mirror of
https://github.com/fluencelabs/assemblyscript
synced 2025-04-25 07:02:13 +00:00
2434 lines
79 KiB
TypeScript
2434 lines
79 KiB
TypeScript
import * as JSMath from "./bindings/Math";
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export { JSMath };
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import {
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abs as builtin_abs,
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ceil as builtin_ceil,
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clz as builtin_clz,
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copysign as builtin_copysign,
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floor as builtin_floor,
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max as builtin_max,
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min as builtin_min,
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sqrt as builtin_sqrt,
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trunc as builtin_trunc
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} from "./builtins";
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// SUN COPYRIGHT NOTICE
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//
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this software
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// is freely granted, provided that this notice is preserved.
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//
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// Applies to all functions marked with a comment referring here.
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// TODO: sin, cos, tan
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function R(z: f64): f64 { // Rational approximation of (asin(x)-x)/x^3
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const // see: musl/src/math/asin.c and SUN COPYRIGHT NOTICE above
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pS0 = reinterpret<f64>(0x3FC5555555555555), // 1.66666666666666657415e-01
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pS1 = reinterpret<f64>(0xBFD4D61203EB6F7D), // -3.25565818622400915405e-01
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pS2 = reinterpret<f64>(0x3FC9C1550E884455), // 2.01212532134862925881e-01
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pS3 = reinterpret<f64>(0xBFA48228B5688F3B), // -4.00555345006794114027e-02
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pS4 = reinterpret<f64>(0x3F49EFE07501B288), // 7.91534994289814532176e-04
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pS5 = reinterpret<f64>(0x3F023DE10DFDF709), // 3.47933107596021167570e-05
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qS1 = reinterpret<f64>(0xC0033A271C8A2D4B), // -2.40339491173441421878e+00
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qS2 = reinterpret<f64>(0x40002AE59C598AC8), // 2.02094576023350569471e+00
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qS3 = reinterpret<f64>(0xBFE6066C1B8D0159), // -6.88283971605453293030e-01
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qS4 = reinterpret<f64>(0x3FB3B8C5B12E9282); // 7.70381505559019352791e-02
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var p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
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var q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
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return p / q;
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}
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@inline function expo2(x: f64): f64 { // exp(x)/2 for x >= log(DBL_MAX)
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const // see: musl/src/math/__expo2.c
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k = <u32>2043,
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kln2 = reinterpret<f64>(0x40962066151ADD8B); // 0x1.62066151add8bp+10
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var scale = reinterpret<f64>(<u64>((<u32>0x3FF + k / 2) << 20) << 32);
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return NativeMath.exp(x - kln2) * scale * scale;
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}
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@lazy var random_seeded = false;
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@lazy var random_state0_64: u64;
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@lazy var random_state1_64: u64;
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@lazy var random_state0_32: u32;
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@lazy var random_state1_32: u32;
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function murmurHash3(h: u64): u64 { // Force all bits of a hash block to avalanche
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h ^= h >> 33; // see: https://github.com/aappleby/smhasher
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h *= 0xFF51AFD7ED558CCD;
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h ^= h >> 33;
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h *= 0xC4CEB9FE1A85EC53;
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h ^= h >> 33;
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return h;
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}
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function splitMix32(h: u32): u32 {
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h += 0x6D2B79F5;
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h = (h ^ (h >> 15)) * (h | 1);
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h ^= h + (h ^ (h >> 7)) * (h | 61);
