math.ts

import * as JSMath from "./bindings/Math";
export { JSMath };

import {
  pow_lut, exp_lut, exp2_lut, log_lut, log2_lut,
  powf_lut, expf_lut, exp2f_lut, logf_lut, log2f_lut
} from "./util/math";

import {
  abs as builtin_abs,
  ceil as builtin_ceil,
  clz as builtin_clz,
  copysign as builtin_copysign,
  floor as builtin_floor,
  max as builtin_max,
  min as builtin_min,
  sqrt as builtin_sqrt,
  trunc as builtin_trunc
} from "./builtins";

// SUN COPYRIGHT NOTICE
//
// 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.
//
// Applies to all functions marked with a comment referring here.

/** @internal */
// @ts-ignore: decorator
@lazy
var rempio2_y0: f64,
    rempio2_y1: f64,
    res128_hi: u64;

/** @internal */
// @ts-ignore: decorator
@lazy @inline
const PIO2_TABLE: StaticArray<u64> = [
  0x00000000A2F9836E, 0x4E441529FC2757D1, 0xF534DDC0DB629599, 0x3C439041FE5163AB,
  0xDEBBC561B7246E3A, 0x424DD2E006492EEA, 0x09D1921CFE1DEB1C, 0xB129A73EE88235F5,
  0x2EBB4484E99C7026, 0xB45F7E413991D639, 0x835339F49C845F8B, 0xBDF9283B1FF897FF,
  0xDE05980FEF2F118B, 0x5A0A6D1F6D367ECF, 0x27CB09B74F463F66, 0x9E5FEA2D7527BAC7,
  0xEBE5F17B3D0739F7, 0x8A5292EA6BFB5FB1, 0x1F8D5D0856033046, 0xFC7B6BABF0CFBC20,
  0x9AF4361DA9E39161, 0x5EE61B086599855F, 0x14A068408DFFD880, 0x4D73273106061557
];

/** @internal */
function R(z: f64): f64 { // Rational approximation of (asin(x)-x)/x^3
  const                   // see: musl/src/math/asin.c and SUN COPYRIGHT NOTICE above
    pS0 = reinterpret<f64>(0x3FC5555555555555), //  1.66666666666666657415e-01
    pS1 = reinterpret<f64>(0xBFD4D61203EB6F7D), // -3.25565818622400915405e-01
    pS2 = reinterpret<f64>(0x3FC9C1550E884455), //  2.01212532134862925881e-01
    pS3 = reinterpret<f64>(0xBFA48228B5688F3B), // -4.00555345006794114027e-02
    pS4 = reinterpret<f64>(0x3F49EFE07501B288), //  7.91534994289814532176e-04
    pS5 = reinterpret<f64>(0x3F023DE10DFDF709), //  3.47933107596021167570e-05
    qS1 = reinterpret<f64>(0xC0033A271C8A2D4B), // -2.40339491173441421878e+00
    qS2 = reinterpret<f64>(0x40002AE59C598AC8), //  2.02094576023350569471e+00
    qS3 = reinterpret<f64>(0xBFE6066C1B8D0159), // -6.88283971605453293030e-01
    qS4 = reinterpret<f64>(0x3FB3B8C5B12E9282); //  7.70381505559019352791e-02
  var p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
  var q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
  return p / q;
}

/** @internal */
// @ts-ignore: decorator
@inline
function expo2(x: f64): f64 { // exp(x)/2 for x >= log(DBL_MAX)
  const                       // see: musl/src/math/__expo2.c
    k    = <u32>2043,
    kln2 = reinterpret<f64>(0x40962066151ADD8B); // 0x1.62066151add8bp+10
  var scale = reinterpret<f64>(<u64>((<u32>0x3FF + k / 2) << 20) << 32);
  return NativeMath.exp(x - kln2) * scale * scale;
}

/** @internal */
/* Helper function to eventually get bits of π/2 * |x|
 *
 * y = π/4 * (frac << clz(frac) >> 11)
 * return clz(frac)
 *
 * Right shift 11 bits to make upper half fit in `double`
 */
// @ts-ignore: decorator
@inline
function pio2_right(q0: u64, q1: u64): u64 { // see: jdh8/metallic/blob/master/src/math/double/rem_pio2.c
  // Bits of π/4
  const p0: u64 = 0xC4C6628B80DC1CD1;
  const p1: u64 = 0xC90FDAA22168C234;

  const Ox1p_64 = reinterpret<f64>(0x3BF0000000000000); // 0x1p-64
  const Ox1p_75 = reinterpret<f64>(0x3B40000000000000); // 0x1p-75

  var shift = clz(q1);

  q1 = q1 << shift | q0 >> (64 - shift);
  q0 <<= shift;

  var lo = umuldi(p1, q1);
  var hi = res128_hi;

  var ahi = hi >> 11;
  var alo = lo >> 11 | hi << 53;
  var blo = <u64>(Ox1p_75 * <f64>p0 * <f64>q1 + Ox1p_75 * <f64>p1 * <f64>q0);

  rempio2_y0 = <f64>(ahi + u64(lo < blo));
  rempio2_y1 = Ox1p_64 * <f64>(alo + blo);

  return shift;
}

/** @internal */
// @ts-ignore: decorator
@inline
function umuldi(u: u64, v: u64): u64 {
  var u1: u64 , v1: u64, w0: u64, w1: u64, t: u64;

  u1 = u & 0xFFFFFFFF;
  v1 = v & 0xFFFFFFFF;

  u >>= 32;
  v >>= 32;

  t  = u1 * v1;
  w0 = t & 0xFFFFFFFF;
  t  = u * v1 + (t >> 32);
  w1 = t >> 32;
  t  = u1 * v + (t & 0xFFFFFFFF);

  res128_hi = u * v + w1 + (t >> 32);
  return (t << 32) + w0;
}

/** @internal */
function pio2_large_quot(x: f64, u: i64): i32 { // see: jdh8/metallic/blob/master/src/math/double/rem_pio2.c
  const bits = changetype<usize>(PIO2_TABLE);

  var magnitude = u & 0x7FFFFFFFFFFFFFFF;
  var offset = (magnitude >> 52) - 1045;
  var shift  = offset & 63;
  var tblPtr = bits + (<i32>(offset >> 6) << 3);
  var s0: u64, s1: u64, s2: u64;

  var b0 = load<u64>(tblPtr, 0 << 3);
  var b1 = load<u64>(tblPtr, 1 << 3);
  var b2 = load<u64>(tblPtr, 2 << 3);

  // Get 192 bits of 0x1p-31 / π with `offset` bits skipped
  if (shift) {
    let rshift = 64 - shift;
    let b3 = load<u64>(tblPtr, 3 << 3);
    s0 = b1 >> rshift | b0 << shift;
    s1 = b2 >> rshift | b1 << shift;
    s2 = b3 >> rshift | b2 << shift;
  } else {
    s0 = b0;
    s1 = b1;
    s2 = b2;
  }

  var significand = (u & 0x000FFFFFFFFFFFFF) | 0x0010000000000000;

  // First 128 bits of fractional part of x/(2π)
  var blo = umuldi(s1, significand);
  var bhi = res128_hi;

  var ahi = s0 * significand;
  var clo = (s2 >> 32) * (significand >> 32);
  var plo = blo + clo;
  var phi = ahi + bhi + u64(plo < clo);

  // r: u128 = p << 2
  var rlo = plo << 2;
  var rhi = phi << 2 | plo >> 62;

  // s: i128 = r >> 127
  var slo = <i64>rhi >> 63;
  var shi = slo >> 1;
  var q   = (<i64>phi >> 62) - slo;

  var shifter = 0x3CB0000000000000 - (pio2_right(rlo ^ slo, rhi ^ shi) << 52);
  var signbit = (u ^ rhi) & 0x8000000000000000;
  var coeff = reinterpret<f64>(shifter | signbit);

  rempio2_y0 *= coeff;
  rempio2_y1 *= coeff;

  return <i32>q;
}

/** @internal */
// @ts-ignore: decorator
@inline
function rempio2(x: f64, u: u64, sign: i32): i32 {
  const pio2_1  = reinterpret<f64>(0x3FF921FB54400000); // 1.57079632673412561417e+00
  const pio2_1t = reinterpret<f64>(0x3DD0B4611A626331); // 6.07710050650619224932e-11
  const pio2_2  = reinterpret<f64>(0x3DD0B4611A600000); // 6.07710050630396597660e-11
  const pio2_2t = reinterpret<f64>(0x3BA3198A2E037073); // 2.02226624879595063154e-21
  const pio2_3  = reinterpret<f64>(0x3BA3198A2E000000); // 2.02226624871116645580e-21
  const pio2_3t = reinterpret<f64>(0x397B839A252049C1); // 8.47842766036889956997e-32
  const invpio2 = reinterpret<f64>(0x3FE45F306DC9C883); // 0.63661977236758134308

  var ix = <u32>(u >> 32) & 0x7FFFFFFF;

  if (ASC_SHRINK_LEVEL < 1) {
    if (ix < 0x4002D97C) { // |x| < 3pi/4, special case with n=+-1
      let q = 1, z: f64, y0: f64, y1: f64;
      if (!sign) {
        z = x - pio2_1;
        if (ix != 0x3FF921FB) { // 33+53 bit pi is good enough
          y0 = z - pio2_1t;
          y1 = (z - y0) - pio2_1t;
        } else { // near pi/2, use 33+33+53 bit pi
          z -= pio2_2;
          y0 = z - pio2_2t;
          y1 = (z - y0) - pio2_2t;
        }
      } else { // negative x
        z = x + pio2_1;
        if (ix != 0x3FF921FB) { // 33+53 bit pi is good enough
          y0 = z + pio2_1t;
          y1 = (z - y0) + pio2_1t;
        } else { // near pi/2, use 33+33+53 bit pi
          z += pio2_2;
          y0 = z + pio2_2t;
          y1 = (z - y0) + pio2_2t;
        }
        q = -1;
      }
      rempio2_y0 = y0;
      rempio2_y1 = y1;
      return q;
    }
  }

  if (ix < 0x413921FB) { // |x| ~< 2^20*pi/2 (1647099)
    // Use precise Cody Waite scheme
    let q  = nearest(x * invpio2);
    let r  = x - q * pio2_1;
    let w  = q * pio2_1t; // 1st round good to 85 bit
    let j  = ix >> 20;
    let y0 = r - w;
    let hi = <u32>(reinterpret<u64>(y0) >> 32);
    let i  = j - ((hi >> 20) & 0x7FF);

    if (i > 16) { // 2nd iteration needed, good to 118
      let t = r;
      w  = q * pio2_2;
      r  = t - w;
      w  = q * pio2_2t - ((t - r) - w);
      y0 = r - w;
      hi = <u32>(reinterpret<u64>(y0) >> 32);
      i = j - ((hi >> 20) & 0x7FF);
      if (i > 49) { // 3rd iteration need, 151 bits acc
        let t = r;
        w  = q * pio2_3;
        r  = t - w;
        w  = q * pio2_3t - ((t - r) - w);
        y0 = r - w;
      }
    }
    let y1 = (r - y0) - w;
    rempio2_y0 = y0;
    rempio2_y1 = y1;
    return <i32>q;
  }
  var q = pio2_large_quot(x, u);
  return select(-q, q, sign);
}

/** @internal */
// @ts-ignore: decorator
@inline
function sin_kern(x: f64, y: f64, iy: i32): f64 { // see: musl/tree/src/math/__sin.c
  const S1 = reinterpret<f64>(0xBFC5555555555549); // -1.66666666666666324348e-01
  const S2 = reinterpret<f64>(0x3F8111111110F8A6); //  8.33333333332248946124e-03
  const S3 = reinterpret<f64>(0xBF2A01A019C161D5); // -1.98412698298579493134e-04
  const S4 = reinterpret<f64>(0x3EC71DE357B1FE7D); //  2.75573137070700676789e-06
  const S5 = reinterpret<f64>(0xBE5AE5E68A2B9CEB); // -2.50507602534068634195e-08
  const S6 = reinterpret<f64>(0x3DE5D93A5ACFD57C); //  1.58969099521155010221e-10

  var z = x * x;
  var w = z * z;
  var r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
  var v = z * x;
  if (!iy) {
    return x + v * (S1 + z * r);
  } else {
    return x - ((z * (0.5 * y - v * r) - y) - v * S1);
  }
}

/** @internal */
// @ts-ignore: decorator
@inline
function cos_kern(x: f64, y: f64): f64 { // see: musl/tree/src/math/__cos.c
  const C1 = reinterpret<f64>(0x3FA555555555554C); //  4.16666666666666019037e-02
  const C2 = reinterpret<f64>(0xBF56C16C16C15177); // -1.38888888888741095749e-03
  const C3 = reinterpret<f64>(0x3EFA01A019CB1590); //  2.48015872894767294178e-05
  const C4 = reinterpret<f64>(0xBE927E4F809C52AD); // -2.75573143513906633035e-07
  const C5 = reinterpret<f64>(0x3E21EE9EBDB4B1C4); //  2.08757232129817482790e-09
  const C6 = reinterpret<f64>(0xBDA8FAE9BE8838D4); // -1.13596475577881948265e-11

  var z = x * x;
  var w = z * z;
  var r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6));
  var hz = 0.5 * z;
  w = 1.0 - hz;
  return w + (((1.0 - w) - hz) + (z * r - x * y));
}

/** @internal */
function tan_kern(x: f64, y: f64, iy: i32): f64 { // see: src/lib/msun/src/k_tan.c
  const T0  = reinterpret<f64>(0x3FD5555555555563); //  3.33333333333334091986e-01
  const T1  = reinterpret<f64>(0x3FC111111110FE7A); //  1.33333333333201242699e-01
  const T2  = reinterpret<f64>(0x3FABA1BA1BB341FE); //  5.39682539762260521377e-02
  const T3  = reinterpret<f64>(0x3F9664F48406D637); //  2.18694882948595424599e-02
  const T4  = reinterpret<f64>(0x3F8226E3E96E8493); //  8.86323982359930005737e-03
  const T5  = reinterpret<f64>(0x3F6D6D22C9560328); //  3.59207910759131235356e-03
  const T6  = reinterpret<f64>(0x3F57DBC8FEE08315); //  1.45620945432529025516e-03
  const T7  = reinterpret<f64>(0x3F4344D8F2F26501); //  5.88041240820264096874e-04
  const T8  = reinterpret<f64>(0x3F3026F71A8D1068); //  2.46463134818469906812e-04
  const T9  = reinterpret<f64>(0x3F147E88A03792A6); //  7.81794442939557092300e-05
  const T10 = reinterpret<f64>(0x3F12B80F32F0A7E9); //  7.14072491382608190305e-05
  const T11 = reinterpret<f64>(0xBEF375CBDB605373); // -1.85586374855275456654e-05
  const T12 = reinterpret<f64>(0x3EFB2A7074BF7AD4); //  2.59073051863633712884e-05

  const one    = reinterpret<f64>(0x3FF0000000000000); // 1.00000000000000000000e+00
  const pio4   = reinterpret<f64>(0x3FE921FB54442D18); // 7.85398163397448278999e-01
  const pio4lo = reinterpret<f64>(0x3C81A62633145C07); // 3.06161699786838301793e-17

  var z: f64, r: f64, v: f64, w: f64, s: f64;
  var hx = <i32>(reinterpret<u64>(x) >> 32); // high word of x
  var ix = hx & 0x7FFFFFFF; // high word of |x|
  var big = ix >= 0x3FE59428;
  if (big) { // |x| >= 0.6744
    if (hx < 0) { x = -x, y = -y; }
    z = pio4 - x;
    w = pio4lo - y;
    x = z + w;
    y = 0.0;
  }
  z = x * x;
  w = z * z;
  r = T1 + w * (T3 + w * (T5 + w * (T7 + w * (T9 + w * T11))));
  v = z * (T2 + w * (T4 + w * (T6 + w * (T8 + w * (T10 + w * T12)))));
  s = z * x;
  r = y + z * (s * (r + v) + y);
  r += T0 * s;
  w = x + r;
  if (big) {
    v = iy;
    return (1 - ((hx >> 30) & 2)) * (v - 2.0 * (x - (w * w / (w + v) - r)));
  }
  if (iy == 1) return w;
  var a: f64, t: f64;
  z = w;
  z = reinterpret<f64>(reinterpret<u64>(z) & 0xFFFFFFFF00000000);
  v = r - (z - x);  // z + v = r + x
  t = a = -one / w; // a = -1.0 / w
  t = reinterpret<f64>(reinterpret<u64>(t) & 0xFFFFFFFF00000000);
  s = one + t * z;
  return t + a * (s + t * v);
}

