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assemblyscript/std/assembly/math.ts
dcodeIO e75d006d26 Implement Math/Mathf.pow
2018-03-26 03:50:06 +02:00

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export declare namespace JSMath {
export const E: f64;
export const LN2: f64;
export const LN10: f64;
export const LOG2E: f64;
export const LOG10E: f64;
export const PI: f64;
export const SQRT1_2: f64;
export const SQRT2: f64;
export function abs(x: f64): f64;
export function acos(x: f64): f64;
export function acosh(x: f64): f64;
export function asin(x: f64): f64;
export function asinh(x: f64): f64;
export function atan(x: f64): f64;
export function atan2(y: f64, x: f64): f64;
export function atanh(x: f64): f64;
export function cbrt(x: f64): f64;
export function ceil(x: f64): f64;
export function clz32(x: f64): i32;
export function cos(x: f64): f64;
export function cosh(x: f64): f64;
export function exp(x: f64): f64;
export function expm1(x: f64): f64;
export function floor(x: f64): f64;
export function fround(x: f64): f32;
export function hypot(value1: f64, value2: f64): f64; // hypot(...values: f64[]): f64;
export function imul(a: f64, b: f64): i32;
export function log(x: f64): f64;
export function log10(x: f64): f64;
export function log1p(x: f64): f64;
export function log2(x: f64): f64;
export function max(value1: f64, value2: f64): f64; // max(...values: f64[]): f64;
export function min(value1: f64, value2: f64): f64; // min(...values: f64[]): f64;
export function pow(base: f64, exponent: f64): f64;
export function random(): f64;
export function round(x: f64): f64;
export function sign(x: f64): f64;
export function sin(x: f64): f64;
export function sinh(x: f64): f64;
export function sqrt(x: f64): f64;
export function tan(x: f64): f64;
export function tanh(x: f64): f64;
export function trunc(x: f64): f64;
}
import {
abs as builtin_abs,
ceil as builtin_ceil,
clz as builtin_clz,
floor as builtin_floor,
max as builtin_max,
min as builtin_min,
nearest as builtin_nearest,
sqrt as builtin_sqrt,
trunc as builtin_trunc
} from "./builtins";
// Math/Mathf.log/exp/pow
// 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;
export const LN2 = 0.69314718055994530942;
export const LN10 = 2.30258509299404568402;
export const LOG2E = 1.4426950408889634074;
export const LOG10E = 0.43429448190325182765;
export const PI = 3.14159265358979323846;
export const SQRT1_2 = 0.70710678118654752440;
export const SQRT2 = 1.41421356237309504880;
export function abs(x: f64): f64 {
return builtin_abs(x);
}
export function ceil(x: f64): f64 {
return builtin_ceil(x);
}
export function clz32(x: f64): i32 {
return builtin_clz(<i32>x);
}
export function exp(x: f64): f64 { // based on musl's implementation of exp
const
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);
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 + copysign<f64>(0.5, x)); // was: [0.5, -0.5][sign_])
} else {
let sign_ = hx >> 31;
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);
}
export function fround(x: f64): f32 {
return <f32>x;
}
export function imul(x: f64, y: f64): i32 {
return <i32>x * <i32>y;
}
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
Lg1 = 6.666666666666735130e-01, // 3FE55555 55555593
Lg2 = 3.999999999940941908e-01, // 3FD99999 9997FA04
Lg3 = 2.857142874366239149e-01, // 3FD24924 94229359
Lg4 = 2.222219843214978396e-01, // 3FCC71C5 1D8E78AF
Lg5 = 1.818357216161805012e-01, // 3FC74664 96CB03DE
