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Side by Side Diff: fusl/src/math/expm1.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/s_expm1.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
2 /* 2 /*
3 * ==================================================== 3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * 5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this 7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice 8 * software is freely granted, provided that this notice
9 * is preserved. 9 * is preserved.
10 * ==================================================== 10 * ====================================================
(...skipping 88 matching lines...) Expand 10 before | Expand all | Expand 10 after
99 * 99 *
100 * Constants: 100 * Constants:
101 * The hexadecimal values are the intended ones for the following 101 * The hexadecimal values are the intended ones for the following
102 * constants. The decimal values may be used, provided that the 102 * constants. The decimal values may be used, provided that the
103 * compiler will convert from decimal to binary accurately enough 103 * compiler will convert from decimal to binary accurately enough
104 * to produce the hexadecimal values shown. 104 * to produce the hexadecimal values shown.
105 */ 105 */
106 106
107 #include "libm.h" 107 #include "libm.h"
108 108
109 static const double 109 static const double o_threshold =
110 o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ 110 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
111 ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ 111 ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
112 ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ 112 ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
113 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ 113 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
114 /* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ 114 /* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2:
115 Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ 115 */
116 Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ 116 Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
117 Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ 117 Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
118 Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ 118 Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
119 Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ 119 Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
120 Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
120 121
121 double expm1(double x) 122 double expm1(double x) {
122 { 123 double_t y, hi, lo, c, t, e, hxs, hfx, r1, twopk;
123 » double_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 124 union {
124 » union {double f; uint64_t i;} u = {x}; 125 double f;
125 » uint32_t hx = u.i>>32 & 0x7fffffff; 126 uint64_t i;
126 » int k, sign = u.i>>63; 127 } u = {x};
128 uint32_t hx = u.i >> 32 & 0x7fffffff;
129 int k, sign = u.i >> 63;
127 130
128 » /* filter out huge and non-finite argument */ 131 /* filter out huge and non-finite argument */
129 » if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ 132 if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */
130 » » if (isnan(x)) 133 if (isnan(x))
131 » » » return x; 134 return x;
132 » » if (sign) 135 if (sign)
133 » » » return -1; 136 return -1;
134 » » if (x > o_threshold) { 137 if (x > o_threshold) {
135 » » » x *= 0x1p1023; 138 x *= 0x1p1023;
136 » » » return x; 139 return x;
137 » » } 140 }
138 » } 141 }
139 142
140 » /* argument reduction */ 143 /* argument reduction */
141 » if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ 144 if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
142 » » if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ 145 if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
143 » » » if (!sign) { 146 if (!sign) {
144 » » » » hi = x - ln2_hi; 147 hi = x - ln2_hi;
145 » » » » lo = ln2_lo; 148 lo = ln2_lo;
146 » » » » k = 1; 149 k = 1;
147 » » » } else { 150 } else {
148 » » » » hi = x + ln2_hi; 151 hi = x + ln2_hi;
149 » » » » lo = -ln2_lo; 152 lo = -ln2_lo;
150 » » » » k = -1; 153 k = -1;
151 » » » } 154 }
152 » » } else { 155 } else {
153 » » » k = invln2*x + (sign ? -0.5 : 0.5); 156 k = invln2 * x + (sign ? -0.5 : 0.5);
154 » » » t = k; 157 t = k;
155 » » » hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 158 hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
156 » » » lo = t*ln2_lo; 159 lo = t * ln2_lo;
157 » » } 160 }
158 » » x = hi-lo; 161 x = hi - lo;
159 » » c = (hi-x)-lo; 162 c = (hi - x) - lo;
160 » } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */ 163 } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */
161 » » if (hx < 0x00100000) 164 if (hx < 0x00100000)
162 » » » FORCE_EVAL((float)x); 165 FORCE_EVAL((float)x);
163 » » return x; 166 return x;
164 » } else 167 } else
165 » » k = 0; 168 k = 0;
166 169
167 » /* x is now in primary range */ 170 /* x is now in primary range */
168 » hfx = 0.5*x; 171 hfx = 0.5 * x;
169 » hxs = x*hfx; 172 hxs = x * hfx;
170 » r1 = 1.0+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 173 r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
171 » t = 3.0-r1*hfx; 174 t = 3.0 - r1 * hfx;
172 » e = hxs*((r1-t)/(6.0 - x*t)); 175 e = hxs * ((r1 - t) / (6.0 - x * t));
173 » if (k == 0) /* c is 0 */ 176 if (k == 0) /* c is 0 */
174 » » return x - (x*e-hxs); 177 return x - (x * e - hxs);
175 » e = x*(e-c) - c; 178 e = x * (e - c) - c;
176 » e -= hxs; 179 e -= hxs;
177 » /* exp(x) ~ 2^k (x_reduced - e + 1) */ 180 /* exp(x) ~ 2^k (x_reduced - e + 1) */
178 » if (k == -1) 181 if (k == -1)
179 » » return 0.5*(x-e) - 0.5; 182 return 0.5 * (x - e) - 0.5;
180 » if (k == 1) { 183 if (k == 1) {
181 » » if (x < -0.25) 184 if (x < -0.25)
182 » » » return -2.0*(e-(x+0.5)); 185 return -2.0 * (e - (x + 0.5));
183 » » return 1.0+2.0*(x-e); 186 return 1.0 + 2.0 * (x - e);
184 » } 187 }
185 » u.i = (uint64_t)(0x3ff + k)<<52; /* 2^k */ 188 u.i = (uint64_t)(0x3ff + k) << 52; /* 2^k */
186 » twopk = u.f; 189 twopk = u.f;
187 » if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ 190 if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
188 » » y = x - e + 1.0; 191 y = x - e + 1.0;
189 » » if (k == 1024) 192 if (k == 1024)
190 » » » y = y*2.0*0x1p1023; 193 y = y * 2.0 * 0x1p1023;
191 » » else 194 else
192 » » » y = y*twopk; 195 y = y * twopk;
193 » » return y - 1.0; 196 return y - 1.0;
194 » } 197 }
195 » u.i = (uint64_t)(0x3ff - k)<<52; /* 2^-k */ 198 u.i = (uint64_t)(0x3ff - k) << 52; /* 2^-k */
196 » if (k < 20) 199 if (k < 20)
197 » » y = (x-e+(1-u.f))*twopk; 200 y = (x - e + (1 - u.f)) * twopk;
198 » else 201 else
199 » » y = (x-(e+u.f)+1)*twopk; 202 y = (x - (e + u.f) + 1) * twopk;
200 » return y; 203 return y;
201 } 204 }
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