--- /dev/null
+Makefile
+b64_add.c
+b64_sft.c
+flt_add.c
+flt_arith.h
+flt_arith2flt.c
+flt_chk.c
+flt_cmp.c
+flt_div.c
+flt_flt2arith.c
+flt_modf.c
+flt_mul.c
+flt_nrm.c
+flt_str2flt.c
+misc.h
+ucmp.c
+flt_arith.3
+
--- /dev/null
+# $Header$
+EMHOME = ../../..
+MODDIR=$(EMHOME)/modules
+INSTALL = $(MODDIR)/install
+COMPARE = $(MODDIR)/compare
+INCLUDES = -I. -I$(MODDIR)/h
+CFLAGS = -O $(INCLUDES) $(COPT)
+AR = ar
+SUF = o
+LIBSUF = a
+
+LIBFLT = libflt.$(LIBSUF)
+
+SRC = b64_add.c flt_arith2flt.c flt_div.c flt_nrm.c b64_sft.c flt_chk.c \
+ flt_flt2arith.c flt_str2flt.c flt_add.c flt_cmp.c flt_mul.c ucmp.c \
+ flt_modf.c
+OBJ = b64_add.$(SUF) flt_arith2flt.$(SUF) flt_div.$(SUF) flt_nrm.$(SUF) \
+ b64_sft.$(SUF) flt_chk.$(SUF) flt_flt2arith.$(SUF) flt_str2flt.$(SUF) \
+ flt_add.$(SUF) flt_cmp.$(SUF) flt_mul.$(SUF) ucmp.$(SUF) \
+ flt_modf.$(SUF)
+
+.SUFFIXES: .$(SUF)
+.c.$(SUF):
+ $(CC) -c $(CFLAGS) $*.c
+
+all: $(LIBFLT)
+
+$(LIBFLT): $(OBJ)
+ rm -f $(LIBFLT)
+ $(AR) r $(LIBFLT) $(OBJ)
+ -sh -c 'ranlib $(LIBFLT)'
+
+install: all
+ $(INSTALL) lib/$(LIBFLT)
+ $(INSTALL) h/flt_arith.h
+ $(INSTALL) man/flt_arith.3
+
+cmp: all
+ -$(COMPARE) lib/$(LIBFLT)
+ -$(COMPARE) h/flt_arith.h
+ -$(COMPARE) man/flt_arith.3
+
+pr:
+ @pr Makefile $(SRC)
+
+opr:
+ make pr | opr
+
+clean:
+ rm -f *.$(SUF) $(LIBFLT)
+
+lintlib:
+ lint $(INCLUDES) -Cflt $(SRC)
+ mv llib-lflt.ln $(MODDIR)/lib
+
+b64_add.$(SUF): misc.h flt_arith.h
+flt_arith2flt.$(SUF): misc.h flt_arith.h
+flt_div.$(SUF): misc.h flt_arith.h
+flt_nrm.$(SUF): misc.h flt_arith.h
+b64_sft.$(SUF): misc.h flt_arith.h
+flt_chk.$(SUF): misc.h flt_arith.h
+flt_flt2arith.$(SUF): misc.h flt_arith.h
+flt_str2flt.$(SUF): misc.h flt_arith.h
+flt_add.$(SUF): misc.h flt_arith.h
+flt_cmp.$(SUF): misc.h flt_arith.h
+flt_mul.$(SUF): misc.h flt_arith.h
+flt_modf.$(SUF): misc.h flt_arith.h
+ucmp.$(SUF): misc.h flt_arith.h
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+# include "misc.h"
+
+int
+b64_add(e1,e2)
+ register struct _mantissa *e1,*e2;
+{
+ int overflow;
+ int carry;
+
+ /* add higher pair of 32 bits */
+ overflow = ucmp(0xFFFFFFFF - e1->flt_h_32, e2->flt_h_32) < 0;
+ e1->flt_h_32 += e2->flt_h_32;
+
+ /* add lower pair of 32 bits */
+ carry = ucmp(0xFFFFFFFF - e1->flt_l_32, e2->flt_l_32) < 0;
+ e1->flt_l_32 += e2->flt_l_32;
+
+ if ((carry) && ((++e1->flt_h_32 &~0xFFFFFFFF) || e1->flt_h_32 == 0)) {
+ e1->flt_h_32 = 0;
+ return(1); /* had a 64 bit overflow */
+ }
+ return(overflow); /* return status from higher add */
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+b64_sft(e,n)
+ register struct _mantissa *e;
+ register int n;
+{
+ if (n > 0) {
+ if (n > 63) {
+ e->flt_l_32 = 0;
+ e->flt_h_32 = 0;
+ return;
+ }
+ if (n >= 32) {
+ e->flt_l_32 = e->flt_h_32;
+ e->flt_h_32 = 0;
+ n -= 32;
+ }
+ if (n > 0) {
+ e->flt_l_32 = (e->flt_l_32 >> 1) & 0x7FFFFFFF;
+ e->flt_l_32 >>= (n - 1);
+ if (e->flt_h_32 != 0) {
+ e->flt_l_32 |= (e->flt_h_32 << (32 - n)) & 0xFFFFFFFF;
+ e->flt_h_32 = (e->flt_h_32 >> 1) & 0x7FFFFFFF;
+ e->flt_h_32 >>= (n - 1);
+ }
+ }
+ return;
+ }
+ n = -n;
+ if (n > 0) {
+ if (n > 63) {
+ e->flt_l_32 = 0;
+ e->flt_h_32 = 0;
+ return;
+ }
+ if (n >= 32) {
+ e->flt_h_32 = e->flt_l_32;
+ e->flt_l_32 = 0;
+ n -= 32;
+ }
+ if (n > 0) {
+ e->flt_h_32 = (e->flt_h_32 << n) & 0xFFFFFFFF;
+ if (e->flt_l_32 != 0) {
+ long l = (e->flt_l_32 >> 1) & 0x7FFFFFFF;
+ e->flt_h_32 |= (l >> (31 - n));
+ e->flt_l_32 = (e->flt_l_32 << n) & 0xFFFFFFFF;
+ }
+ }
+ }
+}
+
+b64_lsft(e)
+ register struct _mantissa *e;
+{
+ /* shift left 1 bit */
+ e->flt_h_32 = (e->flt_h_32 << 1) & 0xFFFFFFFF;
+ if (e->flt_l_32 & 0x80000000L) e->flt_h_32 |= 1;