Lg6 = 1.531383769920937332e-01, // 3FC39A09 D078C69F
Lg7 = 1.479819860511658591e-01, // 3FC2F112 DF3E5244
Ox1p54 = 18014398509481984.0;
var Ux = reinterpret<u64>(x);
var hx = <u32>(Ux >> 32);
var k = 0;
if (hx < 0x00100000 || <bool>(hx >> 31)) {
if (Ux << 1 == 0) return -1 / (x * x); // log(+-0)=-inf
if (hx >> 31) return (x - x) / 0.0; // log(-#) = NaN
// subnormal number, scale x up
k -= 54;
x *= Ox1p54;
Ux = reinterpret<u64>(x);
hx = <u32>(Ux >> 32);
} else if (hx >= 0x7ff00000) return x;
else if (hx == 0x3ff00000 && Ux << 32 == 0) return 0;
// reduce x into [sqrt(2)/2, sqrt(2)]
hx += 0x3ff00000 - 0x3fe6a09e;
k += (<i32>hx >> 20) - 0x3ff;
hx = (hx & 0x000fffff) + 0x3fe6a09e;
Ux = <u64>hx << 32 | (Ux & 0xffffffff);
x = reinterpret<f64>(Ux);
var f = x - 1.0;
var hfsq = 0.5 * f * f;
var s = f / (2.0 + f);
var z = s * s;
var w = z * z;
var t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
var t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
var R = t2 + t1;
var dk = k;
return s * (hfsq + R) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
}
// export function log2(x: f64): f64 {
// return log(x) / LN2;
// }
// export function log10(x: f64): f64 {
// return log(x) / LN10;
// }
export function max(value1: f64, value2: f64): f64 {
return builtin_max(value1, value2);
}
export function min(value1: f64, value2: f64): f64 {
return builtin_min(value1, value2);
}
export function pow(x: f64, y: f64): f64 { // pased on musl's implementation of pow
const
two53 = 9007199254740992.0, // 0x43400000, 0x00000000
huge = 1.0e+300,
tiny = 1.0e-300,
// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
L1 = 5.99999999999994648725e-01, // 0x3FE33333, 0x33333303
L2 = 4.28571428578550184252e-01, // 0x3FDB6DB6, 0xDB6FABFF
L3 = 3.33333329818377432918e-01, // 0x3FD55555, 0x518F264D
L4 = 2.72728123808534006489e-01, // 0x3FD17460, 0xA91D4101
L5 = 2.30660745775561754067e-01, // 0x3FCD864A, 0x93C9DB65
L6 = 2.06975017800338417784e-01, // 0x3FCA7E28, 0x4A454EEF
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
lg2 = 6.93147180559945286227e-01, // 0x3FE62E42, 0xFEFA39EF
lg2_h = 6.93147182464599609375e-01, // 0x3FE62E43, 0x00000000
lg2_l = -1.90465429995776804525e-09, // 0xBE205C61, 0x0CA86C39
ovt = 8.0085662595372944372e-017, // -(1024-log2(ovfl+.5ulp))
cp = 9.61796693925975554329e-01, // 0x3FEEC709, 0xDC3A03FD =2/(3ln2)
cp_h = 9.61796700954437255859e-01, // 0x3FEEC709, 0xE0000000 =(float)cp
cp_l = -7.02846165095275826516e-09, // 0xBE3E2FE0, 0x145B01F5 =tail of cp_h
ivln2 = 1.44269504088896338700e+00, // 0x3FF71547, 0x652B82FE =1/ln2
ivln2_h = 1.44269502162933349609e+00, // 0x3FF71547, 0x60000000 =24b 1/ln2
ivln2_l = 1.92596299112661746887e-0; // 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail
var __u = reinterpret<u64>(x); // EXTRACT_WORDS(hx, lx, x)
var hx = <i32>(__u >> 32);
var lx = <u32>__u;
__u = reinterpret<u64>(y); // EXTRACT_WORDS(hy, ly, y)
var hy = <i32>(__u >> 32);
var ly = <u32>__u;
var ix = hx & 0x7fffffff;
var iy = hy & 0x7fffffff;
// x**0 = 1, even if x is NaN
if ((iy | ly) == 0) return 1.0;
// 1**y = 1, even if y is NaN
if (hx == 0x3ff00000 && lx == 0) return 1.0;
// NaN if either arg is NaN
if (
ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0)
) return x + y;
// determine if y is an odd int when x < 0
// yisint = 0 ... y is not an integer
// yisint = 1 ... y is an odd int
// yisint = 2 ... y is an even int
var yisint = 0, k: i32;
if (hx < 0) {
if (iy >= 0x43400000) yisint = 2; // even integer y
