388 lines
7.9 KiB
C
388 lines
7.9 KiB
C
/* sin.c
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*
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* Circular sine
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, sin();
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*
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* y = sin( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Range reduction is into intervals of pi/4. The reduction
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* error is nearly eliminated by contriving an extended precision
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* modular arithmetic.
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*
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* Two polynomial approximating functions are employed.
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* Between 0 and pi/4 the sine is approximated by
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* x + x**3 P(x**2).
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* Between pi/4 and pi/2 the cosine is represented as
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* 1 - x**2 Q(x**2).
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC 0, 10 150000 3.0e-17 7.8e-18
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* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* sin total loss x > 1.073741824e9 0.0
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*
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* Partial loss of accuracy begins to occur at x = 2**30
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* = 1.074e9. The loss is not gradual, but jumps suddenly to
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* about 1 part in 10e7. Results may be meaningless for
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* x > 2**49 = 5.6e14. The routine as implemented flags a
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* TLOSS error for x > 2**30 and returns 0.0.
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*/
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/* cos.c
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*
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* Circular cosine
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, cos();
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*
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* y = cos( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Range reduction is into intervals of pi/4. The reduction
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* error is nearly eliminated by contriving an extended precision
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* modular arithmetic.
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*
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* Two polynomial approximating functions are employed.
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* Between 0 and pi/4 the cosine is approximated by
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* 1 - x**2 Q(x**2).
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* Between pi/4 and pi/2 the sine is represented as
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* x + x**3 P(x**2).
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
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* DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
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*/
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/* sin.c */
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1985, 1995, 2000 by Stephen L. Moshier
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*/
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#include "mconf.h"
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#ifdef UNK
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const static double sincof[] = {
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1.58962301576546568060E-10,
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-2.50507477628578072866E-8,
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2.75573136213857245213E-6,
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-1.98412698295895385996E-4,
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8.33333333332211858878E-3,
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-1.66666666666666307295E-1,
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};
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const static double coscof[6] = {
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-1.13585365213876817300E-11,
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2.08757008419747316778E-9,
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-2.75573141792967388112E-7,
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2.48015872888517045348E-5,
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-1.38888888888730564116E-3,
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4.16666666666665929218E-2,
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};
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const static double DP1 = 7.85398125648498535156E-1;
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const static double DP2 = 3.77489470793079817668E-8;
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const static double DP3 = 2.69515142907905952645E-15;
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/* const static double lossth = 1.073741824e9; */
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#endif
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#ifdef DEC
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static unsigned short sincof[] = {
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0030056,0143750,0177214,0163153,
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0131727,0027455,0044510,0175352,
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0033470,0167432,0131752,0042414,
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0135120,0006400,0146776,0174027,
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0036410,0104210,0104207,0137202,
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0137452,0125252,0125252,0125103,
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};
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static unsigned short coscof[24] = {
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0127107,0151115,0002060,0152325,
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0031017,0072353,0155161,0174053,
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0132623,0171173,0172542,0057056,
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0034320,0006400,0147102,0023652,
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0135666,0005540,0133012,0076213,
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0037052,0125252,0125252,0125126,
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};
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/* 7.853981629014015197753906250000E-1 */
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static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
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/* 4.960467869796758577649598009884E-10 */
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static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
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/* 2.860594363054915898381331279295E-18 */
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static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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#endif
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#ifdef IBMPC
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static unsigned short sincof[] = {
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0x9ccd,0x1fd1,0xd8fd,0x3de5,
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0x1f5d,0xa929,0xe5e5,0xbe5a,
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0x48a1,0x567d,0x1de3,0x3ec7,
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0xdf03,0x19bf,0x01a0,0xbf2a,
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0xf7d0,0x1110,0x1111,0x3f81,
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0x5548,0x5555,0x5555,0xbfc5,
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};
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static unsigned short coscof[24] = {
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0x1a9b,0xa086,0xfa49,0xbda8,
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0x3f05,0x7b4e,0xee9d,0x3e21,
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0x4bc6,0x7eac,0x7e4f,0xbe92,
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0x44f5,0x19c8,0x01a0,0x3efa,
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0x4f91,0x16c1,0xc16c,0xbf56,
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0x554b,0x5555,0x5555,0x3fa5,
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};
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/*
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7.85398125648498535156E-1,
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3.77489470793079817668E-8,
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2.69515142907905952645E-15,
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*/
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static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
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static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
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static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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#endif
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#ifdef MIEEE
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static unsigned short sincof[] = {
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0x3de5,0xd8fd,0x1fd1,0x9ccd,
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0xbe5a,0xe5e5,0xa929,0x1f5d,
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0x3ec7,0x1de3,0x567d,0x48a1,
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0xbf2a,0x01a0,0x19bf,0xdf03,
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0x3f81,0x1111,0x1110,0xf7d0,
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0xbfc5,0x5555,0x5555,0x5548,
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};
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static unsigned short coscof[24] = {
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0xbda8,0xfa49,0xa086,0x1a9b,
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0x3e21,0xee9d,0x7b4e,0x3f05,
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0xbe92,0x7e4f,0x7eac,0x4bc6,
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0x3efa,0x01a0,0x19c8,0x44f5,
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0xbf56,0xc16c,0x16c1,0x4f91,
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0x3fa5,0x5555,0x5555,0x554b,
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};
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static unsigned short P1[] = {0x3fe9,0x21fb,0x4000,0x0000};