+ e->flt_l_32 = (e->flt_l_32 << 1) & 0xFFFFFFFF;
+}
+
+b64_rsft(e)
+ register struct _mantissa *e;
+{
+ /* shift right 1 bit */
+ e->flt_l_32 = (e->flt_l_32 >> 1) & 0x7FFFFFFF;
+ if (e->flt_h_32 & 1) e->flt_l_32 |= 0x80000000L;
+ e->flt_h_32 = (e->flt_h_32 >> 1) & 0x7FFFFFFF;
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+flt_add(e1,e2,e3)
+ register flt_arith *e1,*e2,*e3;
+{
+ /* Add two extended numbers e1 and e2, and put the result
+ in e3
+ */
+ flt_arith ce2;
+ int diff;
+
+ flt_status = 0;
+ if ((e2->m1 | e2->m2) == 0L) {
+ *e3 = *e1;
+ return;
+ }
+ if ((e1->m1 | e1->m2) == 0L) {
+ *e3 = *e2;
+ return;
+ }
+ ce2 = *e2;
+ *e3 = *e1;
+ e1 = &ce2;
+
+ /* adjust mantissas to equal power */
+ diff = e3->flt_exp - e1->flt_exp;
+ if (diff < 0) {
+ diff = -diff;
+ e3->flt_exp += diff;
+ b64_sft(&(e3->flt_mantissa), diff);
+ }
+ else if (diff > 0) {
+ e1->flt_exp += diff;
+ b64_sft(&(e1->flt_mantissa), diff);
+ }
+ if (e1->flt_sign != e3->flt_sign) {
+ /* e3 + e1 = e3 - (-e1) */
+ int tmp = ucmp(e1->m1, e3->m1);
+ int tmp2 = ucmp(e1->m2, e3->m2);
+ if (tmp > 0 || (tmp == 0 && tmp2 > 0)) {
+ /* abs(e1) > abs(e3) */
+ if (tmp2 < 0) {
+ e1->m1 -= 1; /* carry in */
+ }
+ e1->m1 -= e3->m1;
+ e1->m2 -= e3->m2;
+ *e3 = *e1;
+ }
+ else {
+ if (tmp2 > 0)
+ e3->m1 -= 1; /* carry in */
+ e3->m1 -= e1->m1;
+ e3->m2 -= e1->m2;
+ }
+ }
+ else {
+ if (b64_add(&e3->flt_mantissa,&e1->flt_mantissa)) {/* addition carry */
+ b64_sft(&e3->flt_mantissa,1);/* shift mantissa one bit RIGHT */
+ e3->m1 |= 0x80000000L; /* set max bit */
+ e3->flt_exp++; /* increase the exponent */
+ }
+ }
+ flt_nrm(e3);
+ flt_chk(e3);
+}
+
+flt_sub(e1,e2,e3)
+ flt_arith *e1,*e2,*e3;
+{
+ flt_arith ce2;
+
+ ce2 = *e2;
+ ce2.flt_sign = ! ce2.flt_sign;
+ flt_add(e1,&ce2,e3);
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+#include <em_arith.h>
+
+flt_arith2flt(n, e)
+ register arith n;
+ register flt_arith *e;
+{
+ /* Convert the arith "n" to a flt_arith "e".
+ */
+ register int i;
+
+ if (n == 0) {
+ e->flt_exp = 0;
+ e->flt_sign = 0;
+ e->m1 = e->m2 = 0;
+ return;
+ }
+ if (n < 0) {
+ e->flt_sign = 1;
+ n = -n;
+ }
+ else e->flt_sign = 0;
+ e->flt_exp = 63;
+ e->m1 = e->m2 = 0;
+ if (n < 0) {
+ n = 0x40000000;
+ while ((n << 1) > 0) n <<= 1;
+ e->flt_exp++;
+ }
+ for (i = 64; i > 0 && n != 0; i--) {
+ b64_rsft(&(e->flt_mantissa));
+ e->m1 |= (n & 1) << 31;
+ n >>= 1;
+ }
+
+ if (i > 0) {
+ b64_sft(&(e->flt_mantissa), i);
+ }
+ flt_status = 0;
+ flt_nrm(e);
+}
--- /dev/null
+.TH FLT_ARITH 3ACK " Fri June 30 1989"
+.ad
+.SH NAME
+flt_arith \- high precision floating point arithmetic
+.SH SYNOPSIS
+.nf
+.B #include <flt_arith.h>
+.PP
+.B flt_add(e1, e2, e3)
+.B flt_arith *e1, *e2, *e3;
+.PP
+.B flt_mul(e1, e2, e3)
+.B flt_arith *e1, *e2, *e3;
+.PP
+.B flt_sub(e1, e2, e3)
+.B flt_arith *e1, *e2, *e3;
+.PP
+.B flt_div(e1, e2, e3)
+.B flt_arith *e1, *e2, *e3;
+.PP
+.B flt_modf(e1, intpart, fractpart)
+.B flt_arith *e1, *intpart, *fractpart;
+.PP
+.B int flt_cmp(e1, e2)
+.B flt_arith *e1, *e2;
+.PP
+.B int flt_str2flt(s, e)
+.B char *s;
+.B flt_arith *e;
+.PP
+.B flt_flt2str(e, buf, bufsize)
+.B flt_arith *e;
+.B char *buf;
+.B int bufsize;
+.PP
+.B int flt_status;
+.PP
+.B #include <em_arith.h>
+.B flt_arith2flt(n, e)
+.B arith n;
+.B flt_arith *e;
+.PP
+.B arith flt_flt2arith(e)
+.B flt_arith *e;
+.SH DESCRIPTION
+This set of routines emulates floating point arithmetic, in a high
+precision. It is intended primarily for compilers that need to evaluate
+floating point expressions at compile-time. It could be argued that this
+should be done in the floating point arithmetic of the target machine,
+but EM does not define its floating point arithmetic.
