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gcc/libgcc/config/libbid/bid64_mul.c

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/* Copyright (C) 2007-2015 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 multiply
*****************************************************************************
*
* Algorithm description:
*
* if(number_digits(coefficient_x)+number_digits(coefficient_y) guaranteed
* below 16)
* return get_BID64(sign_x^sign_y, exponent_x + exponent_y - dec_bias,
* coefficient_x*coefficient_y)
* else
* get long product: coefficient_x*coefficient_y
* determine number of digits to round off (extra_digits)
* rounding is performed as a 128x128-bit multiplication by
* 2^M[extra_digits]/10^extra_digits, followed by a shift
* M[extra_digits] is sufficiently large for required accuracy
*
****************************************************************************/
#include "bid_internal.h"
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_mul (UINT64 * pres, UINT64 * px,
UINT64 *
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x, y;
#else
UINT64
bid64_mul (UINT64 x,
UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT128 P, PU, C128, Q_high, Q_low, Stemp;
UINT64 sign_x, sign_y, coefficient_x, coefficient_y;
UINT64 C64, remainder_h, carry, CY, res;
UINT64 valid_x, valid_y;
int_double tempx, tempy;
int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
bin_expon_product;
int rmode, digits_p, bp, amount, amount2, final_exponent, round_up;
unsigned status, uf_status;
#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) {
#ifdef SET_STATUS_FLAGS
if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// x is Inf. or NaN
// 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 0
if (((y & INFINITY_MASK64) != INFINITY_MASK64)
&& !coefficient_y) {
#ifdef SET_STATUS_FLAGS
__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
// y==0 , return NaN
BID_RETURN (NAN_MASK64);
}
// check if y is NaN
if ((y & NAN_MASK64) == NAN_MASK64)
// y==NaN , return NaN
BID_RETURN (coefficient_y & QUIET_MASK64);
// otherwise return +/-Inf
BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
}
// x is 0
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_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) {
// check if x is 0
if (!coefficient_x) {
__set_status_flags (pfpsf, INVALID_EXCEPTION);
// x==0, return NaN
BID_RETURN (NAN_MASK64);
}
// otherwise return +/-Inf
BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
}
// y is 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;
BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
}
//--- 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;
res =
get_BID64_small_mantissa (sign_x ^ sign_y,
exponent_x + exponent_y -
DECIMAL_EXPONENT_BIAS, C64, rnd_mode,
pfpsf);
BID_RETURN (res);
} else {
uf_status = 0;
// 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;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
rmode = rnd_mode;
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
rmode = 3 - rmode;
#else
rmode = 0;
#endif
#else
rmode = 0;
#endif
round_up = 0;
if (((unsigned) final_exponent) >= 3 * 256) {
if (final_exponent < 0) {
// underflow
if (final_exponent + 16 < 0) {
res = sign_x ^ sign_y;
__set_status_flags (pfpsf,
UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
if (rmode == ROUNDING_UP)
res |= 1;
BID_RETURN (res);
}
uf_status = UNDERFLOW_EXCEPTION;
if (final_exponent == -1) {
__add_128_64 (PU, P, round_const_table[rmode][extra_digits]);
if (__unsigned_compare_ge_128
(PU, power10_table_128[extra_digits + 16]))
uf_status = 0;
}
extra_digits -= final_exponent;
final_exponent = 0;
if (extra_digits > 17) {
__mul_128x128_full (Q_high, Q_low, P, reciprocals10_128[16]);
amount = recip_scale[16];
__shr_128 (P, Q_high, amount);
// get sticky bits
amount2 = 64 - amount;
remainder_h = 0;
remainder_h--;
remainder_h >>= amount2;
remainder_h = remainder_h & Q_high.w[0];
extra_digits -= 16;
if (remainder_h || (Q_low.w[1] > reciprocals10_128[16].w[1]
|| (Q_low.w[1] ==
reciprocals10_128[16].w[1]
&& Q_low.w[0] >=
reciprocals10_128[16].w[0]))) {
round_up = 1;
__set_status_flags (pfpsf,
UNDERFLOW_EXCEPTION |
INEXACT_EXCEPTION);
P.w[0] = (P.w[0] << 3) + (P.w[0] << 1);
P.w[0] |= 1;
extra_digits++;
}
}
} else {
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
1000000000000000ull, rnd_mode,
pfpsf);
BID_RETURN (res);
}
}
if (extra_digits > 0) {
// will divide by 10^(digits_p - 16)
// add a constant to P, depending on rounding mode
// 0.5*10^(digits_p - 16) for round-to-nearest
__add_128_64 (P, P, round_const_table[rmode][extra_digits]);
// get P*(2^M[extra_digits])/10^extra_digits
__mul_128x128_full (Q_high, Q_low, P,
reciprocals10_128[extra_digits]);
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
amount = recip_scale[extra_digits];
__shr_128 (C128, Q_high, amount);
C64 = __low_64 (C128);
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
if (rmode == 0) //ROUNDING_TO_NEAREST
#endif
if ((C64 & 1) && !round_up) {
// check whether fractional part of initial_P/10^extra_digits
// is exactly .5
// this is the same as fractional part of
// (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero
// get remainder
remainder_h = Q_high.w[0] << (64 - amount);
// test whether fractional part is 0
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0]))) {
C64--;
}
}
#endif
#ifdef SET_STATUS_FLAGS
status = INEXACT_EXCEPTION | uf_status;
// get remainder
remainder_h = Q_high.w[0] << (64 - amount);
switch (rmode) {
case ROUNDING_TO_NEAREST:
case ROUNDING_TIES_AWAY:
// test whether fractional part is 0
if (remainder_h == 0x8000000000000000ull
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
case ROUNDING_DOWN:
case ROUNDING_TO_ZERO:
if (!remainder_h
&& (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
|| (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
&& Q_low.w[0] <
reciprocals10_128[extra_digits].w[0])))
status = EXACT_STATUS;
break;
default:
// round up
__add_carry_out (Stemp.w[0], CY, Q_low.w[0],
reciprocals10_128[extra_digits].w[0]);
__add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
reciprocals10_128[extra_digits].w[1], CY);
if ((remainder_h >> (64 - amount)) + carry >=
(((UINT64) 1) << amount))
status = EXACT_STATUS;
}
__set_status_flags (pfpsf, status);
#endif
// convert to BID and return
res =
fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, C64,
rmode, pfpsf);
BID_RETURN (res);
}
// go to convert_format and exit
C64 = __low_64 (P);
res =
get_BID64 (sign_x ^ sign_y,
exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64,
rmode, pfpsf);
BID_RETURN (res);
}
}
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