/* Copyright (C) 2007-2020 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/>. */
/*****************************************************************************
*
* Helper add functions (for fma)
*
* __BID_INLINE__ UINT64 get_add64(
* UINT64 sign_x, int exponent_x, UINT64 coefficient_x,
* UINT64 sign_y, int exponent_y, UINT64 coefficient_y,
* int rounding_mode)
*
* __BID_INLINE__ UINT64 get_add128(
* UINT64 sign_x, int exponent_x, UINT64 coefficient_x,
* UINT64 sign_y, int final_exponent_y, UINT128 CY,
* int extra_digits, int rounding_mode)
*
*****************************************************************************
*
* Algorithm description:
*
* get_add64: same as BID64 add, but arguments are unpacked and there
* are no special case checks
*
* get_add128: add 64-bit coefficient to 128-bit product (which contains
* 16+extra_digits decimal digits),
* return BID64 result
* - the exponents are compared and the two coefficients are
* properly aligned for addition/subtraction
* - multiple paths are needed
* - final result exponent is calculated and the lower term is
* rounded first if necessary, to avoid manipulating
* coefficients longer than 128 bits
*
****************************************************************************/
#ifndef _INLINE_BID_ADD_H_
#define _INLINE_BID_ADD_H_
#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
///////////////////////////////////////////////////////////////////////
//
// get_add64() is essentially the same as bid_add(), except that
// the arguments are unpacked
//
//////////////////////////////////////////////////////////////////////
__BID_INLINE__ UINT64
get_add64 (UINT64 sign_x, int exponent_x, UINT64 coefficient_x,
UINT64 sign_y, int exponent_y, UINT64 coefficient_y,
int rounding_mode, unsigned *fpsc) {
UINT128 CA, CT, CT_new;
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,
C64_new;
int_double tempx;
int exponent_a, exponent_b, diff_dec_expon;
int bin_expon_ca, extra_digits, amount, scale_k, scale_ca;
unsigned rmode, status;
// 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 ---
tempx.d = (double) coefficient_a;
bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
if (!coefficient_a) {
return get_BID64 (sign_b, exponent_b, coefficient_b, rounding_mode,
fpsc);
}
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 (fpsc, INEXACT_EXCEPTION);
}
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (((rounding_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST
{
switch (rounding_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--;
}
return get_BID64 (sign_a, exponent_a, coefficient_a,
rounding_mode, fpsc);
}
}
// 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 (rounding_mode == ROUNDING_DOWN && (!coefficient_a)
&& sign_a != sign_b)
sign_s = 0x8000000000000000ull;
#endif
#endif
return get_BID64 (sign_s, exponent_b, coefficient_a,
rounding_mode, fpsc);
}
// 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 = rounding_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 = rounding_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
//P_ca = power10_table_128[scale_ca].w[0];
//P_ca_m1 = power10_table_128[scale_ca-1].w[0];
if (coefficient_a >= power10_table_128[scale_ca].w[0]) {
scale_ca++;
//P_ca_m1 = P_ca;
//P_ca = power10_table_128[scale_ca].w[0];
}
scale_k = 16 - scale_ca;
// apply sign
//Ts = (T1 + sign_ab) ^ sign_ab;
// test range of ca
//X = coefficient_a + Ts - P_ca_m1;
// 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
// the following test is equivalent to
// ( (initial_coefficient_a + Ts) < P_ca &&
// (initial_coefficient_a + Ts) > P_ca_m1 ),
// which 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 +=
