Chromium Code Reviews
chromiumcodereview-hr@appspot.gserviceaccount.com (chromiumcodereview-hr) | Please choose your nickname with Settings | Help | Chromium Project | Gerrit Changes | Sign out
(84)

Unified Diff: third_party/fdlibm/fdlibm.js

Issue 448643002: Reland "Implement trigonometric functions using a fdlibm port." (Closed) Base URL: https://v8.googlecode.com/svn/branches/bleeding_edge
Patch Set: fix windows build and gc mole Created 6 years, 4 months ago
Use n/p to move between diff chunks; N/P to move between comments. Draft comments are only viewable by you.
Jump to:
View side-by-side diff with in-line comments
Download patch
« no previous file with comments | « third_party/fdlibm/fdlibm.cc ('k') | tools/generate-runtime-tests.py » ('j') | no next file with comments »
Expand Comments ('e') | Collapse Comments ('c') | Show Comments Hide Comments ('s')
Index: third_party/fdlibm/fdlibm.js
diff --git a/third_party/fdlibm/fdlibm.js b/third_party/fdlibm/fdlibm.js
new file mode 100644
index 0000000000000000000000000000000000000000..d5dbb72990a5adecafd3697393ca86928ba31970
--- /dev/null
+++ b/third_party/fdlibm/fdlibm.js
@@ -0,0 +1,356 @@
+// The following is adapted from fdlibm (http://www.netlib.org/fdlibm),
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunSoft, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+// The original source code covered by the above license above has been
+// modified significantly by Google Inc.
+// Copyright 2014 the V8 project authors. All rights reserved.
+//
+// The following is a straightforward translation of fdlibm routines for
+// sin, cos, and tan, by Raymond Toy (rtoy@google.com).
+
+
+var kTrig; // Initialized to a Float64Array during genesis and is not writable.
+
+const INVPIO2 = kTrig[0];
+const PIO2_1 = kTrig[1];
+const PIO2_1T = kTrig[2];
+const PIO2_2 = kTrig[3];
+const PIO2_2T = kTrig[4];
+const PIO2_3 = kTrig[5];
+const PIO2_3T = kTrig[6];
+const PIO4 = kTrig[32];
+const PIO4LO = kTrig[33];
+
+// Compute k and r such that x - k*pi/2 = r where |r| < pi/4. For
+// precision, r is returned as two values y0 and y1 such that r = y0 + y1
+// to more than double precision.
+macro REMPIO2(X)
+ var n, y0, y1;
+ var hx = %_DoubleHi(X);
+ var ix = hx & 0x7fffffff;
+
+ if (ix < 0x4002d97c) {
+ // |X| ~< 3*pi/4, special case with n = +/- 1
+ if (hx > 0) {
+ var z = X - PIO2_1;
+ if (ix != 0x3ff921fb) {
+ // 33+53 bit pi is good enough
+ y0 = z - PIO2_1T;
+ y1 = (z - y0) - PIO2_1T;
+ } else {
+ // near pi/2, use 33+33+53 bit pi
+ z -= PIO2_2;
+ y0 = z - PIO2_2T;
+ y1 = (z - y0) - PIO2_2T;
+ }
+ n = 1;
+ } else {
+ // Negative X
+ var z = X + PIO2_1;
+ if (ix != 0x3ff921fb) {
+ // 33+53 bit pi is good enough
+ y0 = z + PIO2_1T;
+ y1 = (z - y0) + PIO2_1T;
+ } else {
+ // near pi/2, use 33+33+53 bit pi
+ z += PIO2_2;
+ y0 = z + PIO2_2T;
+ y1 = (z - y0) + PIO2_2T;
+ }
+ n = -1;
+ }
+ } else if (ix <= 0x413921fb) {
+ // |X| ~<= 2^19*(pi/2), medium size
+ var t = MathAbs(X);
+ n = (t * INVPIO2 + 0.5) | 0;
+ var r = t - n * PIO2_1;
+ var w = n * PIO2_1T;
+ // First round good to 85 bit
+ y0 = r - w;
+ if (ix - (%_DoubleHi(y0) & 0x7ff00000) > 0x1000000) {
+ // 2nd iteration needed, good to 118
+ t = r;
+ w = n * PIO2_2;
+ r = t - w;
+ w = n * PIO2_2T - ((t - r) - w);
+ y0 = r - w;
+ if (ix - (%_DoubleHi(y0) & 0x7ff00000) > 0x3100000) {
+ // 3rd iteration needed. 151 bits accuracy
+ t = r;
+ w = n * PIO2_3;
+ r = t - w;
+ w = n * PIO2_3T - ((t - r) - w);
+ y0 = r - w;
+ }
+ }
+ y1 = (r - y0) - w;
+ if (hx < 0) {
+ n = -n;
+ y0 = -y0;
+ y1 = -y1;
+ }
+ } else {
+ // Need to do full Payne-Hanek reduction here.
