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/* -*- linux-c -*- */
/* Math functions
* Copyright (C) 2005 Red Hat Inc.
* Portions (C) Free Software Foundation, Inc.
*
* This file is part of systemtap, and is free software. You can
* redistribute it and/or modify it under the terms of the GNU General
* Public License (GPL); either version 2, or (at your option) any
* later version.
*/
#ifndef _STAPLINUX_ARITH_C_
#define _STAPLINUX_ARITH_C_
/** @file arith.
* @brief Implements various arithmetic-related helper functions
*/
/* 64-bit division for 64-bit cpus and i386 */
/* Other 32-bit cpus will need to modify this file. */
#if defined (__i386__) || defined(__arm__) || \
(defined(__powerpc__) && !defined(__powerpc64__)) || \
(defined(__mips__) && !defined(__mips64))
static long long _div64 (long long u, long long v);
static long long _mod64 (long long u, long long v);
#endif
/* 31 bit s390 suupport is not yet included, it may never be.
#ifdef __s390__
static long long _div64 (long long u, long long v);
static long long _mod64 (long long u, long long v);
#endif
*/
/** Divide x by y. In case of division-by-zero,
* set context error string, and return 0
*/
static int64_t _stp_div64 (const char **error, int64_t x, int64_t y)
{
// check for division-by-zero
if (unlikely (y == 0)) {
if (error) *error = "division by 0";
return 0;
}
if (unlikely (y == -1))
return -x;
#if defined (__LP64__)
return x/y;
#else
if (likely ((x >= LONG_MIN && x <= LONG_MAX) &&
(y >= LONG_MIN && y <= LONG_MAX))) {
return (long)x / (long)y;
} else
return _div64 (x, y);
#endif
}
/** Modulo x by y. In case of division-by-zero,
* set context error string, and return any 0
*/
static int64_t _stp_mod64 (const char **error, int64_t x, int64_t y)
{
// check for division-by-zero
if (unlikely (y == 0)) {
if (error) *error = "division by 0";
return 0;
}
if (unlikely (y == 1 || y == -1))
return 0;
#if defined (__LP64__)
return x%y;
#else
if (likely ((x >= LONG_MIN && x <= LONG_MAX) &&
(y >= LONG_MIN && y <= LONG_MAX))) {
return (long)x % (long)y;
} else
return _mod64 (x, y);
#endif
}
/** Return a random integer between 0 and n - 1.
* @param n how far from zero to go. Make it positive but less than a million or so.
*/
static unsigned long _stp_random_u (unsigned long n)
{
static unsigned long seed;
static int initialized_p = 0;
if (unlikely (! initialized_p)) {
seed = (unsigned long) jiffies;
initialized_p = 1;
}
/* from glibc rand man page */
seed = seed * 1103515245 + 12345;
return (n == 0 ? 0 : seed % n);
}
/** Return a random integer between -n and n.
* @param n how far from zero to go. Make it positive but less than a million or so.
