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Implement Math/Mathf.exp; Initial math test suite

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dcodeIO
2018-03-25 17:42:56 +02:00
parent 70d2a0a425
commit e26734ef90
12 changed files with 7292 additions and 105 deletions
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206
std/assembly/math.ts
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@ -58,6 +58,13 @@ import {
trunc as builtin_trunc
} from "./builtins";
// Math/Mathf.log/exp
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
export namespace Math {
export const E = 2.7182818284590452354;
@ -81,6 +88,67 @@ export namespace Math {
return builtin_clz(<i32>x);
}
export function exp(x: f64): f64 {
// based on musl's implementation of exp:
const
half = <f64[]>[0.5,-0.5],
ln2hi = 6.93147180369123816490e-01, // 0x3fe62e42, 0xfee00000
ln2lo = 1.90821492927058770002e-10, // 0x3dea39ef, 0x35793c76
invln2 = 1.44269504088896338700e+00, // 0x3ff71547, 0x652b82fe
P1 = 1.66666666666666019037e-01, // 0x3FC55555, 0x5555553E
P2 = -2.77777777770155933842e-03, // 0xBF66C16C, 0x16BEBD93
P3 = 6.61375632143793436117e-05, // 0x3F11566A, 0xAF25DE2C
P4 = -1.65339022054652515390e-06, // 0xBEBBBD41, 0xC5D26BF1
P5 = 4.13813679705723846039e-08, // 0x3E663769, 0x72BEA4D0
Ox1p1023 = 8.98846567431157954e+307;
var hx = <u32>(reinterpret<u64>(x) >> 32);
var sign_ = hx >> 31;
hx &= 0x7fffffff; // high word of |x|
// special cases
if (hx >= 0x4086232b) { // if |x| >= 708.39...
if (isNaN(x)) return x;
if (x > 709.782712893383973096) {
// overflow if x!=inf
x *= Ox1p1023;
return x;
}
if (x < -708.39641853226410622) {
// underflow if x!=-inf
if (x < -745.13321910194110842) return 0;
}
}
// argument reduction
var hi: f64, lo: f64;
var k: i32;
if (hx > 0x3fd62e42) { // if |x| > 0.5 ln2
if (hx >= 0x3ff0a2b2) { // if |x| >= 1.5 ln2
k = <i32>(invln2 * x + half[sign_]);
} else {
k = 1 - sign_ - sign_;
}
hi = x - k * ln2hi; // k * ln2hi is exact here
lo = k * ln2lo;
x = hi - lo;
} else if (hx > 0x3e300000) { // if |x| > 2**-28
k = 0;
hi = x;
lo = 0;
} else {
// inexact if x != 0
return 1 + x;
}
// x is now in primary range
var xx = x * x;
var c = x - xx * (P1 + xx * (P2 + xx * (P3 + xx * (P4 + xx * P5))));
var y: f64 = 1 + (x * c / (2 - c) - lo + hi);
if (k == 0) return y;
return scalbn(y, k);
}
export function floor(x: f64): f64 {
return builtin_floor(x);
}
@ -93,13 +161,7 @@ export namespace Math {
return <i32>x * <i32>y;
}
export function log(x: f64): f64 {
// based on musl's implementation of log:
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
export function log(x: f64): f64 { // based on musl's implementation of log
const
ln2_hi = 6.93147180369123816490e-01, // 3fe62e42 fee00000
ln2_lo = 1.90821492927058770002e-10, // 3dea39ef 35793c76
@ -109,7 +171,8 @@ export namespace Math {
Lg4 = 2.222219843214978396e-01, // 3FCC71C5 1D8E78AF
Lg5 = 1.818357216161805012e-01, // 3FC74664 96CB03DE
Lg6 = 1.531383769920937332e-01, // 3FC39A09 D078C69F
Lg7 = 1.479819860511658591e-01; // 3FC2F112 DF3E5244
Lg7 = 1.479819860511658591e-01, // 3FC2F112 DF3E5244
Ox1p54 = 18014398509481984.0;
var Ux = reinterpret<u64>(x);
var hx = <u32>(Ux >> 32);
@ -119,7 +182,7 @@ export namespace Math {
if (hx >> 31) return (x - x) / 0.0; // log(-#) = NaN
// subnormal number, scale x up
k -= 54;
x *= 1.8014398509481984e16; // 0x1p54
x *= Ox1p54;
Ux = reinterpret<u64>(x);
hx = <u32>(Ux >> 32);
} else if (hx >= 0x7ff00000) return x;
