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android / toolchain / gcc / donut / . / gcc-4.3.1 / libgcc / config / libbid / bid64_div.c
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/* Copyright (C) 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 2, or (at your option) any later
version.
In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file. (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)
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. */
/*****************************************************************************
* BID64 divide
*****************************************************************************
*
* Algorithm description:
*
* if(coefficient_x<coefficient_y)
* p = number_digits(coefficient_y) - number_digits(coefficient_x)
* A = coefficient_x*10^p
* B = coefficient_y
* CA= A*10^(15+j), j=0 for A>=B, 1 otherwise
* Q = 0
* else
* get Q=(int)(coefficient_x/coefficient_y)
* (based on double precision divide)
* check for exact divide case
* Let R = coefficient_x - Q*coefficient_y
* Let m=16-number_digits(Q)
* CA=R*10^m, Q=Q*10^m
* B = coefficient_y
* endif
* if (CA<2^64)
* Q += CA/B (64-bit unsigned divide)
* else
* get final Q using double precision divide, followed by 3 integer
* iterations
* if exact result, eliminate trailing zeros
* check for underflow
* round coefficient to nearest
*
****************************************************************************/
#include "bid_internal.h"
#include "bid_div_macros.h"
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
#include <fenv.h>
#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
#endif
extern UINT32 convert_table[5][128][2];
extern SINT8 factors[][2];
extern UINT8 packed_10000_zeros[];
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_div (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x, y;
#else
UINT64
bid64_div (UINT64 x,
UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 CA, CT;
UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD;
UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res;
UINT64 valid_x, valid_y;
SINT64 D;
int_double t_scale, tempq, temp_b;
int_float tempx, tempy;
double da, db, dq, da_h, da_l;
int exponent_x, exponent_y, bin_expon_cx;
int diff_expon, ed1, ed2, bin_index;
int rmode, amount;
int nzeros, i, j, k, d5;
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
#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
#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 & NAN_MASK64) == NAN_MASK64) {
#ifdef SET_STATUS_FLAGS
if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (coefficient_x & QUIET_MASK64);
}
// x is Infinity?
if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
// check if y is Inf or NaN
if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
// y==Inf, return NaN
if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (NAN_MASK64);
}
} else {
// otherwise return +/-Inf
BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
INFINITY_MASK64);
}
}
// x==0
if (((y & INFINITY_MASK64) != INFINITY_MASK64)
&& !(coefficient_y)) {
// y==0 , return NaN
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (NAN_MASK64);
}
if (((y & INFINITY_MASK64) != INFINITY_MASK64)) {
if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64)
exponent_y = ((UINT32) (y >> 51)) & 0x3ff;
else
exponent_y = ((UINT32) (y >> 53)) & 0x3ff;
sign_y = y & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (exponent_x > DECIMAL_MAX_EXPON_64)
exponent_x = DECIMAL_MAX_EXPON_64;
else if (exponent_x < 0)
exponent_x = 0;
BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
}
}
if (!valid_y) {
// y is Inf. or NaN
// test if y is NaN
if ((y & NAN_MASK64) == NAN_MASK64) {
#ifdef SET_STATUS_FLAGS
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (coefficient_y & QUIET_MASK64);
}
// y is Infinity?
