mirror of
https://github.com/Instadapp/Swap-Aggregator-Subgraph.git
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3286 lines
103 KiB
TypeScript
3286 lines
103 KiB
TypeScript
import * as JSMath from "./bindings/Math";
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export { JSMath };
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import {
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pow_lut, exp_lut, exp2_lut, log_lut, log2_lut,
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powf_lut, expf_lut, exp2f_lut, logf_lut, log2f_lut
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} from "./util/math";
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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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/** @internal */
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// @ts-ignore: decorator
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@lazy var rempio2_y0: f64, rempio2_y1: f64, res128_hi: u64;
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/** @internal */
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// @ts-ignore: decorator
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@lazy @inline const PIO2_TABLE = memory.data<u64>([
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0x00000000A2F9836E, 0x4E441529FC2757D1, 0xF534DDC0DB629599, 0x3C439041FE5163AB,
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0xDEBBC561B7246E3A, 0x424DD2E006492EEA, 0x09D1921CFE1DEB1C, 0xB129A73EE88235F5,
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0x2EBB4484E99C7026, 0xB45F7E413991D639, 0x835339F49C845F8B, 0xBDF9283B1FF897FF,
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0xDE05980FEF2F118B, 0x5A0A6D1F6D367ECF, 0x27CB09B74F463F66, 0x9E5FEA2D7527BAC7,
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0xEBE5F17B3D0739F7, 0x8A5292EA6BFB5FB1, 0x1F8D5D0856033046, 0xFC7B6BABF0CFBC20,
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0x9AF4361DA9E39161, 0x5EE61B086599855F, 0x14A068408DFFD880, 0x4D73273106061557
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]);
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/** @internal */
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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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/** @internal */
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// @ts-ignore: decorator
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@inline
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function expo2(x: f64, sign: 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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// in directed rounding correct sign before rounding or overflow is important
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return NativeMath.exp(x - kln2) * (sign * scale) * scale;
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}
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/** @internal */
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/* Helper function to eventually get bits of π/2 * |x|
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*
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* y = π/4 * (frac << clz(frac) >> 11)
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* return clz(frac)
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*
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* Right shift 11 bits to make upper half fit in `double`
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*/
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// @ts-ignore: decorator
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@inline
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function pio2_right(q0: u64, q1: u64): u64 { // see: jdh8/metallic/blob/master/src/math/double/rem_pio2.c
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// Bits of π/4
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const p0: u64 = 0xC4C6628B80DC1CD1;
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const p1: u64 = 0xC90FDAA22168C234;
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const Ox1p_64 = reinterpret<f64>(0x3BF0000000000000); // 0x1p-64
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const Ox1p_75 = reinterpret<f64>(0x3B40000000000000); // 0x1p-75
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var shift = clz(q1);
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q1 = q1 << shift | q0 >> (64 - shift);
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q0 <<= shift;
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var lo = umuldi(p1, q1);
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var hi = res128_hi;
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var ahi = hi >> 11;
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var alo = lo >> 11 | hi << 53;
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var blo = <u64>(Ox1p_75 * <f64>p0 * <f64>q1 + Ox1p_75 * <f64>p1 * <f64>q0);
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rempio2_y0 = <f64>(ahi + u64(lo < blo));
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rempio2_y1 = Ox1p_64 * <f64>(alo + blo);
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return shift;
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}
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/** @internal */
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// @ts-ignore: decorator
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@inline
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function umuldi(u: u64, v: u64): u64 {
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var u1: u64 , v1: u64, w0: u64, w1: u64, t: u64;
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u1 = u & 0xFFFFFFFF;
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v1 = v & 0xFFFFFFFF;
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u >>= 32;
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v >>= 32;
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t = u1 * v1;
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w0 = t & 0xFFFFFFFF;
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t = u * v1 + (t >> 32);
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w1 = t >> 32;
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t = u1 * v + (t & 0xFFFFFFFF);
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res128_hi = u * v + w1 + (t >> 32);
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return (t << 32) + w0;
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}
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/** @internal */
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function pio2_large_quot(x: f64, u: i64): i32 { // see: jdh8/metallic/blob/master/src/math/double/rem_pio2.c
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var magnitude = u & 0x7FFFFFFFFFFFFFFF;
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var offset = (magnitude >> 52) - 1045;
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var shift = offset & 63;
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var tblPtr = PIO2_TABLE + (<i32>(offset >> 6) << 3);
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var s0: u64, s1: u64, s2: u64;
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var b0 = load<u64>(tblPtr, 0 << 3);
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var b1 = load<u64>(tblPtr, 1 << 3);
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var b2 = load<u64>(tblPtr, 2 << 3);
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// Get 192 bits of 0x1p-31 / π with `offset` bits skipped
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if (shift) {
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let rshift = 64 - shift;
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let b3 = load<u64>(tblPtr, 3 << 3);
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s0 = b1 >> rshift | b0 << shift;
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s1 = b2 >> rshift | b1 << shift;
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s2 = b3 >> rshift | b2 << shift;
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} else {
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s0 = b0;
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s1 = b1;
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s2 = b2;
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}
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var significand = (u & 0x000FFFFFFFFFFFFF) | 0x0010000000000000;
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// First 128 bits of fractional part of x/(2π)
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var blo = umuldi(s1, significand);
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var bhi = res128_hi;
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var ahi = s0 * significand;
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var clo = (s2 >> 32) * (significand >> 32);
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var plo = blo + clo;
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var phi = ahi + bhi + u64(plo < clo);
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// r: u128 = p << 2
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var rlo = plo << 2;
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var rhi = phi << 2 | plo >> 62;
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// s: i128 = r >> 127
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var slo = <i64>rhi >> 63;
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var shi = slo >> 1;
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var q = (<i64>phi >> 62) - slo;
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var shifter = 0x3CB0000000000000 - (pio2_right(rlo ^ slo, rhi ^ shi) << 52);
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var signbit = (u ^ rhi) & 0x8000000000000000;
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var coeff = reinterpret<f64>(shifter | signbit);
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rempio2_y0 *= coeff;
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rempio2_y1 *= coeff;
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return <i32>q;
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}
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/** @internal */
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// @ts-ignore: decorator
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@inline
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function rempio2(x: f64, u: u64, sign: i32): i32 {
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const
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pio2_1 = reinterpret<f64>(0x3FF921FB54400000), // 1.57079632673412561417e+00
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pio2_1t = reinterpret<f64>(0x3DD0B4611A626331), // 6.07710050650619224932e-11
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pio2_2 = reinterpret<f64>(0x3DD0B4611A600000), // 6.07710050630396597660e-11
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pio2_2t = reinterpret<f64>(0x3BA3198A2E037073), // 2.02226624879595063154e-21
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pio2_3 = reinterpret<f64>(0x3BA3198A2E000000), // 2.02226624871116645580e-21
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pio2_3t = reinterpret<f64>(0x397B839A252049C1), // 8.47842766036889956997e-32
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invpio2 = reinterpret<f64>(0x3FE45F306DC9C883); // 0.63661977236758134308
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var ix = <u32>(u >> 32) & 0x7FFFFFFF;
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if (ASC_SHRINK_LEVEL < 1) {
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if (ix < 0x4002D97C) { // |x| < 3pi/4, special case with n=+-1
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let q = 1, z: f64, y0: f64, y1: f64;
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if (!sign) {
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z = x - pio2_1;
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if (ix != 0x3FF921FB) { // 33+53 bit pi is good enough
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y0 = z - pio2_1t;
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y1 = (z - y0) - pio2_1t;
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} else { // near pi/2, use 33+33+53 bit pi
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z -= pio2_2;
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y0 = z - pio2_2t;
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y1 = (z - y0) - pio2_2t;
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}
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} else { // negative x
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z = x + pio2_1;
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if (ix != 0x3FF921FB) { // 33+53 bit pi is good enough
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y0 = z + pio2_1t;
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y1 = (z - y0) + pio2_1t;
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} else { // near pi/2, use 33+33+53 bit pi
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z += pio2_2;
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y0 = z + pio2_2t;
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y1 = (z - y0) + pio2_2t;
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}
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q = -1;
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}
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rempio2_y0 = y0;
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rempio2_y1 = y1;
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return q;
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}
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}
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if (ix < 0x413921FB) { // |x| ~< 2^20*pi/2 (1647099)
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// Use precise Cody Waite scheme
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let q = nearest(x * invpio2);
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let r = x - q * pio2_1;
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let w = q * pio2_1t; // 1st round good to 85 bit
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let j = ix >> 20;
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let y0 = r - w;
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let hi = <u32>(reinterpret<u64>(y0) >> 32);
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let i = j - ((hi >> 20) & 0x7FF);
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if (i > 16) { // 2nd iteration needed, good to 118
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let t = r;
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w = q * pio2_2;
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r = t - w;
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w = q * pio2_2t - ((t - r) - w);
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y0 = r - w;
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hi = <u32>(reinterpret<u64>(y0) >> 32);
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i = j - ((hi >> 20) & 0x7FF);
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if (i > 49) { // 3rd iteration need, 151 bits acc
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let t = r;
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w = q * pio2_3;
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r = t - w;
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w = q * pio2_3t - ((t - r) - w);
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y0 = r - w;
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}
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}
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let y1 = (r - y0) - w;
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rempio2_y0 = y0;
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rempio2_y1 = y1;
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return <i32>q;
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}
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var q = pio2_large_quot(x, u);
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return select(-q, q, sign);
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}
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/** @internal */
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// @ts-ignore: decorator
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@inline
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function sin_kern(x: f64, y: f64, iy: i32): f64 { // see: musl/tree/src/math/__sin.c
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const
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S1 = reinterpret<f64>(0xBFC5555555555549), // -1.66666666666666324348e-01
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S2 = reinterpret<f64>(0x3F8111111110F8A6), // 8.33333333332248946124e-03
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S3 = reinterpret<f64>(0xBF2A01A019C161D5), // -1.98412698298579493134e-04
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S4 = reinterpret<f64>(0x3EC71DE357B1FE7D), // 2.75573137070700676789e-06
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S5 = reinterpret<f64>(0xBE5AE5E68A2B9CEB), // -2.50507602534068634195e-08
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S6 = reinterpret<f64>(0x3DE5D93A5ACFD57C); // 1.58969099521155010221e-10
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var z = x * x;
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var w = z * z;
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var r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
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var v = z * x;
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if (!iy) {
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return x + v * (S1 + z * r);
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} else {
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return x - ((z * (0.5 * y - v * r) - y) - v * S1);
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}
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}
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/** @internal */
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// @ts-ignore: decorator
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@inline
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function cos_kern(x: f64, y: f64): f64 { // see: musl/tree/src/math/__cos.c
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const
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C1 = reinterpret<f64>(0x3FA555555555554C), // 4.16666666666666019037e-02
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C2 = reinterpret<f64>(0xBF56C16C16C15177), // -1.38888888888741095749e-03
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C3 = reinterpret<f64>(0x3EFA01A019CB1590), // 2.48015872894767294178e-05
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C4 = reinterpret<f64>(0xBE927E4F809C52AD), // -2.75573143513906633035e-07
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C5 = reinterpret<f64>(0x3E21EE9EBDB4B1C4), // 2.08757232129817482790e-09
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C6 = reinterpret<f64>(0xBDA8FAE9BE8838D4); // -1.13596475577881948265e-11
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var z = x * x;
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var w = z * z;
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var r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6));
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var hz = 0.5 * z;
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w = 1.0 - hz;
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return w + (((1.0 - w) - hz) + (z * r - x * y));
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}
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/** @internal */
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function tan_kern(x: f64, y: f64, iy: i32): f64 { // see: src/lib/msun/src/k_tan.c
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const
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T0 = reinterpret<f64>(0x3FD5555555555563), // 3.33333333333334091986e-01
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T1 = reinterpret<f64>(0x3FC111111110FE7A), // 1.33333333333201242699e-01
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T2 = reinterpret<f64>(0x3FABA1BA1BB341FE), // 5.39682539762260521377e-02
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T3 = reinterpret<f64>(0x3F9664F48406D637), // 2.18694882948595424599e-02
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T4 = reinterpret<f64>(0x3F8226E3E96E8493), // 8.86323982359930005737e-03
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T5 = reinterpret<f64>(0x3F6D6D22C9560328), // 3.59207910759131235356e-03
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T6 = reinterpret<f64>(0x3F57DBC8FEE08315), // 1.45620945432529025516e-03
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T7 = reinterpret<f64>(0x3F4344D8F2F26501), // 5.88041240820264096874e-04
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T8 = reinterpret<f64>(0x3F3026F71A8D1068), // 2.46463134818469906812e-04
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T9 = reinterpret<f64>(0x3F147E88A03792A6), // 7.81794442939557092300e-05
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T10 = reinterpret<f64>(0x3F12B80F32F0A7E9), // 7.14072491382608190305e-05
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T11 = reinterpret<f64>(0xBEF375CBDB605373), // -1.85586374855275456654e-05
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T12 = reinterpret<f64>(0x3EFB2A7074BF7AD4); // 2.59073051863633712884e-05
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const
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one = reinterpret<f64>(0x3FF0000000000000), // 1.00000000000000000000e+00
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pio4 = reinterpret<f64>(0x3FE921FB54442D18), // 7.85398163397448278999e-01
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pio4lo = reinterpret<f64>(0x3C81A62633145C07); // 3.06161699786838301793e-17
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var z: f64, r: f64, v: f64, w: f64, s: f64;
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var hx = <i32>(reinterpret<u64>(x) >> 32); // high word of x
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var ix = hx & 0x7FFFFFFF; // high word of |x|
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var big = ix >= 0x3FE59428;
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if (big) { // |x| >= 0.6744
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if (hx < 0) { x = -x, y = -y; }
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z = pio4 - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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}
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z = x * x;
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w = z * z;
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r = T1 + w * (T3 + w * (T5 + w * (T7 + w * (T9 + w * T11))));
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v = z * (T2 + w * (T4 + w * (T6 + w * (T8 + w * (T10 + w * T12)))));
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s = z * x;
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r = y + z * (s * (r + v) + y);
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r += T0 * s;
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w = x + r;
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if (big) {
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v = iy;
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return (1 - ((hx >> 30) & 2)) * (v - 2.0 * (x - (w * w / (w + v) - r)));
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}
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if (iy == 1) return w;
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var a: f64, t: f64;
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z = w;
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z = reinterpret<f64>(reinterpret<u64>(z) & 0xFFFFFFFF00000000);
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v = r - (z - x); // z + v = r + x
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t = a = -one / w; // a = -1.0 / w
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t = reinterpret<f64>(reinterpret<u64>(t) & 0xFFFFFFFF00000000);
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s = one + t * z;
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return t + a * (s + t * v);
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}
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/** @internal */
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function dtoi32(x: f64): i32 {
|
|
if (ASC_SHRINK_LEVEL > 0) {
|
|
const inv32 = 1.0 / 4294967296;
|
|
return <i32><i64>(x - 4294967296 * floor(x * inv32));
|
|
} else {
|
|
let result = 0;
|
|
let u = reinterpret<u64>(x);
|
|
let e = (u >> 52) & 0x7FF;
|
|
if (e <= 1023 + 30) {
|
|
result = <i32>x;
|
|
} else if (e <= 1023 + 30 + 53) {
|
|
let v = (u & ((<u64>1 << 52) - 1)) | (<u64>1 << 52);
|
|
v = v << e - 1023 - 52 + 32;
|
|
result = <i32>(v >> 32);
|
|
result = select<i32>(-result, result, u >> 63);
|
|
}
|
|
return result;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy var random_seeded = false;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy var random_state0_64: u64, random_state1_64: u64;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy var random_state0_32: u32, random_state1_32: u32;
|
|
|
|
function murmurHash3(h: u64): u64 { // Force all bits of a hash block to avalanche
|
|
h ^= h >> 33; // see: https://github.com/aappleby/smhasher
|
|
h *= 0xFF51AFD7ED558CCD;
|
|
h ^= h >> 33;
|
|
h *= 0xC4CEB9FE1A85EC53;
|
|
h ^= h >> 33;
|
|
return h;
|
|
}
|
|
|
|
function splitMix32(h: u32): u32 {
|
|
h += 0x6D2B79F5;
|
|
h = (h ^ (h >> 15)) * (h | 1);
|
|
h ^= h + (h ^ (h >> 7)) * (h | 61);
|
|
return h ^ (h >> 14);
|
|
}
|
|
|
|
export namespace NativeMath {
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const E = reinterpret<f64>(0x4005BF0A8B145769); // 2.7182818284590452354
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LN2 = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.69314718055994530942
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LN10 = reinterpret<f64>(0x40026BB1BBB55516); // 2.30258509299404568402
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LOG2E = reinterpret<f64>(0x3FF71547652B82FE); // 1.4426950408889634074
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LOG10E = reinterpret<f64>(0x3FDBCB7B1526E50E); // 0.43429448190325182765
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const PI = reinterpret<f64>(0x400921FB54442D18); // 3.14159265358979323846
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const SQRT1_2 = reinterpret<f64>(0x3FE6A09E667F3BCD); // 0.70710678118654752440
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const SQRT2 = reinterpret<f64>(0x3FF6A09E667F3BCD); // 1.41421356237309504880
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export var sincos_sin: f64 = 0;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export var sincos_cos: f64 = 0;
|
|
|
|
// @ts-ignore: decorator
|
|
@inline export function abs(x: f64): f64 {
|
|
return builtin_abs<f64>(x);
|
|
}
|
|
|
|
export function acos(x: f64): f64 { // see: musl/src/math/acos.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
pio2_hi = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
|
|
pio2_lo = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
|
|
Ox1p_120f = reinterpret<f32>(0x03800000);
|
|
|
|
var hx = <u32>(reinterpret<u64>(x) >> 32);
|
|
var ix = hx & 0x7FFFFFFF;
|
|
if (ix >= 0x3FF00000) {
|
|
let lx = <u32>reinterpret<u64>(x);
|
|
if ((ix - 0x3FF00000 | lx) == 0) {
|
|
if (hx >> 31) return 2 * pio2_hi + Ox1p_120f;
|
|
return 0;
|
|
}
|
|
return 0 / (x - x);
|
|
}
|
|
if (ix < 0x3FE00000) {
|
|
if (ix <= 0x3C600000) return pio2_hi + Ox1p_120f;
|
|
return pio2_hi - (x - (pio2_lo - x * R(x * x)));
|
|
}
|
|
var s: f64, w: f64, z: f64;
|
|
if (hx >> 31) {
|
|
// z = (1.0 + x) * 0.5;
|
|
z = 0.5 + x * 0.5;
|
|
s = builtin_sqrt<f64>(z);
|
|
w = R(z) * s - pio2_lo;
|
|
return 2 * (pio2_hi - (s + w));
|
|
}
|
|
// z = (1.0 - x) * 0.5;
|
|
z = 0.5 - x * 0.5;
|
|
s = builtin_sqrt<f64>(z);
|
|
var df = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
|
|
var c = (z - df * df) / (s + df);
|
|
w = R(z) * s + c;
|
|
return 2 * (df + w);
|
|
}
|
|
|
|
export function acosh(x: f64): f64 { // see: musl/src/math/acosh.c
|
|
const s = reinterpret<f64>(0x3FE62E42FEFA39EF);
|
|
var u = reinterpret<u64>(x);
|
|
// Prevent propagation for all input values less than 1.0.