*/
static int _stp_random_pm (unsigned n)
{
return -(int)n + (int)_stp_random_u (2*n + 1);
}
#if defined (__i386__) || defined (__arm__) || \
(defined(__powerpc__) && !defined(__powerpc64__)) || \
(defined(__mips__) && !defined(__mips64))
/* 64-bit division functions extracted from libgcc */
typedef long long DWtype;
typedef unsigned long long UDWtype;
typedef unsigned long UWtype;
typedef long Wtype;
typedef unsigned int USItype;
typedef unsigned int UQItype __attribute__ ((mode (QI)));
typedef unsigned int UDItype __attribute__ ((mode (DI)));
#ifdef _BIG_ENDIAN
struct DWstruct {Wtype high, low;};
#else
struct DWstruct {Wtype low, high;};
#endif
#define __CLOBBER_CC : "cc"
#define W_TYPE_SIZE 32
#define __BITS4 (W_TYPE_SIZE / 4)
#define __ll_B ((UWtype) 1 << (W_TYPE_SIZE / 2))
#define __ll_lowpart(t) ((UWtype) (t) & (__ll_B - 1))
#define __ll_highpart(t) ((UWtype) (t) >> (W_TYPE_SIZE / 2))
typedef union
{
struct DWstruct s;
DWtype ll;
} DWunion;
#if defined (__i386__)
/* these are the i386 versions of these macros from gcc/longlong.h */
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("mull %3" \
: "=a" ((USItype) (w0)), \
"=d" ((USItype) (w1)) \
: "%0" ((USItype) (u)), \
"rm" ((USItype) (v)))
#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
__asm__ ("subl %5,%1\n\tsbbl %3,%0" \
: "=r" ((USItype) (sh)), \
"=&r" ((USItype) (sl)) \
: "0" ((USItype) (ah)), \
"g" ((USItype) (bh)), \
"1" ((USItype) (al)), \
"g" ((USItype) (bl)))
#define udiv_qrnnd(q, r, n1, n0, dv) \
__asm__ ("divl %4" \
: "=a" ((USItype) (q)), \
"=d" ((USItype) (r)) \
: "0" ((USItype) (n0)), \
"1" ((USItype) (n1)), \
"rm" ((USItype) (dv)))
#define count_leading_zeros(count, x) \
do { \
USItype __cbtmp; \
__asm__ ("bsrl %1,%0" \
: "=r" (__cbtmp) : "rm" ((USItype) (x))); \
(count) = __cbtmp ^ 31; \
} while (0)
#elif defined (__powerpc__)
/* these are the ppc versions of these macros from gcc/longlong.h */
#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
do { \
if (__builtin_constant_p (ah) && (ah) == 0) \
__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{sfze|subfze} %0,%2" \
: "=r" (sh), "=&r" (sl) : "r" (bh), "rI" (al), "r" (bl));\
else if (__builtin_constant_p (ah) && (ah) == ~(USItype) 0) \
__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{sfme|subfme} %0,%2" \
: "=r" (sh), "=&r" (sl) : "r" (bh), "rI" (al), "r" (bl));\
else if (__builtin_constant_p (bh) && (bh) == 0) \
__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{ame|addme} %0,%2" \
: "=r" (sh), "=&r" (sl) : "r" (ah), "rI" (al), "r" (bl));\
else if (__builtin_constant_p (bh) && (bh) == ~(USItype) 0) \
__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{aze|addze} %0,%2" \
: "=r" (sh), "=&r" (sl) : "r" (ah), "rI" (al), "r" (bl));\
else \
__asm__ ("{sf%I4|subf%I4c} %1,%5,%4\n\t{sfe|subfe} %0,%3,%2" \
: "=r" (sh), "=&r" (sl) \
: "r" (ah), "r" (bh), "rI" (al), "r" (bl)); \
} while (0)
#define count_leading_zeros(count, x) \
__asm__ ("{cntlz|cntlzw} %0,%1" : "=r" (count) : "r" (x))
#define COUNT_LEADING_ZEROS_0 32
#define umul_ppmm(ph, pl, m0, m1) \
do { \
