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Fix-up coefficients and smallest denormal value for ieeeDouble in exp()

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Iain Buclaw 2015-06-07 19:51:04 +02:00 • committed by Martin Nowak
parent aebeac9363
commit 73493bbb49
1 changed files with 44 additions and 25 deletions
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69
std/math.d
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@ -1574,36 +1574,55 @@ real exp(real x) @trusted pure nothrow @nogc
} }
else else
{ {
// Coefficients for exp(x) alias F = floatTraits!T;
static immutable real[3] P = [ static if (F.realFormat == RealFormat.ieeeDouble)
9.9999999999999999991025E-1L,
3.0299440770744196129956E-2L,
1.2617719307481059087798E-4L,
];
static immutable real[4] Q = [
2.0000000000000000000897E0L,
2.2726554820815502876593E-1L,
2.5244834034968410419224E-3L,
3.0019850513866445504159E-6L,
];
// C1 + C2 = LN2.
enum real C1 = 6.9314575195312500000000E-1L;
enum real C2 = 1.428606820309417232121458176568075500134E-6L;
// Overflow and Underflow limits.
static if (real.mant_dig == 64) // 80-bit reals
{ {
enum real OF = 1.1356523406294143949492E4L; // ln((1-2^-64) * 2^16384) ≈ 0x1.62e42fefa39efp+13 // Coefficients for exp(x)
enum real UF = -1.1398805384308300613366E4L; // ln(2^-16445) ≈ -0x1.6436716d5406ep+13 static immutable real[3] P = [
9.99999999999999999910E-1L,
3.02994407707441961300E-2L,
1.26177193074810590878E-4L,
];
static immutable real[4] Q = [
2.00000000000000000009E0L,
2.27265548208155028766E-1L,
2.52448340349684104192E-3L,
3.00198505138664455042E-6L,
];
// C1 + C2 = LN2.
enum real C1 = 6.93145751953125E-1;
enum real C2 = 1.42860682030941723212E-6;
// Overflow and Underflow limits.
enum real OF = 7.09782712893383996732E2; // ln((1-2^-53) * 2^1024)
enum real UF = -7.451332191019412076235E2; // ln(2^-1075)
} }
else static if (real.mant_dig == 53) // 64-bit reals else static if (F.realFormat == RealFormat.ieeeExtended)
{ {
enum real OF = 0x1.62e42fefa39efp+9L; // ln((1-2^-53) * 2^1024) = 709.78271... // Coefficients for exp(x)
enum real UF = -0x1.74385446d71c3p+9L; // ln(2^-1074) = -744.44007... static immutable real[3] P = [
9.9999999999999999991025E-1L,
3.0299440770744196129956E-2L,
1.2617719307481059087798E-4L,
];
static immutable real[4] Q = [
2.0000000000000000000897E0L,
2.2726554820815502876593E-1L,
2.5244834034968410419224E-3L,
3.0019850513866445504159E-6L,
];
// C1 + C2 = LN2.
enum real C1 = 6.9314575195312500000000E-1L;
enum real C2 = 1.4286068203094172321215E-6L;
// Overflow and Underflow limits.
enum real OF = 1.1356523406294143949492E4L; // ln((1-2^-64) * 2^16384)
enum real UF = -1.13994985314888605586758E4L; // ln(2^-16446)
} }
else else
static assert(0, "No over-/underflow limits for real type!"); static assert(0, "Not implemented for this architecture");
// Special cases. // Special cases.
// FIXME: set IEEE flags accordingly // FIXME: set IEEE flags accordingly