else if (iy >= 0x3ff00000) {
k = (iy >> 20) - 0x3ff; // exponent
if (k > 20) {
let jj = ly >> (52 - k);
if ((jj << (52 - k)) == ly) yisint = 2 - (jj & 1);
} else if (ly == 0) {
let jj = iy >> (20 - k);
if ((jj << (20 - k)) == iy) yisint = 2 - (jj & 1);
}
}
}
// special value of y
if (ly == 0) {
if (iy == 0x7ff00000) { // y is +-inf
if (((ix - 0x3ff00000) | lx) == 0) return 1.0; // (-1)**+-inf is 1
else if (ix >= 0x3ff00000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
}
if (iy == 0x3ff00000) { // y is +-1
if (hy >= 0) return x;
return 1 / x;
}
if (hy == 0x40000000) return x * x; // y is 2
if (hy == 0x3fe00000) { // y is 0.5
if (hx >= 0) return sqrt(x); // x >= +0
}
}
var ax = builtin_abs(x), z: f64;
// special value of x
if (lx == 0) {
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { // x is +-0,+-inf,+-1
z = ax;
if (hy < 0) z = 1.0 / z; // z = (1/|x|)
if (hx < 0) {
if (((ix - 0x3ff00000) | yisint) == 0) z = (z - z) / (z - z); // (-1)**non-int is NaN
else if (yisint == 1) z = -z; // (x<0)**odd = -(|x|**odd)
}
return z;
}
}
var s = 1.0; // sign of result
if (hx < 0) {
if (yisint == 0) return (x - x) / (x - x); // (x<0)**(non-int) is NaN
if (yisint == 1) s = -1.0; // (x<0)**(odd int)
}
// |y| is huge
var t1: f64, t2: f64, p_h: f64, p_l: f64, r: f64, t: f64, u: f64, v: f64, w: f64;
var j: i32, n: i32;
if (iy > 0x41e00000) { // if |y| > 2**31
if (iy > 0x43f00000) { // if |y| > 2**64, must o/uflow
if (ix <= 0x3fefffff) return hy < 0 ? huge * huge : tiny * tiny;
if (ix >= 0x3ff00000) return hy > 0 ? huge * huge : tiny * tiny;
}
// over/underflow if x is not close to one
if (ix < 0x3fefffff) return hy < 0 ? s * huge * huge : s * tiny * tiny;
if (ix > 0x3ff00000) return hy > 0 ? s * huge * huge : s * tiny * tiny;
// now |1-x| is tiny <= 2**-20, suffice to compute
// log(x) by x-x^2/2+x^3/3-x^4/4
t = ax - 1.0; // t has 20 trailing zeros
w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
u = ivln2_h * t; // ivln2_h has 21 sig. bits
v = t * ivln2_l - w * ivln2;
t1 = u + v;
t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xffffffff00000000); // SET_LOW_WORD(t1, 0)
t2 = v - (t1 - u);
} else {
let ss: f64, s2: f64, s_h: f64, s_l: f64, t_h: f64, t_l: f64;
n = 0;
// take care subnormal number
if (ix < 0x00100000) {
ax *= two53;
n -= 53;
ix = <u32>(reinterpret<u64>(ax) >> 32);
}
n += (ix >> 20) - 0x3ff;
j = ix & 0x000fffff;
// determine interval
ix = j | 0x3ff00000; // normalize ix
if (j <= 0x3988E) k = 0; // |x|<sqrt(3/2)
else if (j < 0xBB67A) k = 1; // |x|<sqrt(3)
else {
k = 0;
n += 1;
ix -= 0x00100000;
}
ax = reinterpret<f64>(reinterpret<u64>(ax) & 0xffffffff | (<u64>ix << 32)); // SET_HIGH_WORD(ax, ix)
// compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
let bp = select<f64>(1.5, 1.0, k); // bp[k], bp[0]=1.0, bp[1]=1.5
u = ax - bp;
v = 1.0 / (ax + bp);
ss = u * v;
s_h = ss;
s_h = reinterpret<f64>(reinterpret<u64>(s_h) & 0xffffffff00000000); // SET_LOW_WORD(s_h, 0)
// t_h=ax+bp[k] High
t_h = reinterpret<f64>(<u64>(((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)) << 32); // SET_HIGH_WORD
t_l = ax - (t_h - bp);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
// compute log(ax)
s2 = ss * ss;
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + ss);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
t_h = reinterpret<f64>(reinterpret<u64>(t_h) & 0xffffffff00000000); // SET_LOW_WORD(t_h, 0)
t_l = r - ((t_h - 3.0) - s2);
// u+v = ss*(1+...)
