1 /*
2
3 fp_trig.c: floating-point math routines for the Linux-m68k
4 floating point emulator.
5
6 Copyright (c) 1998-1999 David Huggins-Daines / Roman Zippel.
7
8 I hereby give permission, free of charge, to copy, modify, and
9 redistribute this software, in source or binary form, provided that
10 the above copyright notice and the following disclaimer are included
11 in all such copies.
12
13 THIS SOFTWARE IS PROVIDED "AS IS", WITH ABSOLUTELY NO WARRANTY, REAL
14 OR IMPLIED.
15
16 */
17
18 #include "fp_emu.h"
19
20 static const struct fp_ext fp_one =
21 {
22 .exp = 0x3fff,
23 };
24
25 extern struct fp_ext *fp_fadd(struct fp_ext *dest, const struct fp_ext *src);
26 extern struct fp_ext *fp_fdiv(struct fp_ext *dest, const struct fp_ext *src);
27
28 struct fp_ext *
fp_fsqrt(struct fp_ext * dest,struct fp_ext * src)29 fp_fsqrt(struct fp_ext *dest, struct fp_ext *src)
30 {
31 struct fp_ext tmp, src2;
32 int i, exp;
33
34 dprint(PINSTR, "fsqrt\n");
35
36 fp_monadic_check(dest, src);
37
38 if (IS_ZERO(dest))
39 return dest;
40
41 if (dest->sign) {
42 fp_set_nan(dest);
43 return dest;
44 }
45 if (IS_INF(dest))
46 return dest;
47
48 /*
49 * sqrt(m) * 2^(p) , if e = 2*p
50 * sqrt(m*2^e) =
51 * sqrt(2*m) * 2^(p) , if e = 2*p + 1
52 *
53 * So we use the last bit of the exponent to decide whether to
54 * use the m or 2*m.
55 *
56 * Since only the fractional part of the mantissa is stored and
57 * the integer part is assumed to be one, we place a 1 or 2 into
58 * the fixed point representation.
59 */
60 exp = dest->exp;
61 dest->exp = 0x3FFF;
62 if (!(exp & 1)) /* lowest bit of exponent is set */
63 dest->exp++;
64 fp_copy_ext(&src2, dest);
65
66 /*
67 * The taylor row around a for sqrt(x) is:
68 * sqrt(x) = sqrt(a) + 1/(2*sqrt(a))*(x-a) + R
69 * With a=1 this gives:
70 * sqrt(x) = 1 + 1/2*(x-1)
71 * = 1/2*(1+x)
72 */
73 fp_fadd(dest, &fp_one);
74 dest->exp--; /* * 1/2 */
75
76 /*
77 * We now apply the newton rule to the function
78 * f(x) := x^2 - r
79 * which has a null point on x = sqrt(r).
80 *
81 * It gives:
82 * x' := x - f(x)/f'(x)
83 * = x - (x^2 -r)/(2*x)
84 * = x - (x - r/x)/2
85 * = (2*x - x + r/x)/2
86 * = (x + r/x)/2
87 */
88 for (i = 0; i < 9; i++) {
89 fp_copy_ext(&tmp, &src2);
90
91 fp_fdiv(&tmp, dest);
92 fp_fadd(dest, &tmp);
93 dest->exp--;
94 }
95
96 dest->exp += (exp - 0x3FFF) / 2;
97
98 return dest;
99 }
100
101 struct fp_ext *
fp_fetoxm1(struct fp_ext * dest,struct fp_ext * src)102 fp_fetoxm1(struct fp_ext *dest, struct fp_ext *src)
103 {
104 uprint("fetoxm1\n");
105
106 fp_monadic_check(dest, src);
107
108 return dest;
109 }
110
111 struct fp_ext *
fp_fetox(struct fp_ext * dest,struct fp_ext * src)112 fp_fetox(struct fp_ext *dest, struct fp_ext *src)
113 {
114 uprint("fetox\n");
115
116 fp_monadic_check(dest, src);
117
118 return dest;
119 }
120
121 struct fp_ext *
fp_ftwotox(struct fp_ext * dest,struct fp_ext * src)122 fp_ftwotox(struct fp_ext *dest, struct fp_ext *src)
123 {
124 uprint("ftwotox\n");
125
126 fp_monadic_check(dest, src);
127
128 return dest;
129 }
130
131 struct fp_ext *
fp_ftentox(struct fp_ext * dest,struct fp_ext * src)132 fp_ftentox(struct fp_ext *dest, struct fp_ext *src)
133 {
134 uprint("ftentox\n");
135
136 fp_monadic_check(dest, src);
137
138 return dest;
139 }
140
141 struct fp_ext *
fp_flogn(struct fp_ext * dest,struct fp_ext * src)142 fp_flogn(struct fp_ext *dest, struct fp_ext *src)
143 {
144 uprint("flogn\n");
145
146 fp_monadic_check(dest, src);
147
148 return dest;
149 }
150
151 struct fp_ext *
fp_flognp1(struct fp_ext * dest,struct fp_ext * src)152 fp_flognp1(struct fp_ext *dest, struct fp_ext *src)
153 {
154 uprint("flognp1\n");
155
156 fp_monadic_check(dest, src);
157
158 return dest;
159 }
160
161 struct fp_ext *
fp_flog10(struct fp_ext * dest,struct fp_ext * src)162 fp_flog10(struct fp_ext *dest, struct fp_ext *src)
163 {
164 uprint("flog10\n");
165
166 fp_monadic_check(dest, src);
167
168 return dest;
169 }
170
171 struct fp_ext *
fp_flog2(struct fp_ext * dest,struct fp_ext * src)172 fp_flog2(struct fp_ext *dest, struct fp_ext *src)
173 {
174 uprint("flog2\n");
175
176 fp_monadic_check(dest, src);
177
178 return dest;
179 }
180
181 struct fp_ext *
fp_fgetexp(struct fp_ext * dest,struct fp_ext * src)182 fp_fgetexp(struct fp_ext *dest, struct fp_ext *src)
183 {
184 dprint(PINSTR, "fgetexp\n");
185
186 fp_monadic_check(dest, src);
187
188 if (IS_INF(dest)) {
189 fp_set_nan(dest);
190 return dest;
191 }
192 if (IS_ZERO(dest))
193 return dest;
194
195 fp_conv_long2ext(dest, (int)dest->exp - 0x3FFF);
196
197 fp_normalize_ext(dest);
198
199 return dest;
200 }
201
202 struct fp_ext *
fp_fgetman(struct fp_ext * dest,struct fp_ext * src)203 fp_fgetman(struct fp_ext *dest, struct fp_ext *src)
204 {
205 dprint(PINSTR, "fgetman\n");
206
207 fp_monadic_check(dest, src);
208
209 if (IS_ZERO(dest))
210 return dest;
211
212 if (IS_INF(dest))
213 return dest;
214
215 dest->exp = 0x3FFF;
216
217 return dest;
218 }
219
220