1 /* Copyright (C) 2007-2023 Free Software Foundation, Inc.
2
3 This file is part of GCC.
4
5 GCC is free software; you can redistribute it and/or modify it under
6 the terms of the GNU General Public License as published by the Free
7 Software Foundation; either version 3, or (at your option) any later
8 version.
9
10 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11 WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
13 for more details.
14
15 Under Section 7 of GPL version 3, you are granted additional
16 permissions described in the GCC Runtime Library Exception, version
17 3.1, as published by the Free Software Foundation.
18
19 You should have received a copy of the GNU General Public License and
20 a copy of the GCC Runtime Library Exception along with this program;
21 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
22 <http://www.gnu.org/licenses/>. */
23
24 /*****************************************************************************
25 * BID64 multiply
26 *****************************************************************************
27 *
28 * Algorithm description:
29 *
30 * if(number_digits(coefficient_x)+number_digits(coefficient_y) guaranteed
31 * below 16)
32 * return get_BID64(sign_x^sign_y, exponent_x + exponent_y - dec_bias,
33 * coefficient_x*coefficient_y)
34 * else
35 * get long product: coefficient_x*coefficient_y
36 * determine number of digits to round off (extra_digits)
37 * rounding is performed as a 128x128-bit multiplication by
38 * 2^M[extra_digits]/10^extra_digits, followed by a shift
39 * M[extra_digits] is sufficiently large for required accuracy
40 *
41 ****************************************************************************/
42
43 #include "bid_internal.h"
44
45 #if DECIMAL_CALL_BY_REFERENCE
46
47 void
48 bid64_mul (UINT64 * pres, UINT64 * px,
49 UINT64 *
50 py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
51 _EXC_INFO_PARAM) {
52 UINT64 x, y;
53 #else
54
55 UINT64
56 bid64_mul (UINT64 x,
57 UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
58 _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
59 #endif
60 UINT128 P, PU, C128, Q_high, Q_low, Stemp;
61 UINT64 sign_x, sign_y, coefficient_x, coefficient_y;
62 UINT64 C64, remainder_h, carry, CY, res;
63 UINT64 valid_x, valid_y;
64 int_double tempx, tempy;
65 int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
66 bin_expon_product;
67 int rmode, digits_p, bp, amount, amount2, final_exponent, round_up;
68 unsigned status, uf_status;
69
70 #if DECIMAL_CALL_BY_REFERENCE
71 #if !DECIMAL_GLOBAL_ROUNDING
72 _IDEC_round rnd_mode = *prnd_mode;
73 #endif
74 x = *px;
75 y = *py;
76 #endif
77
78 valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
79 valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
80
81 // unpack arguments, check for NaN or Infinity
82 if (!valid_x) {
83
84 #ifdef SET_STATUS_FLAGS
85 if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN
86 __set_status_flags (pfpsf, INVALID_EXCEPTION);
87 #endif
88 // x is Inf. or NaN
89
90 // test if x is NaN
91 if ((x & NAN_MASK64) == NAN_MASK64) {
92 #ifdef SET_STATUS_FLAGS
93 if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
94 __set_status_flags (pfpsf, INVALID_EXCEPTION);
95 #endif
96 BID_RETURN (coefficient_x & QUIET_MASK64);
97 }
98 // x is Infinity?
99 if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
100 // check if y is 0
101 if (((y & INFINITY_MASK64) != INFINITY_MASK64)
102 && !coefficient_y) {
103 #ifdef SET_STATUS_FLAGS
104 __set_status_flags (pfpsf, INVALID_EXCEPTION);
105 #endif
106 // y==0 , return NaN
107 BID_RETURN (NAN_MASK64);
108 }
109 // check if y is NaN
110 if ((y & NAN_MASK64) == NAN_MASK64)
111 // y==NaN , return NaN
112 BID_RETURN (coefficient_y & QUIET_MASK64);
113 // otherwise return +/-Inf
114 BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
115 }
116 // x is 0
117 if (((y & INFINITY_MASK64) != INFINITY_MASK64)) {
118 if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64)
119 exponent_y = ((UINT32) (y >> 51)) & 0x3ff;
120 else
121 exponent_y = ((UINT32) (y >> 53)) & 0x3ff;
122 sign_y = y & 0x8000000000000000ull;
123
124 exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
125 if (exponent_x > DECIMAL_MAX_EXPON_64)
126 exponent_x = DECIMAL_MAX_EXPON_64;
127 else if (exponent_x < 0)
128 exponent_x = 0;
129 BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
130 }
131 }
132 if (!valid_y) {
133 // y is Inf. or NaN
134
135 // test if y is NaN
136 if ((y & NAN_MASK64) == NAN_MASK64) {
137 #ifdef SET_STATUS_FLAGS
138 if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN
139 __set_status_flags (pfpsf, INVALID_EXCEPTION);
140 #endif
141 BID_RETURN (coefficient_y & QUIET_MASK64);
142 }
143 // y is Infinity?