|
|
// Note musl lib didn't fix this yet.
|
|
if (<i64>u < 0x3FF0000000000000) return (x - x) / 0.0;
|
|
var e = u >> 52 & 0x7FF;
|
|
if (e < 0x3FF + 1) return log1p(x - 1 + builtin_sqrt<f64>((x - 1) * (x - 1) + 2 * (x - 1)));
|
|
if (e < 0x3FF + 26) return log(2 * x - 1 / (x + builtin_sqrt<f64>(x * x - 1)));
|
|
return log(x) + s;
|
|
}
|
|
|
|
export function asin(x: f64): f64 { // see: musl/src/math/asin.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
pio2_hi = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
|
|
pio2_lo = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
|
|
Ox1p_120f = reinterpret<f32>(0x03800000);
|
|
|
|
var hx = <u32>(reinterpret<u64>(x) >> 32);
|
|
var ix = hx & 0x7FFFFFFF;
|
|
if (ix >= 0x3FF00000) {
|
|
let lx = <u32>reinterpret<u64>(x);
|
|
if ((ix - 0x3FF00000 | lx) == 0) return x * pio2_hi + Ox1p_120f;
|
|
return 0 / (x - x);
|
|
}
|
|
if (ix < 0x3FE00000) {
|
|
if (ix < 0x3E500000 && ix >= 0x00100000) return x;
|
|
return x + x * R(x * x);
|
|
}
|
|
// var z = (1.0 - builtin_abs<f64>(x)) * 0.5;
|
|
var z = 0.5 - builtin_abs<f64>(x) * 0.5;
|
|
var s = builtin_sqrt<f64>(z);
|
|
var r = R(z);
|
|
if (ix >= 0x3FEF3333) x = pio2_hi - (2 * (s + s * r) - pio2_lo);
|
|
else {
|
|
let f = reinterpret<f64>(reinterpret<u64>(s) & 0xFFFFFFFF00000000);
|
|
let c = (z - f * f) / (s + f);
|
|
x = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f));
|
|
}
|
|
if (hx >> 31) return -x;
|
|
return x;
|
|
}
|
|
|
|
export function asinh(x: f64): f64 { // see: musl/src/math/asinh.c
|
|
const c = reinterpret<f64>(0x3FE62E42FEFA39EF); // 0.693147180559945309417232121458176568
|
|
var u = reinterpret<u64>(x);
|
|
var e = u >> 52 & 0x7FF;
|
|
var y = reinterpret<f64>(u & 0x7FFFFFFFFFFFFFFF);
|
|
if (e >= 0x3FF + 26) y = log(y) + c;
|
|
else if (e >= 0x3FF + 1) y = log(2 * y + 1 / (builtin_sqrt<f64>(y * y + 1) + y));
|
|
else if (e >= 0x3FF - 26) y = log1p(y + y * y / (builtin_sqrt<f64>(y * y + 1) + 1));
|
|
return builtin_copysign(y, x);
|
|
}
|
|
|
|
export function atan(x: f64): f64 { // see musl/src/math/atan.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
atanhi0 = reinterpret<f64>(0x3FDDAC670561BB4F), // 4.63647609000806093515e-01
|
|
atanhi1 = reinterpret<f64>(0x3FE921FB54442D18), // 7.85398163397448278999e-01
|
|
atanhi2 = reinterpret<f64>(0x3FEF730BD281F69B), // 9.82793723247329054082e-01
|
|
atanhi3 = reinterpret<f64>(0x3FF921FB54442D18), // 1.57079632679489655800e+00
|
|
atanlo0 = reinterpret<f64>(0x3C7A2B7F222F65E2), // 2.26987774529616870924e-17
|
|
atanlo1 = reinterpret<f64>(0x3C81A62633145C07), // 3.06161699786838301793e-17
|
|
atanlo2 = reinterpret<f64>(0x3C7007887AF0CBBD), // 1.39033110312309984516e-17
|
|
atanlo3 = reinterpret<f64>(0x3C91A62633145C07), // 6.12323399573676603587e-17
|
|
aT0 = reinterpret<f64>(0x3FD555555555550D), // 3.33333333333329318027e-01
|
|
aT1 = reinterpret<f64>(0xBFC999999998EBC4), // -1.99999999998764832476e-01
|
|
aT2 = reinterpret<f64>(0x3FC24924920083FF), // 1.42857142725034663711e-01
|
|
aT3 = reinterpret<f64>(0xBFBC71C6FE231671), // -1.11111104054623557880e-01,
|
|
aT4 = reinterpret<f64>(0x3FB745CDC54C206E), // 9.09088713343650656196e-02
|
|
aT5 = reinterpret<f64>(0xBFB3B0F2AF749A6D), // -7.69187620504482999495e-02
|
|
aT6 = reinterpret<f64>(0x3FB10D66A0D03D51), // 6.66107313738753120669e-02
|
|
aT7 = reinterpret<f64>(0xBFADDE2D52DEFD9A), // -5.83357013379057348645e-02
|
|
aT8 = reinterpret<f64>(0x3FA97B4B24760DEB), // 4.97687799461593236017e-02
|
|
aT9 = reinterpret<f64>(0xBFA2B4442C6A6C2F), // -3.65315727442169155270e-02
|
|
aT10 = reinterpret<f64>(0x3F90AD3AE322DA11), // 1.62858201153657823623e-02
|
|
Ox1p_120f = reinterpret<f32>(0x03800000);
|
|
|
|
var ix = <u32>(reinterpret<u64>(x) >> 32);
|
|
var sx = x;
|
|
ix &= 0x7FFFFFFF;
|
|
var z: f64;
|
|
if (ix >= 0x44100000) {
|
|
if (isNaN(x)) return x;
|
|
z = atanhi3 + Ox1p_120f;
|
|
return builtin_copysign<f64>(z, sx);
|
|
}
|
|
var id: i32;
|
|
if (ix < 0x3FDC0000) {
|
|
if (ix < 0x3E400000) return x;
|
|
id = -1;
|
|
} else {
|
|
x = builtin_abs<f64>(x);
|
|
if (ix < 0x3FF30000) {
|
|
if (ix < 0x3FE60000) {
|
|
id = 0;
|
|
x = (2.0 * x - 1.0) / (2.0 + x);
|
|
} else {
|
|
id = 1;
|
|
x = (x - 1.0) / (x + 1.0);
|
|
}
|
|
} else {
|
|
if (ix < 0x40038000) {
|
|
id = 2;
|
|
x = (x - 1.5) / (1.0 + 1.5 * x);
|
|
} else {
|
|
id = 3;
|
|
x = -1.0 / x;
|
|
}
|
|
}
|
|
}
|
|
z = x * x;
|
|
var w = z * z;
|
|
var s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
|
|
var s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
|
|
var s3 = x * (s1 + s2);
|
|
if (id < 0) return x - s3;
|
|
switch (id) {
|
|
case 0: { z = atanhi0 - ((s3 - atanlo0) - x); break; }
|
|
case 1: { z = atanhi1 - ((s3 - atanlo1) - x); break; }
|
|
case 2: { z = atanhi2 - ((s3 - atanlo2) - x); break; }
|
|
case 3: { z = atanhi3 - ((s3 - atanlo3) - x); break; }
|
|
default: unreachable();
|
|
}
|
|
return builtin_copysign<f64>(z, sx);
|
|
}
|
|
|
|
export function atanh(x: f64): f64 { // see: musl/src/math/atanh.c
|
|
var u = reinterpret<u64>(x);
|
|
var e = u >> 52 & 0x7FF;
|
|
var y = builtin_abs(x);
|
|
if (e < 0x3FF - 1) {
|
|
if (e >= 0x3FF - 32) y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y));
|
|
} else {
|
|
y = 0.5 * log1p(2 * (y / (1 - y)));
|
|
}
|
|
return builtin_copysign<f64>(y, x);
|
|
}
|
|
|
|
export function atan2(y: f64, x: f64): f64 { // see: musl/src/math/atan2.c and SUN COPYRIGHT NOTICE above
|
|
const pi_lo = reinterpret<f64>(0x3CA1A62633145C07); // 1.2246467991473531772E-16
|
|
if (isNaN(x) || isNaN(y)) return x + y;
|
|
var u = reinterpret<u64>(x);
|
|
var ix = <u32>(u >> 32);
|
|
var lx = <u32>u;
|
|
u = reinterpret<u64>(y);
|
|
var iy = <u32>(u >> 32);
|
|
var ly = <u32>u;
|
|
if ((ix - 0x3FF00000 | lx) == 0) return atan(y);
|
|
var m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
|
|
ix = ix & 0x7FFFFFFF;
|
|
iy = iy & 0x7FFFFFFF;
|
|
if ((iy | ly) == 0) {
|
|
switch (m) {
|
|
case 0:
|
|
case 1: return y;
|
|
case 2: return PI;
|
|
case 3: return -PI;
|
|
}
|
|
}
|
|
if ((ix | lx) == 0) return m & 1 ? -PI / 2 : PI / 2;
|
|
if (ix == 0x7FF00000) {
|
|
if (iy == 0x7FF00000) {
|
|
let t = m & 2 ? 3 * PI / 4 : PI / 4;
|
|
return m & 1 ? -t : t;
|
|
} else {
|
|
let t = m & 2 ? PI : 0;
|
|
return m & 1 ? -t : t;
|
|
}
|
|
}
|
|
var z: f64;
|
|
if (ix + (64 << 20) < iy || iy == 0x7FF00000) return m & 1 ? -PI / 2 : PI / 2;
|
|
if ((m & 2) && iy + (64 << 20) < ix) z = 0;
|
|
else z = atan(builtin_abs<f64>(y / x));
|
|
switch (m) {
|
|
case 0: return z;
|
|
case 1: return -z;
|
|
case 2: return PI - (z - pi_lo);
|
|
case 3: return (z - pi_lo) - PI;
|
|
}
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
export function cbrt(x: f64): f64 { // see: musl/src/math/cbrt.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
B1 = <u32>715094163,
|
|
B2 = <u32>696219795,
|
|
P0 = reinterpret<f64>(0x3FFE03E60F61E692), // 1.87595182427177009643
|
|
P1 = reinterpret<f64>(0xBFFE28E092F02420), // -1.88497979543377169875
|
|
P2 = reinterpret<f64>(0x3FF9F1604A49D6C2), // 1.621429720105354466140
|
|
P3 = reinterpret<f64>(0xBFE844CBBEE751D9), // -0.758397934778766047437
|
|
P4 = reinterpret<f64>(0x3FC2B000D4E4EDD7), // 0.145996192886612446982
|
|
Ox1p54 = reinterpret<f64>(0x4350000000000000); // 0x1p54
|
|
|
|
var u = reinterpret<u64>(x);
|
|
var hx = <u32>(u >> 32) & 0x7FFFFFFF;
|
|
if (hx >= 0x7FF00000) return x + x;
|
|
if (hx < 0x00100000) {
|
|
u = reinterpret<u64>(x * Ox1p54);
|
|
hx = <u32>(u >> 32) & 0x7FFFFFFF;
|
|
if (hx == 0) return x;
|
|
hx = hx / 3 + B2;
|
|
} else {
|
|
hx = hx / 3 + B1;
|
|
}
|
|
u &= 1 << 63;
|
|
u |= <u64>hx << 32;
|
|
var t = reinterpret<f64>(u);
|
|
var r = (t * t) * (t / x);
|
|
t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
|
|
t = reinterpret<f64>((reinterpret<u64>(t) + 0x80000000) & 0xFFFFFFFFC0000000);
|
|
var s = t * t;
|
|
r = x / s;
|
|
r = (r - t) / (2 * t + r);
|
|
t = t + t * r;
|
|
return t;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function ceil(x: f64): f64 {
|
|
return builtin_ceil<f64>(x);
|
|
}
|
|
|
|
export function clz32(x: f64): f64 {
|
|
if (!isFinite(x)) return 32;
|
|
/*
|
|
* Wasm (MVP) and JS have different approaches for double->int conversions.
|
|
*
|
|
* For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
|
|
* our float-point arguments before actual convertion to integers.