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return h ^ (h >> 14);
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}
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export namespace NativeMath {
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@lazy export const E = reinterpret<f64>(0x4005BF0A8B145769); // 2.7182818284590452354
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@lazy export const LN2 = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.69314718055994530942
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@lazy export const LN10 = reinterpret<f64>(0x40026BB1BBB55516); // 2.30258509299404568402
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@lazy export const LOG2E = reinterpret<f64>(0x3FF71547652B82FE); // 1.4426950408889634074
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@lazy export const LOG10E = reinterpret<f64>(0x3FDBCB7B1526E50E); // 0.43429448190325182765
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@lazy export const PI = reinterpret<f64>(0x400921FB54442D18); // 3.14159265358979323846
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@lazy export const SQRT1_2 = reinterpret<f64>(0x3FE6A09E667F3BCD); // 0.70710678118654752440
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@lazy export const SQRT2 = reinterpret<f64>(0x3FF6A09E667F3BCD); // 1.41421356237309504880
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@inline
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export function abs(x: f64): f64 {
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return builtin_abs<f64>(x);
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}
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export function acos(x: f64): f64 { // see: musl/src/math/acos.c and SUN COPYRIGHT NOTICE above
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const
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pio2_hi = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
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pio2_lo = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
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Ox1p_120f = reinterpret<f32>(0x03800000);
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var hx = <u32>(reinterpret<u64>(x) >> 32);
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var ix = hx & 0x7FFFFFFF;
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if (ix >= 0x3FF00000) {
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let lx = <u32>reinterpret<u64>(x);
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if ((ix - 0x3FF00000 | lx) == 0) {
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if (hx >> 31) return 2 * pio2_hi + Ox1p_120f;
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return 0;
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}
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return 0 / (x - x);
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}
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if (ix < 0x3FE00000) {
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if (ix <= 0x3C600000) return pio2_hi + Ox1p_120f;
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return pio2_hi - (x - (pio2_lo - x * R(x * x)));
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}
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var s: f64, w: f64, z: f64;
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if (hx >> 31) {
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// z = (1.0 + x) * 0.5;
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z = 0.5 + x * 0.5;
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s = builtin_sqrt<f64>(z);
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w = R(z) * s - pio2_lo;
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return 2 * (pio2_hi - (s + w));
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}
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// z = (1.0 - x) * 0.5;
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z = 0.5 - x * 0.5;
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s = builtin_sqrt<f64>(z);
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var df = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
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var c = (z - df * df) / (s + df);
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w = R(z) * s + c;
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return 2 * (df + w);
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}
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export function acosh(x: f64): f64 { // see: musl/src/math/acosh.c
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const s = reinterpret<f64>(0x3FE62E42FEFA39EF);
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var e = reinterpret<u64>(x) >> 52 & 0x7FF;
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if (e < 0x3FF + 1) return log1p(x - 1 + builtin_sqrt<f64>((x - 1) * (x - 1) + 2 * (x - 1)));
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if (e < 0x3FF + 26) return log(2 * x - 1 / (x + builtin_sqrt<f64>(x * x - 1)));
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return log(x) + s;
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}
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export function asin(x: f64): f64 { // see: musl/src/math/asin.c and SUN COPYRIGHT NOTICE above
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const
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pio2_hi = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
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pio2_lo = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