+.PP
+.B flt_add
+adds the numbers indicated by
+.I e1
+and
+.I e2
+and stores the result indirectly through
+.IR e3 .
+.PP
+.B flt_mul
+multiplies the numbers indicated by
+.I e1
+and
+.I e2
+and stores the result indirectly through
+.IR e3 .
+.PP
+.B flt_sub
+subtracts the number indicated by
+.I e2
+from the one indicated by
+.I e1
+and stores the result indirectly through
+.IR e3 .
+.PP
+.B flt_div
+divides the number indicated by
+.I e1
+by the one indicated by
+.I e2
+and stores the result indirectly through
+.IR e3 .
+.PP
+.B flt_modf
+splits the number indicated by
+.I e
+in an integer and a fraction part, and stores the integer part through
+.I intpart
+and the fraction part through
+.IR fractpart .
+So, adding the numbers indicated by
+.I intpart
+and
+.I fractpart
+results (in the absence of rounding error) in the number
+indicated by
+.IR e .
+Also, the absolute value of the number indicated by
+.I intpart
+is less than or equal to the absolute value of the number indicated by
+.IR e .
+The absolute value of the number indicated by
+.I fractpart
+is less than 1.
+.PP
+.B flt_cmp
+compares the numbers indicated by
+.I e1
+and
+.I e2
+and returns -1 if
+.I e1
+<
+.IR e2 ,
+0 if
+.I e1
+=
+.IR e2 ,
+and 1 if
+.I e1
+>
+.IR e2 .
+.PP
+.B flt_str2flt
+converts the string indicated by
+.I s
+to a floating point number, and stores this number through
+.IR e.
+The string should contain a floating point constant, which consists of
+an integer part, a decimal point, a fraction part, an \f(CWe\fP or an
+\f(CWE\fP, and an optionally signed integer exponent. The integer and
+fraction parts both consist of a sequence of digits. They may not both be
+missing. The decimal point, the \f(CWe\fP and the exponent may be
+missing.
+.PP
+.B flt_flt2str
+converts the number indicated by
+.I e
+into a string, in a scientific notation acceptable for EM. The result is
+stored in
+.IR buf .
+At most
+.I bufsize
+characters are stored.
+.PP
+.B flt_arith2flt
+converts the number
+.I n
+to the floating point format use in this package and returns the result
+in
+.IR e .
+.PP
+.B flt_flt2arith
+truncates the number indicated by
+.I e
+to the largest integer value smaller than or equal to the number indicated by
+.IR e .
+It returns this value.
+.PP
+Before each operation, the
+.I flt_status
+variable is reset to 0. After an operation, it can be checked for one
+of the following values:
+.IP FLT_OVFL
+.br
+an overflow occurred. The result is a large value with the correct sign.
+This can occur with the routines
+.IR flt_add ,
+.IR flt_sub ,
+.IR flt_div ,
+.IR flt_mul ,
+.IR flt_flt2arith ,
+and
+.IR flt_str2flt .
+.IP FLT_UNFL
+.br
+an underflow occurred. The result is 0.
+This can occur with the routines
+.IR flt_div ,
+.IR flt_mul ,
+.IR flt_sub ,
+.IR flt_add ,
+and
+.IR flt_str2flt .
+.IP FLT_DIV0
+.br
+divide by 0. The result is a large value with the sign of the dividend.
+This can only occur with the routine
+.IR flt_div .
+.IP FLT_NOFLT
+.br
+indicates that the string did not represent a floating point number. The
+result is 0.
+This can only occur with the routine
+.IR flt_str2flt .
+.IP FLT_BTSM
+.br
+indicates that the buffer is too small. The contents of the buffer is
+undefined. This can only occur with the routine
+.IR flt_flt2str .
+.SH FILES
+~em/modules/h/flt_arith.h
+.br
+~em/modules/h/em_arith.h
+.br
+~em/modules/lib/libflt.a
--- /dev/null
+/*
+ * (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ * See the copyright notice in the ACK home directory, in the file "Copyright".