|
|
*/
|
|
return builtin_clz(dtoi32(x));
|
|
}
|
|
|
|
export function cos(x: f64): f64 { // see: musl/src/math/cos.c
|
|
var u = reinterpret<u64>(x);
|
|
var ix = <u32>(u >> 32);
|
|
var sign = ix >> 31;
|
|
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
// |x| ~< pi/4
|
|
if (ix <= 0x3FE921FB) {
|
|
if (ix < 0x3E46A09E) { // |x| < 2**-27 * sqrt(2)
|
|
return 1.0;
|
|
}
|
|
return cos_kern(x, 0);
|
|
}
|
|
|
|
// sin(Inf or NaN) is NaN
|
|
if (ix >= 0x7FF00000) return x - x;
|
|
|
|
// argument reduction needed
|
|
var n = rempio2(x, u, sign);
|
|
var y0 = rempio2_y0;
|
|
var y1 = rempio2_y1;
|
|
|
|
x = n & 1 ? sin_kern(y0, y1, 1) : cos_kern(y0, y1);
|
|
return (n + 1) & 2 ? -x : x;
|
|
}
|
|
|
|
export function cosh(x: f64): f64 { // see: musl/src/math/cosh.c
|
|
var u = reinterpret<u64>(x);
|
|
u &= 0x7FFFFFFFFFFFFFFF;
|
|
x = reinterpret<f64>(u);
|
|
var w = <u32>(u >> 32);
|
|
var t: f64;
|
|
if (w < 0x3FE62E42) {
|
|
if (w < 0x3FF00000 - (26 << 20)) return 1;
|
|
t = expm1(x);
|
|
// return 1 + t * t / (2 * (1 + t));
|
|
return 1 + t * t / (2 + 2 * t);
|
|
}
|
|
if (w < 0x40862E42) {
|
|
t = exp(x);
|
|
return 0.5 * (t + 1 / t);
|
|
}
|
|
t = expo2(x, 1);
|
|
return t;
|
|
}
|
|
|
|
export function exp(x: f64): f64 { // see: musl/src/math/exp.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return exp_lut(x);
|
|
} else {
|
|
const
|
|
ln2hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
|
|
ln2lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
|
|
invln2 = reinterpret<f64>(0x3FF71547652B82FE), // 1.44269504088896338700e+00
|
|
P1 = reinterpret<f64>(0x3FC555555555553E), // 1.66666666666666019037e-01
|
|
P2 = reinterpret<f64>(0xBF66C16C16BEBD93), // -2.77777777770155933842e-03
|
|
P3 = reinterpret<f64>(0x3F11566AAF25DE2C), // 6.61375632143793436117e-05
|
|
P4 = reinterpret<f64>(0xBEBBBD41C5D26BF1), // -1.65339022054652515390e-06
|
|
P5 = reinterpret<f64>(0x3E66376972BEA4D0), // 4.13813679705723846039e-08
|
|
overflow = reinterpret<f64>(0x40862E42FEFA39EF), // 709.782712893383973096
|
|
underflow = reinterpret<f64>(0xC0874910D52D3051), // -745.13321910194110842
|
|
Ox1p1023 = reinterpret<f64>(0x7FE0000000000000); // 0x1p1023
|
|
|
|
let hx = <u32>(reinterpret<u64>(x) >> 32);
|
|
let sign_ = <i32>(hx >> 31);
|
|
hx &= 0x7FFFFFFF;
|
|
if (hx >= 0x4086232B) {
|
|
if (isNaN(x)) return x;
|
|
if (x > overflow) return x * Ox1p1023;
|
|
if (x < underflow) return 0;
|
|
}
|
|
let hi: f64, lo: f64 = 0;
|
|
let k = 0;
|
|
if (hx > 0x3FD62E42) {
|
|
if (hx >= 0x3FF0A2B2) {
|
|
k = <i32>(invln2 * x + builtin_copysign<f64>(0.5, x));
|
|
} else {
|
|
k = 1 - (sign_ << 1);
|
|
}
|
|
hi = x - k * ln2hi;
|
|
lo = k * ln2lo;
|
|
x = hi - lo;
|
|
} else if (hx > 0x3E300000) {
|
|
hi = x;
|
|
} else return 1.0 + x;
|
|
let xs = x * x;
|
|
// var c = x - xp2 * (P1 + xp2 * (P2 + xp2 * (P3 + xp2 * (P4 + xp2 * P5))));
|
|
let xq = xs * xs;
|
|
let c = x - (xs * P1 + xq * ((P2 + xs * P3) + xq * (P4 + xs * P5)));
|
|
let y = 1.0 + (x * c / (2 - c) - lo + hi);
|
|
return k == 0 ? y : scalbn(y, k);
|
|
}
|
|
}
|
|
|
|
export function exp2(x: f64): f64 {
|
|
return exp2_lut(x);
|
|
}
|
|
|
|
export function expm1(x: f64): f64 { // see: musl/src/math/expm1.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
o_threshold = reinterpret<f64>(0x40862E42FEFA39EF), // 7.09782712893383973096e+02
|
|
ln2_hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
|
|
ln2_lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
|
|
invln2 = reinterpret<f64>(0x3FF71547652B82FE), // 1.44269504088896338700e+00
|
|
Q1 = reinterpret<f64>(0xBFA11111111110F4), // -3.33333333333331316428e-02
|
|
Q2 = reinterpret<f64>(0x3F5A01A019FE5585), // 1.58730158725481460165e-03
|
|
Q3 = reinterpret<f64>(0xBF14CE199EAADBB7), // -7.93650757867487942473e-05
|
|
Q4 = reinterpret<f64>(0x3ED0CFCA86E65239), // 4.00821782732936239552e-06
|
|
Q5 = reinterpret<f64>(0xBE8AFDB76E09C32D), // -2.01099218183624371326e-07
|
|
Ox1p1023 = reinterpret<f64>(0x7FE0000000000000); // 0x1p1023
|
|
|
|
var u = reinterpret<u64>(x);
|
|
var hx = <u32>(u >> 32 & 0x7FFFFFFF);
|
|
var k = 0, sign_ = <i32>(u >> 63);
|
|
if (hx >= 0x4043687A) {
|
|
if (isNaN(x)) return x;
|
|
if (sign_) return -1;
|
|
if (x > o_threshold) return x * Ox1p1023;
|
|
}
|
|
var c = 0.0, t: f64;
|
|
if (hx > 0x3FD62E42) {
|
|
k = select<i32>(
|
|
1 - (sign_ << 1),
|
|
<i32>(invln2 * x + builtin_copysign<f64>(0.5, x)),
|
|
hx < 0x3FF0A2B2
|
|
);
|
|
t = <f64>k;
|
|
let hi = x - t * ln2_hi;
|
|
let lo = t * ln2_lo;
|
|
x = hi - lo;
|
|
c = (hi - x) - lo;
|
|
} else if (hx < 0x3C900000) return x;
|
|
var hfx = 0.5 * x;
|
|
var hxs = x * hfx;
|
|
// var r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
|
|
var hxq = hxs * hxs;
|
|
var r1 = (1.0 + hxs * Q1) + hxq * ((Q2 + hxs * Q3) + hxq * (Q4 + hxs * Q5));
|
|
t = 3.0 - r1 * hfx;
|
|
var e = hxs * ((r1 - t) / (6.0 - x * t));
|
|
if (k == 0) return x - (x * e - hxs);
|
|
e = x * (e - c) - c;
|
|
e -= hxs;
|
|
if (k == -1) return 0.5 * (x - e) - 0.5;
|
|
if (k == 1) {
|
|
if (x < -0.25) return -2.0 * (e - (x + 0.5));
|
|
return 1.0 + 2.0 * (x - e);
|
|
}
|
|
u = (0x3FF + k) << 52;
|
|
var twopk = reinterpret<f64>(u);
|
|
var y: f64;
|
|
if (k < 0 || k > 56) {
|
|
y = x - e + 1.0;
|
|
if (k == 1024) y = y * 2.0 * Ox1p1023;
|
|
else y = y * twopk;
|
|
return y - 1.0;
|
|
}
|
|
u = (0x3FF - k) << 52;
|
|
y = reinterpret<f64>(u);
|
|
if (k < 20) y = (1 - y) - e;
|
|
else y = 1 - (e + y);
|
|
return (x + y) * twopk;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function floor(x: f64): f64 {
|
|
return builtin_floor<f64>(x);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function fround(x: f64): f64 {
|
|
return <f32>x;
|
|
}
|
|
|
|
export function hypot(x: f64, y: f64): f64 { // see: musl/src/math/hypot.c
|
|
const
|
|
SPLIT = reinterpret<f64>(0x41A0000000000000) + 1, // 0x1p27 + 1
|
|
Ox1p700 = reinterpret<f64>(0x6BB0000000000000),
|
|
Ox1p_700 = reinterpret<f64>(0x1430000000000000);
|
|
|
|
var ux = reinterpret<u64>(x);
|
|
var uy = reinterpret<u64>(y);
|
|
ux &= 0x7FFFFFFFFFFFFFFF;
|
|
uy &= 0x7FFFFFFFFFFFFFFF;
|
|
if (ux < uy) {
|
|
let ut = ux;
|
|
ux = uy;
|
|
uy = ut;
|
|
}
|
|
var ex = <i32>(ux >> 52);
|
|
var ey = <i32>(uy >> 52);
|
|
y = reinterpret<f64>(uy);
|
|
if (ey == 0x7FF) return y;
|
|
x = reinterpret<f64>(ux);
|
|
if (ex == 0x7FF || uy == 0) return x;
|
|
if (ex - ey > 64) return x + y;
|
|
var z = 1.0;
|
|
if (ex > 0x3FF + 510) {
|
|
z = Ox1p700;
|
|
x *= Ox1p_700;
|
|
y *= Ox1p_700;
|
|
} else if (ey < 0x3FF - 450) {
|
|
z = Ox1p_700;
|
|
x *= Ox1p700;
|
|
y *= Ox1p700;
|
|
}
|
|
var c = x * SPLIT;
|
|
var h = x - c + c;
|
|
var l = x - h;
|
|
var hx = x * x;
|
|
var lx = h * h - hx + (2 * h + l) * l;
|
|
c = y * SPLIT;
|
|
h = y - c + c;
|
|
l = y - h;
|
|
var hy = y * y;
|
|
var ly = h * h - hy + (2 * h + l) * l;
|
|
return z * builtin_sqrt(ly + lx + hy + hx);
|
|
}
|
|
|
|
export function imul(x: f64, y: f64): f64 {
|
|
/*
|
|
* Wasm (MVP) and JS have different approaches for double->int conversions.
|
|
*
|
|
* For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
|
|
* our float-point arguments before actual convertion to integers.
|
|
*/
|
|
if (!isFinite(x + y)) return 0;
|
|
return dtoi32(x) * dtoi32(y);
|
|
}
|
|
|
|
export function log(x: f64): f64 { // see: musl/src/math/log.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return log_lut(x);
|
|
} else {
|
|
const
|
|
ln2_hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
|
|
ln2_lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
|
|
Lg1 = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
|
|
Lg2 = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
|
|
Lg3 = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
|
|
Lg4 = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
|
|
Lg5 = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
|
|
Lg6 = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
|
|
Lg7 = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
|
|
Ox1p54 = reinterpret<f64>(0x4350000000000000); // 0x1p54
|
|
|
|
let u = reinterpret<u64>(x);
|
|
let hx = <u32>(u >> 32);
|
|
let k = 0;
|
|
if (hx < 0x00100000 || <bool>(hx >> 31)) {
|
|
if (u << 1 == 0) return -1 / (x * x);
|
|
if (hx >> 31) return (x - x) / 0.0;
|
|
k -= 54;
|
|
x *= Ox1p54;
|
|
u = reinterpret<u64>(x);
|
|
hx = <u32>(u >> 32);
|
|
} else if (hx >= 0x7FF00000) {
|
|
return x;
|
|
} else if (hx == 0x3FF00000 && u << 32 == 0) {
|
|
return 0;
|
|
}
|
|
hx += 0x3FF00000 - 0x3FE6A09E;
|
|
k += (<i32>hx >> 20) - 0x3FF;
|
|
hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
|
|
u = <u64>hx << 32 | (u & 0xFFFFFFFF);
|
|
x = reinterpret<f64>(u);
|
|
let f = x - 1.0;
|
|
let hfsq = 0.5 * f * f;
|
|
let s = f / (2.0 + f);
|
|
let z = s * s;
|
|
let w = z * z;
|
|
let t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
|
let t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
|
let r = t2 + t1;
|
|
let dk = <f64>k;
|
|
return s * (hfsq + r) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
|
|
}
|
|
}
|
|
|
|
export function log10(x: f64): f64 { // see: musl/src/math/log10.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
ivln10hi = reinterpret<f64>(0x3FDBCB7B15200000), // 4.34294481878168880939e-01
|
|
ivln10lo = reinterpret<f64>(0x3DBB9438CA9AADD5), // 2.50829467116452752298e-11
|
|
log10_2hi = reinterpret<f64>(0x3FD34413509F6000), // 3.01029995663611771306e-01
|
|
log10_2lo = reinterpret<f64>(0x3D59FEF311F12B36), // 3.69423907715893078616e-13
|
|
Lg1 = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
|
|
Lg2 = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
|
|
Lg3 = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
|
|
Lg4 = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
|
|
Lg5 = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
|
|
Lg6 = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
|
|
Lg7 = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
|
|
Ox1p54 = reinterpret<f64>(0x4350000000000000); // 0x1p54
|
|
|
|
var u = reinterpret<u64>(x);
|
|
var hx = <u32>(u >> 32);
|
|
var k = 0;
|
|
if (hx < 0x00100000 || <bool>(hx >> 31)) {
|
|
if (u << 1 == 0) return -1 / (x * x);
|
|
if (hx >> 31) return (x - x) / 0.0;
|
|
k -= 54;
|
|
x *= Ox1p54;
|
|
u = reinterpret<u64>(x);
|
|
hx = <u32>(u >> 32);
|
|
} else if (hx >= 0x7FF00000) {
|
|
return x;
|
|
} else if (hx == 0x3FF00000 && u << 32 == 0) {
|
|
return 0;
|
|
}
|
|
hx += 0x3FF00000 - 0x3FE6A09E;
|
|
k += <i32>(hx >> 20) - 0x3FF;
|
|
hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
|
|
u = <u64>hx << 32 | (u & 0xFFFFFFFF);
|
|
x = reinterpret<f64>(u);
|
|
var f = x - 1.0;
|
|
var hfsq = 0.5 * f * f;
|
|
var s = f / (2.0 + f);
|
|
var z = s * s;
|
|
var w = z * z;
|
|
var t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
|
var t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
|
var r = t2 + t1;
|
|
var hi = f - hfsq;
|
|
u = reinterpret<u64>(hi);
|
|
u &= 0xFFFFFFFF00000000;
|
|
hi = reinterpret<f64>(u);
|
|
var lo = f - hi - hfsq + s * (hfsq + r);
|
|
var val_hi = hi * ivln10hi;
|
|
var dk = <f64>k;
|
|
var y = dk * log10_2hi;
|
|
var val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;
|
|
w = y + val_hi;
|
|
val_lo += (y - w) + val_hi;
|
|
return val_lo + w;
|
|
}
|
|
|
|
export function log1p(x: f64): f64 { // see: musl/src/math/log1p.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
ln2_hi = reinterpret<f64>(0x3FE62E42FEE00000), // 6.93147180369123816490e-01
|
|
ln2_lo = reinterpret<f64>(0x3DEA39EF35793C76), // 1.90821492927058770002e-10
|
|
Lg1 = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
|
|
Lg2 = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
|
|
Lg3 = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
|
|
Lg4 = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
