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math: long double trigonometric cleanup (cosl, sinl, sincosl, tanl)

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ld128 support was added to internal kernel functions (__cosl, __sinl,
__tanl, __rem_pio2l) from freebsd (not tested, but should be a good
start for when ld128 arch arrives)

__rem_pio2l had some code cleanup, the freebsd ld128 code seems to
gather the results of a large reduction with precision loss (fixed
the bug but a todo comment was added for later investigation)

the old copyright was removed from the non-kernel wrapper functions
(cosl, sinl, sincosl, tanl) since these are trivial and the interesting
parts and comments had been already rewritten.
This commit is contained in:
Szabolcs Nagy 2013-09-03 18:50:58 +00:00
parent bcd797a5ba
commit ea9bb95a5b
8 changed files with 228 additions and 236 deletions
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37
src/math/__cosl.c
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@ -1,4 +1,5 @@
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */
/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -14,7 +15,8 @@
#include "libm.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
/*
* ld80 version of __cos.c. See __cos.c for most comments.
*/
@ -43,7 +45,6 @@
*/
static const long double
C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
static const double
C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
@ -51,13 +52,43 @@ C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */
#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))))
#elif LDBL_MANT_DIG == 113
/*
* ld128 version of __cos.c. See __cos.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
* |cos(x) - c(x))| < 2**-122.0
*
* 113-bit precision requires more care than 64-bit precision, since
* simple methods give a minimax polynomial with coefficient for x^2
* that is 1 ulp below 0.5, but we want it to be precisely 0.5. See
* above for more details.
*/
static const long double
C1 = 0.04166666666666666666666666666666658424671L,
C2 = -0.001388888888888888888888888888863490893732L,
C3 = 0.00002480158730158730158730158600795304914210L,
C4 = -0.2755731922398589065255474947078934284324e-6L,
C5 = 0.2087675698786809897659225313136400793948e-8L,
C6 = -0.1147074559772972315817149986812031204775e-10L,
C7 = 0.4779477332386808976875457937252120293400e-13L;
static const double
C8 = -0.1561920696721507929516718307820958119868e-15,
C9 = 0.4110317413744594971475941557607804508039e-18,
C10 = -0.8896592467191938803288521958313920156409e-21,
C11 = 0.1601061435794535138244346256065192782581e-23;
#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \
z*(C8+z*(C9+z*(C10+z*C11)))))))))))
#endif
long double __cosl(long double x, long double y)
{
long double hz,z,r,w;
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))));
r = POLY(z);
hz = 0.5*z;
w = 1.0-hz;
return w + (((1.0-w)-hz) + (z*r-x*y));