+ */
+/* $Header$ */
+
+#ifndef __FLT_INCLUDED__
+#define __FLT_INCLUDED__
+
+struct _mantissa {
+ long flt_h_32;
+ long flt_l_32;
+};
+
+struct _EXTEND {
+ short flt_sign;
+ short flt_exp;
+ struct _mantissa flt_mantissa;
+};
+
+typedef struct _EXTEND flt_arith;
+
+extern int flt_status;
+#define FLT_OVFL 001
+#define FLT_UNFL 002
+#define FLT_DIV0 004
+#define FLT_NOFLT 010
+#define FLT_BTSM 020
+
+#endif __FLT_INCLUDED__
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+int flt_status = 0;
+
+flt_chk(e)
+ register flt_arith *e;
+{
+ if (e->flt_exp >= EXT_MAX) {
+ flt_status = FLT_OVFL;
+ e->flt_exp = EXT_MAX;
+ e->m1 = e->m2 = 0;
+ }
+ if (e->flt_exp <= EXT_MIN) {
+ flt_status = FLT_UNFL;
+ e->flt_exp = 0;
+ e->m1 = e->m2 = 0;
+ e->flt_sign = 0;
+ }
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+int
+flt_cmp(e1, e2)
+ register flt_arith *e1, *e2;
+{
+ int sign = e1->flt_sign ? -1 : 1;
+ int tmp;
+
+ if (e1->flt_sign > e2->flt_sign) return -1;
+ if (e1->flt_sign < e2->flt_sign) return 1;
+ if (e1->flt_exp < e2->flt_exp) return -sign;
+ if (e1->flt_exp > e2->flt_exp) return sign;
+ if ((tmp = ucmp(e1->m1, e2->m1)) < 0) return -sign;
+ if (tmp > 0) return sign;
+ if ((tmp = ucmp(e1->m2, e2->m2)) < 0) return -sign;
+ if (tmp > 0) return sign;
+ return 0;
+}
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+flt_div(e1,e2,e3)
+ register flt_arith *e1,*e2,*e3;
+{
+ short error = 0;
+ long result[2];
+ register long *lp;
+ unsigned short u[9], v[5];
+ register int j;
+ register unsigned short *u_p = u;
+ int maxv = 4;
+
+ flt_status = 0;
+ e3->flt_sign = e1->flt_sign ^ e2->flt_sign;
+ if ((e2->m1 | e2->m2) == 0) {
+ flt_status = FLT_DIV0;
+ e3->flt_exp = EXT_MAX;
+ e3->m1 = e3->m2 = 0L;
+ return;
+ }
+ if ((e1->m1 | e1->m2) == 0) { /* 0 / anything == 0 */
+ e3->flt_exp = 0; /* make sure */
+ e3->m1 = e3->m2 = 0L;
+ e3->flt_sign = 0;
+ return;
+ }
+ e3->flt_exp = e1->flt_exp - e2->flt_exp + 2;
+
+ u[4] = (e1->m2 & 1) << 15;
+ b64_rsft(&(e1->flt_mantissa));
+ u[0] = (e1->m1 >> 16) & 0xFFFF;
+ u[1] = e1->m1 & 0xFFFF;
+ u[2] = (e1->m2 >> 16) & 0xFFFF;
+ u[3] = e1->m2 & 0xFFFF;
+ u[5] = 0; u[6] = 0; u[7] = 0;
+ v[1] = (e2->m1 >> 16) & 0xFFFF;
+ v[2] = e2->m1 & 0xFFFF;
+ v[3] = (e2->m2 >> 16) & 0xFFFF;
+ v[4] = e2->m2 & 0xFFFF;
+ while (! v[maxv]) maxv--;
+ result[0] = 0;
+ result[1] = 0;
+ lp = result;
+
+ /*
+ * Use an algorithm of Knuth (The art of programming, Seminumerical
+ * algorithms), to divide u by v. u and v are both seen as numbers
+ * with base 65536.
+ */
+ for (j = 0; j <= 3; j++, u_p++) {
+ long q_est, temp;
+
+ if (j == 2) lp++;
+ if (u_p[0] == 0 && u_p[1] < v[1]) continue;
+ temp = ((long)u_p[0] << 16) + u_p[1];
+ if (u_p[0] >= v[1]) {
+ q_est = 0x0000FFFF;
+ }
+ else if (v[1] == 1) {
+ q_est = temp;
+ }
+ else if (temp >= 0) {
+ q_est = temp / v[1];
+ }
+ else {
+ long rem;
+ q_est = (0x7FFFFFFF/v[1])+((temp&0x7FFFFFFF)/v[1]);
+ rem = (0x7FFFFFFF%v[1])+((temp&0x7FFFFFFF)%v[1])+1;
+ while (rem > v[1]) {
+ q_est++;
+ rem -= v[1];
+ }
+ }
+ temp -= q_est * v[1];
+ while (!(temp&0xFFFF0000) && ucmp(v[2]*q_est,((temp<<16)+u_p[2])) > 0) {
+ q_est--;
+ temp += v[1];
+ }
+ /* Now, according to Knuth, we have an estimate of the
+ quotient, that is either correct or one too big, but
+ almost always correct.
+ */
+ if (q_est != 0) {
+ int i;
+ long k = 0;
+ int borrow = 0;
+
+ for (i = maxv; i > 0; i--) {
+ long tmp = q_est * v[i] + k + borrow;
+ unsigned short md = tmp & 0xFFFF;
+
+ borrow = (md > u_p[i]);
+ u_p[i] -= md;
+ k = (tmp >> 16) & 0xFFFF;
+ }
+ k += borrow;
+ borrow = u_p[0] < k;
+ u_p[0] -= k;
+
+ if (borrow) {
+ /* So, this does not happen often; the estimate
+ was one too big; correct this
+ */
+ *lp |= (j & 1) ? (q_est - 1) : ((q_est-1)<<16);
+ borrow = 0;
+ for (i = maxv; i > 0; i--) {
+ long tmp
+ = v[i]+(long)u_p[i]+borrow;
+
+ u_p[i] = tmp & 0xFFFF;
+ borrow = (tmp >> 16) & 0xFFFF;
+ }
+ u_p[0] += borrow;
+ }
+ else *lp |= (j & 1) ? q_est : (q_est<<16);
+ }
+ }
+ e3->m1 = result[0];
+ e3->m2 = result[1];
+
+ flt_nrm(e3);
+ flt_chk(e3);
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+#include <em_arith.h>
+
+arith
+flt_flt2arith(e)
+ register flt_arith *e;
+{
+ /* Convert the flt_arith "n" to an arith.
+ */
+ arith n;
+ struct _mantissa a;
+
+ flt_status = 0;
+ if (e->flt_exp < 0) {
+ /* absolute value of result < 1.