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Ox1p_120f = reinterpret<f32>(0x03800000);
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var hx = <u32>(reinterpret<u64>(x) >> 32);
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var ix = hx & 0x7FFFFFFF;
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if (ix >= 0x3FF00000) {
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let lx = <u32>reinterpret<u64>(x);
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if ((ix - 0x3FF00000 | lx) == 0) return x * pio2_hi + Ox1p_120f;
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return 0 / (x - x);
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}
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if (ix < 0x3FE00000) {
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if (ix < 0x3E500000 && ix >= 0x00100000) return x;
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return x + x * R(x * x);
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}
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// var z = (1.0 - builtin_abs<f64>(x)) * 0.5;
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var z = 0.5 - builtin_abs<f64>(x) * 0.5;
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var s = builtin_sqrt<f64>(z);
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var r = R(z);
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if (ix >= 0x3FEF3333) x = pio2_hi - (2 * (s + s * r) - pio2_lo);
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else {
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let f = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
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let c = (z - f * f) / (s + f);
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x = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f));
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}
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if (hx >> 31) return -x;
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return x;
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}
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export function asinh(x: f64): f64 { // see: musl/src/math/asinh.c
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const c = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.693147180559945309417232121458176568
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var u = reinterpret<u64>(x);
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var e = u >> 52 & 0x7FF;
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var y = reinterpret<f64>(u & 0x7FFFFFFFFFFFFFFF);
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if (e >= 0x3FF + 26) y = log(y) + c;
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else if (e >= 0x3FF + 1) y = log(2 * y + 1 / (builtin_sqrt<f64>(y * y + 1) + y));
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else if (e >= 0x3FF - 26) y = log1p(y + y * y / (builtin_sqrt<f64>(y * y + 1) + 1));
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return builtin_copysign(y, x);
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}
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export function atan(x: f64): f64 { // see musl/src/math/atan.c and SUN COPYRIGHT NOTICE above
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const
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atanhi0 = reinterpret<f64>(0x3FDDAC670561BB4F), // 4.63647609000806093515e-01
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atanhi1 = reinterpret<f64>(0x3FE921FB54442D18), // 7.85398163397448278999e-01
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atanhi2 = reinterpret<f64>(0x3FEF730BD281F69B), // 9.82793723247329054082e-01
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atanhi3 = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
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atanlo0 = reinterpret<f64>(0x3C7A2B7F222F65E2), // 2.26987774529616870924e-17
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atanlo1 = reinterpret<f64>(0x3C81A62633145C07), // 3.06161699786838301793e-17
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atanlo2 = reinterpret<f64>(0x3C7007887AF0CBBD), // 1.39033110312309984516e-17
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atanlo3 = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
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aT0 = reinterpret<f64>(0x3FD555555555550D), // 3.33333333333329318027e-01
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aT1 = reinterpret<f64>(0xBFC999999998EBC4), // -1.99999999998764832476e-01
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aT2 = reinterpret<f64>(0x3FC24924920083FF), // 1.42857142725034663711e-01
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aT3 = reinterpret<f64>(0xBFBC71C6FE231671), // -1.11111104054623557880e-01,
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aT4 = reinterpret<f64>(0x3FB745CDC54C206E), // 9.09088713343650656196e-02
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aT5 = reinterpret<f64>(0xBFB3B0F2AF749A6D), // -7.69187620504482999495e-02
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aT6 = reinterpret<f64>(0x3FB10D66A0D03D51), // 6.66107313738753120669e-02
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aT7 = reinterpret<f64>(0xBFADDE2D52DEFD9A), // -5.83357013379057348645e-02
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aT8 = reinterpret<f64>(0x3FA97B4B24760DEB), // 4.97687799461593236017e-02
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aT9 = reinterpret<f64>(0xBFA2B4442C6A6C2F), // -3.65315727442169155270e-02