if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
// return +/-0
BID_RETURN (((x ^ y) & 0x8000000000000000ull));
}
// y is 0
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (coefficient_x < coefficient_y) {
// get number of decimal digits for c_x, c_y
//--- get number of bits in the coefficients of x and y ---
tempx.d = (float) coefficient_x;
tempy.d = (float) coefficient_y;
bin_index = (tempy.i - tempx.i) >> 23;
A = coefficient_x * power10_index_binexp[bin_index];
B = coefficient_y;
temp_b.d = (double) B;
// compare A, B
DU = (A - B) >> 63;
ed1 = 15 + (int) DU;
ed2 = estimate_decimal_digits[bin_index] + ed1;
T = power10_table_128[ed1].w[0];
__mul_64x64_to_128 (CA, A, T);
Q = 0;
diff_expon = diff_expon - ed2;
// adjust double precision db, to ensure that later A/B - (int)(da/db) > -1
if (coefficient_y < 0x0020000000000000ull) {
temp_b.i += 1;
db = temp_b.d;
} else
db = (double) (B + 2 + (B & 1));
} else {
// get c_x/c_y
// set last bit before conversion to DP
A2 = coefficient_x | 1;
da = (double) A2;
db = (double) coefficient_y;
tempq.d = da / db;
Q = (UINT64) tempq.d;
R = coefficient_x - coefficient_y * Q;
// will use to get number of dec. digits of Q
bin_expon_cx = (tempq.i >> 52) - 0x3ff;
// R<0 ?
D = ((SINT64) R) >> 63;
Q += D;
R += (coefficient_y & D);
// exact result ?
if (((SINT64) R) <= 0) {
// can have R==-1 for coeff_y==1
res =
get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
// get decimal digits of Q
DU = power10_index_binexp[bin_expon_cx] - Q - 1;
DU >>= 63;
ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU;
T = power10_table_128[ed2].w[0];
__mul_64x64_to_128 (CA, R, T);
B = coefficient_y;
Q *= power10_table_128[ed2].w[0];
diff_expon -= ed2;
}
if (!CA.w[1]) {
Q2 = CA.w[0] / B;
B2 = B + B;
B4 = B2 + B2;
R = CA.w[0] - Q2 * B;
Q += Q2;
} else {
// 2^64
t_scale.i = 0x43f0000000000000ull;
// convert CA to DP
da_h = CA.w[1];
da_l = CA.w[0];
da = da_h * t_scale.d + da_l;
// quotient
dq = da / db;
Q2 = (UINT64) dq;
// get w[0] remainder
R = CA.w[0] - Q2 * B;
// R<0 ?
D = ((SINT64) R) >> 63;
Q2 += D;
R += (B & D);
// now R<6*B
// quick divide
// 4*B
B2 = B + B;
B4 = B2 + B2;
R = R - B4;
// R<0 ?
D = ((SINT64) R) >> 63;
// restore R if negative
R += (B4 & D);
Q2 += ((~D) & 4);
R = R - B2;
// R<0 ?
D = ((SINT64) R) >> 63;
// restore R if negative
R += (B2 & D);
Q2 += ((~D) & 2);
R = R - B;
// R<0 ?
D = ((SINT64) R) >> 63;
// restore R if negative
R += (B & D);
Q2 += ((~D) & 1);
Q += Q2;
}
#ifdef SET_STATUS_FLAGS
if (R) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#ifndef LEAVE_TRAILING_ZEROS
else
#endif
#else
#ifndef LEAVE_TRAILING_ZEROS
if (!R)
#endif
#endif
#ifndef LEAVE_TRAILING_ZEROS
{
// eliminate trailing zeros
// check whether CX, CY are short
if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) {
i = (int) coefficient_y - 1;
j = (int) coefficient_x - 1;
// difference in powers of 2 factors for Y and X
nzeros = ed2 - factors[i][0] + factors[j][0];
// difference in powers of 5 factors
d5 = ed2 - factors[i][1] + factors[j][1];
if (d5 < nzeros)
nzeros = d5;
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[nzeros];
Q = CT.w[1] >> amount;
diff_expon += nzeros;
} else {
tdigit[0] = Q & 0x3ffffff;
tdigit[1] = 0;
QX = Q >> 26;
QX32 = QX;
nzeros = 0;
for (j = 0; QX32; j++, QX32 >>= 7) {
k = (QX32 & 127);
tdigit[0] += convert_table[j][k][0];
tdigit[1] += convert_table[j][k][1];
if (tdigit[0] >= 100000000) {
tdigit[0] -= 100000000;
tdigit[1]++;
}
}
digit = tdigit[0];
if (!digit && !tdigit[1])
nzeros += 16;
else {
if (!digit) {
nzeros += 8;
digit = tdigit[1];
}
// decompose digit
PD = (UINT64) digit *0x068DB8BBull;
digit_h = (UINT32) (PD >> 40);
digit_low = digit - digit_h * 10000;
if (!digit_low)
nzeros += 4;
else
digit_h = digit_low;
if (!(digit_h & 1))
nzeros +=
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
(digit_h & 7));
}
if (nzeros) {
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
amount = short_recip_scale[nzeros];
Q = CT.w[1] >> amount;
}
diff_expon += nzeros;
}
if (diff_expon >= 0) {
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q,
rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
#endif
if (diff_expon >= 0) {
#ifdef IEEE_ROUND_NEAREST
// round to nearest code
// R*10
R += R;
R = (R << 2) + R;
B5 = B4 + B;
// compare 10*R to 5*B
R = B5 - R;
// correction for (R==0 && (Q&1))
R -= (Q & 1);
// R<0 ?
