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gcc/libgcc/config/libbid/bid64_div.c
Jakub Jelinek 748086b7b2 Licensing changes to GPLv3 resp. GPLv3 with GCC Runtime Exception. 
From-SVN: r145841
2009-04-09 17:00:19 +02:00

1796 lines
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/* Copyright (C) 2007, 2009 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 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);
}
}
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