1 /*
2   (C) Copyright 2001,2006,
3   International Business Machines Corporation,
4   Sony Computer Entertainment, Incorporated,
5   Toshiba Corporation,
6 
7   All rights reserved.
8 
9   Redistribution and use in source and binary forms, with or without
10   modification, are permitted provided that the following conditions are met:
11 
12     * Redistributions of source code must retain the above copyright notice,
13   this list of conditions and the following disclaimer.
14     * Redistributions in binary form must reproduce the above copyright
15   notice, this list of conditions and the following disclaimer in the
16   documentation and/or other materials provided with the distribution.
17     * Neither the names of the copyright holders nor the names of their
18   contributors may be used to endorse or promote products derived from this
19   software without specific prior written permission.
20 
21   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
22   IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
23   TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
24   PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
25   OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
26   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
27   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
28   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
29   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
30   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
31   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32 */
33 #ifndef _REMAINDER_H_
34 #define _REMAINDER_H_	1
35 
36 #include <spu_intrinsics.h>
37 #include "headers/vec_literal.h"
38 
_remainder(double x,double y)39 static __inline double _remainder(double x, double y)
40 {
41   int n, shift;
42   vec_uchar16 swap_words = VEC_LITERAL(vec_uchar16, 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11);
43   vec_uchar16 propagate = VEC_LITERAL(vec_uchar16, 4,5,6,7, 192,192,192,192, 12,13,14,15, 192,192,192,192);
44   vec_uchar16 splat_hi = VEC_LITERAL(vec_uchar16, 0,1,2,3,0,1,2,3, 8,9,10,11, 8,9,10,11);
45   vec_uchar16 splat_lo = VEC_LITERAL(vec_uchar16, 4,5,6,7,4,5,6,7, 12,13,14,15, 12,13,14,15);
46   vec_uint4 vx, vy, z;
47   vec_uint4 x_hi, y_hi, y_lo;
48   vec_uint4 abs_x, abs_y, abs_2x, abs_2y;
49   vec_uint4 exp_x, exp_y;
50   vec_uint4 zero_x, zero_y;
51   vec_uint4 logb_x, logb_y;
52   vec_uint4 mant_x, mant_y;
53   vec_uint4 normal, norm, denorm;
54   vec_uint4 gt, eq, bias, y2_hi;
55   vec_uint4 nan_out;
56   vec_uint4 result, result0, resultx, cnt, sign, borrow;
57   vec_uint4 exp_special = VEC_SPLAT_U32(0x7FF00000);
58   vec_uint4 half_smax = VEC_SPLAT_U32(0x7FEFFFFF);
59   vec_uint4 lsb       = (vec_uint4)(VEC_SPLAT_U64(0x0000000000000001ULL));
60   vec_uint4 sign_mask = (vec_uint4)(VEC_SPLAT_U64(0x8000000000000000ULL));
61   vec_uint4 implied_1 = (vec_uint4)(VEC_SPLAT_U64(0x0010000000000000ULL));
62   vec_uint4 mant_mask = (vec_uint4)(VEC_SPLAT_U64(0x000FFFFFFFFFFFFFULL));
63 
64   vx = (vec_uint4)spu_promote(x, 0);
65   vy = (vec_uint4)spu_promote(y, 0);
66 
67   abs_x = spu_andc(vx, sign_mask);
68   abs_y = spu_andc(vy, sign_mask);
69 
70   abs_2y = spu_add(abs_y, implied_1);
71 
72   sign = spu_and(vx, sign_mask);
73 
74 
75   /* Compute abs_x = fmodf(abs_x, 2*abs_y). If y is greater than 0.5*SMAX (SMAX is the maximum
76    * representable float), then return abs_x.
77    */
78   {
79     x_hi = spu_shuffle(abs_x, abs_x, splat_hi);
80     y_lo = spu_shuffle(abs_y, abs_y, splat_lo);
81     y_hi = spu_shuffle(abs_y, abs_y, splat_hi);
82     y2_hi = spu_shuffle(abs_2y, abs_2y, splat_hi);
83 
84     /* Force a NaN output if (1) abs_x is infinity or NaN or (2)
85      * abs_y is a NaN.
86      */
87     nan_out = spu_or(spu_cmpgt(x_hi, half_smax),
88                      spu_or(spu_cmpgt(y_hi, exp_special),
89                             spu_and(spu_cmpeq(y_hi, exp_special),
90                                     spu_cmpgt(y_lo, 0))));
91 
92     /* Determine ilogb of abs_x and abs_y and
93      * extract the mantissas (mant_x, mant_y)
94      */
95     exp_x  = spu_rlmask(x_hi, -20);
96     exp_y  = spu_rlmask(y2_hi, -20);
97 
98     resultx = spu_or(spu_cmpgt(y2_hi, x_hi), spu_cmpgt(y_hi, half_smax));
99 
100     zero_x = spu_cmpeq(exp_x, 0);
101     zero_y = spu_cmpeq(exp_y, 0);
102 
103     logb_x = spu_add(exp_x, -1023);
104     logb_y = spu_add(exp_y, -1023);
105 
106     mant_x = spu_andc(spu_sel(implied_1, abs_x, mant_mask), zero_x);
107     mant_y = spu_andc(spu_sel(implied_1, abs_2y, mant_mask), zero_y);
108 
109     /* Compute fixed point fmod of mant_x and mant_y. Set the flag,
110      * result0, to all ones if we detect that the final result is
111      * ever 0.
