author | Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com> |
Fri, 11 Jun 2010 15:26:22 +0300 | |
changeset 34 | 5fae379060a7 |
parent 0 | e4d67989cc36 |
permissions | -rw-r--r-- |
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/*-------------------------------------------------------------------- |
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*© Portions copyright (c) 2006 Nokia Corporation. All rights reserved. |
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*-------------------------------------------------------------------- |
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*/ |
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/* @(#)e_rem_pio2.c 1.4 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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* |
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*/ |
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#ifndef __SYMBIAN32__ |
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#ifndef lint |
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static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_rem_pio2.c,v 1.8 2005/02/04 18:26:06 das Exp $"; |
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#endif |
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#endif //__SYMBIAN32__ |
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/* __ieee754_rem_pio2(x,y) |
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* |
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* return the remainder of x rem pi/2 in y[0]+y[1] |
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* use __kernel_rem_pio2() |
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*/ |
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#include <math.h> |
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#include "math_private.h" |
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/* |
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* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
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*/ |
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static const int32_t two_over_pi[] = { |
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
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}; |
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|
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static const int32_t npio2_hw[] = { |
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0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
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0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
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0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
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0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
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0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
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0x404858EB, 0x404921FB, |
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}; |
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/* |
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* invpio2: 53 bits of 2/pi |
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* pio2_1: first 33 bit of pi/2 |
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* pio2_1t: pi/2 - pio2_1 |
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* pio2_2: second 33 bit of pi/2 |
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* pio2_2t: pi/2 - (pio2_1+pio2_2) |
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* pio2_3: third 33 bit of pi/2 |
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
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*/ |
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static const double |
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zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
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invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
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pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
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pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
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pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
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pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
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pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
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int32_t __ieee754_rem_pio2(double x, double *y) |
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{ |
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double z = 0,w,t,r,fn; |
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double tx[3]; |
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int32_t e0,i,j,nx,n,ix,hx; |
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u_int32_t low; |
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GET_HIGH_WORD(hx,x); /* high word of x */ |
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ix = hx&0x7fffffff; |
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if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
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{y[0] = x; y[1] = 0; return 0;} |
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if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
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|
93 |
if(hx>0) { |
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|
94 |
z = x - pio2_1; |
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|
95 |
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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|
96 |
y[0] = z - pio2_1t; |
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|
97 |
y[1] = (z-y[0])-pio2_1t; |
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|
98 |
} else { /* near pi/2, use 33+33+53 bit pi */ |
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|
99 |
z -= pio2_2; |
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|
100 |
y[0] = z - pio2_2t; |
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|
101 |
y[1] = (z-y[0])-pio2_2t; |
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|
102 |
} |
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|
103 |
return 1; |
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|
104 |
} else { /* negative x */ |
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|
105 |
z = x + pio2_1; |
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|
106 |
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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|
107 |
y[0] = z + pio2_1t; |
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|
108 |
y[1] = (z-y[0])+pio2_1t; |
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|
109 |
} else { /* near pi/2, use 33+33+53 bit pi */ |
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110 |
z += pio2_2; |
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111 |
y[0] = z + pio2_2t; |
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112 |
y[1] = (z-y[0])+pio2_2t; |
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|
113 |
} |
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114 |
return -1; |
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115 |
} |
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116 |
} |
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117 |
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
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118 |
t = fabs(x); |
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119 |
n = (int32_t) (t*invpio2+half); |
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120 |
fn = (double)n; |
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121 |
r = t-fn*pio2_1; |
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122 |
w = fn*pio2_1t; /* 1st round good to 85 bit */ |
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123 |
if(n<32&&ix!=npio2_hw[n-1]) { |
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124 |
y[0] = r-w; /* quick check no cancellation */ |
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125 |
} else { |
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126 |
u_int32_t high; |
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127 |
j = ix>>20; |
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128 |
y[0] = r-w; |
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129 |
GET_HIGH_WORD(high,y[0]); |
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130 |
i = j-((high>>20)&0x7ff); |
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131 |
if(i>16) { /* 2nd iteration needed, good to 118 */ |
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132 |
t = r; |
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133 |
w = fn*pio2_2; |
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134 |
r = t-w; |
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135 |
w = fn*pio2_2t-((t-r)-w); |
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136 |
y[0] = r-w; |
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137 |
GET_HIGH_WORD(high,y[0]); |
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138 |
i = j-((high>>20)&0x7ff); |
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139 |
if(i>49) { /* 3rd iteration need, 151 bits acc */ |
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140 |
t = r; /* will cover all possible cases */ |
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141 |
w = fn*pio2_3; |
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142 |
r = t-w; |
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143 |
w = fn*pio2_3t-((t-r)-w); |
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144 |
y[0] = r-w; |
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145 |
} |
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146 |
} |
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|
147 |
} |
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|
148 |
y[1] = (r-y[0])-w; |
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|
149 |
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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150 |
else return n; |
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|
151 |
} |
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|
152 |
/* |
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153 |
* all other (large) arguments |
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|
154 |
*/ |
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|
155 |
if(ix>=0x7ff00000) { /* x is inf or NaN */ |
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|
156 |
y[0]=y[1]=x-x; return 0; |
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|
157 |
} |
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|
158 |
/* set z = scalbn(|x|,ilogb(x)-23) */ |
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|
159 |
GET_LOW_WORD(low,x); |
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Revision: 201002
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|
160 |
SET_LOW_WORD(z,low); |
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|
161 |
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
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|
162 |
SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); |
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|
163 |
for(i=0;i<2;i++) { |
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Revision: 201002
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|
164 |
tx[i] = (double)((int32_t)(z)); |
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Revision: 201002
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|
165 |
z = (z-tx[i])*two24; |
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parents:
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|
166 |
} |
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|
167 |
tx[2] = z; |
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Revision: 201002
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|
168 |
nx = 3; |
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Revision: 201002
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|
169 |
while(tx[nx-1]==zero) nx--; /* skip zero term */ |
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Revision: 201002
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|
170 |
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
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|
171 |
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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|
172 |
return n; |
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|
173 |
} |