_bool y
- depends on 64BIT
+ depends on !ARM_32
+ select 64BIT
select HAS_FAST_MULTIPLY
config ARM
diff --git a/xen/arch/x86/Kconfig b/xen/arch/x86/Kconfig
index cb401fa2e5..57776d5106 100644
--- a/xen/arch/x86/Kconfig
+++ b/xen/arch/x86/Kconfig
@@ -1,5 +1,6 @@
config X86_64
def_bool y
+ select 64BIT
config X86
def_bool y
diff --git a/xen/common/Makefile b/xen/common/Makefile
index 71c1d466bd..e2a7e62d14 100644
--- a/xen/common/Makefile
+++ b/xen/common/Makefile
@@ -21,7 +21,6 @@ obj-y += kernel.o
obj-y += keyhandler.o
obj-$(CONFIG_KEXEC) += kexec.o
obj-$(CONFIG_KEXEC) += kimage.o
-obj-y += lib.o
obj-$(CONFIG_LIVEPATCH) += livepatch.o livepatch_elf.o
obj-$(CONFIG_MEM_ACCESS) += mem_access.o
obj-y += memory.o
diff --git a/xen/common/lib.c b/xen/common/lib.c
deleted file mode 100644
index 5b8f49153d..0000000000
--- a/xen/common/lib.c
+++ /dev/null
@@ -1,404 +0,0 @@
-#include <xen/lib.h>
-#include <xen/types.h>
-#include <asm/byteorder.h>
-
-/*
- * A couple of 64 bit operations ported from FreeBSD.
- * The code within the '#if BITS_PER_LONG == 32' block below, and no other
- * code in this file, is distributed under the following licensing terms
- * This is the modified '3-clause' BSD license with the obnoxious
- * advertising clause removed, as permitted by University of California.
- *
- * 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 BITS_PER_LONG == 32
-
-/*
- * Depending on the desired operation, we view a `long long' (aka quad_t) in
- * one or more of the following formats.
- */
-union uu {
- s64 q; /* as a (signed) quad */
- s64 uq; /* as an unsigned quad */
- long sl[2]; /* as two signed longs */
- unsigned long ul[2]; /* as two unsigned longs */
-};
-
-#ifdef __BIG_ENDIAN
-#define _QUAD_HIGHWORD 0
-#define _QUAD_LOWWORD 1
-#else /* __LITTLE_ENDIAN */
-#define _QUAD_HIGHWORD 1
-#define _QUAD_LOWWORD 0
-#endif
-
-/*
- * 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 CHAR_BIT 8 /* number of bits in a char */
-#define QUAD_BITS (sizeof(s64) * 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
- * unsigned 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) & ((1 << HALF_BITS) - 1))
-#define LHUP(x) ((x) << HALF_BITS)
-
-/*
- * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
- * section 4.3.1, pp. 257--259.
- */
-#define B (1 << HALF_BITS) /* digit base */
-
-/* Combine two `digits' to make a single two-digit number. */
-#define COMBINE(a, b) (((unsigned long)(a) << HALF_BITS) | (b))
-
-/* select a type for digits in base B */
-typedef unsigned long digit;
-
-/*
- * 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(register digit *p, register int len, register int sh)
-{
- register 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 unsigned long. As a consequence, the maximum length dividend
- * and divisor are 4 `digits' in this base (they are shorter if they have
- * leading zeros).
- */
-u64 __qdivrem(u64 uq, u64 vq, u64 *arq)
-{
- union uu tmp;
- digit *u, *v, *q;
- register digit v1, v2;
- unsigned 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) {
- unsigned 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 {
- register 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 {
- unsigned long nn = COMBINE(uj0, uj1);
-
- qhat = nn / v1;
- rhat = nn % 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);
-}
-
-/*
- * Divide two signed quads.
- * Truncates towards zero, as required by C99.
- */
-s64 __divdi3(s64 a, s64 b)
-{
- u64 ua, ub, uq;
- int neg = (a < 0) ^ (b < 0);
- ua = (a < 0) ? -(u64)a : a;
- ub = (b < 0) ? -(u64)b : b;
- uq = __qdivrem(ua, ub, (u64 *)0);
- return (neg ? -uq : uq);
-}
-
-
-/*
- * Divide two unsigned quads.
- */
-u64 __udivdi3(u64 a, u64 b)
-{
- return __qdivrem(a, b, (u64 *)0);
-}
-
-/*
- * Remainder of unsigned quad division
- */
-u64 __umoddi3(u64 a, u64 b)
-{
- u64 rem;
- __qdivrem(a, b, &rem);
- return rem;
-}
-
-/*
- * Remainder of signed quad division.
