--- /dev/null
+/* Simple data type for positive real numbers for the GNU compiler.
+ Copyright (C) 2002, 2003, 2004, 2007 Free Software Foundation, Inc.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 3, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING3. If not see
+<http://www.gnu.org/licenses/>. */
+
+/* This library supports positive real numbers and 0;
+ inf and nan are NOT supported.
+ It is written to be simple and fast.
+
+ Value of sreal is
+ x = sig * 2 ^ exp
+ where
+ sig = significant
+ (for < 64-bit machines sig = sig_lo + sig_hi * 2 ^ SREAL_PART_BITS)
+ exp = exponent
+
+ One HOST_WIDE_INT is used for the significant on 64-bit (and more than
+ 64-bit) machines,
+ otherwise two HOST_WIDE_INTs are used for the significant.
+ Only a half of significant bits is used (in normalized sreals) so that we do
+ not have problems with overflow, for example when c->sig = a->sig * b->sig.
+ So the precision for 64-bit and 32-bit machines is 32-bit.
+
+ Invariant: The numbers are normalized before and after each call of sreal_*.
+
+ Normalized sreals:
+ All numbers (except zero) meet following conditions:
+ SREAL_MIN_SIG <= sig && sig <= SREAL_MAX_SIG
+ -SREAL_MAX_EXP <= exp && exp <= SREAL_MAX_EXP
+
+ If the number would be too large, it is set to upper bounds of these
+ conditions.
+
+ If the number is zero or would be too small it meets following conditions:
+ sig == 0 && exp == -SREAL_MAX_EXP
+*/
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "tm.h"
+#include "sreal.h"
+
+static inline void copy (sreal *, sreal *);
+static inline void shift_right (sreal *, int);
+static void normalize (sreal *);
+
+/* Print the content of struct sreal. */
+
+void
+dump_sreal (FILE *file, sreal *x)
+{
+#if SREAL_PART_BITS < 32
+ fprintf (file, "((" HOST_WIDE_INT_PRINT_UNSIGNED " * 2^16 + "
+ HOST_WIDE_INT_PRINT_UNSIGNED ") * 2^%d)",
+ x->sig_hi, x->sig_lo, x->exp);
+#else
+ fprintf (file, "(" HOST_WIDE_INT_PRINT_UNSIGNED " * 2^%d)", x->sig, x->exp);
+#endif
+}
+
+/* Copy the sreal number. */
+
+static inline void
+copy (sreal *r, sreal *a)
+{
+#if SREAL_PART_BITS < 32
+ r->sig_lo = a->sig_lo;
+ r->sig_hi = a->sig_hi;
+#else
+ r->sig = a->sig;
+#endif
+ r->exp = a->exp;
+}
+
+/* Shift X right by S bits. Needed: 0 < S <= SREAL_BITS.
+ When the most significant bit shifted out is 1, add 1 to X (rounding). */
+
+static inline void
+shift_right (sreal *x, int s)
+{
+ gcc_assert (s > 0);
+ gcc_assert (s <= SREAL_BITS);
+ /* Exponent should never be so large because shift_right is used only by
+ sreal_add and sreal_sub ant thus the number cannot be shifted out from
+ exponent range. */
+ gcc_assert (x->exp + s <= SREAL_MAX_EXP);
+
+ x->exp += s;
+
+#if SREAL_PART_BITS < 32
