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gcc/libgcc/config/libbid/bid128_div.c
Jakub Jelinek 7adcbafe45 Update copyright years.
2022-01-03 10:42:10 +01:00

1852 lines
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/* Copyright (C) 2007-2022 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/>. */
#define BID_128RES
#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[];
BID128_FUNCTION_ARG2 (bid128_div, x, y)
UINT256 CA4, CA4r, P256;
UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res;
UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD,
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;
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
res.w[1] = (CX.w[1]) & QUIET_MASK64;
res.w[0] = CX.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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// y is NaN?
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull))
// return NaN
{
// return +/-Inf
res.w[1] = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) |
0x7800000000000000ull;
res.w[0] = 0;
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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// return 0
res.w[1] = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
if (exponent_x > DECIMAL_MAX_EXPON_128)
exponent_x = DECIMAL_MAX_EXPON_128;
else if (exponent_x < 0)
exponent_x = 0;
res.w[1] |= (((UINT64) exponent_x) << 49);
res.w[0] = 0;
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
res.w[1] = CY.w[1] & QUIET_MASK64;
res.w[0] = CY.w[0];
BID_RETURN (res);
}
// y is Infinity?
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res.w[1] = sign_x ^ sign_y;
res.w[0] = 0;
BID_RETURN (res);
}
// y is 0, return +/-Inf
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
res.w[1] =
((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
res.w[0] = 0;
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;
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 = 33;
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);
if (!CR.w[1] && !CR.w[0]) {
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
// 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++;
ed2 = 34 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
T128.w[1] = power10_table_128[ed2].w[1];
__mul_128x128_to_256 (CA4, CR, T128);
diff_expon = diff_expon - ed2;
__mul_128x128_low (CQ, CQ, T128);
}
__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_high (Qh, 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
//T128 = reciprocals10_128[17];
T128.w[0] = 0x44909befeb9fad49ull;
T128.w[1] = 0x000b877aa3236a4bull;
__mul_128x128_to_256 (P256, CQ, T128);
//amount = recip_scale[17];
Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44));
Q_low = CQ.w[0] - Q_high * 100000000000000000ull;
if (!Q_low) {
diff_expon += 17;
tdigit[0] = Q_high & 0x3ffffff;
tdigit[1] = 0;
QX = Q_high >> 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) {
__mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-64
amount = short_recip_scale[nzeros];
CQ.w[0] = CQ.w[1] >> amount;
} else
CQ.w[0] = Q_high;
CQ.w[1] = 0;
diff_expon += nzeros;
} else {
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_high (Qh, 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;
}
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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
} else {
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ,
CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
//#define LEAVE_TRAILING_ZEROS
TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2 (UINT128, bid128dd_div, UINT64, x,
UINT64, y)
UINT256 CA4, CA4r, P256;
UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res;
UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD,
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;
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
CX.w[1] = 0;
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) {
#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
res.w[0] = (CX.w[0] & 0x0003ffffffffffffull);
__mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull);
BID_RETURN (res);
}
// x is Infinity?
if (((x) & 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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
if ((((y) & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
// otherwise return +/-Inf
res.w[1] =
(((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
}
// x is 0
if ((((y) & 0x7800000000000000ull) != 0x7800000000000000ull)) {
if(!CY.w[0]) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x=y=0, return NaN
res.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// return 0
res.w[1] = ((x) ^ (y)) & 0x8000000000000000ull;
if (((y) & 0x6000000000000000ull) == 0x6000000000000000ull)
exponent_y = ((UINT32) ((y) >> 51)) & 0x3ff;
else
exponent_y = ((UINT32) ((y) >> 53)) & 0x3ff;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128;
if (exponent_x > DECIMAL_MAX_EXPON_128)
exponent_x = DECIMAL_MAX_EXPON_128;
else if (exponent_x < 0)
exponent_x = 0;
res.w[1] |= (((UINT64) exponent_x) << 49);
res.w[0] = 0;
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
res.w[0] = (CY.w[0] & 0x0003ffffffffffffull);
__mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull);
BID_RETURN (res);
}
// y is Infinity?
if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res.w[1] = sign_x ^ sign_y;
res.w[0] = 0;
BID_RETURN (res);
}
// y is 0, return +/-Inf
res.w[1] =
(((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull;
res.w[0] = 0;
#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;
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 = 33;
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);
if (!CR.w[1] && !CR.w[0]) {
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
// 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++;
ed2 = 34 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
T128.w[1] = power10_table_128[ed2].w[1];
__mul_128x128_to_256 (CA4, CR, T128);
diff_expon = diff_expon - ed2;
__mul_128x128_low (CQ, CQ, T128);
}
__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_high (Qh, 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];
T128.w[0] = 0x44909befeb9fad49ull;
T128.w[1] = 0x000b877aa3236a4bull;
__mul_128x128_to_256 (P256, CQ, T128);
//amount = recip_scale[17];
Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44));
Q_low = CQ.w[0] - Q_high * 100000000000000000ull;
if (!Q_low) {
diff_expon += 17;
tdigit[0] = Q_high & 0x3ffffff;
tdigit[1] = 0;
QX = Q_high >> 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) {
__mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-64
amount = short_recip_scale[nzeros];
CQ.w[0] = CQ.w[1] >> amount;
} else
CQ.w[0] = Q_high;
CQ.w[1] = 0;
diff_expon += nzeros;
} else {
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_high (Qh, 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;
}
}
get_BID128(&res, sign_x ^ sign_y, diff_expon, CQ, &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
} else {
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ,
CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
BID128_FUNCTION_ARGTYPE1_ARG128 (bid128dq_div, UINT64, x, y)
UINT256 CA4, CA4r, P256;
UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res;
UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, valid_y,
PD;
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;
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
__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
res.w[0] = (CX.w[0] & 0x0003ffffffffffffull);
__mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull);
BID_RETURN (res);
}
// 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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) {
// otherwise return +/-Inf
res.w[1] =
((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
res.w[0] = 0;
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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// return 0
res.w[1] = (x ^ y.w[1]) & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + (DECIMAL_EXPONENT_BIAS_128<<1) - DECIMAL_EXPONENT_BIAS;
if (exponent_x > DECIMAL_MAX_EXPON_128)
exponent_x = DECIMAL_MAX_EXPON_128;
else if (exponent_x < 0)
exponent_x = 0;
res.w[1] |= (((UINT64) exponent_x) << 49);
res.w[0] = 0;
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
res.w[1] = CY.w[1] & QUIET_MASK64;
res.w[0] = CY.w[0];
BID_RETURN (res);
}
// y is Infinity?