/** @internal */
function dtoi32(x: f64): i32 {
  if (ASC_SHRINK_LEVEL > 0) {
    const inv32 = 1.0 / 4294967296;
    return <i32><i64>(x - 4294967296 * floor(x * inv32));
  } else {
    let result = 0;
    let u = reinterpret<u64>(x);
    let e = (u >> 52) & 0x7FF;
    if (e <= 1023 + 30) {
      result = <i32>x;
    } else if (e <= 1023 + 30 + 53) {
      let v = (u & ((<u64>1 << 52) - 1)) | (<u64>1 << 52);
      v = v << e - 1023 - 52 + 32;
      result = <i32>(v >> 32);
      result = select<i32>(-result, result, u >> 63);
    }
    return result;
  }
}

// @ts-ignore: decorator
@lazy
var random_seeded = false;

// @ts-ignore: decorator
@lazy
var random_state0_64: u64;

// @ts-ignore: decorator
@lazy
var random_state1_64: u64;

// @ts-ignore: decorator
@lazy
var random_state0_32: u32;

// @ts-ignore: decorator
@lazy
var random_state1_32: u32;

function murmurHash3(h: u64): u64 { // Force all bits of a hash block to avalanche
  h ^= h >> 33;                     // see: https://github.com/aappleby/smhasher
  h *= 0xFF51AFD7ED558CCD;
  h ^= h >> 33;
  h *= 0xC4CEB9FE1A85EC53;
  h ^= h >> 33;
  return h;
}

function splitMix32(h: u32): u32 {
  h += 0x6D2B79F5;
  h  = (h ^ (h >> 15)) * (h | 1);
  h ^= h + (h ^ (h >> 7)) * (h | 61);
  return h ^ (h >> 14);
}

export namespace NativeMath {

  // @ts-ignore: decorator
  @lazy
  export const E       = reinterpret<f64>(0x4005BF0A8B145769); // 2.7182818284590452354

  // @ts-ignore: decorator
  @lazy
  export const LN2     = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.69314718055994530942

  // @ts-ignore: decorator
  @lazy
  export const LN10    = reinterpret<f64>(0x40026BB1BBB55516); // 2.30258509299404568402

  // @ts-ignore: decorator
  @lazy
  export const LOG2E   = reinterpret<f64>(0x3FF71547652B82FE); // 1.4426950408889634074

  // @ts-ignore: decorator
  @lazy
  export const LOG10E  = reinterpret<f64>(0x3FDBCB7B1526E50E); // 0.43429448190325182765

  // @ts-ignore: decorator
  @lazy
  export const PI      = reinterpret<f64>(0x400921FB54442D18); // 3.14159265358979323846

  // @ts-ignore: decorator
  @lazy
  export const SQRT1_2 = reinterpret<f64>(0x3FE6A09E667F3BCD); // 0.70710678118654752440

  // @ts-ignore: decorator
  @lazy
  export const SQRT2   = reinterpret<f64>(0x3FF6A09E667F3BCD); // 1.41421356237309504880

  // @ts-ignore: decorator
  @lazy
  export var sincos_sin: f64 = 0;

  // @ts-ignore: decorator
  @lazy
  export var sincos_cos: f64 = 0;

  // @ts-ignore: decorator
  @inline export function abs(x: f64): f64 {
    return builtin_abs<f64>(x);
  }

  export function acos(x: f64): f64 { // see: musl/src/math/acos.c and SUN COPYRIGHT NOTICE above
    const
      pio2_hi   = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
      pio2_lo   = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var hx = <u32>(reinterpret<u64>(x) >> 32);
    var ix = hx & 0x7FFFFFFF;
    if (ix >= 0x3FF00000) {
      let lx = <u32>reinterpret<u64>(x);
      if ((ix - 0x3FF00000 | lx) == 0) {
        if (hx >> 31) return 2 * pio2_hi + Ox1p_120f;
        return 0;
      }
      return 0 / (x - x);
    }
    if (ix < 0x3FE00000) {
      if (ix <= 0x3C600000) return pio2_hi + Ox1p_120f;
      return pio2_hi - (x - (pio2_lo - x * R(x * x)));
    }
    var s: f64, w: f64, z: f64;
    if (hx >> 31) {
      // z = (1.0 + x) * 0.5;
      z = 0.5 + x * 0.5;
      s = builtin_sqrt<f64>(z);
      w = R(z) * s - pio2_lo;
      return 2 * (pio2_hi - (s + w));
    }
    // z = (1.0 - x) * 0.5;
    z = 0.5 - x * 0.5;
    s = builtin_sqrt<f64>(z);
    var df = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
    var c = (z - df * df) / (s + df);
    w = R(z) * s + c;
    return 2 * (df + w);
  }

  export function acosh(x: f64): f64 { // see: musl/src/math/acosh.c
    const s = reinterpret<f64>(0x3FE62E42FEFA39EF);
    var e = reinterpret<u64>(x) >> 52 & 0x7FF;
    if (e < 0x3FF + 1) return log1p(x - 1 + builtin_sqrt<f64>((x - 1) * (x - 1) + 2 * (x - 1)));
    if (e < 0x3FF + 26) return log(2 * x - 1 / (x + builtin_sqrt<f64>(x * x - 1)));
    return log(x) + s;
  }

  export function asin(x: f64): f64 { // see: musl/src/math/asin.c and SUN COPYRIGHT NOTICE above
    const
      pio2_hi   = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
      pio2_lo   = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var hx = <u32>(reinterpret<u64>(x) >> 32);
    var ix = hx & 0x7FFFFFFF;
    if (ix >= 0x3FF00000) {
      let lx = <u32>reinterpret<u64>(x);
      if ((ix - 0x3FF00000 | lx) == 0) return x * pio2_hi + Ox1p_120f;
      return 0 / (x - x);
    }
    if (ix < 0x3FE00000) {
      if (ix < 0x3E500000 && ix >= 0x00100000) return x;
      return x + x * R(x * x);
    }
    // var z = (1.0 - builtin_abs<f64>(x)) * 0.5;
    var z = 0.5 - builtin_abs<f64>(x) * 0.5;
    var s = builtin_sqrt<f64>(z);
    var r = R(z);
    if (ix >= 0x3FEF3333) x = pio2_hi - (2 * (s + s * r) - pio2_lo);
    else {
      let f = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
      let c = (z - f * f) / (s + f);
      x = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f));
    }
    if (hx >> 31) return -x;
    return x;
  }

  export function asinh(x: f64): f64 { // see: musl/src/math/asinh.c
    const c = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.693147180559945309417232121458176568
    var u = reinterpret<u64>(x);
    var e = u >> 52 & 0x7FF;
    var y = reinterpret<f64>(u & 0x7FFFFFFFFFFFFFFF);
    if (e >= 0x3FF + 26) y = log(y) + c;
    else if (e >= 0x3FF + 1)  y =   log(2 * y + 1 / (builtin_sqrt<f64>(y * y + 1) + y));
    else if (e >= 0x3FF - 26) y = log1p(y + y * y / (builtin_sqrt<f64>(y * y + 1) + 1));
    return builtin_copysign(y, x);
  }

  export function atan(x: f64): f64 { // see musl/src/math/atan.c and SUN COPYRIGHT NOTICE above
    const
      atanhi0   = reinterpret<f64>(0x3FDDAC670561BB4F), //  4.63647609000806093515e-01
      atanhi1   = reinterpret<f64>(0x3FE921FB54442D18), //  7.85398163397448278999e-01
      atanhi2   = reinterpret<f64>(0x3FEF730BD281F69B), //  9.82793723247329054082e-01
      atanhi3   = reinterpret<f64>(0x3FF921FB54442D18), //  1.57079632679489655800e+00
      atanlo0   = reinterpret<f64>(0x3C7A2B7F222F65E2), //  2.26987774529616870924e-17
      atanlo1   = reinterpret<f64>(0x3C81A62633145C07), //  3.06161699786838301793e-17
      atanlo2   = reinterpret<f64>(0x3C7007887AF0CBBD), //  1.39033110312309984516e-17
      atanlo3   = reinterpret<f64>(0x3C91A62633145C07), //  6.12323399573676603587e-17
      aT0       = reinterpret<f64>(0x3FD555555555550D), //  3.33333333333329318027e-01
      aT1       = reinterpret<f64>(0xBFC999999998EBC4), // -1.99999999998764832476e-01
      aT2       = reinterpret<f64>(0x3FC24924920083FF), //  1.42857142725034663711e-01
      aT3       = reinterpret<f64>(0xBFBC71C6FE231671), // -1.11111104054623557880e-01,
      aT4       = reinterpret<f64>(0x3FB745CDC54C206E), //  9.09088713343650656196e-02
      aT5       = reinterpret<f64>(0xBFB3B0F2AF749A6D), // -7.69187620504482999495e-02
      aT6       = reinterpret<f64>(0x3FB10D66A0D03D51), //  6.66107313738753120669e-02
      aT7       = reinterpret<f64>(0xBFADDE2D52DEFD9A), // -5.83357013379057348645e-02
      aT8       = reinterpret<f64>(0x3FA97B4B24760DEB), //  4.97687799461593236017e-02
      aT9       = reinterpret<f64>(0xBFA2B4442C6A6C2F), // -3.65315727442169155270e-02
      aT10      = reinterpret<f64>(0x3F90AD3AE322DA11), //  1.62858201153657823623e-02
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var ix = <u32>(reinterpret<u64>(x) >> 32);
    var sx = x;
    ix &= 0x7FFFFFFF;
    var z: f64;
    if (ix >= 0x44100000) {
      if (isNaN(x)) return x;
      z = atanhi3 + Ox1p_120f;
      return builtin_copysign<f64>(z, sx);
    }
    var id: i32;
    if (ix < 0x3FDC0000) {
      if (ix < 0x3E400000) return x;
      id = -1;
    } else {
      x = builtin_abs<f64>(x);
      if (ix < 0x3FF30000) {
        if (ix < 0x3FE60000) {
          id = 0;
          x = (2.0 * x - 1.0) / (2.0 + x);
        } else {
          id = 1;
          x = (x - 1.0) / (x + 1.0);
        }
      } else {
        if (ix < 0x40038000) {
          id = 2;
          x = (x - 1.5) / (1.0 + 1.5 * x);
        } else {
          id = 3;
          x = -1.0 / x;
        }
      }
    }
    z = x * x;
    var w = z * z;
    var s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
    var s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
    var s3 = x * (s1 + s2);
    if (id < 0) return x - s3;
    switch (id) {
      case 0: { z = atanhi0 - ((s3 - atanlo0) - x); break; }
      case 1: { z = atanhi1 - ((s3 - atanlo1) - x); break; }
      case 2: { z = atanhi2 - ((s3 - atanlo2) - x); break; }
      case 3: { z = atanhi3 - ((s3 - atanlo3) - x); break; }
      default: unreachable();
    }
    return builtin_copysign<f64>(z, sx);
  }

  export function atanh(x: f64): f64 { // see: musl/src/math/atanh.c
    var u = reinterpret<u64>(x);
    var e = u >> 52 & 0x7FF;
    var y = builtin_abs(x);
    if (e < 0x3FF - 1) {
      if (e >= 0x3FF - 32) y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y));
    } else {
      y = 0.5 * log1p(2 * (y / (1 - y)));
    }
    return builtin_copysign<f64>(y, x);
  }

  export function atan2(y: f64, x: f64): f64 { // see: musl/src/math/atan2.c and SUN COPYRIGHT NOTICE above
    const pi_lo = reinterpret<f64>(0x3CA1A62633145C07); // 1.2246467991473531772E-16
    if (isNaN(x) || isNaN(y)) return x + y;
    var u = reinterpret<u64>(x);
    var ix = <u32>(u >> 32);
    var lx = <u32>u;
    u = reinterpret<u64>(y);
    var iy = <u32>(u >> 32);
    var ly = <u32>u;
    if ((ix - 0x3FF00000 | lx) == 0) return atan(y);
    var m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
    ix = ix & 0x7FFFFFFF;
    iy = iy & 0x7FFFFFFF;
    if ((iy | ly) == 0) {
      switch (m) {
        case 0:
        case 1: return  y;
        case 2: return  PI;
        case 3: return -PI;
      }
    }
    if ((ix | lx) == 0) return m & 1 ? -PI / 2 : PI / 2;
    if (ix == 0x7FF00000) {
      if (iy == 0x7FF00000) {
        let t = m & 2 ? 3 * PI / 4 : PI / 4;
        return m & 1 ? -t : t;
      } else {
        let t = m & 2 ? PI : 0;
        return m & 1 ? -t : t;
      }
    }
    var z: f64;
    if (ix + (64 << 20) < iy || iy == 0x7FF00000) return m & 1 ? -PI / 2 : PI / 2;
    if ((m & 2) && iy + (64 << 20) < ix) z = 0;
    else z = atan(builtin_abs<f64>(y / x));
    switch (m) {
      case 0: return  z;
      case 1: return -z;
      case 2: return PI - (z - pi_lo);
      case 3: return (z - pi_lo) - PI;
    }
    unreachable();
    return 0;
  }

  export function cbrt(x: f64): f64 { // see: musl/src/math/cbrt.c and SUN COPYRIGHT NOTICE above
    const
      B1     = <u32>715094163,
      B2     = <u32>696219795,
      P0     = reinterpret<f64>(0x3FFE03E60F61E692), //  1.87595182427177009643
      P1     = reinterpret<f64>(0xBFFE28E092F02420), // -1.88497979543377169875
      P2     = reinterpret<f64>(0x3FF9F1604A49D6C2), //  1.621429720105354466140
      P3     = reinterpret<f64>(0xBFE844CBBEE751D9), // -0.758397934778766047437
      P4     = reinterpret<f64>(0x3FC2B000D4E4EDD7), //  0.145996192886612446982
      Ox1p54 = reinterpret<f64>(0x4350000000000000);
    var u = reinterpret<u64>(x);
    var hx = <u32>(u >> 32) & 0x7FFFFFFF;
    if (hx >= 0x7FF00000) return x + x;
    if (hx < 0x00100000) {
      u = reinterpret<u64>(x * Ox1p54);
      hx = <u32>(u >> 32) & 0x7FFFFFFF;
      if (hx == 0) return x;
      hx = hx / 3 + B2;
    } else {
      hx = hx / 3 + B1;
    }
    u &= 1 << 63;
    u |= <u64>hx << 32;
    var t = reinterpret<f64>(u);
    var r = (t * t) * (t / x);
    t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
    t = reinterpret<f64>((reinterpret<u64>(t) + 0x80000000) & 0xFFFFFFFFC0000000);
    var s = t * t;
    r = x / s;
    r = (r - t) / (2 * t + r);
    t = t + t * r;
    return t;
  }

