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Diffstat (limited to 'mini-os/lib/math.c')
| -rw-r--r-- | mini-os/lib/math.c | 385 |
1 files changed, 385 insertions, 0 deletions
diff --git a/mini-os/lib/math.c b/mini-os/lib/math.c new file mode 100644 index 0000000000..29e1cc933e --- /dev/null +++ b/mini-os/lib/math.c @@ -0,0 +1,385 @@ +/* -*- Mode:C; c-basic-offset:4; tab-width:4 -*- + **************************************************************************** + * (C) 2003 - Rolf Neugebauer - Intel Research Cambridge + **************************************************************************** + * + * File: math.c + * Author: Rolf Neugebauer (neugebar@dcs.gla.ac.uk) + * Changes: + * + * Date: Aug 2003 + * + * Environment: Xen Minimal OS + * Description: Library functions for 64bit arith and other + * from freebsd, files in sys/libkern/ (qdivrem.c, etc) + * + **************************************************************************** + * $Id: c-insert.c,v 1.7 2002/11/08 16:04:34 rn 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. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. 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. + * + * $FreeBSD: src/sys/libkern/divdi3.c,v 1.6 1999/08/28 00:46:31 peter Exp $ +*/ + +#include <types.h> + +/* + * 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 */ +}; +/* XXX RN: Yuck hardcoded endianess :) */ +#define _QUAD_HIGHWORD 1 +#define _QUAD_LOWWORD 0 +/* + * 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 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) & ((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) (((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(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 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). + */ +u64 +__qdivrem(uq, vq, arq) + u64 uq, vq, *arq; +{ + union uu tmp; + digit *u, *v, *q; + register 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 { + 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 { + u_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. + * ??? if -1/2 should produce -1 on this machine, this code is wrong + */ +s64 +__divdi3(s64 a, s64 b) +{ + u64 ua, ub, uq; + int neg; + + if (a < 0) + ua = -(u64)a, neg = 1; + else + ua = a, neg = 0; + if (b < 0) + ub = -(u64)b, neg ^= 1; + else + ub = b; + uq = __qdivrem(ua, ub, (u64 *)0); + return (neg ? -uq : uq); +} + +/* + * Divide two unsigned quads. + */ +u64 +__udivdi3(a, b) + u64 a, b; +{ + return (__qdivrem(a, b, (u64 *)0)); +} + + +/* + * Return remainder after dividing two unsigned quads. + */ +u_quad_t +__umoddi3(a, b) + u_quad_t a, b; +{ + u_quad_t r; + + (void)__qdivrem(a, b, &r); + return (r); +} + |