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Add docs and tests for fp classificators

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This commit is contained in:
Eugen Wissner 2017-09-18 11:31:37 +02:00
parent 586d12b6c7
commit be551e9349
2 changed files with 534 additions and 304 deletions
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304
source/tanya/math/fp.d
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@ -1,304 +0,0 @@
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/**
* Copyright: Eugene Wissner 2017.
* License: $(LINK2 https://www.mozilla.org/en-US/MPL/2.0/,
* Mozilla Public License, v. 2.0).
* Authors: $(LINK2 mailto:info@caraus.de, Eugene Wissner)
* Source: $(LINK2 https://github.com/caraus-ecms/tanya/blob/master/source/tanya/math/fp.d,
* tanya/math/fp.d)
*/
module tanya.math.fp;
import tanya.math.nbtheory;
/**
* Floating-point number precisions according to IEEE-754.
*/
enum IEEEPrecision : ubyte
{
/// Single precision: 64-bit.
single = 4,
/// Single precision: 64-bit.
double_ = 8,
/// Extended precision: 80-bit.
extended = 10,
}
/**
* Tests the precision of floating-point type $(D_PARAM F).
*
* For $(D_KEYWORD float), $(D_PSYMBOL ieeePrecision) always evaluates to
* $(D_INLINECODE IEEEPrecision.single); for $(D_KEYWORD double) - to
* $(D_INLINECODE IEEEPrecision.double). It returns different values only
* for $(D_KEYWORD real), since $(D_KEYWORD real) is a platform-dependent type.
*
* If $(D_PARAM F) is a $(D_KEYWORD real) and the target platform isn't
* currently supported, static assertion error will be raised (you can use
* $(D_INLINECODE is(typeof(ieeePrecision!F))) for testing the platform support
* without a compilation error).
*
* Params:
* F = Type to be tested.
*
* Returns: Precision according to IEEE-754.
*
* See_Also: $(D_PSYMBOL IEEEPrecision).
*/
template ieeePrecision(F)
if (isFloatingPoint!F)
{
static if (F.sizeof == float.sizeof)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.single;
}
else static if (F.sizeof == double.sizeof)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.double_;
}
else version (X86)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.extended;
}
else version (X86_64)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.extended;
}
else
{
static assert(false, "Unsupported IEEE 754 floating point precision");
}
}
private union FloatBits(F)
{
F floating;
static if (ieeePrecision!F == IEEEPrecision.single)
{
uint integral;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
ulong integral;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
struct // Little-endian.
{
ulong mantissa;
ushort exp;
}
}
else
{
static assert(false, "Unsupported IEEE 754 floating point precision");
}
}
enum FloatingPointClass : ubyte
{
nan,
zero,
infinite,
subnormal,
normal,
}
FloatingPointClass classify(F)(F x)
if (isFloatingPoint!F)
{
if (x == 0)
{
return FloatingPointClass.zero;
}
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
if (bits.integral > 0x7f800000)
{
return FloatingPointClass.nan;
}
else if (bits.integral == 0x7f800000)
{
return FloatingPointClass.infinite;
}
else if (bits.integral < 0x800000)
{
return FloatingPointClass.subnormal;
}
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
if (bits.integral > 0x7ff0000000000000)
{
return FloatingPointClass.nan;
}
else if (bits.integral == 0x7ff0000000000000)
{
return FloatingPointClass.infinite;
}
else if (bits.integral < 0x10000000000000)
{
return FloatingPointClass.subnormal;
}
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
if (bits.exp == 0x7fff)
{
if ((bits.mantissa & 0x7fffffffffffffff) == 0)
{
return FloatingPointClass.infinite;
}
else
{
return FloatingPointClass.nan;
}
}
else if (bits.exp == 0)
{
return FloatingPointClass.subnormal;
}
else if (bits.mantissa < 0x8000000000000000) // "Unnormal".