D = ((UINT64) R) >> 63;
Q += D;
#else
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
// round to nearest code
// R*10
R += R;
R = (R << 2) + R;
B5 = B4 + B;
// compare 10*R to 5*B
R = B5 - R;
// correction for (R==0 && (Q&1))
R -= (Q & 1);
// R<0 ?
D = ((UINT64) R) >> 63;
Q += D;
#else
rmode = rnd_mode;
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
switch (rmode) {
case 0: // round to nearest code
case ROUNDING_TIES_AWAY:
// R*10
R += R;
R = (R << 2) + R;
B5 = B4 + B;
// compare 10*R to 5*B
R = B5 - R;
// correction for (R==0 && (Q&1))
R -= ((Q | (rmode >> 2)) & 1);
// R<0 ?
D = ((UINT64) R) >> 63;
Q += D;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
break;
default: // rounding up
Q++;
break;
}
#endif
#endif
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
} else {
// UF occurs
#ifdef SET_STATUS_FLAGS
if ((diff_expon + 16 < 0)) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
rmode = rnd_mode;
res =
get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y)
UINT256 CA4 =
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
int_float fx, fy, f64;
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
digits_q, amount;
int nzeros, i, j, k, d5, done = 0;
unsigned rmode;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
// unpack arguments, check for NaN or Infinity
CX.w[1] = 0;
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) {
#ifdef SET_STATUS_FLAGS
if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN
((x & SNAN_MASK64) == SNAN_MASK64))
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// test if x is NaN
if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
res = CX.w[0];
BID_RETURN (res & QUIET_MASK64);
}
// x is Infinity?
if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) {
// check if y is Inf.
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
// return NaN
{
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
// otherwise return +/-Inf
res =
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
BID_RETURN (res);
}
}
// x is 0
if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) {
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x=y=0, return NaN
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
// return 0
res = ((x) ^ y.w[1]) & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
if (exponent_x > DECIMAL_MAX_EXPON_64)
exponent_x = DECIMAL_MAX_EXPON_64;
else if (exponent_x < 0)
exponent_x = 0;
res |= (((UINT64) exponent_x) << 53);
BID_RETURN (res);
}
}
exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS);
if (!valid_y) {
// y is Inf. or NaN
// test if y is NaN
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
Tmp.w[0] = CY.w[0];
TP128 = reciprocals10_128[18];
__mul_128x128_full (Qh, Ql, Tmp, TP128);
amount = recip_scale[18];
__shr_128 (Tmp, Qh, amount);
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
BID_RETURN (res);
}
// y is Infinity?
