/* Copyright (C) 2007-2020 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#define BID_128RES
#include "bid_internal.h"
#include "bid_sqrt_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
BID128_FUNCTION_ARG1 (bid128_sqrt, x)
UINT256 M256, C256, C4, C8;
UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
UINT64 sign_x, Carry;
SINT64 D;
int_float fx, f64;
int exponent_x, bin_expon_cx;
int digits, scale, exponent_q;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
// unpack arguments, check for NaN or Infinity
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
res.w[1] = CX.w[1];
res.w[0] = CX.w[0];
// NaN ?
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef SET_STATUS_FLAGS
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
res.w[1] = CX.w[1] & QUIET_MASK64;
BID_RETURN (res);
}
// x is Infinity?
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
res.w[1] = CX.w[1];
if (sign_x) {
// -Inf, return NaN
res.w[1] = 0x7c00000000000000ull;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
}
BID_RETURN (res);
}
// x is 0 otherwise
res.w[1] =
sign_x |
((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) << 49);
res.w[0] = 0;
BID_RETURN (res);
}
if (sign_x) {
res.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
// 2^64
f64.i = 0x5f800000;
// fx ~ CX
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
digits = estimate_decimal_digits[bin_expon_cx];
A10 = CX;
if (exponent_x & 1) {
A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
A10.w[0] = CX.w[0] << 3;
CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
CX2.w[0] = CX.w[0] << 1;
__add_128_128 (A10, A10, CX2);
}
CS.w[0] = short_sqrt128 (A10);
CS.w[1] = 0;
// check for exact result
if (CS.w[0] * CS.w[0] == A10.w[0]) {
__mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
if (S2.w[1] == A10.w[1]) // && S2.w[0]==A10.w[0])
{
get_BID128_very_fast (&res, 0,
(exponent_x +
DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
// get number of digits in CX
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
if (D > 0
|| (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
digits++;
// if exponent is odd, scale coefficient by 10
scale = 67 - digits;
exponent_q = exponent_x - scale;
scale += (exponent_q & 1); // exp. bias is even
if (scale > 38) {
T128 = power10_table_128[scale - 37];
__mul_128x128_low (CX1, CX, T128);
TP128 = power10_table_128[37];
__mul_128x128_to_256 (C256, CX1, TP128);
} else {
T128 = power10_table_128[scale];
__mul_128x128_to_256 (C256, CX, T128);
}
// 4*C256
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
C4.w[0] = C256.w[0] << 2;
long_sqrt128 (&CS, C256);
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (!((rnd_mode) & 3)) {
#endif
#endif
// compare to midpoints
CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
// CSM^2
//__mul_128x128_to_256(M256, CSM, CSM);
__sqr128_to_256 (M256, CSM);
if (C4.w[3] > M256.w[3]
|| (C4.w[3] == M256.w[3]
&& (C4.w[2] > M256.w[2]
|| (C4.w[2] == M256.w[2]
&& (C4.w[1] > M256.w[1]
|| (C4.w[1] == M256.w[1]
&& C4.w[0] > M256.w[0])))))) {
// round up
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
} else {
C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
C8.w[0] = CS.w[0] << 3;
// M256 - 8*CSM
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] - Carry;
// if CSM' > C256, round up
if (M256.w[3] > C4.w[3]
|| (M256.w[3] == C4.w[3]
&& (M256.w[2] > C4.w[2]
|| (M256.w[2] == C4.w[2]
&& (M256.w[1] > C4.w[1]
|| (M256.w[1] == C4.w[1]
&& M256.w[0] > C4.w[0])))))) {
// round down
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
}
}
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
} else {
__sqr128_to_256 (M256, CS);
C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
C8.w[0] = CS.w[0] << 1;
if (M256.w[3] > C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] > C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] > C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] > C256.w[0])))))) {
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] - Carry;
M256.w[0]++;
if (!M256.w[0]) {
M256.w[1]++;
if (!M256.w[1]) {
M256.w[2]++;
if (!M256.w[2])
M256.w[3]++;
}
}
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
if (M256.w[3] > C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] > C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] > C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] > C256.w[0])))))) {
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
}
}
else {
__add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] + Carry;
M256.w[0]++;
if (!M256.w[0]) {
M256.w[1]++;
if (!M256.w[1]) {
M256.w[2]++;
if (!M256.w[2])
M256.w[3]++;
}
}
if (M256.w[3] < C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] < C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] < C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] <= C256.w[0])))))) {
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
}
}
// RU?
if ((rnd_mode) == ROUNDING_UP) {
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
}
}
#endif
#endif
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
#endif
get_BID128_fast (&res, 0,
(exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
BID128_FUNCTION_ARGTYPE1 (bid128d_sqrt, UINT64, x)
UINT256 M256, C256, C4, C8;
UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
UINT64 sign_x, Carry;
SINT64 D;
int_float fx, f64;
int exponent_x, bin_expon_cx;
int digits, scale, exponent_q;
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
fexcept_t binaryflags = 0;
#endif
// unpack arguments, check for NaN or Infinity
// unpack arguments, check for NaN or Infinity
CX.w[1] = 0;
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) {
res.w[1] = CX.w[0];
res.w[0] = 0;
// NaN ?
