e_atan2.c 3.9 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130
  1. /* @(#)e_atan2.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_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $";
  14. #endif
  15. /* __ieee754_atan2(y,x)
  16. * Method :
  17. * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  18. * 2. Reduce x to positive by (if x and y are unexceptional):
  19. * ARG (x+iy) = arctan(y/x) ... if x > 0,
  20. * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
  21. *
  22. * Special cases:
  23. *
  24. * ATAN2((anything), NaN ) is NaN;
  25. * ATAN2(NAN , (anything) ) is NaN;
  26. * ATAN2(+-0, +(anything but NaN)) is +-0 ;
  27. * ATAN2(+-0, -(anything but NaN)) is +-pi ;
  28. * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  29. * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  30. * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  31. * ATAN2(+-INF,+INF ) is +-pi/4 ;
  32. * ATAN2(+-INF,-INF ) is +-3pi/4;
  33. * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  34. *
  35. * Constants:
  36. * The hexadecimal values are the intended ones for the following
  37. * constants. The decimal values may be used, provided that the
  38. * compiler will convert from decimal to binary accurately enough
  39. * to produce the hexadecimal values shown.
  40. */
  41. #include "math.h"
  42. #include "math_private.h"
  43. #ifdef __STDC__
  44. static const double
  45. #else
  46. static double
  47. #endif
  48. tiny = 1.0e-300,
  49. zero = 0.0,
  50. pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  51. pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  52. pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  53. pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  54. #ifdef __STDC__
  55. double __ieee754_atan2(double y, double x)
  56. #else
  57. double __ieee754_atan2(y,x)
  58. double y,x;
  59. #endif
  60. {
  61. double z;
  62. int32_t k,m,hx,hy,ix,iy;
  63. u_int32_t lx,ly;
  64. EXTRACT_WORDS(hx,lx,x);
  65. ix = hx&0x7fffffff;
  66. EXTRACT_WORDS(hy,ly,y);
  67. iy = hy&0x7fffffff;
  68. if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  69. ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
  70. return x+y;
  71. if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
  72. m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
  73. /* when y = 0 */
  74. if((iy|ly)==0) {
  75. switch(m) {
  76. case 0:
  77. case 1: return y; /* atan(+-0,+anything)=+-0 */
  78. case 2: return pi+tiny;/* atan(+0,-anything) = pi */
  79. case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  80. }
  81. }
  82. /* when x = 0 */
  83. if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  84. /* when x is INF */
  85. if(ix==0x7ff00000) {
  86. if(iy==0x7ff00000) {
  87. switch(m) {
  88. case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
  89. case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  90. case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  91. case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  92. }
  93. } else {
  94. switch(m) {
  95. case 0: return zero ; /* atan(+...,+INF) */
  96. case 1: return -zero ; /* atan(-...,+INF) */
  97. case 2: return pi+tiny ; /* atan(+...,-INF) */
  98. case 3: return -pi-tiny ; /* atan(-...,-INF) */
  99. }
  100. }
  101. }
  102. /* when y is INF */
  103. if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  104. /* compute y/x */
  105. k = (iy-ix)>>20;
  106. if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
  107. else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
  108. else z=atan(fabs(y/x)); /* safe to do y/x */
  109. switch (m) {
  110. case 0: return z ; /* atan(+,+) */
  111. case 1: {
  112. u_int32_t zh;
  113. GET_HIGH_WORD(zh,z);
  114. SET_HIGH_WORD(z,zh ^ 0x80000000);
  115. }
  116. return z ; /* atan(-,+) */
  117. case 2: return pi-(z-pi_lo);/* atan(+,-) */
  118. default: /* case 3 */
  119. return (z-pi_lo)-pi;/* atan(-,-) */
  120. }
  121. }