USItype __m0 = (m0), __m1 = (m1); \
__asm__ ("mulhwu %0,%1,%2" : "=r" (ph) : "%r" (m0), "r" (m1)); \
(pl) = __m0 * __m1; \
} while (0)
#elif defined (__arm__)
#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
__asm__ ("subs %1, %4, %5\n\tsbc %0, %2, %3" \
: "=r" ((USItype) (sh)), \
"=&r" ((USItype) (sl)) \
: "r" ((USItype) (ah)), \
"rI" ((USItype) (bh)), \
"r" ((USItype) (al)), \
"rI" ((USItype) (bl)) __CLOBBER_CC)
#define umul_ppmm(xh, xl, a, b) \
{register USItype __t0, __t1, __t2; \
__asm__ ("%@ Inlined umul_ppmm\n" \
" mov %2, %5, lsr #16\n" \
" mov %0, %6, lsr #16\n" \
" bic %3, %5, %2, lsl #16\n" \
" bic %4, %6, %0, lsl #16\n" \
" mul %1, %3, %4\n" \
" mul %4, %2, %4\n" \
" mul %3, %0, %3\n" \
" mul %0, %2, %0\n" \
" adds %3, %4, %3\n" \
" addcs %0, %0, #65536\n" \
" adds %1, %1, %3, lsl #16\n" \
" adc %0, %0, %3, lsr #16" \
: "=&r" ((USItype) (xh)), \
"=r" ((USItype) (xl)), \
"=&r" (__t0), "=&r" (__t1), "=r" (__t2) \
: "r" ((USItype) (a)), \
"r" ((USItype) (b)) __CLOBBER_CC );}
#elif (defined(__mips) && __mips >= 3) && W_TYPE_SIZE == 64
#if (__GNUC__ >= 5) || (__GNUC__ >= 4 && __GNUC_MINOR__ >= 4)
#define umul_ppmm(w1, w0, u, v) \
do { \
typedef unsigned int __ll_UTItype __attribute__((mode(TI))); \
__ll_UTItype __ll = (__ll_UTItype)(u) * (v); \
w1 = __ll >> 64; \
w0 = __ll; \
} while (0)
#elif __GNUC__ > 2 || __GNUC_MINOR__ >= 7
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("dmultu %2,%3" \
: "=l" ((UDItype)(w0)), \
"=h" ((UDItype)(w1)) \
: "d" ((UDItype)(u)), \
"d" ((UDItype)(v)))
#else
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("dmultu %2,%3\n" \
"mflo %0\n" \
"mfhi %1" \
: "=d" ((UDItype)(w0)), \
"=d" ((UDItype)(w1)) \
: "d" ((UDItype)(u)), \
"d" ((UDItype)(v)))
#endif
/* This comes from lib/mpi/longlong.h */
#elif defined(__mips__) && W_TYPE_SIZE == 32
#if (__GNUC__ >= 5) || (__GNUC__ >= 4 && __GNUC_MINOR__ >= 4)
#define umul_ppmm(w1, w0, u, v) \
do { \
UDItype __ll = (UDItype)(u) * (v); \
w1 = __ll >> 32; \
w0 = __ll; \
} while (0)
#elif __GNUC__ > 2 || __GNUC_MINOR__ >= 7
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("multu %2,%3" \
: "=l" ((USItype)(w0)), \
"=h" ((USItype)(w1)) \
: "d" ((USItype)(u)), \
"d" ((USItype)(v)))
#else
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("multu %2,%3\n" \
"mflo %0\n" \
"mfhi %1" \
: "=d" ((USItype)(w0)), \
"=d" ((USItype)(w1)) \
: "d" ((USItype)(u)), \
"d" ((USItype)(v)))
#endif
#if !defined (sub_ddmmss)
#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
do { \
UWtype __x; \
__x = (al) - (bl); \
(sh) = (ah) - (bh) - (__x > (al)); \
(sl) = __x; \
} while (0)
#endif
#elif (defined(__mips) && __mips >= 3) && W_TYPE_SIZE == 64
#if (__GNUC__ >= 5) || (__GNUC__ >= 4 && __GNUC_MINOR__ >= 4)
#define umul_ppmm(w1, w0, u, v) \
do { \
typedef unsigned int __ll_UTItype __attribute__((mode(TI))); \
__ll_UTItype __ll = (__ll_UTItype)(u) * (v); \
w1 = __ll >> 64; \
w0 = __ll; \
} while (0)
#elif __GNUC__ > 2 || __GNUC_MINOR__ >= 7
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("dmultu %2,%3" \
: "=l" ((UDItype)(w0)), \
"=h" ((UDItype)(w1)) \