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res = sign_x ^ sign_y;
BID_RETURN (res);
}
// y is 0, return +/-Inf
res =
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (__unsigned_compare_gt_128 (CY, CX)) {
// CX < CY
// 2^64
f64.i = 0x5f800000;
// fx ~ CX, fy ~ CY
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
// expon_cy - expon_cx
bin_index = (fy.i - fx.i) >> 23;
if (CX.w[1]) {
T = power10_index_binexp_128[bin_index].w[0];
__mul_64x128_short (CA, T, CX);
} else {
T128 = power10_index_binexp_128[bin_index];
__mul_64x128_short (CA, CX.w[0], T128);
}
ed2 = 15;
if (__unsigned_compare_gt_128 (CY, CA))
ed2++;
T128 = power10_table_128[ed2];
__mul_128x128_to_256 (CA4, CA, T128);
ed2 += estimate_decimal_digits[bin_index];
CQ.w[0] = CQ.w[1] = 0;
diff_expon = diff_expon - ed2;
} else {
// get CQ = CX/CY
__div_128_by_128 (&CQ, &CR, CX, CY);
// get number of decimal digits in CQ
// 2^64
f64.i = 0x5f800000;
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
// binary expon. of CQ
bin_expon = (fx.i - 0x3f800000) >> 23;
digits_q = estimate_decimal_digits[bin_expon];
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
if (__unsigned_compare_ge_128 (CQ, TP128))
digits_q++;
if (digits_q <= 16) {
if (!CR.w[1] && !CR.w[0]) {
res = get_BID64 (sign_x ^ sign_y, diff_expon,
CQ.w[0], rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
ed2 = 16 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
diff_expon = diff_expon - ed2;
CQ.w[0] *= T128.w[0];
} else {
ed2 = digits_q - 16;
diff_expon += ed2;
T128 = reciprocals10_128[ed2];
__mul_128x128_to_256 (P256, CQ, T128);
amount = recip_scale[ed2];
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
CQ.w[1] = 0;
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
CA4.w[1] = CX.w[1] - QB256.w[1];
CA4.w[0] = CX.w[0] - QB256.w[0];
if (CX.w[0] < QB256.w[0])
CA4.w[1]--;
if (CR.w[0] || CR.w[1])
CA4.w[0] |= 1;
done = 1;
}
}
if (!done) {
__div_256_by_128 (&CQ, &CA4, CY);
}
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#ifndef LEAVE_TRAILING_ZEROS
else
#endif
#else
#ifndef LEAVE_TRAILING_ZEROS
if (!CA4.w[0] && !CA4.w[1])
#endif
#endif
#ifndef LEAVE_TRAILING_ZEROS
// check whether result is exact
{
// check whether CX, CY are short
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
i = (int) CY.w[0] - 1;
j = (int) CX.w[0] - 1;
// difference in powers of 2 factors for Y and X
nzeros = ed2 - factors[i][0] + factors[j][0];
// difference in powers of 5 factors
d5 = ed2 - factors[i][1] + factors[j][1];
if (d5 < nzeros)
nzeros = d5;
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128_long (CQ, Qh, amount);
diff_expon += nzeros;
} else {
// decompose Q as Qh*10^17 + Ql
Q_low = CQ.w[0];
{
tdigit[0] = Q_low & 0x3ffffff;
tdigit[1] = 0;
QX = Q_low >> 26;
QX32 = QX;
nzeros = 0;
for (j = 0; QX32; j++, QX32 >>= 7) {
k = (QX32 & 127);
tdigit[0] += convert_table[j][k][0];
tdigit[1] += convert_table[j][k][1];
if (tdigit[0] >= 100000000) {
tdigit[0] -= 100000000;
tdigit[1]++;
}
}
if (tdigit[1] >= 100000000) {
tdigit[1] -= 100000000;
if (tdigit[1] >= 100000000)
tdigit[1] -= 100000000;
}
digit = tdigit[0];
if (!digit && !tdigit[1])
nzeros += 16;
else {
if (!digit) {
nzeros += 8;
digit = tdigit[1];
}
// decompose digit
PD = (UINT64) digit *0x068DB8BBull;
digit_h = (UINT32) (PD >> 40);
digit_low = digit - digit_h * 10000;
if (!digit_low)
nzeros += 4;
else
digit_h = digit_low;
if (!(digit_h & 1))
nzeros +=
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
(digit_h & 7));
}
if (nzeros) {
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128 (CQ, Qh, amount);
}
diff_expon += nzeros;
}
}
if(diff_expon>=0){
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
#endif
if (diff_expon >= 0) {
#ifdef IEEE_ROUND_NEAREST
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
#else
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
#else
rmode = rnd_mode;
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
switch (rmode) {
case ROUNDING_TO_NEAREST: // round to nearest code
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_TIES_AWAY:
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
break;
default: // rounding up