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aT10 = reinterpret<f64>(0x3F90AD3AE322DA11), // 1.62858201153657823623e-02
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Ox1p_120f = reinterpret<f32>(0x03800000);
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var ix = <u32>(reinterpret<u64>(x) >> 32);
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var sx = x;
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ix &= 0x7FFFFFFF;
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var z: f64;
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if (ix >= 0x44100000) {
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if (isNaN(x)) return x;
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z = atanhi3 + Ox1p_120f;
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return builtin_copysign<f64>(z, sx);
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}
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var id: i32;
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if (ix < 0x3FDC0000) {
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if (ix < 0x3E400000) return x;
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id = -1;
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} else {
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x = builtin_abs<f64>(x);
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if (ix < 0x3FF30000) {
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if (ix < 0x3FE60000) {
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id = 0;
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x = (2.0 * x - 1.0) / (2.0 + x);
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} else {
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id = 1;
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x = (x - 1.0) / (x + 1.0);
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}
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} else {
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if (ix < 0x40038000) {
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id = 2;
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x = (x - 1.5) / (1.0 + 1.5 * x);
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} else {
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id = 3;
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x = -1.0 / x;
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}
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}
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}
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z = x * x;
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var w = z * z;
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var s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
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var s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
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var s3 = x * (s1 + s2);
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if (id < 0) return x - s3;
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switch (id) {
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case 0: { z = atanhi0 - ((s3 - atanlo0) - x); break; }
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case 1: { z = atanhi1 - ((s3 - atanlo1) - x); break; }
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case 2: { z = atanhi2 - ((s3 - atanlo2) - x); break; }
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case 3: { z = atanhi3 - ((s3 - atanlo3) - x); break; }
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default: unreachable();
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}
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return builtin_copysign<f64>(z, sx);
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}
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export function atanh(x: f64): f64 { // see: musl/src/math/atanh.c
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var u = reinterpret<u64>(x);
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var e = u >> 52 & 0x7FF;
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var s = u >> 63;
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u &= 0x7FFFFFFFFFFFFFFF;
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var y = reinterpret<f64>(u);
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if (e < 0x3FF - 1) {
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if (e >= 0x3FF - 32) y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y));
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} else {
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y = 0.5 * log1p(2 * (y / (1 - y)));
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}
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return builtin_copysign<f64>(y, x);
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}
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export function atan2(y: f64, x: f64): f64 { // see: musl/src/math/atan2.c and SUN COPYRIGHT NOTICE above
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const pi_lo = reinterpret<f64>(0x3CA1A62633145C07); // 1.2246467991473531772E-16
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if (isNaN(x) || isNaN(y)) return x + y;
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var u = reinterpret<u64>(x);
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var ix = <u32>(u >> 32);
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var lx = <u32>u;
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u = reinterpret<u64>(y);