112      */
113     result0 = spu_or(zero_x, zero_y);
114 
115     n = spu_extract(spu_sub(logb_x, logb_y), 0);
116 
117     while (n-- > 0) {
118       borrow = spu_genb(mant_x, mant_y);
119       borrow = spu_shuffle(borrow, borrow, propagate);
120       z = spu_subx(mant_x, mant_y, borrow);
121 
122       result0 = spu_or(spu_cmpeq(spu_or(z, spu_shuffle(z, z, swap_words)), 0), result0);
123 
124       mant_x = spu_sel(spu_slqw(mant_x, 1), spu_andc(spu_slqw(z, 1), lsb), spu_cmpgt((vec_int4)spu_shuffle(z, z, splat_hi), -1));
125     }
126 
127 
128     borrow = spu_genb(mant_x, mant_y);
129     borrow = spu_shuffle(borrow, borrow, propagate);
130     z = spu_subx(mant_x, mant_y, borrow);
131 
132     mant_x = spu_sel(mant_x, z, spu_cmpgt((vec_int4)spu_shuffle(z, z, splat_hi), -1));
133     mant_x = spu_andc(mant_x, VEC_LITERAL(vec_uint4, 0,0,-1,-1));
134 
135     result0 = spu_or(spu_cmpeq(spu_or(mant_x, spu_shuffle(mant_x, mant_x, swap_words)), 0), result0);
136 
137     /* Convert the result back to floating point and restore
138      * the sign. If we flagged the result to be zero (result0),
139      * zero it. If we flagged the result to equal its input x,
140      * (resultx) then return x.
141      *
142      * Double precision generates a denorm for an output.
143      */
144     cnt = spu_cntlz(mant_x);
145     cnt = spu_add(cnt, spu_and(spu_rlqwbyte(cnt, 4), spu_cmpeq(cnt, 32)));
146     cnt = spu_add(spu_shuffle(cnt, cnt, splat_hi), -11);
147 
148     shift = spu_extract(exp_y, 0) - 1;
149     denorm = spu_slqwbytebc(spu_slqw(mant_x, shift), shift);
150 
151     exp_y = spu_sub(exp_y, cnt);
152 
153     normal = spu_cmpgt((vec_int4)exp_y, 0);
154 
155     /* Normalize normal results, denormalize denorm results.
156      */
157     shift = spu_extract(cnt, 0);
158     norm = spu_slqwbytebc(spu_slqw(spu_andc(mant_x, VEC_LITERAL(vec_uint4, 0x00100000, 0, -1, -1)), shift), shift);
159 
160     mant_x = spu_sel(denorm, norm, normal);
161 
162     exp_y = spu_and(spu_rl(exp_y, 20), normal);
163 
164     result = spu_sel(exp_y, mant_x, mant_mask);
165 
166     abs_x = spu_sel(spu_andc(result, spu_rlmask(result0, -1)), abs_x, resultx);
167 
168   }
169 
170   /* if (2*x > y)
171    *     x -= y
172    *     if (2*x >= y) x -= y
173    */
174   abs_2x = spu_and(spu_add(abs_x, implied_1), normal);
175 
176   gt = spu_cmpgt(abs_2x, abs_y);
177   eq = spu_cmpeq(abs_2x, abs_y);
178   bias = spu_or(gt, spu_and(eq, spu_rlqwbyte(gt, 4)));
179   bias = spu_shuffle(bias, bias, splat_hi);
180   abs_x = spu_sel(abs_x, (vec_uint4)spu_sub((vec_double2)abs_x, (vec_double2)abs_y), bias);
181 
182   bias = spu_andc(bias, spu_rlmaska((vec_uint4)spu_msub((vec_double2)abs_x, VEC_SPLAT_F64(2.0), (vec_double2)abs_y), -31));
183   bias = spu_shuffle(bias, bias, splat_hi);
184   abs_x = spu_sel(abs_x, (vec_uint4)spu_sub((vec_double2)abs_x, (vec_double2)abs_y), bias);
185 
186   /* Generate a correct final sign
187    */
188   result = spu_sel(spu_xor(abs_x, sign), exp_special, nan_out);
189 
190   return (spu_extract((vec_double2)result, 0));
191 }
192 #endif /* _REMAINDER_H_ */
193