144 if ((y & INFINITY_MASK64) == INFINITY_MASK64) {
145 // check if x is 0
146 if (!coefficient_x) {
147 __set_status_flags (pfpsf, INVALID_EXCEPTION);
148 // x==0, return NaN
149 BID_RETURN (NAN_MASK64);
150 }
151 // otherwise return +/-Inf
152 BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64);
153 }
154 // y is 0
155 exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
156 if (exponent_x > DECIMAL_MAX_EXPON_64)
157 exponent_x = DECIMAL_MAX_EXPON_64;
158 else if (exponent_x < 0)
159 exponent_x = 0;
160 BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53));
161 }
162 //--- get number of bits in the coefficients of x and y ---
163 // version 2 (original)
164 tempx.d = (double) coefficient_x;
165 bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52);
166 tempy.d = (double) coefficient_y;
167 bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52);
168
169 // magnitude estimate for coefficient_x*coefficient_y is
170 // 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx)
171 bin_expon_product = bin_expon_cx + bin_expon_cy;
172
173 // check if coefficient_x*coefficient_y<2^(10*k+3)
174 // equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1
175 if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) {
176 // easy multiply
177 C64 = coefficient_x * coefficient_y;
178
179 res =
180 get_BID64_small_mantissa (sign_x ^ sign_y,
181 exponent_x + exponent_y -
182 DECIMAL_EXPONENT_BIAS, C64, rnd_mode,
183 pfpsf);
184 BID_RETURN (res);
185 } else {
186 uf_status = 0;
187 // get 128-bit product: coefficient_x*coefficient_y
188 __mul_64x64_to_128 (P, coefficient_x, coefficient_y);
189
190 // tighten binary range of P: leading bit is 2^bp
191 // unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1
192 bin_expon_product -= 2 * BINARY_EXPONENT_BIAS;
193
194 __tight_bin_range_128 (bp, P, bin_expon_product);
195
196 // get number of decimal digits in the product
197 digits_p = estimate_decimal_digits[bp];
198 if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P)))
199 digits_p++; // if power10_table_128[digits_p] <= P
200
201 // determine number of decimal digits to be rounded out
202 extra_digits = digits_p - MAX_FORMAT_DIGITS;
203 final_exponent =
204 exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS;
205
206 #ifndef IEEE_ROUND_NEAREST_TIES_AWAY
207 #ifndef IEEE_ROUND_NEAREST
208 rmode = rnd_mode;
209 if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2)
210 rmode = 3 - rmode;
211 #else
212 rmode = 0;
213 #endif
214 #else
215 rmode = 0;
216 #endif
217
218 round_up = 0;
219 if (((unsigned) final_exponent) >= 3 * 256) {
220 if (final_exponent < 0) {
221 // underflow
222 if (final_exponent + 16 < 0) {
223 res = sign_x ^ sign_y;
224 __set_status_flags (pfpsf,
225 UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
226 if (rmode == ROUNDING_UP)
227 res |= 1;
228 BID_RETURN (res);
229 }
230
231 uf_status = UNDERFLOW_EXCEPTION;
232 if (final_exponent == -1) {
233 __add_128_64 (PU, P, round_const_table[rmode][extra_digits]);
234 if (__unsigned_compare_ge_128
235 (PU, power10_table_128[extra_digits + 16]))
236 uf_status = 0;
237 }
238 extra_digits -= final_exponent;
239 final_exponent = 0;
240
241 if (extra_digits > 17) {
242 __mul_128x128_full (Q_high, Q_low, P, reciprocals10_128[16]);
243
244 amount = recip_scale[16];
245 __shr_128 (P, Q_high, amount);
246
247 // get sticky bits
248 amount2 = 64 - amount;
249 remainder_h = 0;
250 remainder_h--;
251 remainder_h >>= amount2;