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var iy = <u32>(u >> 32);
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var ly = <u32>u;
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if ((ix - 0x3FF00000 | lx) == 0) return atan(y);
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var m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
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ix = ix & 0x7FFFFFFF;
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iy = iy & 0x7FFFFFFF;
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if ((iy | ly) == 0) {
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switch (m) {
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case 0:
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case 1: return y;
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case 2: return PI;
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case 3: return -PI;
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}
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}
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if ((ix | lx) == 0) return m & 1 ? -PI / 2 : PI / 2;
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if (ix == 0x7FF00000) {
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if (iy == 0x7FF00000) {
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switch (m) {
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case 0: return PI / 4;
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case 1: return -PI / 4;
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case 2: return 3 * PI / 4;
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case 3: return -3 * PI / 4;
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}
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} else {
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switch (m) {
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case 0: return 0.0;
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case 1: return -0.0;
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case 2: return PI;
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case 3: return -PI;
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}
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}
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}
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var z: f64;
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if (ix + (64 << 20) < iy || iy == 0x7FF00000) return m & 1 ? -PI / 2 : PI / 2;
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if ((m & 2) && iy + (64 << 20) < ix) z = 0;
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else z = atan(builtin_abs<f64>(y / x));
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switch (m) {
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case 0: return z;
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case 1: return -z;
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case 2: return PI - (z - pi_lo);
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case 3: return (z - pi_lo) - PI;
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}
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unreachable();
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return 0;
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}
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export function cbrt(x: f64): f64 { // see: musl/src/math/cbrt.c and SUN COPYRIGHT NOTICE above
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const
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B1 = <u32>715094163,
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B2 = <u32>696219795,
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P0 = reinterpret<f64>(0x3FFE03E60F61E692), // 1.87595182427177009643
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P1 = reinterpret<f64>(0xBFFE28E092F02420), // -1.88497979543377169875
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P2 = reinterpret<f64>(0x3FF9F1604A49D6C2), // 1.621429720105354466140
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P3 = reinterpret<f64>(0xBFE844CBBEE751D9), // -0.758397934778766047437
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P4 = reinterpret<f64>(0x3FC2B000D4E4EDD7), // 0.145996192886612446982
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Ox1p54 = reinterpret<f64>(0x4350000000000000);
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var u = reinterpret<u64>(x);
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var hx = <u32>(u >> 32) & 0x7FFFFFFF;
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if (hx >= 0x7FF00000) return x + x;
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if (hx < 0x00100000) {
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u = reinterpret<u64>(x * Ox1p54);
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hx = <u32>(u >> 32) & 0x7FFFFFFF;
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if (hx == 0) return x;
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hx = hx / 3 + B2;
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} else {
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hx = hx / 3 + B1;
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}
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u &= 1 << 63;
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u |= <u64>hx << 32;
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var t = reinterpret<f64>(u);
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var r = (t * t) * (t / x);
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t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
