mirror of
https://github.com/fluencelabs/assemblyscript
synced 2025-06-12 06:21:29 +00:00
Implement Math/Mathf.pow
This commit is contained in:
dcodeIO
@ -58,7 +58,7 @@ import {
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trunc as builtin_trunc
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} from "./builtins";
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// Math/Mathf.log/exp
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// Math/Mathf.log/exp/pow
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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
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@ -88,10 +88,8 @@ export namespace Math {
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return builtin_clz(<i32>x);
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}
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export function exp(x: f64): f64 {
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// based on musl's implementation of exp:
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export function exp(x: f64): f64 { // based on musl's implementation of exp
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const
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half = <f64[]>[0.5,-0.5],
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ln2hi = 6.93147180369123816490e-01, // 0x3fe62e42, 0xfee00000
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ln2lo = 1.90821492927058770002e-10, // 0x3dea39ef, 0x35793c76
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invln2 = 1.44269504088896338700e+00, // 0x3ff71547, 0x652b82fe
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@ -103,7 +101,6 @@ export namespace Math {
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Ox1p1023 = 8.98846567431157954e+307;
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var hx = <u32>(reinterpret<u64>(x) >> 32);
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var sign_ = hx >> 31;
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hx &= 0x7fffffff; // high word of |x|
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// special cases
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@ -125,8 +122,9 @@ export namespace Math {
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var k: i32;
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if (hx > 0x3fd62e42) { // if |x| > 0.5 ln2
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if (hx >= 0x3ff0a2b2) { // if |x| >= 1.5 ln2
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k = <i32>(invln2 * x + half[sign_]);
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k = <i32>(invln2 * x + copysign<f64>(0.5, x)); // was: [0.5, -0.5][sign_])
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} else {
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let sign_ = hx >> 31;
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k = 1 - sign_ - sign_;
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}
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hi = x - k * ln2hi; // k * ln2hi is exact here
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@ -223,6 +221,236 @@ export namespace Math {
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return builtin_min(value1, value2);
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}
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export function pow(x: f64, y: f64): f64 { // pased on musl's implementation of pow
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const
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two53 = 9007199254740992.0, // 0x43400000, 0x00000000
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huge = 1.0e+300,
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tiny = 1.0e-300,
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// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
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L1 = 5.99999999999994648725e-01, // 0x3FE33333, 0x33333303
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L2 = 4.28571428578550184252e-01, // 0x3FDB6DB6, 0xDB6FABFF
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L3 = 3.33333329818377432918e-01, // 0x3FD55555, 0x518F264D
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L4 = 2.72728123808534006489e-01, // 0x3FD17460, 0xA91D4101
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L5 = 2.30660745775561754067e-01, // 0x3FCD864A, 0x93C9DB65
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L6 = 2.06975017800338417784e-01, // 0x3FCA7E28, 0x4A454EEF
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P1 = 1.66666666666666019037e-01, // 0x3FC55555, 0x5555553E
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P2 = -2.77777777770155933842e-03, // 0xBF66C16C, 0x16BEBD93
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P3 = 6.61375632143793436117e-05, // 0x3F11566A, 0xAF25DE2C
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P4 = -1.65339022054652515390e-06, // 0xBEBBBD41, 0xC5D26BF1
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P5 = 4.13813679705723846039e-08, // 0x3E663769, 0x72BEA4D0
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lg2 = 6.93147180559945286227e-01, // 0x3FE62E42, 0xFEFA39EF
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lg2_h = 6.93147182464599609375e-01, // 0x3FE62E43, 0x00000000
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lg2_l = -1.90465429995776804525e-09, // 0xBE205C61, 0x0CA86C39
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ovt = 8.0085662595372944372e-017, // -(1024-log2(ovfl+.5ulp))
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cp = 9.61796693925975554329e-01, // 0x3FEEC709, 0xDC3A03FD =2/(3ln2)
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cp_h = 9.61796700954437255859e-01, // 0x3FEEC709, 0xE0000000 =(float)cp
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cp_l = -7.02846165095275826516e-09, // 0xBE3E2FE0, 0x145B01F5 =tail of cp_h
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ivln2 = 1.44269504088896338700e+00, // 0x3FF71547, 0x652B82FE =1/ln2
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ivln2_h = 1.44269502162933349609e+00, // 0x3FF71547, 0x60000000 =24b 1/ln2
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ivln2_l = 1.92596299112661746887e-0; // 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail
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var __u = reinterpret<u64>(x); // EXTRACT_WORDS(hx, lx, x)
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var hx = <i32>(__u >> 32);