CQ.w[0]++;
if (!CQ.w[0])
CQ.w[1]++;
break;
}
#endif
#endif
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
} else {
// UF occurs
#ifdef SET_STATUS_FLAGS
if ((diff_expon + 16 < 0)) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
rmode = rnd_mode;
res =
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
//#define LEAVE_TRAILING_ZEROS
TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y)
UINT256 CA4 =
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y;
int_float fx, fy, f64;
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
digits_q, amount;
int nzeros, i, j, k, d5, done = 0;
unsigned rmode;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y));
// unpack arguments, check for NaN or Infinity
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
// test if x is NaN
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
(y & 0x7e00000000000000ull) == 0x7e00000000000000ull)
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
Tmp.w[0] = CX.w[0];
TP128 = reciprocals10_128[18];
__mul_128x128_full (Qh, Ql, Tmp, TP128);
amount = recip_scale[18];
__shr_128 (Tmp, Qh, amount);
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
BID_RETURN (res);
}
// x is Infinity?
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// check if y is Inf.
if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull))
// return NaN
{
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
// otherwise return +/-Inf
res =
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
BID_RETURN (res);
}
}
// x is 0
if (((y & INFINITY_MASK64) != INFINITY_MASK64) &&
!(CY.w[0])) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x=y=0, return NaN
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
// return 0
if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) {
if (!CY.w[0]) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
exponent_x =
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
(DECIMAL_EXPONENT_BIAS << 1);
if (exponent_x > DECIMAL_MAX_EXPON_64)
exponent_x = DECIMAL_MAX_EXPON_64;
else if (exponent_x < 0)
exponent_x = 0;
res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53);
BID_RETURN (res);
}
}
CY.w[1] = 0;
if (!valid_y) {
// y is Inf. or NaN
// test if y is NaN
if ((y & NAN_MASK64) == NAN_MASK64) {
#ifdef SET_STATUS_FLAGS
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (CY.w[0] & QUIET_MASK64);
}
// y is Infinity?
if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res = sign_x ^ sign_y;
BID_RETURN (res);
}
// y is 0, return +/-Inf
res =
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
diff_expon =
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 +
(DECIMAL_EXPONENT_BIAS << 1);
if (__unsigned_compare_gt_128 (CY, CX)) {
// CX < CY
// 2^64
f64.i = 0x5f800000;
// fx ~ CX, fy ~ CY
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
// expon_cy - expon_cx
bin_index = (fy.i - fx.i) >> 23;
if (CX.w[1]) {
T = power10_index_binexp_128[bin_index].w[0];
__mul_64x128_short (CA, T, CX);
} else {
T128 = power10_index_binexp_128[bin_index];
__mul_64x128_short (CA, CX.w[0], T128);
}
ed2 = 15;
if (__unsigned_compare_gt_128 (CY, CA))
ed2++;
T128 = power10_table_128[ed2];
__mul_128x128_to_256 (CA4, CA, T128);
ed2 += estimate_decimal_digits[bin_index];
CQ.w[0] = CQ.w[1] = 0;
diff_expon = diff_expon - ed2;
} else {
// get CQ = CX/CY
__div_128_by_128 (&CQ, &CR, CX, CY);
// get number of decimal digits in CQ
// 2^64
f64.i = 0x5f800000;
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
// binary expon. of CQ
bin_expon = (fx.i - 0x3f800000) >> 23;
digits_q = estimate_decimal_digits[bin_expon];
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
if (__unsigned_compare_ge_128 (CQ, TP128))
digits_q++;
if (digits_q <= 16) {
if (!CR.w[1] && !CR.w[0]) {
res = get_BID64 (sign_x ^ sign_y, diff_expon,
CQ.w[0], rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
ed2 = 16 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
diff_expon = diff_expon - ed2;
CQ.w[0] *= T128.w[0];
} else {
ed2 = digits_q - 16;
diff_expon += ed2;
T128 = reciprocals10_128[ed2];
__mul_128x128_to_256 (P256, CQ, T128);
amount = recip_scale[ed2];