|
|
Lg5 = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
|
|
Lg6 = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
|
|
Lg7 = reinterpret<f64>(0x3FC2F112DF3E5244); // 1.479819860511658591e-01
|
|
|
|
var u = reinterpret<u64>(x);
|
|
var hx = <u32>(u >> 32);
|
|
var k = 1;
|
|
var c = 0.0, f = 0.0;
|
|
if (hx < 0x3FDA827A || <bool>(hx >> 31)) {
|
|
if (hx >= 0xBFF00000) {
|
|
if (x == -1) return x / 0.0;
|
|
return (x - x) / 0.0;
|
|
}
|
|
if (hx << 1 < 0x3CA00000 << 1) return x;
|
|
if (hx <= 0xBFD2BEC4) {
|
|
k = 0;
|
|
c = 0;
|
|
f = x;
|
|
}
|
|
} else if (hx >= 0x7FF00000) return x;
|
|
if (k) {
|
|
u = reinterpret<u64>(1 + x);
|
|
let hu = <u32>(u >> 32);
|
|
hu += 0x3FF00000 - 0x3FE6A09E;
|
|
k = <i32>(hu >> 20) - 0x3FF;
|
|
if (k < 54) {
|
|
let uf = reinterpret<f64>(u);
|
|
c = k >= 2 ? 1 - (uf - x) : x - (uf - 1);
|
|
c /= uf;
|
|
} else c = 0;
|
|
hu = (hu & 0x000FFFFF) + 0x3FE6A09E;
|
|
u = <u64>hu << 32 | (u & 0xFFFFFFFF);
|
|
f = reinterpret<f64>(u) - 1;
|
|
}
|
|
var hfsq = 0.5 * f * f;
|
|
var s = f / (2.0 + f);
|
|
var z = s * s;
|
|
var w = z * z;
|
|
var t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
|
var t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
|
var r = t2 + t1;
|
|
var dk = <f64>k;
|
|
return s * (hfsq + r) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
|
|
}
|
|
|
|
export function log2(x: f64): f64 { // see: musl/src/math/log2.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return log2_lut(x);
|
|
} else {
|
|
const
|
|
ivln2hi = reinterpret<f64>(0x3FF7154765200000), // 1.44269504072144627571e+00
|
|
ivln2lo = reinterpret<f64>(0x3DE705FC2EEFA200), // 1.67517131648865118353e-10
|
|
Lg1 = reinterpret<f64>(0x3FE5555555555593), // 6.666666666666735130e-01
|
|
Lg2 = reinterpret<f64>(0x3FD999999997FA04), // 3.999999999940941908e-01
|
|
Lg3 = reinterpret<f64>(0x3FD2492494229359), // 2.857142874366239149e-01
|
|
Lg4 = reinterpret<f64>(0x3FCC71C51D8E78AF), // 2.222219843214978396e-01
|
|
Lg5 = reinterpret<f64>(0x3FC7466496CB03DE), // 1.818357216161805012e-01
|
|
Lg6 = reinterpret<f64>(0x3FC39A09D078C69F), // 1.531383769920937332e-01
|
|
Lg7 = reinterpret<f64>(0x3FC2F112DF3E5244), // 1.479819860511658591e-01
|
|
Ox1p54 = reinterpret<f64>(0x4350000000000000); // 1p54
|
|
|
|
let u = reinterpret<u64>(x);
|
|
let hx = <u32>(u >> 32);
|
|
let k = 0;
|
|
if (hx < 0x00100000 || <bool>(hx >> 31)) {
|
|
if (u << 1 == 0) return -1 / (x * x);
|
|
if (hx >> 31) return (x - x) / 0.0;
|
|
k -= 54;
|
|
x *= Ox1p54;
|
|
u = reinterpret<u64>(x);
|
|
hx = <u32>(u >> 32);
|
|
} else if (hx >= 0x7FF00000) {
|
|
return x;
|
|
} else if (hx == 0x3FF00000 && u << 32 == 0) {
|
|
return 0;
|
|
}
|
|
hx += 0x3FF00000 - 0x3FE6A09E;
|
|
k += <i32>(hx >> 20) - 0x3FF;
|
|
hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
|
|
u = <u64>hx << 32 | (u & 0xFFFFFFFF);
|
|
x = reinterpret<f64>(u);
|
|
let f = x - 1.0;
|
|
let hfsq = 0.5 * f * f;
|
|
let s = f / (2.0 + f);
|
|
let z = s * s;
|
|
let w = z * z;
|
|
let t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
|
let t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
|
let r = t2 + t1;
|
|
let hi = f - hfsq;
|
|
u = reinterpret<u64>(hi);
|
|
u &= 0xFFFFFFFF00000000;
|
|
hi = reinterpret<f64>(u);
|
|
let lo = f - hi - hfsq + s * (hfsq + r);
|
|
let val_hi = hi * ivln2hi;
|
|
let val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
|
|
let y = <f64>k;
|
|
w = y + val_hi;
|
|
val_lo += (y - w) + val_hi;
|
|
val_hi = w;
|
|
return val_lo + val_hi;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function max(value1: f64, value2: f64): f64 {
|
|
return builtin_max<f64>(value1, value2);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function min(value1: f64, value2: f64): f64 {
|
|
return builtin_min<f64>(value1, value2);
|
|
}
|
|
|
|
export function pow(x: f64, y: f64): f64 { // see: musl/src/math/pow.c and SUN COPYRIGHT NOTICE above
|
|
// TODO: remove this fast pathes after introduced own mid-end IR with "stdlib call simplify" transforms
|
|
if (builtin_abs<f64>(y) <= 2) {
|
|
if (y == 2.0) return x * x;
|
|
if (y == 0.5) {
|
|
return select<f64>(
|
|
builtin_abs<f64>(builtin_sqrt<f64>(x)),
|
|
Infinity,
|
|
x != -Infinity
|
|
);
|
|
}
|
|
if (y == -1.0) return 1 / x;
|
|
if (y == 1.0) return x;
|
|
if (y == 0.0) return 1.0;
|
|
}
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return pow_lut(x, y);
|
|
} else {
|
|
const
|
|
dp_h1 = reinterpret<f64>(0x3FE2B80340000000), // 5.84962487220764160156e-01
|
|
dp_l1 = reinterpret<f64>(0x3E4CFDEB43CFD006), // 1.35003920212974897128e-08
|
|
two53 = reinterpret<f64>(0x4340000000000000), // 9007199254740992.0
|
|
huge = reinterpret<f64>(0x7E37E43C8800759C), // 1e+300
|
|
tiny = reinterpret<f64>(0x01A56E1FC2F8F359), // 1e-300
|
|
L1 = reinterpret<f64>(0x3FE3333333333303), // 5.99999999999994648725e-01
|
|
L2 = reinterpret<f64>(0x3FDB6DB6DB6FABFF), // 4.28571428578550184252e-01
|
|
L3 = reinterpret<f64>(0x3FD55555518F264D), // 3.33333329818377432918e-01
|
|
L4 = reinterpret<f64>(0x3FD17460A91D4101), // 2.72728123808534006489e-01
|
|
L5 = reinterpret<f64>(0x3FCD864A93C9DB65), // 2.30660745775561754067e-01
|
|
L6 = reinterpret<f64>(0x3FCA7E284A454EEF), // 2.06975017800338417784e-01
|
|
P1 = reinterpret<f64>(0x3FC555555555553E), // 1.66666666666666019037e-01
|
|
P2 = reinterpret<f64>(0xBF66C16C16BEBD93), // -2.77777777770155933842e-03
|
|
P3 = reinterpret<f64>(0x3F11566AAF25DE2C), // 6.61375632143793436117e-05
|
|
P4 = reinterpret<f64>(0xBEBBBD41C5D26BF1), // -1.65339022054652515390e-06
|
|
P5 = reinterpret<f64>(0x3E66376972BEA4D0), // 4.13813679705723846039e-08
|
|
lg2 = reinterpret<f64>(0x3FE62E42FEFA39EF), // 6.93147180559945286227e-01
|
|
lg2_h = reinterpret<f64>(0x3FE62E4300000000), // 6.93147182464599609375e-01
|
|
lg2_l = reinterpret<f64>(0xBE205C610CA86C39), // -1.90465429995776804525e-09
|
|
ovt = reinterpret<f64>(0x3C971547652B82FE), // 8.0085662595372944372e-017
|
|
cp = reinterpret<f64>(0x3FEEC709DC3A03FD), // 9.61796693925975554329e-01
|
|
cp_h = reinterpret<f64>(0x3FEEC709E0000000), // 9.61796700954437255859e-01
|
|
cp_l = reinterpret<f64>(0xBE3E2FE0145B01F5), // -7.02846165095275826516e-09
|
|
ivln2 = reinterpret<f64>(0x3FF71547652B82FE), // 1.44269504088896338700e+00
|
|
ivln2_h = reinterpret<f64>(0x3FF7154760000000), // 1.44269502162933349609e+00
|
|
ivln2_l = reinterpret<f64>(0x3E54AE0BF85DDF44), // 1.92596299112661746887e-08
|
|
inv3 = reinterpret<f64>(0x3FD5555555555555); // 0.3333333333333333333333
|
|
|
|
let u_ = reinterpret<u64>(x);
|
|
let hx = <i32>(u_ >> 32);
|
|
let lx = <u32>u_;
|
|
u_ = reinterpret<u64>(y);
|
|
let hy = <i32>(u_ >> 32);
|
|
let ly = <u32>u_;
|
|
let ix = hx & 0x7FFFFFFF;
|
|
let iy = hy & 0x7FFFFFFF;
|
|
if ((iy | ly) == 0) return 1.0; // x**0 = 1, even if x is NaN
|
|
// if (hx == 0x3FF00000 && lx == 0) return 1.0; // C: 1**y = 1, even if y is NaN, JS: NaN
|
|
if ( // NaN if either arg is NaN
|
|
ix > 0x7FF00000 || (ix == 0x7FF00000 && lx != 0) ||
|
|
iy > 0x7FF00000 || (iy == 0x7FF00000 && ly != 0)
|
|
) return x + y;
|
|
let yisint = 0, k: i32;
|
|
if (hx < 0) {
|
|
if (iy >= 0x43400000) yisint = 2;
|
|
else if (iy >= 0x3FF00000) {
|
|
k = (iy >> 20) - 0x3FF;
|
|
let offset = select<u32>(52, 20, k > 20) - k;
|
|
let Ly = select<u32>(ly, iy, k > 20);
|
|
let jj = Ly >> offset;
|
|
if ((jj << offset) == Ly) yisint = 2 - (jj & 1);
|
|
}
|
|
}
|
|
if (ly == 0) {
|
|
if (iy == 0x7FF00000) { // y is +-inf
|
|
if (((ix - 0x3FF00000) | lx) == 0) return NaN; // C: (-1)**+-inf is 1, JS: NaN
|
|
else if (ix >= 0x3FF00000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
|
|
else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
|
|
}
|
|
if (iy == 0x3FF00000) {
|
|
if (hy >= 0) return x;
|
|
return 1 / x;
|
|
}
|
|
if (hy == 0x40000000) return x * x;
|
|
if (hy == 0x3FE00000) {
|
|
if (hx >= 0) return builtin_sqrt(x);
|
|
}
|
|
}
|
|
let ax = builtin_abs<f64>(x), z: f64;
|
|
if (lx == 0) {
|
|
if (ix == 0 || ix == 0x7FF00000 || ix == 0x3FF00000) {
|
|
z = ax;
|
|
if (hy < 0) z = 1.0 / z;
|
|
if (hx < 0) {
|
|
if (((ix - 0x3FF00000) | yisint) == 0) {
|
|
let d = z - z;
|
|
z = d / d;
|
|
} else if (yisint == 1) z = -z;
|
|
}
|
|
return z;
|
|
}
|
|
}
|
|
let s = 1.0;
|
|
if (hx < 0) {
|
|
if (yisint == 0) {
|
|
let d = x - x;
|
|
return d / d;
|
|
}
|
|
if (yisint == 1) s = -1.0;
|
|
}
|
|
let t1: f64, t2: f64, p_h: f64, p_l: f64, r: f64, t: f64, u: f64, v: f64, w: f64;
|
|
let j: i32, n: i32;
|
|
if (iy > 0x41E00000) {
|
|
if (iy > 0x43F00000) {
|
|
if (ix <= 0x3FEFFFFF) return hy < 0 ? huge * huge : tiny * tiny;
|
|
if (ix >= 0x3FF00000) return hy > 0 ? huge * huge : tiny * tiny;
|
|
}
|
|
if (ix < 0x3FEFFFFF) return hy < 0 ? s * huge * huge : s * tiny * tiny;
|
|
if (ix > 0x3FF00000) return hy > 0 ? s * huge * huge : s * tiny * tiny;
|
|
t = ax - 1.0;
|
|
w = (t * t) * (0.5 - t * (inv3 - t * 0.25));
|
|
u = ivln2_h * t;
|
|
v = t * ivln2_l - w * ivln2;
|
|
t1 = u + v;
|
|
t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xFFFFFFFF00000000);
|
|
t2 = v - (t1 - u);
|
|
} else {
|
|
let ss: f64, s2: f64, s_h: f64, s_l: f64, t_h: f64, t_l: f64;
|
|
n = 0;
|
|
if (ix < 0x00100000) {
|
|
ax *= two53;
|
|
n -= 53;
|
|
ix = <u32>(reinterpret<u64>(ax) >> 32);
|
|
}
|
|
n += (ix >> 20) - 0x3FF;
|
|
j = ix & 0x000FFFFF;
|
|
ix = j | 0x3FF00000;
|
|
if (j <= 0x3988E) k = 0;
|
|
else if (j < 0xBB67A) k = 1;
|
|
else {
|
|
k = 0;
|
|
n += 1;
|
|
ix -= 0x00100000;
|
|
}
|
|
ax = reinterpret<f64>(reinterpret<u64>(ax) & 0xFFFFFFFF | (<u64>ix << 32));
|
|
let bp = select<f64>(1.5, 1.0, k); // k ? 1.5 : 1.0
|
|
u = ax - bp;
|
|
v = 1.0 / (ax + bp);
|
|
ss = u * v;
|
|
s_h = ss;
|
|
s_h = reinterpret<f64>(reinterpret<u64>(s_h) & 0xFFFFFFFF00000000);
|
|
t_h = reinterpret<f64>(<u64>(((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)) << 32);
|
|
t_l = ax - (t_h - bp);
|
|
s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
|
s2 = ss * ss;
|
|
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
|
r += s_l * (s_h + ss);
|
|
s2 = s_h * s_h;
|
|
t_h = 3.0 + s2 + r;
|
|
t_h = reinterpret<f64>(reinterpret<u64>(t_h) & 0xFFFFFFFF00000000);
|
|
t_l = r - ((t_h - 3.0) - s2);
|
|
u = s_h * t_h;
|
|
v = s_l * t_h + t_l * ss;
|
|
p_h = u + v;
|
|
p_h = reinterpret<f64>(reinterpret<u64>(p_h) & 0xFFFFFFFF00000000);
|
|
p_l = v - (p_h - u);
|
|
let z_h = cp_h * p_h;
|
|
let dp_l = select<f64>(dp_l1, 0.0, k);
|
|
let z_l = cp_l * p_h + p_l * cp + dp_l;
|
|
t = <f64>n;
|
|
let dp_h = select<f64>(dp_h1, 0.0, k);
|
|
t1 = ((z_h + z_l) + dp_h) + t;
|
|
t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xFFFFFFFF00000000);
|
|
t2 = z_l - (((t1 - t) - dp_h) - z_h);
|
|
}
|
|
let y1 = y;
|
|
y1 = reinterpret<f64>(reinterpret<u64>(y1) & 0xFFFFFFFF00000000);
|
|
p_l = (y - y1) * t1 + y * t2;
|
|
p_h = y1 * t1;
|
|
z = p_l + p_h;
|
|
u_ = reinterpret<u64>(z);
|
|
j = <u32>(u_ >> 32);
|
|
let i = <i32>u_;
|
|
if (j >= 0x40900000) {
|
|
if (((j - 0x40900000) | i) != 0) return s * huge * huge;
|
|
if (p_l + ovt > z - p_h) return s * huge * huge;
|
|
} else if ((j & 0x7FFFFFFF) >= 0x4090CC00) {
|
|
if (((j - 0xC090CC00) | i) != 0) return s * tiny * tiny;
|
|
if (p_l <= z - p_h) return s * tiny * tiny;
|
|
}
|
|
i = j & 0x7FFFFFFF;
|
|
k = (i >> 20) - 0x3FF;
|
|
n = 0;
|
|
if (i > 0x3FE00000) {
|
|
n = j + (0x00100000 >> (k + 1));
|
|
k = ((n & 0x7FFFFFFF) >> 20) - 0x3FF;
|
|
t = 0.0;
|
|
t = reinterpret<f64>(<u64>(n & ~(0x000FFFFF >> k)) << 32);
|
|
n = ((n & 0x000FFFFF) | 0x00100000) >> (20 - k);
|
|
if (j < 0) n = -n;
|
|
p_h -= t;
|
|
}
|
|
t = p_l + p_h;
|
|
t = reinterpret<f64>(reinterpret<u64>(t) & 0xFFFFFFFF00000000);
|
|
u = t * lg2_h;
|
|
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
|
z = u + v;
|
|
w = v - (z - u);
|
|
t = z * z;
|
|