  // @ts-ignore: decorator
  @inline
  export function ceil(x: f64): f64 {
    return builtin_ceil<f64>(x);
  }

  export function clz32(x: f64): f64 {
    if (!isFinite(x)) return 32;
    /*
     * Wasm (MVP) and JS have different approaches for double->int conversions.
     *
     * For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
     * our float-point arguments before actual convertion to integers.
     */
    return builtin_clz(dtoi32(x));
  }

  export function cos(x: f64): f64 { // see: musl/src/math/cos.c
    var u  = reinterpret<u64>(x);
    var ix = <u32>(u >> 32);
    var sign = ix >> 31;

    ix &= 0x7FFFFFFF;

    // |x| ~< pi/4
    if (ix <= 0x3FE921FB) {
      if (ix < 0x3E46A09E) {  // |x| < 2**-27 * sqrt(2)
        return 1.0;
      }
      return cos_kern(x, 0);
    }

    // sin(Inf or NaN) is NaN
    if (ix >= 0x7FF00000) return x - x;

    // argument reduction needed
    var n  = rempio2(x, u, sign);
    var y0 = rempio2_y0;
    var y1 = rempio2_y1;

    x = n & 1 ? sin_kern(y0, y1, 1) : cos_kern(y0, y1);
    return (n + 1) & 2 ? -x : x;
  }

  export function cosh(x: f64): f64 { // see: musl/src/math/cosh.c
    var u = reinterpret<u64>(x);
    u &= 0x7FFFFFFFFFFFFFFF;
    x = reinterpret<f64>(u);
    var w = <u32>(u >> 32);
    var t: f64;
    if (w < 0x3FE62E42) {
      if (w < 0x3FF00000 - (26 << 20)) return 1;
      t = expm1(x);
      // return 1 + t * t / (2 * (1 + t));
      return 1 + t * t / (2 + 2 * t);
    }
    if (w < 0x40862E42) {
      t = exp(x);
      return 0.5 * (t + 1 / t);
    }
    t = expo2(x);
    return t;
  }

  export function exp(x: f64): f64 { // see: musl/src/math/exp.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return exp_lut(x);
    } else {
      const
        ln2hi     = reinterpret<f64>(0x3FE62E42FEE00000), //  6.93147180369123816490e-01
        ln2lo     = reinterpret<f64>(0x3DEA39EF35793C76), //  1.90821492927058770002e-10
        invln2    = reinterpret<f64>(0x3FF71547652B82FE), //  1.44269504088896338700e+00
        P1        = reinterpret<f64>(0x3FC555555555553E), //  1.66666666666666019037e-01
        P2        = reinterpret<f64>(0xBF66C16C16BEBD93), // -2.77777777770155933842e-03
        P3        = reinterpret<f64>(0x3F11566AAF25DE2C), //  6.61375632143793436117e-05
        P4        = reinterpret<f64>(0xBEBBBD41C5D26BF1), // -1.65339022054652515390e-06
        P5        = reinterpret<f64>(0x3E66376972BEA4D0), //  4.13813679705723846039e-08
        overflow  = reinterpret<f64>(0x40862E42FEFA39EF), //  709.782712893383973096
        underflow = reinterpret<f64>(0xC0874910D52D3051), // -745.13321910194110842
        Ox1p1023  = reinterpret<f64>(0x7FE0000000000000);
      let hx = <u32>(reinterpret<u64>(x) >> 32);
      let sign_ = <i32>(hx >> 31);
      hx &= 0x7FFFFFFF;
      if (hx >= 0x4086232B) {
        if (isNaN(x)) return x;
        if (x > overflow)  return x * Ox1p1023;
        if (x < underflow) return 0;
      }
      let hi: f64, lo: f64 = 0;
      let k = 0;
      if (hx > 0x3FD62E42) {
        if (hx >= 0x3FF0A2B2) {
          k = <i32>(invln2 * x + builtin_copysign<f64>(0.5, x));
        } else {
          k = 1 - (sign_ << 1);
        }
        hi = x - k * ln2hi;
        lo = k * ln2lo;
        x = hi - lo;
      } else if (hx > 0x3E300000) {
        hi = x;
      } else return 1.0 + x;
      let xs = x * x;
      // var c = x - xp2 * (P1 + xp2 * (P2 + xp2 * (P3 + xp2 * (P4 + xp2 * P5))));
      let xq = xs * xs;
      let c = x - (xs * P1 + xq * ((P2 + xs * P3) + xq * (P4 + xs * P5)));
      let y = 1.0 + (x * c / (2 - c) - lo + hi);
      return k == 0 ? y : scalbn(y, k);
    }
  }

  export function exp2(x: f64): f64 {
    return exp2_lut(x);
  }

  export function expm1(x: f64): f64 { // see: musl/src/math/expm1.c and SUN COPYRIGHT NOTICE above
    const
      o_threshold = reinterpret<f64>(0x40862E42FEFA39EF), //  7.09782712893383973096e+02
      ln2_hi      = reinterpret<f64>(0x3FE62E42FEE00000), //  6.93147180369123816490e-01
      ln2_lo      = reinterpret<f64>(0x3DEA39EF35793C76), //  1.90821492927058770002e-10
      invln2      = reinterpret<f64>(0x3FF71547652B82FE), //  1.44269504088896338700e+00
      Q1          = reinterpret<f64>(0xBFA11111111110F4), // -3.33333333333331316428e-02
      Q2          = reinterpret<f64>(0x3F5A01A019FE5585), //  1.58730158725481460165e-03
      Q3          = reinterpret<f64>(0xBF14CE199EAADBB7), // -7.93650757867487942473e-05
      Q4          = reinterpret<f64>(0x3ED0CFCA86E65239), //  4.00821782732936239552e-06
      Q5          = reinterpret<f64>(0xBE8AFDB76E09C32D), // -2.01099218183624371326e-07
      Ox1p1023    = reinterpret<f64>(0x7FE0000000000000);
    var u = reinterpret<u64>(x);
    var hx = <u32>(u >> 32 & 0x7FFFFFFF);
    var k = 0, sign_ = <i32>(u >> 63);
    if (hx >= 0x4043687A) {
      if (isNaN(x)) return x;
      if (sign_) return -1;
      if (x > o_threshold) return x * Ox1p1023;
    }
    var c = 0.0, t: f64;
    if (hx > 0x3FD62E42) {
      k = select<i32>(
        1 - (sign_ << 1),
        <i32>(invln2 * x + builtin_copysign<f64>(0.5, x)),
        hx < 0x3FF0A2B2
      );
      t = <f64>k;
      let hi = x - t * ln2_hi;
      let lo = t * ln2_lo;
      x = hi - lo;
      c = (hi - x) - lo;
    } else if (hx < 0x3C900000) return x;
    var hfx = 0.5 * x;
    var hxs = x * hfx;
    // var r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
    var hxq = hxs * hxs;
    var r1 = (1.0 + hxs * Q1) + hxq * ((Q2 + hxs * Q3) + hxq * (Q4 + hxs * Q5));
    t = 3.0 - r1 * hfx;
    var e = hxs * ((r1 - t) / (6.0 - x * t));
    if (k == 0) return x - (x * e - hxs);
    e = x * (e - c) - c;
    e -= hxs;
    if (k == -1) return 0.5 * (x - e) - 0.5;
    if (k == 1) {
      if (x < -0.25) return -2.0 * (e - (x + 0.5));
      return 1.0 + 2.0 * (x - e);
    }
    u = (0x3FF + k) << 52;
    var twopk = reinterpret<f64>(u);
    var y: f64;
    if (k < 0 || k > 56) {
      y = x - e + 1.0;
      if (k == 1024) y = y * 2.0 * Ox1p1023;
      else y = y * twopk;
      return y - 1.0;
    }
    u = (0x3FF - k) << 52;
    y = reinterpret<f64>(u);
    if (k < 20) y = (1 - y) - e;
    else y = 1 - (e + y);
    return (x + y) * twopk;
  }

  // @ts-ignore: decorator
  @inline
  export function floor(x: f64): f64 {
    return builtin_floor<f64>(x);
  }

  // @ts-ignore: decorator
  @inline
  export function fround(x: f64): f64 {
    return <f32>x;
  }

  export function hypot(x: f64, y: f64): f64 { // see: musl/src/math/hypot.c
    const
      SPLIT    = reinterpret<f64>(0x41A0000000000000) + 1, // 0x1p27 + 1
      Ox1p700  = reinterpret<f64>(0x6BB0000000000000),
      Ox1p_700 = reinterpret<f64>(0x1430000000000000);
    var ux = reinterpret<u64>(x);
    var uy = reinterpret<u64>(y);
    ux &= 0x7FFFFFFFFFFFFFFF;
    uy &= 0x7FFFFFFFFFFFFFFF;
    if (ux < uy) {
      let ut = ux;
      ux = uy;
      uy = ut;
    }
    var ex = <i32>(ux >> 52);
    var ey = <i32>(uy >> 52);
    y = reinterpret<f64>(uy);
    if (ey == 0x7FF) return y;
    x = reinterpret<f64>(ux);
    if (ex == 0x7FF || uy == 0) return x;
    if (ex - ey > 64) return x + y;
    var z = 1.0;
    if (ex > 0x3FF + 510) {
      z  = Ox1p700;
      x *= Ox1p_700;
      y *= Ox1p_700;
    } else if (ey < 0x3FF - 450) {
      z  = Ox1p_700;
      x *= Ox1p700;
      y *= Ox1p700;
    }
    var c = x * SPLIT;
    var h = x - c + c;
    var l = x - h;
    var hx = x * x;
    var lx = h * h - hx + (2 * h + l) * l;
    c = y * SPLIT;
    h = y - c + c;
    l = y - h;
    var hy = y * y;
    var ly = h * h - hy + (2 * h + l) * l;
    return z * builtin_sqrt(ly + lx + hy + hx);
  }

  export function imul(x: f64, y: f64): f64 {
    /*
     * Wasm (MVP) and JS have different approaches for double->int conversions.
     *
     * For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
     * our float-point arguments before actual convertion to integers.
     */
    if (!isFinite(x + y)) return 0;
    return dtoi32(x) * dtoi32(y);
  }

  export function log(x: f64): f64 { // see: musl/src/math/log.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return log_lut(x);
    } else {
      const
        ln2_hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
        ln2_lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
        Lg1    = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
        Lg2    = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
        Lg3    = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
        Lg4    = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
        Lg5    = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
        Lg6    = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
        Lg7    = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
        Ox1p54 = reinterpret<f64>(0x4350000000000000);
      let u = reinterpret<u64>(x);
      let hx = <u32>(u >> 32);
      let k = 0;
      if (hx < 0x00100000 || <bool>(hx >> 31)) {
        if (u << 1 == 0) return -1 / (x * x);
        if (hx >> 31)    return (x - x) / 0.0;
        k -= 54;
        x *= Ox1p54;
        u = reinterpret<u64>(x);
        hx = <u32>(u >> 32);
      } else if (hx >= 0x7FF00000) return x;
        else if (hx == 0x3FF00000 && u << 32 == 0) return 0;
      hx += 0x3FF00000 - 0x3FE6A09E;
      k += (<i32>hx >> 20) - 0x3FF;
      hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
      u = <u64>hx << 32 | (u & 0xFFFFFFFF);
      x = reinterpret<f64>(u);
      let f = x - 1.0;
      let hfsq = 0.5 * f * f;
      let s = f / (2.0 + f);
      let z = s * s;
      let w = z * z;
      let t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
      let t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
      let r = t2 + t1;
      let dk = <f64>k;
      return s * (hfsq + r) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
    }
  }

  export function log10(x: f64): f64 { // see: musl/src/math/log10.c and SUN COPYRIGHT NOTICE above
    const
      ivln10hi  = reinterpret<f64>(0x3FDBCB7B15200000), // 4.34294481878168880939e-01
      ivln10lo  = reinterpret<f64>(0x3DBB9438CA9AADD5), // 2.50829467116452752298e-11
      log10_2hi = reinterpret<f64>(0x3FD34413509F6000), // 3.01029995663611771306e-01
      log10_2lo = reinterpret<f64>(0x3D59FEF311F12B36), // 3.69423907715893078616e-13
      Lg1       = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
      Lg2       = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
      Lg3       = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
      Lg4       = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
      Lg5       = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
      Lg6       = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
      Lg7       = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
      Ox1p54    = reinterpret<f64>(0x4350000000000000);
    var u = reinterpret<u64>(x);
    var hx = <u32>(u >> 32);
    var k = 0;
    if (hx < 0x00100000 || <bool>(hx >> 31)) {
      if (u << 1 == 0) return -1 / (x * x);
      if (hx >> 31) return (x - x) / 0.0;
      k -= 54;
      x *= Ox1p54;
      u = reinterpret<u64>(x);
      hx = <u32>(u >> 32);
    } else if (hx >= 0x7FF00000) return x;
      else if (hx == 0x3FF00000 && u << 32 == 0) return 0;
    hx += 0x3FF00000 - 0x3FE6A09E;
    k += <i32>(hx >> 20) - 0x3FF;
    hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
    u = <u64>hx << 32 | (u & 0xFFFFFFFF);
    x = reinterpret<f64>(u);
    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 hi = f - hfsq;
    u = reinterpret<u64>(hi);
    u &= 0xFFFFFFFF00000000;
    hi = reinterpret<f64>(u);
    var lo = f - hi - hfsq + s * (hfsq + r);
    var val_hi = hi * ivln10hi;
    var dk = <f64>k;
    var y = dk * log10_2hi;
    var val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;
    w = y + val_hi;
    val_lo += (y - w) + val_hi;
    return val_lo + w;
  }

  export function log1p(x: f64): f64 { // see: musl/src/math/log1p.c and SUN COPYRIGHT NOTICE above
    const
      ln2_hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
      ln2_lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
      Lg1    = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
      Lg2    = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
      Lg3    = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
      Lg4    = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
      Lg5    = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
      Lg6    = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
      Lg7    = reinterpret<f64>(0x3FC2F112DF3E5244); // 1.479819860511658591e-01
    var u = reinterpret<u64>(x);
    var hx = <u32>(u >> 32);
    var k = 1;
    var c = 0.0, f = 0.0;
    if (hx < 0x3FDA827A || <bool>(hx >> 31)) {
      if (hx >= 0xBFF00000) {
        if (x == -1) return x / 0.0;
        return (x - x) / 0.0;
      }
      if (hx << 1 < 0x3CA00000 << 1) return x;
      if (hx <= 0xBFD2BEC4) {
        k = 0;
        c = 0;
        f = x;
      }
    } else if (hx >= 0x7FF00000) return x;
    if (k) {
      u = reinterpret<u64>(1 + x);
      let hu = <u32>(u >> 32);
      hu += 0x3FF00000 - 0x3FE6A09E;
      k = <i32>(hu >> 20) - 0x3FF;
      if (k < 54) {
        let uf = reinterpret<f64>(u);
        c = k >= 2 ? 1 - (uf - x) : x - (uf - 1);
        c /= uf;
      } else c = 0;
      hu = (hu & 0x000FFFFF) + 0x3FE6A09E;
      u = <u64>hu << 32 | (u & 0xFFFFFFFF);
      f = reinterpret<f64>(u) - 1;
    }
    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 = <f64>k;
    return s * (hfsq + r) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
  }

  export function log2(x: f64): f64 { // see: musl/src/math/log2.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return log2_lut(x);
    } else {
      const
        ivln2hi = reinterpret<f64>(0x3FF7154765200000), // 1.44269504072144627571e+00
        ivln2lo = reinterpret<f64>(0x3DE705FC2EEFA200), // 1.67517131648865118353e-10
        Lg1     = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
        Lg2     = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
        Lg3     = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
        Lg4     = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
        Lg5     = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
        Lg6     = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
        Lg7     = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
        Ox1p54  = reinterpret<f64>(0x4350000000000000);
      let u = reinterpret<u64>(x);
      let hx = <u32>(u >> 32);
      let k = 0;
      if (hx < 0x00100000 || <bool>(hx >> 31)) {
        if (u << 1 == 0) return -1 / (x * x);
        if (hx >> 31) return (x - x) / 0.0;
        k -= 54;
        x *= Ox1p54;
        u = reinterpret<u64>(x);
        hx = <u32>(u >> 32);
      } else if (hx >= 0x7FF00000) return x;
        else if (hx == 0x3FF00000 && u << 32 == 0) return 0;
      hx += 0x3FF00000 - 0x3FE6A09E;
      k += <i32>(hx >> 20) - 0x3FF;
      hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
      u = <u64>hx << 32 | (u & 0xFFFFFFFF);
      x = reinterpret<f64>(u);
      let f = x - 1.0;
      let hfsq = 0.5 * f * f;
      let s = f / (2.0 + f);
      let z = s * s;
      let w = z * z;
      let t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
      let t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
      let r = t2 + t1;
      let hi = f - hfsq;
      u = reinterpret<u64>(hi);
      u &= 0xFFFFFFFF00000000;
      hi = reinterpret<f64>(u);
      let lo = f - hi - hfsq + s * (hfsq + r);
      let val_hi = hi * ivln2hi;
      let val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
      let y = <f64>k;
      w = y + val_hi;
      val_lo += (y - w) + val_hi;
      val_hi = w;
      return val_lo + val_hi;
    }
  }

