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Side by Side Diff: fusl/src/math/j0f.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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1 /* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */
2 /* 2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */ 4 */
5 /* 5 /*
6 * ==================================================== 6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * 8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this 10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice 11 * software is freely granted, provided that this notice
12 * is preserved. 12 * is preserved.
13 * ==================================================== 13 * ====================================================
14 */ 14 */
15 15
16 #define _GNU_SOURCE 16 #define _GNU_SOURCE
17 #include "libm.h" 17 #include "libm.h"
18 18
19 static float pzerof(float), qzerof(float); 19 static float pzerof(float), qzerof(float);
20 20
21 static const float 21 static const float invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
22 invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */ 22 tpi = 6.3661974669e-01; /* 0x3f22f983 */
23 tpi = 6.3661974669e-01; /* 0x3f22f983 */
24 23
25 static float common(uint32_t ix, float x, int y0) 24 static float common(uint32_t ix, float x, int y0) {
26 { 25 float z, s, c, ss, cc;
27 » float z,s,c,ss,cc; 26 /*
28 » /* 27 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
29 » * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 28 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
30 » * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 29 */
31 » */ 30 s = sinf(x);
32 » s = sinf(x); 31 c = cosf(x);
33 » c = cosf(x); 32 if (y0)
34 » if (y0) 33 c = -c;
35 » » c = -c; 34 cc = s + c;
36 » cc = s+c; 35 if (ix < 0x7f000000) {
37 » if (ix < 0x7f000000) { 36 ss = s - c;
38 » » ss = s-c; 37 z = -cosf(2 * x);
39 » » z = -cosf(2*x); 38 if (s * c < 0)
40 » » if (s*c < 0) 39 cc = z / ss;
41 » » » cc = z/ss; 40 else
42 » » else 41 ss = z / cc;
43 » » » ss = z/cc; 42 if (ix < 0x58800000) {
44 » » if (ix < 0x58800000) { 43 if (y0)
45 » » » if (y0) 44 ss = -ss;
46 » » » » ss = -ss; 45 cc = pzerof(x) * cc - qzerof(x) * ss;
47 » » » cc = pzerof(x)*cc-qzerof(x)*ss; 46 }
48 » » } 47 }
49 » } 48 return invsqrtpi * cc / sqrtf(x);
50 » return invsqrtpi*cc/sqrtf(x);
51 } 49 }
52 50
53 /* R0/S0 on [0, 2.00] */ 51 /* R0/S0 on [0, 2.00] */
54 static const float 52 static const float R02 = 1.5625000000e-02, /* 0x3c800000 */
55 R02 = 1.5625000000e-02, /* 0x3c800000 */ 53 R03 = -1.8997929874e-04, /* 0xb947352e */
56 R03 = -1.8997929874e-04, /* 0xb947352e */ 54 R04 = 1.8295404516e-06, /* 0x35f58e88 */
57 R04 = 1.8295404516e-06, /* 0x35f58e88 */ 55 R05 = -4.6183270541e-09, /* 0xb19eaf3c */
58 R05 = -4.6183270541e-09, /* 0xb19eaf3c */ 56 S01 = 1.5619102865e-02, /* 0x3c7fe744 */
59 S01 = 1.5619102865e-02, /* 0x3c7fe744 */ 57 S02 = 1.1692678527e-04, /* 0x38f53697 */
60 S02 = 1.1692678527e-04, /* 0x38f53697 */ 58 S03 = 5.1354652442e-07, /* 0x3509daa6 */
61 S03 = 5.1354652442e-07, /* 0x3509daa6 */ 59 S04 = 1.1661400734e-09; /* 0x30a045e8 */
62 S04 = 1.1661400734e-09; /* 0x30a045e8 */
63 60
64 float j0f(float x) 61 float j0f(float x) {
65 { 62 float z, r, s;
66 » float z,r,s; 63 uint32_t ix;