/*90000000000000000 */ +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;
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 (fpsc, status);
#endif
return get_BID64 (sign_s, exponent_b + extra_digits, C64,
rounding_mode, fpsc);
}
///////////////////////////////////////////////////////////////////
// round 128-bit coefficient and return result in BID64 format
// do not worry about midpoint cases
//////////////////////////////////////////////////////////////////
static UINT64
__bid_simple_round64_sticky (UINT64 sign, int exponent, UINT128 P,
int extra_digits, int rounding_mode,
unsigned *fpsc) {
UINT128 Q_high, Q_low, C128;
UINT64 C64;
int amount, rmode;
rmode = rounding_mode;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (sign && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#endif
#endif
__add_128_64 (P, P, round_const_table[rmode][extra_digits]);
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Q_high, Q_low, P,
reciprocals10_128[extra_digits]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[extra_digits];
__shr_128 (C128, Q_high, amount);
C64 = __low_64 (C128);
#ifdef SET_STATUS_FLAGS
__set_status_flags (fpsc, INEXACT_EXCEPTION);
#endif
return get_BID64 (sign, exponent, C64, rounding_mode, fpsc);
}
///////////////////////////////////////////////////////////////////
// round 128-bit coefficient and return result in BID64 format
///////////////////////////////////////////////////////////////////
static UINT64
__bid_full_round64 (UINT64 sign, int exponent, UINT128 P,
int extra_digits, int rounding_mode,
unsigned *fpsc) {
UINT128 Q_high, Q_low, C128, Stemp, PU;
UINT64 remainder_h, C64, carry, CY;
int amount, amount2, rmode, status = 0;
if (exponent < 0) {
if (exponent >= -16 && (extra_digits + exponent < 0)) {
extra_digits = -exponent;
#ifdef SET_STATUS_FLAGS
if (extra_digits > 0) {
rmode = rounding_mode;
if (sign && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
__add_128_128 (PU, P,
round_const_table_128[rmode][extra_digits]);
if (__unsigned_compare_gt_128
(power10_table_128[extra_digits + 15], PU))
status = UNDERFLOW_EXCEPTION;
}
#endif
}
}
if (extra_digits > 0) {
exponent += extra_digits;
rmode = rounding_mode;
if (sign && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
__add_128_128 (P, P, round_const_table_128[rmode][extra_digits]);
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Q_high, Q_low, P,
reciprocals10_128[extra_digits]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[extra_digits];
__shr_128_long (C128, Q_high, amount);
C64 = __low_64 (C128);
#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
// get remainder
amount2 = 64 - amount;
remainder_h = 0;
remainder_h--;
remainder_h >>= amount2;
remainder_h = remainder_h & Q_high.w[0];
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0]))) {
C64--;
}
}
#endif
#ifdef SET_STATUS_FLAGS
status |= INEXACT_EXCEPTION;
// get remainder
remainder_h = Q_high.w[0] << (64 - amount);
switch (rmode) {
case ROUNDING_TO_NEAREST:
case ROUNDING_TIES_AWAY:
// test whether fractional part is 0
if (remainder_h == 0x8000000000000000ull
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
default:
// round up
__add_carry_out (Stemp.w[0], CY, Q_low.w[0],
reciprocals10_128[extra_digits].w[0]);
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
reciprocals10_128[extra_digits].w[1], CY);
if ((remainder_h >> (64 - amount)) + carry >=
(((UINT64) 1) << amount))
status = EXACT_STATUS;
}
__set_status_flags (fpsc, status);
#endif
} else {
C64 = P.w[0];
if (!C64) {
sign = 0;
if (rounding_mode == ROUNDING_DOWN)
sign = 0x8000000000000000ull;
}
}
return get_BID64 (sign, exponent, C64, rounding_mode, fpsc);
}
