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lib/msun/src/k_sincosl.h

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/*-
* ====================================================
lidlUnsubmitted
Done
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And here, /*-

lidl: And here, /*-
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* k_sinl.c and k_cosl.c merged by Steven G. Kargl
*/
#if LDBL_MANT_DIG == 64 /* ld80 version of k_sincosl.c. */
#if defined(__amd64__) || defined(__i386__)
/* Long double constants are slow on these arches, and broken on i386. */
static const volatile double
C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */
C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */
S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */
S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */
#define S1 ((long double)S1hi + S1lo)
#define C1 ((long double)C1hi + C1lo)
#else
static const long double
C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
S1 = -0.166666666666666666671L, /* -0xaaaaaaaaaaaaaaab.0p-66 */
#endif
static const double
C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
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 */
S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
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 */
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
{
long double hz, r, v, w, z;
z = x * x;
v = z * x;
/*
* XXX Replace Horner scheme with an algorithm suitable for CPUs
* with more complex pipelines.
*/
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))));
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
*sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
z * C7))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}
#elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */
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,
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
C8 = -0.1561920696721507929516718307820958119868e-15,
C9 = 0.4110317413744594971475941557607804508039e-18,
C10 = -0.8896592467191938803288521958313920156409e-21,
C11 = 0.1601061435794535138244346256065192782581e-23,
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
{
long double hz, r, v, w, z;
z = x * x;
v = z * x;
/*
* XXX Replace Horner scheme with an algorithm suitable for CPUs
* with more complex pipelines.
*/
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
*cs = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}
#else
#error "Unsupported long double format"
#endif