https://github.com/ifduyue/musl/blob/master/src/math/__cos.c Skip to content Toggle navigation Sign up * Product + Actions Automate any workflow + Packages Host and manage packages + Security Find and fix vulnerabilities + Codespaces Instant dev environments + Copilot Write better code with AI + Code review Manage code changes + Issues Plan and track work + Discussions Collaborate outside of code + Explore + All features + Documentation + GitHub Skills + Blog * Solutions + For + Enterprise + Teams + Startups + Education + By Solution + CI/CD & Automation + DevOps + DevSecOps + Case Studies + Customer Stories + Resources * Open Source + GitHub Sponsors Fund open source developers + The ReadME Project GitHub community articles + Repositories + Topics + Trending + Collections * Pricing [ ] * # In this repository All GitHub | Jump to | * No suggested jump to results * # In this repository All GitHub | Jump to | * # In this user All GitHub | Jump to | * # In this repository All GitHub | Jump to | Sign in Sign up {{ message }} ifduyue / musl Public * Notifications * Fork 28 * Star 148 * Code * Pull requests 0 * Actions * Security * Insights More * Code * Pull requests * Actions * Security * Insights Permalink master Switch branches/tags [ ] Branches Tags Could not load branches Nothing to show {{ refName }} default View all branches Could not load tags Nothing to show {{ refName }} default View all tags Name already in use A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch? Cancel Create musl/src/math/__cos.c Go to file * Go to file T * Go to line L * * Copy path * Copy permalink This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. # Szabolcs Nagy math: use double_t for temporaries to avoid stores on i386 ... Latest commit e216951 May 15, 2013 History When FLT_EVAL_METHOD!=0 (only i386 with x87 fp) the excess precision of an expression must be removed in an assignment. (gcc needs -fexcess-precision=standard or -std=c99 for this) This is done by extra load/store instructions which adds code bloat when lot of temporaries are used and it makes the result less precise in many cases. Using double_t and float_t avoids these issues on i386 and it makes no difference on other archs. For now only a few functions are modified where the excess precision is clearly beneficial (mostly polynomial evaluations with temporaries). object size differences on i386, gcc-4.8: old new __cosdf.o 123 95 __cos.o 199 169 __sindf.o 131 95 __sin.o 225 203 __tandf.o 207 151 __tan.o 605 499 erff.o 1470 1416 erf.o 1703 1649 j0f.o 1779 1745 j0.o 2308 2274 j1f.o 1602 1568 j1.o 2286 2252 tgamma.o 1431 1424 math/*.o 64164 63635 0 contributors Users who have contributed to this file 71 lines (67 sloc) 2.82 KB Raw Blame Edit this file E Open in GitHub Desktop * Open with Desktop * View raw * * View blame This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters Show hidden characters /* origin: FreeBSD /usr/src/lib/msun/src/k_cos.c */ /* * ==================================================== * 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. * ==================================================== */ /* * __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. * * Algorithm * 1. Since cos(-x) = cos(x), we need only to consider positive x. * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. * 3. 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 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 * | | * * 4 6 8 10 12 14 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then * cos(x) ~ 1 - x*x/2 + r * since cos(x+y) ~ cos(x) - sin(x)*y * ~ cos(x) - x*y, * a correction term is necessary in cos(x) and hence * cos(x+y) = 1 - (x*x/2 - (r - x*y)) * For better accuracy, rearrange to * cos(x+y) ~ w + (tmp + (r-x*y)) * where w = 1 - x*x/2 and tmp is a tiny correction term * (1 - x*x/2 == w + tmp exactly in infinite precision). * The exactness of w + tmp in infinite precision depends on w * and tmp having the same precision as x. If they have extra * precision due to compiler bugs, then the extra precision is * only good provided it is retained in all terms of the final * expression for cos(). Retention happens in all cases tested * under FreeBSD, so don't pessimize things by forcibly clipping * any extra precision in w. */ #include "libm.h" static const double C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ double __cos(double x, double y) { double_t hz,z,r,w; z = x*x; w = z*z; r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); hz = 0.5*z; w = 1.0-hz; return w + (((1.0-w)-hz) + (z*r-x*y)); } * Copy lines * Copy permalink * View git blame [ ] Go Footer (c) 2023 GitHub, Inc. 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