e_rem_pio2.c 5.1 KB

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