/* 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 . */ /***************************************************************************** * BID64 remainder ***************************************************************************** * * Algorithm description: * * if(exponent_x < exponent_y) * scale coefficient_y so exponents are aligned * perform coefficient divide (64-bit integer divide), unless * coefficient_y is longer than 64 bits (clearly larger * than coefficient_x) * else // exponent_x > exponent_y * use a loop to scale coefficient_x to 18_digits, divide by * coefficient_y (64-bit integer divide), calculate remainder * as new_coefficient_x and repeat until final remainder is obtained * (when new_exponent_x < exponent_y) * ****************************************************************************/ #include "bid_internal.h" #define MAX_FORMAT_DIGITS 16 #define DECIMAL_EXPONENT_BIAS 398 #define MASK_BINARY_EXPONENT 0x7ff0000000000000ull #define BINARY_EXPONENT_BIAS 0x3ff #define UPPER_EXPON_LIMIT 51 #if DECIMAL_CALL_BY_REFERENCE void bid64_rem (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x, y; #else UINT64 bid64_rem (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 CY; UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res; UINT64 Q, R, R2, T, valid_y, valid_x; int_float tempx; int exponent_x, exponent_y, bin_expon, e_scale; int digits_x, diff_expon; #if DECIMAL_CALL_BY_REFERENCE x = *px; y = *py; #endif valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); // unpack arguments, check for NaN or Infinity if (!valid_x) { // x is Inf. or NaN or 0 #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // test if x is NaN if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if (((x & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = coefficient_x & QUIET_MASK64;; BID_RETURN (res); } // x is Infinity? if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { if (((y & NAN_MASK64) != NAN_MASK64)) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } } // x is 0 // return x if y != 0 if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) && coefficient_y) { if ((y & 0x6000000000000000ull) == 0x6000000000000000ull) exponent_y = (y >> 51) & 0x3ff; else exponent_y = (y >> 53) & 0x3ff; if (exponent_y < exponent_x) exponent_x = exponent_y; x = exponent_x; x <<= 53; res = x | sign_x; BID_RETURN (res); } } if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if (((y & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = coefficient_y & QUIET_MASK64;; BID_RETURN (res); } // y is Infinity? if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) { res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x); BID_RETURN (res); } // y is 0, return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } } diff_expon = exponent_x - exponent_y; if (diff_expon <= 0) { diff_expon = -diff_expon; if (diff_expon > 16) { // |x|<|y| in this case res = x; BID_RETURN (res); } // set exponent of y to exponent_x, scale coefficient_y T = power10_table_128[diff_expon].w[0]; __mul_64x64_to_128 (CY, coefficient_y, T); if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) { res = x; BID_RETURN (res); } Q = coefficient_x / CY.w[0]; R = coefficient_x - Q * CY.w[0]; R2 = R + R; if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) { R = CY.w[0] - R; sign_x ^= 0x8000000000000000ull; } res = very_fast_get_BID64 (sign_x, exponent_x, R); BID_RETURN (res); } while (diff_expon > 0) { // get number of digits in coeff_x tempx.d = (float) coefficient_x; bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f; digits_x = estimate_decimal_digits[bin_expon]; // will not use this test, dividend will have 18 or 19 digits //if(coefficient_x >= power10_table_128[digits_x].w[0]) // digits_x++; e_scale = 18 - digits_x; if (diff_expon >= e_scale) { diff_expon -= e_scale; } else { e_scale = diff_expon; diff_expon = 0; } // scale dividend to 18 or 19 digits coefficient_x *= power10_table_128[e_scale].w[0]; // quotient Q = coefficient_x / coefficient_y; // remainder coefficient_x -= Q * coefficient_y; // check for remainder == 0 if (!coefficient_x) { res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0); BID_RETURN (res); } } R2 = coefficient_x + coefficient_x; if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) { coefficient_x = coefficient_y - coefficient_x; sign_x ^= 0x8000000000000000ull; } res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x); BID_RETURN (res); }