u = s_h * t_h;
v = s_l * t_h + t_l * ss;
// 2/(3log2)*(ss+...)
p_h = u + v;
p_h = reinterpret<f64>(reinterpret<u64>(p_h) & 0xffffffff00000000); // SET_LOW_WORD(p_h, 0)
p_l = v - (p_h - u);
let z_h = cp_h * p_h; // cp_h+cp_l = 2/(3*log2)
let dp_l = select<f64>(1.35003920212974897128e-08, 0.0, k); // dp_l[k]
let z_l = cp_l * p_h + p_l * cp + dp_l;
// log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l
t = <f64>n;
let dp_h = select<f64>(5.84962487220764160156e-01, 0.0, k); // dp_h[k]
t1 = ((z_h + z_l) + dp_h) + t;
t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xffffffff00000000); // SET_LOW_WORD(t1, 0);
t2 = z_l - (((t1 - t) - dp_h) - z_h);
}
// split up y into y1+y2 and compute (y1+y2)*(t1+t2)
var y1 = y;
y1 = reinterpret<f64>(reinterpret<u64>(y1) & 0xffffffff00000000); // SET_LOW_WORD(y1, 0)
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
__u = reinterpret<u64>(z); // EXTRACT_WORDS(j, i, z) ...
j = <u32>(__u >> 32);
var i = <i32>__u;
if (j >= 0x40900000) { // z >= 1024
if (((j - 0x40900000) | i) != 0) return s * huge * huge; // if z > 1024, overflow
if (p_l + ovt > z - p_h) return s * huge * huge; // overflow
} else if ((j & 0x7fffffff) >= 0x4090cc00) { // z <= -1075, FIXME: instead of abs(j) use unsigned j
if (((j - 0xc090cc00) | i) != 0) return s * tiny * tiny; // z < -1075, underflow
if (p_l <= z - p_h) return s * tiny * tiny; // underflow
}
// compute 2**(p_h+p_l)
i = j & 0x7fffffff;
k = (i >> 20) - 0x3ff;
n = 0;
if (i > 0x3fe00000) { // if |z| > 0.5, set n = [z+0.5]
n = j + (0x00100000 >> (k + 1));
k = ((n & 0x7fffffff) >> 20) - 0x3ff; // new k for n
t = 0.0;
t = reinterpret<f64>(<u64>(n & ~(0x000fffff >> k)) << 32); // SET_HIGH_WORD(t, n & ~(0x000fffff>>k))
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
if (j < 0) n = -n;
p_h -= t;
}
t = p_l + p_h;
t = reinterpret<f64>(reinterpret<u64>(t) & 0xffffffff00000000); // SET_LOW_WORD(t, 0)
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
r = (z * t1) / (t1 - 2.0) - (w + z * w);
z = 1.0 - (r - z);
j = <u32>(reinterpret<u64>(z) >> 32); // GET_HIGH_WORD(j, z)
j += n << 20;
if ((j >> 20) <= 0) z = scalbn(z, n); // subnormal output
else z = reinterpret<f64>(reinterpret<u64>(z) & 0xffffffff | (<u64>j << 32)); // SET_HIGH_WORD(z, j)
return s * z;
}
export function round(x: f64): f64 {
return builtin_nearest(x);
}
export function sign(x: f64): f64 {
return x > 0 ? 1 : x < 0 ? -1 : x;
}
export function sqrt(x: f64): f64 {
return builtin_sqrt(x);
}
export function trunc(x: f64): f64 {
return builtin_trunc(x);
}
}
export namespace Mathf {
export const E = <f32>Math.E;
export const LN2 = <f32>Math.LN2;
export const LN10 = <f32>Math.LN10;
export const LOG2E = <f32>Math.LOG2E;
export const LOG10E = <f32>Math.LOG10E;
export const PI = <f32>Math.PI;
export const SQRT1_2 = <f32>Math.SQRT1_2;
export const SQRT2 = <f32>Math.SQRT2;
export function abs(x: f32): f32 {
return builtin_abs(x);
}
export function ceil(x: f32): f32 {
return builtin_ceil(x);
}
export function clz32(x: f32): i32 {
return builtin_clz(<i32>x);
}
export function floor(x: f32): f32 {
return builtin_floor(x);
}
export function exp(x: f32): f32 { // based on musl's implementation of expf
const