{
return FloatingPointClass.nan;
}
}
return FloatingPointClass.normal;
}
bool isFinite(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
static if (ieeePrecision!F == IEEEPrecision.single)
{
bits.floating = x;
bits.integral &= 0x7f800000;
return bits.integral != 0x7f800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
bits.floating = x;
bits.integral &= 0x7ff0000000000000;
return bits.integral != 0x7ff0000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
bits.floating = abs(x);
return (bits.exp != 0x7fff) && (bits.mantissa >= 0x8000000000000000);
}
}
bool isNaN(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
return bits.integral > 0x7f800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral > 0x7ff0000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
if ((bits.exp == 0x7fff && (bits.mantissa & 0x7fffffffffffffff) != 0)
|| ((bits.exp != 0) && (bits.mantissa < 0x8000000000000000)))
{
return true;
}
return false;
}
}
bool isInfinity(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
return bits.integral == 0x7f800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral == 0x7ff0000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
return (bits.exp == 0x7fff)
&& ((bits.mantissa & 0x7fffffffffffffff) == 0);
}
}
bool isSubnormal(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
return bits.integral < 0x800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral < 0x10000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
return bits.exp == 0;
}
}
bool isNormal(F)(F x)
if (isFloatingPoint!F)
{
static if (ieeePrecision!F == IEEEPrecision.single)
{
FloatBits!F bits;
bits.floating = x;
bits.integral &= 0x7f800000;
return bits.integral != 0 && bits.integral != 0x7f800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
FloatBits!F bits;
bits.floating = x;
bits.integral &= 0x7ff0000000000000;
return bits.integral != 0 && bits.integral != 0x7ff0000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
return classify(x) == FloatingPointClass.normal;
}
}
bool signBit(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = x;
static if (ieeePrecision!F == IEEEPrecision.single)
{
return (bits.integral & (1 << 31)) != 0;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return (bits.integral & (1 << 63)) != 0;
}
else static if (ieeePrecision!F == IEEEPrecision.extended)
{
return (bits.exp & (1 << 15)) != 0;
}
}

534
source/tanya/math/package.d
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@ -19,6 +19,540 @@ public import tanya.math.nbtheory;
public import tanya.math.random; public import tanya.math.random;
import tanya.meta.trait; import tanya.meta.trait;
/// Floating-point number precisions according to IEEE-754.
enum IEEEPrecision : ubyte
{
single = 4, /// Single precision: 64-bit.
double_ = 8, /// Single precision: 64-bit.
doubleExtended = 10, /// Double extended precision: 80-bit.
}
/**
* Tests the precision of floating-point type $(D_PARAM F).
*
* For $(D_KEYWORD float), $(D_PSYMBOL ieeePrecision) always evaluates to
* $(D_INLINECODE IEEEPrecision.single); for $(D_KEYWORD double) - to
* $(D_INLINECODE IEEEPrecision.double). It returns different values only
* for $(D_KEYWORD real), since $(D_KEYWORD real) is a platform-dependent type.
*
* If $(D_PARAM F) is a $(D_KEYWORD real) and the target platform isn't
* currently supported, static assertion error will be raised (you can use
* $(D_INLINECODE is(typeof(ieeePrecision!F))) for testing the platform support
* without a compilation error).
*
* Params:
* F = Type to be tested.
*
* Returns: Precision according to IEEE-754.
*
* See_Also: $(D_PSYMBOL IEEEPrecision).
*/
template ieeePrecision(F)
if (isFloatingPoint!F)
{
static if (F.sizeof == float.sizeof)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.single;
}
else static if (F.sizeof == double.sizeof)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.double_;
}
else version (X86)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.doubleExtended;
}
else version (X86_64)
{
enum IEEEPrecision ieeePrecision = IEEEPrecision.doubleExtended;
}
else
{
static assert(false, "Unsupported IEEE 754 floating point precision");
}
}
///
pure nothrow @safe @nogc unittest
{
static assert(ieeePrecision!float == IEEEPrecision.single);
static assert(ieeePrecision!double == IEEEPrecision.double_);
}
private union FloatBits(F)
{
F floating;
static if (ieeePrecision!F == IEEEPrecision.single)
{
uint integral;
enum uint expMask = 0x7f800000;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
ulong integral;
enum ulong expMask = 0x7ff0000000000000;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
struct // Little-endian.
{
ulong mantissa;
ushort exp;
}
enum ulong mantissaMask = 0x7fffffffffffffff;
enum uint expMask = 0x7fff;
}
else
{
static assert(false, "Unsupported IEEE 754 floating point precision");
}
}
/**
* Floating-point number classifications.
*/
enum FloatingPointClass : ubyte
{
/**
* Not a Number.
*
* See_Also: $(D_PSYMBOL isNaN).
*/
nan,
/// Zero.
zero,
/**
* Infinity.
*
* See_Also: $(D_PSYMBOL isInfinity).
*/
infinite,
/**
* Denormalized number.
*
* See_Also: $(D_PSYMBOL isSubnormal).
*/
subnormal,
/**
* Normalized number.
*
* See_Also: $(D_PSYMBOL isNormal).
*/
normal,
}
/**
* Returns whether $(D_PARAM x) is a NaN, zero, infinity, subnormal or
* normalized number.
*
* This function doesn't distinguish between negative and positive infinity,
* negative and positive NaN or negative and positive zero.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: Classification of $(D_PARAM x).