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t = reinterpret<f64>((reinterpret<u64>(t) + 0x80000000) & 0xFFFFFFFFC0000000);
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var s = t * t;
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r = x / s;
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r = (r - t) / (2 * t + r);
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t = t + t * r;
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return t;
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}
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@inline
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export function ceil(x: f64): f64 {
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return builtin_ceil<f64>(x);
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}
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export function clz32(x: f64): f64 {
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if (!isFinite(x)) return 32;
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/*
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* Wasm (MVP) and JS have different approaches for double->int conversions.
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*
|
|
* 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(
|
|
<i32><i64>(x - 4294967296 * builtin_floor(x * (1.0 / 4294967296)))
|
|
);
|
|
}
|
|
|
|
export function cos(x: f64): f64 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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
|
|
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);
|
|
var hx = <u32>(reinterpret<u64>(x) >> 32);
|
|
var 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;
|
|
}
|
|
var hi: f64, lo: f64 = 0;
|
|
var 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;
|
|
var xs = x * x;
|
|
// var c = x - xp2 * (P1 + xp2 * (P2 + xp2 * (P3 + xp2 * (P4 + xp2 * P5))));
|
|
var xq = xs * xs;
|
|
var c = x - (xs * P1 + xq * ((P2 + xs * P3) + xq * (P4 + xs * P5)));
|
|
var y = 1.0 + (x * c / (2 - c) - lo + hi);
|
|
if (k == 0) return y;
|
|
return scalbn(y, k);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
@inline
|
|
export function floor(x: f64): f64 {
|
|
return builtin_floor<f64>(x);
|
|
}
|
|
|
|
@inline
|
|
export function fround(x: f64): f32 {
|
|
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;
|
|
const inv32 = 1.0 / 4294967296;
|
|
return (
|
|
<i32><i64>(x - 4294967296 * builtin_floor(x * inv32)) *
|
|
<i32><i64>(y - 4294967296 * builtin_floor(y * inv32))
|
|
);
|
|
}
|
|
|
|
export function log(x: f64): f64 { // see: musl/src/math/log.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
|
|
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 dk = 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
|
|
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);
|
|
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 * ivln2hi;
|
|
var val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
|
|
var y = <f64>k;
|
|
w = y + val_hi;
|
|
val_lo += (y - w) + val_hi;
|
|
val_hi = w;
|
|
return val_lo + val_hi;
|
|
}
|
|
|
|
@inline
|
|
export function max(value1: f64, value2: f64): f64 {
|
|
return builtin_max<f64>(value1, value2);
|
|
}
|
|
|
|
@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
|
|
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
|
|
var u_ = reinterpret<u64>(x);
|
|
var hx = <i32>(u_ >> 32);
|
|
var lx = <u32>u_;
|
|
u_ = reinterpret<u64>(y);
|
|
var hy = <i32>(u_ >> 32);
|
|
var ly = <u32>u_;
|
|
var ix = hx & 0x7FFFFFFF;
|
|
var 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;
|
|
var yisint = 0, k: i32;
|
|
if (hx < 0) {
|
|
if (iy >= 0x43400000) yisint = 2;
|
|
else if (iy >= 0x3FF00000) {
|
|
k = (iy >> 20) - 0x3FF;
|
|
let kcond = k > 20;
|
|
let offset = select<i32>(52, 20, kcond) - k;
|
|
let Ly = select<i32>(ly, iy, kcond);
|
|
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);
|
|
}
|
|
}
|
|
var 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;
|
|
}
|
|
}
|
|
var s = 1.0;
|
|
if (hx < 0) {
|
|
if (yisint == 0) {
|
|
let d = x - x;
|
|
return d / d;
|
|
}
|
|
if (yisint == 1) s = -1.0;
|
|
}
|
|
var t1: f64, t2: f64, p_h: f64, p_l: f64, r: f64, t: f64, u: f64, v: f64, w: f64;
|
|
var j: i32, n: i32;
|
|
if (iy > 0x41E00000) {
|
|
if (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);
|
|
}
|
|
var 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);
|
|
var 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 {
|
|
assert(value);
|
|
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);
|
|
}
|
|
|
|
export function random(): f64 { // see: v8/src/base/random-number-generator.cc
|
|
if (!random_seeded) throw new Error("PRNG must be seeded.");
|
|
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 + s1) & 0x000FFFFFFFFFFFFF) | 0x3FF0000000000000;
|
|
return reinterpret<f64>(r) - 1;
|
|
}
|
|
|
|
@inline
|
|
export function round(x: f64): f64 {
|
|
return builtin_copysign<f64>(builtin_floor<f64>(x + 0.5), x);
|
|
}
|
|
|
|
@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;
|
|
}
|
|
}
|
|
|
|
@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) & (x == x));
|
|
}
|
|
|
|
export function sin(x: f64): f64 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
@inline
|
|
export function sqrt(x: f64): f64 {
|
|
return builtin_sqrt<f64>(x);
|
|
}
|
|
|
|
export function tan(x: f64): f64 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
@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;
|
|
}
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
@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;
