/* Copyright (C) 2007-2015 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 add
*****************************************************************************
*
* Algorithm description:
*
* if(exponent_a < exponent_b)
* switch a, b
* diff_expon = exponent_a - exponent_b
* if(diff_expon > 16)
* return normalize(a)
* if(coefficient_a*10^diff_expon guaranteed below 2^62)
* S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b
* if(|S|<10^16)
* return get_BID64(sign(S),exponent_b,|S|)
* else
* determine number of extra digits in S (1, 2, or 3)
* return rounded result
* else // large exponent difference
* if(number_digits(coefficient_a*10^diff_expon) +/- 10^16)
* guaranteed the same as
* number_digits(coefficient_a*10^diff_expon) )
* S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon))
* corr = 10^16 + (sign_a^sign_b)*coefficient_b
* corr*10^exponent_b is rounded so it aligns with S*10^exponent_S
* return get_BID64(sign_a,exponent(S),S+rounded(corr))
* else
* add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b
* in 128-bit integer arithmetic, then round to 16 decimal digits
*
*
****************************************************************************/
#include "bid_internal.h"
#if DECIMAL_CALL_BY_REFERENCE
void bid64_add (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM);
#else
UINT64 bid64_add (UINT64 x,
UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM);
#endif
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_sub (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
_IDEC_round rnd_mode = *prnd_mode;
#endif
// check if y is not NaN
if (((y & NAN_MASK64) != NAN_MASK64))
y ^= 0x8000000000000000ull;
bid64_add (pres, px,
&y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
_EXC_INFO_ARG);
}
#else
UINT64
bid64_sub (UINT64 x,
UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
// check if y is not NaN
if (((y & NAN_MASK64) != NAN_MASK64))
y ^= 0x8000000000000000ull;
return bid64_add (x,
y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
_EXC_INFO_ARG);
}
#endif
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_add (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x, y;
#else
UINT64
bid64_add (UINT64 x,
UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 CA, CT, CT_new;
UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new;
UINT64 valid_x, valid_y;
UINT64 res;
UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab,
rem_a;
UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp;
int_double tempx;
int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon;
int bin_expon_ca, extra_digits, amount, scale_k, scale_ca;
unsigned rmode, status;
#if DECIMAL_CALL_BY_REFERENCE
#if !DECIMAL_GLOBAL_ROUNDING
_IDEC_round rnd_mode = *prnd_mode;
#endif
x = *px;
y = *py;
#endif
valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
// unpack arguments, check for NaN or Infinity
if (!valid_x) {
// x is Inf. or NaN
// test if x is NaN
if ((x & NAN_MASK64) == NAN_MASK64) {
#ifdef SET_STATUS_FLAGS
if (((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
|| ((y & SNAN_MASK64) == SNAN_MASK64))
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = coefficient_x & QUIET_MASK64;
BID_RETURN (res);
}
// x is Infinity?
if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
// check if y is Inf
if (((y & NAN_MASK64) == INFINITY_MASK64)) {
if (sign_x == (y & 0x8000000000000000ull)) {
res = coefficient_x;
BID_RETURN (res);
}
// return NaN
{
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = NAN_MASK64;
BID_RETURN (res);
}
}
// check if y is NaN
if (((y & NAN_MASK64) == NAN_MASK64)) {
res = coefficient_y & QUIET_MASK64;
#ifdef SET_STATUS_FLAGS
if (((y & SNAN_MASK64) == SNAN_MASK64))
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (res);
}
// otherwise return +/-Inf
{
res = coefficient_x;
BID_RETURN (res);
}
}
// x is 0
{
if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y) {
if (exponent_y <= exponent_x) {
res = y;
BID_RETURN (res);
}
}
}
}
if (!valid_y) {
// y is Inf. or NaN?
