octave-kai/gnulib-hg: lib/tanl.c annotate

annotate lib/tanl.c @ 15941:83c276c24d2a

tanl: Simplify for platforms where 'long double' == 'double'. * lib/tanl.c (tanl) [HAVE_SAME_LONG_DOUBLE_AS_DOUBLE]: New alternative implementation. * m4/tanl.m4 (gl_FUNC_TANL): Require gl_LONG_DOUBLE_VS_DOUBLE. Determine TANL_LIBM according to HAVE_SAME_LONG_DOUBLE_AS_DOUBLE. * modules/tanl (Depends-on): Add tan. Update conditions. (configure.ac): Don't compile trigl.c if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE.

author	Bruno Haible <bruno@clisp.org>
date	Tue, 11 Oct 2011 02:57:05 +0200
parents	094f6cfdb5c3
children	2074f2bf7216

rev	line source
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	1 /* s_tanl.c -- long double version of s_tan.c.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	2 * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	3 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	4
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	5 /* @(#)s_tan.c 5.1 93/09/24 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	6 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	7 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	9 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	10 * Developed at SunPro, a Sun Microsystems, Inc. business.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	11 * Permission to use, copy, modify, and distribute this
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	12 * software is freely granted, provided that this notice
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	13 * is preserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	14 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	15 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	16
8186 c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	17 #include <config.h>
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	18
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	19 /* Specification. */
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	20 #include <math.h>
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	21
15941 83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	22 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	23
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	24 long double
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	25 tanl (long double x)
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	26 {
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	27 return tan (x);
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	28 }
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	29
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	30 #else
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	31
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	32 /* tanl(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	33 * Return tangent function of x.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	34 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	35 * kernel function:
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	36 * __kernel_tanl ... tangent function on [-pi/4,pi/4]
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	37 * __ieee754_rem_pio2l ... argument reduction routine
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	38 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	39 * Method.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	40 * Let S,C and T denote the sin, cos and tan respectively on
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	41 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	42 * in [-pi/4 , +pi/4], and let n = k mod 4.
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	43 * We have
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	44 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	45 * n sin(x) cos(x) tan(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	46 * ----------------------------------------------------------
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	47 * 0 S C T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	48 * 1 C -S -1/T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	49 * 2 -S -C T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	50 * 3 -C S -1/T
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	51 * ----------------------------------------------------------
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	52 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	53 * Special cases:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	54 * Let trig be any of sin, cos, or tan.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	55 * trig(+-INF) is NaN, with signals;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	56 * trig(NaN) is that NaN;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	57 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	58 * Accuracy:
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	59 * TRIG(x) returns trig(x) nearly rounded
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	60 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	61
15941 83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	62 # include "trigl.h"
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	63
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	64 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	65 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	66 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	67 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	68 * Developed at SunPro, a Sun Microsystems, Inc. business.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	69 * Permission to use, copy, modify, and distribute this
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	70 * software is freely granted, provided that this notice
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	71 * is preserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	72 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	73 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	74
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	75 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	76 Long double expansions contributed by
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	77 Stephen L. Moshier <moshier@na-net.ornl.gov>
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	78 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	79
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	80 /* __kernel_tanl( x, y, k )
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	81 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	82 * Input x is assumed to be bounded by ~pi/4 in magnitude.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	83 * Input y is the tail of x.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	84 * Input k indicates whether tan (if k=1) or
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	85 * -1/tan (if k= -1) is returned.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	86 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	87 * Algorithm
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	88 * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	89 * 2. if x < 2^-57, return x with inexact if x!=0.
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	90 * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	91 * on [0,0.67433].
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	92 *
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	93 * Note: tan(x+y) = tan(x) + tan'(x)*y
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	94 * ~ tan(x) + (1+xx)y
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	95 * Therefore, for better accuracy in computing tan(x+y), let
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	96 * r = x^3 * R(x^2)
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	97 * then
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	98 * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	99 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	100 * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	101 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	102 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	103 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	104
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	105
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	106 static const long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	107 pio4hi = 7.8539816339744830961566084581987569936977E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	108 pio4lo = 2.1679525325309452561992610065108379921906E-35L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	109
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	110 /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	111 0 <= x <= 0.6743316650390625
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	112 Peak relative error 8.0e-36 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	113 TH = 3.333333333333333333333333333333333333333E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	114 T0 = -1.813014711743583437742363284336855889393E7L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	115 T1 = 1.320767960008972224312740075083259247618E6L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	116 T2 = -2.626775478255838182468651821863299023956E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	117 T3 = 1.764573356488504935415411383687150199315E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	118 T4 = -3.333267763822178690794678978979803526092E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	119