+ var r = %RemPiO2(X);
+ n = r[0];
+ y0 = r[1];
+ y1 = r[2];
+ }
+endmacro
+
+
+// __kernel_sin(X, Y, IY)
+// kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
+// Input X is assumed to be bounded by ~pi/4 in magnitude.
+// Input Y is the tail of X so that x = X + Y.
+//
+// Algorithm
+// 1. Since ieee_sin(-x) = -ieee_sin(x), we need only to consider positive x.
+// 2. ieee_sin(x) is approximated by a polynomial of degree 13 on
+// [0,pi/4]
+// 3 13
+// sin(x) ~ x + S1*x + ... + S6*x
+// where
+//
+// |ieee_sin(x) 2 4 6 8 10 12 | -58
+// |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
+// | x |
+//
+// 3. ieee_sin(X+Y) = ieee_sin(X) + sin'(X')*Y
+// ~ ieee_sin(X) + (1-X*X/2)*Y
+// For better accuracy, let
+// 3 2 2 2 2
+// r = X *(S2+X *(S3+X *(S4+X *(S5+X *S6))))
+// then 3 2
+// sin(x) = X + (S1*X + (X *(r-Y/2)+Y))
+//
+macro KSIN(x)
+kTrig[7+x]
+endmacro
+
+macro RETURN_KERNELSIN(X, Y, SIGN)
+ var z = X * X;
+ var v = z * X;
+ var r = KSIN(1) + z * (KSIN(2) + z * (KSIN(3) +
+ z * (KSIN(4) + z * KSIN(5))));
+ return (X - ((z * (0.5 * Y - v * r) - Y) - v * KSIN(0))) SIGN;
+endmacro
+
+// __kernel_cos(X, Y)
+// kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+// Input X is assumed to be bounded by ~pi/4 in magnitude.
+// Input Y is the tail of X so that x = X + Y.
+//
+// Algorithm
+// 1. Since ieee_cos(-x) = ieee_cos(x), we need only to consider positive x.
+// 2. ieee_cos(x) is approximated by a polynomial of degree 14 on
+// [0,pi/4]
+// 4 14
+// cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+// where the remez error is
+//
+// | 2 4 6 8 10 12 14 | -58
+// |ieee_cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
+// | |
+//
+// 4 6 8 10 12 14
+// 3. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
+// ieee_cos(x) = 1 - x*x/2 + r
+// since ieee_cos(X+Y) ~ ieee_cos(X) - ieee_sin(X)*Y
+// ~ ieee_cos(X) - X*Y,
+// a correction term is necessary in ieee_cos(x) and hence
+// cos(X+Y) = 1 - (X*X/2 - (r - X*Y))
+// For better accuracy when x > 0.3, let qx = |x|/4 with
+// the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
+// Then
+// cos(X+Y) = (1-qx) - ((X*X/2-qx) - (r-X*Y)).
+// Note that 1-qx and (X*X/2-qx) is EXACT here, and the
+// magnitude of the latter is at least a quarter of X*X/2,
+// thus, reducing the rounding error in the subtraction.
+//
+macro KCOS(x)
+kTrig[13+x]
+endmacro
+
+macro RETURN_KERNELCOS(X, Y, SIGN)
+ var ix = %_DoubleHi(X) & 0x7fffffff;
+ var z = X * X;
+ var r = z * (KCOS(0) + z * (KCOS(1) + z * (KCOS(2)+
+ z * (KCOS(3) + z * (KCOS(4) + z * KCOS(5))))));
+ if (ix < 0x3fd33333) { // |x| ~< 0.3
+ return (1 - (0.5 * z - (z * r - X * Y))) SIGN;
+ } else {
+ var qx;
+ if (ix > 0x3fe90000) { // |x| > 0.78125
+ qx = 0.28125;
+ } else {
+ qx = %_ConstructDouble(%_DoubleHi(0.25 * X), 0);
+ }
+ var hz = 0.5 * z - qx;
+ return (1 - qx - (hz - (z * r - X * Y))) SIGN;
+ }
+endmacro
+
+// kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+// Input x is assumed to be bounded by ~pi/4 in magnitude.
+// Input y is the tail of x.
+// Input k indicates whether ieee_tan (if k = 1) or -1/tan (if k = -1)
+// is returned.
+//
+// Algorithm
+// 1. Since ieee_tan(-x) = -ieee_tan(x), we need only to consider positive x.
+// 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
+// 3. ieee_tan(x) is approximated by a odd polynomial of degree 27 on
+// [0,0.67434]
+// 3 27
+// tan(x) ~ x + T1*x + ... + T13*x
+// where
+//
+// |ieee_tan(x) 2 4 26 | -59.2
+// |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
+// | x |
+//
+// Note: ieee_tan(x+y) = ieee_tan(x) + tan'(x)*y
+// ~ ieee_tan(x) + (1+x*x)*y
+// Therefore, for better accuracy in computing ieee_tan(x+y), let
+// 3 2 2 2 2
+// r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+// then
+// 3 2
+// tan(x+y) = x + (T1*x + (x *(r+y)+y))
+//
+// 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
+// tan(x) = ieee_tan(pi/4-y) = (1-ieee_tan(y))/(1+ieee_tan(y))
+// = 1 - 2*(ieee_tan(y) - (ieee_tan(y)^2)/(1+ieee_tan(y)))
+//
+// Set returnTan to 1 for tan; -1 for cot. Anything else is illegal
+// and will cause incorrect results.
