/GCC/gcc/sreal.c
C | 544 lines | 414 code | 53 blank | 77 comment | 62 complexity | 6a56ac3bbfe2a815de336d7a27c1cbdf MD5 | raw file
Possible License(s): GPL-2.0
- /* Simple data type for positive real numbers for the GNU compiler.
- Copyright (C) 2002, 2003, 2004 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 2, 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 COPYING. If not, write to the Free
- Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
- 02110-1301, USA. */
- /* 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;
- }