From: mdw Date: Sat, 17 Jun 2000 11:46:19 +0000 (+0000) Subject: New and much faster stack-based algorithm for reading integers. Support X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/commitdiff_plain/2b26f2d79b3c5342a0daaba359cc00e13de2a9ca New and much faster stack-based algorithm for reading integers. Support reading and writing binary integers in bases between 2 and 256. --- diff --git a/mptext.c b/mptext.c index c5d20e4..f408b90 100644 --- a/mptext.c +++ b/mptext.c @@ -1,6 +1,6 @@ /* -*-c-*- * - * $Id: mptext.c,v 1.4 1999/12/22 15:56:56 mdw Exp $ + * $Id: mptext.c,v 1.5 2000/06/17 11:46:19 mdw Exp $ * * Textual representation of multiprecision numbers * @@ -30,6 +30,10 @@ /*----- Revision history --------------------------------------------------* * * $Log: mptext.c,v $ + * Revision 1.5 2000/06/17 11:46:19 mdw + * New and much faster stack-based algorithm for reading integers. Support + * reading and writing binary integers in bases between 2 and 256. + * * Revision 1.4 1999/12/22 15:56:56 mdw * Use clever recursive algorithm for writing numbers out. * @@ -47,12 +51,37 @@ /*----- Header files ------------------------------------------------------*/ #include +#include #include #include "mp.h" #include "mptext.h" #include "paranoia.h" +/*----- Magical numbers ---------------------------------------------------*/ + +/* --- Maximum recursion depth --- * + * + * This is the number of bits in a @size_t@ object. Why? + * + * Just to convince yourself that this is correct: let @b = MPW_MAX + 1@. + * Then the largest possible @mp@ is %$M - 1$% where %$M = b^Z$%. Let %$r$% + * be a radix to read or write. Since the recursion squares the radix at + * each step, the highest number reached by the recursion is %$d$%, where: + * + * %$r^(2^d) = b^Z$%. + * + * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum, + * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%. + * + * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an + * overestimate, since a @size_t@ representation may contain `holes'. + * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient + * for `some time to come'. + */ + +#define DEPTH (CHAR_BIT * sizeof(size_t) + 10) + /*----- Main code ---------------------------------------------------------*/ /* --- @mp_read@ --- * @@ -73,22 +102,57 @@ * before the number is ignored. */ +/* --- About the algorithm --- * + * + * The algorithm here is rather aggressive. I maintain an array of + * successive squarings of the radix, and a stack of partial results, each + * with a counter attached indicating which radix square to multiply by. + * Once the item at the top of the stack reaches the same counter level as + * the next item down, they are combined together and the result is given a + * counter level one higher than either of the results. + * + * Gluing the results together at the end is slightly tricky. Pay attention + * to the code. + * + * This is more complicated because of the need to handle the slightly + * bizarre syntax. + */ + mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) { - int r; - int ch; - unsigned f = 0; + int ch; /* Current char being considered */ + unsigned f = 0; /* Flags about the current number */ + int r; /* Radix to switch over to */ + mpw rd; /* Radix as an @mp@ digit */ + mp rr; /* The @mp@ for the radix */ + unsigned nf = m ? m->f & MP_BURN : 0; /* New @mp@ flags */ + + /* --- Stacks --- */ + + mp *pow[DEPTH]; /* List of powers */ + unsigned pows; /* Next index to fill */ + struct { unsigned i; mp *m; } s[DEPTH]; /* Main stack */ + unsigned sp; /* Current stack pointer */ + + /* --- Flags --- */ enum { f_neg = 1u, f_ok = 2u }; + /* --- Initialize the stacks --- */ + + mp_build(&rr, &rd, &rd + 1); + pow[0] = &rr; + pows = 1; + + sp = 0; + /* --- Initialize the destination number --- */ - MP_MODIFY(m, 4); - m->vl = m->v; - m->f &= ~MP_UNDEF; + if (m) + MP_DROP(m); /* --- Read an initial character --- */ @@ -107,18 +171,24 @@ mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) /* --- If the radix is zero, look for leading zeros --- */ - if (radix) + if (radix > 0) { + assert(((void)"ascii radix must be <= 36", radix <= 36)); + rd = radix; + r = -1; + } else if (radix < 0) { + rd = -radix; + assert(((void)"binary radix must fit in a byte ", rd < UCHAR_MAX)); r = -1; - else if (ch != '0') { - radix = 10; + } else if (ch != '0') { + rd = 10; r = 0; } else { ch = ops->get(p); if (ch == 'x') { ch = ops->get(p); - radix = 16; + rd = 16; } else { - radix = 8; + rd = 8; f |= f_ok; } r = -1; @@ -132,8 +202,20 @@ mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) /* --- An underscore indicates a numbered base --- */ if (ch == '_' && r > 0 && r <= 36) { - radix = r; - m->vl = m->v; + unsigned i; + + /* --- Clear out the stacks --- */ + + for (i = 1; i < pows; i++) + MP_DROP(pow[i]); + pows = 1; + for (i = 0; i < sp; i++) + MP_DROP(s[i].m); + sp = 0; + + /* --- Restart the search --- */ + + rd = r; r = -1; f &= ~f_ok; continue; @@ -141,23 +223,27 @@ mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) /* --- Check that the character is a digit and in range --- */ - if (!isalnum(ch)) - break; - if (ch >= '0' && ch <= '9') - x = ch - '0'; + if (radix < 0) + x = ch; else { - ch = tolower(ch); - if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ - x = ch - 'a' + 10; - else + if (!isalnum(ch)) break; + if (ch >= '0' && ch <= '9') + x = ch - '0'; + else { + ch = tolower(ch); + if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ + x = ch - 'a' + 10; + else + break; + } } /* --- Sort out what to do with the character --- */ if (x >= 10 && r >= 0) r = -1; - if (x >= radix) + if (x >= rd) break; if (r >= 0) @@ -165,25 +251,92 @@ mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) /* --- Stick the character on the end of my integer --- */ - mp_ensure(m, MP_LEN(m) + 1); - mpx_umuln(m->v, m->vl, m->v, m->vl - 1, radix); - mpx_uaddn(m->v, m->vl, x); - mp_shrink(m); + assert(((void)"Number is too unimaginably huge", sp < DEPTH)); + s[sp].m = m = mp_new(1, nf); + m->v[0] = x; + s[sp].i = 0; + + /* --- Now grind through the stack --- */ + + while (sp > 0 && s[sp - 1].i == s[sp].i) { + + /* --- Combine the top two items --- */ + + sp--; + m = s[sp].m; + m = mp_mul(m, m, pow[s[sp].i]); + m = mp_add(m, m, s[sp + 1].m); + s[sp].m = m; + MP_DROP(s[sp + 1].m); + s[sp].i++; + + /* --- Make a new radix power if necessary --- */ + + if (s[sp].i >= pows) { + assert(((void)"Number is too unimaginably huge", pows < DEPTH)); + pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); + pows++; + } + } f |= f_ok; + sp++; } ops->unget(ch, p); + /* --- If we're done, compute the rest of the number --- */ + + if (f & f_ok) { + if (!sp) + return (MP_ZERO); + else { + mp *z = MP_ONE; + sp--; + + while (sp > 0) { + + /* --- Combine the top two items --- */ + + sp--; + m = s[sp].m; + z = mp_mul(z, z, pow[s[sp + 1].i]); + m = mp_mul(m, m, z); + m = mp_add(m, m, s[sp + 1].m); + s[sp].m = m; + MP_DROP(s[sp + 1].m); + + /* --- Make a new radix power if necessary --- */ + + if (s[sp].i >= pows) { + assert(((void)"Number is too unimaginably huge", pows < DEPTH)); + pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); + pows++; + } + } + MP_DROP(z); + m = s[0].m; + } + } else { + unsigned i; + for (i = 0; i < sp; i++) + MP_DROP(s[i].m); + } + + /* --- Clear the radix power list --- */ + + { + unsigned i; + for (i = 1; i < pows; i++) + MP_DROP(pow[i]); + } + /* --- Bail out if the number was bad --- */ - if (!(f & f_ok)) { - MP_DROP(m); + if (!