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Begin work on core:math/cmplx
`complex*` types only at the moment, `quaternion*` types coming later
This commit is contained in:
gingerBill
@@ -0,0 +1,513 @@
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package math_cmplx
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import "core:builtin"
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import "core:math"
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// The original C code, the long comment, and the constants
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// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
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// The go code is a simplified version of the original C.
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//
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// Cephes Math Library Release 2.8: June, 2000
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// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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//
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// The readme file at http://netlib.sandia.gov/cephes/ says:
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// Some software in this archive may be from the book _Methods and
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// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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// International, 1989) or from the Cephes Mathematical Library, a
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// commercial product. In either event, it is copyrighted by the author.
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// What you see here may be used freely but it comes with no support or
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// guarantee.
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//
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// The two known misprints in the book are repaired here in the
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// source listings for the gamma function and the incomplete beta
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// integral.
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//
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// Stephen L. Moshier
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// moshier@na-net.ornl.gov
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abs :: builtin.abs
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conj :: builtin.conj
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real :: builtin.real
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imag :: builtin.imag
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jmag :: builtin.jmag
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kmag :: builtin.kmag
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sin :: proc{
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sin_complex128,
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}
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cos :: proc{
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cos_complex128,
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}
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tan :: proc{
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tan_complex128,
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}
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cot :: proc{
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cot_complex128,
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}
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sinh :: proc{
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sinh_complex128,
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}
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cosh :: proc{
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cosh_complex128,
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}
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tanh :: proc{
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tanh_complex128,
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}
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// sqrt returns the square root of x.
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// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
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sqrt :: proc{
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sqrt_complex32,
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sqrt_complex64,
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sqrt_complex128,
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}
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ln :: proc{
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ln_complex32,
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ln_complex64,
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ln_complex128,
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}
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log10 :: proc{
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log10_complex32,
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log10_complex64,
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log10_complex128,
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}
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exp :: proc{
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exp_complex32,
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exp_complex64,
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exp_complex128,
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}
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pow :: proc{
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pow_complex32,
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pow_complex64,
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pow_complex128,
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}
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phase :: proc{
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phase_complex32,
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phase_complex64,
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phase_complex128,
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}
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polar :: proc{
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polar_complex32,
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polar_complex64,
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polar_complex128,
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}
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is_inf :: proc{
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is_inf_complex32,
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is_inf_complex64,
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is_inf_complex128,
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}
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is_nan :: proc{
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is_nan_complex32,
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is_nan_complex64,
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is_nan_complex128,
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}
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// sqrt_complex32 returns the square root of x.
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// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
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sqrt_complex32 :: proc "contextless" (x: complex32) -> complex32 {
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return complex32(sqrt_complex128(complex128(x)))
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}
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// sqrt_complex64 returns the square root of x.
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// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
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sqrt_complex64 :: proc "contextless" (x: complex64) -> complex64 {
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return complex64(sqrt_complex128(complex128(x)))
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}
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// sqrt_complex128 returns the square root of x.
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// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
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sqrt_complex128 :: proc "contextless" (x: complex128) -> complex128 {
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// The original C code, the long comment, and the constants
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// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
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// The go code is a simplified version of the original C.
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//
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// Cephes Math Library Release 2.8: June, 2000
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// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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//
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// The readme file at http://netlib.sandia.gov/cephes/ says:
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// Some software in this archive may be from the book _Methods and
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// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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// International, 1989) or from the Cephes Mathematical Library, a
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// commercial product. In either event, it is copyrighted by the author.
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// What you see here may be used freely but it comes with no support or
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// guarantee.
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//
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// The two known misprints in the book are repaired here in the
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// source listings for the gamma function and the incomplete beta
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// integral.
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//
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// Stephen L. Moshier
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// moshier@na-net.ornl.gov
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// Complex square root
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//
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// DESCRIPTION:
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//
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// If z = x + iy, r = |z|, then
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//
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// 1/2
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// Re w = [ (r + x)/2 ] ,
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//
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// 1/2
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// Im w = [ (r - x)/2 ] .
