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-rw-r--r--libm/float/cmplxf.c407
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diff --git a/libm/float/cmplxf.c b/libm/float/cmplxf.c
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-/* cmplxf.c
- *
- * Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- * float r; real part
- * float i; imaginary part
- * }cmplxf;
- *
- * cmplxf *a, *b, *c;
- *
- * caddf( a, b, c ); c = b + a
- * csubf( a, b, c ); c = b - a
- * cmulf( a, b, c ); c = b * a
- * cdivf( a, b, c ); c = b / a
- * cnegf( c ); c = -c
- * cmovf( b, c ); c = b
- *
- *
- *
- * DESCRIPTION:
- *
- * Addition:
- * c.r = b.r + a.r
- * c.i = b.i + a.i
- *
- * Subtraction:
- * c.r = b.r - a.r
- * c.i = b.i - a.i
- *
- * Multiplication:
- * c.r = b.r * a.r - b.i * a.i
- * c.i = b.r * a.i + b.i * a.r
- *
- * Division:
- * d = a.r * a.r + a.i * a.i
- * c.r = (b.r * a.r + b.i * a.i)/d
- * c.i = (b.i * a.r - b.r * a.i)/d
- * ACCURACY:
- *
- * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
- * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
- * peak relative error 8.3e-17, rms 2.1e-17.
- *
- * Tests in the rectangle {-10,+10}:
- * Relative error:
- * arithmetic function # trials peak rms
- * IEEE cadd 30000 5.9e-8 2.6e-8
- * IEEE csub 30000 6.0e-8 2.6e-8
- * IEEE cmul 30000 1.1e-7 3.7e-8
- * IEEE cdiv 30000 2.1e-7 5.7e-8
- */
- /* cmplx.c
- * complex number arithmetic
- */
-
-
-/*
-Cephes Math Library Release 2.1: December, 1988
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-extern float MAXNUMF, MACHEPF, PIF, PIO2F;
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-#ifdef ANSIC
-float sqrtf(float), frexpf(float, int *);
-float ldexpf(float, int);
-float cabsf(cmplxf *), atan2f(float, float), cosf(float), sinf(float);
-#else
-float sqrtf(), frexpf(), ldexpf();
-float cabsf(), atan2f(), cosf(), sinf();
-#endif
-/*
-typedef struct
- {
- float r;
- float i;
- }cmplxf;
-*/
-cmplxf czerof = {0.0, 0.0};
-extern cmplxf czerof;
-cmplxf conef = {1.0, 0.0};
-extern cmplxf conef;
-
-/* c = b + a */
-
-void caddf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-
-c->r = b->r + a->r;
-c->i = b->i + a->i;
-}
-
-
-/* c = b - a */
-
-void csubf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-
-c->r = b->r - a->r;
-c->i = b->i - a->i;
-}
-
-/* c = b * a */
-
-void cmulf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-register float y;
-
-y = b->r * a->r - b->i * a->i;
-c->i = b->r * a->i + b->i * a->r;
-c->r = y;
-}
-
-
-
-/* c = b / a */
-
-void cdivf( a, b, c )
-register cmplxf *a, *b;
-cmplxf *c;
-{
-float y, p, q, w;
-
-
-y = a->r * a->r + a->i * a->i;
-p = b->r * a->r + b->i * a->i;
-q = b->i * a->r - b->r * a->i;
-
-if( y < 1.0f )
- {
- w = MAXNUMF * y;
- if( (fabsf(p) > w) || (fabsf(q) > w) || (y == 0.0f) )
- {
- c->r = MAXNUMF;
- c->i = MAXNUMF;
- mtherr( "cdivf", OVERFLOW );
- return;
- }
- }
-c->r = p/y;
-c->i = q/y;
-}
-
-
-/* b = a */
-
-void cmovf( a, b )
-register short *a, *b;
-{
-int i;
-
-
-i = 8;
-do
- *b++ = *a++;
-while( --i );
-}
-
-
-void cnegf( a )
-register cmplxf *a;
-{
-
-a->r = -a->r;
-a->i = -a->i;
-}
-
-/* cabsf()
- *
- * Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * float cabsf();
- * cmplxf z;
- * float a;
- *
- * a = cabsf( &z );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy
- *
- * then
- *
- * a = sqrt( x**2 + y**2 ).