67 » uint32_t ix;
68 64
69 » GET_FLOAT_WORD(ix, x); 65 GET_FLOAT_WORD(ix, x);
70 » ix &= 0x7fffffff; 66 ix &= 0x7fffffff;
71 » if (ix >= 0x7f800000) 67 if (ix >= 0x7f800000)
72 » » return 1/(x*x); 68 return 1 / (x * x);
73 » x = fabsf(x); 69 x = fabsf(x);
74 70
75 » if (ix >= 0x40000000) { /* |x| >= 2 */ 71 if (ix >= 0x40000000) { /* |x| >= 2 */
76 » » /* large ulp error near zeros */ 72 /* large ulp error near zeros */
77 » » return common(ix, x, 0); 73 return common(ix, x, 0);
78 » } 74 }
79 » if (ix >= 0x3a000000) { /* |x| >= 2**-11 */ 75 if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
80 » » /* up to 4ulp error near 2 */ 76 /* up to 4ulp error near 2 */
81 » » z = x*x; 77 z = x * x;
82 » » r = z*(R02+z*(R03+z*(R04+z*R05))); 78 r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
83 » » s = 1+z*(S01+z*(S02+z*(S03+z*S04))); 79 s = 1 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
84 » » return (1+x/2)*(1-x/2) + z*(r/s); 80 return (1 + x / 2) * (1 - x / 2) + z * (r / s);
85 » } 81 }
86 » if (ix >= 0x21800000) /* |x| >= 2**-60 */ 82 if (ix >= 0x21800000) /* |x| >= 2**-60 */
87 » » x = 0.25f*x*x; 83 x = 0.25f * x * x;
88 » return 1 - x; 84 return 1 - x;
89 } 85 }
90 86
91 static const float 87 static const float u00 = -7.3804296553e-02, /* 0xbd9726b5 */
92 u00 = -7.3804296553e-02, /* 0xbd9726b5 */ 88 u01 = 1.7666645348e-01, /* 0x3e34e80d */
93 u01 = 1.7666645348e-01, /* 0x3e34e80d */ 89 u02 = -1.3818567619e-02, /* 0xbc626746 */
94 u02 = -1.3818567619e-02, /* 0xbc626746 */ 90 u03 = 3.4745343146e-04, /* 0x39b62a69 */
95 u03 = 3.4745343146e-04, /* 0x39b62a69 */ 91 u04 = -3.8140706238e-06, /* 0xb67ff53c */
96 u04 = -3.8140706238e-06, /* 0xb67ff53c */ 92 u05 = 1.9559013964e-08, /* 0x32a802ba */
97 u05 = 1.9559013964e-08, /* 0x32a802ba */ 93 u06 = -3.9820518410e-11, /* 0xae2f21eb */
98 u06 = -3.9820518410e-11, /* 0xae2f21eb */ 94 v01 = 1.2730483897e-02, /* 0x3c509385 */
99 v01 = 1.2730483897e-02, /* 0x3c509385 */ 95 v02 = 7.6006865129e-05, /* 0x389f65e0 */
100 v02 = 7.6006865129e-05, /* 0x389f65e0 */ 96 v03 = 2.5915085189e-07, /* 0x348b216c */
101 v03 = 2.5915085189e-07, /* 0x348b216c */ 97 v04 = 4.4111031494e-10; /* 0x2ff280c2 */
102 v04 = 4.4111031494e-10; /* 0x2ff280c2 */
103 98
104 float y0f(float x) 99 float y0f(float x) {
105 { 100 float z, u, v;
106 » float z,u,v; 101 uint32_t ix;
107 » uint32_t ix;
108 102
109 » GET_FLOAT_WORD(ix, x); 103 GET_FLOAT_WORD(ix, x);
110 » if ((ix & 0x7fffffff) == 0) 104 if ((ix & 0x7fffffff) == 0)
111 » » return -1/0.0f; 105 return -1 / 0.0f;
112 » if (ix>>31) 106 if (ix >> 31)
113 » » return 0/0.0f; 107 return 0 / 0.0f;
114 » if (ix >= 0x7f800000) 108 if (ix >= 0x7f800000)
115 » » return 1/x; 109 return 1 / x;
116 » if (ix >= 0x40000000) { /* |x| >= 2.0 */ 110 if (ix >= 0x40000000) { /* |x| >= 2.0 */
117 » » /* large ulp error near zeros */ 111 /* large ulp error near zeros */
118 » » return common(ix,x,1); 112 return common(ix, x, 1);
119 » } 113 }
120 » if (ix >= 0x39000000) { /* x >= 2**-13 */ 114 if (ix >= 0x39000000) { /* x >= 2**-13 */
121 » » /* large ulp error at x ~= 0.89 */ 115 /* large ulp error at x ~= 0.89 */
122 » » z = x*x; 116 z = x * x;
123 » » u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 117 u = u00 +
124 » » v = 1+z*(v01+z*(v02+z*(v03+z*v04))); 118 z * (u01 + z * (u02 + z * (u03 + z * (u04 + z * (u05 + z * u06)))));
