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4973 | right-hear | 1 | /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
2 | /* @(#)e_rem_pio2.c 5.1 93/09/24 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | */ |
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13 | |||
14 | #if defined(LIBM_SCCS) && !defined(lint) |
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15 | static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 jtc Exp $"; |
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16 | #endif |
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17 | |||
18 | /* __ieee754_rem_pio2(x,y) |
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19 | * |
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20 | * return the remainder of x rem pi/2 in y[0]+y[1] |
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21 | * use __kernel_rem_pio2() |
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22 | */ |
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23 | |||
24 | #include "math.h" |
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25 | #include "math_private.h" |
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26 | |||
27 | /* |
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28 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
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29 | */ |
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30 | #ifdef __STDC__ |
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31 | static const int32_t two_over_pi[] = { |
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32 | #else |
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33 | static int32_t two_over_pi[] = { |
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34 | #endif |
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35 | 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
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36 | 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
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37 | 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
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38 | 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
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39 | 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
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40 | 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
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41 | 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
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42 | 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
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43 | 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
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44 | 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
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45 | 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
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46 | }; |
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47 | |||
48 | #ifdef __STDC__ |
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49 | static const int32_t npio2_hw[] = { |
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50 | #else |
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51 | static int32_t npio2_hw[] = { |
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52 | #endif |
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53 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
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54 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
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55 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
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56 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
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57 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
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58 | 0x404858EB, 0x404921FB, |
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59 | }; |
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60 | |||
61 | /* |
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62 | * invpio2: 53 bits of 2/pi |
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63 | * pio2_1: first 33 bit of pi/2 |
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64 | * pio2_1t: pi/2 - pio2_1 |
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65 | * pio2_2: second 33 bit of pi/2 |
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66 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
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67 | * pio2_3: third 33 bit of pi/2 |
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68 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
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69 | */ |
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70 | |||
71 | #ifdef __STDC__ |
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72 | static const double |
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73 | #else |
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74 | static double |
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75 | #endif |
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76 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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77 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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78 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
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79 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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80 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
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81 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
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82 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
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83 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
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84 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
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85 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
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86 | |||
87 | #ifdef __STDC__ |
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88 | int32_t __ieee754_rem_pio2(double x, double *y) |
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89 | #else |
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90 | int32_t __ieee754_rem_pio2(x,y) |
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91 | double x,y[]; |
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92 | #endif |
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93 | { |
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94 | double z,w,t,r,fn; |
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95 | double tx[3]; |
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96 | int32_t e0,i,j,nx,n,ix,hx; |
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97 | u_int32_t low; |
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98 | |||
99 | GET_HIGH_WORD(hx,x); /* high word of x */ |
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100 | ix = hx&0x7fffffff; |
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101 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
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102 | {y[0] = x; y[1] = 0; return 0;} |
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103 | if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
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104 | t = fabs(x); |
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105 | n = (int32_t) (t*invpio2+half); |
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106 | fn = (double)n; |
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107 | r = t-fn*pio2_1; |
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108 | w = fn*pio2_1t; /* 1st round good to 85 bit */ |
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109 | if(n<32&&ix!=npio2_hw[n-1]) { |
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110 | y[0] = r-w; /* quick check no cancellation */ |
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111 | } else { |
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112 | u_int32_t high; |
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113 | j = ix>>20; |
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114 | y[0] = r-w; |
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115 | GET_HIGH_WORD(high,y[0]); |
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116 | i = j-((high>>20)&0x7ff); |
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117 | if(i>16) { /* 2nd iteration needed, good to 118 */ |
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118 | t = r; |
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119 | w = fn*pio2_2; |
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120 | r = t-w; |
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121 | w = fn*pio2_2t-((t-r)-w); |
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122 | y[0] = r-w; |
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123 | GET_HIGH_WORD(high,y[0]); |
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124 | i = j-((high>>20)&0x7ff); |
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125 | if(i>49) { /* 3rd iteration need, 151 bits acc */ |
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126 | t = r; /* will cover all possible cases */ |
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127 | w = fn*pio2_3; |
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128 | r = t-w; |
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129 | w = fn*pio2_3t-((t-r)-w); |
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130 | y[0] = r-w; |
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131 | } |
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132 | } |
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133 | } |
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134 | y[1] = (r-y[0])-w; |
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135 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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136 | else return n; |
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137 | } |
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138 | /* |
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139 | * all other (large) arguments |
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140 | */ |
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141 | if(ix>=0x7ff00000) { /* x is inf or NaN */ |
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142 | y[0]=y[1]=x-x; return 0; |
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143 | } |
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144 | /* set z = scalbn(|x|,ilogb(x)-23) */ |
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145 | GET_LOW_WORD(low,x); |
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146 | SET_LOW_WORD(z,low); |
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147 | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
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148 | SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); |
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149 | for(i=0;i<2;i++) { |
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150 | tx[i] = (double)((int32_t)(z)); |
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151 | z = (z-tx[i])*two24; |
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152 | } |
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153 | tx[2] = z; |
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154 | nx = 3; |
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155 | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
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156 | n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
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157 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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158 | return n; |
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159 | }0)>2;i++)>20))); |