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
CQ.w[1] = 0;
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
CA4.w[1] = CX.w[1] - QB256.w[1];
CA4.w[0] = CX.w[0] - QB256.w[0];
if (CX.w[0] < QB256.w[0])
CA4.w[1]--;
if (CR.w[0] || CR.w[1])
CA4.w[0] |= 1;
done = 1;
if(CA4.w[1]|CA4.w[0]) {
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
}
}
}
if (!done) {
__div_256_by_128 (&CQ, &CA4, CY);
}
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#ifndef LEAVE_TRAILING_ZEROS
else
#endif
#else
#ifndef LEAVE_TRAILING_ZEROS
if (!CA4.w[0] && !CA4.w[1])
#endif
#endif
#ifndef LEAVE_TRAILING_ZEROS
// check whether result is exact
{
if(!done) {
// check whether CX, CY are short
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
i = (int) CY.w[0] - 1;
j = (int) CX.w[0] - 1;
// difference in powers of 2 factors for Y and X
nzeros = ed2 - factors[i][0] + factors[j][0];
// difference in powers of 5 factors
d5 = ed2 - factors[i][1] + factors[j][1];
if (d5 < nzeros)
nzeros = d5;
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128_long (CQ, Qh, amount);
diff_expon += nzeros;
} else {
// decompose Q as Qh*10^17 + Ql
//T128 = reciprocals10_128[17];
Q_low = CQ.w[0];
{
tdigit[0] = Q_low & 0x3ffffff;
tdigit[1] = 0;
QX = Q_low >> 26;
QX32 = QX;
nzeros = 0;
for (j = 0; QX32; j++, QX32 >>= 7) {
k = (QX32 & 127);
tdigit[0] += convert_table[j][k][0];
tdigit[1] += convert_table[j][k][1];
if (tdigit[0] >= 100000000) {
tdigit[0] -= 100000000;
tdigit[1]++;
}
}
if (tdigit[1] >= 100000000) {
tdigit[1] -= 100000000;
if (tdigit[1] >= 100000000)
tdigit[1] -= 100000000;
}
digit = tdigit[0];
if (!digit && !tdigit[1])
nzeros += 16;
else {
if (!digit) {
nzeros += 8;
digit = tdigit[1];
}
// decompose digit
PD = (UINT64) digit *0x068DB8BBull;
digit_h = (UINT32) (PD >> 40);
digit_low = digit - digit_h * 10000;
if (!digit_low)
nzeros += 4;
else
digit_h = digit_low;
if (!(digit_h & 1))
nzeros +=
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
(digit_h & 7));
}
if (nzeros) {
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128 (CQ, Qh, amount);
}
diff_expon += nzeros;
}
}
}
if(diff_expon>=0){
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
#endif
if (diff_expon >= 0) {
#ifdef IEEE_ROUND_NEAREST
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
//if(CQ.w[0]<carry64)
//CQ.w[1] ++;
#else
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
#else
rmode = rnd_mode;
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
switch (rmode) {
case ROUNDING_TO_NEAREST: // round to nearest code
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_TIES_AWAY:
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
break;
default: // rounding up
CQ.w[0]++;
if (!CQ.w[0])
CQ.w[1]++;
break;
}
#endif
#endif
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
} else {
// UF occurs
#ifdef SET_STATUS_FLAGS
if ((diff_expon + 16 < 0)) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
rmode = rnd_mode;
res =
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
//#define LEAVE_TRAILING_ZEROS
extern UINT32 convert_table[5][128][2];
extern SINT8 factors[][2];
extern UINT8 packed_10000_zeros[];
//UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf)
TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y)
UINT256 CA4 =
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256;
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp;
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res;
int_float fx, fy, f64;
UINT32 QX32, tdigit[3], digit, digit_h, digit_low;
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2,
digits_q, amount;
int nzeros, i, j, k, d5, done = 0;
unsigned rmode;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y);
// unpack arguments, check for NaN or Infinity
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
// test if x is NaN
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN
(y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
Tmp.w[0] = CX.w[0];
TP128 = reciprocals10_128[18];
__mul_128x128_full (Qh, Ql, Tmp, TP128);
amount = recip_scale[18];
__shr_128 (Tmp, Qh, amount);
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
BID_RETURN (res);
}
// x is Infinity?
