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/* Copyright (C) 2007-2014 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.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
/*****************************************************************************
* BID64 remainder
*****************************************************************************
*
* Algorithm description:
*
* if(exponent_x < exponent_y)
* scale coefficient_y so exponents are aligned
* perform coefficient divide (64-bit integer divide), unless
* coefficient_y is longer than 64 bits (clearly larger
* than coefficient_x)
* else // exponent_x > exponent_y
* use a loop to scale coefficient_x to 18_digits, divide by
* coefficient_y (64-bit integer divide), calculate remainder
* as new_coefficient_x and repeat until final remainder is obtained
* (when new_exponent_x < exponent_y)
*
****************************************************************************/
#include "bid_internal.h"
#define MAX_FORMAT_DIGITS 16
#define DECIMAL_EXPONENT_BIAS 398
#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull
#define BINARY_EXPONENT_BIAS 0x3ff
#define UPPER_EXPON_LIMIT 51
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_rem (UINT64 * pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x, y;
#else
UINT64
bid64_rem (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 CY;
UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
UINT64 Q, R, R2, T, valid_y, valid_x;
int_float tempx;
int exponent_x, exponent_y, bin_expon, e_scale;
int digits_x, diff_expon;
#if DECIMAL_CALL_BY_REFERENCE
x = *px;
y = *py;
#endif
valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
// unpack arguments, check for NaN or Infinity
if (!valid_x) {
// x is Inf. or NaN or 0
#ifdef SET_STATUS_FLAGS
if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// test if x is NaN
if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if (((x & SNAN_MASK64) == SNAN_MASK64))
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = coefficient_x & QUIET_MASK64;;
BID_RETURN (res);
}
// x is Infinity?
if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
if (((y & NAN_MASK64) != NAN_MASK64)) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// return NaN
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
}
// x is 0
// return x if y != 0
if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
coefficient_y) {
if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
exponent_y = (y >> 51) & 0x3ff;
else
exponent_y = (y >> 53) & 0x3ff;
if (exponent_y < exponent_x)
exponent_x = exponent_y;
x = exponent_x;
x <<= 53;
res = x | sign_x;
BID_RETURN (res);
}
}
if (!valid_y) {
// y is Inf. or NaN
// test if y is NaN
if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if (((y & SNAN_MASK64) == SNAN_MASK64))
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = coefficient_y & QUIET_MASK64;;
BID_RETURN (res);
}
// y is Infinity?
if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
BID_RETURN (res);
}
// y is 0, return NaN
{
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
}
diff_expon = exponent_x - exponent_y;
if (diff_expon <= 0) {
diff_expon = -diff_expon;
if (diff_expon > 16) {
// |x|<|y| in this case
res = x;
BID_RETURN (res);
}
// set exponent of y to exponent_x, scale coefficient_y
T = power10_table_128[diff_expon].w[0];
__mul_64x64_to_128 (CY, coefficient_y, T);
if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
res = x;
BID_RETURN (res);
}
Q = coefficient_x / CY.w[0];
R = coefficient_x - Q * CY.w[0];
R2 = R + R;
if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
R = CY.w[0] - R;
sign_x ^= 0x8000000000000000ull;
}
res = very_fast_get_BID64 (sign_x, exponent_x, R);
BID_RETURN (res);
}
while (diff_expon > 0) {
// get number of digits in coeff_x
tempx.d = (float) coefficient_x;
bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
digits_x = estimate_decimal_digits[bin_expon];
// will not use this test, dividend will have 18 or 19 digits
//if(coefficient_x >= power10_table_128[digits_x].w[0])
// digits_x++;
e_scale = 18 - digits_x;
if (diff_expon >= e_scale) {
diff_expon -= e_scale;
} else {
e_scale = diff_expon;
diff_expon = 0;
}
// scale dividend to 18 or 19 digits
coefficient_x *= power10_table_128[e_scale].w[0];
// quotient
Q = coefficient_x / coefficient_y;
// remainder
coefficient_x -= Q * coefficient_y;
// check for remainder == 0
if (!coefficient_x) {
res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
BID_RETURN (res);
}
}
R2 = coefficient_x + coefficient_x;
if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
coefficient_x = coefficient_y - coefficient_x;
sign_x ^= 0x8000000000000000ull;
}
res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
BID_RETURN (res);
}
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