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//
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// Cancellation error in r-x or r+x is avoided by using the
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// identity 2 Re w Im w = y.
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//
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// Note that -w is also a square root of z. The root chosen
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// is always in the right half plane and Im w has the same sign as y.
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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 -10,+10 25000 3.2e-17 9.6e-18
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// IEEE -10,+10 1,000,000 2.9e-16 6.1e-17
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if imag(x) == 0 {
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// Ensure that imag(r) has the same sign as imag(x) for imag(x) == signed zero.
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if real(x) == 0 {
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return complex(0, imag(x))
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}
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if real(x) < 0 {
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return complex(0, math.copy_sign(math.sqrt(-real(x)), imag(x)))
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}
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return complex(math.sqrt(real(x)), imag(x))
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} else if math.is_inf(imag(x), 0) {
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return complex(math.inf_f64(1.0), imag(x))
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}
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if real(x) == 0 {
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if imag(x) < 0 {
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r := math.sqrt(-0.5 * imag(x))
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return complex(r, -r)
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}
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r := math.sqrt(0.5 * imag(x))
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return complex(r, r)
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}
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a := real(x)
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b := imag(x)
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scale: f64
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// Rescale to avoid internal overflow or underflow.
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if abs(a) > 4 || abs(b) > 4 {
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a *= 0.25
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b *= 0.25
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scale = 2
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} else {
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a *= 1.8014398509481984e16 // 2**54
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b *= 1.8014398509481984e16
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scale = 7.450580596923828125e-9 // 2**-27
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}
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r := math.hypot(a, b)
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t: f64
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if a > 0 {
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t = math.sqrt(0.5*r + 0.5*a)
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r = scale * abs((0.5*b)/t)
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t *= scale
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} else {
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r = math.sqrt(0.5*r - 0.5*a)
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t = scale * abs((0.5*b)/r)
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r *= scale
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}
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if b < 0 {
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return complex(t, -r)
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}
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return complex(t, r)
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}
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ln_complex32 :: proc "contextless" (x: complex32) -> complex32 {
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return complex(math.ln(abs(x)), phase(x))
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}
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ln_complex64 :: proc "contextless" (x: complex64) -> complex64 {
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return complex(math.ln(abs(x)), phase(x))
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}
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ln_complex128 :: proc "contextless" (x: complex128) -> complex128 {
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return complex(math.ln(abs(x)), phase(x))
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}
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exp_complex32 :: proc "contextless" (x: complex32) -> complex32 {
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switch re, im := real(x), imag(x); {
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case math.is_inf(re, 0):
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switch {
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case re > 0 && im == 0:
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return x
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case math.is_inf(im, 0) || math.is_nan(im):
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if re < 0 {
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return complex(0, math.copy_sign(0, im))
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} else {
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return complex(math.inf_f64(1.0), math.nan_f64())
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}
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}
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case math.is_nan(re):
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if im == 0 {
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return complex(math.nan_f16(), im)
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}
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}
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r := math.exp(real(x))
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s, c := math.sincos(imag(x))
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return complex(r*c, r*s)
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}
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exp_complex64 :: proc "contextless" (x: complex64) -> complex64 {
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switch re, im := real(x), imag(x); {
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case math.is_inf(re, 0):
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switch {
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case re > 0 && im == 0:
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return x
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case math.is_inf(im, 0) || math.is_nan(im):
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if re < 0 {
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return complex(0, math.copy_sign(0, im))
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} else {
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return complex(math.inf_f64(1.0), math.nan_f64())
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}
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}
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case math.is_nan(re):
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if im == 0 {
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return complex(math.nan_f32(), im)
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}
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}
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r := math.exp(real(x))
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s, c := math.sincos(imag(x))
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return complex(r*c, r*s)
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}
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exp_complex128 :: proc "contextless" (x: complex128) -> complex128 {
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switch re, im := real(x), imag(x); {
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case math.is_inf(re, 0):
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switch {
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case re > 0 && im == 0:
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return x
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case math.is_inf(im, 0) || math.is_nan(im):
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if re < 0 {
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return complex(0, math.copy_sign(0, im))
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} else {
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return complex(math.inf_f64(1.0), math.nan_f64())
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}
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}
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case math.is_nan(re):
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if im == 0 {
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return complex(math.nan_f64(), im)
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}
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}
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r := math.exp(real(x))
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s, c := math.sincos(imag(x))
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return complex(r*c, r*s)
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}
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pow_complex32 :: proc "contextless" (x, y: complex32) -> complex32 {
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if x == 0 { // Guaranteed also true for x == -0.