- * Truncates towards zero, as required by C99:
- * 11 % 5 = 1
- * -11 % 5 = -1
- * 11 % -5 = 1
- * -11 % -5 = -1
- */
-s64 __moddi3(s64 a, s64 b)
-{
- u64 ua, ub, urem;
- int neg = (a < 0);
- ua = neg ? -(u64)a : a;
- ub = (b < 0) ? -(u64)b : b;
- __qdivrem(ua, ub, &urem);
- return (neg ? -urem : urem);
-}
-
-/*
- * Quotient and remainder of unsigned long long division
- */
-s64 __ldivmod_helper(s64 a, s64 b, s64 *r)
-{
- u64 ua, ub, rem, quot;
-
- ua = ABS(a);
- ub = ABS(b);
- quot = __qdivrem(ua, ub, &rem);
- if ( a < 0 )
- *r = -rem;
- else
- *r = rem;
- if ( (a < 0) ^ (b < 0) )
- return -quot;
- else
- return quot;
-}
-#endif /* BITS_PER_LONG == 32 */
-
-/*
- * Local variables:
- * mode: C
- * c-file-style: "BSD"
- * c-basic-offset: 4
- * tab-width: 4
- * indent-tabs-mode: nil
- * End:
- */
diff --git a/xen/lib/Makefile b/xen/lib/Makefile
index 0b274583ef..a5dc1442a4 100644
--- a/xen/lib/Makefile
+++ b/xen/lib/Makefile
@@ -10,3 +10,7 @@ lib-y += rbtree.o
lib-y += sort.o
lib-$(CONFIG_X86) += xxhash32.o
lib-$(CONFIG_X86) += xxhash64.o
+
+lib32-y := divmod.o
+lib32-$(CONFIG_64BIT) :=
+lib-y += $(lib32-y)
diff --git a/xen/lib/divmod.c b/xen/lib/divmod.c
new file mode 100644
index 0000000000..0be6ccc700
--- /dev/null
+++ b/xen/lib/divmod.c
@@ -0,0 +1,402 @@
+#include <xen/lib.h>
+#include <xen/types.h>
+#include <asm/byteorder.h>
+
+/*
+ * A couple of 64 bit operations ported from FreeBSD.
+ * The code within the '#if BITS_PER_LONG == 32' block below, and no other
+ * code in this file, is distributed under the following licensing terms
+ * This is the modified '3-clause' BSD license with the obnoxious
+ * advertising clause removed, as permitted by University of California.
+ *
+ * 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.
+ */
+
+/*
+ * Depending on the desired operation, we view a `long long' (aka quad_t) in
+ * one or more of the following formats.
+ */
+union uu {
+ s64 q; /* as a (signed) quad */
+ s64 uq; /* as an unsigned quad */
+ long sl[2]; /* as two signed longs */
+ unsigned long ul[2]; /* as two unsigned longs */
+};
+
+#ifdef __BIG_ENDIAN
+#define _QUAD_HIGHWORD 0
+#define _QUAD_LOWWORD 1
+#else /* __LITTLE_ENDIAN */
+#define _QUAD_HIGHWORD 1
+#define _QUAD_LOWWORD 0
+#endif
+
+/*
+ * 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 CHAR_BIT 8 /* number of bits in a char */
+#define QUAD_BITS (sizeof(s64) * 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
+ * unsigned 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) & ((1 << HALF_BITS) - 1))
+#define LHUP(x) ((x) << HALF_BITS)
+
+/*
+ * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
+ * section 4.3.1, pp. 257--259.
+ */
+#define B (1 << HALF_BITS) /* digit base */
+
+/* Combine two `digits' to make a single two-digit number. */
+#define COMBINE(a, b) (((unsigned long)(a) << HALF_BITS) | (b))
+
+/* select a type for digits in base B */
+typedef unsigned long digit;
+
+/*
+ * 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(register digit *p, register int len, register int sh)
+{
+ register 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 unsigned long. As a consequence, the maximum length dividend
+ * and divisor are 4 `digits' in this base (they are shorter if they have
+ * leading zeros).
+ */
+u64 __qdivrem(u64 uq, u64 vq, u64 *arq)
+{
+ union uu tmp;
+ digit *u, *v, *q;
+ register digit v1, v2;
+ unsigned 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) {
+ unsigned 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 {
+ register 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 {
+ unsigned long nn = COMBINE(uj0, uj1);
+
+ qhat = nn / v1;
+ rhat = nn % 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);
+}
+
+/*
+ * Divide two signed quads.
+ * Truncates towards zero, as required by C99.
+ */
+s64 __divdi3(s64 a, s64 b)
+{
+ u64 ua, ub, uq;
+ int neg = (a < 0) ^ (b < 0);
+ ua = (a < 0) ? -(u64)a : a;
+ ub = (b < 0) ? -(u64)b : b;
+ uq = __qdivrem(ua, ub, (u64 *)0);
+ return (neg ? -uq : uq);
+}
+
+
+/*
+ * Divide two unsigned quads.
+ */
+u64 __udivdi3(u64 a, u64 b)
+{
+ return __qdivrem(a, b, (u64 *)0);
+}
+
+/*
+ * Remainder of unsigned quad division
+ */
+u64 __umoddi3(u64 a, u64 b)
+{
+ u64 rem;
+ __qdivrem(a, b, &rem);
+ return rem;
+}
+
+/*
+ * Remainder of signed quad division.
+ * Truncates towards zero, as required by C99:
+ * 11 % 5 = 1
+ * -11 % 5 = -1
+ * 11 % -5 = 1
+ * -11 % -5 = -1
+ */
+s64 __moddi3(s64 a, s64 b)
+{
+ u64 ua, ub, urem;
+ int neg = (a < 0);
+ ua = neg ? -(u64)a : a;
+ ub = (b < 0) ? -(u64)b : b;
+ __qdivrem(ua, ub, &urem);
+ return (neg ? -urem : urem);
+}
+
+/*
+ * Quotient and remainder of unsigned long long division
+ */
+s64 __ldivmod_helper(s64 a, s64 b, s64 *r)
+{
+ u64 ua, ub, rem, quot;
+
+ ua = ABS(a);
+ ub = ABS(b);
+ quot = __qdivrem(ua, ub, &rem);
+ if ( a < 0 )
+ *r = -rem;
+ else
+ *r = rem;
+ if ( (a < 0) ^ (b < 0) )
+ return -quot;
+ else
+ return quot;
+}
+
+/*
+ * Local variables:
+ * mode: C
+ * c-file-style: "BSD"
+ * c-basic-offset: 4
+ * tab-width: 4
+ * indent-tabs-mode: nil
+ * End:
+ */
--
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