|
|
}
|
|
|
|
export namespace NativeMathf {
|
|
|
|
@lazy export const E = <f32>NativeMath.E;
|
|
@lazy export const LN2 = <f32>NativeMath.LN2;
|
|
@lazy export const LN10 = <f32>NativeMath.LN10;
|
|
@lazy export const LOG2E = <f32>NativeMath.LOG2E;
|
|
@lazy export const LOG10E = <f32>NativeMath.LOG10E;
|
|
@lazy export const PI = <f32>NativeMath.PI;
|
|
@lazy export const SQRT1_2 = <f32>NativeMath.SQRT1_2;
|
|
@lazy export const SQRT2 = <f32>NativeMath.SQRT2;
|
|
|
|
@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);
|
|
u &= 0x7FFFFFFF;
|
|
var y = reinterpret<f32>(u);
|
|
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) {
|
|
switch (m) {
|
|
case 0: return pi / 4;
|
|
case 1: return -pi / 4;
|
|
case 2: return 3 * pi / 4;
|
|
case 3: return -3 * pi / 4;
|
|
}
|
|
} else {
|
|
switch (m) {
|
|
case 0: return 0;
|
|
case 1: return -0;
|
|
case 2: return pi;
|
|
case 3: return -pi;
|
|
}
|
|
}
|
|
}
|
|
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;
|
|
}
|
|
|
|
@inline
|
|
export function ceil(x: f32): f32 {
|
|
return builtin_ceil<f32>(x);
|
|
}
|
|
|
|
export function clz32(x: f32): f32 {
|
|
if (!isFinite(x)) return 32;
|
|
return builtin_clz(
|
|
<i32><i64>(x - 4294967296 * builtin_floor(x * (1.0 / 4294967296)))
|
|
);
|
|
}
|
|
|
|
export function cos(x: f32): f32 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
@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
|
|
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);
|
|
var hx = reinterpret<u32>(x);
|
|
var sign_ = <i32>(hx >> 31);
|
|
hx &= 0x7FFFFFFF;
|
|
if (hx >= 0x42AEAC50) {
|
|
if (hx >= 0x42B17218) {
|
|
if (!sign_) return x * Ox1p127f;
|
|
else if (hx >= 0x42CFF1B5) return 0;
|
|
}
|
|
}
|
|
var hi: f32, lo: f32;
|
|
var 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;
|
|
}
|
|
var xx = x * x;
|
|
var c = x - xx * (P1 + xx * P2);
|
|
var y: f32 = 1 + (x * c / (2 - c) - lo + hi);
|
|
if (k == 0) return y;
|
|
return scalbn(y, k);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
@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));
|
|
}
|
|
|
|
@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;
|
|
const inv32 = 1.0 / 4294967296;
|
|
return (
|
|
<i32><i64>(x - 4294967296 * builtin_floor(x * inv32)) *
|
|
<i32><i64>(y - 4294967296 * builtin_floor(y * inv32))
|
|
);
|
|
}
|
|
|
|
export function log(x: f32): f32 { // see: musl/src/math/logf.c and SUN COPYRIGHT NOTICE above
|
|
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);
|
|
var u = reinterpret<u32>(x);
|
|
var 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);
|
|
var f = x - 1.0;
|
|
var s = f / (2.0 + f);
|
|
var z = s * s;
|
|
var w = z * z;
|
|
var t1 = w * (Lg2 + w * Lg4);
|
|
var t2 = z * (Lg1 + w * Lg3);
|
|
var r = t2 + t1;
|
|
var hfsq = <f32>0.5 * f * f;
|
|
var dk = <f32>k;
|
|
return s * (hfsq + r) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
|
|
}
|
|
|
|
export function 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
|
|
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);
|
|
var ix = reinterpret<u32>(x);
|
|
var 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);
|
|
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;
|
|
var u = reinterpret<u32>(hi);
|
|
u &= 0xFFFFF000;
|
|
hi = reinterpret<f32>(u);
|
|
var lo: f32 = f - hi - hfsq + s * (hfsq + r);
|
|
var dk = <f32>k;
|
|
return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + dk;
|
|
}
|
|
|
|
@inline
|
|
export function max(value1: f32, value2: f32): f32 {
|
|
return builtin_max<f32>(value1, value2);
|
|
}
|
|
|
|
@inline
|
|
export function min(value1: f32, value2: f32): f32 {
|
|
return builtin_min<f32>(value1, value2);
|
|
}
|
|
|
|
export function pow(x: f32, y: f32): f32 { // see: musl/src/math/powf.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
dp_h1 = reinterpret<f32>(0x3F15C000), // 5.84960938e-01f
|
|
dp_l1 = reinterpret<f32>(0x35D1CFDC), // 1.56322085e-06f
|
|
two24 = reinterpret<f32>(0x4B800000), // 16777216f
|
|
huge = reinterpret<f32>(0x7149F2CA), // 1.0e+30f
|
|
tiny = reinterpret<f32>(0x0DA24260), // 1.0e-30f
|
|
L1 = reinterpret<f32>(0x3F19999A), // 6.0000002384e-01f
|
|
L2 = reinterpret<f32>(0x3EDB6DB7), // 4.2857143283e-01f
|
|
L3 = reinterpret<f32>(0x3EAAAAAB), // 3.3333334327e-01f
|
|
L4 = reinterpret<f32>(0x3E8BA305), // 2.7272811532e-01f
|
|
L5 = reinterpret<f32>(0x3E6C3255), // 2.3066075146e-01f
|
|
L6 = reinterpret<f32>(0x3E53F142), // 2.0697501302e-01f
|
|
P1 = reinterpret<f32>(0x3E2AAAAB), // 1.6666667163e-01f
|
|
P2 = reinterpret<f32>(0xBB360B61), // -2.7777778450e-03f
|
|
P3 = reinterpret<f32>(0x388AB355), // 6.6137559770e-05f
|
|
P4 = reinterpret<f32>(0xB5DDEA0E), // -1.6533901999e-06f
|
|
P5 = reinterpret<f32>(0x3331BB4C), // 4.1381369442e-08f
|
|
lg2 = reinterpret<f32>(0x3F317218), // 6.9314718246e-01f
|
|
lg2_h = reinterpret<f32>(0x3F317200), // 6.93145752e-01f
|
|
lg2_l = reinterpret<f32>(0x35BFBE8C), // 1.42860654e-06f
|
|
ovt = reinterpret<f32>(0x3338AA3C), // 4.2995665694e-08f
|
|
cp = reinterpret<f32>(0x3F76384F), // 9.6179670095e-01
|
|
cp_h = reinterpret<f32>(0x3F764000), // 9.6191406250e-01
|
|
cp_l = reinterpret<f32>(0xB8F623C6), // -1.1736857402e-04
|
|
ivln2 = reinterpret<f32>(0x3FB8AA3B), // 1.4426950216e+00
|
|
ivln2_h = reinterpret<f32>(0x3FB8AA00), // 1.4426879883e+00
|
|
ivln2_l = reinterpret<f32>(0x36ECA570), // 7.0526075433e-06
|
|
inv3 = reinterpret<f32>(0x3EAAAAAB); // 0.333333333333
|
|
var hx = reinterpret<i32>(x);
|
|
var hy = reinterpret<i32>(y);
|
|
var ix = hx & 0x7FFFFFFF;
|
|
var iy = hy & 0x7FFFFFFF;
|
|
if (iy == 0) return 1.0; // x**0 = 1, even if x is NaN
