gnulib: lib/tanl.c annotate

annotate lib/tanl.c @ 40231:9b3c79fdfe0b

strtod: fix clash with strtold Problem reported for RHEL 5 by Jesse Caldwell (Bug#34817). * lib/strtod.c (compute_minus_zero, minus_zero): Simplify by remving the macro / external variable, and having just a function. User changed. This avoids the need for an external variable that might clash.

author	Paul Eggert <eggert@cs.ucla.edu>
date	Mon, 11 Mar 2019 16:40:29 -0700
parents	2074f2bf7216
children

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
16511 2074f2bf7216 math code: Add comments. Bruno Haible <bruno@clisp.org> parents: 15941 diff changeset	32 /* Code based on glibc/sysdeps/ieee754/ldbl-128/s_tanl.c
2074f2bf7216 math code: Add comments. Bruno Haible <bruno@clisp.org> parents: 15941 diff changeset	33 and glibc/sysdeps/ieee754/ldbl-128/k_tanl.c. */
2074f2bf7216 math code: Add comments. Bruno Haible <bruno@clisp.org> parents: 15941 diff changeset	34
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	35 /* tanl(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	36 * Return tangent function of x.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	37 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	38 * kernel function:
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	39 * __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	40 * __ieee754_rem_pio2l ... argument reduction routine
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	41 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	42 * Method.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	43 * 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	44 * [-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	45 * 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	46 * We have
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	47 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	48 * n sin(x) cos(x) tan(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	49 * ----------------------------------------------------------
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	50 * 0 S C T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	51 * 1 C -S -1/T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	52 * 2 -S -C T
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	53 * 3 -C S -1/T
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	54 * ----------------------------------------------------------
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	55 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	56 * Special cases:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	57 * 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	58 * trig(+-INF) is NaN, with signals;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	59 * trig(NaN) is that NaN;
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 * Accuracy:
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	62 * 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	63 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	64
15941 83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	65 # include "trigl.h"
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	66
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 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	69 * 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	70 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	71 * 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	72 * 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	73 * 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	74 * is preserved.
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 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	77
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 Long double expansions contributed by
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	80 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	81 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	82
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	83 /* __kernel_tanl( x, y, k )
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	84 * 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	85 * 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	86 * Input y is the tail of x.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	87 * 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	88 * -1/tan (if k= -1) is returned.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	89 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	90 * Algorithm
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	91 * 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	92 * 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	93 * 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	94 * on [0,0.67433].
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	95 *
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	96 * 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	97 * ~ tan(x) + (1+xx)y
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	98 * 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	99 * r = x^3 * R(x^2)
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	100 * then
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	101 * 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	102 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	103 * 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	104 * 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	105 * = 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	106 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	107
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	108
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	109 static const long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	110 pio4hi = 7.8539816339744830961566084581987569936977E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	111 pio4lo = 2.1679525325309452561992610065108379921906E-35L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	112
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	113 /* 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	114 0 <= x <= 0.6743316650390625
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	115 Peak relative error 8.0e-36 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	116 TH = 3.333333333333333333333333333333333333333E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	117 T0 = -1.813014711743583437742363284336855889393E7L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	118 T1 = 1.320767960008972224312740075083259247618E6L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	119 T2 = -2.626775478255838182468651821863299023956E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	120 T3 = 1.764573356488504935415411383687150199315E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	121 T4 = -3.333267763822178690794678978979803526092E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	122
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	123 U0 = -1.359761033807687578306772463253710042010E8L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	124 U1 = 6.494370630656893175666729313065113194784E7L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	125 U2 = -4.180787672237927475505536849168729386782E6L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	126 U3 = 8.031643765106170040139966622980914621521E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	127 U4 = -5.323131271912475695157127875560667378597E2L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	128 /* 1.000000000000000000000000000000000000000E0 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	129
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	130
12752 73d9dd27dc41 New modules acosl, asinl, atanl, cosl, expl, logl, sinl, sqrtl, tanl. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	131 static long double
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	132 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	133 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	134 long double z, r, v, w, s, u, u1;
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	135 int invert = 0, sign;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	136
8544 245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	137 sign = 1;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	138 if (x < 0)
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	139 {
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	140 x = -x;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	141 y = -y;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	142 sign = -1;
245a3653b197 Fix indentation. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	143 }
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	144
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	145 if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* x < 2*-57 /
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	146 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	147 if ((int) x == 0)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	148 { /* generate inexact */
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	149 if (iy == -1 && x == 0.0)
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	150 return 1.0L / fabs (x);
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	151 else
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	152 return (iy == 1) ? x : -1.0L / x;
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	153 }
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	154 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	155 if (x >= 0.6743316650390625) /* \|x\| >= 0.6743316650390625 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	156 {
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	157 invert = 1;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	158
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	159 z = pio4hi - x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	160 w = pio4lo - y;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	161 x = z + w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	162 y = 0.0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	163 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	164 z = x * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	165 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	166 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	167 r = r / v;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	168
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	169 s = z * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	170 r = y + z * (s * r + y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	171 r += TH * s;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	172 w = x + r;
9923 810b08d769f8 fix typos in mathl Paolo Bonzini <bonzini@gnu.org> parents: 8563 diff changeset	173 if (invert)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	174 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	175 v = (long double) iy;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	176 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	177 if (sign < 0)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	178 w = -w;
4239 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 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	181 if (iy == 1)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	182 return w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	183 else
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	184 { /* if allow error up to 2 ulp,
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	185 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	186 /* compute -1.0/(x+r) accurately */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	187 u1 = (double) w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	188 v = r - (u1 - x);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	189 z = -1.0 / w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	190 u = (double) z;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	191 s = 1.0 + u * u1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	192 return u + z * (s + u * v);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	193 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	194 }
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
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	197 tanl (long double x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	198 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	199 long double y[2], z = 0.0L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	200 int n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	201
8563 c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	202 /* tanl(NaN) is NaN */
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	203 if (isnanl (x))
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	204 return x;
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	205
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	206 /* \|x\| ~< pi/4 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	207 if (x >= -0.7853981633974483096156608458198757210492 &&
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	208 x <= 0.7853981633974483096156608458198757210492)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	209 return kernel_tanl (x, z, 1);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	210
8563 c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	211 /* tanl(Inf) is NaN, tanl(0) is 0 */
c3d334708928 Better support of signalling NaNs. Bruno Haible <bruno@clisp.org> parents: 8544 diff changeset	212 else if (x + x == x)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 10667 diff changeset	213 return x - x; /* NaN */
4239 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 /* argument reduction needed */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	216 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	217 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	218 n = ieee754_rem_pio2l (x, y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	219 /* 1 -- n even, -1 -- n odd */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	220 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	221 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	222 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	223
15941 83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	224 #endif
83c276c24d2a tanl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	225
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	226 #if 0
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	227 int
4652 b09c3f1225b6 Remove K&R cruft. Paul Eggert <eggert@cs.ucla.edu> parents: 4239 diff changeset	228 main (void)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	229 {
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	230 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	231 printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	232 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 *3));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	233 printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492 *31));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	234 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 / 2));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	235 printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 3/2));
094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12752 diff changeset	236 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	237 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	238 #endif

Mercurial > gnulib

annotate lib/tanl.c @ 40231:9b3c79fdfe0b