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// Written in the D programming language.
/**
* Builtin mathematical intrinsics
*
* Source: $(DRUNTIMESRC core/_math.d)
* Macros:
* TABLE_SV = <table border="1" cellpadding="4" cellspacing="0">
* <caption>Special Values</caption>
* $0</table>
*
* NAN = $(RED NAN)
* SUP = <span style="vertical-align:super;font-size:smaller">$0</span>
* POWER = $1<sup>$2</sup>
* PLUSMN = ±
* INFIN = ∞
* PLUSMNINF = ±∞
* LT = <
* GT = >
*
* Copyright: Copyright Digital Mars 2000 - 2011.
* License: $(WEB www.boost.org/LICENSE_1_0.txt, Boost License 1.0).
* Authors: $(WEB digitalmars.com, Walter Bright),
* Don Clugston
*/
module core.math;
public:
@nogc:
/***********************************
* Returns cosine of x. x is in radians.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH cos(x)) $(TH invalid?))
* $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
* $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes) )
* )
* Bugs:
* Results are undefined if |x| >= $(POWER 2,64).
*/
real cos(real x) @safe pure nothrow; /* intrinsic */
/***********************************
* Returns sine of x. x is in radians.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH sin(x)) $(TH invalid?))
* $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
* $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
* $(TR $(TD $(PLUSMNINF)) $(TD $(NAN)) $(TD yes))
* )
* Bugs:
* Results are undefined if |x| >= $(POWER 2,64).
*/
real sin(real x) @safe pure nothrow; /* intrinsic */
/*****************************************
* Returns x rounded to a long value using the current rounding mode.
* If the integer value of x is
* greater than long.max, the result is
* indeterminate.
*/
long rndtol(real x) @safe pure nothrow; /* intrinsic */
/*****************************************
* Returns x rounded to a long value using the FE_TONEAREST rounding mode.
* If the integer value of x is
* greater than long.max, the result is
* indeterminate.
*/
extern (C) real rndtonl(real x);
/***************************************
* Compute square root of x.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH sqrt(x)) $(TH invalid?))
* $(TR $(TD -0.0) $(TD -0.0) $(TD no))
* $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD yes))
* $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
* )
*/
@safe pure nothrow
{
float sqrt(float x); /* intrinsic */
double sqrt(double x); /* intrinsic */ /// ditto
real sqrt(real x); /* intrinsic */ /// ditto
}
/*******************************************
* Compute n * 2$(SUPERSCRIPT exp)
* References: frexp
*/
real ldexp(real n, int exp) @safe pure nothrow; /* intrinsic */
unittest {
static if (real.mant_dig == 113)
{
assert(ldexp(1, -16384) == 0x1p-16384L);
assert(ldexp(1, -16382) == 0x1p-16382L);
}
else static if (real.mant_dig == 106)
{
assert(ldexp(1, 1023) == 0x1p1023L);
assert(ldexp(1, -1022) == 0x1p-1022L);
assert(ldexp(1, -1021) == 0x1p-1021L);
}
else static if (real.mant_dig == 64)
{
assert(ldexp(1, -16384) == 0x1p-16384L);
assert(ldexp(1, -16382) == 0x1p-16382L);
}
else static if (real.mant_dig == 53)
{
assert(ldexp(1, 1023) == 0x1p1023L);
assert(ldexp(1, -1022) == 0x1p-1022L);
assert(ldexp(1, -1021) == 0x1p-1021L);
}
else
assert(false, "Only 128bit, 80bit and 64bit reals expected here");
}
/*******************************
* Returns |x|
*
* $(TABLE_SV
* $(TR $(TH x) $(TH fabs(x)))
* $(TR $(TD $(PLUSMN)0.0) $(TD +0.0) )
* $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
* )
*/
real fabs(real x) @safe pure nothrow; /* intrinsic */
/**********************************
* Rounds x to the nearest integer value, using the current rounding
* mode.
* If the return value is not equal to x, the FE_INEXACT
* exception is raised.
* $(B nearbyint) performs
* the same operation, but does not set the FE_INEXACT exception.
*/
real rint(real x) @safe pure nothrow; /* intrinsic */
/***********************************
* Building block functions, they
* translate to a single x87 instruction.
*/
real yl2x(real x, real y) @safe pure nothrow; // y * log2(x)
real yl2xp1(real x, real y) @safe pure nothrow; // y * log2(x + 1)
unittest
{
version (INLINE_YL2X)
{
assert(yl2x(1024, 1) == 10);
assert(yl2xp1(1023, 1) == 10);
}
}
/*************************************
* Round argument to a specific precision.
*
* D language types specify a minimum precision, not a maximum. The
* `toPrec()` function forces rounding of the argument `f` to the
* precision of the specified floating point type `T`.
*
* Params:
* T = precision type to round to
* f = value to convert
* Returns:
* f in precision of type `T`
*/
@safe pure nothrow
T toPrec(T:float)(float f) { pragma(inline, false); return f; }
/// ditto
@safe pure nothrow
T toPrec(T:float)(double f) { pragma(inline, false); return cast(T) f; }
/// ditto
@safe pure nothrow
T toPrec(T:float)(real f) { pragma(inline, false); return cast(T) f; }
/// ditto
@safe pure nothrow
T toPrec(T:double)(float f) { pragma(inline, false); return f; }
/// ditto
@safe pure nothrow
T toPrec(T:double)(double f) { pragma(inline, false); return f; }
/// ditto
@safe pure nothrow
T toPrec(T:double)(real f) { pragma(inline, false); return cast(T) f; }
/// ditto
@safe pure nothrow
T toPrec(T:real)(float f) { pragma(inline, false); return f; }
/// ditto
@safe pure nothrow
T toPrec(T:real)(double f) { pragma(inline, false); return f; }
/// ditto
@safe pure nothrow
T toPrec(T:real)(real f) { pragma(inline, false); return f; }
@safe unittest
{
static float f = 1.1f;
static double d = 1.1;
static real r = 1.1L;
f = toPrec!float(f + f);
f = toPrec!float(d + d);
f = toPrec!float(r + r);
d = toPrec!double(f + f);
d = toPrec!double(d + d);
d = toPrec!double(r + r);
r = toPrec!real(f + f);
r = toPrec!real(d + d);
r = toPrec!real(r + r);
/+ Uncomment these once compiler support has been added.
enum real PIR = 0xc.90fdaa22168c235p-2;
enum double PID = 0x1.921fb54442d18p+1;
enum float PIF = 0x1.921fb6p+1;
assert(toPrec!float(PIR) == PIF);
assert(toPrec!double(PIR) == PID);
assert(toPrec!real(PIR) == PIR);
assert(toPrec!float(PID) == PIF);
assert(toPrec!double(PID) == PID);
assert(toPrec!real(PID) == PID);
assert(toPrec!float(PIF) == PIF);
assert(toPrec!double(PIF) == PIF);
assert(toPrec!real(PIF) == PIF);
+/
}
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