+ Return value only depends on sign:
+ */
+ return -e->flt_sign;
+ }
+
+ if (e->flt_exp > (8*sizeof(arith)-2)) {
+ /* probably overflow, but there is one exception:
+ */
+ if (e->flt_sign) {
+ n = 0x80;
+ while (n << 8) n <<= 8;
+ if (e->flt_exp == 8*sizeof(arith)-1 &&
+ e->m2 == 0 &&
+ e->m1 == 0x80000000) {
+ /* No overflow in this case */
+ }
+ else flt_status = FLT_OVFL;
+ return n;
+ }
+ n = 0x7F;
+ while ((n << 8) > 0) {
+ n <<= 8;
+ n |= 0xFF;
+ }
+ return n;
+ }
+
+ a = e->flt_mantissa;
+ b64_sft(&a, 63-e->flt_exp);
+ n = a.flt_l_32 | ((a.flt_h_32 << 16) << 16);
+ /* not << 32; this could be an undefined operation */
+ return n;
+}
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+flt_modf(e, ipart, fpart)
+ register flt_arith *e, *ipart, *fpart;
+{
+ if (e->flt_exp < 0) {
+ *fpart = *e;
+ ipart->flt_sign = 0;
+ ipart->flt_exp = 0;
+ ipart->m1 = ipart->m2 = 0;
+ return;
+ }
+ if (e->flt_exp >= 63) {
+ fpart->flt_sign = 0;
+ fpart->flt_exp = 0;
+ fpart->m1 = fpart->m2 = 0;
+ *ipart = *e;
+ return;
+ }
+ *ipart = *e;
+ /* "loose" low order bits */
+ b64_sft(&(ipart->flt_mantissa), 63 - e->flt_exp);
+ b64_sft(&(ipart->flt_mantissa), e->flt_exp - 63);
+ flt_sub(e, ipart, fpart);
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+flt_mul(e1,e2,e3)
+ register flt_arith *e1,*e2,*e3;
+{
+ /* Multiply the extended numbers e1 and e2, and put the
+ result in e3.
+ */
+ register int i,j; /* loop control */
+ unsigned short mp[4];
+ unsigned short mc[4];
+ unsigned short result[8]; /* result */
+
+ register unsigned short *pres;
+
+ flt_status = 0;
+
+ /* first save the sign (XOR) */
+ e3->flt_sign = e1->flt_sign ^ e2->flt_sign;
+
+ /* compute new exponent */
+ e3->flt_exp = e1->flt_exp + e2->flt_exp + 1;
+
+ /* 128 bit multiply of mantissas */
+
+ /* assign unknown long formats */
+ /* to known unsigned word formats */
+ mp[0] = (e1->m1 >> 16) & 0xFFFF;
+ mp[1] = e1->m1 & 0xFFFF;
+ mp[2] = (e1->m2 >> 16) & 0xFFFF;
+ mp[3] = e1->m2 & 0xFFFF;
+ mc[0] = (e2->m1 >> 16) & 0xFFFF;
+ mc[1] = e2->m1 & 0xFFFF;
+ mc[2] = (e2->m2 >> 16) & 0xFFFF;
+ mc[3] = e2->m2 & 0xFFFF;
+ for (i = 8; i--;) {
+ result[i] = 0;
+ }
+ /*
+ * fill registers with their components
+ */
+ for(i=4, pres = &result[4];i--;pres--) if (mp[i]) {
+ unsigned short k = 0;
+ long mpi = mp[i];
+ for(j=4;j--;) {
+ long tmp = (long)pres[j] + k;
+ if (mc[j]) tmp += mpi * mc[j];
+ pres[j] = tmp & 0xFFFF;
+ k = (tmp >> 16) & 0xFFFF;
+ }
+ pres[-1] = k;
+ }
+
+ if (! (result[0] & 0x8000)) {
+ e3->flt_exp--;
+ for (i = 0; i <= 3; i++) {
+ result[i] <<= 1;
+ if (result[i+1]&0x8000) result[i] |= 1;
+ }
+ result[4] <<= 1;
+ }
+ /*
+ * combine the registers to a total
+ */
+ e3->m1 = ((long)result[0] << 16) + result[1];
+ e3->m2 = ((long)result[2] << 16) + result[3];
+ if (result[4] & 0x8000) {
+ if (++e3->m2 == 0) {
+ if (++e3->m1 == 0) {
+ e3->m1 = 0x80000000;
+ e3->flt_exp++;
+ }
+ }
+ }
+ flt_chk(e3);
+}
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+flt_nrm(e)
+ register flt_arith *e;
+{
+ if ((e->m1 | e->m2) == 0L)
+ return;
+
+ /* if top word is zero mov low word */
+ /* to top word, adjust exponent value */
+ if (e->m1 == 0L) {
+ e->m1 = e->m2;
+ e->m2 = 0L;
+ e->flt_exp -= 32;
+ }
+ if ((e->m1 & 0x80000000) == 0) {
+ long l = 0x40000000;
+ int cnt = -1;
+
+ while (! (l & e->m1)) {
+ l >>= 1;
+ cnt--;
+ }
+ e->flt_exp += cnt;
+ b64_sft(&(e->flt_mantissa), cnt);
+ }
+}
--- /dev/null
+/*
+ (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+/* The following tables can be computed with the following bc(1)