*/
FloatingPointClass classify(F)(F x)
if (isFloatingPoint!F)
{
if (x == 0)
{
return FloatingPointClass.zero;
}
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
if (bits.integral > bits.expMask)
{
return FloatingPointClass.nan;
}
else if (bits.integral == bits.expMask)
{
return FloatingPointClass.infinite;
}
else if (bits.integral < (1 << 23))
{
return FloatingPointClass.subnormal;
}
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
if (bits.integral > bits.expMask)
{
return FloatingPointClass.nan;
}
else if (bits.integral == bits.expMask)
{
return FloatingPointClass.infinite;
}
else if (bits.integral < (1L << 52))
{
return FloatingPointClass.subnormal;
}
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
if (bits.exp == bits.expMask)
{
if ((bits.mantissa & bits.mantissaMask) == 0)
{
return FloatingPointClass.infinite;
}
else
{
return FloatingPointClass.nan;
}
}
else if (bits.exp == 0)
{
return FloatingPointClass.subnormal;
}
else if (bits.mantissa < (1L << 63)) // "Unnormal".
{
return FloatingPointClass.nan;
}
}
return FloatingPointClass.normal;
}
///
pure nothrow @safe @nogc unittest
{
assert(classify(0.0) == FloatingPointClass.zero);
assert(classify(double.nan) == FloatingPointClass.nan);
assert(classify(double.infinity) == FloatingPointClass.infinite);
assert(classify(-double.infinity) == FloatingPointClass.infinite);
assert(classify(1.4) == FloatingPointClass.normal);
assert(classify(1.11254e-307 / 10) == FloatingPointClass.subnormal);
assert(classify(0.0f) == FloatingPointClass.zero);
assert(classify(float.nan) == FloatingPointClass.nan);
assert(classify(float.infinity) == FloatingPointClass.infinite);
assert(classify(-float.infinity) == FloatingPointClass.infinite);
assert(classify(0.3) == FloatingPointClass.normal);
assert(classify(5.87747e-38f / 10) == FloatingPointClass.subnormal);
assert(classify(0.0L) == FloatingPointClass.zero);
assert(classify(real.nan) == FloatingPointClass.nan);
assert(classify(real.infinity) == FloatingPointClass.infinite);
assert(classify(-real.infinity) == FloatingPointClass.infinite);
}
private pure nothrow @nogc @safe unittest
{
static if (ieeePrecision!float == IEEEPrecision.doubleExtended)
{
assert(classify(1.68105e-10) == FloatingPointClass.normal);
assert(classify(1.68105e-4932L) == FloatingPointClass.subnormal);
// Emulate unnormals, because they aren't generated anymore since i386
FloatBits!real unnormal;
unnormal.exp = 0x123;
unnormal.mantissa = 0x1;
assert(classify(unnormal) == FloatingPointClass.subnormal);
}
}
/**
* Determines whether $(D_PARAM x) is a finite number.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is a finite number,
* $(D_KEYWORD false) otherwise.
*
* See_Also: $(D_PSYMBOL isInfinity).
*/
bool isFinite(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
static if (ieeePrecision!F == IEEEPrecision.single
|| ieeePrecision!F == IEEEPrecision.double_)
{
bits.floating = x;
bits.integral &= bits.expMask;
return bits.integral != bits.expMask;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
bits.floating = abs(x);
return (bits.exp != bits.expMask)
&& (bits.exp == 0 || bits.mantissa >= (1L << 63));
}
}
///
pure nothrow @safe @nogc unittest
{
assert(!isFinite(float.infinity));
assert(!isFinite(-double.infinity));
assert(isFinite(0.0));
assert(!isFinite(float.nan));
assert(isFinite(5.87747e-38f / 10));
assert(isFinite(1.11254e-307 / 10));
assert(isFinite(0.5));
}
/**
* Determines whether $(D_PARAM x) is $(B n)ot $(B a) $(B n)umber (NaN).
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is not a number,
* $(D_KEYWORD false) otherwise.
*/
bool isNaN(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single
|| ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral > bits.expMask;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
const maskedMantissa = bits.mantissa & bits.mantissaMask;
if ((bits.exp == bits.expMask && maskedMantissa != 0)
|| ((bits.exp != 0) && (bits.mantissa < (1L << 63))))
{
return true;
}
return false;
}
}
///
pure nothrow @safe @nogc unittest
{
assert(isNaN(float.init));
assert(isNaN(double.init));
assert(isNaN(real.init));
}
/**
* Determines whether $(D_PARAM x) is a positive or negative infinity.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is infinity, $(D_KEYWORD false)
* otherwise.
*
* See_Also: $(D_PSYMBOL isFinite).