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 + copysign<f32>(0.5, x)); // was: [0.5, -0.5][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
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
Ox1p25f = <f32>33554432.0;
var ux = reinterpret<u32>(x);
var k = 0;
if (ux < 0x00800000 || <bool>(ux >> 31)) { // x < 2**-126
if (ux << 1 == 0) return -1 / (x * x); // log(+-0)=-inf
if (ux >> 31) return (x - x) / 0; // log(-#) = NaN
// subnormal number, scale up x
k -= 25;
x *= Ox1p25f;
ux = reinterpret<u32>(x);
} else if (ux >= 0x7f800000) return x;
else if (ux == 0x3f800000) return 0;
// reduce x into [sqrt(2)/2, sqrt(2)]
ux += 0x3f800000 - 0x3f3504f3;
k += <u32>(<i32>ux >> 23) - 0x7f;
ux = (ux & 0x007fffff) + 0x3f3504f3;
x = reinterpret<f32>(ux);
var f = x - 1.0;
var s = f / (2.0 + f);
var z = s * s;
var w = z * z;
var t1 = w * (Lg2 + w * Lg4);
var t2 = z * (Lg1 + w * Lg3);
var R = t2 + t1;
var hfsq = <f32>0.5 * f * f;
var dk = <f32>k;
return s * (hfsq + R) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
}
// export function log2(x: f32): f32 {
// return log(x) / LN2;
// }
// export function log10(x: f32): f32 {
// return log(x) / LN10;
// }
export function max(value1: f32, value2: f32): f32 {
return builtin_max(value1, value2);
}
export function min(value1: f32, value2: f32): f32 {
return builtin_min(value1, value2);
}
export function pow(x: f32, y: f32): f32 { // based on musl's implementation of powf
const
two24 = <f32>16777216.0, // 0x4b800000
huge = <f32>1.0e30,
tiny = <f32>1.0e-30,
// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
L1 = <f32>6.0000002384e-01, // 0x3f19999a
L2 = <f32>4.2857143283e-01, // 0x3edb6db7
L3 = <f32>3.3333334327e-01, // 0x3eaaaaab
L4 = <f32>2.7272811532e-01, // 0x3e8ba305
L5 = <f32>2.3066075146e-01, // 0x3e6c3255
L6 = <f32>2.0697501302e-01, // 0x3e53f142
P1 = <f32>1.6666667163e-01, // 0x3e2aaaab
P2 = <f32>-2.7777778450e-03, // 0xbb360b61
P3 = <f32>6.6137559770e-05, // 0x388ab355
P4 = <f32>-1.6533901999e-06, // 0xb5ddea0e
P5 = <f32>4.1381369442e-08, // 0x3331bb4c
lg2 = <f32>6.9314718246e-01, // 0x3f317218
lg2_h = <f32>6.93145752e-01, // 0x3f317200
lg2_l = <f32>1.42860654e-06, // 0x35bfbe8c
ovt = <f32>4.2995665694e-08, // -(128-log2(ovfl+.5ulp))
cp = <f32>9.6179670095e-01, // 0x3f76384f =2/(3ln2)
cp_h = <f32>9.6191406250e-01, // 0x3f764000 =12b cp
cp_l = <f32>-1.1736857402e-04, // 0xb8f623c6 =tail of cp_h
ivln2 = <f32>1.4426950216e+00, // 0x3fb8aa3b =1/ln2
ivln2_h = <f32>1.4426879883e+00, // 0x3fb8aa00 =16b 1/ln2
ivln2_l = <f32>7.0526075433e-06; // 0x36eca570 =1/ln2 tail
var hx = reinterpret<i32>(x); // GET_FLOAT_WORD(hx, x)
var hy = reinterpret<i32>(y); // GET_FLOAT_WORD(hy, y)
var ix = hx & 0x7fffffff;
var iy = hy & 0x7fffffff;
// x**0 = 1, even if x is NaN
if (iy == 0) return 1.0;
// 1**y = 1, even if y is NaN
if (hx == 0x3f800000) return 1.0;
// NaN if either arg is NaN
if (ix > 0x7f800000 || iy > 0x7f800000) return x + y;
// determine if y is an odd int when x < 0
// yisint = 0 ... y is not an integer
// yisint = 1 ... y is an odd int
// yisint = 2 ... y is an even int
var yisint = 0, j: i32, k: i32;
if (hx < 0) {
if (iy >= 0x4b800000) yisint = 2; // even integer y
else if (iy >= 0x3f800000) {