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var lx = <u32>__u;
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__u = reinterpret<u64>(y); // EXTRACT_WORDS(hy, ly, y)
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var hy = <i32>(__u >> 32);
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var ly = <u32>__u;
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var ix = hx & 0x7fffffff;
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var iy = hy & 0x7fffffff;
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// x**0 = 1, even if x is NaN
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if ((iy | ly) == 0) return 1.0;
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// 1**y = 1, even if y is NaN
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if (hx == 0x3ff00000 && lx == 0) return 1.0;
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// NaN if either arg is NaN
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if (
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ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
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iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0)
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) return x + y;
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// determine if y is an odd int when x < 0
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// yisint = 0 ... y is not an integer
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// yisint = 1 ... y is an odd int
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// yisint = 2 ... y is an even int
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var yisint = 0, k: i32;
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if (hx < 0) {
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if (iy >= 0x43400000) yisint = 2; // even integer y
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else if (iy >= 0x3ff00000) {
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k = (iy >> 20) - 0x3ff; // exponent
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if (k > 20) {
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let jj = ly >> (52 - k);
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if ((jj << (52 - k)) == ly) yisint = 2 - (jj & 1);
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} else if (ly == 0) {
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let jj = iy >> (20 - k);
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if ((jj << (20 - k)) == iy) yisint = 2 - (jj & 1);
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}
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}
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}
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// special value of y
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if (ly == 0) {
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if (iy == 0x7ff00000) { // y is +-inf
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if (((ix - 0x3ff00000) | lx) == 0) return 1.0; // (-1)**+-inf is 1
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else if (ix >= 0x3ff00000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
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else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
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}
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if (iy == 0x3ff00000) { // y is +-1
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if (hy >= 0) return x;
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return 1 / x;
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}
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if (hy == 0x40000000) return x * x; // y is 2
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if (hy == 0x3fe00000) { // y is 0.5
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if (hx >= 0) return sqrt(x); // x >= +0
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}
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}
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var ax = builtin_abs(x), z: f64;
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// special value of x
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if (lx == 0) {
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if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { // x is +-0,+-inf,+-1
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z = ax;
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if (hy < 0) z = 1.0 / z; // z = (1/|x|)
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if (hx < 0) {
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if (((ix - 0x3ff00000) | yisint) == 0) z = (z - z) / (z - z); // (-1)**non-int is NaN
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else if (yisint == 1) z = -z; // (x<0)**odd = -(|x|**odd)
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}
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return z;
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}
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}
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var s = 1.0; // sign of result
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if (hx < 0) {
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if (yisint == 0) return (x - x) / (x - x); // (x<0)**(non-int) is NaN
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if (yisint == 1) s = -1.0; // (x<0)**(odd int)
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}
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// |y| is huge
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var t1: f64, t2: f64, p_h: f64, p_l: f64, r: f64, t: f64, u: f64, v: f64, w: f64;
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var j: i32, n: i32;
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if (iy > 0x41e00000) { // if |y| > 2**31
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if (iy > 0x43f00000) { // if |y| > 2**64, must o/uflow
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if (ix <= 0x3fefffff) return hy < 0 ? huge * huge : tiny * tiny;
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if (ix >= 0x3ff00000) return hy > 0 ? huge * huge : tiny * tiny;
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}
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// over/underflow if x is not close to one
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if (ix < 0x3fefffff) return hy < 0 ? s * huge * huge : s * tiny * tiny;
