bid64_rem.c revision 1.1 
1/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
2
3This file is part of GCC.
4
5GCC is free software; you can redistribute it and/or modify it under
6the terms of the GNU General Public License as published by the Free
7Software Foundation; either version 3, or (at your option) any later
8version.
9
10GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11WARRANTY; without even the implied warranty of MERCHANTABILITY or
12FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
13for more details.
14
15Under Section 7 of GPL version 3, you are granted additional
16permissions described in the GCC Runtime Library Exception, version
173.1, as published by the Free Software Foundation.
18
19You should have received a copy of the GNU General Public License and
20a copy of the GCC Runtime Library Exception along with this program;
21see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
22<http://www.gnu.org/licenses/>.  */
23
24/*****************************************************************************
25 *    BID64 remainder
26 *****************************************************************************
27 *
28 *  Algorithm description:
29 *
30 *  if(exponent_x < exponent_y)
31 *    scale coefficient_y so exponents are aligned
32 *    perform coefficient divide (64-bit integer divide), unless
33 *            coefficient_y is longer than 64 bits (clearly larger
34 *                                               than coefficient_x)
35 *  else  // exponent_x > exponent_y
36 *     use a loop to scale coefficient_x to 18_digits, divide by
37 *         coefficient_y (64-bit integer divide), calculate remainder
38 *         as new_coefficient_x and repeat until final remainder is obtained
39 *         (when new_exponent_x < exponent_y)
40 *
41 ****************************************************************************/
42
43#include "bid_internal.h"
44
45#define MAX_FORMAT_DIGITS     16
46#define DECIMAL_EXPONENT_BIAS 398
47#define MASK_BINARY_EXPONENT  0x7ff0000000000000ull
48#define BINARY_EXPONENT_BIAS  0x3ff
49#define UPPER_EXPON_LIMIT     51
50
51#if DECIMAL_CALL_BY_REFERENCE
52
53void
54bid64_rem (UINT64 * pres, UINT64 * px,
55	   UINT64 *
56	   py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
57  UINT64 x, y;
58#else
59
60UINT64
61bid64_rem (UINT64 x,
62	   UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
63#endif
64  UINT128 CY;
65  UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
66  UINT64 Q, R, R2, T, valid_y, valid_x;
67  int_float tempx;
68  int exponent_x, exponent_y, bin_expon, e_scale;
69  int digits_x, diff_expon;
70
71#if DECIMAL_CALL_BY_REFERENCE
72  x = *px;
73  y = *py;
74#endif
75
76  valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
77  valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
78
79  // unpack arguments, check for NaN or Infinity
80  if (!valid_x) {
81    // x is Inf. or NaN or 0
82#ifdef SET_STATUS_FLAGS
83    if ((y & SNAN_MASK64) == SNAN_MASK64)	// y is sNaN
84      __set_status_flags (pfpsf, INVALID_EXCEPTION);
85#endif
86
87    // test if x is NaN
88    if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
89#ifdef SET_STATUS_FLAGS
90      if (((x & SNAN_MASK64) == SNAN_MASK64))
91	__set_status_flags (pfpsf, INVALID_EXCEPTION);
92#endif
93      res = coefficient_x & QUIET_MASK64;;
94      BID_RETURN (res);
95    }
96    // x is Infinity?
97    if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
98      if (((y & NAN_MASK64) != NAN_MASK64)) {
99#ifdef SET_STATUS_FLAGS
100	__set_status_flags (pfpsf, INVALID_EXCEPTION);
101#endif
102	// return NaN
103	res = 0x7c00000000000000ull;
104	BID_RETURN (res);
105      }
106    }
107    // x is 0
108    // return x if y != 0
109    if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
110	coefficient_y) {
111      if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
112	exponent_y = (y >> 51) & 0x3ff;
113      else
114	exponent_y = (y >> 53) & 0x3ff;
115
116      if (exponent_y < exponent_x)
117	exponent_x = exponent_y;
118
119      x = exponent_x;
120      x <<= 53;
121
122      res = x | sign_x;
123      BID_RETURN (res);
124    }
125
126  }
127  if (!valid_y) {
128    // y is Inf. or NaN
129
130    // test if y is NaN
131    if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
132#ifdef SET_STATUS_FLAGS
133      if (((y & SNAN_MASK64) == SNAN_MASK64))
134	__set_status_flags (pfpsf, INVALID_EXCEPTION);
135#endif
136      res = coefficient_y & QUIET_MASK64;;
137      BID_RETURN (res);
138    }
139    // y is Infinity?
140    if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
141      res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
142      BID_RETURN (res);
143    }
144    // y is 0, return NaN
145    {
146#ifdef SET_STATUS_FLAGS
147      __set_status_flags (pfpsf, INVALID_EXCEPTION);
148#endif
149      res = 0x7c00000000000000ull;
150      BID_RETURN (res);
151    }
152  }
153
154
155  diff_expon = exponent_x - exponent_y;
156  if (diff_expon <= 0) {
157    diff_expon = -diff_expon;
158
159    if (diff_expon > 16) {
160      // |x|<|y| in this case
161      res = x;
162      BID_RETURN (res);
163    }
164    // set exponent of y to exponent_x, scale coefficient_y
165    T = power10_table_128[diff_expon].w[0];
166    __mul_64x64_to_128 (CY, coefficient_y, T);
167
168    if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
169      res = x;
170      BID_RETURN (res);
171    }
172
173    Q = coefficient_x / CY.w[0];
174    R = coefficient_x - Q * CY.w[0];
175
176    R2 = R + R;
177    if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
178      R = CY.w[0] - R;
179      sign_x ^= 0x8000000000000000ull;
180    }
181
182    res = very_fast_get_BID64 (sign_x, exponent_x, R);
183    BID_RETURN (res);
184  }
185
186
187  while (diff_expon > 0) {
188    // get number of digits in coeff_x
189    tempx.d = (float) coefficient_x;
190    bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
191    digits_x = estimate_decimal_digits[bin_expon];
192    // will not use this test, dividend will have 18 or 19 digits
193    //if(coefficient_x >= power10_table_128[digits_x].w[0])
194    //      digits_x++;
195
196    e_scale = 18 - digits_x;
197    if (diff_expon >= e_scale) {
198      diff_expon -= e_scale;
199    } else {
200      e_scale = diff_expon;
201      diff_expon = 0;
202    }
203
204    // scale dividend to 18 or 19 digits
205    coefficient_x *= power10_table_128[e_scale].w[0];
206
207    // quotient
208    Q = coefficient_x / coefficient_y;
209    // remainder
210    coefficient_x -= Q * coefficient_y;
211
212    // check for remainder == 0
213    if (!coefficient_x) {
214      res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
215      BID_RETURN (res);
216    }
217  }
218
219  R2 = coefficient_x + coefficient_x;
220  if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
221    coefficient_x = coefficient_y - coefficient_x;
222    sign_x ^= 0x8000000000000000ull;
223  }
224
225  res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
226  BID_RETURN (res);
227
228}
229