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if is_nan(y) {
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return nan_complex32()
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}
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r, i := real(y), imag(y)
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switch {
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case r == 0:
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return 1
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case r < 0:
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if i == 0 {
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return complex(math.inf_f16(1), 0)
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}
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return inf_complex32()
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case r > 0:
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return 0
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}
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unreachable()
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}
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modulus := abs(x)
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if modulus == 0 {
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return complex(0, 0)
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}
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r := math.pow(modulus, real(y))
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arg := phase(x)
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theta := real(y) * arg
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if imag(y) != 0 {
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r *= math.exp(-imag(y) * arg)
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theta += imag(y) * math.ln(modulus)
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}
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s, c := math.sincos(theta)
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return complex(r*c, r*s)
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}
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pow_complex64 :: proc "contextless" (x, y: complex64) -> complex64 {
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if x == 0 { // Guaranteed also true for x == -0.
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if is_nan(y) {
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return nan_complex64()
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}
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r, i := real(y), imag(y)
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switch {
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case r == 0:
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return 1
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case r < 0:
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if i == 0 {
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return complex(math.inf_f32(1), 0)
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}
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return inf_complex64()
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case r > 0:
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return 0
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}
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unreachable()
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}
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modulus := abs(x)
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if modulus == 0 {
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return complex(0, 0)
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}
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r := math.pow(modulus, real(y))
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arg := phase(x)
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theta := real(y) * arg
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if imag(y) != 0 {
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r *= math.exp(-imag(y) * arg)
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theta += imag(y) * math.ln(modulus)
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}
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s, c := math.sincos(theta)
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return complex(r*c, r*s)
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}
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pow_complex128 :: proc "contextless" (x, y: complex128) -> complex128 {
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if x == 0 { // Guaranteed also true for x == -0.
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if is_nan(y) {
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return nan_complex128()
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}
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r, i := real(y), imag(y)
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switch {
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case r == 0:
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return 1
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case r < 0:
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if i == 0 {
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return complex(math.inf_f64(1), 0)
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}
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return inf_complex128()
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case r > 0:
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return 0
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}
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unreachable()
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}
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modulus := abs(x)
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if modulus == 0 {
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return complex(0, 0)
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}
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r := math.pow(modulus, real(y))
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arg := phase(x)
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theta := real(y) * arg