@ -204,24 +267,79 @@ export namespace Mathf {
return builtin_floor(x);
}
export function exp(x: f32): f32 { // based on musl's implementation of expf
const
half = <f32[]>[0.5,-0.5],
ln2hi = <f32>6.9314575195e-1, // 0x3f317200
ln2lo = <f32>1.4286067653e-6, // 0x35bfbe8e
invln2 = <f32>1.4426950216e+0, // 0x3fb8aa3b
// Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
// |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
P1 = <f32>1.6666625440e-1, // 0xaaaa8f.0p-26
P2 = <f32>-2.7667332906e-3, // -0xb55215.0p-32
Ox1p127f = <f32>1.701411835e+38;
var hx = reinterpret<u32>(x);
var sign_ = <i32>(hx >> 31); // sign bit of x
hx &= 0x7fffffff; // high word of |x|
// special cases
if (hx >= 0x42aeac50) { // if |x| >= -87.33655f or NaN
if (hx >= 0x42b17218 && !sign_) { // x >= 88.722839f
// overflow
x *= Ox1p127f;
return x;
}
if (sign_) {
// underflow
if (hx >= 0x42cff1b5) { // x <= -103.972084f */
return 0;
}
}
}
// argument reduction
var hi: f32, lo: f32;
var k: i32;
if (hx > 0x3eb17218) { // if |x| > 0.5 ln2
if (hx > 0x3f851592) { // if |x| > 1.5 ln2
k = <i32>(invln2 * x + half[sign_]);
} else {
k = 1 - sign_ - sign_;
}
hi = x - <f32>k * ln2hi; // k * ln2hi is exact here
lo = <f32>k * ln2lo;
x = hi - lo;
} else if (hx > 0x39000000) { // |x| > 2**-14
k = 0;
hi = x;
lo = 0;
} else {
// raise inexact
return 1 + x;
}
// x is now in primary range
var xx = x * x;
var c = x - xx * (P1 + xx * P2);
var y: f32 = 1 + (x * c / (2 - c) - lo + hi);
if (k == 0) return y;
return scalbnf(y, k);
}
export function imul(x: f32, y: f32): i32 {
return <i32>x * <i32>y;
}
export function log(x: f32): f32 {
// based on musl's implementaion of logf:
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
export function log(x: f32): f32 { // based on musl's implementaion of logf
const
ln2_hi = <f32>6.9313812256e-01, // 0x3f317180
ln2_lo = <f32>9.0580006145e-06, // 0x3717f7d1
Lg1 = <f32>0.66666662693, // 0xaaaaaa.0p-24
Lg2 = <f32>0.40000972152, // 0xccce13.0p-25
Lg3 = <f32>0.28498786688, // 0x91e9ee.0p-25
Lg4 = <f32>0.24279078841; // 0xf89e26.0p-26
Lg4 = <f32>0.24279078841, // 0xf89e26.0p-26
Ox1p25f = <f32>33554432.0;
var ux = reinterpret<u32>(x);
var k = 0;
@ -230,7 +348,7 @@ export namespace Mathf {
if (ux >> 31) return (x - x) / 0; // log(-#) = NaN
// subnormal number, scale up x
k -= 25;
x *= 3.3554432; // 0x1p25f;
x *= Ox1p25f;
ux = reinterpret<u32>(x);
} else if (ux >= 0x7f800000) return x;
else if (ux == 0x3f800000) return 0;
@ -285,3 +403,55 @@ export namespace Mathf {
return builtin_trunc(x);
}
}
function scalbn(x: f64, n: i32): f64 { // based on musl's implementation of scalbn
const
Ox1p1023 = 8.98846567431157954e+307,
Ox1p_1022 = 2.22507385850720138e-308;
var y = x;
if (n > 1023) {
y *= Ox1p1023;
n -= 1023;
if (n > 1023) {
y *= Ox1p1023;
n -= 1023;
if (n > 1023) n = 1023;
}
} else if (n < -1022) {
y *= Ox1p_1022;
n += 1022;
if (n < -1022) {
y *= Ox1p_1022;
n += 1022;
if (n < -1022) n = -1022;
}
}
return y * reinterpret<f64>(<u64>(0x3ff + n) << 52);
}
function scalbnf(x: f32, n: i32): f32 { // based on musl's implementation of scalbnf
const
Ox1p127f = <f32>1.701411835e+38,
Ox1p_126f = <f32>1.175494351e-38;
var y = x;
if (n > 127) {
y *= Ox1p127f;
n -= 127;
if (n > 127) {
y *= Ox1p127f;
n -= 127;
if (n > 127) n = 127;
}
} else if (n < -126) {
y *= Ox1p_126f;
n += 126;
if (n < -126) {
y *= Ox1p_126f;
n += 126;
if (n < -126) n = -126;
}
}
return y * reinterpret<f32>(<u32>(0x7f + n) << 23);
}