`11210 libm should be cstyle(1ONBLD) clean`
 ``` `````` 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 /* 31 * long double __k_tanl(long double x; long double y, int k); 32 * kernel tan/cotan function on [-pi/4, pi/4], pi/4 ~ 0.785398164 33 * Input x is assumed to be bounded by ~pi/4 in magnitude. 34 * Input y is the tail of x. 35 * Input k indicate -- tan if k=0; else -1/tan 36 * 37 * Table look up algorithm 38 * 1. by tan(-x) = -tan(x), need only to consider positive x 39 * 2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then 40 * if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x != 0 41 * else 42 * z = x*x; 43 * w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6)))))) 44 * return (k == 0)? w: 1/w; `````` 51 * tan(t+x') 52 * = (tan(t)+tan(x'))/(1-tan(x')tan(t)) 53 * We have 54 * sin(x')+tan(t)*(tan(t)*sin(x')) 55 * = tan(t) + ------------------------------- for k=0 56 * cos(x') - tan(t)*sin(x') 57 * 58 * cos(x') - tan(t)*sin(x') 59 * = - -------------------------------------- for k=1 60 * tan(t) + tan(t)*(cos(x')-1) + sin(x') 61 * 62 * 63 * where tan(t) is from the table, 64 * sin(x') = x + pp1*x^3 + ...+ pp5*x^11 65 * cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10 66 */ 67 68 #include "libm.h" 69 70 extern const long double _TBL_tanl_hi[], _TBL_tanl_lo[]; 71 static const long double 72 one = 1.0L, 73 /* 74 * 3 11 -122.32 75 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 76 */ 77 pp1 = -1.666666666666666666666666666586782940810e-0001L, 78 pp2 = +8.333333333333333333333003723660929317540e-0003L, 79 pp3 = -1.984126984126984076045903483778337804470e-0004L, 80 pp4 = +2.755731922361906641319723106210900949413e-0006L, 81 pp5 = -2.505198398570947019093998469135012057673e-0008L, 82 /* 83 * 2 10 -123.84 84 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 85 */ 86 qq1 = -4.999999999999999999999999999999378373641e-0001L, 87 qq2 = +4.166666666666666666666665478399327703130e-0002L, 88 qq3 = -1.388888888888888888058211230618051613494e-0003L, 89 qq4 = +2.480158730156105377771585658905303111866e-0005L, 90 qq5 = -2.755728099762526325736488376695157008736e-0007L, 91 /* 92 * |tan(x) - (x+t1*x^3+...+t6*x^13)| 93 * |------------------------------ | <= 2^-59.73 for |x|<0.15625 94 * | x | 95 */ 96 t1 = +3.333333333333333333333333333333423342490e-0001L, 97 t2 = +1.333333333333333333333333333093838744537e-0001L, 98 t3 = +5.396825396825396825396827906318682662250e-0002L, 99 t4 = +2.186948853615520282185576976994418486911e-0002L, 100 t5 = +8.863235529902196573354554519991152936246e-0003L, 101 t6 = +3.592128036572480064652191427543994878790e-0003L, 102 t7 = +1.455834387051455257856833807581901305474e-0003L, 103 t8 = +5.900274409318599857829983256201725587477e-0004L, 104 t9 = +2.391291152117265181501116961901122362937e-0004L, 105 t10 = +9.691533169382729742394024173194981882375e-0005L, 106 t11 = +3.927994733186415603228178184225780859951e-0005L, 107 t12 = +1.588300018848323824227640064883334101288e-0005L, 108 t13 = +6.916271223396808311166202285131722231723e-0006L; 109 110 #define i0 0 111 112 long double 113 __k_tanl(long double x, long double y, int k) { 114 long double a, t, z, w = 0, s, c; 115 int *pt = (int *) &t, *px = (int *) &x; 116 int i, j, hx, ix; 117 118 t = 1.0L; 119 hx = px[i0]; 120 ix = hx & 0x7fffffff; 121 if (ix < 0x3ffc4000) { 122 *(3 - i0 + (int *) &t) = 1; /* make t = one+ulp */ 123 if (ix < 0x3fc60000) { 124 if (((int) (x * t)) < 1) /* generate inexact */ 125 w = x; /* generate underflow if subnormal */ 126 } else { 127 z = x * x; 128 if (ix < 0x3ff30000) /* 2**-12 */ 129 t = z * (t1 + z * (t2 + z * (t3 + z * t4))); 130 else 131 t = z * (t1 + z * (t2 + z * (t3 + z * (t4 + 132 z * (t5 + z * (t6 + z * (t7 + z * (t8 + 133 z * (t9 + z * (t10 + z * (t11 + 134 z * (t12 + z * t13)))))))))))); 135 t = y + x * t; 136 w = x + t; 137 } 138 return (k == 0 ? w : -one / w); 139 } 140 j = (ix + 0x400) & 0x7ffff800; 141 i = (j - 0x3ffc4000) >> 11; 142 pt[i0] = j; 143 if (hx > 0) 144 x = y - (t - x); 145 else 146 x = (-y) - (t + x); 147 a = _TBL_tanl_hi[i]; 148 z = x * x; 149 /* cos(x)-1 */ 150 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 151 /* sin(x) */ 152 s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); 153 if (k == 0) { 154 w = a * s; 155 t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t)); 156 return (hx < 0 ? -a - t : a + t); 157 } else { 158 w = s + a * t; 159 c = w + _TBL_tanl_lo[i]; 160 z = one - (a * s - t); 161 return (hx >= 0 ? z / (-a - c) : z / (a + c)); 162 } 163 } ``` ``` `````` 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 26 /* 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 28 * Use is subject to license terms. 