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if (ix > 0x3ff00000) return hy > 0 ? s * huge * huge : s * tiny * tiny;
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// now |1-x| is tiny <= 2**-20, suffice to compute
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// log(x) by x-x^2/2+x^3/3-x^4/4
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t = ax - 1.0; // t has 20 trailing zeros
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w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
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u = ivln2_h * t; // ivln2_h has 21 sig. bits
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v = t * ivln2_l - w * ivln2;
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t1 = u + v;
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t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xffffffff00000000); // SET_LOW_WORD(t1, 0)
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t2 = v - (t1 - u);
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} else {
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let ss: f64, s2: f64, s_h: f64, s_l: f64, t_h: f64, t_l: f64;
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n = 0;
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// take care subnormal number
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if (ix < 0x00100000) {
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ax *= two53;
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n -= 53;
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ix = <u32>(reinterpret<u64>(ax) >> 32);
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}
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n += (ix >> 20) - 0x3ff;
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j = ix & 0x000fffff;
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// determine interval
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ix = j | 0x3ff00000; // normalize ix
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if (j <= 0x3988E) k = 0; // |x|<sqrt(3/2)
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else if (j < 0xBB67A) k = 1; // |x|<sqrt(3)
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else {
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k = 0;
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n += 1;
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ix -= 0x00100000;
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}
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ax = reinterpret<f64>(reinterpret<u64>(ax) & 0xffffffff | (<u64>ix << 32)); // SET_HIGH_WORD(ax, ix)
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// compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
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let bp = select<f64>(1.5, 1.0, k); // bp[k], bp[0]=1.0, bp[1]=1.5
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u = ax - bp;
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v = 1.0 / (ax + bp);
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ss = u * v;
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s_h = ss;
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s_h = reinterpret<f64>(reinterpret<u64>(s_h) & 0xffffffff00000000); // SET_LOW_WORD(s_h, 0)
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// t_h=ax+bp[k] High
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t_h = reinterpret<f64>(<u64>(((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)) << 32); // SET_HIGH_WORD
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t_l = ax - (t_h - bp);
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s_l = v * ((u - s_h * t_h) - s_h * t_l);
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// compute log(ax)
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s2 = ss * ss;
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r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
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r += s_l * (s_h + ss);
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s2 = s_h * s_h;
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t_h = 3.0 + s2 + r;
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t_h = reinterpret<f64>(reinterpret<u64>(t_h) & 0xffffffff00000000); // SET_LOW_WORD(t_h, 0)
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t_l = r - ((t_h - 3.0) - s2);
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// u+v = ss*(1+...)
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u = s_h * t_h;
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v = s_l * t_h + t_l * ss;
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// 2/(3log2)*(ss+...)
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p_h = u + v;
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p_h = reinterpret<f64>(reinterpret<u64>(p_h) & 0xffffffff00000000); // SET_LOW_WORD(p_h, 0)
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p_l = v - (p_h - u);
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let z_h = cp_h * p_h; // cp_h+cp_l = 2/(3*log2)
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let dp_l = select<f64>(1.35003920212974897128e-08, 0.0, k); // dp_l[k]
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let z_l = cp_l * p_h + p_l * cp + dp_l;
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// log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l
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t = <f64>n;
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let dp_h = select<f64>(5.84962487220764160156e-01, 0.0, k); // dp_h[k]
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t1 = ((z_h + z_l) + dp_h) + t;
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t1 = reinterpret<f64>(reinterpret<u64>(t1) & 0xffffffff00000000); // SET_LOW_WORD(t1, 0);
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t2 = z_l - (((t1 - t) - dp_h) - z_h);
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}
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// split up y into y1+y2 and compute (y1+y2)*(t1+t2)
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var y1 = y;
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y1 = reinterpret<f64>(reinterpret<u64>(y1) & 0xffffffff00000000); // SET_LOW_WORD(y1, 0)
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p_l = (y - y1) * t1 + y * t2;
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p_h = y1 * t1;
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z = p_l + p_h;
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__u = reinterpret<u64>(z); // EXTRACT_WORDS(j, i, z) ...