if (((y & INFINITY_MASK64) == INFINITY_MASK64)) {
#ifdef SET_STATUS_FLAGS
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = coefficient_y & QUIET_MASK64;
BID_RETURN (res);
}
// y is 0
if (!coefficient_x) { // x==0
if (exponent_x <= exponent_y)
res = ((UINT64) exponent_x) << 53;
else
res = ((UINT64) exponent_y) << 53;
if (sign_x == sign_y)
res |= sign_x;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rnd_mode == ROUNDING_DOWN && sign_x != sign_y)
res |= 0x8000000000000000ull;
#endif
#endif
BID_RETURN (res);
} else if (exponent_y >= exponent_x) {
res = x;
BID_RETURN (res);
}
}
// sort arguments by exponent
if (exponent_x < exponent_y) {
sign_a = sign_y;
exponent_a = exponent_y;
coefficient_a = coefficient_y;
sign_b = sign_x;
exponent_b = exponent_x;
coefficient_b = coefficient_x;
} else {
sign_a = sign_x;
exponent_a = exponent_x;
coefficient_a = coefficient_x;
sign_b = sign_y;
exponent_b = exponent_y;
coefficient_b = coefficient_y;
}
// exponent difference
diff_dec_expon = exponent_a - exponent_b;
/* get binary coefficients of x and y */
//--- get number of bits in the coefficients of x and y ---
// version 2 (original)
tempx.d = (double) coefficient_a;
bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
if (diff_dec_expon > MAX_FORMAT_DIGITS) {
// normalize a to a 16-digit coefficient
scale_ca = estimate_decimal_digits[bin_expon_ca];
if (coefficient_a >= power10_table_128[scale_ca].w[0])
scale_ca++;
scale_k = 16 - scale_ca;
coefficient_a *= power10_table_128[scale_k].w[0];
diff_dec_expon -= scale_k;
exponent_a -= scale_k;
/* get binary coefficients of x and y */
//--- get number of bits in the coefficients of x and y ---
tempx.d = (double) coefficient_a;
bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
if (diff_dec_expon > MAX_FORMAT_DIGITS) {
#ifdef SET_STATUS_FLAGS
if (coefficient_b) {
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (((rnd_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST
{
switch (rnd_mode) {
case ROUNDING_DOWN:
if (sign_b) {
coefficient_a -= ((((SINT64) sign_a) >> 63) | 1);
if (coefficient_a < 1000000000000000ull) {
exponent_a--;
coefficient_a = 9999999999999999ull;
} else if (coefficient_a >= 10000000000000000ull) {
exponent_a++;
coefficient_a = 1000000000000000ull;
}
}
break;
case ROUNDING_UP:
if (!sign_b) {
coefficient_a += ((((SINT64) sign_a) >> 63) | 1);
if (coefficient_a < 1000000000000000ull) {
exponent_a--;
coefficient_a = 9999999999999999ull;
} else if (coefficient_a >= 10000000000000000ull) {
exponent_a++;
coefficient_a = 1000000000000000ull;
}
}
break;
default: // RZ
if (sign_a != sign_b) {
coefficient_a--;
if (coefficient_a < 1000000000000000ull) {
exponent_a--;
coefficient_a = 9999999999999999ull;
}
}
break;
}
} else
#endif
#endif
// check special case here
if ((coefficient_a == 1000000000000000ull)
&& (diff_dec_expon == MAX_FORMAT_DIGITS + 1)
&& (sign_a ^ sign_b)
&& (coefficient_b > 5000000000000000ull)) {
coefficient_a = 9999999999999999ull;
exponent_a--;
}
res =
fast_get_BID64_check_OF (sign_a, exponent_a, coefficient_a,
rnd_mode, pfpsf);
BID_RETURN (res);
}
}
// test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62
if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) {
// coefficient_a*10^(exponent_a-exponent_b)<2^63
// multiply by 10^(exponent_a-exponent_b)
coefficient_a *= power10_table_128[diff_dec_expon].w[0];
// sign mask
sign_b = ((SINT64) sign_b) >> 63;
// apply sign to coeff. of b
coefficient_b = (coefficient_b + sign_b) ^ sign_b;
// apply sign to coefficient a
sign_a = ((SINT64) sign_a) >> 63;
coefficient_a = (coefficient_a + sign_a) ^ sign_a;
coefficient_a += coefficient_b;
// get sign
sign_s = ((SINT64) coefficient_a) >> 63;
coefficient_a = (coefficient_a + sign_s) ^ sign_s;
sign_s &= 0x8000000000000000ull;
// coefficient_a < 10^16 ?
if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) {
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rnd_mode == ROUNDING_DOWN && (!coefficient_a)
&& sign_a != sign_b)
sign_s = 0x8000000000000000ull;
#endif
#endif
res = very_fast_get_BID64 (sign_s, exponent_b, coefficient_a);
BID_RETURN (res);
}
// otherwise rounding is necessary
// already know coefficient_a<10^19
// coefficient_a < 10^17 ?