/////////////////////////////////////////////////////////////////////////////////
// round 192-bit coefficient (P, remainder_P) and return result in BID64 format
// the lowest 64 bits (remainder_P) are used for midpoint checking only
////////////////////////////////////////////////////////////////////////////////
static UINT64
__bid_full_round64_remainder (UINT64 sign, int exponent, UINT128 P,
int extra_digits, UINT64 remainder_P,
int rounding_mode, unsigned *fpsc,
unsigned uf_status) {
UINT128 Q_high, Q_low, C128, Stemp;
UINT64 remainder_h, C64, carry, CY;
int amount, amount2, rmode, status = uf_status;
rmode = rounding_mode;
if (sign && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
if (rmode == ROUNDING_UP && remainder_P) {
P.w[0]++;
if (!P.w[0])
P.w[1]++;
}
if (extra_digits) {
__add_128_64 (P, P, round_const_table[rmode][extra_digits]);
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Q_high, Q_low, P,
reciprocals10_128[extra_digits]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[extra_digits];
__shr_128 (C128, Q_high, amount);
C64 = __low_64 (C128);
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rmode == 0) //ROUNDING_TO_NEAREST
#endif
if (!remainder_P && (C64 & 1)) {
// check whether fractional part of initial_P/10^extra_digits
// is exactly .5
// get remainder
amount2 = 64 - amount;
remainder_h = 0;
remainder_h--;
remainder_h >>= amount2;
remainder_h = remainder_h & Q_high.w[0];
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0]))) {
C64--;
}
}
#endif
#ifdef SET_STATUS_FLAGS
status |= INEXACT_EXCEPTION;
if (!remainder_P) {
// get remainder
remainder_h = Q_high.w[0] << (64 - amount);
switch (rmode) {
case ROUNDING_TO_NEAREST:
case ROUNDING_TIES_AWAY:
// test whether fractional part is 0
if (remainder_h == 0x8000000000000000ull
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
default:
// round up
__add_carry_out (Stemp.w[0], CY, Q_low.w[0],
reciprocals10_128[extra_digits].w[0]);
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
reciprocals10_128[extra_digits].w[1], CY);
if ((remainder_h >> (64 - amount)) + carry >=
(((UINT64) 1) << amount))
status = EXACT_STATUS;
}
}
__set_status_flags (fpsc, status);
#endif
} else {
C64 = P.w[0];
#ifdef SET_STATUS_FLAGS
if (remainder_P) {
__set_status_flags (fpsc, uf_status | INEXACT_EXCEPTION);
}
#endif
}
return get_BID64 (sign, exponent + extra_digits, C64, rounding_mode,
fpsc);
}
///////////////////////////////////////////////////////////////////
// get P/10^extra_digits
// result fits in 64 bits
///////////////////////////////////////////////////////////////////
__BID_INLINE__ UINT64
__truncate (UINT128 P, int extra_digits)
// extra_digits <= 16
{
UINT128 Q_high, Q_low, C128;
UINT64 C64;
int amount;
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Q_high, Q_low, P,
reciprocals10_128[extra_digits]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[extra_digits];
__shr_128 (C128, Q_high, amount);
C64 = __low_64 (C128);
return C64;
}
///////////////////////////////////////////////////////////////////
// return number of decimal digits in 128-bit value X
///////////////////////////////////////////////////////////////////
__BID_INLINE__ int
__get_dec_digits64 (UINT128 X) {
int_double tempx;
int digits_x, bin_expon_cx;
if (!X.w[1]) {
//--- get number of bits in the coefficients of x and y ---
tempx.d = (double) X.w[0];
bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
// get number of decimal digits in the coeff_x
digits_x = estimate_decimal_digits[bin_expon_cx];
if (X.w[0] >= power10_table_128[digits_x].w[0])
digits_x++;
return digits_x;
}
tempx.d = (double) X.w[1];
bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