- *
- * Overflow and underflow are avoided by testing the magnitudes
- * of x and y before squaring. If either is outside half of
- * the floating point full scale range, both are rescaled.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 30000 1.2e-7 3.4e-8
- */
-
-
-/*
-Cephes Math Library Release 2.1: January, 1989
-Copyright 1984, 1987, 1989 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/*
-typedef struct
- {
- float r;
- float i;
- }cmplxf;
-*/
-/* square root of max and min numbers */
-#define SMAX 1.3043817825332782216E+19
-#define SMIN 7.6664670834168704053E-20
-#define PREC 12
-#define MAXEXPF 128
-
-
-#define SMAXT (2.0f * SMAX)
-#define SMINT (0.5f * SMIN)
-
-float cabsf( z )
-register cmplxf *z;
-{
-float x, y, b, re, im;
-int ex, ey, e;
-
-re = fabsf( z->r );
-im = fabsf( z->i );
-
-if( re == 0.0f )
- {
- return( im );
- }
-if( im == 0.0f )
- {
- return( re );
- }
-
-/* Get the exponents of the numbers */
-x = frexpf( re, &ex );
-y = frexpf( im, &ey );
-
-/* Check if one number is tiny compared to the other */
-e = ex - ey;
-if( e > PREC )
- return( re );
-if( e < -PREC )
- return( im );
-
-/* Find approximate exponent e of the geometric mean. */
-e = (ex + ey) >> 1;
-
-/* Rescale so mean is about 1 */
-x = ldexpf( re, -e );
-y = ldexpf( im, -e );
-
-/* Hypotenuse of the right triangle */
-b = sqrtf( x * x + y * y );
-
-/* Compute the exponent of the answer. */
-y = frexpf( b, &ey );
-ey = e + ey;
-
-/* Check it for overflow and underflow. */
-if( ey > MAXEXPF )
- {
- mtherr( "cabsf", OVERFLOW );
- return( MAXNUMF );
- }
-if( ey < -MAXEXPF )
- return(0.0f);
-
-/* Undo the scaling */
-b = ldexpf( b, e );
-return( b );
-}
- /* csqrtf()
- *
- * Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtf();
- * cmplxf z, w;
- *
- * csqrtf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * If z = x + iy, r = |z|, then
- *
- * 1/2
- * Im w = [ (r - x)/2 ] ,
- *
- * Re w = y / 2 Im w.
- *
- *
- * Note that -w is also a square root of z. The solution
- * reported is always in the upper half plane.
- *
- * Because of the potential for cancellation error in r - x,
- * the result is sharpened by doing a Heron iteration
- * (see sqrt.c) in complex arithmetic.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,+10 100000 1.8e-7 4.2e-8
- *
- */
-
-
-void csqrtf( z, w )
-cmplxf *z, *w;
-{
-cmplxf q, s;
-float x, y, r, t;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0f )
- {
- if( x < 0.0f )
- {
- w->r = 0.0f;
- w->i = sqrtf(-x);
- return;
- }
- else
- {
- w->r = sqrtf(x);
- w->i = 0.0f;
- return;
- }
- }
-
-if( x == 0.0f )
- {
- r = fabsf(y);
- r = sqrtf(0.5f*r);
- if( y > 0 )
- w->r = r;
- else
- w->r = -r;
- w->i = r;
- return;
- }
-
-/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
- * The relative error in the first term is approximately y^2/12x^2 .
- */
-if( (fabsf(y) < fabsf(0.015f*x))
- && (x > 0) )
- {
- t = 0.25f*y*(y/x);
- }
-else
- {
- r = cabsf(z);
- t = 0.5f*(r - x);
- }
-
-r = sqrtf(t);
-q.i = r;
-q.r = 0.5f*y/r;
-
-/* Heron iteration in complex arithmetic:
- * q = (q + z/q)/2
- */
-cdivf( &q, z, &s );
-caddf( &q, &s, w );
-w->r *= 0.5f;
-w->i *= 0.5f;
-}
-
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