e_rem_pio2.c 5.5 KB

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  1. /* @(#)e_rem_pio2.c 5.1 93/09/24 */
  2. /*
  3. * ====================================================
  4. * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  5. *
  6. * Developed at SunPro, a Sun Microsystems, Inc. business.
  7. * Permission to use, copy, modify, and distribute this
  8. * software is freely granted, provided that this notice
  9. * is preserved.
  10. * ====================================================
  11. */
  12. #if defined(LIBM_SCCS) && !defined(lint)
  13. static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
  14. #endif
  15. /* __ieee754_rem_pio2(x,y)
  16. *
  17. * return the remainder of x rem pi/2 in y[0]+y[1]
  18. * use __kernel_rem_pio2()
  19. */
  20. #include "math.h"
  21. #include "math_private.h"
  22. /*
  23. * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  24. */
  25. #ifdef __STDC__
  26. static const int32_t two_over_pi[] = {
  27. #else
  28. static int32_t two_over_pi[] = {
  29. #endif
  30. 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
  31. 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
  32. 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
  33. 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
  34. 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
  35. 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
  36. 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
  37. 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
  38. 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
  39. 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
  40. 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
  41. };
  42. #ifdef __STDC__
  43. static const int32_t npio2_hw[] = {
  44. #else
  45. static int32_t npio2_hw[] = {
  46. #endif
  47. 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
  48. 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
  49. 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
  50. 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
  51. 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
  52. 0x404858EB, 0x404921FB,
  53. };
  54. /*
  55. * invpio2: 53 bits of 2/pi
  56. * pio2_1: first 33 bit of pi/2
  57. * pio2_1t: pi/2 - pio2_1
  58. * pio2_2: second 33 bit of pi/2
  59. * pio2_2t: pi/2 - (pio2_1+pio2_2)
  60. * pio2_3: third 33 bit of pi/2
  61. * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
  62. */
  63. #ifdef __STDC__
  64. static const double
  65. #else
  66. static double
  67. #endif
  68. zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  69. half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  70. two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  71. invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  72. pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  73. pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
  74. pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
  75. pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
  76. pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
  77. pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
  78. #ifdef __STDC__
  79. int32_t __ieee754_rem_pio2(double x, double *y)
  80. #else
  81. int32_t __ieee754_rem_pio2(x,y)
  82. double x,y[];
  83. #endif
  84. {
  85. double z=0.0,w,t,r,fn;
  86. double tx[3];
  87. int32_t e0,i,j,nx,n,ix,hx;
  88. u_int32_t low;
  89. GET_HIGH_WORD(hx,x); /* high word of x */
  90. ix = hx&0x7fffffff;
  91. if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
  92. {y[0] = x; y[1] = 0; return 0;}
  93. if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
  94. if(hx>0) {
  95. z = x - pio2_1;
  96. if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
  97. y[0] = z - pio2_1t;
  98. y[1] = (z-y[0])-pio2_1t;
  99. } else { /* near pi/2, use 33+33+53 bit pi */
  100. z -= pio2_2;
  101. y[0] = z - pio2_2t;
  102. y[1] = (z-y[0])-pio2_2t;
  103. }
  104. return 1;
  105. } else { /* negative x */
  106. z = x + pio2_1;
  107. if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
  108. y[0] = z + pio2_1t;
  109. y[1] = (z-y[0])+pio2_1t;
  110. } else { /* near pi/2, use 33+33+53 bit pi */
  111. z += pio2_2;
  112. y[0] = z + pio2_2t;
  113. y[1] = (z-y[0])+pio2_2t;
  114. }
  115. return -1;
  116. }
  117. }
  118. if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
  119. t = fabs(x);
  120. n = (int32_t) (t*invpio2+half);
  121. fn = (double)n;
  122. r = t-fn*pio2_1;
  123. w = fn*pio2_1t; /* 1st round good to 85 bit */
  124. if(n<32&&ix!=npio2_hw[n-1]) {
  125. y[0] = r-w; /* quick check no cancellation */
  126. } else {
  127. u_int32_t high;
  128. j = ix>>20;
  129. y[0] = r-w;
  130. GET_HIGH_WORD(high,y[0]);
  131. i = j-((high>>20)&0x7ff);
  132. if(i>16) { /* 2nd iteration needed, good to 118 */
  133. t = r;
  134. w = fn*pio2_2;
  135. r = t-w;
  136. w = fn*pio2_2t-((t-r)-w);
  137. y[0] = r-w;
  138. GET_HIGH_WORD(high,y[0]);
  139. i = j-((high>>20)&0x7ff);
  140. if(i>49) { /* 3rd iteration need, 151 bits acc */
  141. t = r; /* will cover all possible cases */
  142. w = fn*pio2_3;
  143. r = t-w;
  144. w = fn*pio2_3t-((t-r)-w);
  145. y[0] = r-w;
  146. }
  147. }
  148. }
  149. y[1] = (r-y[0])-w;
  150. if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  151. else return n;
  152. }
  153. /*
  154. * all other (large) arguments
  155. */
  156. if(ix>=0x7ff00000) { /* x is inf or NaN */
  157. y[0]=y[1]=x-x; return 0;
  158. }
  159. /* set z = scalbn(|x|,ilogb(x)-23) */
  160. GET_LOW_WORD(low,x);
  161. SET_LOW_WORD(z,low);
  162. e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
  163. SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
  164. for(i=0;i<2;i++) {
  165. tx[i] = (double)((int32_t)(z));
  166. z = (z-tx[i])*two24;
  167. }
  168. tx[2] = z;
  169. nx = 3;
  170. while(tx[nx-1]==zero) nx--; /* skip zero term */
  171. n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
  172. if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  173. return n;
  174. }