// get number of decimal digits in the coeff_x
digits_x = estimate_decimal_digits[bin_expon_cx + 64];
if (__unsigned_compare_ge_128 (X, power10_table_128[digits_x]))
digits_x++;
return digits_x;
}
////////////////////////////////////////////////////////////////////////////////
//
// add 64-bit coefficient to 128-bit coefficient, return result in BID64 format
//
////////////////////////////////////////////////////////////////////////////////
__BID_INLINE__ UINT64
get_add128 (UINT64 sign_x, int exponent_x, UINT64 coefficient_x,
UINT64 sign_y, int final_exponent_y, UINT128 CY,
int extra_digits, int rounding_mode, unsigned *fpsc) {
UINT128 CY_L, CX, FS, F, CT, ST, T2;
UINT64 CYh, CY0L, T, S, coefficient_y, remainder_y;
SINT64 D = 0;
int_double tempx;
int diff_dec_expon, extra_digits2, exponent_y, status;
int extra_dx, diff_dec2, bin_expon_cx, digits_x, rmode;
// CY has more than 16 decimal digits
exponent_y = final_exponent_y - extra_digits;
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
rounding_mode = 0;
#endif
#ifdef IEEE_ROUND_NEAREST
rounding_mode = 0;
#endif
if (exponent_x > exponent_y) {
// normalize x
//--- get number of bits in the coefficients of x and y ---
tempx.d = (double) coefficient_x;
bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
// get number of decimal digits in the coeff_x
digits_x = estimate_decimal_digits[bin_expon_cx];
if (coefficient_x >= power10_table_128[digits_x].w[0])
digits_x++;
extra_dx = 16 - digits_x;
coefficient_x *= power10_table_128[extra_dx].w[0];
if ((sign_x ^ sign_y) && (coefficient_x == 1000000000000000ull)) {
extra_dx++;
coefficient_x = 10000000000000000ull;
}
exponent_x -= extra_dx;
if (exponent_x > exponent_y) {
// exponent_x > exponent_y
diff_dec_expon = exponent_x - exponent_y;
if (exponent_x <= final_exponent_y + 1) {
__mul_64x64_to_128 (CX, coefficient_x,
power10_table_128[diff_dec_expon].w[0]);
if (sign_x == sign_y) {
__add_128_128 (CT, CY, CX);
if ((exponent_x >
final_exponent_y) /*&& (final_exponent_y>0) */ )
extra_digits++;
if (__unsigned_compare_ge_128
(CT, power10_table_128[16 + extra_digits]))
extra_digits++;
} else {
__sub_128_128 (CT, CY, CX);
if (((SINT64) CT.w[1]) < 0) {
CT.w[0] = 0 - CT.w[0];
CT.w[1] = 0 - CT.w[1];
if (CT.w[0])
CT.w[1]--;
sign_y = sign_x;
} else if (!(CT.w[1] | CT.w[0])) {
sign_y =
(rounding_mode !=
ROUNDING_DOWN) ? 0 : 0x8000000000000000ull;
}
if ((exponent_x + 1 >=
final_exponent_y) /*&& (final_exponent_y>=0) */ ) {
extra_digits = __get_dec_digits64 (CT) - 16;
if (extra_digits <= 0) {
if (!CT.w[0] && rounding_mode == ROUNDING_DOWN)
sign_y = 0x8000000000000000ull;
return get_BID64 (sign_y, exponent_y, CT.w[0],
rounding_mode, fpsc);
}
} else
if (__unsigned_compare_gt_128
(power10_table_128[15 + extra_digits], CT))
extra_digits--;
}
return __bid_full_round64 (sign_y, exponent_y, CT, extra_digits,
rounding_mode, fpsc);
}
// diff_dec2+extra_digits is the number of digits to eliminate from
// argument CY
diff_dec2 = exponent_x - final_exponent_y;
if (diff_dec2 >= 17) {
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if ((rounding_mode) & 3) {
switch (rounding_mode) {
case ROUNDING_UP:
if (!sign_y) {
D = ((SINT64) (sign_x ^ sign_y)) >> 63;
D = D + D + 1;
coefficient_x += D;
}
break;
case ROUNDING_DOWN:
if (sign_y) {
D = ((SINT64) (sign_x ^ sign_y)) >> 63;
D = D + D + 1;
coefficient_x += D;
}
break;
case ROUNDING_TO_ZERO:
if (sign_y != sign_x) {
D = 0 - 1;
coefficient_x += D;
}
break;
}
if (coefficient_x < 1000000000000000ull) {
coefficient_x -= D;
coefficient_x =
D + (coefficient_x << 1) + (coefficient_x << 3);
exponent_x--;
}
}
#endif
#endif
#ifdef SET_STATUS_FLAGS
if (CY.w[1] | CY.w[0])
