123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228 |
- /* Copyright (C) 2007-2022 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 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);
- }
|