+ program:
+
+obase=16
+scale=0
+define t(x){
+ auto a, b, c
+ a=2;b=1;c=2^32;n=1
+ while(a<x) {
+ b=a;n+=n;a*=a
+ }
+ n/=2
+ a=b
+ while(b<x) {
+ a=b;b*=c;n+=32
+ }
+ n-=32
+ b=a
+ while(a<x) {
+ b=a;a+=a;n+=1
+ }
+ n-=1
+ x*=16^16
+ b=x%a
+ x/=a
+ if(a<=(2*b)) x+=1
+ obase=10
+ n
+ obase=16
+ return(x)
+}
+for (i=1;i<28;i++) {
+ t(10^i)
+}
+0
+for (i=1;i<20;i++) {
+ t(10^(28*i))
+}
+0
+define r(x){
+ auto a, b, c
+ a=2;b=1;c=2^32;n=1
+ while(a<x) {
+ b=a;n+=n;a*=a
+ }
+ n/=2
+ a=b
+ while(b<x) {
+ a=b;b*=c;n+=32
+ }
+ n-=32
+ b=a
+ while(a<x) {
+ b=a;a+=a;n+=1
+ }
+ a=b
+ a*=16^16
+ b=a%x
+ a/=x
+ if(x<=(2*b)) a+=1
+ obase=10
+ -n
+ obase=16
+ return(a)
+}
+for (i=1;i<28;i++) {
+ r(10^i)
+}
+0
+for (i=1;i<20;i++) {
+ r(10^(28*i))
+}
+0
+
+*/
+static flt_arith s10pow[] = { /* representation of 10 ** i */
+ { 0, 0, 0x80000000, 0 },
+ { 0, 3, 0xA0000000, 0 },
+ { 0, 6, 0xC8000000, 0 },
+ { 0, 9, 0xFA000000, 0 },
+ { 0, 13, 0x9C400000, 0 },
+ { 0, 16, 0xC3500000, 0 },
+ { 0, 19, 0xF4240000, 0 },
+ { 0, 23, 0x98968000, 0 },
+ { 0, 26, 0xBEBC2000, 0 },
+ { 0, 29, 0xEE6B2800, 0 },
+ { 0, 33, 0x9502F900, 0 },
+ { 0, 36, 0xBA43B740, 0 },
+ { 0, 39, 0xE8D4A510, 0 },
+ { 0, 43, 0x9184E72A, 0 },
+ { 0, 46, 0xB5E620F4, 0x80000000 },
+ { 0, 49, 0xE35FA931, 0xA0000000 },
+ { 0, 53, 0x8E1BC9BF, 0x04000000 },
+ { 0, 56, 0xB1A2BC2E, 0xC5000000 },
+ { 0, 59, 0xDE0B6B3A, 0x76400000 },
+ { 0, 63, 0x8AC72304, 0x89E80000 },
+ { 0, 66, 0xAD78EBC5, 0xAC620000 },
+ { 0, 69, 0xD8D726B7, 0x177A8000 },
+ { 0, 73, 0x87867832, 0x6EAC9000 },
+ { 0, 76, 0xA968163F, 0x0A57B400 },
+ { 0, 79, 0xD3C21BCE, 0xCCEDA100 },
+ { 0, 83, 0x84595161, 0x401484A0 },
+ { 0, 86, 0xA56FA5B9, 0x9019A5C8 },
+ { 0, 89, 0xCECB8F27, 0xF4200F3A }
+};
+static flt_arith big_10pow[] = { /* representation of 10 ** (28*i) */
+ { 0, 0, 0x80000000, 0 },
+ { 0, 93, 0x813F3978, 0xF8940984 },
+ { 0, 186, 0x82818F12, 0x81ED44A0 },
+ { 0, 279, 0x83C7088E, 0x1AAB65DB },
+ { 0, 372, 0x850FADC0, 0x9923329E },
+ { 0, 465, 0x865B8692, 0x5B9BC5C2 },
+ { 0, 558, 0x87AA9AFF, 0x79042287 },
+ { 0, 651, 0x88FCF317, 0xF22241E2 },
+ { 0, 744, 0x8A5296FF, 0xE33CC930 },
+ { 0, 837, 0x8BAB8EEF, 0xB6409C1A },
+ { 0, 930, 0x8D07E334, 0x55637EB3 },
+ { 0, 1023, 0x8E679C2F, 0x5E44FF8F },
+ { 0, 1116, 0x8FCAC257, 0x558EE4E6 },
+ { 0, 1209, 0x91315E37, 0xDB165AA9 },
+ { 0, 1302, 0x929B7871, 0xDE7F22B9 },
+ { 0, 1395, 0x940919BB, 0xD4620B6D },
+ { 0, 1488, 0x957A4AE1, 0xEBF7F3D4 },
+ { 0, 1581, 0x96EF14C6, 0x454AA840 },
+ { 0, 1674, 0x98678061, 0x27ECE4F5 },
+ { 0, 1767, 0x99E396C1, 0x3A3ACFF2 }
+};
+
+static flt_arith r_10pow[] = { /* representation of 10 ** -i */
+ { 0, 0, 0x80000000, 0 },
+ { 0, -4, 0xCCCCCCCC, 0xCCCCCCCD },
+ { 0, -7, 0xA3D70A3D, 0x70A3D70A },
+ { 0, -10, 0x83126E97, 0x8D4FDF3B },
+ { 0, -14, 0xD1B71758, 0xE219652C },
+ { 0, -17, 0xA7C5AC47, 0x1B478423 },
+ { 0, -20, 0x8637BD05, 0xAF6C69B6 },
+ { 0, -24, 0xD6BF94D5, 0xE57A42BC },
+ { 0, -27, 0xABCC7711, 0x8461CEFD },
+ { 0, -30, 0x89705F41, 0x36B4A597 },
+ { 0, -34, 0xDBE6FECE, 0xBDEDD5BF },
+ { 0, -37, 0xAFEBFF0B, 0xCB24AAFF },
+ { 0, -40, 0x8CBCCC09, 0x6F5088CC },
+ { 0, -44, 0xE12E1342, 0x4BB40E13 },
+ { 0, -47, 0xB424DC35, 0x095CD80F },
+ { 0, -50, 0x901D7CF7, 0x3AB0ACD9 },
+ { 0, -54, 0xE69594BE, 0xC44DE15B },
+ { 0, -57, 0xB877AA32, 0x36A4B449 },
+ { 0, -60, 0x9392EE8E, 0x921D5D07 },
+ { 0, -64, 0xEC1E4A7D, 0xB69561A5 },
+ { 0, -67, 0xBCE50864, 0x92111AEB },
+ { 0, -70, 0x971DA050, 0x74DA7BEF },
+ { 0, -74, 0xF1C90080, 0xBAF72CB1 },
+ { 0, -77, 0xC16D9A00, 0x95928A27 },