125 » » return u/v + tpi*(j0f(x)*logf(x)); 119 v = 1 + z * (v01 + z * (v02 + z * (v03 + z * v04)));
126 » } 120 return u / v + tpi * (j0f(x) * logf(x));
127 » return u00 + tpi*logf(x); 121 }
122 return u00 + tpi * logf(x);
128 } 123 }
129 124
130 /* The asymptotic expansions of pzero is 125 /* The asymptotic expansions of pzero is
131 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 126 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
132 * For x >= 2, We approximate pzero by 127 * For x >= 2, We approximate pzero by
133 * pzero(x) = 1 + (R/S) 128 * pzero(x) = 1 + (R/S)
134 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 129 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
135 * S = 1 + pS0*s^2 + ... + pS4*s^10 130 * S = 1 + pS0*s^2 + ... + pS4*s^10
136 * and 131 * and
137 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 132 * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
138 */ 133 */
139 static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 134 static const float pR8[6] = {
140 0.0000000000e+00, /* 0x00000000 */ 135 /* for x in [inf, 8]=1/[0,0.125] */
141 -7.0312500000e-02, /* 0xbd900000 */ 136 0.0000000000e+00, /* 0x00000000 */
142 -8.0816707611e+00, /* 0xc1014e86 */ 137 -7.0312500000e-02, /* 0xbd900000 */
143 -2.5706311035e+02, /* 0xc3808814 */ 138 -8.0816707611e+00, /* 0xc1014e86 */
144 -2.4852163086e+03, /* 0xc51b5376 */ 139 -2.5706311035e+02, /* 0xc3808814 */
145 -5.2530439453e+03, /* 0xc5a4285a */ 140 -2.4852163086e+03, /* 0xc51b5376 */
141 -5.2530439453e+03, /* 0xc5a4285a */
146 }; 142 };
147 static const float pS8[5] = { 143 static const float pS8[5] = {
148 1.1653436279e+02, /* 0x42e91198 */ 144 1.1653436279e+02, /* 0x42e91198 */
149 3.8337448730e+03, /* 0x456f9beb */ 145 3.8337448730e+03, /* 0x456f9beb */
150 4.0597855469e+04, /* 0x471e95db */ 146 4.0597855469e+04, /* 0x471e95db */
151 1.1675296875e+05, /* 0x47e4087c */ 147 1.1675296875e+05, /* 0x47e4087c */
152 4.7627726562e+04, /* 0x473a0bba */ 148 4.7627726562e+04, /* 0x473a0bba */
153 }; 149 };
154 static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 150 static const float pR5[6] = {
155 -1.1412546255e-11, /* 0xad48c58a */ 151 /* for x in [8,4.5454]=1/[0.125,0.22001] */
156 -7.0312492549e-02, /* 0xbd8fffff */ 152 -1.1412546255e-11, /* 0xad48c58a */
157 -4.1596107483e+00, /* 0xc0851b88 */ 153 -7.0312492549e-02, /* 0xbd8fffff */
158 -6.7674766541e+01, /* 0xc287597b */ 154 -4.1596107483e+00, /* 0xc0851b88 */
159 -3.3123129272e+02, /* 0xc3a59d9b */ 155 -6.7674766541e+01, /* 0xc287597b */
160 -3.4643338013e+02, /* 0xc3ad3779 */ 156 -3.3123129272e+02, /* 0xc3a59d9b */
157 -3.4643338013e+02, /* 0xc3ad3779 */
161 }; 158 };
162 static const float pS5[5] = { 159 static const float pS5[5] = {
163 6.0753936768e+01, /* 0x42730408 */ 160 6.0753936768e+01, /* 0x42730408 */
164 1.0512523193e+03, /* 0x44836813 */ 161 1.0512523193e+03, /* 0x44836813 */
165 5.9789707031e+03, /* 0x45bad7c4 */ 162 5.9789707031e+03, /* 0x45bad7c4 */
166 9.6254453125e+03, /* 0x461665c8 */ 163 9.6254453125e+03, /* 0x461665c8 */
167 2.4060581055e+03, /* 0x451660ee */ 164 2.4060581055e+03, /* 0x451660ee */
168 }; 165 };
169 166
170 static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 167 static const float pR3[6] = {