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j = <u32>(__u >> 32);
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var i = <i32>__u;
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if (j >= 0x40900000) { // z >= 1024
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if (((j - 0x40900000) | i) != 0) return s * huge * huge; // if z > 1024, overflow
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if (p_l + ovt > z - p_h) return s * huge * huge; // overflow
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} else if ((j & 0x7fffffff) >= 0x4090cc00) { // z <= -1075, FIXME: instead of abs(j) use unsigned j
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if (((j - 0xc090cc00) | i) != 0) return s * tiny * tiny; // z < -1075, underflow
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if (p_l <= z - p_h) return s * tiny * tiny; // underflow
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}
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// compute 2**(p_h+p_l)
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i = j & 0x7fffffff;
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k = (i >> 20) - 0x3ff;
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n = 0;
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if (i > 0x3fe00000) { // if |z| > 0.5, set n = [z+0.5]
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n = j + (0x00100000 >> (k + 1));
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k = ((n & 0x7fffffff) >> 20) - 0x3ff; // new k for n
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t = 0.0;
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t = reinterpret<f64>(<u64>(n & ~(0x000fffff >> k)) << 32); // SET_HIGH_WORD(t, n & ~(0x000fffff>>k))
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n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
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if (j < 0) n = -n;
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p_h -= t;
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}
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t = p_l + p_h;
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t = reinterpret<f64>(reinterpret<u64>(t) & 0xffffffff00000000); // SET_LOW_WORD(t, 0)
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u = t * lg2_h;
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v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
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z = u + v;
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w = v - (z - u);
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t = z * z;
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t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
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r = (z * t1) / (t1 - 2.0) - (w + z * w);
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z = 1.0 - (r - z);
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j = <u32>(reinterpret<u64>(z) >> 32); // GET_HIGH_WORD(j, z)
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j += n << 20;
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if ((j >> 20) <= 0) z = scalbn(z, n); // subnormal output
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else z = reinterpret<f64>(reinterpret<u64>(z) & 0xffffffff | (<u64>j << 32)); // SET_HIGH_WORD(z, j)
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return s * z;
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}
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export function round(x: f64): f64 {
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return builtin_nearest(x);
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}
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@ -269,7 +497,6 @@ export namespace Mathf {
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export function exp(x: f32): f32 { // based on musl's implementation of expf
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const
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half = <f32[]>[0.5,-0.5],
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ln2hi = <f32>6.9314575195e-1, // 0x3f317200
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ln2lo = <f32>1.4286067653e-6, // 0x35bfbe8e
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invln2 = <f32>1.4426950216e+0, // 0x3fb8aa3b