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if imag(y) != 0 {
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r *= math.exp(-imag(y) * arg)
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theta += imag(y) * math.ln(modulus)
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}
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s, c := math.sincos(theta)
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return complex(r*c, r*s)
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}
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log10_complex32 :: proc "contextless" (x: complex32) -> complex32 {
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return math.LN10*ln(x)
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}
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log10_complex64 :: proc "contextless" (x: complex64) -> complex64 {
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return math.LN10*ln(x)
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}
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log10_complex128 :: proc "contextless" (x: complex128) -> complex128 {
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return math.LN10*ln(x)
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}
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phase_complex32 :: proc "contextless" (x: complex32) -> f16 {
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return math.atan2(imag(x), real(x))
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}
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phase_complex64 :: proc "contextless" (x: complex64) -> f32 {
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return math.atan2(imag(x), real(x))
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}
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phase_complex128 :: proc "contextless" (x: complex128) -> f64 {
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return math.atan2(imag(x), real(x))
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}
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rect_complex32 :: proc "contextless" (r, θ: f16) -> complex32 {
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s, c := math.sincos(θ)
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return complex(r*c, r*s)
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}
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rect_complex64 :: proc "contextless" (r, θ: f32) -> complex64 {
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s, c := math.sincos(θ)
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return complex(r*c, r*s)
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}
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rect_complex128 :: proc "contextless" (r, θ: f64) -> complex128 {
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s, c := math.sincos(θ)
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return complex(r*c, r*s)
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}
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polar_complex32 :: proc "contextless" (x: complex32) -> (r, θ: f16) {
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return abs(x), phase(x)
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}
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polar_complex64 :: proc "contextless" (x: complex64) -> (r, θ: f32) {
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return abs(x), phase(x)
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}
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polar_complex128 :: proc "contextless" (x: complex128) -> (r, θ: f64) {
|
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return abs(x), phase(x)
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||||
}
|
||||
|
||||
|
||||
|
||||
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nan_complex32 :: proc "contextless" () -> complex32 {
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return complex(math.nan_f16(), math.nan_f16())
|
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}
|
||||
nan_complex64 :: proc "contextless" () -> complex64 {
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return complex(math.nan_f32(), math.nan_f32())
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}
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nan_complex128 :: proc "contextless" () -> complex128 {
|
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return complex(math.nan_f64(), math.nan_f64())
|
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}
|
||||
|
||||
|
||||
inf_complex32 :: proc "contextless" () -> complex32 {
|
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inf := math.inf_f16(1)
|
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return complex(inf, inf)
|
||||
}
|
||||
inf_complex64 :: proc "contextless" () -> complex64 {
|
||||
inf := math.inf_f32(1)
|
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return complex(inf, inf)
|
||||
}
|
||||
inf_complex128 :: proc "contextless" () -> complex128 {
|
||||
inf := math.inf_f64(1)
|
||||
return complex(inf, inf)
|
||||
}
|
||||
|
||||
|
||||
is_inf_complex32 :: proc "contextless" (x: complex32) -> bool {
|
||||
return math.is_inf(real(x), 0) || math.is_inf(imag(x), 0)
|
||||
}
|
||||
is_inf_complex64 :: proc "contextless" (x: complex64) -> bool {
|
||||
return math.is_inf(real(x), 0) || math.is_inf(imag(x), 0)
|
||||
}
|
||||
is_inf_complex128 :: proc "contextless" (x: complex128) -> bool {
|
||||
return math.is_inf(real(x), 0) || math.is_inf(imag(x), 0)
|
||||
}
|
||||
|
||||
|
||||
is_nan_complex32 :: proc "contextless" (x: complex32) -> bool {
|
||||
if math.is_inf(real(x), 0) || math.is_inf(imag(x), 0) {
|
||||
return false
|
||||
}
|
||||
return math.is_nan(real(x)) || math.is_nan(imag(x))
|
||||
}
|
||||
is_nan_complex64 :: proc "contextless" (x: complex64) -> bool {
|
||||
if math.is_inf(real(x), 0) || math.is_inf(imag(x), 0) {
|
||||
return false
|
||||
}
|
||||
return math.is_nan(real(x)) || math.is_nan(imag(x))
|
||||
}
|
||||
is_nan_complex128 :: proc "contextless" (x: complex128) -> bool {
|
||||
if math.is_inf(real(x), 0) || math.is_inf(imag(x), 0) {
|
||||
return false
|
||||
}
|
||||
return math.is_nan(real(x)) || math.is_nan(imag(x))
|
||||
}
|
||||
Reference in New Issue
Block a user