171 -2.5470459075e-09, /* 0xb12f081b */ 168 /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
172 -7.0311963558e-02, /* 0xbd8fffb8 */ 169 -2.5470459075e-09, /* 0xb12f081b */
173 -2.4090321064e+00, /* 0xc01a2d95 */ 170 -7.0311963558e-02, /* 0xbd8fffb8 */
174 -2.1965976715e+01, /* 0xc1afba52 */ 171 -2.4090321064e+00, /* 0xc01a2d95 */
175 -5.8079170227e+01, /* 0xc2685112 */ 172 -2.1965976715e+01, /* 0xc1afba52 */
176 -3.1447946548e+01, /* 0xc1fb9565 */ 173 -5.8079170227e+01, /* 0xc2685112 */
174 -3.1447946548e+01, /* 0xc1fb9565 */
177 }; 175 };
178 static const float pS3[5] = { 176 static const float pS3[5] = {
179 3.5856033325e+01, /* 0x420f6c94 */ 177 3.5856033325e+01, /* 0x420f6c94 */
180 3.6151397705e+02, /* 0x43b4c1ca */ 178 3.6151397705e+02, /* 0x43b4c1ca */
181 1.1936077881e+03, /* 0x44953373 */ 179 1.1936077881e+03, /* 0x44953373 */
182 1.1279968262e+03, /* 0x448cffe6 */ 180 1.1279968262e+03, /* 0x448cffe6 */
183 1.7358093262e+02, /* 0x432d94b8 */ 181 1.7358093262e+02, /* 0x432d94b8 */
184 }; 182 };
185 183
186 static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 184 static const float pR2[6] = {
187 -8.8753431271e-08, /* 0xb3be98b7 */ 185 /* for x in [2.8570,2]=1/[0.3499,0.5] */
188 -7.0303097367e-02, /* 0xbd8ffb12 */ 186 -8.8753431271e-08, /* 0xb3be98b7 */
189 -1.4507384300e+00, /* 0xbfb9b1cc */ 187 -7.0303097367e-02, /* 0xbd8ffb12 */
190 -7.6356959343e+00, /* 0xc0f4579f */ 188 -1.4507384300e+00, /* 0xbfb9b1cc */
191 -1.1193166733e+01, /* 0xc1331736 */ 189 -7.6356959343e+00, /* 0xc0f4579f */
192 -3.2336456776e+00, /* 0xc04ef40d */ 190 -1.1193166733e+01, /* 0xc1331736 */
191 -3.2336456776e+00, /* 0xc04ef40d */
193 }; 192 };
194 static const float pS2[5] = { 193 static const float pS2[5] = {
195 2.2220300674e+01, /* 0x41b1c32d */ 194 2.2220300674e+01, /* 0x41b1c32d */
196 1.3620678711e+02, /* 0x430834f0 */ 195 1.3620678711e+02, /* 0x430834f0 */
197 2.7047027588e+02, /* 0x43873c32 */ 196 2.7047027588e+02, /* 0x43873c32 */
198 1.5387539673e+02, /* 0x4319e01a */ 197 1.5387539673e+02, /* 0x4319e01a */
199 1.4657617569e+01, /* 0x416a859a */ 198 1.4657617569e+01, /* 0x416a859a */
200 }; 199 };
201 200
202 static float pzerof(float x) 201 static float pzerof(float x) {
203 { 202 const float *p, *q;
204 » const float *p,*q; 203 float_t z, r, s;
205 » float_t z,r,s; 204 uint32_t ix;
206 » uint32_t ix;
207 205
208 » GET_FLOAT_WORD(ix, x); 206 GET_FLOAT_WORD(ix, x);
209 » ix &= 0x7fffffff; 207 ix &= 0x7fffffff;
210 » if (ix >= 0x41000000){p = pR8; q = pS8;} 208 if (ix >= 0x41000000) {
211 » else if (ix >= 0x40f71c58){p = pR5; q = pS5;} 209 p = pR8;
212 » else if (ix >= 0x4036db68){p = pR3; q = pS3;} 210 q = pS8;
213 » else /*ix >= 0x40000000*/ {p = pR2; q = pS2;} 211 } else if (ix >= 0x40f71c58) {
214 » z = 1.0f/(x*x); 212 p = pR5;
215 » r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 213 q = pS5;
216 » s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 214 } else if (ix >= 0x4036db68) {
217 » return 1.0f + r/s; 215 p = pR3;
216 q = pS3;
217 } else /*ix >= 0x40000000*/ {
218 p = pR2;
219 q = pS2;
220 }
221 z = 1.0f / (x * x);
222 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
223 s = 1.0f + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
224 return 1.0f + r / s;
218 } 225 }
219 226
220