*/
bool isInfinity(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single
|| ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral == bits.expMask;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
return (bits.exp == bits.expMask)
&& ((bits.mantissa & bits.mantissaMask) == 0);
}
}
///
pure nothrow @safe @nogc unittest
{
assert(isInfinity(float.infinity));
assert(isInfinity(-float.infinity));
assert(isInfinity(double.infinity));
assert(isInfinity(-double.infinity));
assert(isInfinity(real.infinity));
assert(isInfinity(-real.infinity));
}
/**
* Determines whether $(D_PARAM x) is a denormilized number or not.
* Denormalized number is a number between `0` and `1` that cannot be
* represented as
*
* <pre>
* m*2<sup>e</sup>
* </pre>
*
* where $(I m) is the mantissa and $(I e) is an exponent that fits into the
* exponent field of the type $(D_PARAM F).
*
* `0` is neither normalized nor denormalized.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is a denormilized number,
* $(D_KEYWORD false) otherwise.
*
* See_Also: $(D_PSYMBOL isNormal).
*/
bool isSubnormal(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = abs(x);
static if (ieeePrecision!F == IEEEPrecision.single)
{
return bits.integral < (1 << 23) && bits.integral > 0;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return bits.integral < (1L << 52) && bits.integral > 0;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
return bits.exp == 0 && bits.mantissa != 0;
}
}
///
pure nothrow @safe @nogc unittest
{
assert(!isSubnormal(0.0f));
assert(!isSubnormal(float.nan));
assert(!isSubnormal(float.infinity));
assert(!isSubnormal(0.3f));
assert(isSubnormal(5.87747e-38f / 10));
assert(!isSubnormal(0.0));
assert(!isSubnormal(double.nan));
assert(!isSubnormal(double.infinity));
assert(!isSubnormal(1.4));
assert(isSubnormal(1.11254e-307 / 10));
assert(!isSubnormal(0.0L));
assert(!isSubnormal(real.nan));
assert(!isSubnormal(real.infinity));
}
/**
* Determines whether $(D_PARAM x) is a normilized number or not.
* Normalized number is a number that can be represented as
*
* <pre>
* m*2<sup>e</sup>
* </pre>
*
* where $(I m) is the mantissa and $(I e) is an exponent that fits into the
* exponent field of the type $(D_PARAM F).
*
* `0` is neither normalized nor denormalized.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is a normilized number,
* $(D_KEYWORD false) otherwise.
*
* See_Also: $(D_PSYMBOL isSubnormal).
*/
bool isNormal(F)(F x)
if (isFloatingPoint!F)
{
static if (ieeePrecision!F == IEEEPrecision.single
|| ieeePrecision!F == IEEEPrecision.double_)
{
FloatBits!F bits;
bits.floating = x;
bits.integral &= bits.expMask;
return bits.integral != 0 && bits.integral != bits.expMask;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
return classify(x) == FloatingPointClass.normal;
}
}
///
pure nothrow @safe @nogc unittest
{
assert(!isNormal(0.0f));
assert(!isNormal(float.nan));
assert(!isNormal(float.infinity));
assert(isNormal(0.3f));
assert(!isNormal(5.87747e-38f / 10));
assert(!isNormal(0.0));
assert(!isNormal(double.nan));
assert(!isNormal(double.infinity));
assert(isNormal(1.4));
assert(!isNormal(1.11254e-307 / 10));
assert(!isNormal(0.0L));
assert(!isNormal(real.nan));
assert(!isNormal(real.infinity));
}
/**
* Determines whether the sign bit of $(D_PARAM x) is set or not.
*
* If the sign bit, $(D_PARAM x) is a negative number, otherwise positive.
*
* Params:
* F = Type of the floating point number.
* x = Floating point number.
*
* Returns: $(D_KEYWORD true) if the sign bit of $(D_PARAM x) is set,
* $(D_KEYWORD false) otherwise.
*/
bool signBit(F)(F x)
if (isFloatingPoint!F)
{
FloatBits!F bits;
bits.floating = x;
static if (ieeePrecision!F == IEEEPrecision.single)
{
return (bits.integral & (1 << 31)) != 0;
}
else static if (ieeePrecision!F == IEEEPrecision.double_)
{
return (bits.integral & (1L << 63)) != 0;
}
else static if (ieeePrecision!F == IEEEPrecision.doubleExtended)
{
return (bits.exp & (1 << 15)) != 0;
}
}
///
pure nothrow @safe @nogc unittest
{
assert(signBit(-1.0f));
assert(!signBit(1.0f));
assert(signBit(-1.0));
assert(!signBit(1.0));
assert(signBit(-1.0L));
assert(!signBit(1.0L));
}
/** /**
* Computes $(D_PARAM x) to the power $(D_PARAM y) modulo $(D_PARAM z). * Computes $(D_PARAM x) to the power $(D_PARAM y) modulo $(D_PARAM z).
* *