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// check if y is Inf.
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull))
// return NaN
{
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
// otherwise return +/-Inf
res =
((x.w[1] ^ y.
w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
BID_RETURN (res);
}
}
// x is 0
if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) {
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x=y=0, return NaN
res = 0x7c00000000000000ull;
BID_RETURN (res);
}
// return 0
res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (exponent_x > DECIMAL_MAX_EXPON_64)
exponent_x = DECIMAL_MAX_EXPON_64;
else if (exponent_x < 0)
exponent_x = 0;
res |= (((UINT64) exponent_x) << 53);
BID_RETURN (res);
}
}
if (!valid_y) {
// y is Inf. or NaN
// test if y is NaN
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull);
Tmp.w[0] = CY.w[0];
TP128 = reciprocals10_128[18];
__mul_128x128_full (Qh, Ql, Tmp, TP128);
amount = recip_scale[18];
__shr_128 (Tmp, Qh, amount);
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
BID_RETURN (res);
}
// y is Infinity?
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res = sign_x ^ sign_y;
BID_RETURN (res);
}
// y is 0, return +/-Inf
res =
((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (__unsigned_compare_gt_128 (CY, CX)) {
// CX < CY
// 2^64
f64.i = 0x5f800000;
// fx ~ CX, fy ~ CY
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0];
// expon_cy - expon_cx
bin_index = (fy.i - fx.i) >> 23;
if (CX.w[1]) {
T = power10_index_binexp_128[bin_index].w[0];
__mul_64x128_short (CA, T, CX);
} else {
T128 = power10_index_binexp_128[bin_index];
__mul_64x128_short (CA, CX.w[0], T128);
}
ed2 = 15;
if (__unsigned_compare_gt_128 (CY, CA))
ed2++;
T128 = power10_table_128[ed2];
__mul_128x128_to_256 (CA4, CA, T128);
ed2 += estimate_decimal_digits[bin_index];
CQ.w[0] = CQ.w[1] = 0;
diff_expon = diff_expon - ed2;
} else {
// get CQ = CX/CY
__div_128_by_128 (&CQ, &CR, CX, CY);
// get number of decimal digits in CQ
// 2^64
f64.i = 0x5f800000;
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0];
// binary expon. of CQ
bin_expon = (fx.i - 0x3f800000) >> 23;
digits_q = estimate_decimal_digits[bin_expon];
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0];
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1];
if (__unsigned_compare_ge_128 (CQ, TP128))
digits_q++;
if (digits_q <= 16) {
if (!CR.w[1] && !CR.w[0]) {
res = get_BID64 (sign_x ^ sign_y, diff_expon,
CQ.w[0], rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
ed2 = 16 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
__mul_64x128_to_192 (CA4, (T128.w[0]), CR);
diff_expon = diff_expon - ed2;
CQ.w[0] *= T128.w[0];
} else {
ed2 = digits_q - 16;
diff_expon += ed2;
T128 = reciprocals10_128[ed2];
__mul_128x128_to_256 (P256, CQ, T128);
amount = recip_scale[ed2];
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount));
CQ.w[1] = 0;
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0]));
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]);
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0];
CA4.w[1] = CX.w[1] - QB256.w[1];
CA4.w[0] = CX.w[0] - QB256.w[0];
if (CX.w[0] < QB256.w[0])
CA4.w[1]--;
if (CR.w[0] || CR.w[1])
CA4.w[0] |= 1;
done = 1;
if(CA4.w[1]|CA4.w[0]) {
