0,0 → 1,506 |
/* Copyright (C) 2007-2015 Free Software Foundation, Inc. |
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This file is part of GCC. |
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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. |
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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/>. */ |
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/***************************************************************************** |
* 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 |
* |
****************************************************************************/ |
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#include "bid_inline_add.h" |
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#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); |
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// unpack arguments, check for NaN, Infinity, or 0 |
if (!valid_x || !valid_y || !valid_z) { |
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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) |
} |
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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)) { |
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if (coefficient_z) { |
exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y; |
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sign_z = z & 0x8000000000000000ull; |
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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; |
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sign_z = z & 0x8000000000000000ull; |
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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); |
} |
} |
} |
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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); |
} |
} |
} |
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/* get binary coefficients of x and y */ |
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//--- 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); |
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tempy.d = (double) coefficient_y; |
bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52); |
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// 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]); |
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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); |
} |
} |