--- /dev/null
+/* Copyright (C) 2007, 2009 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);
+ }
+}
projects / msp430-gcc.git / blobdiff