  // @ts-ignore: decorator
  @inline
  export function max(value1: f64, value2: f64): f64 {
    return builtin_max<f64>(value1, value2);
  }

  // @ts-ignore: decorator
  @inline
  export function min(value1: f64, value2: f64): f64 {
    return builtin_min<f64>(value1, value2);
  }

  export function pow(x: f64, y: f64): f64 { // see: musl/src/math/pow.c and SUN COPYRIGHT NOTICE above
    // TODO: remove this fast pathes after introduced own mid-end IR with "stdlib call simplify" transforms
    if (builtin_abs<f64>(y) <= 2) {
      if (y == 2.0) return x * x;
      if (y == 0.5) {
        return select<f64>(
          builtin_abs<f64>(builtin_sqrt<f64>(x)),
          Infinity,
          x != -Infinity
        );
      }
      if (y == -1.0) return 1 / x;
      if (y == 1.0) return x;
      if (y == 0.0) return 1.0;
    }
    if (ASC_SHRINK_LEVEL < 1) {
      return pow_lut(x, y);
    } else {
      const
        dp_h1   = reinterpret<f64>(0x3FE2B80340000000), //  5.84962487220764160156e-01
        dp_l1   = reinterpret<f64>(0x3E4CFDEB43CFD006), //  1.35003920212974897128e-08
        two53   = reinterpret<f64>(0x4340000000000000), //  9007199254740992.0
        huge    = reinterpret<f64>(0x7E37E43C8800759C), //  1e+300
        tiny    = reinterpret<f64>(0x01A56E1FC2F8F359), //  1e-300
        L1      = reinterpret<f64>(0x3FE3333333333303), //  5.99999999999994648725e-01
        L2      = reinterpret<f64>(0x3FDB6DB6DB6FABFF), //  4.28571428578550184252e-01
        L3      = reinterpret<f64>(0x3FD55555518F264D), //  3.33333329818377432918e-01
        L4      = reinterpret<f64>(0x3FD17460A91D4101), //  2.72728123808534006489e-01
        L5      = reinterpret<f64>(0x3FCD864A93C9DB65), //  2.30660745775561754067e-01
        L6      = reinterpret<f64>(0x3FCA7E284A454EEF), //  2.06975017800338417784e-01
        P1      = reinterpret<f64>(0x3FC555555555553E), //  1.66666666666666019037e-01
        P2      = reinterpret<f64>(0xBF66C16C16BEBD93), // -2.77777777770155933842e-03
        P3      = reinterpret<f64>(0x3F11566AAF25DE2C), //  6.61375632143793436117e-05
        P4      = reinterpret<f64>(0xBEBBBD41C5D26BF1), // -1.65339022054652515390e-06
        P5      = reinterpret<f64>(0x3E66376972BEA4D0), //  4.13813679705723846039e-08
        lg2     = reinterpret<f64>(0x3FE62E42FEFA39EF), //  6.93147180559945286227e-01
        lg2_h   = reinterpret<f64>(0x3FE62E4300000000), //  6.93147182464599609375e-01
        lg2_l   = reinterpret<f64>(0xBE205C610CA86C39), // -1.90465429995776804525e-09
        ovt     = reinterpret<f64>(0x3C971547652B82FE), //  8.0085662595372944372e-017
        cp      = reinterpret<f64>(0x3FEEC709DC3A03FD), //  9.61796693925975554329e-01
        cp_h    = reinterpret<f64>(0x3FEEC709E0000000), //  9.61796700954437255859e-01
        cp_l    = reinterpret<f64>(0xBE3E2FE0145B01F5), // -7.02846165095275826516e-09
        ivln2   = reinterpret<f64>(0x3FF71547652B82FE), //  1.44269504088896338700e+00
        ivln2_h = reinterpret<f64>(0x3FF7154760000000), //  1.44269502162933349609e+00
        ivln2_l = reinterpret<f64>(0x3E54AE0BF85DDF44), //  1.92596299112661746887e-08
        inv3    = reinterpret<f64>(0x3FD5555555555555); //  0.3333333333333333333333
      let u_ = reinterpret<u64>(x);
      let hx = <i32>(u_ >> 32);
      let lx = <u32>u_;
      u_ = reinterpret<u64>(y);
      let hy = <i32>(u_ >> 32);
      let ly = <u32>u_;
      let ix = hx & 0x7FFFFFFF;
      let iy = hy & 0x7FFFFFFF;
      if ((iy | ly) == 0) return 1.0; // x**0 = 1, even if x is NaN
      // if (hx == 0x3FF00000 && lx == 0) return 1.0; // C: 1**y = 1, even if y is NaN, JS: NaN
      if ( // NaN if either arg is NaN
        ix > 0x7FF00000 || (ix == 0x7FF00000 && lx != 0) ||
        iy > 0x7FF00000 || (iy == 0x7FF00000 && ly != 0)
      ) return x + y;
      let yisint = 0, k: i32;
      if (hx < 0) {
        if (iy >= 0x43400000) yisint = 2;
        else if (iy >= 0x3FF00000) {
          k = (iy >> 20) - 0x3FF;
          let offset = select<u32>(52, 20, k > 20) - k;
          let Ly = select<u32>(ly, iy, k > 20);
          let jj = Ly >> offset;
          if ((jj << offset) == Ly) yisint = 2 - (jj & 1);
        }
      }
      if (ly == 0) {
        if (iy == 0x7FF00000) { // y is +-inf
          if (((ix - 0x3FF00000) | lx) == 0) return NaN; // C: (-1)**+-inf is 1, JS: NaN
          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) {
          if (hy >= 0) return x;
          return 1 / x;
        }
        if (hy == 0x40000000) return x * x;
        if (hy == 0x3FE00000) {
          if (hx >= 0) return builtin_sqrt(x);
        }
      }
      let ax = builtin_abs<f64>(x), z: f64;
      if (lx == 0) {
        if (ix == 0 || ix == 0x7FF00000 || ix == 0x3FF00000) {
          z = ax;
          if (hy < 0) z = 1.0 / z;
          if (hx < 0) {
            if (((ix - 0x3FF00000) | yisint) == 0) {
              let d = z - z;
              z = d / d;
            } else if (yisint == 1) z = -z;
          }
          return z;
        }
      }
      let s = 1.0;
      if (hx < 0) {
        if (yisint == 0) {
          let d = x - x;
          return d / d;
        }
        if (yisint == 1) s = -1.0;
      }
      let t1: f64, t2: f64, p_h: f64, p_l: f64, r: f64, t: f64, u: f64, v: f64, w: f64;
      let j: i32, n: i32;
      if (iy > 0x41E00000) {
        if (iy > 0x43F00000) {
          if (ix <= 0x3FEFFFFF) return hy < 0 ? huge * huge : tiny * tiny;
          if (ix >= 0x3FF00000) return hy > 0 ? huge * huge : tiny * tiny;
        }
        if (ix < 0x3FEFFFFF) return hy < 0 ? s * huge * huge : s * tiny * tiny;
        if (ix > 0x3FF00000) return hy > 0 ? s * huge * huge : s * tiny * tiny;
        t = ax - 1.0;
        w = (t * t) * (0.5 - t * (inv3 - t * 0.25));
        u = ivln2_h * t;
        v = t * ivln2_l - w * ivln2;
        t1 = u + v;
        t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xFFFFFFFF00000000);
        t2 = v - (t1 - u);
      } else {
        let ss: f64, s2: f64, s_h: f64, s_l: f64, t_h: f64, t_l: f64;
        n = 0;
        if (ix < 0x00100000) {
          ax *= two53;
          n -= 53;
          ix = <u32>(reinterpret<u64>(ax) >> 32);
        }
        n += (ix >> 20) - 0x3FF;
        j = ix & 0x000FFFFF;
        ix = j | 0x3FF00000;
        if (j <= 0x3988E) k = 0;
        else if (j < 0xBB67A) k = 1;
        else {
          k = 0;
          n += 1;
          ix -= 0x00100000;
        }
        ax = reinterpret<f64>(reinterpret<u64>(ax) & 0xFFFFFFFF | (<u64>ix << 32));
        let bp = select<f64>(1.5, 1.0, k); // k ? 1.5 : 1.0
        u = ax - bp;
        v = 1.0 / (ax + bp);
        ss = u * v;
        s_h = ss;
        s_h = reinterpret<f64>(reinterpret<u64>(s_h) & 0xFFFFFFFF00000000);
        t_h = reinterpret<f64>(<u64>(((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)) << 32);
        t_l = ax - (t_h - bp);
        s_l = v * ((u - s_h * t_h) - s_h * t_l);
        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);
        t_l = r - ((t_h - 3.0) - s2);
        u = s_h * t_h;
        v = s_l * t_h + t_l * ss;
        p_h = u + v;
        p_h = reinterpret<f64>(reinterpret<u64>(p_h) & 0xFFFFFFFF00000000);
        p_l = v - (p_h - u);
        let z_h = cp_h * p_h;
        let dp_l = select<f64>(dp_l1, 0.0, k);
        let z_l = cp_l * p_h + p_l * cp + dp_l;
        t = <f64>n;
        let dp_h = select<f64>(dp_h1, 0.0, k);
        t1 = ((z_h + z_l) + dp_h) + t;
        t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xFFFFFFFF00000000);
        t2 = z_l - (((t1 - t) - dp_h) - z_h);
      }
      let y1 = y;
      y1 = reinterpret<f64>(reinterpret<u64>(y1) & 0xFFFFFFFF00000000);
      p_l = (y - y1) * t1 + y * t2;
      p_h = y1 * t1;
      z = p_l + p_h;
      u_ = reinterpret<u64>(z);
      j = <u32>(u_ >> 32);
      let i = <i32>u_;
      if (j >= 0x40900000) {
        if (((j - 0x40900000) | i) != 0) return s * huge * huge;
        if (p_l + ovt > z - p_h) return s * huge * huge;
      } else if ((j & 0x7FFFFFFF) >= 0x4090CC00) {
        if (((j - 0xC090CC00) | i) != 0) return s * tiny * tiny;
        if (p_l <= z - p_h) return s * tiny * tiny;
      }
      i = j & 0x7FFFFFFF;
      k = (i >> 20) - 0x3FF;
      n = 0;
      if (i > 0x3FE00000) {
        n = j + (0x00100000 >> (k + 1));
        k = ((n & 0x7FFFFFFF) >> 20) - 0x3FF;
        t = 0.0;
        t = reinterpret<f64>(<u64>(n & ~(0x000FFFFF >> k)) << 32);
        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);
      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);
      j += n << 20;
      if ((j >> 20) <= 0) z = scalbn(z, n);
      else z = reinterpret<f64>(reinterpret<u64>(z) & 0xFFFFFFFF | (<u64>j << 32));
      return s * z;
    }
  }

  export function seedRandom(value: i64): void {
    random_seeded = true;
    random_state0_64 = murmurHash3(value);
    random_state1_64 = murmurHash3(~random_state0_64);
    random_state0_32 = splitMix32(<u32>value);
    random_state1_32 = splitMix32(random_state0_32);
    assert(
      random_state0_64 != 0 && random_state1_64 != 0 &&
      random_state0_32 != 0 && random_state1_32 != 0
    );
  }

  export function random(): f64 { // see: v8/src/base/utils/random-number-generator.cc
    if (!random_seeded) seedRandom(reinterpret<i64>(seed()));
    var s1 = random_state0_64;
    var s0 = random_state1_64;
    random_state0_64 = s0;
    s1 ^= s1 << 23;
    s1 ^= s1 >> 17;
    s1 ^= s0;
    s1 ^= s0 >> 26;
    random_state1_64 = s1;
    var r = (s0 >> 12) | 0x3FF0000000000000;
    return reinterpret<f64>(r) - 1;
  }

  // @ts-ignore: decorator
  @inline
  export function round(x: f64): f64 {
    return builtin_copysign<f64>(builtin_floor<f64>(x + 0.5), x);
  }

  // @ts-ignore: decorator
  @inline
  export function sign(x: f64): f64 {
    if (ASC_SHRINK_LEVEL > 0) {
      return builtin_abs(x) > 0 ? builtin_copysign<f64>(1, x) : x;
    } else {
      return x > 0 ? 1 : x < 0 ? -1 : x;
    }
  }

  // @ts-ignore: decorator
  @inline
  export function signbit(x: f64): bool {
    // In ECMAScript all NaN values are indistinguishable from each other
    // so we need handle NaN and negative NaN in similar way
    return <bool>(<i32>(reinterpret<u64>(x) >>> 63) & i32(x == x));
  }

  export function sin(x: f64): f64 { // see: musl/src/math/sin.c
    var u  = reinterpret<u64>(x);
    var ix = <u32>(u >> 32);
    var sign = ix >> 31;

    ix &= 0x7FFFFFFF;

    // |x| ~< pi/4
    if (ix <= 0x3FE921FB) {
      if (ix < 0x3E500000) { // |x| < 2**-26
        return x;
      }
      return sin_kern(x, 0.0, 0);
    }

    // sin(Inf or NaN) is NaN
    if (ix >= 0x7FF00000) return x - x;

    // argument reduction needed
    var n  = rempio2(x, u, sign);
    var y0 = rempio2_y0;
    var y1 = rempio2_y1;

    x = n & 1 ? cos_kern(y0, y1) : sin_kern(y0, y1, 1);
    return n & 2 ? -x : x;
  }

  export function sinh(x: f64): f64 { // see: musl/src/math/sinh.c
    var u = reinterpret<u64>(x) & 0x7FFFFFFFFFFFFFFF;
    var absx = reinterpret<f64>(u);
    var w = <u32>(u >> 32);
    var t: f64;
    var h = builtin_copysign(0.5, x);
    if (w < 0x40862E42) {
      t = expm1(absx);
      if (w < 0x3FF00000) {
        if (w < 0x3FF00000 - (26 << 20)) return x;
        return h * (2 * t - t * t / (t + 1));
      }
      return h * (t + t / (t + 1));
    }
    t = 2 * h * expo2(absx);
    return t;
  }

  // @ts-ignore: decorator
  @inline
  export function sqrt(x: f64): f64 {
    return builtin_sqrt<f64>(x);
  }

  export function tan(x: f64): f64 { // see: musl/src/math/tan.c
    var u = reinterpret<u64>(x);
    var ix = <i32>(u >> 32);
    var sign = ix >>> 31;

    ix &= 0x7FFFFFFF;