k = (iy >> 23) - 0x7f; // exponent
j = iy >> (23 - k);
if ((j << (23 - k)) == iy) yisint = 2 - (j & 1);
}
}
// special value of y
if (iy == 0x7f800000) { // y is +-inf
if (ix == 0x3f800000) return 1.0; // (-1)**+-inf is 1
else if (ix > 0x3f800000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
}
if (iy == 0x3f800000) return hy >= 0 ? x : 1.0 / x; // y is +-1
if (hy == 0x40000000) return x * x; // y is 2
if (hy == 0x3f000000) { // y is 0.5
if (hx >= 0) return builtin_sqrt<f32>(x); // x >= +0
}
var ax = builtin_abs<f32>(x);
// special value of x
var z: f32;
if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { // x is +-0,+-inf,+-1
z = ax;
if (hy < 0) z = 1.0 / z; // z = (1/|x|)
if (hx < 0) {
if (((ix - 0x3f800000) | yisint) == 0) z = (z - z) / (z - z); // (-1)**non-int is NaN
else if (yisint == 1) z = -z; // (x<0)**odd = -(|x|**odd)
}
return z;
}
var sn = <f32>1.0; // sign of result
if (hx < 0) {
if (yisint == 0) return (x - x) / (x - x); // (x<0)**(non-int) is NaN
if (yisint == 1) sn = -1.0; // (x<0)**(odd int)
}
// |y| is huge
var t1: f32, t2: f32, r: f32, s: f32, t: f32, u: f32, v: f32, w: f32, p_h: f32, p_l: f32;
var n: i32, is: i32;
if (iy > 0x4d000000) { // if |y| > 2**27
// over/underflow if x is not close to one
if (ix < 0x3f7ffff8) return hy < 0 ? sn * huge * huge : sn * tiny * tiny;
if (ix > 0x3f800007) return hy > 0 ? sn * huge * huge : sn * tiny * tiny;
// now |1-x| is tiny <= 2**-20, suffice to compute
// log(x) by x-x^2/2+x^3/3-x^4/4
t = ax - 1; // t has 20 trailing zeros
w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
u = ivln2_h * t; // ivln2_h has 16 sig. bits
v = t * ivln2_l - w * ivln2;
t1 = u + v;
is = reinterpret<i32>(t1); // GET_FLOAT_WORD(is, t1)
t1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t1, is & 0xfffff000)
t2 = v - (t1 - u);
} else {
let s2: f32, s_h: f32, s_l: f32, t_h: f32, t_l: f32;
n = 0;
// take care subnormal number
if (ix < 0x00800000) {
ax *= two24;
n -= 24;
ix = reinterpret<i32>(ax); // GET_FLOAT_WORD(ix, ax)
}
n += (ix >> 23) - 0x7f;
j = ix & 0x007fffff;
// determine interval
ix = j | 0x3f800000; // normalize ix
if (j <= 0x1cc471) k = 0; // |x|<sqrt(3/2)
else if (j < 0x5db3d7) k = 1; // |x|<sqrt(3)
else {
k = 0;
n += 1;
ix -= 0x00800000;
}
ax = reinterpret<f32>(ix); // SET_FLOAT_WORD(ax, ix)
// compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
let bp = select<f32>(1.5, 1.0, k); // bp[k], [1.0, 1.5]
u = ax - bp;
v = 1.0 / (ax + bp);
s = u * v;
s_h = s;
is = reinterpret<u32>(s_h); // GET_FLOAT_WORD(is, s_h)
s_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(s_h, is & 0xfffff000)
// t_h=ax+bp[k] High
is = ((ix >> 1) & 0xfffff000) | 0x20000000;
t_h = reinterpret<f32>(is + 0x00400000 + (k << 21)); // SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21))
t_l = ax - (t_h - bp);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
// compute log(ax)
s2 = s * s;
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + s);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
is = reinterpret<u32>(t_h); // GET_FLOAT_WORD(is, t_h)
t_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t_h, is & 0xfffff000)
t_l = r - ((t_h - 3.0) - s2);
// u+v = s*(1+...)