117
src/math/__rem_pio2l.c
View File

@ -13,15 +13,22 @@
* Optimized by Bruce D. Evans.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
/* ld80 version of __rem_pio2(x,y)
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
/* ld80 and ld128 version of __rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __rem_pio2_large() for large x
*/
#define BIAS (LDBL_MAX_EXP - 1)
#if LDBL_MANT_DIG == 64
/* u ~< 0x1p25*pi/2 */
#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))
#define TOINT 0x1.8p63
#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
#define ROUND1 22
#define ROUND2 61
#define NX 3
#define NY 2
/*
* invpio2: 64 bits of 2/pi
* pio2_1: first 39 bits of pi/2
@ -32,60 +39,61 @@
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
static const long double
invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
#elif LDBL_MANT_DIG == 113
/* u ~< 0x1p45*pi/2 */
#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))
#define TOINT 0x1.8p112
#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
#define ROUND1 51
#define ROUND2 119
#define NX 5
#define NY 3
static const long double
invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */
pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */
pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */
pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */
pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */
pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */
#endif
int __rem_pio2l(long double x, long double *y)
{
union IEEEl2bits u,u1;
union ldshape u,uz;
long double z,w,t,r,fn;
double tx[3],ty[2];
int e0,ex,i,j,nx,n;
int16_t expsign;
double tx[NX],ty[NY];
int ex,ey,n,i;
u.e = x;
expsign = u.xbits.expsign;
ex = expsign & 0x7fff;
if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
union IEEEl2bits u2;
int ex1;
/* |x| ~< 2^25*(pi/2), medium size */
/* Use a specialized rint() to get fn. Assume round-to-nearest. */
fn = x*invpio2 + 0x1.8p63;
fn = fn - 0x1.8p63;
// FIXME
//#ifdef HAVE_EFFICIENT_IRINT
// n = irint(fn);
//#else
n = fn;
//#endif
u.f = x;
ex = u.i.se & 0x7fff;
if (SMALL(u)) {
/* rint(x/(pi/2)), Assume round-to-nearest. */
fn = x*invpio2 + TOINT - TOINT;
n = QUOBITS(fn);
r = x-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 102 bit */
j = ex;
w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if (i > 22) { /* 2nd iteration needed, good to 141 */
u.f = y[0];
ey = u.i.se & 0x7fff;
if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if (i > 61) { /* 3rd iteration need, 180 bits acc */
t = r; /* will cover all possible cases */
u.f = y[0];
ey = u.i.se & 0x7fff;
if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
t = r; /* will cover all possible cases (not verified for ld128) */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
@ -102,23 +110,26 @@ int __rem_pio2l(long double x, long double *y)
y[0] = y[1] = x - x;
return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
u1.e = x;
e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
u1.xbits.expsign = ex - e0;
z = u1.e;
for (i=0; i<2; i++) {
/* set z = scalbn(|x|,-ilogb(x)+23) */
uz.f = x;
uz.i.se = 0x3fff + 23;
z = uz.f;
for (i=0; i < NX - 1; i++) {
tx[i] = (double)(int32_t)z;
z = (z-tx[i])*two24;
z = (z-tx[i])*0x1p24;
}
tx[2] = z;
nx = 3;
while (tx[nx-1] == 0.0)
nx--; /* skip zero term */
n = __rem_pio2_large(tx,ty,e0,nx,2);
r = (long double)ty[0] + ty[1];
w = ty[1] - (r - ty[0]);
if (expsign < 0) {
tx[i] = z;
while (tx[i] == 0)
i--;
n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY);
w = ty[1];
if (NY == 3)
w += ty[2];
r = ty[0] + w;
/* TODO: for ld128 this does not follow the recommendation of the
comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
w -= r - ty[0];
if (u.i.se >> 15) {
y[0] = -r;
y[1] = -w;
return -n;

36
src/math/__sinl.c
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@ -1,4 +1,5 @@
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */
/* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
@ -13,7 +14,8 @@
#include "libm.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
/*
* ld80 version of __sin.c. See __sin.c for most comments.
*/
@ -23,10 +25,8 @@
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */
static const double
S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
@ -35,6 +35,34 @@ S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8))))))
#elif LDBL_MANT_DIG == 113
/*
* ld128 version of __sin.c. See __sin.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
* |sin(x)/x - s(x)| < 2**-122.1
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 = 0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
S4 = 0.27557319223985890652557316053039946268333231205686e-5L,
S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
S6 = 0.16059043836821614596571832194524392581082444805729e-9L,
S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
static const double
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ \
z*(S9+z*(S10+z*(S11+z*S12))))))))))
#endif
long double __sinl(long double x, long double y, int iy)
{
@ -42,7 +70,7 @@ long double __sinl(long double x, long double y, int iy)
z = x*x;
v = z*x;
r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))));
r = POLY(z);
if (iy == 0)
return x+v*(S1+z*r);
return x-((z*(0.5*y-v*r)-y)-v*S1);

66
src/math/__tanl.c
View File

@ -1,4 +1,5 @@
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
/* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */
/*
* ====================================================
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
@ -12,7 +13,8 @@
#include "libm.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
/*
* ld80 version of __tan.c. See __tan.c for most comments.
*/
@ -22,14 +24,12 @@
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */
T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */
T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */
pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */
pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */
static const double
T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */
T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */
@ -44,6 +44,59 @@ T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */
T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
w * (T25 + w * (T29 + w * T33)))))))
#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
w * (T27 + w * T31))))))
#elif LDBL_MANT_DIG == 113
/*
* ld128 version of __tan.c. See __tan.c for most comments.
*/
/*
* Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
* |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
T3 = 0x1.5555555555555555555555555553p-2L,
T5 = 0x1.1111111111111111111111111eb5p-3L,
T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
T17 = 0x1.355824803674477dfcf726649efep-11L,
T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
static const double
T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 + \
w * (T45 + w * (T49 + w * (T53 + w * T57)))))))))))))
#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 + \
w * (T47 + w * (T51 + w * T55))))))))))))
#endif
long double __tanl(long double x, long double y, int odd) {
long double z, r, v, w, s, a, t;
@ -62,10 +115,8 @@ long double __tanl(long double x, long double y, int odd) {
}
z = x * x;
w = z * z;
r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
w * (T25 + w * (T29 + w * T33))))));
v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
w * (T27 + w * T31))))));
r = RPOLY(w);
v = z * VPOLY(w);
s = z * x;
r = y + z * (s * (r + v) + y) + T3 * s;
w = x + r;
@ -76,7 +127,6 @@ long double __tanl(long double x, long double y, int odd) {
}
if (!odd)
return w;
/*
* if allow error up to 2 ulp, simply return
* -1.0 / (x+r) here