: "d" ((UDItype)(u)), \
"d" ((UDItype)(v)))
#else
#define umul_ppmm(w1, w0, u, v) \
__asm__ ("dmultu %2,%3\n" \
"mflo %0\n" \
"mfhi %1" \
: "=d" ((UDItype)(w0)), \
"=d" ((UDItype)(w1)) \
: "d" ((UDItype)(u)), \
"d" ((UDItype)(v)))
#endif
#endif
#define __udiv_qrnnd_c(q, r, n1, n0, d) \
do { \
UWtype __d1, __d0, __q1, __q0; \
UWtype __r1, __r0, __m; \
__d1 = __ll_highpart (d); \
__d0 = __ll_lowpart (d); \
\
__r1 = (n1) % __d1; \
__q1 = (n1) / __d1; \
__m = (UWtype) __q1 * __d0; \
__r1 = __r1 * __ll_B | __ll_highpart (n0); \
if (__r1 < __m) \
{ \
__q1--, __r1 += (d); \
if (__r1 >= (d)) /* i.e. we didn't get carry when adding to __r1 */\
if (__r1 < __m) \
__q1--, __r1 += (d); \
} \
__r1 -= __m; \
\
__r0 = __r1 % __d1; \
__q0 = __r1 / __d1; \
__m = (UWtype) __q0 * __d0; \
__r0 = __r0 * __ll_B | __ll_lowpart (n0); \
if (__r0 < __m) \
{ \
__q0--, __r0 += (d); \
if (__r0 >= (d)) \
if (__r0 < __m) \
__q0--, __r0 += (d); \
} \
__r0 -= __m; \
\
(q) = (UWtype) __q1 * __ll_B | __q0; \
(r) = __r0; \
} while (0)
#if !defined (udiv_qrnnd)
#define UDIV_NEEDS_NORMALIZATION 1
#define udiv_qrnnd __udiv_qrnnd_c
#else
#define UDIV_NEEDS_NORMALIZATION 0
#endif
#if !defined (count_leading_zeros)
static const UQItype _stp_clz_tab[256] =
{
0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
};
#define count_leading_zeros(count, x) \
do { \
UWtype __xr = (x); \
UWtype __a; \
\
if (W_TYPE_SIZE <= 32) \
{ \
__a = __xr < ((UWtype)1<<2*__BITS4) \
? (__xr < ((UWtype)1<<__BITS4) ? 0 : __BITS4) \
: (__xr < ((UWtype)1<<3*__BITS4) ? 2*__BITS4 : 3*__BITS4); \
} \
else \
{ \
for (__a = W_TYPE_SIZE - 8; __a > 0; __a -= 8) \
if (((__xr >> __a) & 0xff) != 0) \
break; \
} \
\
(count) = W_TYPE_SIZE - (_stp_clz_tab[__xr >> __a] + __a); \
} while (0)
#define COUNT_LEADING_ZEROS_0 W_TYPE_SIZE
#endif
static UDWtype
_stp_udivmoddi4 (UDWtype n, UDWtype d, UDWtype *rp)
{
const DWunion nn = {.ll = n};
const DWunion dd = {.ll = d};
DWunion ww, rr;
UWtype d0, d1, n0, n1, n2;
UWtype q0, q1;
UWtype b, bm;
d0 = dd.s.low;
d1 = dd.s.high;
n0 = nn.s.low;
n1 = nn.s.high;
#if !UDIV_NEEDS_NORMALIZATION
if (d1 == 0)
{
if (d0 > n1)
{
/* 0q = nn / 0D */
udiv_qrnnd (q0, n0, n1, n0, d0);
q1 = 0;
/* Remainder in n0. */
}
else
{
/* qq = NN / 0d */
if (d0 == 0)
d0 = 1 / d0; /* Divide intentionally by zero. */
udiv_qrnnd (q1, n1, 0, n1, d0);
udiv_qrnnd (q0, n0, n1, n0, d0);
/* Remainder in n0. */
}
if (rp != 0)
{
rr.s.low = n0;
rr.s.high = 0;
*rp = rr.ll;
}
}
#else /* UDIV_NEEDS_NORMALIZATION */
if (d1 == 0)
{
if (d0 > n1)
{
/* 0q = nn / 0D */
count_leading_zeros (bm, d0);
if (bm != 0)
{
/* Normalize, i.e. make the most significant bit of the
denominator set. */
d0 = d0 << bm;
n1 = (n1 << bm) | (n0 >> (W_TYPE_SIZE - bm));
n0 = n0 << bm;
}
udiv_qrnnd (q0, n0, n1, n0, d0);
q1 = 0;
/* Remainder in n0 >> bm. */
}
else
{
/* qq = NN / 0d */
if (d0 == 0)
d0 = 1 / d0; /* Divide intentionally by zero. */
count_leading_zeros (bm, d0);
if (bm == 0)
{
/* From (n1 >= d0) /\ (the most significant bit of d0 is set),
conclude (the most significant bit of n1 is set) /\ (the
leading quotient digit q1 = 1).