+//
+macro KTAN(x)
+kTrig[19+x]
+endmacro
+
+function KernelTan(x, y, returnTan) {
+ var z;
+ var w;
+ var hx = %_DoubleHi(x);
+ var ix = hx & 0x7fffffff;
+
+ if (ix < 0x3e300000) { // |x| < 2^-28
+ if (((ix | %_DoubleLo(x)) | (returnTan + 1)) == 0) {
+ // x == 0 && returnTan = -1
+ return 1 / MathAbs(x);
+ } else {
+ if (returnTan == 1) {
+ return x;
+ } else {
+ // Compute -1/(x + y) carefully
+ var w = x + y;
+ var z = %_ConstructDouble(%_DoubleHi(w), 0);
+ var v = y - (z - x);
+ var a = -1 / w;
+ var t = %_ConstructDouble(%_DoubleHi(a), 0);
+ var s = 1 + t * z;
+ return t + a * (s + t * v);
+ }
+ }
+ }
+ if (ix >= 0x3fe59429) { // |x| > .6744
+ if (x < 0) {
+ x = -x;
+ y = -y;
+ }
+ z = PIO4 - x;
+ w = PIO4LO - y;
+ x = z + w;
+ y = 0;
+ }
+ z = x * x;
+ w = z * z;
+
+ // Break x^5 * (T1 + x^2*T2 + ...) into
+ // x^5 * (T1 + x^4*T3 + ... + x^20*T11) +
+ // x^5 * (x^2 * (T2 + x^4*T4 + ... + x^22*T12))
+ var r = KTAN(1) + w * (KTAN(3) + w * (KTAN(5) +
+ w * (KTAN(7) + w * (KTAN(9) + w * KTAN(11)))));
+ var v = z * (KTAN(2) + w * (KTAN(4) + w * (KTAN(6) +
+ w * (KTAN(8) + w * (KTAN(10) + w * KTAN(12))))));
+ var s = z * x;
+ r = y + z * (s * (r + v) + y);
+ r = r + KTAN(0) * s;
+ w = x + r;
+ if (ix >= 0x3fe59428) {
+ return (1 - ((hx >> 30) & 2)) *
+ (returnTan - 2.0 * (x - (w * w / (w + returnTan) - r)));
+ }
+ if (returnTan == 1) {
+ return w;
+ } else {
+ z = %_ConstructDouble(%_DoubleHi(w), 0);
+ v = r - (z - x);
+ var a = -1 / w;
+ var t = %_ConstructDouble(%_DoubleHi(a), 0);
+ s = 1 + t * z;
+ return t + a * (s + t * v);
+ }
+}
+
+function MathSinSlow(x) {
+ REMPIO2(x);
+ var sign = 1 - (n & 2);
+ if (n & 1) {
+ RETURN_KERNELCOS(y0, y1, * sign);
+ } else {
+ RETURN_KERNELSIN(y0, y1, * sign);
+ }
+}
+
+function MathCosSlow(x) {
+ REMPIO2(x);
+ if (n & 1) {
+ var sign = (n & 2) - 1;
+ RETURN_KERNELSIN(y0, y1, * sign);
+ } else {
+ var sign = 1 - (n & 2);
+ RETURN_KERNELCOS(y0, y1, * sign);
+ }
+}
+
+// ECMA 262 - 15.8.2.16
+function MathSin(x) {
+ x = x * 1; // Convert to number.
+ if ((%_DoubleHi(x) & 0x7fffffff) <= 0x3fe921fb) {
+ // |x| < pi/4, approximately. No reduction needed.
+ RETURN_KERNELSIN(x, 0, /* empty */);
+ }
+ return MathSinSlow(x);
+}
+
+// ECMA 262 - 15.8.2.7
+function MathCos(x) {
+ x = x * 1; // Convert to number.
+ if ((%_DoubleHi(x) & 0x7fffffff) <= 0x3fe921fb) {
+ // |x| < pi/4, approximately. No reduction needed.
+ RETURN_KERNELCOS(x, 0, /* empty */);
+ }
+ return MathCosSlow(x);
+}
+
+// ECMA 262 - 15.8.2.18
+function MathTan(x) {
+ x = x * 1; // Convert to number.
+ if ((%_DoubleHi(x) & 0x7fffffff) <= 0x3fe921fb) {
+ // |x| < pi/4, approximately. No reduction needed.
+ return KernelTan(x, 0, 1);
+ }
+ REMPIO2(x);
+ return KernelTan(y0, y1, (n & 1) ? -1 : 1);
+}
« no previous file with comments | « third_party/fdlibm/fdlibm.cc ('k') | tools/generate-runtime-tests.py » ('j') | no next file with comments »

Powered by Google App Engine
This is Rietveld 408576698