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gcc/libgcc/config/libbid/bid64_fma.c

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/* Copyright (C) 2007-2016 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 fma
*****************************************************************************
*
* Algorithm description:
*
* if multiplication is guranteed exact (short coefficients)
* call the unpacked arg. equivalent of bid64_add(x*y, z)
* else
* get full coefficient_x*coefficient_y product
* call subroutine to perform addition of 64-bit argument
* to 128-bit product
*
****************************************************************************/
#include "bid_inline_add.h"
#if DECIMAL_CALL_BY_REFERENCE
extern void bid64_mul (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM);
#else
extern UINT64 bid64_mul (UINT64 x,
UINT64 y _RND_MODE_PARAM
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM);
#endif
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_fma (UINT64 * pres, UINT64 * px, UINT64 * py,
UINT64 *
pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x, y, z;
#else
UINT64
bid64_fma (UINT64 x, UINT64 y,
UINT64 z _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 P, PU, CT, CZ;
UINT64 sign_x, sign_y, coefficient_x, coefficient_y, sign_z,
coefficient_z;
UINT64 C64, remainder_y, res;
UINT64 CYh, CY0L, T, valid_x, valid_y, valid_z;
int_double tempx, tempy;
int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
bin_expon_product, rmode;
int digits_p, bp, final_exponent, exponent_z, digits_z, ez, ey,
scale_z, uf_status;
#if DECIMAL_CALL_BY_REFERENCE
#if !DECIMAL_GLOBAL_ROUNDING
_IDEC_round rnd_mode = *prnd_mode;
#endif
x = *px;
y = *py;
z = *pz;
#endif
valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
valid_z = unpack_BID64 (&sign_z, &exponent_z, &coefficient_z, z);
// unpack arguments, check for NaN, Infinity, or 0
if (!valid_x || !valid_y || !valid_z) {
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
// if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y)
// check first for non-canonical NaN payload
y = y & 0xfe03ffffffffffffull; // clear G6-G12
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
}
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return quiet (y)
res = y & 0xfdffffffffffffffull;
} else { // y is QNaN
// return y
res = y;
// if z = SNaN or x = SNaN signal invalid exception
if ((z & MASK_SNAN) == MASK_SNAN
|| (x & MASK_SNAN) == MASK_SNAN) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
}
}
BID_RETURN (res)
} else if ((z & MASK_NAN) == MASK_NAN) { // z is NAN
// if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z)
// check first for non-canonical NaN payload
z = z & 0xfe03ffffffffffffull; // clear G6-G12
if ((z & 0x0003ffffffffffffull) > 999999999999999ull) {
z = z & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
}
if ((z & MASK_SNAN) == MASK_SNAN) { // z is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return quiet (z)
res = z & 0xfdffffffffffffffull;
} else { // z is QNaN
// return z
res = z;
// if x = SNaN signal invalid exception
if ((x & MASK_SNAN) == MASK_SNAN) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
}
}
BID_RETURN (res)
} else if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
// if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x)
// check first for non-canonical NaN payload
x = x & 0xfe03ffffffffffffull; // clear G6-G12
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
}
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return quiet (x)
res = x & 0xfdffffffffffffffull;
} else { // x is QNaN
// return x
res = x; // clear out G[6]-G[16]
}
BID_RETURN (res)
}
if (!valid_x) {
// x is Inf. or 0
// x is Infinity?
if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
// check if y is 0
if (!coefficient_y) {
// y==0, return NaN
#ifdef SET_STATUS_FLAGS
if ((z & 0x7e00000000000000ull) != 0x7c00000000000000ull)
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (0x7c00000000000000ull);
}
// test if z is Inf of oposite sign
if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
&& (((x ^ y) ^ z) & 0x8000000000000000ull)) {
// return NaN
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (0x7c00000000000000ull);
}
// otherwise return +/-Inf
BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
0x7800000000000000ull);
}
// x is 0
if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)
&& ((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {
if (coefficient_z) {
exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y;
sign_z = z & 0x8000000000000000ull;
if (exponent_y >= exponent_z)
BID_RETURN (z);
res =
add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
&rnd_mode, pfpsf);
BID_RETURN (res);
}
}
}
if (!valid_y) {
// y is Inf. or 0
// y is Infinity?