This special case is necessary, not an optimization.
(Shifts counts of W_TYPE_SIZE are undefined.) */
n1 -= d0;
q1 = 1;
}
else
{
/* Normalize. */
b = W_TYPE_SIZE - bm;
d0 = d0 << bm;
n2 = n1 >> b;
n1 = (n1 << bm) | (n0 >> b);
n0 = n0 << bm;
udiv_qrnnd (q1, n1, n2, n1, d0);
}
/* n1 != d0... */
udiv_qrnnd (q0, n0, n1, n0, d0);
/* Remainder in n0 >> bm. */
}
if (rp != 0)
{
rr.s.low = n0 >> bm;
rr.s.high = 0;
*rp = rr.ll;
}
}
#endif /* UDIV_NEEDS_NORMALIZATION */
else
{
if (d1 > n1)
{
/* 00 = nn / DD */
q0 = 0;
q1 = 0;
/* Remainder in n1n0. */
if (rp != 0)
{
rr.s.low = n0;
rr.s.high = n1;
*rp = rr.ll;
}
}
else
{
/* 0q = NN / dd */
count_leading_zeros (bm, d1);
if (bm == 0)
{
/* From (n1 >= d1) /\ (the most significant bit of d1 is set),
conclude (the most significant bit of n1 is set) /\ (the
quotient digit q0 = 0 or 1).
This special case is necessary, not an optimization. */
/* The condition on the next line takes advantage of that
n1 >= d1 (true due to program flow). */
if (n1 > d1 || n0 >= d0)
{
q0 = 1;
sub_ddmmss (n1, n0, n1, n0, d1, d0);
}
else
q0 = 0;
q1 = 0;
if (rp != 0)
{
rr.s.low = n0;
rr.s.high = n1;
*rp = rr.ll;
}
}
else
{
UWtype m1, m0;
/* Normalize. */
b = W_TYPE_SIZE - bm;
d1 = (d1 << bm) | (d0 >> b);
d0 = d0 << bm;
n2 = n1 >> b;
n1 = (n1 << bm) | (n0 >> b);
n0 = n0 << bm;
udiv_qrnnd (q0, n1, n2, n1, d1);
umul_ppmm (m1, m0, q0, d0);
if (m1 > n1 || (m1 == n1 && m0 > n0))
{
q0--;
sub_ddmmss (m1, m0, m1, m0, d1, d0);
}
q1 = 0;
/* Remainder in (n1n0 - m1m0) >> bm. */
if (rp != 0)
{
sub_ddmmss (n1, n0, n1, n0, m1, m0);
rr.s.low = (n1 << b) | (n0 >> bm);
rr.s.high = n1 >> bm;
*rp = rr.ll;
}
}
}
}
ww.s.low = q0; ww.s.high = q1;
return ww.ll;
}
static long long _div64 (long long u, long long v)
{
long c = 0;
DWunion uu = {.ll = u};
DWunion vv = {.ll = v};
DWtype w;
if (uu.s.high < 0)
c = ~c,
uu.ll = -uu.ll;
if (vv.s.high < 0)
c = ~c,
vv.ll = -vv.ll;
w = _stp_udivmoddi4 (uu.ll, vv.ll, (UDWtype *) 0);
if (c)
w = -w;
return w;
}
static long long _mod64 (long long u, long long v)
{
long c = 0;
DWunion uu = {.ll = u};
DWunion vv = {.ll = v};
DWtype w;
if (uu.s.high < 0)
c = ~c,
uu.ll = -uu.ll;
if (vv.s.high < 0)
vv.ll = -vv.ll;
(void) _stp_udivmoddi4 (uu.ll, vv.ll, (UDWtype*)&w);
if (c)
w = -w;
return w;
}
#endif /* __i386__ || __arm__ || (__powerpc__ && !__powerpc64__) */
#endif /* _STAPLINUX_ARITH_C_ */