/* Copyright (C) 2007 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 2, or (at your option) any later version. In addition to the permissions in the GNU General Public License, the Free Software Foundation gives you unlimited permission to link the compiled version of this file into combinations with other programs, and to distribute those combinations without any restriction coming from the use of this file. (The General Public License restrictions do apply in other respects; for example, they cover modification of the file, and distribution when not linked into a combine executable.) 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. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING. If not, write to the Free Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /***************************************************************************** * BID64 add ***************************************************************************** * * Algorithm description: * * if(exponent_a < exponent_b) * switch a, b * diff_expon = exponent_a - exponent_b * if(diff_expon > 16) * return normalize(a) * if(coefficient_a*10^diff_expon guaranteed below 2^62) * S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b * if(|S|<10^16) * return get_BID64(sign(S),exponent_b,|S|) * else * determine number of extra digits in S (1, 2, or 3) * return rounded result * else // large exponent difference * if(number_digits(coefficient_a*10^diff_expon) +/- 10^16) * guaranteed the same as * number_digits(coefficient_a*10^diff_expon) ) * S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon)) * corr = 10^16 + (sign_a^sign_b)*coefficient_b * corr*10^exponent_b is rounded so it aligns with S*10^exponent_S * return get_BID64(sign_a,exponent(S),S+rounded(corr)) * else * add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b * in 128-bit integer arithmetic, then round to 16 decimal digits * * ****************************************************************************/ #include "bid_internal.h" #if DECIMAL_CALL_BY_REFERENCE void bid64_add (UINT64 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM); #else UINT64 bid64_add (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM); #endif #if DECIMAL_CALL_BY_REFERENCE void bid64_sub (UINT64 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 y = *py; #if !DECIMAL_GLOBAL_ROUNDING _IDEC_round rnd_mode = *prnd_mode; #endif // check if y is not NaN if (((y & NAN_MASK64) != NAN_MASK64)) y ^= 0x8000000000000000ull; bid64_add (pres, px, &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); } #else UINT64 bid64_sub (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { // check if y is not NaN if (((y & NAN_MASK64) != NAN_MASK64)) y ^= 0x8000000000000000ull; return bid64_add (x, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); } #endif #if DECIMAL_CALL_BY_REFERENCE void bid64_add (UINT64 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x, y; #else UINT64 bid64_add (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 CA, CT, CT_new; UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new; UINT64 valid_x, valid_y; UINT64 res; UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab, rem_a; UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp; int_double tempx; int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon; int bin_expon_ca, extra_digits, amount, scale_k, scale_ca; unsigned rmode, 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) { // 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 || ((y & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = coefficient_x & QUIET_MASK64; BID_RETURN (res); } // x is Infinity? if ((x & INFINITY_MASK64) == INFINITY_MASK64) { // check if y is Inf if (((y & NAN_MASK64) == INFINITY_MASK64)) { if (sign_x == (y & 0x8000000000000000ull)) { res = coefficient_x; BID_RETURN (res); } // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = NAN_MASK64; BID_RETURN (res); } } // check if y is NaN if (((y & NAN_MASK64) == NAN_MASK64)) { res = coefficient_y & QUIET_MASK64; #ifdef SET_STATUS_FLAGS if (((y & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (res); } // otherwise return +/-Inf { res = coefficient_x; BID_RETURN (res); } } // x is 0 { if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y) { if (exponent_y <= exponent_x) { res = y; BID_RETURN (res); } } } } if (!valid_y) { // y is Inf. or NaN? if (((y & INFINITY_MASK64) == INFINITY_MASK64)) { #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = coefficient_y & QUIET_MASK64; BID_RETURN (res); } // y is 0 if (!coefficient_x) { // x==0 if (exponent_x <= exponent_y) res = ((UINT64) exponent_x) << 53; else res = ((UINT64) exponent_y) << 53; if (sign_x == sign_y) res |= sign_x; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rnd_mode == ROUNDING_DOWN && sign_x != sign_y) res |= 0x8000000000000000ull; #endif #endif BID_RETURN (res); } else if (exponent_y >= exponent_x) { res = x; BID_RETURN (res); } } // sort arguments by exponent if (exponent_x < exponent_y) { sign_a = sign_y; exponent_a = exponent_y; coefficient_a = coefficient_y; sign_b = sign_x; exponent_b = exponent_x; coefficient_b = coefficient_x; } else { sign_a = sign_x; exponent_a = exponent_x; coefficient_a = coefficient_x; sign_b = sign_y; exponent_b = exponent_y; coefficient_b = coefficient_y; } // exponent difference diff_dec_expon = exponent_a - exponent_b; /* 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_a; bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; if (diff_dec_expon > MAX_FORMAT_DIGITS) { // normalize a to a 16-digit coefficient scale_ca = estimate_decimal_digits[bin_expon_ca]; if (coefficient_a >= power10_table_128[scale_ca].w[0]) scale_ca++; scale_k = 16 - scale_ca; coefficient_a *= power10_table_128[scale_k].w[0]; diff_dec_expon -= scale_k; exponent_a -= scale_k; /* get binary coefficients of x and y */ //--- get number of bits in the coefficients of x and y --- tempx.d = (double) coefficient_a; bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; if (diff_dec_expon > MAX_FORMAT_DIGITS) { #ifdef SET_STATUS_FLAGS if (coefficient_b) { __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (((rnd_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST { switch (rnd_mode) { case ROUNDING_DOWN: if (sign_b) { coefficient_a -= ((((SINT64) sign_a) >> 63) | 1); if (coefficient_a < 1000000000000000ull) { exponent_a--; coefficient_a = 9999999999999999ull; } else if (coefficient_a >= 10000000000000000ull) { exponent_a++; coefficient_a = 1000000000000000ull; } } break; case ROUNDING_UP: if (!sign_b) { coefficient_a += ((((SINT64) sign_a) >> 63) | 1); if (coefficient_a < 1000000000000000ull) { exponent_a--; coefficient_a = 9999999999999999ull; } else if (coefficient_a >= 10000000000000000ull) { exponent_a++; coefficient_a = 1000000000000000ull; } } break; default: // RZ if (sign_a != sign_b) { coefficient_a--; if (coefficient_a < 1000000000000000ull) { exponent_a--; coefficient_a = 9999999999999999ull; } } break; } } else #endif #endif // check special case here if ((coefficient_a == 1000000000000000ull) && (diff_dec_expon == MAX_FORMAT_DIGITS + 1) && (sign_a ^ sign_b) && (coefficient_b > 5000000000000000ull)) { coefficient_a = 9999999999999999ull; exponent_a--; } res = fast_get_BID64_check_OF (sign_a, exponent_a, coefficient_a, rnd_mode, pfpsf); BID_RETURN (res); } } // test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62 if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) { // coefficient_a*10^(exponent_a-exponent_b)<2^63 // multiply by 10^(exponent_a-exponent_b) coefficient_a *= power10_table_128[diff_dec_expon].w[0]; // sign mask sign_b = ((SINT64) sign_b) >> 63; // apply sign to coeff. of b coefficient_b = (coefficient_b + sign_b) ^ sign_b; // apply sign to coefficient a sign_a = ((SINT64) sign_a) >> 63; coefficient_a = (coefficient_a + sign_a) ^ sign_a; coefficient_a += coefficient_b; // get sign sign_s = ((SINT64) coefficient_a) >> 63; coefficient_a = (coefficient_a + sign_s) ^ sign_s; sign_s &= 0x8000000000000000ull; // coefficient_a < 10^16 ? if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) { #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rnd_mode == ROUNDING_DOWN && (!coefficient_a) && sign_a != sign_b) sign_s = 0x8000000000000000ull; #endif #endif res = very_fast_get_BID64 (sign_s, exponent_b, coefficient_a); BID_RETURN (res); } // otherwise rounding is necessary // already know coefficient_a<10^19 // coefficient_a < 10^17 ? if (coefficient_a < power10_table_128[17].w[0]) extra_digits = 1; else if (coefficient_a < power10_table_128[18].w[0]) extra_digits = 2; else extra_digits = 3; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST rmode = rnd_mode; if (sign_s && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif coefficient_a += round_const_table[rmode][extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits __mul_64x64_to_128 (CT, coefficient_a, reciprocals10_64[extra_digits]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[extra_digits]; C64 = CT.w[1] >> amount; } else { // coefficient_a*10^(exponent_a-exponent_b) is large sign_s = sign_a; #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST rmode = rnd_mode; if (sign_s && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif // check whether we can take faster path scale_ca = estimate_decimal_digits[bin_expon_ca]; sign_ab = sign_a ^ sign_b; sign_ab = ((SINT64) sign_ab) >> 63; // T1 = 10^(16-diff_dec_expon) T1 = power10_table_128[16 - diff_dec_expon].w[0]; // get number of digits in coefficient_a if (coefficient_a >= power10_table_128[scale_ca].w[0]) { scale_ca++; } scale_k = 16 - scale_ca; // addition saved_ca = coefficient_a - T1; coefficient_a = (SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0]; extra_digits = diff_dec_expon - scale_k; // apply sign saved_cb = (coefficient_b + sign_ab) ^ sign_ab; // add 10^16 and rounding constant coefficient_b = saved_cb + 10000000000000000ull + round_const_table[rmode][extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits __mul_64x64_to_128 (CT, coefficient_b, reciprocals10_64[extra_digits]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[extra_digits]; C0_64 = CT.w[1] >> amount; // result coefficient C64 = C0_64 + coefficient_a; // filter out difficult (corner) cases // this test ensures the number of digits in coefficient_a does not change // after adding (the appropriately scaled and rounded) coefficient_b if ((UINT64) (C64 - 1000000000000000ull - 1) > 9000000000000000ull - 2) { if (C64 >= 10000000000000000ull) { // result has more than 16 digits if (!scale_k) { // must divide coeff_a by 10 saved_ca = saved_ca + T1; __mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull); //reciprocals10_64[1]); coefficient_a = CA.w[1] >> 1; rem_a = saved_ca - (coefficient_a << 3) - (coefficient_a << 1); coefficient_a = coefficient_a - T1; saved_cb += rem_a * power10_table_128[diff_dec_expon].w[0]; } else coefficient_a = (SINT64) (saved_ca - T1 - (T1 << 3)) * (SINT64) power10_table_128[scale_k - 1].w[0]; extra_digits++; coefficient_b = saved_cb + 100000000000000000ull + round_const_table[rmode][extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits __mul_64x64_to_128 (CT, coefficient_b, reciprocals10_64[extra_digits]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[extra_digits]; C0_64 = CT.w[1] >> amount; // result coefficient C64 = C0_64 + coefficient_a; } else if (C64 <= 1000000000000000ull) { // less than 16 digits in result coefficient_a = (SINT64) saved_ca *(SINT64) power10_table_128[scale_k + 1].w[0]; //extra_digits --; exponent_b--; coefficient_b = (saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull + round_const_table[rmode][extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits __mul_64x64_to_128 (CT_new, coefficient_b, reciprocals10_64[extra_digits]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[extra_digits]; C0_64 = CT_new.w[1] >> amount; // result coefficient C64_new = C0_64 + coefficient_a; if (C64_new < 10000000000000000ull) { C64 = C64_new; #ifdef SET_STATUS_FLAGS CT = CT_new; #endif } else exponent_b++; } } } #ifndef IEEE_ROUND_NEAREST_TIES_AWAY #ifndef IEEE_ROUND_NEAREST if (rmode == 0) //ROUNDING_TO_NEAREST #endif if (C64 & 1) { // 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 = CT.w[1] << (64 - amount); // test whether fractional part is 0 if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) { C64--; } } #endif #ifdef SET_STATUS_FLAGS status = INEXACT_EXCEPTION; // get remainder remainder_h = CT.w[1] << (64 - amount); switch (rmode) { case ROUNDING_TO_NEAREST: case ROUNDING_TIES_AWAY: // test whether fractional part is 0 if ((remainder_h == 0x8000000000000000ull) && (CT.w[0] < reciprocals10_64[extra_digits])) status = EXACT_STATUS; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) status = EXACT_STATUS; //if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y; break; default: // round up __add_carry_out (tmp, carry, CT.w[0], reciprocals10_64[extra_digits]); if ((remainder_h >> (64 - amount)) + carry >= (((UINT64) 1) << amount)) status = EXACT_STATUS; break; } __set_status_flags (pfpsf, status); #endif res = fast_get_BID64_check_OF (sign_s, exponent_b + extra_digits, C64, rnd_mode, pfpsf); BID_RETURN (res); }