29 */ 30 31 /* 32 * long double __k_tanl(long double x; long double y, int k); 33 * kernel tan/cotan function on [-pi/4, pi/4], pi/4 ~ 0.785398164 34 * Input x is assumed to be bounded by ~pi/4 in magnitude. 35 * Input y is the tail of x. 36 * Input k indicate -- tan if k=0; else -1/tan 37 * 38 * Table look up algorithm 39 * 1. by tan(-x) = -tan(x), need only to consider positive x 40 * 2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then 41 * if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x != 0 42 * else 43 * z = x*x; 44 * w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6)))))) 45 * return (k == 0)? w: 1/w; `````` 52 * tan(t+x') 53 * = (tan(t)+tan(x'))/(1-tan(x')tan(t)) 54 * We have 55 * sin(x')+tan(t)*(tan(t)*sin(x')) 56 * = tan(t) + ------------------------------- for k=0 57 * cos(x') - tan(t)*sin(x') 58 * 59 * cos(x') - tan(t)*sin(x') 60 * = - -------------------------------------- for k=1 61 * tan(t) + tan(t)*(cos(x')-1) + sin(x') 62 * 63 * 64 * where tan(t) is from the table, 65 * sin(x') = x + pp1*x^3 + ...+ pp5*x^11 66 * cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10 67 */ 68 69 #include "libm.h" 70 71 extern const long double _TBL_tanl_hi[], _TBL_tanl_lo[]; 72 static const long double one = 1.0L; 73 74 /* 75 * 3 11 -122.32 76 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 77 */ 78 static const long double 79 pp1 = -1.666666666666666666666666666586782940810e-0001L, 80 pp2 = +8.333333333333333333333003723660929317540e-0003L, 81 pp3 = -1.984126984126984076045903483778337804470e-0004L, 82 pp4 = +2.755731922361906641319723106210900949413e-0006L, 83 pp5 = -2.505198398570947019093998469135012057673e-0008L; 84 85 /* 86 * 2 10 -123.84 87 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 88 */ 89 static const long double 90 qq1 = -4.999999999999999999999999999999378373641e-0001L, 91 qq2 = +4.166666666666666666666665478399327703130e-0002L, 92 qq3 = -1.388888888888888888058211230618051613494e-0003L, 93 qq4 = +2.480158730156105377771585658905303111866e-0005L, 94 qq5 = -2.755728099762526325736488376695157008736e-0007L; 95 96 /* 97 * |tan(x) - (x+t1*x^3+...+t6*x^13)| 98 * |------------------------------ | <= 2^-59.73 for |x|<0.15625 99 * | x | 100 */ 101 static const long double 102 t1 = +3.333333333333333333333333333333423342490e-0001L, 103 t2 = +1.333333333333333333333333333093838744537e-0001L, 104 t3 = +5.396825396825396825396827906318682662250e-0002L, 105 t4 = +2.186948853615520282185576976994418486911e-0002L, 106 t5 = +8.863235529902196573354554519991152936246e-0003L, 107 t6 = +3.592128036572480064652191427543994878790e-0003L, 108 t7 = +1.455834387051455257856833807581901305474e-0003L, 109 t8 = +5.900274409318599857829983256201725587477e-0004L, 110 t9 = +2.391291152117265181501116961901122362937e-0004L, 111 t10 = +9.691533169382729742394024173194981882375e-0005L, 112 t11 = +3.927994733186415603228178184225780859951e-0005L, 113 t12 = +1.588300018848323824227640064883334101288e-0005L, 114 t13 = +6.916271223396808311166202285131722231723e-0006L; 115 116 #define i0 0 117 118 long double 119 __k_tanl(long double x, long double y, int k) 120 { 121 long double a, t, z, w = 0, s, c; 122 int *pt = (int *)&t, *px = (int *)&x; 123 int i, j, hx, ix; 124 125 t = 1.0L; 126 hx = px[i0]; 127 ix = hx & 0x7fffffff; 128 129 if (ix < 0x3ffc4000) { 130 *(3 - i0 + (int *)&t) = 1; /* make t = one+ulp */ 131 132 if (ix < 0x3fc60000) { 133 if (((int)(x * t)) < 1) /* generate inexact */ 134 w = x; /* generate underflow if subnormal */ 135 } else { 136 z = x * x; 137 138 if (ix < 0x3ff30000) { /* 2**-12 */ 139 t = z * (t1 + z * (t2 + z * (t3 + z * t4))); 140 } else { 141 t = z * (t1 + z * (t2 + z * (t3 + z * (t4 + z * 142 (t5 + z * (t6 + z * (t7 + z * (t8 + z * 143 (t9 + z * (t10 + z * (t11 + z * (t12 + z * 144 t13)))))))))))); 145 } 146 147 t = y + x * t; 148 w = x + t; 149 } 150 151 return (k == 0 ? w : -one / w); 152 } 153 154 j = (ix + 0x400) & 0x7ffff800; 155 i = (j - 0x3ffc4000) >> 11; 156 pt[i0] = j; 157 158 if (hx > 0) 159 x = y - (t - x); 160 else 161 x = (-y) - (t + x); 162 163 a = _TBL_tanl_hi[i]; 164 z = x * x; 165 /* cos(x)-1 */ 166 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 167 /* sin(x) */ 168 s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); 169 170 if (k == 0) { 171 w = a * s; 172 t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t)); 173 return (hx < 0 ? -a - t : a + t); 174 } else { 175 w = s + a * t; 176 c = w + _TBL_tanl_lo[i]; 177 z = one - (a * s - t); 178 return (hx >= 0 ? z / (-a - c) : z / (a + c)); 179 } 180 } ```