221 /* For x >= 8, the asymptotic expansions of qzero is 227 /* For x >= 8, the asymptotic expansions of qzero is
222 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 228 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
223 * We approximate pzero by 229 * We approximate pzero by
224 * qzero(x) = s*(-1.25 + (R/S)) 230 * qzero(x) = s*(-1.25 + (R/S))
225 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 231 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
226 * S = 1 + qS0*s^2 + ... + qS5*s^12 232 * S = 1 + qS0*s^2 + ... + qS5*s^12
227 * and 233 * and
228 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 234 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
229 */ 235 */
230 static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 236 static const float qR8[6] = {
231 0.0000000000e+00, /* 0x00000000 */ 237 /* for x in [inf, 8]=1/[0,0.125] */
232 7.3242187500e-02, /* 0x3d960000 */ 238 0.0000000000e+00, /* 0x00000000 */
233 1.1768206596e+01, /* 0x413c4a93 */ 239 7.3242187500e-02, /* 0x3d960000 */
234 5.5767340088e+02, /* 0x440b6b19 */ 240 1.1768206596e+01, /* 0x413c4a93 */
235 8.8591972656e+03, /* 0x460a6cca */ 241 5.5767340088e+02, /* 0x440b6b19 */
236 3.7014625000e+04, /* 0x471096a0 */ 242 8.8591972656e+03, /* 0x460a6cca */
243 3.7014625000e+04, /* 0x471096a0 */
237 }; 244 };
238 static const float qS8[6] = { 245 static const float qS8[6] = {
239 1.6377603149e+02, /* 0x4323c6aa */ 246 1.6377603149e+02, /* 0x4323c6aa */
240 8.0983447266e+03, /* 0x45fd12c2 */ 247 8.0983447266e+03, /* 0x45fd12c2 */
241 1.4253829688e+05, /* 0x480b3293 */ 248 1.4253829688e+05, /* 0x480b3293 */
242 8.0330925000e+05, /* 0x49441ed4 */ 249 8.0330925000e+05, /* 0x49441ed4 */
243 8.4050156250e+05, /* 0x494d3359 */ 250 8.4050156250e+05, /* 0x494d3359 */
244 -3.4389928125e+05, /* 0xc8a7eb69 */ 251 -3.4389928125e+05, /* 0xc8a7eb69 */
245 }; 252 };
246 253
247 static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 254 static const float qR5[6] = {
248 1.8408595828e-11, /* 0x2da1ec79 */ 255 /* for x in [8,4.5454]=1/[0.125,0.22001] */
249 7.3242180049e-02, /* 0x3d95ffff */ 256 1.8408595828e-11, /* 0x2da1ec79 */
250 5.8356351852e+00, /* 0x40babd86 */ 257 7.3242180049e-02, /* 0x3d95ffff */
251 1.3511157227e+02, /* 0x43071c90 */ 258 5.8356351852e+00, /* 0x40babd86 */
252 1.0272437744e+03, /* 0x448067cd */ 259 1.3511157227e+02, /* 0x43071c90 */
253 1.9899779053e+03, /* 0x44f8bf4b */ 260 1.0272437744e+03, /* 0x448067cd */
261 1.9899779053e+03, /* 0x44f8bf4b */
254 }; 262 };
255 static const float qS5[6] = { 263 static const float qS5[6] = {
256 8.2776611328e+01, /* 0x42a58da0 */ 264 8.2776611328e+01, /* 0x42a58da0 */
257 2.0778142090e+03, /* 0x4501dd07 */ 265 2.0778142090e+03, /* 0x4501dd07 */
258 1.8847289062e+04, /* 0x46933e94 */ 266 1.8847289062e+04, /* 0x46933e94 */
259 5.6751113281e+04, /* 0x475daf1d */ 267 5.6751113281e+04, /* 0x475daf1d */
260 3.5976753906e+04, /* 0x470c88c1 */ 268 3.5976753906e+04, /* 0x470c88c1 */
261 -5.3543427734e+03, /* 0xc5a752be */ 269 -5.3543427734e+03, /* 0xc5a752be */
262 }; 270 };
263 271
264 static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 272 static const float qR3[6] = {
265 4.3774099900e-09, /* 0x3196681b */ 273 /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
266 7.3241114616e-02, /* 0x3d95ff70 */ 274 4.3774099900e-09, /* 0x3196681b */
