constants.d

// Written in the D programming language.

/**
This is a submodule of $(MREF std, math).

It contains several useful mathematical constants.

Copyright: Copyright The D Language Foundation 2000 - 2011.
License:   $(HTTP www.boost.org/LICENSE_1_0.txt, Boost License 1.0).
Authors:   $(HTTP digitalmars.com, Walter Bright), Don Clugston
Source: $(PHOBOSSRC std/math/constants.d)

Macros:
     SUB = $1<sub>$2</sub>
     PI = &pi;
     SQRT = &radic;
     HALF = &frac12;
 */
module std.math.constants;

// Values obtained from Wolfram Alpha. 116 bits ought to be enough for anybody.
// Wolfram Alpha LLC. 2011. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=e+in+base+16 (access July 6, 2011).
enum real E =          0x1.5bf0a8b1457695355fb8ac404e7a8p+1L; /** e = 2.718281... */
enum real LOG2T =      0x1.a934f0979a3715fc9257edfe9b5fbp+1L; /** $(SUB log, 2)10 = 3.321928... */
enum real LOG2E =      0x1.71547652b82fe1777d0ffda0d23a8p+0L; /** $(SUB log, 2)e = 1.442695... */
enum real LOG2 =       0x1.34413509f79fef311f12b35816f92p-2L; /** $(SUB log, 10)2 = 0.301029... */
enum real LOG10E =     0x1.bcb7b1526e50e32a6ab7555f5a67cp-2L; /** $(SUB log, 10)e = 0.434294... */
enum real LN2 =        0x1.62e42fefa39ef35793c7673007e5fp-1L; /** ln 2  = 0.693147... */
enum real LN10 =       0x1.26bb1bbb5551582dd4adac5705a61p+1L; /** ln 10 = 2.302585... */
enum real PI =         0x1.921fb54442d18469898cc51701b84p+1L; /** &pi; = 3.141592... */
enum real PI_2 =       PI/2;                                  /** $(PI) / 2 = 1.570796... */
enum real PI_4 =       PI/4;                                  /** $(PI) / 4 = 0.785398... */
enum real M_1_PI =     0x1.45f306dc9c882a53f84eafa3ea69cp-2L; /** 1 / $(PI) = 0.318309... */
enum real M_2_PI =     2*M_1_PI;                              /** 2 / $(PI) = 0.636619... */
enum real M_2_SQRTPI = 0x1.20dd750429b6d11ae3a914fed7fd8p+0L; /** 2 / $(SQRT)$(PI) = 1.128379... */
enum real SQRT2 =      0x1.6a09e667f3bcc908b2fb1366ea958p+0L; /** $(SQRT)2 = 1.414213... */
enum real SQRT1_2 =    SQRT2/2;                               /** $(SQRT)$(HALF) = 0.707106... */
// Note: Make sure the magic numbers in compiler backend for x87 match these.