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
|
r = (z * t1) / (t1 - 2.0) - (w + z * w);
|
|
z = 1.0 - (r - z);
|
|
j = <u32>(reinterpret<u64>(z) >> 32);
|
|
j += n << 20;
|
|
if ((j >> 20) <= 0) z = scalbn(z, n);
|
|
else z = reinterpret<f64>(reinterpret<u64>(z) & 0xFFFFFFFF | (<u64>j << 32));
|
|
return s * z;
|
|
}
|
|
}
|
|
|
|
export function seedRandom(value: i64): void {
|
|
random_seeded = true;
|
|
random_state0_64 = murmurHash3(value);
|
|
random_state1_64 = murmurHash3(~random_state0_64);
|
|
random_state0_32 = splitMix32(<u32>value);
|
|
random_state1_32 = splitMix32(random_state0_32);
|
|
assert(
|
|
random_state0_64 != 0 && random_state1_64 != 0 &&
|
|
random_state0_32 != 0 && random_state1_32 != 0
|
|
);
|
|
}
|
|
|
|
export function random(): f64 { // see: v8/src/base/utils/random-number-generator.cc
|
|
if (!random_seeded) seedRandom(reinterpret<i64>(seed()));
|
|
var s1 = random_state0_64;
|
|
var s0 = random_state1_64;
|
|
random_state0_64 = s0;
|
|
s1 ^= s1 << 23;
|
|
s1 ^= s1 >> 17;
|
|
s1 ^= s0;
|
|
s1 ^= s0 >> 26;
|
|
random_state1_64 = s1;
|
|
var r = (s0 >> 12) | 0x3FF0000000000000;
|
|
return reinterpret<f64>(r) - 1;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function round(x: f64): f64 {
|
|
let roundUp = builtin_ceil<f64>(x);
|
|
return select<f64>(roundUp, roundUp - 1.0, roundUp - 0.5 <= x);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function sign(x: f64): f64 {
|
|
if (ASC_SHRINK_LEVEL > 0) {
|
|
return builtin_abs(x) > 0 ? builtin_copysign<f64>(1, x) : x;
|
|
} else {
|
|
return x > 0 ? 1 : x < 0 ? -1 : x;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function signbit(x: f64): bool {
|
|
return <bool>(reinterpret<u64>(x) >>> 63);
|
|
}
|
|
|
|
export function sin(x: f64): f64 { // see: musl/src/math/sin.c
|
|
var u = reinterpret<u64>(x);
|
|
var ix = <u32>(u >> 32);
|
|
var sign = ix >> 31;
|
|
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
// |x| ~< pi/4
|
|
if (ix <= 0x3FE921FB) {
|
|
if (ix < 0x3E500000) { // |x| < 2**-26
|
|
return x;
|
|
}
|
|
return sin_kern(x, 0.0, 0);
|
|
}
|
|
|
|
// sin(Inf or NaN) is NaN
|
|
if (ix >= 0x7FF00000) return x - x;
|
|
|
|
// argument reduction needed
|
|
var n = rempio2(x, u, sign);
|
|
var y0 = rempio2_y0;
|
|
var y1 = rempio2_y1;
|
|
|
|
x = n & 1 ? cos_kern(y0, y1) : sin_kern(y0, y1, 1);
|
|
return n & 2 ? -x : x;
|
|
}
|
|
|
|
export function sinh(x: f64): f64 { // see: musl/src/math/sinh.c
|
|
var u = reinterpret<u64>(x) & 0x7FFFFFFFFFFFFFFF;
|
|
var a = reinterpret<f64>(u);
|
|
var w = <u32>(u >> 32);
|
|
var h = builtin_copysign(0.5, x);
|
|
if (w < 0x40862E42) {
|
|
let t = expm1(a);
|
|
if (w < 0x3FF00000) {
|
|
if (w < 0x3FF00000 - (26 << 20)) return x;
|
|
return h * (2 * t - t * t / (t + 1));
|
|
}
|
|
return h * (t + t / (t + 1));
|
|
}
|
|
return expo2(a, 2 * h);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function sqrt(x: f64): f64 {
|
|
return builtin_sqrt<f64>(x);
|
|
}
|
|
|
|
export function tan(x: f64): f64 { // see: musl/src/math/tan.c
|
|
var u = reinterpret<u64>(x);
|
|
var ix = <i32>(u >> 32);
|
|
var sign = ix >>> 31;
|
|
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
// |x| ~< pi/4
|
|
if (ix <= 0x3FE921FB) {
|
|
if (ix < 0x3E400000) { // |x| < 2**-27
|
|
return x;
|
|
}
|
|
return tan_kern(x, 0.0, 1);
|
|
}
|
|
|
|
// tan(Inf or NaN) is NaN
|
|
if (ix >= 0x7FF00000) return x - x;
|
|
|
|
var n = rempio2(x, u, sign);
|
|
return tan_kern(rempio2_y0, rempio2_y1, 1 - ((n & 1) << 1));
|
|
}
|
|
|
|
export function tanh(x: f64): f64 { // see: musl/src/math/tanh.c
|
|
var u = reinterpret<u64>(x);
|
|
u &= 0x7FFFFFFFFFFFFFFF;
|
|
var y = reinterpret<f64>(u);
|
|
var w = <u32>(u >> 32);
|
|
var t: f64;
|
|
if (w > 0x3FE193EA) {
|
|
if (w > 0x40340000) {
|
|
t = 1 - 0 / y;
|
|
} else {
|
|
t = expm1(2 * y);
|
|
t = 1 - 2 / (t + 2);
|
|
}
|
|
} else if (w > 0x3FD058AE) {
|
|
t = expm1(2 * y);
|
|
t = t / (t + 2);
|
|
} else if (w >= 0x00100000) {
|
|
t = expm1(-2 * y);
|
|
t = -t / (t + 2);
|
|
} else t = y;
|
|
return builtin_copysign<f64>(t, x);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function trunc(x: f64): f64 {
|
|
return builtin_trunc<f64>(x);
|
|
}
|
|
|
|
export function scalbn(x: f64, n: i32): f64 { // see: https://git.musl-libc.org/cgit/musl/tree/src/math/scalbn.c
|
|
const
|
|
Ox1p53 = reinterpret<f64>(0x4340000000000000),
|
|
Ox1p1023 = reinterpret<f64>(0x7FE0000000000000),
|
|
Ox1p_1022 = reinterpret<f64>(0x0010000000000000);
|
|
|
|
var y = x;
|
|
if (n > 1023) {
|
|
y *= Ox1p1023;
|
|
n -= 1023;
|
|
if (n > 1023) {
|
|
y *= Ox1p1023;
|
|
n = builtin_min<i32>(n - 1023, 1023);
|
|
}
|
|
} else if (n < -1022) {
|
|
// make sure final n < -53 to avoid double
|
|
// rounding in the subnormal range
|
|
y *= Ox1p_1022 * Ox1p53;
|
|
n += 1022 - 53;
|
|
if (n < -1022) {
|
|
y *= Ox1p_1022 * Ox1p53;
|
|
n = builtin_max<i32>(n + 1022 - 53, -1022);
|
|
}
|
|
}
|
|
return y * reinterpret<f64>(<u64>(0x3FF + n) << 52);
|
|
}
|
|
|
|
export function mod(x: f64, y: f64): f64 { // see: musl/src/math/fmod.c
|
|
if (builtin_abs<f64>(y) == 1.0) {
|
|
// x % 1, x % -1 ==> sign(x) * abs(x - 1.0 * trunc(x / 1.0))
|
|
// TODO: move this rule to compiler's optimization pass.
|
|
// It could be apply for any x % C_pot, where "C_pot" is pow of two const.
|
|
return builtin_copysign<f64>(x - builtin_trunc<f64>(x), x);
|
|
}
|
|
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) {
|
|
return x * f64(ux1 != uy1);
|
|
}
|
|
if (!ex) {
|
|
ex -= builtin_clz<i64>(ux << 12);
|
|
ux <<= 1 - ex;
|
|
} else {
|
|
ux &= <u64>-1 >> 12;
|
|
ux |= 1 << 52;
|
|
}
|
|
if (!ey) {
|
|
ey -= builtin_clz<i64>(uy << 12);
|
|
uy <<= 1 - ey;
|
|
} 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;
|
|
}
|
|
return reinterpret<f64>(ux | (sx << 63));
|
|
}
|
|
|
|
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 <<= 1 - ex;
|
|
} else {
|
|
uxi &= <u64>-1 >> 12;
|
|
uxi |= 1 << 52;
|
|
}
|
|
if (!ey) {
|
|
ey -= builtin_clz<i64>(uy << 12);
|
|
uy <<= 1 - ey;
|
|
} else {
|
|
uy &= <u64>-1 >> 12;
|
|
uy |= 1 << 52;
|
|
}
|
|
var q: u32 = 0;
|
|
do {
|
|
if (ex < ey) {
|
|
if (ex + 1 == ey) break; // goto end
|
|
return x;
|
|
}
|
|
while (ex > ey) {
|
|
if (uxi >= uy) {
|
|
uxi -= uy;
|
|
++q;
|
|
}
|
|
uxi <<= 1;
|
|
q <<= 1;
|
|
--ex;
|
|
}
|
|
if (uxi >= uy) {
|
|
uxi -= uy;
|
|
++q;
|
|
}
|
|
if (uxi == 0) ex = -60;
|
|
else {
|
|
let shift = builtin_clz<i64>(uxi << 11);
|
|
ex -= shift;
|
|
uxi <<= shift;
|
|
}
|
|
break;
|
|
} while (false);
|
|
// end:
|
|
if (ex > 0) {
|
|
uxi -= 1 << 52;
|
|
uxi |= ex << 52;
|
|
} else {
|
|
uxi >>= -ex + 1;
|
|
}
|
|
x = reinterpret<f64>(uxi);
|
|
y = builtin_abs<f64>(y);
|
|
var x2 = x + x;
|
|
if (ex == ey || (ex + 1 == ey && (x2 > y || (x2 == y && <bool>(q & 1))))) {
|
|
x -= y;
|
|
// ++q;
|
|
}
|
|
return sx ? -x : x;
|
|
}
|
|
|
|
export function sincos(x: f64): void { // see: musl/tree/src/math/sincos.c
|
|
var u = reinterpret<u64>(x);
|
|
var ix = <u32>(u >> 32);
|
|
var sign = ix >> 31;
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
if (ix <= 0x3FE921FB) { // |x| ~<= π/4
|
|
if (ix < 0x3E46A09E) { // if |x| < 2**-27 * sqrt(2)
|
|
sincos_sin = x;
|
|
sincos_cos = 1;
|
|
return;
|
|
}
|
|
sincos_sin = sin_kern(x, 0, 0);
|
|
sincos_cos = cos_kern(x, 0);
|
|
return;
|
|
}
|
|
// sin(Inf or NaN) is NaN
|
|
if (ix >= 0x7F800000) {
|
|
let xx = x - x;
|
|
sincos_sin = xx;
|
|
sincos_cos = xx;
|
|
return;
|
|
}
|
|
// general argument reduction needed
|
|
var n = rempio2(x, u, sign);
|
|
var y0 = rempio2_y0;
|
|
var y1 = rempio2_y1;
|
|
var s = sin_kern(y0, y1, 1);
|
|
var c = cos_kern(y0, y1);
|
|
var sin = s, cos = c;
|
|
if (n & 1) {
|
|
sin = c;
|
|
cos = -s;
|
|
}
|
|
if (n & 2) {
|
|
sin = -sin;
|
|
cos = -cos;
|
|
}
|
|
sincos_sin = sin;
|
|
sincos_cos = cos;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy var rempio2f_y: f64;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy @inline const PIO2F_TABLE = memory.data<u64>([
|
|
0xA2F9836E4E441529,
|
|
0xFC2757D1F534DDC0,
|
|
0xDB6295993C439041,
|
|
0xFE5163ABDEBBC561
|
|
]);
|
|
|
|
function Rf(z: f32): f32 { // Rational approximation of (asin(x)-x)/x^3
|
|
const // see: musl/src/math/asinf.c and SUN COPYRIGHT NOTICE above
|
|
pS0 = reinterpret<f32>(0x3E2AAA75), // 1.6666586697e-01f
|
|
pS1 = reinterpret<f32>(0xBD2F13BA), // -4.2743422091e-02f
|
|
pS2 = reinterpret<f32>(0xBC0DD36B), // -8.6563630030e-03f
|
|
qS1 = reinterpret<f32>(0xBF34E5AE); // -7.0662963390e-01f
|
|
|
|
var p = z * (pS0 + z * (pS1 + z * pS2));
|
|
var q: f32 = 1 + z * qS1;
|
|
return p / q;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function expo2f(x: f32, sign: 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);
|
|
// in directed rounding correct sign before rounding or overflow is important
|
|
return NativeMathf.exp(x - kln2) * (sign * scale) * scale;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function pio2f_large_quot(x: f32, u: i32): i32 { // see: jdh8/metallic/blob/master/src/math/float/rem_pio2f.c
|
|
const coeff = reinterpret<f64>(0x3BF921FB54442D18); // π * 0x1p-65 = 8.51530395021638647334e-20
|
|
|
|
var offset = (u >> 23) - 152;
|
|
var shift = <u64>(offset & 63);
|
|
var tblPtr = PIO2F_TABLE + (offset >> 6 << 3);
|
|
|
|
var b0 = load<u64>(tblPtr, 0 << 3);
|
|
var b1 = load<u64>(tblPtr, 1 << 3);
|
|
var lo: u64;
|
|
|
|
if (shift > 32) {
|
|
let b2 = load<u64>(tblPtr, 2 << 3);
|
|
lo = b2 >> (96 - shift);
|
|
lo |= b1 << (shift - 32);
|
|
} else {
|
|
lo = b1 >> (32 - shift);
|
|
}
|
|
|
|
var hi = (b1 >> (64 - shift)) | (b0 << shift);
|
|
var mantissa: u64 = (u & 0x007FFFFF) | 0x00800000;
|
|
var product = mantissa * hi + (mantissa * lo >> 32);
|
|
var r: i64 = product << 2;
|
|
var q = <i32>((product >> 62) + (r >>> 63));
|
|
rempio2f_y = copysign<f64>(coeff, x) * <f64>r;
|
|
return q;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function rempio2f(x: f32, u: u32, sign: i32): i32 { // see: jdh8/metallic/blob/master/src/math/float/rem_pio2f.c
|
|
const
|
|
pi2hi = reinterpret<f64>(0x3FF921FB50000000), // 1.57079631090164184570
|
|
pi2lo = reinterpret<f64>(0x3E5110B4611A6263), // 1.58932547735281966916e-8
|
|
_2_pi = reinterpret<f64>(0x3FE45F306DC9C883); // 0.63661977236758134308
|
|
|
|
if (u < 0x4DC90FDB) { // π * 0x1p28
|
|
let q = nearest(x * _2_pi);
|
|
rempio2f_y = x - q * pi2hi - q * pi2lo;
|
|
return <i32>q;
|
|
}
|
|
|
|
var q = pio2f_large_quot(x, u);
|
|
return select(-q, q, sign);
|
|
}
|
|
|
|
// |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]).
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function sin_kernf(x: f64): f32 { // see: musl/tree/src/math/__sindf.c
|
|
const
|
|
S1 = reinterpret<f64>(0xBFC5555554CBAC77), // -0x15555554cbac77.0p-55
|
|
S2 = reinterpret<f64>(0x3F811110896EFBB2), // 0x111110896efbb2.0p-59
|
|
S3 = reinterpret<f64>(0xBF2A00F9E2CAE774), // -0x1a00f9e2cae774.0p-65
|
|
S4 = reinterpret<f64>(0x3EC6CD878C3B46A7); // 0x16cd878c3b46a7.0p-71
|
|
|
|
var z = x * x;
|
|
var w = z * z;
|
|
var r = S3 + z * S4;
|
|
var s = z * x;
|
|
return <f32>((x + s * (S1 + z * S2)) + s * w * r);
|
|
}
|
|
|
|
// |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]).
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function cos_kernf(x: f64): f32 { // see: musl/tree/src/math/__cosdf.c
|
|
const
|
|
C0 = reinterpret<f64>(0xBFDFFFFFFD0C5E81), // -0x1ffffffd0c5e81.0p-54
|
|
C1 = reinterpret<f64>(0x3FA55553E1053A42), // 0x155553e1053a42.0p-57
|
|
C2 = reinterpret<f64>(0xBF56C087E80F1E27), // -0x16c087e80f1e27.0p-62
|
|
C3 = reinterpret<f64>(0x3EF99342E0EE5069); // 0x199342e0ee5069.0p-68
|
|
|
|
var z = x * x;
|
|
var w = z * z;
|
|
var r = C2 + z * C3;
|
|
return <f32>(((1 + z * C0) + w * C1) + (w * z) * r);
|
|
}
|
|
|
|
// |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]).