    // |x| ~< pi/4
    if (ix <= 0x3FE921FB) {
      if (ix < 0x3E400000) { // |x| < 2**-27
        return x;
      }
      return tan_kern(x, 0.0, 1);
    }

    // tan(Inf or NaN) is NaN
    if (ix >= 0x7FF00000) return x - x;

    var n = rempio2(x, u, sign);
    return tan_kern(rempio2_y0, rempio2_y1, 1 - ((n & 1) << 1));
  }

  export function tanh(x: f64): f64 { // see: musl/src/math/tanh.c
    var u = reinterpret<u64>(x);
    u &= 0x7FFFFFFFFFFFFFFF;
    var y = reinterpret<f64>(u);
    var w = <u32>(u >> 32);
    var t: f64;
    if (w > 0x3FE193EA) {
      if (w > 0x40340000) {
        t = 1 - 0 / y;
      } else {
        t = expm1(2 * y);
        t = 1 - 2 / (t + 2);
      }
    } else if (w > 0x3FD058AE) {
      t = expm1(2 * y);
      t = t / (t + 2);
    } else if (w >= 0x00100000) {
      t = expm1(-2 * y);
      t = -t / (t + 2);
    } else t = y;
    return builtin_copysign<f64>(t, x);
  }

  // @ts-ignore: decorator
  @inline
  export function trunc(x: f64): f64 {
    return builtin_trunc<f64>(x);
  }

  export function scalbn(x: f64, n: i32): f64 { // see: https://git.musl-libc.org/cgit/musl/tree/src/math/scalbn.c
    const
      Ox1p53    = reinterpret<f64>(0x4340000000000000),
      Ox1p1023  = reinterpret<f64>(0x7FE0000000000000),
      Ox1p_1022 = reinterpret<f64>(0x0010000000000000);
    var y = x;
    if (n > 1023) {
      y *= Ox1p1023;
      n -= 1023;
      if (n > 1023) {
        y *= Ox1p1023;
        n = builtin_min<i32>(n - 1023, 1023);
      }
    } else if (n < -1022) {
      // make sure final n < -53 to avoid double
      // rounding in the subnormal range
      y *= Ox1p_1022 * Ox1p53;
      n += 1022 - 53;
      if (n < -1022) {
        y *= Ox1p_1022 * Ox1p53;
        n = builtin_max<i32>(n + 1022 - 53, -1022);
      }
    }
    return y * reinterpret<f64>(<u64>(0x3FF + n) << 52);
  }

  export function mod(x: f64, y: f64): f64 { // see: musl/src/math/fmod.c
    var ux = reinterpret<u64>(x);
    var uy = reinterpret<u64>(y);
    var ex = <i64>(ux >> 52 & 0x7FF);
    var ey = <i64>(uy >> 52 & 0x7FF);
    var sx = ux >> 63;
    var uy1 = uy << 1;
    if (uy1 == 0 || ex == 0x7FF || isNaN<f64>(y)) {
      let m = x * y;
      return m / m;
    }
    var ux1 = ux << 1;
    if (ux1 <= uy1) {
      if (ux1 == uy1) return 0 * x;
      return x;
    }
    if (!ex) {
      ex -= builtin_clz<i64>(ux << 12);
      ux <<= -ex + 1;
    } else {
      ux &= <u64>-1 >> 12;
      ux |= 1 << 52;
    }
    if (!ey) {
      ey -= builtin_clz<i64>(uy << 12);
      uy <<= -ey + 1;
    } else {
      uy &= <u64>-1 >> 12;
      uy |= 1 << 52;
    }
    while (ex > ey) {
      if (ux >= uy) {
        if (ux == uy) return 0 * x;
        ux -= uy;
      }
      ux <<= 1;
      --ex;
    }
    if (ux >= uy) {
      if (ux == uy) return 0 * x;
      ux -= uy;
    }
    // for (; !(ux >> 52); ux <<= 1) --ex;
    var shift = builtin_clz<i64>(ux << 11);
    ex -= shift;
    ux <<= shift;
    if (ex > 0) {
      ux -= 1 << 52;
      ux |= ex << 52;
    } else {
      ux >>= -ex + 1;
    }
    ux |= sx << 63;
    return reinterpret<f64>(ux);
  }

  export function rem(x: f64, y: f64): f64 { // see: musl/src/math/remquo.c
    var ux = reinterpret<u64>(x);
    var uy = reinterpret<u64>(y);
    var ex = <i64>(ux >> 52 & 0x7FF);
    var ey = <i64>(uy >> 52 & 0x7FF);
    var sx = <i32>(ux >> 63);
    if (uy << 1 == 0 || ex == 0x7FF || isNaN(y)) {
      let m = x * y;
      return m / m;
    }
    if (ux << 1 == 0) return x;
    var uxi = ux;
    if (!ex) {
      ex -= builtin_clz<i64>(uxi << 12);
      uxi <<= -ex + 1;
    } else {
      uxi &= <u64>-1 >> 12;
      uxi |= 1 << 52;
    }
    if (!ey) {
      ey -= builtin_clz<i64>(uy << 12);
      uy <<= -ey + 1;
    } else {
      uy &= <u64>-1 >> 12;
      uy |= 1 << 52;
    }
    var q: u32 = 0;
    do {
      if (ex < ey) {
        if (ex + 1 == ey) break; // goto end
        return x;
      }
      while (ex > ey) {
        if (uxi >= uy) {
          uxi -= uy;
          ++q;
        }
        uxi <<= 1;
        q <<= 1;
        --ex;
      }
      if (uxi >= uy) {
        uxi -= uy;
        ++q;
      }
      if (uxi == 0) ex = -60;
      else {
        let shift = builtin_clz<i64>(uxi << 11);
        ex -= shift;
        uxi <<= shift;
      }
      break;
    } while (false);
  // end:
    if (ex > 0) {
      uxi -= 1 << 52;
      uxi |= ex << 52;
    } else {
      uxi >>= -ex + 1;
    }
    x = reinterpret<f64>(uxi);
    y = builtin_abs<f64>(y);
    var x2 = x + x;
    if (ex == ey || (ex + 1 == ey && (x2 > y || (x2 == y && <bool>(q & 1))))) {
      x -= y;
      // ++q;
    }
    return sx ? -x : x;
  }

  export function sincos(x: f64): void { // see: musl/tree/src/math/sincos.c
    var u = reinterpret<u64>(x);
    var ix = <u32>(u >> 32);
    var sign = ix >> 31;
    ix &= 0x7FFFFFFF;

    if (ix <= 0x3FE921FB) {  // |x| ~<= π/4
      if (ix < 0x3E46A09E) { // if |x| < 2**-27 * sqrt(2)
        sincos_sin = x;
        sincos_cos = 1;
        return;
      }
      sincos_sin = sin_kern(x, 0, 0);
      sincos_cos = cos_kern(x, 0);
      return;
    }
    // sin(Inf or NaN) is NaN
    if (ix >= 0x7F800000) {
      let xx = x - x;
      sincos_sin = xx;
      sincos_cos = xx;
      return;
    }
    // general argument reduction needed
    var n = rempio2(x, u, sign);
    var y0 = rempio2_y0;
    var y1 = rempio2_y1;
    var s = sin_kern(y0, y1, 1);
    var c = cos_kern(y0, y1);
    var sin = s, cos = c;
    if (n & 1) {
      sin =  c;
      cos = -s;
    }
    if (n & 2) {
      sin = -sin;
      cos = -cos;
    }
    sincos_sin = sin;
    sincos_cos = cos;
  }
}

// @ts-ignore: decorator
@lazy
var rempio2f_y: f64;

// @ts-ignore: decorator
@lazy @inline
const PIO2F_TABLE: StaticArray<u64> = [
  0xA2F9836E4E441529,
  0xFC2757D1F534DDC0,
  0xDB6295993C439041,
  0xFE5163ABDEBBC561
];

function Rf(z: f32): f32 { // Rational approximation of (asin(x)-x)/x^3
  const                    // see: musl/src/math/asinf.c and SUN COPYRIGHT NOTICE above
    pS0 = reinterpret<f32>(0x3E2AAA75), //  1.6666586697e-01f
    pS1 = reinterpret<f32>(0xBD2F13BA), // -4.2743422091e-02f
    pS2 = reinterpret<f32>(0xBC0DD36B), // -8.6563630030e-03f
    qS1 = reinterpret<f32>(0xBF34E5AE); // -7.0662963390e-01f
  var p = z * (pS0 + z * (pS1 + z * pS2));
  var q: f32 = 1 + z * qS1;
  return p / q;
}

// @ts-ignore: decorator
@inline
function expo2f(x: f32): f32 { // exp(x)/2 for x >= log(DBL_MAX)
  const                                // see: musl/src/math/__expo2f.c
    k    = <u32>235,
    kln2 = reinterpret<f32>(0x4322E3BC); // 0x1.45c778p+7f
  var scale = reinterpret<f32>(<u32>(0x7F + (k >> 1)) << 23);
  return NativeMathf.exp(x - kln2) * scale * scale;
}

// @ts-ignore: decorator
@inline
function pio2f_large_quot(x: f32, u: i32): i32 { // see: jdh8/metallic/blob/master/src/math/float/rem_pio2f.c
  const coeff = reinterpret<f64>(0x3BF921FB54442D18); // π * 0x1p-65 = 8.51530395021638647334e-20
  const bits = changetype<usize>(PIO2F_TABLE);

  var offset = (u >> 23) - 152;
  var shift  = <u64>(offset & 63);
  var tblPtr = bits + (offset >> 6 << 3);

  var b0 = load<u64>(tblPtr, 0 << 3);
  var b1 = load<u64>(tblPtr, 1 << 3);
  var lo: u64;

  if (shift > 32) {
    let b2 = load<u64>(tblPtr, 2 << 3);
    lo  = b2 >> (96 - shift);
    lo |= b1 << (shift - 32);
  } else {
    lo = b1 >> (32 - shift);
  }

  var hi = (b1 >> (64 - shift)) | (b0 << shift);
  var mantissa: u64 = (u & 0x007FFFFF) | 0x00800000;
  var product = mantissa * hi + (mantissa * lo >> 32);
  var r: i64 = product << 2;
  var q = <i32>((product >> 62) + (r >>> 63));
  rempio2f_y = copysign<f64>(coeff, x) * <f64>r;
  return q;
}

// @ts-ignore: decorator
@inline
function rempio2f(x: f32, u: u32, sign: i32): i32 { // see: jdh8/metallic/blob/master/src/math/float/rem_pio2f.c
  const pi2hi = reinterpret<f64>(0x3FF921FB50000000); // 1.57079631090164184570
  const pi2lo = reinterpret<f64>(0x3E5110B4611A6263); // 1.58932547735281966916e-8
  const _2_pi = reinterpret<f64>(0x3FE45F306DC9C883); // 0.63661977236758134308

  if (u < 0x4DC90FDB) { // π * 0x1p28
    let q = nearest(x * _2_pi);
    rempio2f_y = x - q * pi2hi - q * pi2lo;
    return <i32>q;
  }

  var q = pio2f_large_quot(x, u);
  return select(-q, q, sign);
}

// |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]).
// @ts-ignore: decorator
@inline
function sin_kernf(x: f64): f32 { // see: musl/tree/src/math/__sindf.c
  const S1 = reinterpret<f64>(0xBFC5555554CBAC77); // -0x15555554cbac77.0p-55
  const S2 = reinterpret<f64>(0x3F811110896EFBB2); //  0x111110896efbb2.0p-59
  const S3 = reinterpret<f64>(0xBF2A00F9E2CAE774); // -0x1a00f9e2cae774.0p-65
  const S4 = reinterpret<f64>(0x3EC6CD878C3B46A7); //  0x16cd878c3b46a7.0p-71

  var z = x * x;
  var w = z * z;
  var r = S3 + z * S4;
  var s = z * x;
  return <f32>((x + s * (S1 + z * S2)) + s * w * r);
}

// |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]).
// @ts-ignore: decorator
@inline
function cos_kernf(x: f64): f32 { // see: musl/tree/src/math/__cosdf.c
  const C0 = reinterpret<f64>(0xBFDFFFFFFD0C5E81); // -0x1ffffffd0c5e81.0p-54
  const C1 = reinterpret<f64>(0x3FA55553E1053A42); //  0x155553e1053a42.0p-57
  const C2 = reinterpret<f64>(0xBF56C087E80F1E27); // -0x16c087e80f1e27.0p-62
  const C3 = reinterpret<f64>(0x3EF99342E0EE5069); //  0x199342e0ee5069.0p-68

  var z = x * x;
  var w = z * z;
  var r = C2 + z * C3;
  return <f32>(((1 + z * C0) + w * C1) + (w * z) * r);
}

// |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]).
// @ts-ignore: decorator
@inline
function tan_kernf(x: f64, odd: i32): f32 { // see: musl/tree/src/math/__tandf.c

  const T0 = reinterpret<f64>(0x3FD5554D3418C99F); // 0x15554d3418c99f.0p-54
  const T1 = reinterpret<f64>(0x3FC112FD38999F72); // 0x1112fd38999f72.0p-55
  const T2 = reinterpret<f64>(0x3FAB54C91D865AFE); // 0x1b54c91d865afe.0p-57
  const T3 = reinterpret<f64>(0x3F991DF3908C33CE); // 0x191df3908c33ce.0p-58
  const T4 = reinterpret<f64>(0x3F685DADFCECF44E); // 0x185dadfcecf44e.0p-61
  const T5 = reinterpret<f64>(0x3F8362B9BF971BCD); // 0x1362b9bf971bcd.0p-59

  var z = x * x;
  var r = T4 + z * T5;
  var t = T2 + z * T3;
  var w = z * z;
  var s = z * x;
  var u = T0 + z * T1;

  r = (x + s * u) + (s * w) * (t + w * r);
  return <f32>(odd ? -1 / r : r);
}

// See: jdh8/metallic/src/math/float/log2f.c and jdh8/metallic/src/math/float/kernel/atanh.h
// @ts-ignore: decorator
@inline
function log2f(x: f64): f64 {
  const
    log2e = reinterpret<f64>(0x3FF71547652B82FE), // 1.44269504088896340736
    c0 = reinterpret<f64>(0x3FD555554FD9CAEF),    // 0.33333332822728226129
    c1 = reinterpret<f64>(0x3FC999A7A8AF4132),    // 0.20000167595436263505
    c2 = reinterpret<f64>(0x3FC2438D79437030),    // 0.14268654271188685375
    c3 = reinterpret<f64>(0x3FBE2F663B001C97);    // 0.11791075649681414150

  var i = reinterpret<i64>(x);
  var exponent = (i - 0x3FE6A09E667F3BCD) >> 52;
  x = reinterpret<f64>(i - (exponent << 52));
  x = (x - 1) / (x + 1);
  var xx = x * x;
  var y = x + x * xx * (c0 + c1 * xx + (c2 + c3 * xx) * (xx * xx));
  return (2 * log2e) * y + <f64>exponent;
}

// See: jdh8/metallic/src/math/float/exp2f.h and jdh8/metallic/blob/master/src/math/float/kernel/exp2f.h
// @ts-ignore: decorator
@inline
function exp2f(x: f64): f64 {
  const
    c0 = reinterpret<f64>(0x3FE62E4302FCC24A), // 6.931471880289532425e-1
    c1 = reinterpret<f64>(0x3FCEBFBE07D97B91), // 2.402265108421173406e-1
    c2 = reinterpret<f64>(0x3FAC6AF6CCFC1A65), // 5.550357105498874537e-2
    c3 = reinterpret<f64>(0x3F83B29E3CE9AEF6), // 9.618030771171497658e-3
    c4 = reinterpret<f64>(0x3F55F0896145A89F), // 1.339086685300950937e-3
    c5 = reinterpret<f64>(0x3F2446C81E384864); // 1.546973499989028719e-4

  if (x < -1022) return 0;
  if (x >= 1024) return Infinity;

  var n = nearest(x);
  x -= n;
  var xx = x * x;
  var y = 1 + x * (c0 + c1 * x + (c2 + c3 * x) * xx + (c4 + c5 * x) * (xx * xx));
  return reinterpret<f64>(reinterpret<i64>(y) + (<i64>n << 52));
}

export namespace NativeMathf {

  // @ts-ignore: decorator
  @lazy
  export const E       = <f32>NativeMath.E;