70
src/math/cosl.c
View File

@ -1,34 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_cosl.c */
/*-
* Copyright (c) 2007 Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
* an accuracy of <= 0.7412 ULP.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -38,44 +7,33 @@ long double cosl(long double x) {
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double cosl(long double x)
{
union IEEEl2bits z;
union ldshape u = {x};
unsigned n;
long double y[2];
long double hi, lo;
long double y[2], hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64)
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
x = u.f;
if (x < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(z.e, 0);
return __cosl(x, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
hi = __cosl(hi, lo);
break;
return __cosl(hi, lo);
case 1:
hi = -__sinl(hi, lo, 1);
break;
return -__sinl(hi, lo, 1);
case 2:
hi = -__cosl(hi, lo);
break;
return -__cosl(hi, lo);
case 3:
hi = __sinl(hi, lo, 1);
break;
default:
return __sinl(hi, lo, 1);
}
return hi;
}
#endif

19
src/math/sincosl.c
View File

@ -9,25 +9,19 @@ void sincosl(long double x, long double *sin, long double *cos)
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
void sincosl(long double x, long double *sin, long double *cos)
{
union IEEEl2bits u;
union ldshape u = {x};
unsigned n;
long double y[2], s, c;
u.e = x;
u.bits.sign = 0;
/* x = nan or inf */
if (u.bits.exp == 0x7fff) {
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff) {
*sin = *cos = x - x;
return;
}
/* |x| < (double)pi/4 */
if (u.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (u.bits.exp < 0x3fff - 64) {
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG) {
/* raise underflow if subnormal */
if (u.bits.exp == 0) FORCE_EVAL(x*0x1p-120f);
if (u.i.se == 0) FORCE_EVAL(x*0x1p-120f);
*sin = x;
/* raise inexact if x!=0 */
*cos = 1.0 + x;
@ -37,7 +31,6 @@ void sincosl(long double x, long double *sin, long double *cos)
*cos = __cosl(x, 0);
return;
}
n = __rem_pio2l(x, y);
s = __sinl(y[0], y[1], 1);
c = __cosl(y[0], y[1]);

66
src/math/sinl.c
View File

@ -1,31 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_sinl.c */
/*-
* Copyright (c) 2007 Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -36,46 +8,34 @@ long double sinl(long double x)
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double sinl(long double x)
{
union IEEEl2bits z;
union ldshape u = {x};
unsigned n;
long double y[2];
long double hi, lo;
long double y[2], hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = NaN or Inf, then sin(x) = NaN. */
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64) {
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(z.bits.exp == 0 ? x/0x1p120f : x+0x1p120f);
FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
return x;
}
return __sinl(x, 0.0, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
hi = __sinl(hi, lo, 1);
break;
return __sinl(hi, lo, 1);
case 1:
hi = __cosl(hi, lo);
break;
return __cosl(hi, lo);
case 2:
hi = -__sinl(hi, lo, 1);
break;
return -__sinl(hi, lo, 1);
case 3:
hi = -__cosl(hi, lo);
break;
default:
return -__cosl(hi, lo);
}
return hi;
}
#endif

53
src/math/tanl.c
View File

@ -1,35 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_tanl.c */
/*-
* Copyright (c) 2007 Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Limited testing on pseudorandom numbers drawn within [0:4e8] shows
* an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
* possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -40,28 +8,21 @@ long double tanl(long double x)
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double tanl(long double x)
{
union IEEEl2bits z;
union ldshape u = {x};
long double y[2];
unsigned n;
z.e = x;
z.bits.sign = 0;
/* If x = NaN or Inf, then tan(x) = NaN. */
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64) {
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(z.bits.exp == 0 ? x/0x1p120f : x+0x1p120f);
FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
return x;
}
return __tanl(x, 0, 0);
}
n = __rem_pio2l(x, y);
return __tanl(y[0], y[1], n&1);
}