267 3.3442313671e+00, /* 0x405607e3 */ 275 7.3241114616e-02, /* 0x3d95ff70 */
268 4.2621845245e+01, /* 0x422a7cc5 */ 276 3.3442313671e+00, /* 0x405607e3 */
269 1.7080809021e+02, /* 0x432acedf */ 277 4.2621845245e+01, /* 0x422a7cc5 */
270 1.6673394775e+02, /* 0x4326bbe4 */ 278 1.7080809021e+02, /* 0x432acedf */
279 1.6673394775e+02, /* 0x4326bbe4 */
271 }; 280 };
272 static const float qS3[6] = { 281 static const float qS3[6] = {
273 4.8758872986e+01, /* 0x42430916 */ 282 4.8758872986e+01, /* 0x42430916 */
274 7.0968920898e+02, /* 0x44316c1c */ 283 7.0968920898e+02, /* 0x44316c1c */
275 3.7041481934e+03, /* 0x4567825f */ 284 3.7041481934e+03, /* 0x4567825f */
276 6.4604252930e+03, /* 0x45c9e367 */ 285 6.4604252930e+03, /* 0x45c9e367 */
277 2.5163337402e+03, /* 0x451d4557 */ 286 2.5163337402e+03, /* 0x451d4557 */
278 -1.4924745178e+02, /* 0xc3153f59 */ 287 -1.4924745178e+02, /* 0xc3153f59 */
279 }; 288 };
280 289
281 static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 290 static const float qR2[6] = {
282 1.5044444979e-07, /* 0x342189db */ 291 /* for x in [2.8570,2]=1/[0.3499,0.5] */
283 7.3223426938e-02, /* 0x3d95f62a */ 292 1.5044444979e-07, /* 0x342189db */
284 1.9981917143e+00, /* 0x3fffc4bf */ 293 7.3223426938e-02, /* 0x3d95f62a */
285 1.4495602608e+01, /* 0x4167edfd */ 294 1.9981917143e+00, /* 0x3fffc4bf */
286 3.1666231155e+01, /* 0x41fd5471 */ 295 1.4495602608e+01, /* 0x4167edfd */
287 1.6252708435e+01, /* 0x4182058c */ 296 3.1666231155e+01, /* 0x41fd5471 */
297 1.6252708435e+01, /* 0x4182058c */
288 }; 298 };
289 static const float qS2[6] = { 299 static const float qS2[6] = {
290 3.0365585327e+01, /* 0x41f2ecb8 */ 300 3.0365585327e+01, /* 0x41f2ecb8 */
291 2.6934811401e+02, /* 0x4386ac8f */ 301 2.6934811401e+02, /* 0x4386ac8f */
292 8.4478375244e+02, /* 0x44533229 */ 302 8.4478375244e+02, /* 0x44533229 */
293 8.8293585205e+02, /* 0x445cbbe5 */ 303 8.8293585205e+02, /* 0x445cbbe5 */
294 2.1266638184e+02, /* 0x4354aa98 */ 304 2.1266638184e+02, /* 0x4354aa98 */
295 -5.3109550476e+00, /* 0xc0a9f358 */ 305 -5.3109550476e+00, /* 0xc0a9f358 */
296 }; 306 };
297 307
298 static float qzerof(float x) 308 static float qzerof(float x) {
299 { 309 const float *p, *q;
300 » const float *p,*q; 310 float_t s, r, z;
301 » float_t s,r,z; 311 uint32_t ix;
302 » uint32_t ix;
303 312
304 » GET_FLOAT_WORD(ix, x); 313 GET_FLOAT_WORD(ix, x);
305 » ix &= 0x7fffffff; 314 ix &= 0x7fffffff;
306 » if (ix >= 0x41000000){p = qR8; q = qS8;} 315 if (ix >= 0x41000000) {
307 » else if (ix >= 0x40f71c58){p = qR5; q = qS5;} 316 p = qR8;
308 » else if (ix >= 0x4036db68){p = qR3; q = qS3;} 317 q = qS8;
309 » else /*ix >= 0x40000000*/ {p = qR2; q = qS2;} 318 } else if (ix >= 0x40f71c58) {
310 » z = 1.0f/(x*x); 319 p = qR5;
311 » r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 320 q = qS5;
312 » s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 321 } else if (ix >= 0x4036db68) {
313 » return (-.125f + r/s)/x; 322 p = qR3;
323 q = qS3;
324 } else /*ix >= 0x40000000*/ {
325 p = qR2;
326 q = qS2;
327 }
328 z = 1.0f / (x * x);
329 r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
330 s = 1.0f +
331 z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
332 return (-.125f + r / s) / x;
314 } 333 }
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