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
// return +/-0
res.w[1] = sign_x ^ sign_y;
res.w[0] = 0;
BID_RETURN (res);
}
// y is 0, return +/-Inf
res.w[1] =
((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull;
res.w[0] = 0;
#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;
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 = 33;
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);
if (!CR.w[1] && !CR.w[0]) {
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
// 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++;
ed2 = 34 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
T128.w[1] = power10_table_128[ed2].w[1];
__mul_128x128_to_256 (CA4, CR, T128);
diff_expon = diff_expon - ed2;
__mul_128x128_low (CQ, CQ, T128);
}
__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
{
//printf("ed2=%d,nz=%d,a=%d,CQ="LX16","LX16", RH="LX16", RL="LX16"\n",ed2,nzeros,amount,CQ.w[1],CQ.w[0],reciprocals10_128[nzeros].w[1],reciprocals10_128[nzeros].w[0]);fflush(stdout);
// 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_high (Qh, 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];
T128.w[0] = 0x44909befeb9fad49ull;
T128.w[1] = 0x000b877aa3236a4bull;
__mul_128x128_to_256 (P256, CQ, T128);
//amount = recip_scale[17];
Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44));
Q_low = CQ.w[0] - Q_high * 100000000000000000ull;
if (!Q_low) {
diff_expon += 17;
tdigit[0] = Q_high & 0x3ffffff;
tdigit[1] = 0;
QX = Q_high >> 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);
//printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout);
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 (CQ, Q_high, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-64
amount = short_recip_scale[nzeros];
CQ.w[0] = CQ.w[1] >> amount;
} else
CQ.w[0] = Q_high;
CQ.w[1] = 0;
diff_expon += nzeros;
} else {
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);
//printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout);
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_high (Qh, 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;
}
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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
} else {
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ,
CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
BID128_FUNCTION_ARG128_ARGTYPE2 (bid128qd_div, x, UINT64, y)
UINT256 CA4, CA4r, P256;
UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, res;
UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD,
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, 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
res.w[1] = (CX.w[1]) & QUIET_MASK64;
res.w[0] = CX.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.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// y is NaN?
if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull))
// return NaN
{
// return +/-Inf
res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull) |
0x7800000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
}
// x is 0
if ((y & 0x7800000000000000ull) < 0x7800000000000000ull) {
if (!CY.w[0]) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x=y=0, return NaN
res.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
BID_RETURN (res);
}
// return 0
res.w[1] = (x.w[1] ^ y) & 0x8000000000000000ull;
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS;
if (exponent_x > DECIMAL_MAX_EXPON_128)
exponent_x = DECIMAL_MAX_EXPON_128;
else if (exponent_x < 0)
exponent_x = 0;
res.w[1] |= (((UINT64) exponent_x) << 49);
res.w[0] = 0;
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
res.w[0] = (CY.w[0] & 0x0003ffffffffffffull);
__mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull);
BID_RETURN (res);
}
// y is Infinity?
if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
// return +/-0
res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull);
res.w[0] = 0;
BID_RETURN (res);
}
// y is 0
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION);
#endif
res.w[1] = (sign_x ^ sign_y) | INFINITY_MASK64;
res.w[0] = 0;
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 = 33;
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);
if (!CR.w[1] && !CR.w[0]) {
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,
pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
// 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++;
ed2 = 34 - digits_q;
T128.w[0] = power10_table_128[ed2].w[0];
T128.w[1] = power10_table_128[ed2].w[1];
__mul_128x128_to_256 (CA4, CR, T128);
diff_expon = diff_expon - ed2;
__mul_128x128_low (CQ, CQ, T128);
}
__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_high (Qh, 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];
T128.w[0] = 0x44909befeb9fad49ull;
T128.w[1] = 0x000b877aa3236a4bull;
__mul_128x128_to_256 (P256, CQ, T128);
//amount = recip_scale[17];
Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44));
Q_low = CQ.w[0] - Q_high * 100000000000000000ull;
if (!Q_low) {
diff_expon += 17;
tdigit[0] = Q_high & 0x3ffffff;
tdigit[1] = 0;
QX = Q_high >> 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) {
__mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]);
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-64
amount = short_recip_scale[nzeros];
CQ.w[0] = CQ.w[1] >> amount;
} else
CQ.w[0] = Q_high;
CQ.w[1] = 0;
diff_expon += nzeros;
} else {
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_high (Qh, 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;
}
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &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
} else {
#ifdef SET_STATUS_FLAGS
if (CA4.w[0] || CA4.w[1]) {
// set status flags
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
}
#endif
handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ,
CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
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