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@ -292,7 +519,7 @@ export namespace Mathf {
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}
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if (sign_) {
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// underflow
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if (hx >= 0x42cff1b5) { // x <= -103.972084f */
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if (hx >= 0x42cff1b5) { // x <= -103.972084f
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return 0;
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}
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}
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@ -303,7 +530,7 @@ export namespace Mathf {
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var k: i32;
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if (hx > 0x3eb17218) { // if |x| > 0.5 ln2
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if (hx > 0x3f851592) { // if |x| > 1.5 ln2
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k = <i32>(invln2 * x + half[sign_]);
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k = <i32>(invln2 * x + copysign<f32>(0.5, x)); // was: [0.5, -0.5][sign_])
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} else {
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k = 1 - sign_ - sign_;
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}
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@ -387,6 +614,219 @@ export namespace Mathf {
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return builtin_min(value1, value2);
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}
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export function pow(x: f32, y: f32): f32 { // based on musl's implementation of powf
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const
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two24 = <f32>16777216.0, // 0x4b800000
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huge = <f32>1.0e30,
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tiny = <f32>1.0e-30,
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// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
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L1 = <f32>6.0000002384e-01, // 0x3f19999a
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L2 = <f32>4.2857143283e-01, // 0x3edb6db7
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L3 = <f32>3.3333334327e-01, // 0x3eaaaaab
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L4 = <f32>2.7272811532e-01, // 0x3e8ba305
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L5 = <f32>2.3066075146e-01, // 0x3e6c3255
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L6 = <f32>2.0697501302e-01, // 0x3e53f142
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P1 = <f32>1.6666667163e-01, // 0x3e2aaaab
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P2 = <f32>-2.7777778450e-03, // 0xbb360b61
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P3 = <f32>6.6137559770e-05, // 0x388ab355
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P4 = <f32>-1.6533901999e-06, // 0xb5ddea0e
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P5 = <f32>4.1381369442e-08, // 0x3331bb4c
|
||||
lg2 = <f32>6.9314718246e-01, // 0x3f317218
|
||||
lg2_h = <f32>6.93145752e-01, // 0x3f317200
|
||||
lg2_l = <f32>1.42860654e-06, // 0x35bfbe8c
|
||||
ovt = <f32>4.2995665694e-08, // -(128-log2(ovfl+.5ulp))
|
||||
cp = <f32>9.6179670095e-01, // 0x3f76384f =2/(3ln2)
|
||||
cp_h = <f32>9.6191406250e-01, // 0x3f764000 =12b cp
|
||||
cp_l = <f32>-1.1736857402e-04, // 0xb8f623c6 =tail of cp_h
|
||||
ivln2 = <f32>1.4426950216e+00, // 0x3fb8aa3b =1/ln2
|
||||
ivln2_h = <f32>1.4426879883e+00, // 0x3fb8aa00 =16b 1/ln2
|
||||
ivln2_l = <f32>7.0526075433e-06; // 0x36eca570 =1/ln2 tail
|
||||
|
||||
var hx = reinterpret<i32>(x); // GET_FLOAT_WORD(hx, x)
|
||||
var hy = reinterpret<i32>(y); // GET_FLOAT_WORD(hy, y)
|
||||
var ix = hx & 0x7fffffff;
|
||||
var iy = hy & 0x7fffffff;
|
||||
|
||||
// x**0 = 1, even if x is NaN
|
||||
if (iy == 0) return 1.0;
|
||||
// 1**y = 1, even if y is NaN
|
||||
if (hx == 0x3f800000) return 1.0;
|
||||
// NaN if either arg is NaN
|
||||
if (ix > 0x7f800000 || iy > 0x7f800000) return x + y;
|
||||
|
||||