u = s_h * t_h;
v = s_l * t_h + t_l * s;
// 2/(3log2)*(s+...)
p_h = u + v;
is = reinterpret<u32>(p_h); // GET_FLOAT_WORD(is, p_h)
p_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(p_h, is & 0xfffff000)
p_l = v - (p_h - u);
let z_h = cp_h * p_h; // cp_h+cp_l = 2/(3*log2)
let dp_l = select<f32>(1.56322085e-06, 0.0, k); // dp_l[k], [0.0, 1.56322085e-06]
let z_l = cp_l * p_h + p_l * cp + dp_l;
// log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l
t = <f32>n;
let dp_h = select<f32>(5.84960938e-01, 0.0, k); // dp_h[k], [0.0, 5.84960938e-01]
t1 = (((z_h + z_l) + dp_h) + t);
is = reinterpret<u32>(t1); // GET_FLOAT_WORD(is, t1)
t1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t1, is & 0xfffff000)
t2 = z_l - (((t1 - t) - dp_h) - z_h);
}
// split up y into y1+y2 and compute (y1+y2)*(t1+t2)
is = reinterpret<u32>(y); // GET_FLOAT_WORD(is, y)
var y1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(y1, is & 0xfffff000)
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
j = reinterpret<u32>(z); // GET_FLOAT_WORD(j, z)
if (j > 0x43000000) { // if z > 128, overflow
return sn * huge * huge;
} else if (j == 0x43000000) { // if z == 128
if (p_l + ovt > z - p_h) return sn * huge * huge; // overflow
} else if ((j & 0x7fffffff) > 0x43160000) { // z < -150, FIXME: check should be (uint32_t)j > 0xc3160000
return sn * tiny * tiny; // underflow
} else if (j == 0xc3160000) { // z == -150
if (p_l <= z - p_h) return sn * tiny * tiny; // underflow
}
// compute 2**(p_h+p_l)
var i = j & 0x7fffffff;
k = (i >> 23) - 0x7f;
n = 0;
if (i > 0x3f000000) { // if |z| > 0.5, set n = [z+0.5]
n = j + (0x00800000 >> (k + 1));
k = ((n & 0x7fffffff) >> 23) - 0x7f; // new k for n
t = reinterpret<f32>(n & ~(0x007fffff >> k)); // SET_FLOAT_WORD(t, n & ~(0x007fffff>>k))
n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
if (j < 0) n = -n;
p_h -= t;
}
t = p_l + p_h;
is = reinterpret<u32>(t); // GET_FLOAT_WORD(is, t)
t = reinterpret<f32>(is & 0xffff8000); // SET_FLOAT_WORD(t, is & 0xffff8000);
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
r = (z * t1) / (t1 - 2.0) - (w + z * w);
z = 1.0 - (r - z);
j = reinterpret<u32>(z); // GET_FLOAT_WORD(j, z)
j += n << 23;
if ((j >> 23) <= 0) z = scalbnf(z, n); // subnormal output
else z = reinterpret<f32>(j); // SET_FLOAT_WORD(z, j)
return sn * z;
}
export function round(x: f32): f32 {
return builtin_nearest(x);
}
export function sign(x: f32): f32 {
return x > 0 ? 1 : x < 0 ? -1 : x;
}
export function sqrt(x: f32): f32 {
return builtin_sqrt(x);
}
export function trunc(x: f32): f32 {
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);
}
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