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	120 U0 = -1.359761033807687578306772463253710042010E8L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	121 U1 = 6.494370630656893175666729313065113194784E7L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	122 U2 = -4.180787672237927475505536849168729386782E6L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	123 U3 = 8.031643765106170040139966622980914621521E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	124 U4 = -5.323131271912475695157127875560667378597E2L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	125 /* 1.000000000000000000000000000000000000000E0 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	126
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	127
12752 73d9dd27dc41 New modules acosl, asinl, atanl, cosl, expl, logl, sinl, sqrtl, tanl. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	128 static long double
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	129 kernel_tanl (long double x, long double y, int iy)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	130 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	131 long double z, r, v, w, s, u, u1;
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	132 int invert = 0, sign;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	133
8544 245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	134 sign = 1;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	135 if (x < 0)
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	136 {
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	137 x = -x;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	138 y = -y;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	139 sign = -1;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	140 }
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	141
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	142 if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* x < 2*-57 /
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	143 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	144 if ((int) x == 0)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	145 { /* generate inexact */
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	146 if (iy == -1 && x == 0.0)
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	147 return 1.0L / fabs (x);
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	148 else
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	149 return (iy == 1) ? x : -1.0L / x;
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	150 }
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	151 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	152 if (x >= 0.6743316650390625) /* \|x\| >= 0.6743316650390625 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	153 {
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	154 invert = 1;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	155
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	156 z = pio4hi - x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	157 w = pio4lo - y;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	158 x = z + w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	159 y = 0.0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	160 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	161 z = x * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	162 r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	163 v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	164 r = r / v;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	165
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	166 s = z * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	167 r = y + z * (s * r + y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	168 r += TH * s;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	169 w = x + r;
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	170 if (invert)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	171 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	172 v = (long double) iy;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	173 w = (v - 2.0 * (x - (w * w / (w + v) - r)));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	174 if (sign < 0)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	175 w = -w;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	176 return w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	177 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	178 if (iy == 1)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	179 return w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	180 else
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	181 { /* if allow error up to 2 ulp,
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	182 simply return -1.0/(x+r) here */
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	183 /* compute -1.0/(x+r) accurately */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	184 u1 = (double) w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	185 v = r - (u1 - x);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	186 z = -1.0 / w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	187 u = (double) z;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	188 s = 1.0 + u * u1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	189 return u + z * (s + u * v);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	190 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	191 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	192
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	193 long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	194 tanl (long double x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	195 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	196 long double y[2], z = 0.0L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	197 int n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	198
8563 c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	199 /* tanl(NaN) is NaN */
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	200 if (isnanl (x))
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	201 return x;
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	202
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	203 /* \|x\| ~< pi/4 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	204 if (x >= -0.7853981633974483096156608458198757210492 &&
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	205 x <= 0.7853981633974483096156608458198757210492)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	206 return kernel_tanl (x, z, 1);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	207
8563 c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	208 /* tanl(Inf) is NaN, tanl(0) is 0 */
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	209 else if (x + x == x)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	210 return x - x; /* NaN */
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	211
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	212 /* argument reduction needed */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	213 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	214 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	215 n = ieee754_rem_pio2l (x, y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	216 /* 1 -- n even, -1 -- n odd */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	217 return kernel_tanl (y[0], y[1], 1 - ((n & 1) << 1));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	218 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	219 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	220
15941 83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	221 #endif
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	222
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	223 #if 0
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	224 int
4652 b09c3f1225b6 Remove K&R cruft. Paul Eggert <eggert@cs.ucla.edu> parents: 4239 diff changeset	225 main (void)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	226 {
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	227 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	228 printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	229 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 *3));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	230 printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492 *31));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	231 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 / 2));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	232 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 3/2));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	233 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 5/2));
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	234 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	235 #endif

Mercurial > hg > octave-kai > gnulib-hg

annotate lib/tanl.c @ 15941:83c276c24d2a