if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#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) {
if (sign_x) {
// -Inf, return NaN
res.w[1] = 0x7c00000000000000ull;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
}
BID_RETURN (res);
}
// x is 0 otherwise
exponent_x =
exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
res.w[1] =
sign_x | ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1)
<< 49);
res.w[0] = 0;
BID_RETURN (res);
}
if (sign_x) {
res.w[1] = 0x7c00000000000000ull;
res.w[0] = 0;
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (res);
}
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
exponent_x =
exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
// 2^64
f64.i = 0x5f800000;
// fx ~ CX
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
digits = estimate_decimal_digits[bin_expon_cx];
A10 = CX;
if (exponent_x & 1) {
A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
A10.w[0] = CX.w[0] << 3;
CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
CX2.w[0] = CX.w[0] << 1;
__add_128_128 (A10, A10, CX2);
}
CS.w[0] = short_sqrt128 (A10);
CS.w[1] = 0;
// check for exact result
if (CS.w[0] * CS.w[0] == A10.w[0]) {
__mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
if (S2.w[1] == A10.w[1]) {
get_BID128_very_fast (&res, 0,
(exponent_x + DECIMAL_EXPONENT_BIAS_128) >> 1,
CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}
}
// get number of digits in CX
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
if (D > 0
|| (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
digits++;
// if exponent is odd, scale coefficient by 10
scale = 67 - digits;
exponent_q = exponent_x - scale;
scale += (exponent_q & 1); // exp. bias is even
if (scale > 38) {
T128 = power10_table_128[scale - 37];
__mul_128x128_low (CX1, CX, T128);
TP128 = power10_table_128[37];
__mul_128x128_to_256 (C256, CX1, TP128);
} else {
T128 = power10_table_128[scale];
__mul_128x128_to_256 (C256, CX, T128);
}
// 4*C256
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
C4.w[0] = C256.w[0] << 2;
long_sqrt128 (&CS, C256);
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
if (!((rnd_mode) & 3)) {
#endif
#endif
// compare to midpoints
CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
// CSM^2
//__mul_128x128_to_256(M256, CSM, CSM);
__sqr128_to_256 (M256, CSM);
if (C4.w[3] > M256.w[3]
|| (C4.w[3] == M256.w[3]
&& (C4.w[2] > M256.w[2]
|| (C4.w[2] == M256.w[2]
&& (C4.w[1] > M256.w[1]
|| (C4.w[1] == M256.w[1]
&& C4.w[0] > M256.w[0])))))) {
// round up
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
} else {
C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
C8.w[0] = CS.w[0] << 3;
// M256 - 8*CSM
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] - Carry;
// if CSM' > C256, round up
if (M256.w[3] > C4.w[3]
|| (M256.w[3] == C4.w[3]
&& (M256.w[2] > C4.w[2]
|| (M256.w[2] == C4.w[2]
&& (M256.w[1] > C4.w[1]
|| (M256.w[1] == C4.w[1]
&& M256.w[0] > C4.w[0])))))) {
// round down
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
}
}
#ifndef IEEE_ROUND_NEAREST
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
} else {
__sqr128_to_256 (M256, CS);
C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
C8.w[0] = CS.w[0] << 1;
if (M256.w[3] > C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] > C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] > C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] > C256.w[0])))))) {
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] - Carry;
M256.w[0]++;
if (!M256.w[0]) {
M256.w[1]++;
if (!M256.w[1]) {
M256.w[2]++;
if (!M256.w[2])
M256.w[3]++;
}
}
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
if (M256.w[3] > C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] > C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] > C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] > C256.w[0])))))) {
if (!CS.w[0])
CS.w[1]--;
CS.w[0]--;
}
}
else {
__add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
__add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
__add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
M256.w[3] = M256.w[3] + Carry;
M256.w[0]++;
if (!M256.w[0]) {
M256.w[1]++;
if (!M256.w[1]) {
M256.w[2]++;
if (!M256.w[2])
M256.w[3]++;
}
}
if (M256.w[3] < C256.w[3]
|| (M256.w[3] == C256.w[3]
&& (M256.w[2] < C256.w[2]
|| (M256.w[2] == C256.w[2]
&& (M256.w[1] < C256.w[1]
|| (M256.w[1] == C256.w[1]
&& M256.w[0] <= C256.w[0])))))) {
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
}
}
// RU?
if ((rnd_mode) == ROUNDING_UP) {
CS.w[0]++;
if (!CS.w[0])
CS.w[1]++;
}
}
#endif
#endif
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
#endif
get_BID128_fast (&res, 0, (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1,
CS);
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
#endif
BID_RETURN (res);
}