+ if (s > SREAL_PART_BITS)
+ {
+ s -= SREAL_PART_BITS;
+ x->sig_hi += (uhwi) 1 << (s - 1);
+ x->sig_lo = x->sig_hi >> s;
+ x->sig_hi = 0;
+ }
+ else
+ {
+ x->sig_lo += (uhwi) 1 << (s - 1);
+ if (x->sig_lo & ((uhwi) 1 << SREAL_PART_BITS))
+ {
+ x->sig_hi++;
+ x->sig_lo -= (uhwi) 1 << SREAL_PART_BITS;
+ }
+ x->sig_lo >>= s;
+ x->sig_lo |= (x->sig_hi & (((uhwi) 1 << s) - 1)) << (SREAL_PART_BITS - s);
+ x->sig_hi >>= s;
+ }
+#else
+ x->sig += (uhwi) 1 << (s - 1);
+ x->sig >>= s;
+#endif
+}
+
+/* Normalize *X. */
+
+static void
+normalize (sreal *x)
+{
+#if SREAL_PART_BITS < 32
+ int shift;
+ HOST_WIDE_INT mask;
+
+ if (x->sig_lo == 0 && x->sig_hi == 0)
+ {
+ x->exp = -SREAL_MAX_EXP;
+ }
+ else if (x->sig_hi < SREAL_MIN_SIG)
+ {
+ if (x->sig_hi == 0)
+ {
+ /* Move lower part of significant to higher part. */
+ x->sig_hi = x->sig_lo;
+ x->sig_lo = 0;
+ x->exp -= SREAL_PART_BITS;
+ }
+ shift = 0;
+ while (x->sig_hi < SREAL_MIN_SIG)
+ {
+ x->sig_hi <<= 1;
+ x->exp--;
+ shift++;
+ }
+ /* Check underflow. */
+ if (x->exp < -SREAL_MAX_EXP)
+ {
+ x->exp = -SREAL_MAX_EXP;
+ x->sig_hi = 0;
+ x->sig_lo = 0;
+ }
+ else if (shift)
+ {
+ mask = (1 << SREAL_PART_BITS) - (1 << (SREAL_PART_BITS - shift));
+ x->sig_hi |= (x->sig_lo & mask) >> (SREAL_PART_BITS - shift);
+ x->sig_lo = (x->sig_lo << shift) & (((uhwi) 1 << SREAL_PART_BITS) - 1);
+ }
+ }
+ else if (x->sig_hi > SREAL_MAX_SIG)
+ {
+ unsigned HOST_WIDE_INT tmp = x->sig_hi;
+
+ /* Find out how many bits will be shifted. */
+ shift = 0;
+ do
+ {
+ tmp >>= 1;
+ shift++;
+ }
+ while (tmp > SREAL_MAX_SIG);
+
+ /* Round the number. */
+ x->sig_lo += (uhwi) 1 << (shift - 1);
+
+ x->sig_lo >>= shift;
+ x->sig_lo += ((x->sig_hi & (((uhwi) 1 << shift) - 1))
+ << (SREAL_PART_BITS - shift));
+ x->sig_hi >>= shift;
+ x->exp += shift;
+ if (x->sig_lo & ((uhwi) 1 << SREAL_PART_BITS))
+ {
+ x->sig_lo -= (uhwi) 1 << SREAL_PART_BITS;
+ x->sig_hi++;
+ if (x->sig_hi > SREAL_MAX_SIG)
+ {
+ /* x->sig_hi was SREAL_MAX_SIG before increment
+ so now last bit is zero. */
+ x->sig_hi >>= 1;
+ x->sig_lo >>= 1;
+ x->exp++;
+ }
+ }
+
+ /* Check overflow. */
+ if (x->exp > SREAL_MAX_EXP)
+ {
+ x->exp = SREAL_MAX_EXP;
+ x->sig_hi = SREAL_MAX_SIG;
+ x->sig_lo = SREAL_MAX_SIG;
+ }
+ }
+#else
+ if (x->sig == 0)
+ {
+ x->exp = -SREAL_MAX_EXP;
+ }
+ else if (x->sig < SREAL_MIN_SIG)
+ {
+ do
+ {
+ x->sig <<= 1;
+ x->exp--;
+ }
+ while (x->sig < SREAL_MIN_SIG);
+
+ /* Check underflow. */
+ if (x->exp < -SREAL_MAX_EXP)
+ {
+ x->exp = -SREAL_MAX_EXP;
+ x->sig = 0;
+ }
+ }
+ else if (x->sig > SREAL_MAX_SIG)
+ {
+ int last_bit;
+ do
+ {
+ last_bit = x->sig & 1;
+ x->sig >>= 1;
+ x->exp++;
+ }
+ while (x->sig > SREAL_MAX_SIG);
+
+ /* Round the number. */
+ x->sig += last_bit;
+ if (x->sig > SREAL_MAX_SIG)