  // @ts-ignore: decorator
  @lazy
  export const LN2     = <f32>NativeMath.LN2;

  // @ts-ignore: decorator
  @lazy
  export const LN10    = <f32>NativeMath.LN10;

  // @ts-ignore: decorator
  @lazy
  export const LOG2E   = <f32>NativeMath.LOG2E;

  // @ts-ignore: decorator
  @lazy
  export const LOG10E  = <f32>NativeMath.LOG10E;

  // @ts-ignore: decorator
  @lazy
  export const PI      = <f32>NativeMath.PI;

  // @ts-ignore: decorator
  @lazy
  export const SQRT1_2 = <f32>NativeMath.SQRT1_2;

  // @ts-ignore: decorator
  @lazy
  export const SQRT2   = <f32>NativeMath.SQRT2;

  // @ts-ignore: decorator
  @lazy
  export var sincos_sin: f32 = 0;

  // @ts-ignore: decorator
  @lazy
  export var sincos_cos: f32 = 0;

  // @ts-ignore: decorator
  @inline
  export function abs(x: f32): f32 {
    return builtin_abs<f32>(x);
  }

  export function acos(x: f32): f32 { // see: musl/src/math/acosf.c and SUN COPYRIGHT NOTICE above
    const
      pio2_hi   = reinterpret<f32>(0x3FC90FDA), // 1.5707962513e+00f
      pio2_lo   = reinterpret<f32>(0x33A22168), // 7.5497894159e-08f
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var hx = reinterpret<u32>(x);
    var ix = hx & 0x7FFFFFFF;
    if (ix >= 0x3F800000) {
      if (ix == 0x3F800000) {
        if (hx >> 31) return 2 * pio2_hi + Ox1p_120f;
        return 0;
      }
      return 0 / (x - x);
    }
    if (ix < 0x3F000000) {
      if (ix <= 0x32800000) return pio2_hi + Ox1p_120f;
      return pio2_hi - (x - (pio2_lo - x * Rf(x * x)));
    }
    var z: f32, w: f32, s: f32;
    if (hx >> 31) {
      // z = (1 + x) * 0.5;
      z = 0.5 + x * 0.5;
      s = builtin_sqrt<f32>(z);
      w = Rf(z) * s - pio2_lo;
      return 2 * (pio2_hi - (s + w));
    }
    // z = (1 - x) * 0.5;
    z = 0.5 - x * 0.5;
    s = builtin_sqrt<f32>(z);
    hx = reinterpret<u32>(s);
    var df = reinterpret<f32>(hx & 0xFFFFF000);
    var c = (z - df * df) / (s + df);
    w = Rf(z) * s + c;
    return 2 * (df + w);
  }

  export function acosh(x: f32): f32 { // see: musl/src/math/acoshf.c
    const s = reinterpret<f32>(0x3F317218); // 0.693147180559945309417232121458176568f
    var u = reinterpret<u32>(x);
    var a = u & 0x7FFFFFFF;
    if (a < 0x3F800000 + (1 << 23)) {
      let xm1 = x - 1;
      return log1p(xm1 + builtin_sqrt(xm1 * (xm1 + 2)));
    }
    if (a < 0x3F800000 + (12 << 23)) return log(2 * x - 1 / (x + builtin_sqrt<f32>(x * x - 1)));
    return log(x) + s;
  }

  export function asin(x: f32): f32 { // see: musl/src/math/asinf.c and SUN COPYRIGHT NOTICE above
    const
      pio2      = reinterpret<f32>(0x3FC90FDB), // 1.570796326794896558e+00f
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var sx = x;
    var hx = reinterpret<u32>(x) & 0x7FFFFFFF;
    if (hx >= 0x3F800000) {
      if (hx == 0x3F800000) return x * pio2 + Ox1p_120f;
      return 0 / (x - x);
    }
    if (hx < 0x3F000000) {
      if (hx < 0x39800000 && hx >= 0x00800000) return x;
      return x + x * Rf(x * x);
    }
    // var z: f32 = (1 - builtin_abs<f32>(x)) * 0.5;
    var z: f32 = 0.5 - builtin_abs<f32>(x) * 0.5;
    var s = builtin_sqrt<f64>(z); // sic
    x = <f32>(pio2 - 2 * (s + s * Rf(z)));
    return builtin_copysign(x, sx);
  }

  export function asinh(x: f32): f32 { // see: musl/src/math/asinhf.c
    const c = reinterpret<f32>(0x3F317218); // 0.693147180559945309417232121458176568f
    var u = reinterpret<u32>(x) & 0x7FFFFFFF;
    var y = reinterpret<f32>(u);
    if (u >= 0x3F800000 + (12 << 23)) y = log(y) + c;
    else if (u >= 0x3F800000 + (1 << 23))  y =   log(2 * y + 1 / (builtin_sqrt<f32>(y * y + 1) + y));
    else if (u >= 0x3F800000 - (12 << 23)) y = log1p(y + y * y / (builtin_sqrt<f32>(y * y + 1) + 1));
    return builtin_copysign(y, x);
  }

  export function atan(x: f32): f32 { // see: musl/src/math/atanf.c and SUN COPYRIGHT NOTICE above
    const
      atanhi0   = reinterpret<f32>(0x3EED6338), //  4.6364760399e-01f
      atanhi1   = reinterpret<f32>(0x3F490FDA), //  7.8539812565e-01f
      atanhi2   = reinterpret<f32>(0x3F7B985E), //  9.8279368877e-01f
      atanhi3   = reinterpret<f32>(0x3FC90FDA), //  1.5707962513e+00f
      atanlo0   = reinterpret<f32>(0x31AC3769), //  5.0121582440e-09f
      atanlo1   = reinterpret<f32>(0x33222168), //  3.7748947079e-08f
      atanlo2   = reinterpret<f32>(0x33140FB4), //  3.4473217170e-08f
      atanlo3   = reinterpret<f32>(0x33A22168), //  7.5497894159e-08f
      aT0       = reinterpret<f32>(0x3EAAAAA9), //  3.3333328366e-01f
      aT1       = reinterpret<f32>(0xBE4CCA98), // -1.9999158382e-01f
      aT2       = reinterpret<f32>(0x3E11F50D), //  1.4253635705e-01f
      aT3       = reinterpret<f32>(0xBDDA1247), // -1.0648017377e-01f
      aT4       = reinterpret<f32>(0x3D7CAC25), //  6.1687607318e-02f
      Ox1p_120f = reinterpret<f32>(0x03800000);
    var ix = reinterpret<u32>(x);
    var sx = x;
    ix &= 0x7FFFFFFF;
    var z: f32;
    if (ix >= 0x4C800000) {
      if (isNaN(x)) return x;
      z = atanhi3 + Ox1p_120f;
      return builtin_copysign(z, sx);
    }
    var id: i32;
    if (ix < 0x3EE00000) {
      if (ix < 0x39800000) return x;
      id = -1;
    } else {
      x = builtin_abs<f32>(x);
      if (ix < 0x3F980000) {
        if (ix < 0x3F300000) {
          id = 0;
          x = (2.0 * x - 1.0) / (2.0 + x);
        } else {
          id = 1;
          x = (x - 1.0) / (x + 1.0);
        }
      } else {
        if (ix < 0x401C0000) {
          id = 2;
          x = (x - 1.5) / (1.0 + 1.5 * x);
        } else {
          id = 3;
          x = -1.0 / x;
        }
      }
    }
    z = x * x;
    var w = z * z;
    var s1 = z * (aT0 + w * (aT2 + w * aT4));
    var s2 = w * (aT1 + w * aT3);
    var s3 = x * (s1 + s2);
    if (id < 0) return x - s3;
    switch (id) {
      case 0: { z = atanhi0 - ((s3 - atanlo0) - x); break; }
      case 1: { z = atanhi1 - ((s3 - atanlo1) - x); break; }
      case 2: { z = atanhi2 - ((s3 - atanlo2) - x); break; }
      case 3: { z = atanhi3 - ((s3 - atanlo3) - x); break; }
      default: unreachable();
    }
    return builtin_copysign(z, sx);
  }

  export function atanh(x: f32): f32 { // see: musl/src/math/atanhf.c
    var u = reinterpret<u32>(x);
    var y = builtin_abs(x);
    if (u < 0x3F800000 - (1 << 23)) {
      if (u >= 0x3F800000 - (32 << 23)) y = 0.5 * log1p(2 * y * (1.0 + y / (1 - y)));
    } else y = 0.5 * log1p(2 * (y / (1 - y)));
    return builtin_copysign(y, x);
  }

  export function atan2(y: f32, x: f32): f32 { // see: musl/src/math/atan2f.c and SUN COPYRIGHT NOTICE above
    const
      pi    = reinterpret<f32>(0x40490FDB), //  3.1415927410e+00f
      pi_lo = reinterpret<f32>(0xB3BBBD2E); // -8.7422776573e-08f
    if (isNaN(x) || isNaN(y)) return x + y;
    var ix = reinterpret<u32>(x);
    var iy = reinterpret<u32>(y);
    if (ix == 0x3F800000) return atan(y);
    var m = <u32>(((iy >> 31) & 1) | ((ix >> 30) & 2));
    ix &= 0x7FFFFFFF;
    iy &= 0x7FFFFFFF;
    if (iy == 0) {
      switch (m) {
        case 0:
        case 1: return  y;
        case 2: return  pi;
        case 3: return -pi;
      }
    }
    if (ix == 0) return m & 1 ? -pi / 2 : pi / 2;
    if (ix == 0x7F800000) {
      if (iy == 0x7F800000) {
        let t: f32 = m & 2 ? 3 * pi / 4 : pi / 4;
        return m & 1 ? -t : t;
      } else {
        let t: f32 = m & 2 ? pi : 0.0;
        return m & 1 ? -t : t;
      }
    }
    if (ix + (26 << 23) < iy || iy == 0x7F800000) return m & 1 ? -pi / 2 : pi / 2;
    var z: f32;
    if ((m & 2) && iy + (26 << 23) < ix) z = 0.0;
    else z = atan(builtin_abs<f32>(y / x));
    switch (m) {
      case 0: return  z;
      case 1: return -z;
      case 2: return pi - (z - pi_lo);
      case 3: return (z - pi_lo) - pi;
    }
    unreachable();
    return 0;
  }

  export function cbrt(x: f32): f32 { // see: musl/src/math/cbrtf.c and SUN COPYRIGHT NOTICE above
    const
      B1      = <u32>709958130,
      B2      = <u32>642849266,
      Ox1p24f = reinterpret<f32>(0x4B800000);
    var u = reinterpret<u32>(x);
    var hx = u & 0x7FFFFFFF;
    if (hx >= 0x7F800000) return x + x;
    if (hx < 0x00800000) {
      if (hx == 0) return x;
      u = reinterpret<u32>(x * Ox1p24f);
      hx = u & 0x7FFFFFFF;
      hx = hx / 3 + B2;
    } else {
      hx = hx / 3 + B1;
    }
    u &= 0x80000000;
    u |= hx;
    var t = <f64>reinterpret<f32>(u);
    var r = t * t * t;
    t = t * (<f64>x + x + r) / (x + r + r);
    r = t * t * t;
    t = t * (<f64>x + x + r) / (x + r + r);
    return <f32>t;
  }

  // @ts-ignore: decorator
  @inline
  export function ceil(x: f32): f32 {
    return builtin_ceil<f32>(x);
  }

  export function clz32(x: f32): f32 {
    if (!isFinite(x)) return 32;
    return <f32>builtin_clz(dtoi32(x));
  }

  export function cos(x: f32): f32 { // see: musl/src/math/cosf.c
    const c1pio2 = reinterpret<f64>(0x3FF921FB54442D18); // M_PI_2 * 1
    const c2pio2 = reinterpret<f64>(0x400921FB54442D18); // M_PI_2 * 2
    const c3pio2 = reinterpret<f64>(0x4012D97C7F3321D2); // M_PI_2 * 3
    const c4pio2 = reinterpret<f64>(0x401921FB54442D18); // M_PI_2 * 4

    var ix = reinterpret<u32>(x);
    var sign = ix >> 31;
    ix &= 0x7FFFFFFF;

    if (ix <= 0x3F490FDA) {  // |x| ~<= π/4
      if (ix < 0x39800000) { // |x| < 2**-12
        // raise inexact if x != 0
        return 1;
      }
      return cos_kernf(x);
    }

    if (ASC_SHRINK_LEVEL < 1) {
      if (ix <= 0x407B53D1) {  // |x| ~<= 5π/4
        if (ix > 0x4016CBE3) { // |x|  ~> 3π/4
          return -cos_kernf(sign ? x + c2pio2 : x - c2pio2);
        } else {
          return sign ? sin_kernf(x + c1pio2) : sin_kernf(c1pio2 - x);
        }
      }
      if (ix <= 0x40E231D5) {  // |x| ~<= 9π/4
        if (ix > 0x40AFEDDF) { // |x|  ~> 7π/4
          return cos_kernf(sign ? x + c4pio2 : x - c4pio2);
        } else {
          return sign ? sin_kernf(-x - c3pio2) : sin_kernf(x - c3pio2);
        }
      }
    }

    // cos(Inf or NaN) is NaN
    if (ix >= 0x7F800000) return x - x;

    // general argument reduction needed
    var n = rempio2f(x, ix, sign);
    var y = rempio2f_y;

    var t = n & 1 ? sin_kernf(y) : cos_kernf(y);
    return (n + 1) & 2 ? -t : t;
  }

  export function cosh(x: f32): f32 { // see: musl/src/math/coshf.c
    var u = reinterpret<u32>(x);
    u &= 0x7FFFFFFF;
    x = reinterpret<f32>(u);
    if (u < 0x3F317217) {
      if (u < 0x3F800000 - (12 << 23)) return 1;
      let t = expm1(x);
      // return 1 + t * t / (2 * (1 + t));
      return 1 + t * t / (2 + 2 * t);
    }
    if (u < 0x42B17217) {
      let t = exp(x);
      // return 0.5 * (t + 1 / t);
      return 0.5 * t + 0.5 / t;
    }
    return expo2f(x);
  }