if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
// check if x is 0
if (!coefficient_x) {
// y==0, return NaN
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
BID_RETURN (0x7c00000000000000ull);
}
// test if z is Inf of oposite sign
if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
&& (((x ^ y) ^ z) & 0x8000000000000000ull)) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// return NaN
BID_RETURN (0x7c00000000000000ull);
}
// otherwise return +/-Inf
BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
0x7800000000000000ull);
}
// y is 0
if (((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {
if (coefficient_z) {
exponent_y += exponent_x - DECIMAL_EXPONENT_BIAS;
sign_z = z & 0x8000000000000000ull;
if (exponent_y >= exponent_z)
BID_RETURN (z);
res =
add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
&rnd_mode, pfpsf);
BID_RETURN (res);
}
}
}
if (!valid_z) {
// y is Inf. or 0
// test if y is NaN/Inf
if ((z & 0x7800000000000000ull) == 0x7800000000000000ull) {
BID_RETURN (coefficient_z & QUIET_MASK64);
}
// z is 0, return x*y
if ((!coefficient_x) || (!coefficient_y)) {
//0+/-0
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;
if (exponent_x <= exponent_z)
res = ((UINT64) exponent_x) << 53;
else
res = ((UINT64) exponent_z) << 53;
if ((sign_x ^ sign_y) == sign_z)
res |= sign_z;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
else if (rnd_mode == ROUNDING_DOWN)
res |= 0x8000000000000000ull;
#endif
#endif
BID_RETURN (res);
}
}
}
/* get binary coefficients of x and y */
//--- get number of bits in the coefficients of x and y ---
// version 2 (original)
tempx.d = (double) coefficient_x;
bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52);
tempy.d = (double) coefficient_y;
bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52);
// magnitude estimate for coefficient_x*coefficient_y is
// 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx)
bin_expon_product = bin_expon_cx + bin_expon_cy;
// check if coefficient_x*coefficient_y<2^(10*k+3)
// equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1
if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) {
// easy multiply
C64 = coefficient_x * coefficient_y;
final_exponent = exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS;
if ((final_exponent > 0) || (!coefficient_z)) {
res =
get_add64 (sign_x ^ sign_y,
final_exponent, C64, sign_z, exponent_z, coefficient_z, rnd_mode, pfpsf);
BID_RETURN (res);
} else {
P.w[0] = C64;
P.w[1] = 0;
extra_digits = 0;
}
} else {
if (!coefficient_z) {
#if DECIMAL_CALL_BY_REFERENCE
bid64_mul (&res, px,
py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
_EXC_INFO_ARG);
#else
res =
bid64_mul (x,
y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
_EXC_INFO_ARG);
#endif
BID_RETURN (res);
}
// get 128-bit product: coefficient_x*coefficient_y
__mul_64x64_to_128 (P, coefficient_x, coefficient_y);
// tighten binary range of P: leading bit is 2^bp
// unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1
bin_expon_product -= 2 * BINARY_EXPONENT_BIAS;
__tight_bin_range_128 (bp, P, bin_expon_product);
// get number of decimal digits in the product
digits_p = estimate_decimal_digits[bp];
if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P)))
digits_p++; // if power10_table_128[digits_p] <= P
// determine number of decimal digits to be rounded out
extra_digits = digits_p - MAX_FORMAT_DIGITS;
final_exponent =
exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS;
}
if (((unsigned) final_exponent) >= 3 * 256) {
if (final_exponent < 0) {
//--- get number of bits in the coefficients of z ---
tempx.d = (double) coefficient_z;
bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