(f & f_ok)) return (0); - } /* --- Set the sign and return --- */ - m->f = 0; if (f & f_neg) m->f |= MP_NEG; return (m); @@ -216,17 +369,22 @@ static int simple(mp *m, int radix, unsigned z, int rc = 0; char buf[64]; unsigned i = sizeof(buf); + int rd = radix > 0 ? radix : -radix; do { int ch; mpw x; - x = mpx_udivn(m->v, m->vl, m->v, m->vl, radix); + x = mpx_udivn(m->v, m->vl, m->v, m->vl, rd); MP_SHRINK(m); - if (x < 10) - ch = '0' + x; - else - ch = 'a' + x - 10; + if (radix < 0) + ch = x; + else { + if (x < 10) + ch = '0' + x; + else + ch = 'a' + x - 10; + } buf[--i] = ch; if (z) z--; @@ -295,11 +453,21 @@ int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) m = MP_COPY(m); MP_SPLIT(m); + /* --- Check the radix for sensibleness --- */ + + if (radix > 0) + assert(((void)"ascii radix must be <= 36", radix <= 36)); + else if (radix < 0) + assert(((void)"binary radix must fit in a byte", -radix < UCHAR_MAX)); + else + assert(((void)"radix can't be zero in mp_write", 0)); + /* --- If the number is negative, sort that out --- */ if (m->f & MP_NEG) { if (ops->put("-", 1, p)) return (EOF); + m->f &= ~MP_NEG; } /* --- If the number is small, do it the easy way --- */ @@ -314,24 +482,20 @@ int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) * the number: the quotient and remainder will be approximately the same * size, and I'll have split them on a digit boundary, so I can just emit * the quotient and remainder recursively, in order. - * - * The array size copes with the largest number possibly representable on - * the host machine. Such a large number shouldn't ever arise in real use. */ else { - mp *pr[CHAR_BIT * sizeof(size_t)]; + mp *pr[DEPTH]; size_t target = MP_LEN(m) / 2; unsigned i = 0; - mp *z = mp_create(1); + mp *z = mp_new(1, 0); /* --- Set up the exponent table --- */ - z->v[0] = radix; + z->v[0] = (radix > 0 ? radix : -radix); z->f = 0; for (;;) { - assert(((void)"Number is too unimaginably huge", - i < sizeof(pr) / sizeof(pr[0]))); + assert(((void)"Number is too unimaginably huge", i < DEPTH)); pr[i++] = z; if (MP_LEN(z) > target) break; @@ -369,19 +533,34 @@ static int verify(dstr *v) if (m) { if (!ob) { fprintf(stderr, "*** unexpected successful parse\n" - "*** input [%i] = %s\n", - ib, v[1].buf); + "*** input [%i] = ", ib); + if (ib < 0) + type_hex.dump(&v[1], stderr); + else + fputs(v[1].buf, stderr); mp_writedstr(m, &d, 10); - fprintf(stderr, "*** (value = %s)\n", d.buf); + fprintf(stderr, "\n*** (value = %s)\n", d.buf); ok = 0; } else { mp_writedstr(m, &d, ob); if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) { fprintf(stderr, "*** failed read or write\n" - "*** input [%i] = %s\n" - "*** output [%i] = %s\n" - "*** expected [%i] = %s\n", - ib, v[1].buf, ob, d.buf, ob, v[3].buf); + "*** input [%i] = ", ib); + if (ib < 0) + type_hex.dump(&v[1], stderr); + else + fputs(v[1].buf, stderr); + fprintf(stderr, "\n*** output [%i] = ", ob); + if (ob < 0) + type_hex.dump(&d, stderr); + else + fputs(d.buf, stderr); + fprintf(stderr, "\n*** expected [%i] = ", ob); + if (ob < 0) + type_hex.dump(&v[3], stderr); + else + fputs(v[3].buf, stderr); + fputc('\n', stderr); ok = 0; } } @@ -389,9 +568,17 @@ static int verify(dstr *v) } else { if (ob) { fprintf(stderr, "*** unexpected parse failure\n" - "*** input [%i] = %s\n" - "*** expected [%i] = %s\n", - ib, v[1].buf, ob, v[3].buf); + "*** input [%i] = ", ib); + if (ib < 0) + type_hex.dump(&v[1], stderr); + else + fputs(v[1].buf, stderr); + fprintf(stderr, "\n*** expected [%i] = ", ob); + if (ob < 0) + type_hex.dump(&v[3], stderr); + else + fputs(v[3].buf, stderr); + fputc('\n', stderr); ok = 0; } } @@ -402,8 +589,12 @@ static int verify(dstr *v) } static test_chunk tests[] = { - { "mptext", verify, + { "mptext-ascii", verify, { &type_int, &type_string, &type_int, &type_string, 0 } }, + { "mptext-bin-in", verify, + { &type_int, &type_hex, &type_int, &type_string, 0 } }, + { "mptext-bin-out", verify, + { &type_int, &type_string, &type_int, &type_hex, 0 } }, { 0, 0, { 0 } } };