+ {
+ x->sig >>= 1;
+ x->exp++;
+ }
+
+ /* Check overflow. */
+ if (x->exp > SREAL_MAX_EXP)
+ {
+ x->exp = SREAL_MAX_EXP;
+ x->sig = SREAL_MAX_SIG;
+ }
+ }
+#endif
+}
+
+/* Set *R to SIG * 2 ^ EXP. Return R. */
+
+sreal *
+sreal_init (sreal *r, unsigned HOST_WIDE_INT sig, signed int exp)
+{
+#if SREAL_PART_BITS < 32
+ r->sig_lo = 0;
+ r->sig_hi = sig;
+ r->exp = exp - 16;
+#else
+ r->sig = sig;
+ r->exp = exp;
+#endif
+ normalize (r);
+ return r;
+}
+
+/* Return integer value of *R. */
+
+HOST_WIDE_INT
+sreal_to_int (sreal *r)
+{
+#if SREAL_PART_BITS < 32
+ if (r->exp <= -SREAL_BITS)
+ return 0;
+ if (r->exp >= 0)
+ return MAX_HOST_WIDE_INT;
+ return ((r->sig_hi << SREAL_PART_BITS) + r->sig_lo) >> -r->exp;
+#else
+ if (r->exp <= -SREAL_BITS)
+ return 0;
+ if (r->exp >= SREAL_PART_BITS)
+ return MAX_HOST_WIDE_INT;
+ if (r->exp > 0)
+ return r->sig << r->exp;
+ if (r->exp < 0)
+ return r->sig >> -r->exp;
+ return r->sig;
+#endif
+}
+
+/* Compare *A and *B. Return -1 if *A < *B, 1 if *A > *B and 0 if *A == *B. */
+
+int
+sreal_compare (sreal *a, sreal *b)
+{
+ if (a->exp > b->exp)
+ return 1;
+ if (a->exp < b->exp)
+ return -1;
+#if SREAL_PART_BITS < 32
+ if (a->sig_hi > b->sig_hi)
+ return 1;
+ if (a->sig_hi < b->sig_hi)
+ return -1;
+ if (a->sig_lo > b->sig_lo)
+ return 1;
+ if (a->sig_lo < b->sig_lo)
+ return -1;
+#else
+ if (a->sig > b->sig)
+ return 1;
+ if (a->sig < b->sig)
+ return -1;
+#endif
+ return 0;
+}
+
+/* *R = *A + *B. Return R. */
+
+sreal *
+sreal_add (sreal *r, sreal *a, sreal *b)
+{
+ int dexp;
+ sreal tmp;
+ sreal *bb;
+
+ if (sreal_compare (a, b) < 0)
+ {
+ sreal *swap;
+ swap = a;
+ a = b;
+ b = swap;
+ }
+
+ dexp = a->exp - b->exp;
+ r->exp = a->exp;
+ if (dexp > SREAL_BITS)
+ {
+#if SREAL_PART_BITS < 32
+ r->sig_hi = a->sig_hi;
+ r->sig_lo = a->sig_lo;
+#else
+ r->sig = a->sig;
+#endif
+ return r;
+ }
+
+ if (dexp == 0)
+ bb = b;
+ else
+ {
+ copy (&tmp, b);
+ shift_right (&tmp, dexp);
+ bb = &tmp;
+ }
+
+#if SREAL_PART_BITS < 32
+ r->sig_hi = a->sig_hi + bb->sig_hi;
+ r->sig_lo = a->sig_lo + bb->sig_lo;
+ if (r->sig_lo & ((uhwi) 1 << SREAL_PART_BITS))
+ {
+ r->sig_hi++;
+ r->sig_lo -= (uhwi) 1 << SREAL_PART_BITS;
+ }
+#else
+ r->sig = a->sig + bb->sig;
+#endif
+ normalize (r);
+ return r;
+}
+
+/* *R = *A - *B. Return R. */
+
+sreal *
+sreal_sub (sreal *r, sreal *a, sreal *b)
+{
+ int dexp;
+ sreal tmp;
+ sreal *bb;
+
+ gcc_assert (sreal_compare (a, b) >= 0);
+
+ dexp = a->exp - b->exp;
+ r->exp = a->exp;
+ if (dexp > SREAL_BITS)
+ {
+#if SREAL_PART_BITS < 32
+ r->sig_hi = a->sig_hi;
+ r->sig_lo = a->sig_lo;
+#else
+ r->sig = a->sig;
+#endif
+ return r;
+ }
+ if (dexp == 0)
+ bb = b;
+ else
+ {
+ copy (&tmp, b);
+ shift_right (&tmp, dexp);
+ bb = &tmp;