252 remainder_h = remainder_h & Q_high.w[0];
253
254 extra_digits -= 16;
255 if (remainder_h || (Q_low.w[1] > reciprocals10_128[16].w[1]
256 || (Q_low.w[1] ==
257 reciprocals10_128[16].w[1]
258 && Q_low.w[0] >=
259 reciprocals10_128[16].w[0]))) {
260 round_up = 1;
261 __set_status_flags (pfpsf,
262 UNDERFLOW_EXCEPTION |
263 INEXACT_EXCEPTION);
264 P.w[0] = (P.w[0] << 3) + (P.w[0] << 1);
265 P.w[0] |= 1;
266 extra_digits++;
267 }
268 }
269 } else {
270 res =
271 fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
272 1000000000000000ull, rnd_mode,
273 pfpsf);
274 BID_RETURN (res);
275 }
276 }
277
278
279 if (extra_digits > 0) {
280 // will divide by 10^(digits_p - 16)
281
282 // add a constant to P, depending on rounding mode
283 // 0.5*10^(digits_p - 16) for round-to-nearest
284 __add_128_64 (P, P, round_const_table[rmode][extra_digits]);
285
286 // get P*(2^M[extra_digits])/10^extra_digits
287 __mul_128x128_full (Q_high, Q_low, P,
288 reciprocals10_128[extra_digits]);
289
290 // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
291 amount = recip_scale[extra_digits];
292 __shr_128 (C128, Q_high, amount);
293
294 C64 = __low_64 (C128);
295
296 #ifndef IEEE_ROUND_NEAREST_TIES_AWAY
297 #ifndef IEEE_ROUND_NEAREST
298 if (rmode == 0) //ROUNDING_TO_NEAREST
299 #endif
300 if ((C64 & 1) && !round_up) {
301 // check whether fractional part of initial_P/10^extra_digits
302 // is exactly .5
303 // this is the same as fractional part of
304 // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero
305
306 // get remainder
307 remainder_h = Q_high.w[0] << (64 - amount);
308
309 // test whether fractional part is 0
310 if (!remainder_h
311 && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
312 || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
313 && Q_low.w[0] <
314 reciprocals10_128[extra_digits].w[0]))) {
315 C64--;
316 }
317 }
318 #endif
319
320 #ifdef SET_STATUS_FLAGS
321 status = INEXACT_EXCEPTION | uf_status;
322
323 // get remainder
324 remainder_h = Q_high.w[0] << (64 - amount);
325
326 switch (rmode) {
327 case ROUNDING_TO_NEAREST:
328 case ROUNDING_TIES_AWAY:
329 // test whether fractional part is 0
330 if (remainder_h == 0x8000000000000000ull
331 && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
332 || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
333 && Q_low.w[0] <
334 reciprocals10_128[extra_digits].w[0])))
335 status = EXACT_STATUS;
336 break;
337 case ROUNDING_DOWN:
338 case ROUNDING_TO_ZERO:
339 if (!remainder_h
340 && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1]
341 || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1]
342 && Q_low.w[0] <
343 reciprocals10_128[extra_digits].w[0])))
344 status = EXACT_STATUS;
345 break;
346 default:
347 // round up
348 __add_carry_out (Stemp.w[0], CY, Q_low.w[0],
349 reciprocals10_128[extra_digits].w[0]);
350 __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1],
351 reciprocals10_128[extra_digits].w[1], CY);
352 if ((remainder_h >> (64 - amount)) + carry >=
353 (((UINT64) 1) << amount))
354 status = EXACT_STATUS;
355 }
356
357 __set_status_flags (pfpsf, status);
358 #endif
359
360 // convert to BID and return
361 res =
362 fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, C64,
363 rmode, pfpsf);
364 BID_RETURN (res);
365 }
366 // go to convert_format and exit
367 C64 = __low_64 (P);
368 res =
369 get_BID64 (sign_x ^ sign_y,
370 exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64,
371 rmode, pfpsf);
372 BID_RETURN (res);
373 }
374 }