// get number of decimal digits in the coeff_x
digits_z = estimate_decimal_digits[bin_expon_cx];
if (coefficient_z >= power10_table_128[digits_z].w[0])
digits_z++;
// underflow
if ((final_exponent + 16 < 0)
|| (exponent_z + digits_z > 33 + final_exponent)) {
res =
BID_normalize (sign_z, exponent_z, coefficient_z,
sign_x ^ sign_y, 1, rnd_mode, pfpsf);
BID_RETURN (res);
}
ez = exponent_z + digits_z - 16;
if (ez < 0)
ez = 0;
scale_z = exponent_z - ez;
coefficient_z *= power10_table_128[scale_z].w[0];
ey = final_exponent - extra_digits;
extra_digits = ez - ey;
if (extra_digits > 33) {
res =
BID_normalize (sign_z, exponent_z, coefficient_z,
sign_x ^ sign_y, 1, rnd_mode, pfpsf);
BID_RETURN (res);
}
//else // extra_digits<=32
if (extra_digits > 17) {
CYh = __truncate (P, 16);
// get remainder
T = power10_table_128[16].w[0];
__mul_64x64_to_64 (CY0L, CYh, T);
remainder_y = P.w[0] - CY0L;
extra_digits -= 16;
P.w[0] = CYh;
P.w[1] = 0;
} else
remainder_y = 0;
// align coeff_x, CYh
__mul_64x64_to_128 (CZ, coefficient_z,
power10_table_128[extra_digits].w[0]);
if (sign_z == (sign_y ^ sign_x)) {
__add_128_128 (CT, CZ, P);
if (__unsigned_compare_ge_128
(CT, power10_table_128[16 + extra_digits])) {
extra_digits++;
ez++;
}
} else {
if (remainder_y && (__unsigned_compare_ge_128 (CZ, P))) {
P.w[0]++;
if (!P.w[0])
P.w[1]++;
}
__sub_128_128 (CT, CZ, P);
if (((SINT64) CT.w[1]) < 0) {
sign_z = sign_y ^ sign_x;
CT.w[0] = 0 - CT.w[0];
CT.w[1] = 0 - CT.w[1];
if (CT.w[0])
CT.w[1]--;
} else if(!(CT.w[1]|CT.w[0]))
sign_z = (rnd_mode!=ROUNDING_DOWN)? 0: 0x8000000000000000ull;
if (ez
&&
(__unsigned_compare_gt_128
(power10_table_128[15 + extra_digits], CT))) {
extra_digits--;
ez--;
}
}
#ifdef SET_STATUS_FLAGS
uf_status = 0;
if ((!ez)
&&
__unsigned_compare_gt_128 (power10_table_128
[extra_digits + 15], CT)) {
rmode = rnd_mode;
if (sign_z && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
//__add_128_64(PU, CT, round_const_table[rmode][extra_digits]);
PU = power10_table_128[extra_digits + 15];
PU.w[0]--;
if (__unsigned_compare_gt_128 (PU, CT)
|| (rmode == ROUNDING_DOWN)
|| (rmode == ROUNDING_TO_ZERO))
uf_status = UNDERFLOW_EXCEPTION;
else if (extra_digits < 2) {
if ((rmode == ROUNDING_UP)) {
if (!extra_digits)
uf_status = UNDERFLOW_EXCEPTION;
else {
if (remainder_y && (sign_z != (sign_y ^ sign_x)))
remainder_y = power10_table_128[16].w[0] - remainder_y;
if (power10_table_128[15].w[0] > remainder_y)
uf_status = UNDERFLOW_EXCEPTION;
}
} else // RN or RN_away
{
if (remainder_y && (sign_z != (sign_y ^ sign_x)))
remainder_y = power10_table_128[16].w[0] - remainder_y;
if (!extra_digits) {
remainder_y += round_const_table[rmode][15];
if (remainder_y < power10_table_128[16].w[0])
uf_status = UNDERFLOW_EXCEPTION;
} else {
if (remainder_y < round_const_table[rmode][16])
uf_status = UNDERFLOW_EXCEPTION;
}
}
//__set_status_flags (pfpsf, uf_status);
}
}
#endif
res =
__bid_full_round64_remainder (sign_z, ez - extra_digits, CT,
extra_digits, remainder_y,
rnd_mode, pfpsf, uf_status);
BID_RETURN (res);
} else {
if ((sign_z == (sign_x ^ sign_y))
|| (final_exponent > 3 * 256 + 15)) {
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
1000000000000000ull, rnd_mode,
pfpsf);
BID_RETURN (res);
}
}
}
if (extra_digits > 0) {
res =
get_add128 (sign_z, exponent_z, coefficient_z, sign_x ^ sign_y,
final_exponent, P, extra_digits, rnd_mode, pfpsf);
BID_RETURN (res);
}
// go to convert_format and exit
else {
C64 = __low_64 (P);
res =
get_add64 (sign_x ^ sign_y,
exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64,
sign_z, exponent_z, coefficient_z,
rnd_mode, pfpsf);
BID_RETURN (res);
}
}
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