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY);
}
}
}
if (!done) {
__div_256_by_128 (&CQ, &CA4, CY);
}
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#ifndef LEAVE_TRAILING_ZEROS
else
#endif
#else
#ifndef LEAVE_TRAILING_ZEROS
if (!CA4.w[0] && !CA4.w[1])
#endif
#endif
#ifndef LEAVE_TRAILING_ZEROS
// check whether result is exact
{
if(!done) {
// check whether CX, CY are short
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) {
i = (int) CY.w[0] - 1;
j = (int) CX.w[0] - 1;
// difference in powers of 2 factors for Y and X
nzeros = ed2 - factors[i][0] + factors[j][0];
// difference in powers of 5 factors
d5 = ed2 - factors[i][1] + factors[j][1];
if (d5 < nzeros)
nzeros = d5;
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2];
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128_long (CQ, Qh, amount);
diff_expon += nzeros;
} else {
// decompose Q as Qh*10^17 + Ql
//T128 = reciprocals10_128[17];
Q_low = CQ.w[0];
{
tdigit[0] = Q_low & 0x3ffffff;
tdigit[1] = 0;
QX = Q_low >> 26;
QX32 = QX;
nzeros = 0;
for (j = 0; QX32; j++, QX32 >>= 7) {
k = (QX32 & 127);
tdigit[0] += convert_table[j][k][0];
tdigit[1] += convert_table[j][k][1];
if (tdigit[0] >= 100000000) {
tdigit[0] -= 100000000;
tdigit[1]++;
}
}
if (tdigit[1] >= 100000000) {
tdigit[1] -= 100000000;
if (tdigit[1] >= 100000000)
tdigit[1] -= 100000000;
}
digit = tdigit[0];
if (!digit && !tdigit[1])
nzeros += 16;
else {
if (!digit) {
nzeros += 8;
digit = tdigit[1];
}
// decompose digit
PD = (UINT64) digit *0x068DB8BBull;
digit_h = (UINT32) (PD >> 40);
digit_low = digit - digit_h * 10000;
if (!digit_low)
nzeros += 4;
else
digit_h = digit_low;
if (!(digit_h & 1))
nzeros +=
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >>
(digit_h & 7));
}
if (nzeros) {
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[nzeros];
__shr_128 (CQ, Qh, amount);
}
diff_expon += nzeros;
}
}
}
if(diff_expon>=0){
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0],
rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
#endif
if(diff_expon>=0) {
#ifdef IEEE_ROUND_NEAREST
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
//if(CQ.w[0]<carry64)
//CQ.w[1] ++;
#else
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
#else
rmode = rnd_mode;
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
switch (rmode) {
case ROUNDING_TO_NEAREST: // round to nearest code
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D);
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_TIES_AWAY:
// rounding
// 2*CA4 - CY
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63);
CA4r.w[0] = CA4.w[0] + CA4.w[0];
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]);
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64;
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1;
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D;
CQ.w[0] += carry64;
if (CQ.w[0] < carry64)
CQ.w[1]++;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
break;
default: // rounding up
CQ.w[0]++;
if (!CQ.w[0])
CQ.w[1]++;
break;
}
#endif
#endif
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
} else {
// UF occurs
#ifdef SET_STATUS_FLAGS
if ((diff_expon + 16 < 0)) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
rmode = rnd_mode;
res =
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}