ARM: Implement long division.
* lib/mes/div.c (__mesabi_log2i): New procedure. (__mesabi_uldiv1): New procedure. (__mesabi_uldiv): Use it. Co-Authored-By: Nathalie Kopaczewski <natkopa@gmail.com>
This commit is contained in:
Danny Milosavljevic
Jan (janneke) Nieuwenhuizen
parent
a5f30ee27b
commit
c1dcdc5d7e
163
lib/mes/div.c
163
lib/mes/div.c
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@ -2,6 +2,7 @@
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* GNU Mes --- Maxwell Equations of Software
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* Copyright © 2016,2017,2018,2019 Jan (janneke) Nieuwenhuizen <janneke@gnu.org>
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* Copyright © 2019 Danny Milosavljevic <dannym@scratchpost.org>
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* Copyright © 2020 Nathalie Kopaczewski <natkopa@gmail.com>
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*
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* This file is part of GNU Mes.
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*
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@ -24,24 +25,163 @@
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#include <limits.h>
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#include <signal.h>
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typedef struct
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struct ldiv_t
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{
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long quot;
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long rem;
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} ldiv_t;
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};
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int __raise (int);
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void
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__mesabi_div0 (void)
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{
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if (__raise(SIGFPE) < 0) { /* could not raise SIGFPE */
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if (__raise (SIGFPE) < 0) /* could not raise SIGFPE */
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{
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/* Fail in any way possible */
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unsigned char *x = (unsigned char *) 0;
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*x = 2;
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}
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}
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#define ULONG_HIGHBITMASK LONG_MIN
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#define ULONG_BITCOUNT (sizeof (unsigned long)*8)
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/** Compute the logarithm of base 2 of D. The result is rounded down.
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That is equal to the highest-index set bit in D.
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The idea is to shift D to the right in order to find the index i of the first most-significant digit > 0.
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The computation is done by bisection, for speed.
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Recurse:
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Two halves are determined of the remaining slice.
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The first half checked is the higher-significant half.
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If that higher-significant half is not zero, recurse on that one.
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Otherwise, recurse on the lower-significant half.
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Precondition: D > 0 */
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static unsigned int
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__mesabi_log2i (unsigned long D)
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{
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unsigned int n = ULONG_BITCOUNT;
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unsigned int i = 0U;
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unsigned long D1;
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while (n >= 2U)
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{ /* while still two halves possible */
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n >>= 1U;
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/* D1: higher-significant half of D */
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D1 = D >> n;
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if (D1 > 0UL)
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{
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/* We know that the resulting index has to be in the higher-significant half.
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In that case, lower-significant half of D is superfluous for determination of i,
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therefore scroll and continue with higher-significant half. */
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D = D1;
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i += n;
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}
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}
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return i;
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}
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#if 0
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static void
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test_log2i (void)
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{
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assert (log2i (1) == 0);
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assert (log2i (1) == 0);
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assert (log2i (2) == 1);
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assert (log2i (3) == 1);
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assert (log2i (4) == 2);
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assert (log2i (5) == 2);
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assert (log2i (6) == 2);
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assert (log2i (7) == 2);
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assert (log2i (8) == 3);
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assert (log2i (9) == 3);
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assert (log2i (10) == 3);
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assert (log2i (11) == 3);
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assert (log2i (12) == 3);
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assert (log2i (13) == 3);
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assert (log2i (71) == 6);
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assert (log2i (72) == 6);
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assert (log2i (73) == 6);
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assert (log2i (74) == 6);
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assert (log2i (75) == 6);
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assert (log2i (99) == 6);
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assert (log2i (2147483648) == 31);
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assert (log2i (3221225471) == 31);
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assert (log2i (4294967294) == 31);
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assert (log2i (4294967295) == 31);
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}
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#endif
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/** Perform unsigned integer division of N by D; store the remainder
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into *REMAINDER; return the quotient.
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This is currently implemented as long division.
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R is the remainder. R >= 0. R starts at N.
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QUOTIENT is built up bit by bit starting at the most significant bit [*].
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Values D', starting at D << ULONG_BITCOUNT [*], going down to 1,
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divided by 2 each time, are iterated over, doing: If R >= D',
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subtract D' from R, and append new LSB 1 to the QUOTIENT.