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function tan_kernf(x: f64, odd: i32): f32 { // see: musl/tree/src/math/__tandf.c
|
|
const
|
|
T0 = reinterpret<f64>(0x3FD5554D3418C99F), // 0x15554d3418c99f.0p-54
|
|
T1 = reinterpret<f64>(0x3FC112FD38999F72), // 0x1112fd38999f72.0p-55
|
|
T2 = reinterpret<f64>(0x3FAB54C91D865AFE), // 0x1b54c91d865afe.0p-57
|
|
T3 = reinterpret<f64>(0x3F991DF3908C33CE), // 0x191df3908c33ce.0p-58
|
|
T4 = reinterpret<f64>(0x3F685DADFCECF44E), // 0x185dadfcecf44e.0p-61
|
|
T5 = reinterpret<f64>(0x3F8362B9BF971BCD); // 0x1362b9bf971bcd.0p-59
|
|
|
|
var z = x * x;
|
|
var r = T4 + z * T5;
|
|
var t = T2 + z * T3;
|
|
var w = z * z;
|
|
var s = z * x;
|
|
var u = T0 + z * T1;
|
|
|
|
r = (x + s * u) + (s * w) * (t + w * r);
|
|
return <f32>(odd ? -1 / r : r);
|
|
}
|
|
|
|
// See: jdh8/metallic/src/math/float/log2f.c and jdh8/metallic/src/math/float/kernel/atanh.h
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function log2f(x: f64): f64 {
|
|
const
|
|
log2e = reinterpret<f64>(0x3FF71547652B82FE), // 1.44269504088896340736
|
|
c0 = reinterpret<f64>(0x3FD555554FD9CAEF), // 0.33333332822728226129
|
|
c1 = reinterpret<f64>(0x3FC999A7A8AF4132), // 0.20000167595436263505
|
|
c2 = reinterpret<f64>(0x3FC2438D79437030), // 0.14268654271188685375
|
|
c3 = reinterpret<f64>(0x3FBE2F663B001C97); // 0.11791075649681414150
|
|
|
|
var i = reinterpret<i64>(x);
|
|
var exponent = (i - 0x3FE6A09E667F3BCD) >> 52;
|
|
x = reinterpret<f64>(i - (exponent << 52));
|
|
x = (x - 1) / (x + 1);
|
|
var xx = x * x;
|
|
var y = x + x * xx * (c0 + c1 * xx + (c2 + c3 * xx) * (xx * xx));
|
|
return (2 * log2e) * y + <f64>exponent;
|
|
}
|
|
|
|
// See: jdh8/metallic/src/math/float/exp2f.h and jdh8/metallic/blob/master/src/math/float/kernel/exp2f.h
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
function exp2f(x: f64): f64 {
|
|
const
|
|
c0 = reinterpret<f64>(0x3FE62E4302FCC24A), // 6.931471880289532425e-1
|
|
c1 = reinterpret<f64>(0x3FCEBFBE07D97B91), // 2.402265108421173406e-1
|
|
c2 = reinterpret<f64>(0x3FAC6AF6CCFC1A65), // 5.550357105498874537e-2
|
|
c3 = reinterpret<f64>(0x3F83B29E3CE9AEF6), // 9.618030771171497658e-3
|
|
c4 = reinterpret<f64>(0x3F55F0896145A89F), // 1.339086685300950937e-3
|
|
c5 = reinterpret<f64>(0x3F2446C81E384864); // 1.546973499989028719e-4
|
|
|
|
if (x < -1022) return 0;
|
|
if (x >= 1024) return Infinity;
|
|
|
|
var n = nearest(x);
|
|
x -= n;
|
|
var xx = x * x;
|
|
var y = 1 + x * (c0 + c1 * x + (c2 + c3 * x) * xx + (c4 + c5 * x) * (xx * xx));
|
|
return reinterpret<f64>(reinterpret<i64>(y) + (<i64>n << 52));
|
|
}
|
|
|
|
export namespace NativeMathf {
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const E = <f32>NativeMath.E;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LN2 = <f32>NativeMath.LN2;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LN10 = <f32>NativeMath.LN10;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LOG2E = <f32>NativeMath.LOG2E;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const LOG10E = <f32>NativeMath.LOG10E;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const PI = <f32>NativeMath.PI;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const SQRT1_2 = <f32>NativeMath.SQRT1_2;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export const SQRT2 = <f32>NativeMath.SQRT2;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export var sincos_sin: f32 = 0;
|
|
|
|
// @ts-ignore: decorator
|
|
@lazy
|
|
export var sincos_cos: f32 = 0;
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function abs(x: f32): f32 {
|
|
return builtin_abs<f32>(x);
|
|
}
|
|
|
|
export function acos(x: f32): f32 { // see: musl/src/math/acosf.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
pio2_hi = reinterpret<f32>(0x3FC90FDA), // 1.5707962513e+00f
|
|
pio2_lo = reinterpret<f32>(0x33A22168), // 7.5497894159e-08f
|
|
Ox1p_120f = reinterpret<f32>(0x03800000); // 0x1p-120f
|
|
|
|
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)) { // |x| < 2, invalid if x < 1
|
|
let xm1 = x - 1;
|
|
return log1p(xm1 + builtin_sqrt(xm1 * (xm1 + 2)));
|
|
}
|
|
if (u < 0x3F800000 + (12 << 23)) { // 2 <= x < 0x1p12
|
|
return log(2 * x - 1 / (x + builtin_sqrt<f32>(x * x - 1)));
|
|
}
|
|
// x >= 0x1p12 or x <= -2 or NaN
|
|
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); // 0x1p-120f
|
|
|
|
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); // 0x1p-120f
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var sx = x;
|
|
ix &= 0x7FFFFFFF;
|
|
var z: f32;
|
|
if (ix >= 0x4C800000) {
|
|
if (isNaN(x)) return x;
|
|
z = atanhi3 + Ox1p_120f;
|
|
return builtin_copysign(z, sx);
|
|
}
|
|
var id: i32;
|
|
if (ix < 0x3EE00000) {
|
|
if (ix < 0x39800000) return x;
|
|
id = -1;
|
|
} else {
|
|
x = builtin_abs<f32>(x);
|
|
if (ix < 0x3F980000) {
|
|
if (ix < 0x3F300000) {
|
|
id = 0;
|
|
x = (2.0 * x - 1.0) / (2.0 + x);
|
|
} else {
|
|
id = 1;
|
|
x = (x - 1.0) / (x + 1.0);
|
|
}
|
|
} else {
|
|
if (ix < 0x401C0000) {
|
|
id = 2;
|
|
x = (x - 1.5) / (1.0 + 1.5 * x);
|
|
} else {
|
|
id = 3;
|
|
x = -1.0 / x;
|
|
}
|
|
}
|
|
}
|
|
z = x * x;
|
|
var w = z * z;
|
|
var s1 = z * (aT0 + w * (aT2 + w * aT4));
|
|
var s2 = w * (aT1 + w * aT3);
|
|
var s3 = x * (s1 + s2);
|
|
if (id < 0) return x - s3;
|
|
switch (id) {
|
|
case 0: { z = atanhi0 - ((s3 - atanlo0) - x); break; }
|
|
case 1: { z = atanhi1 - ((s3 - atanlo1) - x); break; }
|
|
case 2: { z = atanhi2 - ((s3 - atanlo2) - x); break; }
|
|
case 3: { z = atanhi3 - ((s3 - atanlo3) - x); break; }
|
|
default: unreachable();
|
|
}
|
|
return builtin_copysign(z, sx);
|
|
}
|
|
|
|
export function atanh(x: f32): f32 { // see: musl/src/math/atanhf.c
|
|
var u = reinterpret<u32>(x);
|
|
var y = builtin_abs(x);
|
|
if (u < 0x3F800000 - (1 << 23)) {
|
|
if (u >= 0x3F800000 - (32 << 23)) y = 0.5 * log1p(2 * y * (1.0 + y / (1 - y)));
|
|
} else y = 0.5 * log1p(2 * (y / (1 - y)));
|
|
return builtin_copysign(y, x);
|
|
}
|
|
|
|
export function atan2(y: f32, x: f32): f32 { // see: musl/src/math/atan2f.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
pi = reinterpret<f32>(0x40490FDB), // 3.1415927410e+00f
|
|
pi_lo = reinterpret<f32>(0xB3BBBD2E); // -8.7422776573e-08f
|
|
|
|
if (isNaN(x) || isNaN(y)) return x + y;
|
|
var ix = reinterpret<u32>(x);
|
|
var iy = reinterpret<u32>(y);
|
|
if (ix == 0x3F800000) return atan(y);
|
|
var m = <u32>(((iy >> 31) & 1) | ((ix >> 30) & 2));
|
|
ix &= 0x7FFFFFFF;
|
|
iy &= 0x7FFFFFFF;
|
|
if (iy == 0) {
|
|
switch (m) {
|
|
case 0:
|
|
case 1: return y;
|
|
case 2: return pi;
|
|
case 3: return -pi;
|
|
}
|
|
}
|
|
if (ix == 0) return m & 1 ? -pi / 2 : pi / 2;
|
|
if (ix == 0x7F800000) {
|
|
if (iy == 0x7F800000) {
|
|
let t: f32 = m & 2 ? 3 * pi / 4 : pi / 4;
|
|
return m & 1 ? -t : t;
|
|
} else {
|
|
let t: f32 = m & 2 ? pi : 0.0;
|
|
return m & 1 ? -t : t;
|
|
}
|
|
}
|
|
if (ix + (26 << 23) < iy || iy == 0x7F800000) return m & 1 ? -pi / 2 : pi / 2;
|
|
var z: f32;
|
|
if ((m & 2) && iy + (26 << 23) < ix) z = 0.0;
|
|
else z = atan(builtin_abs<f32>(y / x));
|
|
switch (m) {
|
|
case 0: return z;
|
|
case 1: return -z;
|
|
case 2: return pi - (z - pi_lo);
|
|
case 3: return (z - pi_lo) - pi;
|
|
}
|
|
unreachable();
|
|
return 0;
|
|
}
|
|
|
|
export function cbrt(x: f32): f32 { // see: musl/src/math/cbrtf.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
B1 = <u32>709958130,
|
|
B2 = <u32>642849266,
|
|
Ox1p24f = reinterpret<f32>(0x4B800000);
|
|
|
|
var u = reinterpret<u32>(x);
|
|
var hx = u & 0x7FFFFFFF;
|
|
if (hx >= 0x7F800000) return x + x;
|
|
if (hx < 0x00800000) {
|
|
if (hx == 0) return x;
|
|
u = reinterpret<u32>(x * Ox1p24f);
|
|
hx = u & 0x7FFFFFFF;
|
|
hx = hx / 3 + B2;
|
|
} else {
|
|
hx = hx / 3 + B1;
|
|
}
|
|
u &= 0x80000000;
|
|
u |= hx;
|
|
var t = <f64>reinterpret<f32>(u);
|
|
var r = t * t * t;
|
|
t = t * (<f64>x + x + r) / (x + r + r);
|
|
r = t * t * t;
|
|
t = t * (<f64>x + x + r) / (x + r + r);
|
|
return <f32>t;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function ceil(x: f32): f32 {
|
|
return builtin_ceil<f32>(x);
|
|
}
|
|
|
|
export function clz32(x: f32): f32 {
|
|
if (!isFinite(x)) return 32;
|
|
return <f32>builtin_clz(dtoi32(x));
|
|
}
|
|
|
|
export function cos(x: f32): f32 { // see: musl/src/math/cosf.c
|
|
const
|
|
c1pio2 = reinterpret<f64>(0x3FF921FB54442D18), // M_PI_2 * 1
|
|
c2pio2 = reinterpret<f64>(0x400921FB54442D18), // M_PI_2 * 2
|
|
c3pio2 = reinterpret<f64>(0x4012D97C7F3321D2), // M_PI_2 * 3
|
|
c4pio2 = reinterpret<f64>(0x401921FB54442D18); // M_PI_2 * 4
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var sign = ix >> 31;
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
if (ix <= 0x3F490FDA) { // |x| ~<= π/4
|
|
if (ix < 0x39800000) { // |x| < 2**-12
|
|
// raise inexact if x != 0
|
|
return 1;
|
|
}
|
|
return cos_kernf(x);
|
|
}
|
|
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (ix <= 0x407B53D1) { // |x| ~<= 5π/4
|
|
if (ix > 0x4016CBE3) { // |x| ~> 3π/4
|
|
return -cos_kernf(sign ? x + c2pio2 : x - c2pio2);
|
|
} else {
|
|
return sign ? sin_kernf(x + c1pio2) : sin_kernf(c1pio2 - x);
|
|
}
|
|
}
|
|
if (ix <= 0x40E231D5) { // |x| ~<= 9π/4
|
|
if (ix > 0x40AFEDDF) { // |x| ~> 7π/4
|
|
return cos_kernf(sign ? x + c4pio2 : x - c4pio2);
|
|
} else {
|
|
return sign ? sin_kernf(-x - c3pio2) : sin_kernf(x - c3pio2);
|
|
}
|
|
}
|
|
}
|
|
|
|
// cos(Inf or NaN) is NaN
|
|
if (ix >= 0x7F800000) return x - x;
|
|
|
|
// general argument reduction needed
|
|
var n = rempio2f(x, ix, sign);
|
|
var y = rempio2f_y;
|
|
|
|
var t = n & 1 ? sin_kernf(y) : cos_kernf(y);
|
|
return (n + 1) & 2 ? -t : t;
|
|
}
|
|
|
|
export function cosh(x: f32): f32 { // see: musl/src/math/coshf.c
|
|
var u = reinterpret<u32>(x);
|
|
u &= 0x7FFFFFFF;
|
|
x = reinterpret<f32>(u);
|
|
if (u < 0x3F317217) {
|
|
if (u < 0x3F800000 - (12 << 23)) return 1;
|
|
let t = expm1(x);
|
|
// return 1 + t * t / (2 * (1 + t));
|
|
return 1 + t * t / (2 + 2 * t);
|
|
}
|
|
if (u < 0x42B17217) {
|
|
let t = exp(x);
|
|
// return 0.5 * (t + 1 / t);
|
|
return 0.5 * t + 0.5 / t;
|
|
}
|
|
return expo2f(x, 1);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function floor(x: f32): f32 {
|
|
return builtin_floor<f32>(x);
|
|
}
|
|
|
|
export function exp(x: f32): f32 { // see: musl/src/math/expf.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return expf_lut(x);
|
|
} else {
|
|
const
|
|
ln2hi = reinterpret<f32>(0x3F317200), // 6.9314575195e-1f
|
|
ln2lo = reinterpret<f32>(0x35BFBE8E), // 1.4286067653e-6f
|
|
invln2 = reinterpret<f32>(0x3FB8AA3B), // 1.4426950216e+0f
|
|
P1 = reinterpret<f32>(0x3E2AAA8F), // 1.6666625440e-1f
|
|
P2 = reinterpret<f32>(0xBB355215), // -2.7667332906e-3f
|
|
Ox1p127f = reinterpret<f32>(0x7F000000); // 0x1p+127f
|
|
|
|
let hx = reinterpret<u32>(x);
|
|
let sign_ = <i32>(hx >> 31);
|
|
hx &= 0x7FFFFFFF;
|
|
if (hx >= 0x42AEAC50) {
|
|
if (hx > 0x7F800000) return x; // NaN
|
|
if (hx >= 0x42B17218) {
|
|
if (!sign_) return x * Ox1p127f;
|
|
else if (hx >= 0x42CFF1B5) return 0;
|
|
}
|
|
}
|
|
let hi: f32, lo: f32;
|
|
let k: i32;
|
|
if (hx > 0x3EB17218) {
|
|
if (hx > 0x3F851592) {
|
|
k = <i32>(invln2 * x + builtin_copysign<f32>(0.5, x));
|
|
} else {
|
|
k = 1 - (sign_ << 1);
|
|
}
|
|
hi = x - <f32>k * ln2hi;
|
|
lo = <f32>k * ln2lo;
|
|
x = hi - lo;
|
|
} else if (hx > 0x39000000) {
|
|
k = 0;
|
|
hi = x;
|
|
lo = 0;
|
|
} else {
|
|
return 1 + x;
|
|
}
|
|
let xx = x * x;
|
|
let c = x - xx * (P1 + xx * P2);
|
|
let y: f32 = 1 + (x * c / (2 - c) - lo + hi);
|
|
return k == 0 ? y : scalbn(y, k);
|
|
}
|
|
}
|
|
|
|
export function exp2(x: f32): f32 {
|
|
return exp2f_lut(x);
|
|
}
|
|
|
|
export function expm1(x: f32): f32 { // see: musl/src/math/expm1f.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
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); // 0x1p+127f
|
|
|
|
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 (hx > 0x42B17217) { // x > log(FLT_MAX)
|
|
x *= Ox1p127f;
|
|
return x;
|
|
}
|
|
}
|
|
var c: f32 = 0.0, t: f32, k: i32;
|
|
if (hx > 0x3EB17218) {
|
|
k = select<i32>(
|
|
1 - (sign_ << 1),
|
|
<i32>(invln2 * x + builtin_copysign<f32>(0.5, x)),
|
|
hx < 0x3F851592
|
|
);
|
|
t = <f32>k;
|
|
let hi = x - t * ln2_hi;
|
|
let lo = t * ln2_lo;
|
|
x = hi - lo;
|
|
c = (hi - x) - lo;
|
|
} else if (hx < 0x33000000) {
|
|
return x;
|
|
} else k = 0;
|
|
var hfx: f32 = 0.5 * x;
|
|
var hxs: f32 = x * hfx;
|
|
var r1: f32 = 1.0 + hxs * (Q1 + hxs * Q2);
|
|
t = 3.0 - r1 * hfx;
|
|
var e = hxs * ((r1 - t) / (6.0 - x * t));
|
|
if (k == 0) return x - (x * e - hxs);
|
|
e = x * (e - c) - c;
|
|
e -= hxs;
|
|
if (k == -1) return 0.5 * (x - e) - 0.5;
|
|
if (k == 1) {
|
|
if (x < -0.25) return -2.0 * (e - (x + 0.5));
|
|
return 1.0 + 2.0 * (x - e);
|
|
}
|
|
u = (0x7F + k) << 23;
|
|
var twopk = reinterpret<f32>(u);
|
|
var y: f32;
|
|
if (k < 0 || k > 56) {
|
|
y = x - e + 1.0;
|
|
if (k == 128) y = y * 2.0 * Ox1p127f;
|
|
else y = y * twopk;
|
|
return y - 1.0;
|
|
}
|
|
u = (0x7F - k) << 23;
|
|
y = reinterpret<f32>(u);
|
|
if (k < 20) y = (1 - y) - e;
|
|
else y = 1 - (e + y);
|
|
return (x + y) * twopk;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function fround(x: f32): f32 {
|
|
return x;
|
|
}
|
|
|
|
export function hypot(x: f32, y: f32): f32 { // see: musl/src/math/hypotf.c
|
|
const
|
|
Ox1p90f = reinterpret<f32>(0x6C800000),
|
|
Ox1p_90f = reinterpret<f32>(0x12800000);
|
|
|
|
var ux = reinterpret<u32>(x);
|
|
var uy = reinterpret<u32>(y);
|
|
ux &= 0x7FFFFFFF;
|
|
uy &= 0x7FFFFFFF;
|
|
if (ux < uy) {
|
|
let ut = ux;
|
|
ux = uy;
|
|
uy = ut;
|
|
}
|
|
x = reinterpret<f32>(ux);
|
|
y = reinterpret<f32>(uy);
|
|
if (uy == 0xFF << 23) return y;
|
|
if (ux >= 0xFF << 23 || uy == 0 || ux - uy >= 25 << 23) return x + y;
|
|
var z: f32 = 1;
|
|
if (ux >= (0x7F + 60) << 23) {
|
|
z = Ox1p90f;
|
|
x *= Ox1p_90f;
|
|
y *= Ox1p_90f;
|
|
} else if (uy < (0x7F - 60) << 23) {
|
|
z = Ox1p_90f;
|
|
x *= Ox1p90f;
|
|
y *= Ox1p90f;
|
|
}
|
|
return z * builtin_sqrt<f32>(<f32>(<f64>x * x + <f64>y * y));
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function imul(x: f32, y: f32): f32 {
|
|
/*
|
|
* Wasm (MVP) and JS have different approaches for double->int conversions.