// determine if y is an odd int when x < 0
|
||||
// yisint = 0 ... y is not an integer
|
||||
// yisint = 1 ... y is an odd int
|
||||
// yisint = 2 ... y is an even int
|
||||
var yisint = 0, j: i32, k: i32;
|
||||
if (hx < 0) {
|
||||
if (iy >= 0x4b800000) yisint = 2; // even integer y
|
||||
else if (iy >= 0x3f800000) {
|
||||
k = (iy >> 23) - 0x7f; // exponent
|
||||
j = iy >> (23 - k);
|
||||
if ((j << (23 - k)) == iy) yisint = 2 - (j & 1);
|
||||
}
|
||||
}
|
||||
|
||||
// special value of y
|
||||
if (iy == 0x7f800000) { // y is +-inf
|
||||
if (ix == 0x3f800000) return 1.0; // (-1)**+-inf is 1
|
||||
else if (ix > 0x3f800000) return hy >= 0 ? y : 0.0; // (|x|>1)**+-inf = inf,0
|
||||
else return hy >= 0 ? 0.0 : -y; // (|x|<1)**+-inf = 0,inf
|
||||
}
|
||||
if (iy == 0x3f800000) return hy >= 0 ? x : 1.0 / x; // y is +-1
|
||||
if (hy == 0x40000000) return x * x; // y is 2
|
||||
if (hy == 0x3f000000) { // y is 0.5
|
||||
if (hx >= 0) return builtin_sqrt<f32>(x); // x >= +0
|
||||
}
|
||||
|
||||
var ax = builtin_abs<f32>(x);
|
||||
// special value of x
|
||||
var z: f32;
|
||||
if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { // x is +-0,+-inf,+-1
|
||||
z = ax;
|
||||
if (hy < 0) z = 1.0 / z; // z = (1/|x|)
|
||||
if (hx < 0) {
|
||||
if (((ix - 0x3f800000) | yisint) == 0) z = (z - z) / (z - z); // (-1)**non-int is NaN
|
||||
else if (yisint == 1) z = -z; // (x<0)**odd = -(|x|**odd)
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
var sn = <f32>1.0; // sign of result
|
||||
if (hx < 0) {
|
||||
if (yisint == 0) return (x - x) / (x - x); // (x<0)**(non-int) is NaN
|
||||
if (yisint == 1) sn = -1.0; // (x<0)**(odd int)
|
||||
}
|
||||
|
||||
// |y| is huge
|
||||
var t1: f32, t2: f32, r: f32, s: f32, t: f32, u: f32, v: f32, w: f32, p_h: f32, p_l: f32;
|
||||
var n: i32, is: i32;
|
||||
if (iy > 0x4d000000) { // if |y| > 2**27
|
||||
// over/underflow if x is not close to one
|
||||
if (ix < 0x3f7ffff8) return hy < 0 ? sn * huge * huge : sn * tiny * tiny;
|
||||
if (ix > 0x3f800007) return hy > 0 ? sn * huge * huge : sn * tiny * tiny;
|
||||
// now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
// log(x) by x-x^2/2+x^3/3-x^4/4
|
||||
t = ax - 1; // t has 20 trailing zeros
|
||||
w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
|
||||
u = ivln2_h * t; // ivln2_h has 16 sig. bits
|
||||
v = t * ivln2_l - w * ivln2;
|
||||
t1 = u + v;
|
||||
is = reinterpret<i32>(t1); // GET_FLOAT_WORD(is, t1)
|
||||
t1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t1, is & 0xfffff000)
|
||||
t2 = v - (t1 - u);
|
||||
} else {
|
||||
let s2: f32, s_h: f32, s_l: f32, t_h: f32, t_l: f32;
|
||||
n = 0;
|
||||
// take care subnormal number
|
||||
if (ix < 0x00800000) {
|
||||
ax *= two24;
|
||||
n -= 24;
|
||||
ix = reinterpret<i32>(ax); // GET_FLOAT_WORD(ix, ax)
|
||||
}
|
||||
n += (ix >> 23) - 0x7f;
|
||||
j = ix & 0x007fffff;
|
||||
// determine interval
|
||||
ix = j | 0x3f800000; // normalize ix
|
||||
if (j <= 0x1cc471) k = 0; // |x|<sqrt(3/2)
|
||||
else if (j < 0x5db3d7) k = 1; // |x|<sqrt(3)
|
||||
else {
|
||||
k = 0;
|
||||
n += 1;
|
||||
ix -= 0x00800000;
|
||||
}
|
||||
ax = reinterpret<f32>(ix); // SET_FLOAT_WORD(ax, ix)
|
||||
|
||||
// compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
|
||||
let bp = select<f32>(1.5, 1.0, k); // bp[k], [1.0, 1.5]
|
||||
u = ax - bp;
|
||||
v = 1.0 / (ax + bp);
|
||||
s = u * v;
|
||||
s_h = s;
|
||||
is = reinterpret<u32>(s_h); // GET_FLOAT_WORD(is, s_h)
|
||||
s_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(s_h, is & 0xfffff000)
|
||||
// t_h=ax+bp[k] High
|
||||
is = ((ix >> 1) & 0xfffff000) | 0x20000000;
|
||||
t_h = reinterpret<f32>(is + 0x00400000 + (k << 21)); // SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21))
|
||||
t_l = ax - (t_h - bp);
|
||||
s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
||||
// compute log(ax)
|
||||
s2 = s * s;
|
||||
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
||||
r += s_l * (s_h + s);
|
||||
s2 = s_h * s_h;
|
||||
t_h = 3.0 + s2 + r;
|
||||
is = reinterpret<u32>(t_h); // GET_FLOAT_WORD(is, t_h)
|
||||
t_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t_h, is & 0xfffff000)
|
||||
t_l = r - ((t_h - 3.0) - s2);
|
||||
// u+v = s*(1+...)
|
||||
u = s_h * t_h;
|
||||
v = s_l * t_h + t_l * s;
|
||||
// 2/(3log2)*(s+...)