__set_status_flags (fpsc, INEXACT_EXCEPTION);
#endif
return get_BID64 (sign_x, exponent_x, coefficient_x,
rounding_mode, fpsc);
}
// here exponent_x <= 16+final_exponent_y
// truncate CY to 16 dec. digits
CYh = __truncate (CY, extra_digits);
// get remainder
T = power10_table_128[extra_digits].w[0];
__mul_64x64_to_64 (CY0L, CYh, T);
remainder_y = CY.w[0] - CY0L;
// align coeff_x, CYh
__mul_64x64_to_128 (CX, coefficient_x,
power10_table_128[diff_dec2].w[0]);
if (sign_x == sign_y) {
__add_128_64 (CT, CX, CYh);
if (__unsigned_compare_ge_128
(CT, power10_table_128[16 + diff_dec2]))
diff_dec2++;
} else {
if (remainder_y)
CYh++;
__sub_128_64 (CT, CX, CYh);
if (__unsigned_compare_gt_128
(power10_table_128[15 + diff_dec2], CT))
diff_dec2--;
}
return __bid_full_round64_remainder (sign_x, final_exponent_y, CT,
diff_dec2, remainder_y,
rounding_mode, fpsc, 0);
}
}
// Here (exponent_x <= exponent_y)
{
diff_dec_expon = exponent_y - exponent_x;
if (diff_dec_expon > MAX_FORMAT_DIGITS) {
rmode = rounding_mode;
if ((sign_x ^ sign_y)) {
if (!CY.w[0])
CY.w[1]--;
CY.w[0]--;
if (__unsigned_compare_gt_128
(power10_table_128[15 + extra_digits], CY)) {
if (rmode & 3) {
extra_digits--;
final_exponent_y--;
} else {
CY.w[0] = 1000000000000000ull;
CY.w[1] = 0;
extra_digits = 0;
}
}
}
__scale128_10 (CY, CY);
extra_digits++;
CY.w[0] |= 1;
return __bid_simple_round64_sticky (sign_y, final_exponent_y, CY,
extra_digits, rmode, fpsc);
}
// apply sign to coeff_x
sign_x ^= sign_y;
sign_x = ((SINT64) sign_x) >> 63;
CX.w[0] = (coefficient_x + sign_x) ^ sign_x;
CX.w[1] = sign_x;
// check whether CY (rounded to 16 digits) and CX have
// any digits in the same position
diff_dec2 = final_exponent_y - exponent_x;
if (diff_dec2 <= 17) {
// align CY to 10^ex
S = power10_table_128[diff_dec_expon].w[0];
__mul_64x128_short (CY_L, S, CY);
__add_128_128 (ST, CY_L, CX);
extra_digits2 = __get_dec_digits64 (ST) - 16;
return __bid_full_round64 (sign_y, exponent_x, ST, extra_digits2,
rounding_mode, fpsc);
}
// truncate CY to 16 dec. digits
CYh = __truncate (CY, extra_digits);
// get remainder
T = power10_table_128[extra_digits].w[0];
__mul_64x64_to_64 (CY0L, CYh, T);
coefficient_y = CY.w[0] - CY0L;
// add rounding constant
rmode = rounding_mode;
if (sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (!(rmode & 3)) //ROUNDING_TO_NEAREST
#endif
#endif
{
coefficient_y += round_const_table[rmode][extra_digits];
}
// align coefficient_y, coefficient_x
S = power10_table_128[diff_dec_expon].w[0];
__mul_64x64_to_128 (F, coefficient_y, S);
// fraction
__add_128_128 (FS, F, CX);
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rmode == 0) //ROUNDING_TO_NEAREST
#endif
{
// rounding code, here RN_EVEN
// 10^(extra_digits+diff_dec_expon)
T2 = power10_table_128[diff_dec_expon + extra_digits];
if (__unsigned_compare_gt_128 (FS, T2)
|| ((CYh & 1) && __test_equal_128 (FS, T2))) {
CYh++;
__sub_128_128 (FS, FS, T2);
}
}
#endif
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (rmode == 4) //ROUNDING_TO_NEAREST
#endif
{
// rounding code, here RN_AWAY
// 10^(extra_digits+diff_dec_expon)
T2 = power10_table_128[diff_dec_expon + extra_digits];
if (__unsigned_compare_ge_128 (FS, T2)) {
CYh++;
__sub_128_128 (FS, FS, T2);
}
}
#endif
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
switch (rmode) {
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
if ((SINT64) FS.w[1] < 0) {
CYh--;
if (CYh < 1000000000000000ull) {
CYh = 9999999999999999ull;
final_exponent_y--;
}
} else {
T2 = power10_table_128[diff_dec_expon + extra_digits];
if (__unsigned_compare_ge_128 (FS, T2)) {
CYh++;
__sub_128_128 (FS, FS, T2);
}
}
break;
case ROUNDING_UP:
if ((SINT64) FS.w[1] < 0)
break;