|
|
*
|
|
* For emulate JS conversion behavior and avoid trapping from wasm we should modulate by MAX_INT
|
|
* our float-point arguments before actual convertion to integers.
|
|
*/
|
|
if (!isFinite(x + y)) return 0;
|
|
return <f32>(dtoi32(x) * dtoi32(y));
|
|
}
|
|
|
|
export function log(x: f32): f32 { // see: musl/src/math/logf.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return logf_lut(x);
|
|
} else {
|
|
const
|
|
ln2_hi = reinterpret<f32>(0x3F317180), // 6.9313812256e-01f
|
|
ln2_lo = reinterpret<f32>(0x3717F7D1), // 9.0580006145e-06f
|
|
Lg1 = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f
|
|
Lg2 = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f
|
|
Lg3 = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f
|
|
Lg4 = reinterpret<f32>(0x3E789E26), // 0xf89e26.0p-26f
|
|
Ox1p25f = reinterpret<f32>(0x4C000000);
|
|
|
|
let u = reinterpret<u32>(x);
|
|
let k = 0;
|
|
if (u < 0x00800000 || <bool>(u >> 31)) {
|
|
if (u << 1 == 0) return -1 / (x * x);
|
|
if (u >> 31) return (x - x) / 0;
|
|
k -= 25;
|
|
x *= Ox1p25f;
|
|
u = reinterpret<u32>(x);
|
|
} else if (u >= 0x7F800000) {
|
|
return x;
|
|
} else if (u == 0x3F800000) {
|
|
return 0;
|
|
}
|
|
u += 0x3F800000 - 0x3F3504F3;
|
|
k += <u32>(<i32>u >> 23) - 0x7F;
|
|
u = (u & 0x007FFFFF) + 0x3F3504F3;
|
|
x = reinterpret<f32>(u);
|
|
let f = x - 1.0;
|
|
let s = f / (2.0 + f);
|
|
let z = s * s;
|
|
let w = z * z;
|
|
let t1 = w * (Lg2 + w * Lg4);
|
|
let t2 = z * (Lg1 + w * Lg3);
|
|
let r = t2 + t1;
|
|
let hfsq = <f32>0.5 * f * f;
|
|
let dk = <f32>k;
|
|
return s * (hfsq + r) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
|
|
}
|
|
}
|
|
|
|
export function log10(x: f32): f32 { // see: musl/src/math/log10f.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
ivln10hi = reinterpret<f32>(0x3EDE6000), // 4.3432617188e-01f
|
|
ivln10lo = reinterpret<f32>(0xB804EAD9), // -3.1689971365e-05f
|
|
log10_2hi = reinterpret<f32>(0x3E9A2080), // 3.0102920532e-01f
|
|
log10_2lo = reinterpret<f32>(0x355427DB), // 7.9034151668e-07f
|
|
Lg1 = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f, 0.66666662693f
|
|
Lg2 = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f, 0.40000972152f
|
|
Lg3 = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f, 0.28498786688f
|
|
Lg4 = reinterpret<f32>(0x3E789E26), // 0xf89e26.0p-26f, 0.24279078841f
|
|
Ox1p25f = reinterpret<f32>(0x4C000000); // 0x1p25f
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var k = 0;
|
|
if (ix < 0x00800000 || <bool>(ix >> 31)) {
|
|
if (ix << 1 == 0) return -1 / (x * x);
|
|
if (ix >> 31) return (x - x) / 0.0;
|
|
k -= 25;
|
|
x *= Ox1p25f;
|
|
ix = reinterpret<u32>(x);
|
|
} else if (ix >= 0x7F800000) {
|
|
return x;
|
|
} else if (ix == 0x3F800000) {
|
|
return 0;
|
|
}
|
|
ix += 0x3F800000 - 0x3F3504F3;
|
|
k += <i32>(ix >> 23) - 0x7F;
|
|
ix = (ix & 0x007FFFFF) + 0x3F3504F3;
|
|
x = reinterpret<f32>(ix);
|
|
var f = x - 1.0;
|
|
var s = f / (2.0 + f);
|
|
var z = s * s;
|
|
var w = z * z;
|
|
var t1 = w * (Lg2 + w * Lg4);
|
|
var t2 = z * (Lg1 + w * Lg3);
|
|
var r = t2 + t1;
|
|
var hfsq: f32 = 0.5 * f * f;
|
|
var hi = f - hfsq;
|
|
ix = reinterpret<u32>(hi);
|
|
ix &= 0xFFFFF000;
|
|
hi = reinterpret<f32>(ix);
|
|
var lo = f - hi - hfsq + s * (hfsq + r);
|
|
var dk = <f32>k;
|
|
return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi + hi * ivln10hi + dk * log10_2hi;
|
|
}
|
|
|
|
export function log1p(x: f32): f32 { // see: musl/src/math/log1pf.c and SUN COPYRIGHT NOTICE above
|
|
const
|
|
ln2_hi = reinterpret<f32>(0x3F317180), // 6.9313812256e-01
|
|
ln2_lo = reinterpret<f32>(0x3717F7D1), // 9.0580006145e-06
|
|
Lg1 = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f, 0.66666662693f
|
|
Lg2 = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f, 0.40000972152f
|
|
Lg3 = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f, 0.28498786688f
|
|
Lg4 = reinterpret<f32>(0x3E789E26); // 0xf89e26.0p-26f, 0.24279078841f
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var c: f32 = 0, f: f32 = 0;
|
|
var k: i32 = 1;
|
|
if (ix < 0x3ED413D0 || <bool>(ix >> 31)) {
|
|
if (ix >= 0xBF800000) {
|
|
if (x == -1) return x / 0.0;
|
|
return (x - x) / 0.0;
|
|
}
|
|
if (ix << 1 < 0x33800000 << 1) return x;
|
|
if (ix <= 0xBE95F619) {
|
|
k = 0;
|
|
c = 0;
|
|
f = x;
|
|
}
|
|
} else if (ix >= 0x7F800000) return x;
|
|
if (k) {
|
|
let uf: f32 = 1 + x;
|
|
let iu = reinterpret<u32>(uf);
|
|
iu += 0x3F800000 - 0x3F3504F3;
|
|
k = <i32>(iu >> 23) - 0x7F;
|
|
if (k < 25) {
|
|
c = k >= 2 ? 1 - (uf - x) : x - (uf - 1);
|
|
c /= uf;
|
|
} else c = 0;
|
|
iu = (iu & 0x007FFFFF) + 0x3F3504F3;
|
|
f = reinterpret<f32>(iu) - 1;
|
|
}
|
|
var s = f / (2.0 + f);
|
|
var z = s * s;
|
|
var w = z * z;
|
|
var t1 = w * (Lg2 + w * Lg4);
|
|
var t2 = z * (Lg1 + w * Lg3);
|
|
var r = t2 + t1;
|
|
var hfsq: f32 = 0.5 * f * f;
|
|
var dk = <f32>k;
|
|
return s * (hfsq + r) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
|
|
}
|
|
|
|
export function log2(x: f32): f32 { // see: musl/src/math/log2f.c and SUN COPYRIGHT NOTICE above
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
return log2f_lut(x);
|
|
} else {
|
|
const
|
|
ivln2hi = reinterpret<f32>(0x3FB8B000), // 1.4428710938e+00f
|
|
ivln2lo = reinterpret<f32>(0xB9389AD4), // -1.7605285393e-04
|
|
Lg1 = reinterpret<f32>(0x3F2AAAAA), // 0xaaaaaa.0p-24f, 0.66666662693f
|
|
Lg2 = reinterpret<f32>(0x3ECCCE13), // 0xccce13.0p-25f, 0.40000972152f
|
|
Lg3 = reinterpret<f32>(0x3E91E9EE), // 0x91e9ee.0p-25f, 0.28498786688f
|
|
Lg4 = reinterpret<f32>(0x3E789E26), // 0xf89e26.0p-26f, 0.24279078841f
|
|
Ox1p25f = reinterpret<f32>(0x4C000000); // 0x1p25f
|
|
|
|
let ix = reinterpret<u32>(x);
|
|
let k: i32 = 0;
|
|
if (ix < 0x00800000 || <bool>(ix >> 31)) {
|
|
if (ix << 1 == 0) return -1 / (x * x);
|
|
if (ix >> 31) return (x - x) / 0.0;
|
|
k -= 25;
|
|
x *= Ox1p25f;
|
|
ix = reinterpret<u32>(x);
|
|
} else if (ix >= 0x7F800000) {
|
|
return x;
|
|
} else if (ix == 0x3F800000) {
|
|
return 0;
|
|
}
|
|
ix += 0x3F800000 - 0x3F3504F3;
|
|
k += <i32>(ix >> 23) - 0x7F;
|
|
ix = (ix & 0x007FFFFF) + 0x3F3504F3;
|
|
x = reinterpret<f32>(ix);
|
|
let f = x - 1.0;
|
|
let s = f / (2.0 + f);
|
|
let z = s * s;
|
|
let w = z * z;
|
|
let t1 = w * (Lg2 + w * Lg4);
|
|
let t2 = z * (Lg1 + w * Lg3);
|
|
let r = t2 + t1;
|
|
let hfsq: f32 = 0.5 * f * f;
|
|
let hi = f - hfsq;
|
|
let u = reinterpret<u32>(hi);
|
|
u &= 0xFFFFF000;
|
|
hi = reinterpret<f32>(u);
|
|
let lo: f32 = f - hi - hfsq + s * (hfsq + r);
|
|
let dk = <f32>k;
|
|
return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + dk;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function max(value1: f32, value2: f32): f32 {
|
|
return builtin_max<f32>(value1, value2);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function min(value1: f32, value2: f32): f32 {
|
|
return builtin_min<f32>(value1, value2);
|
|
}
|
|
|
|
export function pow(x: f32, y: f32): f32 {
|
|
// TODO: remove this fast pathes after introduced own mid-end IR with "stdlib call simplify" transforms
|
|
if (builtin_abs<f32>(y) <= 2) {
|
|
if (y == 2.0) return x * x;
|
|
if (y == 0.5) {
|
|
return select<f32>(
|
|
builtin_abs<f32>(builtin_sqrt<f32>(x)),
|
|
Infinity,
|
|
x != -Infinity
|
|
);
|
|
}
|
|
if (y == -1.0) return 1 / x;
|
|
if (y == 1.0) return x;
|
|
if (y == 0.0) return 1.0;
|
|
}
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
// see: musl/src/math/powf.c
|
|
return powf_lut(x, y);
|
|
} else {
|
|
// based on: jdh8/metallic/src/math/float/powf.c
|
|
if (y == 0) return 1;
|
|
// @ts-ignore: cast
|
|
if (isNaN(x) | isNaN(y)) {
|
|
return NaN;
|
|
}
|
|
let sign: u32 = 0;
|
|
let uy = reinterpret<u32>(y);
|
|
let ux = reinterpret<u32>(x);
|
|
let sx = ux >> 31;
|
|
ux &= 0x7FFFFFFF;
|
|
if (sx && nearest(y) == y) {
|
|
x = -x;
|
|
sx = 0;
|
|
sign = u32(nearest(y * 0.5) != y * 0.5) << 31;
|
|
}
|
|
let m: u32;
|
|
if (ux == 0x3F800000) { // x == 1
|
|
m = sx | u32((uy & 0x7FFFFFFF) == 0x7F800000) ? 0x7FC00000 : 0x3F800000;
|
|
} else if (ux == 0) {
|
|
m = uy >> 31 ? 0x7F800000 : 0;
|
|
} else if (ux == 0x7F800000) {
|
|
m = uy >> 31 ? 0 : 0x7F800000;
|
|
} else if (sx) {
|
|
m = 0x7FC00000;
|
|
} else {
|
|
m = reinterpret<u32>(<f32>exp2f(<f64>y * log2f(x)));
|
|
}
|
|
return reinterpret<f32>(m | sign);
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function seedRandom(value: i64): void {
|
|
NativeMath.seedRandom(value);
|
|
}
|
|
|
|
// Using xoroshiro64starstar from http://xoshiro.di.unimi.it/xoroshiro64starstar.c
|
|
export function random(): f32 {
|
|
if (!random_seeded) seedRandom(reinterpret<i64>(seed()));
|
|
|
|
var s0 = random_state0_32;
|
|
var s1 = random_state1_32;
|
|
var r = rotl<u32>(s0 * 0x9E3779BB, 5) * 5;
|
|
|
|
s1 ^= s0;
|
|
random_state0_32 = rotl<u32>(s0, 26) ^ s1 ^ (s1 << 9);
|
|
random_state1_32 = rotl<u32>(s1, 13);
|
|
|
|
return reinterpret<f32>((r >> 9) | (127 << 23)) - 1.0;
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function round(x: f32): f32 {
|
|
let roundUp = builtin_ceil<f32>(x);
|
|
return select<f32>(roundUp, roundUp - 1.0, roundUp - 0.5 <= x);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function sign(x: f32): f32 {
|
|
if (ASC_SHRINK_LEVEL > 0) {
|
|
return builtin_abs(x) > 0 ? builtin_copysign<f32>(1, x) : x;
|
|
} else {
|
|
return x > 0 ? 1 : x < 0 ? -1 : x;
|
|
}
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function signbit(x: f32): bool {
|
|
return <bool>(reinterpret<u32>(x) >>> 31);
|
|
}
|
|
|
|
export function sin(x: f32): f32 { // see: musl/src/math/sinf.c
|
|
const
|
|
s1pio2 = reinterpret<f64>(0x3FF921FB54442D18), // M_PI_2 * 1
|
|
s2pio2 = reinterpret<f64>(0x400921FB54442D18), // M_PI_2 * 2
|
|
s3pio2 = reinterpret<f64>(0x4012D97C7F3321D2), // M_PI_2 * 3
|
|
s4pio2 = reinterpret<f64>(0x401921FB54442D18); // M_PI_2 * 4
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var sign = ix >> 31;
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
if (ix <= 0x3F490FDA) { // |x| ~<= π/4
|
|
if (ix < 0x39800000) { // |x| < 2**-12
|
|
return x;
|
|
}
|
|
return sin_kernf(x);
|
|
}
|
|
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (ix <= 0x407B53D1) { // |x| ~<= 5π/4
|
|
if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
|
|
return sign ? -cos_kernf(x + s1pio2) : cos_kernf(x - s1pio2);
|
|
}
|
|
return sin_kernf(-(sign ? x + s2pio2 : x - s2pio2));
|
|
}
|
|
|
|
if (ix <= 0x40E231D5) { // |x| ~<= 9π/4
|
|
if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
|
|
return sign ? cos_kernf(x + s3pio2) : -cos_kernf(x - s3pio2);
|
|
}
|
|
return sin_kernf(sign ? x + s4pio2 : x - s4pio2);
|
|
}
|
|
}
|
|
|
|
// sin(Inf or NaN) is NaN
|
|
if (ix >= 0x7F800000) return x - x;
|
|
|
|
var n = rempio2f(x, ix, sign);
|
|
var y = rempio2f_y;
|
|
|
|
var t = n & 1 ? cos_kernf(y) : sin_kernf(y);
|
|
return n & 2 ? -t : t;
|
|
}
|
|
|
|
export function sinh(x: f32): f32 { // see: musl/src/math/sinhf.c
|
|
var u = reinterpret<u32>(x) & 0x7FFFFFFF;
|
|
var a = reinterpret<f32>(u);
|
|
var h = builtin_copysign<f32>(0.5, x);
|
|
if (u < 0x42B17217) {
|
|
let t = expm1(a);
|
|
if (u < 0x3F800000) {
|
|
if (u < 0x3F800000 - (12 << 23)) return x;
|
|
return h * (2 * t - t * t / (t + 1));
|
|
}
|
|
return h * (t + t / (t + 1));
|
|
}
|
|
return expo2f(a, 2 * h);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function sqrt(x: f32): f32 {
|
|
return builtin_sqrt<f32>(x);
|
|
}
|
|
|
|
export function tan(x: f32): f32 { // see: musl/src/math/tanf.c
|
|
const
|
|
t1pio2 = reinterpret<f64>(0x3FF921FB54442D18), // 1 * M_PI_2
|
|
t2pio2 = reinterpret<f64>(0x400921FB54442D18), // 2 * M_PI_2
|
|
t3pio2 = reinterpret<f64>(0x4012D97C7F3321D2), // 3 * M_PI_2
|
|
t4pio2 = reinterpret<f64>(0x401921FB54442D18); // 4 * M_PI_2
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var sign = ix >> 31;