  // @ts-ignore: decorator
  @inline
  export function floor(x: f32): f32 {
    return builtin_floor<f32>(x);
  }

  export function exp(x: f32): f32 { // see: musl/src/math/expf.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return expf_lut(x);
    } else {
      const
        ln2hi    = reinterpret<f32>(0x3F317200), //  6.9314575195e-1f
        ln2lo    = reinterpret<f32>(0x35BFBE8E), //  1.4286067653e-6f
        invln2   = reinterpret<f32>(0x3FB8AA3B), //  1.4426950216e+0f
        P1       = reinterpret<f32>(0x3E2AAA8F), //  1.6666625440e-1f
        P2       = reinterpret<f32>(0xBB355215), // -2.7667332906e-3f
        Ox1p127f = reinterpret<f32>(0x7F000000);
      let hx = reinterpret<u32>(x);
      let sign_ = <i32>(hx >> 31);
      hx &= 0x7FFFFFFF;
      if (hx >= 0x42AEAC50) {
        if (hx > 0x7F800000) return x; // NaN
        if (hx >= 0x42B17218) {
          if (!sign_) return x * Ox1p127f;
          else if (hx >= 0x42CFF1B5) return 0;
        }
      }
      let hi: f32, lo: f32;
      let k: i32;
      if (hx > 0x3EB17218) {
        if (hx > 0x3F851592) {
          k = <i32>(invln2 * x + builtin_copysign<f32>(0.5, x));
        } else {
          k = 1 - (sign_ << 1);
        }
        hi = x - <f32>k * ln2hi;
        lo = <f32>k * ln2lo;
        x = hi - lo;
      } else if (hx > 0x39000000) {
        k = 0;
        hi = x;
        lo = 0;
      } else {
        return 1 + x;
      }
      let xx = x * x;
      let c = x - xx * (P1 + xx * P2);
      let y: f32 = 1 + (x * c / (2 - c) - lo + hi);
      return k == 0 ? y : scalbn(y, k);
    }
  }

  export function exp2(x: f32): f32 {
    return exp2f_lut(x);
  }

  export function expm1(x: f32): f32 { // see: musl/src/math/expm1f.c and SUN COPYRIGHT NOTICE above
    const
      o_threshold = reinterpret<f32>(0x42B17180), //  8.8721679688e+01f
      ln2_hi      = reinterpret<f32>(0x3F317180), //  6.9313812256e-01f
      ln2_lo      = reinterpret<f32>(0x3717F7D1), //  9.0580006145e-06f
      invln2      = reinterpret<f32>(0x3FB8AA3B), //  1.4426950216e+00f
      Q1          = reinterpret<f32>(0xBD088868), // -3.3333212137e-02f
      Q2          = reinterpret<f32>(0x3ACF3010), //  1.5807170421e-03f
      Ox1p127f    = reinterpret<f32>(0x7F000000);
    var u = reinterpret<u32>(x);
    var hx = u & 0x7FFFFFFF;
    var sign_ = <i32>(u >> 31);
    if (hx >= 0x4195B844) {
      if (hx > 0x7F800000) return x;
      if (sign_) return -1;
      if (x > o_threshold) {
        x *= Ox1p127f;
        return x;
      }
    }
    var c: f32 = 0.0, t: f32, k: i32;
    if (hx > 0x3EB17218) {
      k = select<i32>(
        1 - (sign_ << 1),
        <i32>(invln2 * x + builtin_copysign<f32>(0.5, x)),
        hx < 0x3F851592
      );
      t = <f32>k;
      let hi = x - t * ln2_hi;
      let lo = t * ln2_lo;
      x = hi - lo;
      c = (hi - x) - lo;
    } else if (hx < 0x33000000) {
      return x;
    } else k = 0;
    var hfx: f32 = 0.5 * x;
    var hxs: f32 = x * hfx;
    var r1: f32 = 1.0 + hxs * (Q1 + hxs * Q2);
    t  = 3.0 - r1 * hfx;
    var e = hxs * ((r1 - t) / (6.0 - x * t));
    if (k == 0) return x - (x * e - hxs);
    e  = x * (e - c) - c;
    e -= hxs;
    if (k == -1) return 0.5 * (x - e) - 0.5;
    if (k == 1) {
      if (x < -0.25) return -2.0 * (e - (x + 0.5));
      return 1.0 + 2.0 * (x - e);
    }
    u = (0x7F + k) << 23;
    var twopk = reinterpret<f32>(u);
    var y: f32;
    if (k < 0 || k > 56) {
      y = x - e + 1.0;
      if (k == 128) y = y * 2.0 * Ox1p127f;
      else y = y * twopk;
      return y - 1.0;
    }
    u = (0x7F - k) << 23;
    y = reinterpret<f32>(u);
    if (k < 20) y = (1 - y) - e;
    else y = 1 - (e + y);
    return (x + y) * twopk;
  }

  // @ts-ignore: decorator
  @inline
  export function fround(x: f32): f32 {
    return x;
  }

  export function hypot(x: f32, y: f32): f32 { // see: musl/src/math/hypotf.c
    const
      Ox1p90f  = reinterpret<f32>(0x6C800000),
      Ox1p_90f = reinterpret<f32>(0x12800000);
    var ux = reinterpret<u32>(x);
    var uy = reinterpret<u32>(y);
    ux &= 0x7FFFFFFF;
    uy &= 0x7FFFFFFF;
    if (ux < uy) {
      let ut = ux;
      ux = uy;
      uy = ut;
    }
    x = reinterpret<f32>(ux);
    y = reinterpret<f32>(uy);
    if (uy == 0xFF << 23) return y;
    if (ux >= 0xFF << 23 || uy == 0 || ux - uy >= 25 << 23) return x + y;
    var z: f32 = 1;
    if (ux >= (0x7F + 60) << 23) {
      z  = Ox1p90f;
      x *= Ox1p_90f;
      y *= Ox1p_90f;
    } else if (uy < (0x7F - 60) << 23) {
      z  = Ox1p_90f;
      x *= Ox1p90f;
      y *= Ox1p90f;
    }
    return z * builtin_sqrt<f32>(<f32>(<f64>x * x + <f64>y * y));
  }

  // @ts-ignore: decorator
  @inline
  export function imul(x: f32, y: f32): f32 {
    /*
     * Wasm (MVP) and JS have different approaches for double->int conversions.
     *
     * For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
     * our float-point arguments before actual convertion to integers.
     */
    if (!isFinite(x + y)) return 0;
    return <f32>(dtoi32(x) * dtoi32(y));
  }

  export function log(x: f32): f32 { // see: musl/src/math/logf.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return logf_lut(x);
    } else {
      const
        ln2_hi  = reinterpret<f32>(0x3F317180), // 6.9313812256e-01f
        ln2_lo  = reinterpret<f32>(0x3717F7D1), // 9.0580006145e-06f
        Lg1     = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f
        Lg2     = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f
        Lg3     = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f
        Lg4     = reinterpret<f32>(0x3E789E26), // 0xf89e26.0p-26f
        Ox1p25f = reinterpret<f32>(0x4C000000);
      let u = reinterpret<u32>(x);
      let k = 0;
      if (u < 0x00800000 || <bool>(u >> 31)) {
        if (u << 1 == 0) return -1 / (x * x);
        if (u >> 31) return (x - x) / 0;
        k -= 25;
        x *= Ox1p25f;
        u = reinterpret<u32>(x);
      } else if (u >= 0x7F800000) return x;
        else if (u == 0x3F800000) return 0;
      u += 0x3F800000 - 0x3F3504F3;
      k += <u32>(<i32>u >> 23) - 0x7F;
      u = (u & 0x007FFFFF) + 0x3F3504F3;
      x = reinterpret<f32>(u);
      let f = x - 1.0;
      let s = f / (2.0 + f);
      let z = s * s;
      let w = z * z;
      let t1 = w * (Lg2 + w * Lg4);
      let t2 = z * (Lg1 + w * Lg3);
      let r = t2 + t1;
      let hfsq = <f32>0.5 * f * f;
      let dk = <f32>k;
      return s * (hfsq + r) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
    }
  }

  export function log10(x: f32): f32 { // see: musl/src/math/log10f.c and SUN COPYRIGHT NOTICE above
    const
      ivln10hi  = reinterpret<f32>(0x3EDE6000), //  4.3432617188e-01f
      ivln10lo  = reinterpret<f32>(0xB804EAD9), // -3.1689971365e-05f
      log10_2hi = reinterpret<f32>(0x3E9A2080), //  3.0102920532e-01f
      log10_2lo = reinterpret<f32>(0x355427DB), //  7.9034151668e-07f
      Lg1       = reinterpret<f32>(0x3F2AAAAA), //  0xaaaaaa.0p-24f, 0.66666662693f
      Lg2       = reinterpret<f32>(0x3ECCCE13), //  0xccce13.0p-25f, 0.40000972152f
      Lg3       = reinterpret<f32>(0x3E91E9EE), //  0x91e9ee.0p-25f, 0.28498786688f
      Lg4       = reinterpret<f32>(0x3E789E26), //  0xf89e26.0p-26f, 0.24279078841f
      Ox1p25f   = reinterpret<f32>(0x4C000000);
    var ix = reinterpret<u32>(x);
    var k = 0;
    if (ix < 0x00800000 || <bool>(ix >> 31)) {
      if (ix << 1 == 0) return -1 / (x * x);
      if (ix >> 31) return (x - x) / 0.0;
      k -= 25;
      x *= Ox1p25f;
      ix = reinterpret<u32>(x);
    } else if (ix >= 0x7F800000) return x;
      else if (ix == 0x3F800000) return 0;
    ix += 0x3F800000 - 0x3F3504F3;
    k += <i32>(ix >> 23) - 0x7F;
    ix = (ix & 0x007FFFFF) + 0x3F3504F3;
    x = reinterpret<f32>(ix);
    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 hi = f - hfsq;
    ix = reinterpret<u32>(hi);
    ix &= 0xFFFFF000;
    hi = reinterpret<f32>(ix);
    var lo = f - hi - hfsq + s * (hfsq + r);
    var dk = <f32>k;
    return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi + hi * ivln10hi + dk * log10_2hi;
  }

  export function log1p(x: f32): f32 { // see: musl/src/math/log1pf.c and SUN COPYRIGHT NOTICE above
    const
      ln2_hi = reinterpret<f32>(0x3F317180), // 6.9313812256e-01
      ln2_lo = reinterpret<f32>(0x3717F7D1), // 9.0580006145e-06
      Lg1    = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f, 0.66666662693f
      Lg2    = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f, 0.40000972152f
      Lg3    = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f, 0.28498786688f
      Lg4    = reinterpret<f32>(0x3E789E26); // 0xf89e26.0p-26f, 0.24279078841f
    var ix = reinterpret<u32>(x);
    var c: f32 = 0, f: f32 = 0;
    var k: i32 = 1;
    if (ix < 0x3ED413D0 || <bool>(ix >> 31)) {
      if (ix >= 0xBF800000) {
        if (x == -1) return x / 0.0;
        return (x - x) / 0.0;
      }
      if (ix << 1 < 0x33800000 << 1) return x;
      if (ix <= 0xBE95F619) {
        k = 0;
        c = 0;
        f = x;
      }
    } else if (ix >= 0x7F800000) return x;
    if (k) {
      let uf: f32 = 1 + x;
      let iu = reinterpret<u32>(uf);
      iu += 0x3F800000 - 0x3F3504F3;
      k = <i32>(iu >> 23) - 0x7F;
      if (k < 25) {
        c = k >= 2 ? 1 - (uf - x) : x - (uf - 1);
        c /= uf;
      } else c = 0;
      iu = (iu & 0x007FFFFF) + 0x3F3504F3;
      f = reinterpret<f32>(iu) - 1;
    }
    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 + c) - hfsq + f + dk * ln2_hi;
  }

  export function log2(x: f32): f32 { // see: musl/src/math/log2f.c and SUN COPYRIGHT NOTICE above
    if (ASC_SHRINK_LEVEL < 1) {
      return log2f_lut(x);
    } else {
      const
        ivln2hi = reinterpret<f32>(0x3FB8B000), //  1.4428710938e+00f
        ivln2lo = reinterpret<f32>(0xB9389AD4), // -1.7605285393e-04
        Lg1     = reinterpret<f32>(0x3F2AAAAA), //  0xaaaaaa.0p-24f, 0.66666662693f
        Lg2     = reinterpret<f32>(0x3ECCCE13), //  0xccce13.0p-25f, 0.40000972152f
        Lg3     = reinterpret<f32>(0x3E91E9EE), //  0x91e9ee.0p-25f, 0.28498786688f
        Lg4     = reinterpret<f32>(0x3E789E26), //  0xf89e26.0p-26f, 0.24279078841f
        Ox1p25f = reinterpret<f32>(0x4C000000);
      let ix = reinterpret<u32>(x);
      let k: i32 = 0;
      if (ix < 0x00800000 || <bool>(ix >> 31)) {
        if (ix << 1 == 0) return -1 / (x * x);
        if (ix >> 31) return (x - x) / 0.0;
        k -= 25;
        x *= Ox1p25f;
        ix = reinterpret<u32>(x);
      } else if (ix >= 0x7F800000) return x;
        else if (ix == 0x3F800000) return 0;
      ix += 0x3F800000 - 0x3F3504F3;
      k += <i32>(ix >> 23) - 0x7F;
      ix = (ix & 0x007FFFFF) + 0x3F3504F3;
      x = reinterpret<f32>(ix);
      let f = x - 1.0;
      let s = f / (2.0 + f);
      let z = s * s;
      let w = z * z;
      let t1 = w * (Lg2 + w * Lg4);
      let t2 = z * (Lg1 + w * Lg3);
      let r = t2 + t1;
      let hfsq: f32 = 0.5 * f * f;
      let hi = f - hfsq;
      let u = reinterpret<u32>(hi);
      u &= 0xFFFFF000;
      hi = reinterpret<f32>(u);
      let lo: f32 = f - hi - hfsq + s * (hfsq + r);
      let dk = <f32>k;
      return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + dk;
    }
  }

  // @ts-ignore: decorator
  @inline
  export function max(value1: f32, value2: f32): f32 {
    return builtin_max<f32>(value1, value2);
  }

  // @ts-ignore: decorator
  @inline
  export function min(value1: f32, value2: f32): f32 {
    return builtin_min<f32>(value1, value2);
  }

  export function pow(x: f32, y: f32): f32 {
    // TODO: remove this fast pathes after introduced own mid-end IR with "stdlib call simplify" transforms
    if (builtin_abs<f32>(y) <= 2) {
      if (y == 2.0) return x * x;
      if (y == 0.5) {
        return select<f32>(
          builtin_abs<f32>(builtin_sqrt<f32>(x)),
          Infinity,
          x != -Infinity
        );
      }
      if (y == -1.0) return 1 / x;
      if (y == 1.0) return x;
      if (y == 0.0) return 1.0;
    }
    if (ASC_SHRINK_LEVEL < 1) {
      // see: musl/src/math/powf.c
      return powf_lut(x, y);
    } else {
      // based on:  jdh8/metallic/src/math/float/powf.c
      if (y == 0) return 1;
      // @ts-ignore: cast
      if (isNaN(x) | isNaN(y)) {
        return NaN;
      }
      let sign: u32 = 0;
      let uy = reinterpret<u32>(y);
      let ux = reinterpret<u32>(x);
      let sx = ux >> 31;
      ux &= 0x7FFFFFFF;
      if (sx && nearest(y) == y) {
        x = -x;
        sx = 0;
        sign = u32(nearest(y * 0.5) != y * 0.5) << 31;
      }
      let m: u32;
      if (ux == 0x3F800000) { // x == 1
        m = sx | u32((uy & 0x7FFFFFFF) == 0x7F800000) ? 0x7FC00000 : 0x3F800000;
      } else if (ux == 0) {
        m = uy >> 31 ? 0x7F800000 : 0;
      } else if (ux == 0x7F800000) {
        m = uy >> 31 ? 0 : 0x7F800000;
      } else if (sx) {
        m = 0x7FC00000;
      } else {
        m = reinterpret<u32>(<f32>exp2f(<f64>y * log2f(x)));
      }
      return reinterpret<f32>(m | sign);
    }
  }

  // @ts-ignore: decorator
  @inline
  export function seedRandom(value: i64): void {
    NativeMath.seedRandom(value);
  }