|
|
// if (hx == 0x3F800000) return 1.0; // C: 1**y = 1, even if y is NaN, JS: NaN
|
|
if (ix > 0x7F800000 || iy > 0x7F800000) return x + y; // NaN if either arg is NaN
|
|
var yisint = 0, j: i32, k: i32;
|
|
if (hx < 0) {
|
|
if (iy >= 0x4B800000) yisint = 2;
|
|
else if (iy >= 0x3F800000) {
|
|
k = (iy >> 23) - 0x7F;
|
|
let ki = 23 - k;
|
|
j = iy >> ki;
|
|
if ((j << ki) == iy) yisint = 2 - (j & 1);
|
|
}
|
|
}
|
|
if (iy == 0x7F800000) { // y is +-inf
|
|
if (ix == 0x3F800000) return NaN; // C: (-1)**+-inf is 1, JS: NaN
|
|
else if (ix > 0x3F800000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
|
|
else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
|
|
}
|
|
if (iy == 0x3F800000) return hy >= 0 ? x : 1.0 / x;
|
|
if (hy == 0x40000000) return x * x;
|
|
if (hy == 0x3F000000) {
|
|
if (hx >= 0) return builtin_sqrt<f32>(x);
|
|
}
|
|
var ax = builtin_abs<f32>(x);
|
|
var z: f32;
|
|
if (ix == 0x7F800000 || ix == 0 || ix == 0x3F800000) {
|
|
z = ax;
|
|
if (hy < 0) z = 1.0 / z;
|
|
if (hx < 0) {
|
|
if (((ix - 0x3F800000) | yisint) == 0) {
|
|
let d = z - z;
|
|
z = d / d;
|
|
}
|
|
else if (yisint == 1) z = -z;
|
|
}
|
|
return z;
|
|
}
|
|
var sn = <f32>1.0;
|
|
if (hx < 0) {
|
|
if (yisint == 0) {
|
|
let d = x - x;
|
|
return d / d;
|
|
}
|
|
if (yisint == 1) sn = -1.0;
|
|
}
|
|
var t1: f32, t2: f32, r: f32, s: f32, t: f32, u: f32, v: f32, w: f32, p_h: f32, p_l: f32;
|
|
var n: i32, is: i32;
|
|
if (iy > 0x4D000000) {
|
|
if (ix < 0x3F7FFFF8) return hy < 0 ? sn * huge * huge : sn * tiny * tiny;
|
|
if (ix > 0x3F800007) return hy > 0 ? sn * huge * huge : sn * tiny * tiny;
|
|
t = ax - 1;
|
|
w = (t * t) * (0.5 - t * (inv3 - t * 0.25));
|
|
u = ivln2_h * t;
|
|
v = t * ivln2_l - w * ivln2;
|
|
t1 = u + v;
|
|
is = reinterpret<i32>(t1);
|
|
t1 = reinterpret<f32>(is & 0xFFFFF000);
|
|
t2 = v - (t1 - u);
|
|
} else {
|
|
let s2: f32, s_h: f32, s_l: f32, t_h: f32, t_l: f32;
|
|
n = 0;
|
|
if (ix < 0x00800000) {
|
|
ax *= two24;
|
|
n -= 24;
|
|
ix = reinterpret<i32>(ax);
|
|
}
|
|
n += (ix >> 23) - 0x7F;
|
|
j = ix & 0x007FFFFF;
|
|
ix = j | 0x3F800000;
|
|
if (j <= 0x1CC471) k = 0;
|
|
else if (j < 0x5DB3D7) k = 1;
|
|
else {
|
|
k = 0;
|
|
n += 1;
|
|
ix -= 0x00800000;
|
|
}
|
|
ax = reinterpret<f32>(ix);
|
|
let bp = select<f32>(1.5, 1.0, k); // k ? 1.5 : 1.0
|
|
u = ax - bp;
|
|
v = 1.0 / (ax + bp);
|
|
s = u * v;
|
|
s_h = s;
|
|
is = reinterpret<u32>(s_h);
|
|
s_h = reinterpret<f32>(is & 0xFFFFF000);
|
|
is = ((ix >> 1) & 0xFFFFF000) | 0x20000000;
|
|
t_h = reinterpret<f32>(is + 0x00400000 + (k << 21));
|
|
t_l = ax - (t_h - bp);
|
|
s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
|
s2 = s * s;
|
|
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
|
r += s_l * (s_h + s);
|
|
s2 = s_h * s_h;
|
|
t_h = 3.0 + s2 + r;
|
|
is = reinterpret<u32>(t_h);
|
|
t_h = reinterpret<f32>(is & 0xFFFFF000);
|
|
t_l = r - ((t_h - 3.0) - s2);
|
|
u = s_h * t_h;
|
|
v = s_l * t_h + t_l * s;
|
|
p_h = u + v;
|
|
is = reinterpret<u32>(p_h);
|
|
p_h = reinterpret<f32>(is & 0xFFFFF000);
|
|
p_l = v - (p_h - u);
|
|
let z_h = cp_h * p_h;
|
|
let dp_l = select<f32>(dp_l1, 0.0, k);
|
|
let z_l = cp_l * p_h + p_l * cp + dp_l;
|
|
t = <f32>n;
|
|
let dp_h = select<f32>(dp_h1, 0.0, k);
|
|
t1 = (((z_h + z_l) + dp_h) + t);
|
|
is = reinterpret<u32>(t1);
|
|
t1 = reinterpret<f32>(is & 0xFFFFF000);
|
|
t2 = z_l - (((t1 - t) - dp_h) - z_h);
|
|
}
|
|
is = reinterpret<u32>(y);
|
|
var y1 = reinterpret<f32>(is & 0xFFFFF000);
|
|
p_l = (y - y1) * t1 + y * t2;
|
|
p_h = y1 * t1;
|
|
z = p_l + p_h;
|
|
j = reinterpret<u32>(z);
|
|
if (j > 0x43000000) {
|
|
return sn * huge * huge;
|
|
} else if (j == 0x43000000) {
|
|
if (p_l + ovt > z - p_h) return sn * huge * huge;
|
|
} else if ((j & 0x7FFFFFFF) > 0x43160000) {
|
|
return sn * tiny * tiny;
|
|
} else if (j == 0xC3160000) {
|
|
if (p_l <= z - p_h) return sn * tiny * tiny;
|
|
}
|
|
var i = j & 0x7FFFFFFF;
|
|
k = (i >> 23) - 0x7F;
|
|
n = 0;
|
|
if (i > 0x3F000000) {
|
|
n = j + (0x00800000 >> (k + 1));
|
|
k = ((n & 0x7FFFFFFF) >> 23) - 0x7F;
|
|
t = reinterpret<f32>(n & ~(0x007FFFFF >> k));
|
|
n = ((n & 0x007FFFFF) | 0x00800000) >> (23 - k);
|
|
if (j < 0) n = -n;
|
|
p_h -= t;
|
|
}
|
|
t = p_l + p_h;
|
|
is = reinterpret<u32>(t);
|
|
t = reinterpret<f32>(is & 0xFFFF8000);
|
|
u = t * lg2_h;
|
|
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
|
z = u + v;
|
|
w = v - (z - u);
|
|
t = z * z;
|
|
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
|
r = (z * t1) / (t1 - 2.0) - (w + z * w);
|
|
z = 1.0 - (r - z);
|
|
j = reinterpret<u32>(z);
|
|
j += n << 23;
|
|
if ((j >> 23) <= 0) z = scalbn(z, n);
|
|
else z = reinterpret<f32>(j);
|
|
return sn * z;
|
|
}
|
|
|
|
@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) throw new Error("PRNG must be seeded.");
|
|
|
|
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;
|
|
}
|
|
|
|
@inline
|
|
export function round(x: f32): f32 {
|
|
return builtin_copysign<f32>(builtin_floor<f32>(x + 0.5), x);
|
|
}
|
|
|
|
@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;
|
|
}
|
|
}
|
|
|
|
@inline
|
|
export function signbit(x: f32): bool {
|
|
return <bool>((reinterpret<u32>(x) >>> 31) & (x == x));
|
|
}
|
|
|
|
export function sin(x: f32): f32 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
@inline
|
|
export function sqrt(x: f32): f32 {
|
|
return builtin_sqrt<f32>(x);
|
|
}
|
|
|
|
export function tan(x: f32): f32 { // TODO
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
@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 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;
|
|
}
|