+ }
+
+#if SREAL_PART_BITS < 32
+ if (a->sig_lo < bb->sig_lo)
+ {
+ r->sig_hi = a->sig_hi - bb->sig_hi - 1;
+ r->sig_lo = a->sig_lo + ((uhwi) 1 << SREAL_PART_BITS) - bb->sig_lo;
+ }
+ else
+ {
+ r->sig_hi = a->sig_hi - bb->sig_hi;
+ r->sig_lo = a->sig_lo - bb->sig_lo;
+ }
+#else
+ r->sig = a->sig - bb->sig;
+#endif
+ normalize (r);
+ return r;
+}
+
+/* *R = *A * *B. Return R. */
+
+sreal *
+sreal_mul (sreal *r, sreal *a, sreal *b)
+{
+#if SREAL_PART_BITS < 32
+ if (a->sig_hi < SREAL_MIN_SIG || b->sig_hi < SREAL_MIN_SIG)
+ {
+ r->sig_lo = 0;
+ r->sig_hi = 0;
+ r->exp = -SREAL_MAX_EXP;
+ }
+ else
+ {
+ unsigned HOST_WIDE_INT tmp1, tmp2, tmp3;
+ if (sreal_compare (a, b) < 0)
+ {
+ sreal *swap;
+ swap = a;
+ a = b;
+ b = swap;
+ }
+
+ r->exp = a->exp + b->exp + SREAL_PART_BITS;
+
+ tmp1 = a->sig_lo * b->sig_lo;
+ tmp2 = a->sig_lo * b->sig_hi;
+ tmp3 = a->sig_hi * b->sig_lo + (tmp1 >> SREAL_PART_BITS);
+
+ r->sig_hi = a->sig_hi * b->sig_hi;
+ r->sig_hi += (tmp2 >> SREAL_PART_BITS) + (tmp3 >> SREAL_PART_BITS);
+ tmp2 &= ((uhwi) 1 << SREAL_PART_BITS) - 1;
+ tmp3 &= ((uhwi) 1 << SREAL_PART_BITS) - 1;
+ tmp1 = tmp2 + tmp3;
+
+ r->sig_lo = tmp1 & (((uhwi) 1 << SREAL_PART_BITS) - 1);
+ r->sig_hi += tmp1 >> SREAL_PART_BITS;
+
+ normalize (r);
+ }
+#else
+ if (a->sig < SREAL_MIN_SIG || b->sig < SREAL_MIN_SIG)
+ {
+ r->sig = 0;
+ r->exp = -SREAL_MAX_EXP;
+ }
+ else
+ {
+ r->sig = a->sig * b->sig;
+ r->exp = a->exp + b->exp;
+ normalize (r);
+ }
+#endif
+ return r;
+}
+
+/* *R = *A / *B. Return R. */
+
+sreal *
+sreal_div (sreal *r, sreal *a, sreal *b)
+{
+#if SREAL_PART_BITS < 32
+ unsigned HOST_WIDE_INT tmp, tmp1, tmp2;
+
+ gcc_assert (b->sig_hi >= SREAL_MIN_SIG);
+ if (a->sig_hi < SREAL_MIN_SIG)
+ {
+ r->sig_hi = 0;
+ r->sig_lo = 0;
+ r->exp = -SREAL_MAX_EXP;
+ }
+ else
+ {
+ /* Since division by the whole number is pretty ugly to write
+ we are dividing by first 3/4 of bits of number. */
+
+ tmp1 = (a->sig_hi << SREAL_PART_BITS) + a->sig_lo;
+ tmp2 = ((b->sig_hi << (SREAL_PART_BITS / 2))
+ + (b->sig_lo >> (SREAL_PART_BITS / 2)));
+ if (b->sig_lo & ((uhwi) 1 << ((SREAL_PART_BITS / 2) - 1)))
+ tmp2++;
+
+ r->sig_lo = 0;
+ tmp = tmp1 / tmp2;
+ tmp1 = (tmp1 % tmp2) << (SREAL_PART_BITS / 2);
+ r->sig_hi = tmp << SREAL_PART_BITS;
+
+ tmp = tmp1 / tmp2;
+ tmp1 = (tmp1 % tmp2) << (SREAL_PART_BITS / 2);
+ r->sig_hi += tmp << (SREAL_PART_BITS / 2);
+
+ tmp = tmp1 / tmp2;
+ r->sig_hi += tmp;
+
+ r->exp = a->exp - b->exp - SREAL_BITS - SREAL_PART_BITS / 2;
+ normalize (r);
+ }
+#else
+ gcc_assert (b->sig != 0);
+ r->sig = (a->sig << SREAL_PART_BITS) / b->sig;
+ r->exp = a->exp - b->exp - SREAL_PART_BITS;
+ normalize (r);
+#endif
+ return r;
+}
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