  // Using xoroshiro64starstar from http://xoshiro.di.unimi.it/xoroshiro64starstar.c
  export function random(): f32 {
    if (!random_seeded) seedRandom(reinterpret<i64>(seed()));

    var s0 = random_state0_32;
    var s1 = random_state1_32;
    var r  = rotl<u32>(s0 * 0x9E3779BB, 5) * 5;

    s1 ^= s0;
    random_state0_32 = rotl<u32>(s0, 26) ^ s1 ^ (s1 << 9);
    random_state1_32 = rotl<u32>(s1, 13);

    return reinterpret<f32>((r >> 9) | (127 << 23)) - 1.0;
  }

  // @ts-ignore: decorator
  @inline
  export function round(x: f32): f32 {
    return builtin_copysign<f32>(builtin_floor<f32>(x + 0.5), x);
  }

  // @ts-ignore: decorator
  @inline
  export function sign(x: f32): f32 {
    if (ASC_SHRINK_LEVEL > 0) {
      return builtin_abs(x) > 0 ? builtin_copysign<f32>(1, x) : x;
    } else {
      return x > 0 ? 1 : x < 0 ? -1 : x;
    }
  }

  // @ts-ignore: decorator
  @inline
  export function signbit(x: f32): bool {
    // @ts-ignore: type
    return <bool>((reinterpret<u32>(x) >>> 31) & (x == x));
  }

  export function sin(x: f32): f32 { // see: musl/src/math/sinf.c
    const s1pio2 = reinterpret<f64>(0x3FF921FB54442D18); // M_PI_2 * 1
    const s2pio2 = reinterpret<f64>(0x400921FB54442D18); // M_PI_2 * 2
    const s3pio2 = reinterpret<f64>(0x4012D97C7F3321D2); // M_PI_2 * 3
    const s4pio2 = reinterpret<f64>(0x401921FB54442D18); // M_PI_2 * 4

    var ix = reinterpret<u32>(x);
    var sign = ix >> 31;
    ix &= 0x7FFFFFFF;

    if (ix <= 0x3F490FDA) {  // |x| ~<= π/4
      if (ix < 0x39800000) { // |x| < 2**-12
        return x;
      }
      return sin_kernf(x);
    }

    if (ASC_SHRINK_LEVEL < 1) {
      if (ix <= 0x407B53D1) {   // |x| ~<= 5π/4
        if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
          return sign ? -cos_kernf(x + s1pio2) : cos_kernf(x - s1pio2);
        }
        return sin_kernf(-(sign ? x + s2pio2 : x - s2pio2));
      }

      if (ix <= 0x40E231D5) {   // |x| ~<= 9π/4
        if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
          return sign ? cos_kernf(x + s3pio2) : -cos_kernf(x - s3pio2);
        }
        return sin_kernf(sign ? x + s4pio2 : x - s4pio2);
      }
    }

    // sin(Inf or NaN) is NaN
    if (ix >= 0x7F800000) return x - x;

    var n = rempio2f(x, ix, sign);
    var y = rempio2f_y;

    var t = n & 1 ? cos_kernf(y) : sin_kernf(y);
    return n & 2 ? -t : t;
  }

  export function sinh(x: f32): f32 { // see: musl/src/math/sinhf.c
    var u = reinterpret<u32>(x) & 0x7FFFFFFF;
    var absx = reinterpret<f32>(u);
    var t: f32;
    var h = builtin_copysign<f32>(0.5, x);
    if (u < 0x42B17217) {
      t = expm1(absx);
      if (u < 0x3F800000) {
        if (u < 0x3F800000 - (12 << 23)) return x;
        return h * (2 * t - t * t / (t + 1));
      }
      return h * (t + t / (t + 1));
    }
    t = 2 * h * expo2f(absx);
    return t;
  }

  // @ts-ignore: decorator
  @inline
  export function sqrt(x: f32): f32 {
    return builtin_sqrt<f32>(x);
  }

  export function tan(x: f32): f32 { // see: musl/src/math/tanf.c
    const t1pio2 = reinterpret<f64>(0x3FF921FB54442D18); // 1 * M_PI_2
    const t2pio2 = reinterpret<f64>(0x400921FB54442D18); // 2 * M_PI_2
    const t3pio2 = reinterpret<f64>(0x4012D97C7F3321D2); // 3 * M_PI_2
    const t4pio2 = reinterpret<f64>(0x401921FB54442D18); // 4 * M_PI_2

    var ix = reinterpret<u32>(x);
    var sign = ix >> 31;
    ix &= 0x7FFFFFFF;

    if (ix <= 0x3F490FDA) {  // |x| ~<= π/4
      if (ix < 0x39800000) { // |x| < 2**-12
        return x;
      }
      return tan_kernf(x, 0);
    }

    if (ASC_SHRINK_LEVEL < 1) {
      if (ix <= 0x407B53D1) {   // |x| ~<= 5π/4
        if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
          return tan_kernf((sign ? x + t1pio2 : x - t1pio2), 1);
        } else {
          return tan_kernf((sign ? x + t2pio2 : x - t2pio2), 0);
        }
      }
      if (ix <= 0x40E231D5) {   // |x| ~<= 9π/4
        if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
          return tan_kernf((sign ? x + t3pio2 : x - t3pio2), 1);
        } else {
          return tan_kernf((sign ? x + t4pio2 : x - t4pio2), 0);
        }
      }
    }

    // tan(Inf or NaN) is NaN
    if (ix >= 0x7F800000) return x - x;

    // argument reduction
    var n = rempio2f(x, ix, sign);
    var y = rempio2f_y;
    return tan_kernf(y, n & 1);
  }

  export function tanh(x: f32): f32 { // see: musl/src/math/tanhf.c
    var u = reinterpret<u32>(x);
    u &= 0x7FFFFFFF;
    var y = reinterpret<f32>(u);
    var t: f32;
    if (u > 0x3F0C9F54) {
      if (u > 0x41200000) t = 1 + 0 / y;
      else {
        t = expm1(2 * y);
        t = 1 - 2 / (t + 2);
      }
    } else if (u > 0x3E82C578) {
      t = expm1(2 * y);
      t = t / (t + 2);
    } else if (u >= 0x00800000) {
      t = expm1(-2 * y);
      t = -t / (t + 2);
    } else t = y;
    return builtin_copysign<f32>(t, x);
  }

  // @ts-ignore: decorator
  @inline
  export function trunc(x: f32): f32 {
    return builtin_trunc<f32>(x);
  }

  export function scalbn(x: f32, n: i32): f32 { // see: https://git.musl-libc.org/cgit/musl/tree/src/math/scalbnf.c
    const
      Ox1p24f   = reinterpret<f32>(0x4B800000),
      Ox1p127f  = reinterpret<f32>(0x7F000000),
      Ox1p_126f = reinterpret<f32>(0x00800000);
    var y = x;
    if (n > 127) {
      y *= Ox1p127f;
      n -= 127;
      if (n > 127) {
        y *= Ox1p127f;
        n = builtin_min<i32>(n - 127, 127);
      }
    } else if (n < -126) {
      y *= Ox1p_126f * Ox1p24f;
      n += 126 - 24;
      if (n < -126) {
        y *= Ox1p_126f * Ox1p24f;
        n = builtin_max<i32>(n + 126 - 24, -126);
      }
    }
    return y * reinterpret<f32>(<u32>(0x7F + n) << 23);
  }

  export function mod(x: f32, y: f32): f32 { // see: musl/src/math/fmodf.c
    var ux = reinterpret<u32>(x);
    var uy = reinterpret<u32>(y);
    var ex = <i32>(ux >> 23 & 0xFF);
    var ey = <i32>(uy >> 23 & 0xFF);
    var sx = ux & 0x80000000;
    var uy1 = uy << 1;
    if (uy1 == 0 || ex == 0xFF || isNaN<f32>(y)) {
      let m = x * y;
      return m / m;
    }
    var ux1 = ux << 1;
    if (ux1 <= uy1) {
      if (ux1 == uy1) return 0 * x;
      return x;
    }
    if (!ex) {
      ex -= builtin_clz<u32>(ux << 9);
      ux <<= -ex + 1;
    } else {
      ux &= <u32>-1 >> 9;
      ux |= 1 << 23;
    }
    if (!ey) {
      ey -= builtin_clz<u32>(uy << 9);
      uy <<= -ey + 1;
    } else {
      uy &= <u32>-1 >> 9;
      uy |= 1 << 23;
    }
    while (ex > ey) {
      if (ux >= uy) {
        if (ux == uy) return 0 * x;
        ux -= uy;
      }
      ux <<= 1;
      --ex;
    }
    if (ux >= uy) {
      if (ux == uy) return 0 * x;
      ux -= uy;
    }
    // for (; !(ux >> 23); ux <<= 1) --ex;
    var shift = <i32>builtin_clz<u32>(ux << 8);
    ex -= shift;
    ux <<= shift;
    if (ex > 0) {
      ux -= 1 << 23;
      ux |= <u32>ex << 23;
    } else {
      ux >>= -ex + 1;
    }
    ux |= sx;
    return reinterpret<f32>(ux);
  }

  export function rem(x: f32, y: f32): f32 { // see: musl/src/math/remquof.c
    var ux = reinterpret<u32>(x);
    var uy = reinterpret<u32>(y);
    var ex = <i32>(ux >> 23 & 0xFF);
    var ey = <i32>(uy >> 23 & 0xFF);
    var sx = <i32>(ux >> 31);
    var uxi = ux;
    if (uy << 1 == 0 || ex == 0xFF || isNaN(y)) return (x * y) / (x * y);
    if (ux << 1 == 0) return x;
    if (!ex) {
      ex -= builtin_clz<u32>(uxi << 9);
      uxi <<= -ex + 1;
    } else {
      uxi &= <u32>-1 >> 9;
      uxi |= 1 << 23;
    }
    if (!ey) {
      ey -= builtin_clz<u32>(uy << 9);
      uy <<= -ey + 1;
    } else {
      uy &= <u32>-1 >> 9;
      uy |= 1 << 23;
    }
    var q = 0;
    do {
      if (ex < ey) {
        if (ex + 1 == ey) break; // goto end
        return x;
      }
      while (ex > ey) {
        if (uxi >= uy) {
          uxi -= uy;
          ++q;
        }
        uxi <<= 1;
        q <<= 1;
        --ex;
      }
      if (uxi >= uy) {
        uxi -= uy;
        ++q;
      }
      if (uxi == 0) ex = -30;
      else {
        let shift = builtin_clz<i32>(uxi << 8);
        ex -= shift;
        uxi <<= shift;
      }
      break;
    } while (false);
  // end
    if (ex > 0) {
      uxi -= 1 << 23;
      uxi |= <u32>ex << 23;
    } else {
      uxi >>= -ex + 1;
    }
    x = reinterpret<f32>(uxi);
    y = builtin_abs<f32>(y);
    var x2 = x + x;
    if (ex == ey || (ex + 1 == ey && (<f32>x2 > y || (<f32>x2 == y && <bool>(q & 1))))) {
      x -= y;
      // q++;
    }
    return sx ? -x : x;
  }

  export function sincos(x: f32): void { // see: musl/tree/src/math/sincosf.c
    const s1pio2 = reinterpret<f64>(0x3FF921FB54442D18); // 1 * M_PI_2
    const s2pio2 = reinterpret<f64>(0x400921FB54442D18); // 2 * M_PI_2
    const s3pio2 = reinterpret<f64>(0x4012D97C7F3321D2); // 3 * M_PI_2
    const s4pio2 = reinterpret<f64>(0x401921FB54442D18); // 4 * M_PI_2

    var ix = reinterpret<u32>(x);
    var sign = ix >> 31;
    ix &= 0x7FFFFFFF;

    if (ix <= 0x3F490FDA) {  // |x| ~<= π/4
      if (ix < 0x39800000) { // |x| < 2**-12
        sincos_sin = x;
        sincos_cos = 1;
        return;
      }
      sincos_sin = sin_kernf(x);
      sincos_cos = cos_kernf(x);
      return;
    }
    if (ASC_SHRINK_LEVEL < 1) {
      if (ix <= 0x407B53D1) {   // |x| ~<= 5π/4
        if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
          if (sign) {
            sincos_sin = -cos_kernf(x + s1pio2);
            sincos_cos =  sin_kernf(x + s1pio2);
          } else {
            sincos_sin = cos_kernf(s1pio2 - x);
            sincos_cos = sin_kernf(s1pio2 - x);
          }
          return;
        }
        // -sin(x + c) is not correct if x+c could be 0: -0 vs +0
        sincos_sin = -sin_kernf(sign ? x + s2pio2 : x - s2pio2);
        sincos_cos = -cos_kernf(sign ? x + s2pio2 : x - s2pio2);
        return;
      }
      if (ix <= 0x40E231D5) {   // |x| ~<= 9π/4
        if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
          if (sign) {
            sincos_sin =  cos_kernf(x + s3pio2);
            sincos_cos = -sin_kernf(x + s3pio2);
          } else {
            sincos_sin = -cos_kernf(x - s3pio2);
            sincos_cos =  sin_kernf(x - s3pio2);
          }
          return;
        }
        sincos_sin = sin_kernf(sign ? x + s4pio2 : x - s4pio2);
        sincos_cos = cos_kernf(sign ? x + s4pio2 : x - s4pio2);
        return;
      }
    }
    // sin(Inf or NaN) is NaN
    if (ix >= 0x7F800000) {
      let xx = x - x;
      sincos_sin = xx;
      sincos_cos = xx;
      return;
    }
    // general argument reduction needed
    var n = rempio2f(x, ix, sign);
    var y = rempio2f_y;
    var s = sin_kernf(y);
    var c = cos_kernf(y);
    var sin = s, cos = c;
    if (n & 1) {
      sin =  c;
      cos = -s;
    }
    if (n & 2) {
      sin = -sin;
      cos = -cos;
    }
    sincos_sin = sin;
    sincos_cos = cos;
  }
}

export function ipow32(x: i32, e: i32): i32 {
  var out = 1;
  if (ASC_SHRINK_LEVEL < 1) {
    if (e < 0) return 0;

    switch (e) {
      case 0: return 1;
      case 1: return x;
      case 2: return x * x;
    }

    let log = 32 - clz(e);
    if (log <= 5) {
      // 32 = 2 ^ 5, so need only five cases.
      // But some extra cases needs for properly overflowing
      switch (log) {
        case 5: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 4: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 3: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 2: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 1: {
          if (e & 1) out *= x;
        }
      }
      return out;
    }
  }

  while (e > 0) {
    if (e & 1) out *= x;
    e >>= 1;
    x *= x;
  }
  return out;
}

export function ipow64(x: i64, e: i32): i64 {
  var out: i64 = 1;
  if (ASC_SHRINK_LEVEL < 1) {
    if (e < 0) return 0;
    switch (e) {
      case 0: return 1;
      case 1: return x;
      case 2: return x * x;
    }

    let log = 32 - clz(e);
    if (log <= 6) {
      // 64 = 2 ^ 6, so need only six cases.
      // But some extra cases needs for properly overflowing
      switch (log) {
        case 6: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 5: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 4: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 3: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 2: {
          if (e & 1) out *= x;
          e >>= 1;
          x *= x;
        }
        case 1: {
          if (e & 1) out *= x;
        }
      }
      return out;
    }
  }

  while (e > 0) {
    if (e & 1) out *= x;
    e >>= 1;
    x *= x;
  }
  return out;
}

export function ipow32f(x: f32, e: i32): f32 {
  var sign = e >> 31;
  e = (e + sign) ^ sign; // abs(e)
  var out: f32 = 1;
  while (e) {
    out *= select<f32>(x, 1.0, e & 1);
    e >>= 1;
    x *= x;
  }
  return sign ? <f32>1.0 / out : out;
}

export function ipow64f(x: f64, e: i32): f64 {
  var sign = e >> 31;
  e = (e + sign) ^ sign; // abs(e)
  var out = 1.0;
  while (e) {
    out *= select(x, 1.0, e & 1);
    e >>= 1;
    x *= x;
  }
  return sign ? 1.0 / out : out;
}