+ { 0, -80, 0x9ABE14CD, 0x44753B53 },
+ { 0, -84, 0xF79687AE, 0xD3EEC551 },
+ { 0, -87, 0xC6120625, 0x76589DDB },
+ { 0, -90, 0x9E74D1B7, 0x91E07E48 }
+};
+
+static flt_arith r_big_10pow[] = { /* representation of 10 ** -(28*i) */
+ { 0, 0, 0x80000000, 0 },
+ { 0, -94, 0xFD87B5F2, 0x8300CA0E },
+ { 0, -187, 0xFB158592, 0xBE068D2F },
+ { 0, -280, 0xF8A95FCF, 0x88747D94 },
+ { 0, -373, 0xF64335BC, 0xF065D37D },
+ { 0, -466, 0xF3E2F893, 0xDEC3F126 },
+ { 0, -559, 0xF18899B1, 0xBC3F8CA2 },
+ { 0, -652, 0xEF340A98, 0x172AACE5 },
+ { 0, -745, 0xECE53CEC, 0x4A314EBE },
+ { 0, -838, 0xEA9C2277, 0x23EE8BCB },
+ { 0, -931, 0xE858AD24, 0x8F5C22CA },
+ { 0, -1024, 0xE61ACF03, 0x3D1A45DF },
+ { 0, -1117, 0xE3E27A44, 0x4D8D98B8 },
+ { 0, -1210, 0xE1AFA13A, 0xFBD14D6E },
+ { 0, -1303, 0xDF82365C, 0x497B5454 },
+ { 0, -1396, 0xDD5A2C3E, 0xAB3097CC },
+ { 0, -1489, 0xDB377599, 0xB6074245 },
+ { 0, -1582, 0xD91A0545, 0xCDB51186 },
+ { 0, -1675, 0xD701CE3B, 0xD387BF48 },
+ { 0, -1768, 0xD4EEC394, 0xD6258BF8 }
+};
+
+static
+add_exponent(e, exp)
+ register flt_arith *e;
+{
+ int neg = exp < 0;
+ int divsz, modsz;
+ flt_arith x;
+
+ if (neg) exp = -exp;
+ divsz = exp / (sizeof(s10pow)/sizeof(s10pow[0]));
+ modsz = exp % (sizeof(s10pow)/sizeof(s10pow[0]));
+ if (neg) {
+ flt_mul(e, &r_10pow[modsz], &x);
+ while (divsz >= sizeof(r_big_10pow)/sizeof(r_big_10pow[0])) {
+ flt_mul(&x, &r_big_10pow[sizeof(r_big_10pow)/sizeof(r_big_10pow[0])-1],&x);
+ divsz -= sizeof(r_big_10pow)/sizeof(r_big_10pow[0])-1;
+ flt_chk(e);
+ if (flt_status != 0) return;
+ }
+ flt_mul(&x, &r_big_10pow[divsz], e);
+ }
+ else {
+ flt_mul(e, &s10pow[modsz], &x);
+ while (divsz >= sizeof(big_10pow)/sizeof(big_10pow[0])) {
+ flt_mul(&x, &big_10pow[sizeof(big_10pow)/sizeof(big_10pow[0])-1],&x);
+ divsz -= sizeof(big_10pow)/sizeof(big_10pow[0])-1;
+ flt_chk(e);
+ if (flt_status != 0) return;
+ }
+ flt_mul(&x, &big_10pow[divsz], e);
+ }
+}
+
+flt_str2flt(s, e)
+ register char *s;
+ register flt_arith *e;
+{
+ register int c;
+ int dotseen = 0;
+ int digitseen = 0;
+ int exp = 0;
+
+ while (isspace(*s)) s++;
+
+ flt_status = 0;
+
+ e->flt_sign = 0;
+ e->flt_exp = 0;
+ e->m1 = e->m2 = 0;
+
+ c = *s;
+ switch(c) {
+ case '-':
+ e->flt_sign = 1;
+ case '+':
+ s++;
+ }
+ while (c = *s++, isdigit(c) || (c == '.' && ! dotseen++)) {
+ if (c == '.') continue;
+ digitseen = 1;
+ if (e->m1 <= 0x7FFFFFFF/5) {
+ struct _mantissa a1;
+
+ a1 = e->flt_mantissa;
+ b64_sft(&(e->flt_mantissa), -3);
+ b64_sft(&a1, -1);
+ b64_add(&(e->flt_mantissa), &a1);
+ a1.flt_h_32 = 0;
+ a1.flt_l_32 = c - '0';
+ b64_add(&(e->flt_mantissa), &a1);
+ }
+ else exp++;
+ if (dotseen) exp--;
+ }
+ if (! digitseen) {
+ flt_status = FLT_NOFLT;
+ return;
+ }
+
+ if (c == 'E' || c == 'e') {
+ int exp1 = 0;
+ int sign = 1;
+
+ switch(*s) {
+ case '-':
+ sign = -1;
+ case '+':
+ s++;
+ }
+ if (c = *s, isdigit(c)) {
+ do {
+ exp1 = 10 * exp1 + (c - '0');
+ } while (c = *++s, isdigit(c));
+ }
+ exp += sign * exp1;
+ }
+ if (e->m1 == 0 && e->m2 == 0) return;
+ e->flt_exp = 63;
+ flt_nrm(e);
+ add_exponent(e, exp);
+ flt_chk(e);
+}
+
+#define NDIGITS 128
+
+static char *
+flt_ecvt(e, ndigit, decpt, sign)
+ register flt_arith *e;
+ int ndigit, *decpt, *sign;
+{
+ /* Like ecvt(), but for extended precision */
+
+ static char buf[NDIGITS+1];
+ register char *p = buf;
+ register char *pe;
+
+ if (ndigit < 0) ndigit = 0;
+ if (ndigit > NDIGITS) ndigit = NDIGITS;
+ pe = &buf[ndigit];
+ buf[0] = '\0';
+
+ *sign = 0;
+ if (e->flt_sign) {
+ *sign = 1;
+ e->flt_sign = 0;
+ }
+