T2 = power10_table_128[diff_dec_expon + extra_digits];
if (__unsigned_compare_gt_128 (FS, T2)) {
CYh += 2;
__sub_128_128 (FS, FS, T2);
} else if ((FS.w[1] == T2.w[1]) && (FS.w[0] == T2.w[0])) {
CYh++;
FS.w[1] = FS.w[0] = 0;
} else if (FS.w[1] | FS.w[0])
CYh++;
break;
}
#endif
#endif
#ifdef SET_STATUS_FLAGS
status = INEXACT_EXCEPTION;
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (!(rmode & 3))
#endif
#endif
{
// RN modes
if ((FS.w[1] ==
round_const_table_128[0][diff_dec_expon + extra_digits].w[1])
&& (FS.w[0] ==
round_const_table_128[0][diff_dec_expon +
extra_digits].w[0]))
status = EXACT_STATUS;
}
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
else if (!FS.w[1] && !FS.w[0])
status = EXACT_STATUS;
#endif
#endif
__set_status_flags (fpsc, status);
#endif
return get_BID64 (sign_y, final_exponent_y, CYh, rounding_mode,
fpsc);
}
}
//////////////////////////////////////////////////////////////////////////
//
// If coefficient_z is less than 16 digits long, normalize to 16 digits
//
/////////////////////////////////////////////////////////////////////////
static UINT64
BID_normalize (UINT64 sign_z, int exponent_z,
UINT64 coefficient_z, UINT64 round_dir, int round_flag,
int rounding_mode, unsigned *fpsc) {
SINT64 D;
int_double tempx;
int digits_z, bin_expon, scale, rmode;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
rmode = rounding_mode;
if (sign_z && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#else
if (coefficient_z >= power10_table_128[15].w[0])
return z;
#endif
#endif
//--- get number of bits in the coefficients of x and y ---
tempx.d = (double) coefficient_z;
bin_expon = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
// get number of decimal digits in the coeff_x
digits_z = estimate_decimal_digits[bin_expon];
if (coefficient_z >= power10_table_128[digits_z].w[0])
digits_z++;
scale = 16 - digits_z;
exponent_z -= scale;
if (exponent_z < 0) {
scale += exponent_z;
exponent_z = 0;
}
coefficient_z *= power10_table_128[scale].w[0];
#ifdef SET_STATUS_FLAGS
if (round_flag) {
__set_status_flags (fpsc, INEXACT_EXCEPTION);
if (coefficient_z < 1000000000000000ull)
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
else if ((coefficient_z == 1000000000000000ull) && !exponent_z
&& ((SINT64) (round_dir ^ sign_z) < 0) && round_flag
&& (rmode == ROUNDING_DOWN || rmode == ROUNDING_TO_ZERO))
__set_status_flags (fpsc, UNDERFLOW_EXCEPTION);
}
#endif
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (round_flag && (rmode & 3)) {
D = round_dir ^ sign_z;
if (rmode == ROUNDING_UP) {
if (D >= 0)
coefficient_z++;
} else {
if (D < 0)
coefficient_z--;
if (coefficient_z < 1000000000000000ull && exponent_z) {
coefficient_z = 9999999999999999ull;
exponent_z--;
}
}
}
#endif
#endif
return get_BID64 (sign_z, exponent_z, coefficient_z, rounding_mode,
fpsc);
}
//////////////////////////////////////////////////////////////////////////
//
// 0*10^ey + cz*10^ez, ey<ez
//
//////////////////////////////////////////////////////////////////////////
__BID_INLINE__ UINT64
add_zero64 (int exponent_y, UINT64 sign_z, int exponent_z,
UINT64 coefficient_z, unsigned *prounding_mode,
unsigned *fpsc) {
int_double tempx;
int bin_expon, scale_k, scale_cz;
int diff_expon;
diff_expon = exponent_z - exponent_y;
tempx.d = (double) coefficient_z;
bin_expon = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
scale_cz = estimate_decimal_digits[bin_expon];
if (coefficient_z >= power10_table_128[scale_cz].w[0])
scale_cz++;
scale_k = 16 - scale_cz;
if (diff_expon < scale_k)
scale_k = diff_expon;
coefficient_z *= power10_table_128[scale_k].w[0];
return get_BID64 (sign_z, exponent_z - scale_k, coefficient_z,
*prounding_mode, fpsc);
}
#endif