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
if (ix <= 0x3F490FDA) { // |x| ~<= π/4
|
|
if (ix < 0x39800000) { // |x| < 2**-12
|
|
return x;
|
|
}
|
|
return tan_kernf(x, 0);
|
|
}
|
|
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (ix <= 0x407B53D1) { // |x| ~<= 5π/4
|
|
if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
|
|
return tan_kernf((sign ? x + t1pio2 : x - t1pio2), 1);
|
|
} else {
|
|
return tan_kernf((sign ? x + t2pio2 : x - t2pio2), 0);
|
|
}
|
|
}
|
|
if (ix <= 0x40E231D5) { // |x| ~<= 9π/4
|
|
if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
|
|
return tan_kernf((sign ? x + t3pio2 : x - t3pio2), 1);
|
|
} else {
|
|
return tan_kernf((sign ? x + t4pio2 : x - t4pio2), 0);
|
|
}
|
|
}
|
|
}
|
|
|
|
// tan(Inf or NaN) is NaN
|
|
if (ix >= 0x7F800000) return x - x;
|
|
|
|
// argument reduction
|
|
var n = rempio2f(x, ix, sign);
|
|
var y = rempio2f_y;
|
|
return tan_kernf(y, n & 1);
|
|
}
|
|
|
|
export function tanh(x: f32): f32 { // see: musl/src/math/tanhf.c
|
|
var u = reinterpret<u32>(x);
|
|
u &= 0x7FFFFFFF;
|
|
var y = reinterpret<f32>(u);
|
|
var t: f32;
|
|
if (u > 0x3F0C9F54) {
|
|
if (u > 0x41200000) t = 1 + 0 / y;
|
|
else {
|
|
t = expm1(2 * y);
|
|
t = 1 - 2 / (t + 2);
|
|
}
|
|
} else if (u > 0x3E82C578) {
|
|
t = expm1(2 * y);
|
|
t = t / (t + 2);
|
|
} else if (u >= 0x00800000) {
|
|
t = expm1(-2 * y);
|
|
t = -t / (t + 2);
|
|
} else t = y;
|
|
return builtin_copysign<f32>(t, x);
|
|
}
|
|
|
|
// @ts-ignore: decorator
|
|
@inline
|
|
export function trunc(x: f32): f32 {
|
|
return builtin_trunc<f32>(x);
|
|
}
|
|
|
|
export function scalbn(x: f32, n: i32): f32 { // see: https://git.musl-libc.org/cgit/musl/tree/src/math/scalbnf.c
|
|
const
|
|
Ox1p24f = reinterpret<f32>(0x4B800000),
|
|
Ox1p127f = reinterpret<f32>(0x7F000000),
|
|
Ox1p_126f = reinterpret<f32>(0x00800000);
|
|
|
|
var y = x;
|
|
if (n > 127) {
|
|
y *= Ox1p127f;
|
|
n -= 127;
|
|
if (n > 127) {
|
|
y *= Ox1p127f;
|
|
n = builtin_min<i32>(n - 127, 127);
|
|
}
|
|
} else if (n < -126) {
|
|
y *= Ox1p_126f * Ox1p24f;
|
|
n += 126 - 24;
|
|
if (n < -126) {
|
|
y *= Ox1p_126f * Ox1p24f;
|
|
n = builtin_max<i32>(n + 126 - 24, -126);
|
|
}
|
|
}
|
|
return y * reinterpret<f32>(<u32>(0x7F + n) << 23);
|
|
}
|
|
|
|
export function mod(x: f32, y: f32): f32 { // see: musl/src/math/fmodf.c
|
|
if (builtin_abs<f32>(y) == 1.0) {
|
|
// x % 1, x % -1 ==> sign(x) * abs(x - 1.0 * trunc(x / 1.0))
|
|
// TODO: move this rule to compiler's optimization pass.
|
|
// It could be apply for any x % C_pot, where "C_pot" is pow of two const.
|
|
return builtin_copysign<f32>(x - builtin_trunc<f32>(x), x);
|
|
}
|
|
var ux = reinterpret<u32>(x);
|
|
var uy = reinterpret<u32>(y);
|
|
var ex = <i32>(ux >> 23 & 0xFF);
|
|
var ey = <i32>(uy >> 23 & 0xFF);
|
|
var sm = 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) {
|
|
return x * f32(ux1 != uy1);
|
|
}
|
|
if (!ex) {
|
|
ex -= builtin_clz<u32>(ux << 9);
|
|
ux <<= 1 - ex;
|
|
} else {
|
|
ux &= <u32>-1 >> 9;
|
|
ux |= 1 << 23;
|
|
}
|
|
if (!ey) {
|
|
ey -= builtin_clz<u32>(uy << 9);
|
|
uy <<= 1 - ey;
|
|
} 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;
|
|
}
|
|
return reinterpret<f32>(ux | sm);
|
|
}
|
|
|
|
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 <<= 1 - ex;
|
|
} else {
|
|
uxi &= <u32>-1 >> 9;
|
|
uxi |= 1 << 23;
|
|
}
|
|
if (!ey) {
|
|
ey -= builtin_clz<u32>(uy << 9);
|
|
uy <<= 1 - ey;
|
|
} else {
|
|
uy &= <u32>-1 >> 9;
|
|
uy |= 1 << 23;
|
|
}
|
|
var q = 0;
|
|
do {
|
|
if (ex < ey) {
|
|
if (ex + 1 == ey) break; // goto end
|
|
return x;
|
|
}
|
|
while (ex > ey) {
|
|
if (uxi >= uy) {
|
|
uxi -= uy;
|
|
++q;
|
|
}
|
|
uxi <<= 1;
|
|
q <<= 1;
|
|
--ex;
|
|
}
|
|
if (uxi >= uy) {
|
|
uxi -= uy;
|
|
++q;
|
|
}
|
|
if (uxi == 0) ex = -30;
|
|
else {
|
|
let shift = builtin_clz<i32>(uxi << 8);
|
|
ex -= shift;
|
|
uxi <<= shift;
|
|
}
|
|
break;
|
|
} while (false);
|
|
// end:
|
|
if (ex > 0) {
|
|
uxi -= 1 << 23;
|
|
uxi |= <u32>ex << 23;
|
|
} else {
|
|
uxi >>= -ex + 1;
|
|
}
|
|
x = reinterpret<f32>(uxi);
|
|
y = builtin_abs<f32>(y);
|
|
var x2 = x + x;
|
|
if (ex == ey || (ex + 1 == ey && (<f32>x2 > y || (<f32>x2 == y && <bool>(q & 1))))) {
|
|
x -= y;
|
|
// q++;
|
|
}
|
|
return sx ? -x : x;
|
|
}
|
|
|
|
export function sincos(x: f32): void { // see: musl/tree/src/math/sincosf.c
|
|
const
|
|
s1pio2 = reinterpret<f64>(0x3FF921FB54442D18), // 1 * M_PI_2
|
|
s2pio2 = reinterpret<f64>(0x400921FB54442D18), // 2 * M_PI_2
|
|
s3pio2 = reinterpret<f64>(0x4012D97C7F3321D2), // 3 * M_PI_2
|
|
s4pio2 = reinterpret<f64>(0x401921FB54442D18); // 4 * M_PI_2
|
|
|
|
var ix = reinterpret<u32>(x);
|
|
var sign = ix >> 31;
|
|
ix &= 0x7FFFFFFF;
|
|
|
|
if (ix <= 0x3F490FDA) { // |x| ~<= π/4
|
|
if (ix < 0x39800000) { // |x| < 2**-12
|
|
sincos_sin = x;
|
|
sincos_cos = 1;
|
|
return;
|
|
}
|
|
sincos_sin = sin_kernf(x);
|
|
sincos_cos = cos_kernf(x);
|
|
return;
|
|
}
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (ix <= 0x407B53D1) { // |x| ~<= 5π/4
|
|
if (ix <= 0x4016CBE3) { // |x| ~<= 3π/4
|
|
if (sign) {
|
|
sincos_sin = -cos_kernf(x + s1pio2);
|
|
sincos_cos = sin_kernf(x + s1pio2);
|
|
} else {
|
|
sincos_sin = cos_kernf(s1pio2 - x);
|
|
sincos_cos = sin_kernf(s1pio2 - x);
|
|
}
|
|
return;
|
|
}
|
|
// -sin(x + c) is not correct if x+c could be 0: -0 vs +0
|
|
sincos_sin = -sin_kernf(sign ? x + s2pio2 : x - s2pio2);
|
|
sincos_cos = -cos_kernf(sign ? x + s2pio2 : x - s2pio2);
|
|
return;
|
|
}
|
|
if (ix <= 0x40E231D5) { // |x| ~<= 9π/4
|
|
if (ix <= 0x40AFEDDF) { // |x| ~<= 7π/4
|
|
if (sign) {
|
|
sincos_sin = cos_kernf(x + s3pio2);
|
|
sincos_cos = -sin_kernf(x + s3pio2);
|
|
} else {
|
|
sincos_sin = -cos_kernf(x - s3pio2);
|
|
sincos_cos = sin_kernf(x - s3pio2);
|
|
}
|
|
return;
|
|
}
|
|
sincos_sin = sin_kernf(sign ? x + s4pio2 : x - s4pio2);
|
|
sincos_cos = cos_kernf(sign ? x + s4pio2 : x - s4pio2);
|
|
return;
|
|
}
|
|
}
|
|
// sin(Inf or NaN) is NaN
|
|
if (ix >= 0x7F800000) {
|
|
let xx = x - x;
|
|
sincos_sin = xx;
|
|
sincos_cos = xx;
|
|
return;
|
|
}
|
|
// general argument reduction needed
|
|
var n = rempio2f(x, ix, sign);
|
|
var y = rempio2f_y;
|
|
var s = sin_kernf(y);
|
|
var c = cos_kernf(y);
|
|
var sin = s, cos = c;
|
|
if (n & 1) {
|
|
sin = c;
|
|
cos = -s;
|
|
}
|
|
if (n & 2) {
|
|
sin = -sin;
|
|
cos = -cos;
|
|
}
|
|
sincos_sin = sin;
|
|
sincos_cos = cos;
|
|
}
|
|
}
|
|
|
|
export function ipow32(x: i32, e: i32): i32 {
|
|
var out = 1;
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (x == 2) {
|
|
return select<i32>(1 << e, 0, <u32>e < 32);
|
|
}
|
|
if (e <= 0) {
|
|
if (x == -1) return select<i32>(-1, 1, e & 1);
|
|
return i32(e == 0) | i32(x == 1);
|
|
}
|
|
else if (e == 1) return x;
|
|
else if (e == 2) return x * x;
|
|
else if (e < 32) {
|
|
let log = 32 - clz(e);
|
|
// 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) {
|
|
if (e & 1) out *= x;
|
|
e >>>= 1;
|
|
x *= x;
|
|
}
|
|
return out;
|
|
}
|
|
|
|
export function ipow64(x: i64, e: i64): i64 {
|
|
var out: i64 = 1;
|
|
if (ASC_SHRINK_LEVEL < 1) {
|
|
if (x == 2) {
|
|
return select<i64>(1 << e, 0, <u64>e < 64);
|
|
}
|
|
if (e <= 0) {
|
|
if (x == -1) return select<i64>(-1, 1, e & 1);
|
|
return i64(e == 0) | i64(x == 1);
|
|
}
|
|
else if (e == 1) return x;
|
|
else if (e == 2) return x * x;
|
|
else if (e < 64) {
|
|
let log = 64 - <i32>clz(e);
|
|
// 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) {
|
|
if (e & 1) out *= x;
|
|
e >>>= 1;
|
|
x *= x;
|
|
}
|
|
return out;
|
|
}
|
|
|
|
/*
|
|
TODO:
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In compile time if only exponent is constant we could replace ipow32/ipow64 by shortest addition chains
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which usually faster than exponentiation by squaring
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for ipow32 and e < 32:
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let b: i32, c: i32, d: i32, h: i32, k: i32, g: i32;
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switch (e) {
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case 1: return x;
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case 2: return x * x;
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case 3: return x * x * x;
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case 4: return (b = x * x) * b;
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case 5: return (b = x * x) * b * x;
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case 6: return (b = x * x) * b * b;
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case 7: return (b = x * x) * b * b * x;
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case 8: return (d = (b = x * x) * b) * d;
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case 9: return (c = x * x * x) * c * c;
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case 10: return (d = (b = x * x) * b) * d * b;
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case 11: return (d = (b = x * x) * b) * d * b * x;
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case 12: return (d = (b = x * x) * b) * d * d;
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case 13: return (d = (b = x * x) * b) * d * d * x;
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case 14: return (d = (b = x * x) * b) * d * d * b;
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case 15: return (k = (b = x * x) * b * x) * k * k;
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case 16: return (h = (d = (b = x * x) * b) * d) * h;
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case 17: return (h = (d = (b = x * x) * b) * d) * h * x;
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case 18: return (h = (d = (b = x * x) * b) * d * x) * h;
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case 19: return (h = (d = (b = x * x) * b) * d * x) * h * x;
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case 20: return (h = (k = (b = x * x) * b * x) * k) * h;
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case 21: return (h = (k = (b = x * x) * b * x) * k) * h * x;
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case 22: return (g = (h = (k = (b = x * x) * b * x) * k) * x) * g;
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case 23: return (h = (d = (c = (b = x * x) * x) * b) * d) * h * c;
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case 24: return (h = (d = (c = x * x * x) * c) * d) * h;
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case 25: return (h = (d = (c = x * x * x) * c) * d) * h * x;
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case 26: return (g = (h = (d = (c = x * x * x) * c) * d) * x) * g;
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case 27: return (h = (d = (c = x * x * x) * c) * d) * h * c;
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case 28: return (h = (d = (c = x * x * x) * c * x) * d) * h;
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case 29: return (h = (d = (c = x * x * x) * c * x) * d) * h * x;
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case 30: return (h = (d = (c = x * x * x) * c) * d * c) * h;
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case 31: return (h = (d = (c = x * x * x) * c) * d * c) * h * x;
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}
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for ipow64: TODO
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switch (e) {
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case 32:
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...
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case 63:
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}
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*/
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