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Otherwise, subtract 0 from R (implicit), and append new LSB 0 to the
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QUOTIENT (0 is the implicit default).
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[*] As a special consideration for C throwing away bits when
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left-shifting, D' starts at the highest value that will not lose
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bits in this way instead. (ULONG_BITCOUNT - log2i(D) - 1) is
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the number of leading zeroes in D in binary radix.
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Precondition: D > 0 */
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static unsigned long
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__mesabi_uldiv1 (unsigned long N, unsigned long D, unsigned long *remainder)
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{
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// Note: __mesabi_log2i(D) < ULONG_BITCOUNT
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unsigned int j = ULONG_BITCOUNT - __mesabi_log2i (D); /* Note: Or j = __mesabi_log2i(N) + 1 - __mesabi_log2i(D) */
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// Note: assert(j - 1 == __builtin_clzl(D)); on GCC
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unsigned long quotient = 0UL;
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unsigned long R = N;
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for (D <<= (j - 1); j > 0U; --j, D >>= 1U)
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{
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quotient <<= 1U;
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if (R >= D)
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{
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R -= D;
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quotient |= 1UL;
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}
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}
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*remainder = R;
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return quotient;
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}
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#if 0
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static void
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assert_uldiv (unsigned long N, unsigned long D, unsigned long expected_quotient,
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unsigned long expected_remainder)
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{
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unsigned long remainder;
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unsigned long quotient;
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quotient = uldiv (N, D, &remainder);
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printf ("%lu/%lu = %lu;%lu\n", N, D, quotient, remainder);
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assert (quotient == expected_quotient);
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assert (remainder == expected_remainder);
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}
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static void
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test_uldiv (void)
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{
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//assert_uldiv(0, 0, 0, 0);
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assert_uldiv (0, 1, 0, 0);
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assert_uldiv (1, 1, 1, 0);
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assert_uldiv (72, 5, 14, 2);
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assert_uldiv (0xffffffff, 1, 0xffffffff, 0);
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assert_uldiv (0xffffffff, 2, 0x7fffffff, 1);
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}
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#endif
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/* Compare gcc: __udivmoddi4 */
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unsigned long
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__mesabi_uldiv (unsigned long a, unsigned long b, unsigned long *remainder)
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@ -50,7 +190,8 @@ __mesabi_uldiv (unsigned long a, unsigned long b, unsigned long* remainder)
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if (!remainder)
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remainder = &tmp;
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*remainder = 0;
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switch (b) {
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switch (b)
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{
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case 64UL:
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*remainder = a & 63UL;
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return a >> 6UL;
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@ -76,13 +217,7 @@ __mesabi_uldiv (unsigned long a, unsigned long b, unsigned long* remainder)
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__mesabi_div0 ();
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return 0UL;
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default:
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{
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unsigned long x;
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for (x = 0; a >= b; a -= b)
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++x;
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*remainder = a;
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return x;
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}
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return __mesabi_uldiv1 (a, b, remainder);
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}
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}
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@ -90,7 +225,7 @@ __mesabi_uldiv (unsigned long a, unsigned long b, unsigned long* remainder)
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Maintainer: Be careful to satisfy quot * b + rem == a.
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That means that rem can be negative. */
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void
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__mesabi_ldiv(long a, long b, ldiv_t* result)
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__mesabi_ldiv (long a, long b, struct ldiv_t *result)
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{
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int negate_result = (a < 0) ^ (b < 0);
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if (b == LONG_MIN)
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@ -137,7 +272,7 @@ __mesabi_ldiv(long a, long b, ldiv_t* result)
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long
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__mesabi_imod (long a, long b)
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{
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ldiv_t result;
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struct ldiv_t result;
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__mesabi_ldiv (a, b, &result);
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return result.rem;
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}
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@ -145,7 +280,7 @@ __mesabi_imod (long a, long b)
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int
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__mesabi_idiv (int a, int b)
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{
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ldiv_t result;
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struct ldiv_t result;
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__mesabi_ldiv (a, b, &result);
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return result.quot;
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}
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