|
||||
p_h = u + v;
|
||||
is = reinterpret<u32>(p_h); // GET_FLOAT_WORD(is, p_h)
|
||||
p_h = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(p_h, is & 0xfffff000)
|
||||
p_l = v - (p_h - u);
|
||||
let z_h = cp_h * p_h; // cp_h+cp_l = 2/(3*log2)
|
||||
let dp_l = select<f32>(1.56322085e-06, 0.0, k); // dp_l[k], [0.0, 1.56322085e-06]
|
||||
let z_l = cp_l * p_h + p_l * cp + dp_l;
|
||||
// log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l
|
||||
t = <f32>n;
|
||||
let dp_h = select<f32>(5.84960938e-01, 0.0, k); // dp_h[k], [0.0, 5.84960938e-01]
|
||||
t1 = (((z_h + z_l) + dp_h) + t);
|
||||
is = reinterpret<u32>(t1); // GET_FLOAT_WORD(is, t1)
|
||||
t1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(t1, is & 0xfffff000)
|
||||
t2 = z_l - (((t1 - t) - dp_h) - z_h);
|
||||
}
|
||||
|
||||
// split up y into y1+y2 and compute (y1+y2)*(t1+t2)
|
||||
is = reinterpret<u32>(y); // GET_FLOAT_WORD(is, y)
|
||||
var y1 = reinterpret<f32>(is & 0xfffff000); // SET_FLOAT_WORD(y1, is & 0xfffff000)
|
||||
p_l = (y - y1) * t1 + y * t2;
|
||||
p_h = y1 * t1;
|
||||
z = p_l + p_h;
|
||||
j = reinterpret<u32>(z); // GET_FLOAT_WORD(j, z)
|
||||
if (j > 0x43000000) { // if z > 128, overflow
|
||||
return sn * huge * huge;
|
||||
} else if (j == 0x43000000) { // if z == 128
|
||||
if (p_l + ovt > z - p_h) return sn * huge * huge; // overflow
|
||||
} else if ((j & 0x7fffffff) > 0x43160000) { // z < -150, FIXME: check should be (uint32_t)j > 0xc3160000
|
||||
return sn * tiny * tiny; // underflow
|
||||
} else if (j == 0xc3160000) { // z == -150
|
||||
if (p_l <= z - p_h) return sn * tiny * tiny; // underflow
|
||||
}
|
||||
|
||||
// compute 2**(p_h+p_l)
|
||||
var i = j & 0x7fffffff;
|
||||
k = (i >> 23) - 0x7f;
|
||||
n = 0;
|
||||
if (i > 0x3f000000) { // if |z| > 0.5, set n = [z+0.5]
|
||||
n = j + (0x00800000 >> (k + 1));
|
||||
k = ((n & 0x7fffffff) >> 23) - 0x7f; // new k for n
|
||||
t = reinterpret<f32>(n & ~(0x007fffff >> k)); // SET_FLOAT_WORD(t, n & ~(0x007fffff>>k))
|
||||
n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
|
||||
if (j < 0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l + p_h;
|
||||
is = reinterpret<u32>(t); // GET_FLOAT_WORD(is, t)
|
||||
t = reinterpret<f32>(is & 0xffff8000); // SET_FLOAT_WORD(t, is & 0xffff8000);
|
||||
u = t * lg2_h;
|
||||
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
||||
z = u + v;
|
||||
w = v - (z - u);
|
||||
t = z * z;
|
||||
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
||||
r = (z * t1) / (t1 - 2.0) - (w + z * w);
|
||||
z = 1.0 - (r - z);
|
||||
j = reinterpret<u32>(z); // GET_FLOAT_WORD(j, z)
|
||||
j += n << 23;
|
||||
if ((j >> 23) <= 0) z = scalbnf(z, n); // subnormal output
|
||||
else z = reinterpret<f32>(j); // SET_FLOAT_WORD(z, j)
|
||||
return sn * z;
|
||||
}
|
||||
|
||||
export function round(x: f32): f32 {
|
||||
return builtin_nearest(x);
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user