+ *decpt = 0;
+ if (e->m1 != 0) {
+#define BIGSZ (sizeof(big_10pow)/sizeof(big_10pow[0]))
+#define SMALLSZ (sizeof(s10pow)/sizeof(s10pow[0]))
+ register flt_arith *pp = &big_10pow[1];
+
+ while (flt_cmp(e, &big_10pow[BIGSZ-1]) >= 0) {
+ flt_mul(e,&r_big_10pow[BIGSZ-1],e);
+ *decpt += (BIGSZ-1)*SMALLSZ;
+ }
+ while (flt_cmp(e,pp) >= 0) {
+ pp++;
+ }
+ pp--;
+ flt_mul(e,&r_big_10pow[pp-big_10pow],e);
+ *decpt += (pp - big_10pow)*SMALLSZ;
+ pp = &s10pow[1];
+ while (pp < &s10pow[SMALLSZ] && cmp_ext(e, pp) >= 0) pp++;
+ pp--;
+ flt_mul(e, &r_10pow[pp-s10pow], e);
+ *decpt += pp - s10pow;
+
+ if (cmp_ext(e, &s10pow[0]) < 0) {
+ while (flt_cmp(e, &r_big_10pow[BIGSZ-1]) < 0) {
+ flt_mul(e,&big_10pow[BIGSZ-1],e);
+ *decpt -= (BIGSZ-1)*SMALLSZ;
+ }
+ pp = &r_big_10pow[1];
+ while(cmp_ext(e,pp) < 0) pp++;
+ pp--;
+ flt_mul(e,&big_10pow[pp-r_big_10pow],e);
+ *decpt -= (pp - r_big_10pow)*SMALLSZ;
+ /* here, value >= 10 ** -28 */
+ flt_mul(e, &s10pow[1], e);
+ (*decpt)--;
+ pp = &r_10pow[0];
+ while(cmp_ext(e, pp) < 0) pp++;
+ flt_mul(e, &s10pow[pp-r_10pow], e);
+ *decpt -= pp - r_10pow;
+ }
+ (*decpt)++; /* because now value in [1.0, 10.0) */
+ }
+ while (p <= pe) {
+ if (e->flt_exp >= 0) {
+ flt_arith x;
+
+ x.m2 = 0; x.flt_exp = e->flt_exp;
+ x.flt_sign = 1;
+ x.m1 = e->m1>>(31-e->flt_exp);
+ *p++ = (x.m1) + '0';
+ x.m1 = x.m1 << (31-e->flt_exp);
+ add_ext(e, &x, e);
+ }
+ else *p++ = '0';
+ flt_mul(e, &s10pow[1], e);
+ }
+ if (pe >= buf) {
+ p = pe;
+ *p += 5; /* round of at the end */
+ while (*p > '9') {
+ *p = '0';
+ if (p > buf) ++*--p;
+ else {
+ *p = '1';
+ ++*decpt;
+ }
+ }
+ *pe = '\0';
+ }
+ return buf;
+}
+
+flt_flt2str(e, buf, bufsize)
+ flt_arith *e;
+ char *buf;
+{
+
+#define NDIG 25
+ int sign, dp;
+ register int i;
+ register char *s1;
+ char Xbuf[NDIG+12];
+ register char *s = Xbuf;
+
+ flt_status = 0;
+ s1 = flt_ecvt(e,NDIG,&dp,&sign);
+ if (sign)
+ *s++ = '-';
+ *s++ = *s1++;
+ *s++ = '.';
+ for (i = NDIG-1; i > 0; i--) {
+ if (*s1) *s++ = *s1++;
+ else *s++ = '0';
+ }
+ if ((e->m1 | e->m2) || e->flt_exp == EXT_MIN || e->flt_exp == EXT_MAX) {
+ --dp ;
+ }
+ if (dp == 0) {
+ *s = 0;
+ return;
+ }
+ *s++ = 'e';
+ if ( dp<0 ) {
+ *s++ = '-' ; dp= -dp ;
+ } else {
+ *s++ = '+' ;
+ }
+ s1 = &Xbuf[NDIG+12];
+ *--s1 = '\0';
+ do {
+ *--s1 = dp % 10 + '0';
+ dp /= 10;
+ } while (dp != 0);
+ while (*s1) *s++ = *s1++;
+ *s++ = '\0';
+ if (s - Xbuf > bufsize) {
+ flt_status = FLT_BTSM;
+ return;
+ }
+ s = Xbuf;
+ s1 = buf;
+ do {
+ *s1++ = *s++;
+ } while (*s);
+}
--- /dev/null
+/*
+ * (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ * See the copyright notice in the ACK home directory, in the file "Copyright".
+ */
+/* $Header$ */
+
+#include <flt_arith.h>
+
+/* some short-hands ... */
+#define m1 flt_mantissa.flt_h_32
+#define m2 flt_mantissa.flt_l_32
+
+/* some constants */
+#define EXT_MAX 16384 /* max exponent */
+#define EXT_MIN (-16384) /* min exponent */
+
+/* hiding of names: */
+#define ucmp flt__ucmp
+#define flt_nrm flt__nrm
+#define flt_chk flt__chk
+#define b64_add flt__64add
+#define b64_sft flt__64sft
+#define b64_rsft flt__64rsft
+#define b64_lsft flt__64lsft
--- /dev/null
+/*
+ (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ See the copyright notice in the ACK home directory, in the file "Copyright".
+*/
+
+/* $Header$ */
+
+#include "misc.h"
+
+int
+ucmp(l1,l2)
+ long l1,l2;
+{
+ if (l1 == l2) return 0;
+ if (l2 >= 0) {
+ if (l1 > l2) return 1;
+ return -1;
+ }
+ if (l1 > 0 || l1 < l2) return -1;
+ return 1;
+}
public / ack.git / commitdiff