if (coefficient_a < power10_table_128[17].w[0])
extra_digits = 1;
else if (coefficient_a < power10_table_128[18].w[0])
extra_digits = 2;
else
extra_digits = 3;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
rmode = rnd_mode;
if (sign_s && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#else
rmode = 0;
#endif
#else
rmode = 0;
#endif
coefficient_a += round_const_table[rmode][extra_digits];
// get P*(2^M[extra_digits])/10^extra_digits
__mul_64x64_to_128 (CT, coefficient_a,
reciprocals10_64[extra_digits]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[extra_digits];
C64 = CT.w[1] >> amount;
} else {
// coefficient_a*10^(exponent_a-exponent_b) is large
sign_s = sign_a;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
rmode = rnd_mode;
if (sign_s && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#else
rmode = 0;
#endif
#else
rmode = 0;
#endif
// check whether we can take faster path
scale_ca = estimate_decimal_digits[bin_expon_ca];
sign_ab = sign_a ^ sign_b;
sign_ab = ((SINT64) sign_ab) >> 63;
// T1 = 10^(16-diff_dec_expon)
T1 = power10_table_128[16 - diff_dec_expon].w[0];
// get number of digits in coefficient_a
if (coefficient_a >= power10_table_128[scale_ca].w[0]) {
scale_ca++;
}
scale_k = 16 - scale_ca;
// addition
saved_ca = coefficient_a - T1;
coefficient_a =
(SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0];
extra_digits = diff_dec_expon - scale_k;
// apply sign
saved_cb = (coefficient_b + sign_ab) ^ sign_ab;
// add 10^16 and rounding constant
coefficient_b =
saved_cb + 10000000000000000ull +
round_const_table[rmode][extra_digits];
// get P*(2^M[extra_digits])/10^extra_digits
__mul_64x64_to_128 (CT, coefficient_b,
reciprocals10_64[extra_digits]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[extra_digits];
C0_64 = CT.w[1] >> amount;
// result coefficient
C64 = C0_64 + coefficient_a;
// filter out difficult (corner) cases
// this test ensures the number of digits in coefficient_a does not change
// after adding (the appropriately scaled and rounded) coefficient_b
if ((UINT64) (C64 - 1000000000000000ull - 1) >
9000000000000000ull - 2) {
if (C64 >= 10000000000000000ull) {
// result has more than 16 digits
if (!scale_k) {
// must divide coeff_a by 10
saved_ca = saved_ca + T1;
__mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull);
//reciprocals10_64[1]);
coefficient_a = CA.w[1] >> 1;
rem_a =
saved_ca - (coefficient_a << 3) - (coefficient_a << 1);
coefficient_a = coefficient_a - T1;
saved_cb += rem_a * power10_table_128[diff_dec_expon].w[0];
} else
coefficient_a =
(SINT64) (saved_ca - T1 -
(T1 << 3)) * (SINT64) power10_table_128[scale_k -
1].w[0];
extra_digits++;
coefficient_b =
saved_cb + 100000000000000000ull +
round_const_table[rmode][extra_digits];
// get P*(2^M[extra_digits])/10^extra_digits
__mul_64x64_to_128 (CT, coefficient_b,
reciprocals10_64[extra_digits]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[extra_digits];
C0_64 = CT.w[1] >> amount;
// result coefficient
C64 = C0_64 + coefficient_a;
} else if (C64 <= 1000000000000000ull) {
// less than 16 digits in result
coefficient_a =
(SINT64) saved_ca *(SINT64) power10_table_128[scale_k +
1].w[0];
//extra_digits --;
exponent_b--;
coefficient_b =
(saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull +
round_const_table[rmode][extra_digits];
// get P*(2^M[extra_digits])/10^extra_digits
__mul_64x64_to_128 (CT_new, coefficient_b,
reciprocals10_64[extra_digits]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[extra_digits];
C0_64 = CT_new.w[1] >> amount;
// result coefficient
C64_new = C0_64 + coefficient_a;
if (C64_new < 10000000000000000ull) {
C64 = C64_new;
#ifdef SET_STATUS_FLAGS
CT = CT_new;
#endif
} else
exponent_b++;
}
}
}
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rmode == 0) //ROUNDING_TO_NEAREST
#endif
if (C64 & 1) {
// check whether fractional part of initial_P/10^extra_digits is
// exactly .5
// this is the same as fractional part of
// (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero
// get remainder
remainder_h = CT.w[1] << (64 - amount);
// test whether fractional part is 0
if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) {
C64--;
}
}
#endif
#ifdef SET_STATUS_FLAGS
status = INEXACT_EXCEPTION;
// get remainder
remainder_h = CT.w[1] << (64 - amount);
switch (rmode) {
case ROUNDING_TO_NEAREST:
case ROUNDING_TIES_AWAY:
// test whether fractional part is 0
if ((remainder_h == 0x8000000000000000ull)
&& (CT.w[0] < reciprocals10_64[extra_digits]))
status = EXACT_STATUS;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits]))
status = EXACT_STATUS;
//if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y;
break;
default:
// round up
__add_carry_out (tmp, carry, CT.w[0],
reciprocals10_64[extra_digits]);
if ((remainder_h >> (64 - amount)) + carry >=
(((UINT64) 1) << amount))
status = EXACT_STATUS;
break;
}
__set_status_flags (pfpsf, status);
#endif
res =
fast_get_BID64_check_OF (sign_s, exponent_b + extra_digits, C64,
rnd_mode, pfpsf);
BID_RETURN (res);
}