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static unsigned short P2[] = {0x3e64,0x442d,0x0000,0x0000};
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static unsigned short P3[] = {0x3ce8,0x4698,0x98cc,0x5170};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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#endif
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#ifdef ANSIPROT
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double floor ( double );
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extern double ldexp ( double, int );
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extern int isnan ( double );
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extern int isfinite ( double );
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#else
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double polevl(), floor(), ldexp();
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int isnan(), isfinite();
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#endif
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extern double PIO4;
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const static double lossth = 1.073741824e9;
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#ifdef NANS
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extern double NAN;
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#endif
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#ifdef INFINITIES
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extern double INFINITY;
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#endif
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double sin(x)
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double x;
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{
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double y, z, zz;
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int j, sign;
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#ifdef MINUSZERO
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if( x == 0.0 )
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return(x);
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#endif
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#ifdef NANS
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if( isnan(x) )
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return(x);
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if( !isfinite(x) )
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{
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mtherr( "sin", DOMAIN );
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return(NAN);
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}
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#endif
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/* make argument positive but save the sign */
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sign = 1;
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if( x < 0 )
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{
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x = -x;
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sign = -1;
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}
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if( x > lossth )
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{
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mtherr( "sin", TLOSS );
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return(0.0);
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}
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y = floor( x/PIO4 ); /* integer part of x/PIO4 */
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/* strip high bits of integer part to prevent integer overflow */
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z = ldexp( y, -4 );
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z = floor(z); /* integer part of y/8 */
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z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
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j = z; /* convert to integer for tests on the phase angle */
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/* map zeros to origin */
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if( j & 1 )
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{
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j += 1;
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y += 1.0;
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}
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j = j & 07; /* octant modulo 360 degrees */
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/* reflect in x axis */
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if( j > 3)
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{
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sign = -sign;
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j -= 4;
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}
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/* Extended precision modular arithmetic */
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z = ((x - y * DP1) - y * DP2) - y * DP3;
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zz = z * z;
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if( (j==1) || (j==2) )
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{
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y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
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}
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else
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{
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/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
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y = z + z * z * z * polevl( zz, sincof, 5 );
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}
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if(sign < 0)
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y = -y;
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return(y);
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}
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double cos(x)
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double x;
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{
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double y, z, zz;
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long i;
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int j, sign;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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if( !isfinite(x) )
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{
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mtherr( "cos", DOMAIN );
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return(NAN);
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}
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#endif
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/* make argument positive */
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sign = 1;
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if( x < 0 )
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x = -x;
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if( x > lossth )
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{
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mtherr( "cos", TLOSS );
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return(0.0);
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}
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y = floor( x/PIO4 );
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z = ldexp( y, -4 );
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z = floor(z); /* integer part of y/8 */
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z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
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/* integer and fractional part modulo one octant */
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i = z;
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if( i & 1 ) /* map zeros to origin */
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{
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i += 1;
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y += 1.0;
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}
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j = i & 07;
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if( j > 3)
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{
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j -=4;
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sign = -sign;
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}
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if( j > 1 )
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sign = -sign;
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/* Extended precision modular arithmetic */
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z = ((x - y * DP1) - y * DP2) - y * DP3;
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zz = z * z;
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if( (j==1) || (j==2) )
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{
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/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
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y = z + z * z * z * polevl( zz, sincof, 5 );
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}
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else
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{
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y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
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}
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if(sign < 0)
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y = -y;
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return(y);
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}
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/* Degrees, minutes, seconds to radians: */
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/* 1 arc second, in radians = 4.8481368110953599358991410e-5 */
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#ifdef DEC
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static unsigned short P648[] = {034513,054170,0176773,0116043,};
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#define P64800 *(double *)P648
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#else
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const static double P64800 = 4.8481368110953599358991410e-5;
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#endif
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double radian(d,m,s)
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double d,m,s;
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{
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return( ((d*60.0 + m)*60.0 + s)*P64800 );
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}
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