PFE 0.33.70
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-Overview
-The PFE Manual
old manual / (book)
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-Dp of ANS Forth
-The 4thTutor
-Forthprimer.pdf
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- Old Words List
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* Forth Repository
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generated
(C) Guido U. Draheim
guidod@gmx.de
Complex
floating point
R2P1=>"EXTENSIONS"(no description)
primitive code = [r2p1]
T2P1=>"EXTENSIONS"(no description)
primitive code = [t2p1]
LAMBDA/EPSILON=>"EXTENSIONS"(no description)
primitive code = [lambda_slash_epsilon]
Z@( addr -- f: z )=>"EXTENSIONS"-
primitive code = [p4_z_fetch]
Z!( addr f: z -- )=>"EXTENSIONS"-
primitive code = [p4_z_store]
X@( zaddr -- f: x )=>"EXTENSIONS"-
primitive code = [p4_x_fetch]
X!( zaddr f: x -- )=>"EXTENSIONS"-
primitive code = [p4_x_store]
Y@( zaddr -- f: y )=>"EXTENSIONS"-
primitive code = [p4_y_fetch]
Y!( zaddr f: x -- )=>"EXTENSIONS"-
primitive code = [p4_y_store]
Z.(f: z -- )=>"EXTENSIONS"Emit the complex number, including the sign of zero when
signbit()is available.primitive code = [p4_z_dot]
ZS.(f: z -- )=>"EXTENSIONS"Emit the complex number in scientific notation, including the sign of zero when
signbit()is available.primitive code = [p4_z_s_dot]
REAL(f: x y -- x )=>"EXTENSIONS"-
primitive code = [p4_real]
IMAG(f: x y -- y )=>"EXTENSIONS"-
primitive code = [p4_imag]
CONJG(f: x y -- x -y )=>"EXTENSIONS"-
primitive code = [p4_conjg]
ZDROP(f: z -- )=>"EXTENSIONS"-
primitive code = [p4_z_drop]
ZDUP(f: z -- z z )=>"EXTENSIONS"-
primitive code = [p4_z_dup]
ZSWAP(f: z1 z2 -- z2 z1 )=>"EXTENSIONS"-
primitive code = [p4_z_swap]
ZOVER(f: z1 z2 -- z1 z2 z1 )=>"EXTENSIONS"-
primitive code = [p4_z_over]
ZNIP(f: z1 z2 -- z2 )=>"EXTENSIONS"-
primitive code = [p4_z_nip]
ZTUCK(f: z1 z2 -- z2 z1 z2 )=>"EXTENSIONS"-
primitive code = [p4_z_tuck]
ZROT(f: z1 z2 z3 -- z2 z3 z1 )=>"EXTENSIONS"-
primitive code = [p4_z_rot]
-ZROT(f: z1 z2 z3 -- z3 z1 z2 )=>"EXTENSIONS"-
primitive code = [p4_minus_z_rot]
Z+(f: z1 z2 -- z1+z2 )=>"EXTENSIONS"-
primitive code = [p4_z_plus]
Z-(f: z1 z2 -- z1-z2 )=>"EXTENSIONS"-
primitive code = [p4_z_minus]
Z*(f: x y u v -- x*u-y*v x*v+y*u )=>"EXTENSIONS"Uses the algorithm followed by JVN: (x+iy)*(u+iv) = [(x+y)*u - y*(u+v)] + i[(x+y)*u + x*(v-u)] Requires 3 multiplications and 5 additions.
primitive code = [p4_z_star]
Z/(f: u+iv z -- u/z+iv/z )=>"EXTENSIONS"Kahan-like algorithm *without* due attention to spurious over/underflows and zeros and infinities.
primitive code = [p4_z_slash]
ZNEGATE(f: z -- -z )=>"EXTENSIONS"-
primitive code = [p4_z_negate]
Z2*(f: z -- z*2 )=>"EXTENSIONS"-
primitive code = [p4_z_two_star]
Z2/(f: z -- z/2 )=>"EXTENSIONS"-
primitive code = [p4_z_two_slash]
I*(f: x y -- -y x )=>"EXTENSIONS"-
primitive code = [p4_i_star]
-I*(f: x y -- y -x )=>"EXTENSIONS"-
primitive code = [p4_minus_i_star]
1/Z(f: z -- 1/z )=>"EXTENSIONS"Kahan algorithm *without* due attention to spurious over/underflows and zeros and infinities.
primitive code = [p4_one_slash_z]
Z^2(f: z -- z^2 )=>"EXTENSIONS"Kahan algorithm without removal of any spurious NaN created by overflow. It deliberately uses (x-y)(x+y) instead of x^2-y^2 for the real part.
primitive code = [p4_z_hat_two]
|Z|^2(f: x y -- |z|^2 )=>"EXTENSIONS"-
primitive code = [p4_z_abs_hat_two]
Z^N( n f: z -- z^n )=>"EXTENSIONS"-
primitive code = [p4_z_hat_n]
X+(f: z a -- x+a y )=>"EXTENSIONS"-
primitive code = [p4_x_plus]
X-(f: z a -- x-a y )=>"EXTENSIONS"-
primitive code = [p4_x_minus]
Y+(f: z a -- x y+a )=>"EXTENSIONS"-
primitive code = [p4_y_plus]
Y-(f: z a -- x y-a )=>"EXTENSIONS"-
primitive code = [p4_y_minus]
Z*F(f: x y f -- x*f y*f )=>"EXTENSIONS"-
primitive code = [p4_z_star_f]
Z/F(f: x y f -- x/f y/f )=>"EXTENSIONS"-
primitive code = [p4_z_slash_f]
F*Z(f: f x y -- f*x f*y )=>"EXTENSIONS"-
primitive code = [p4_f_star_z]
F/Z(f: f z -- f/z )=>"EXTENSIONS"Kahan algorithm *without* due attention to spurious over/underflows and zeros and infinities.
primitive code = [p4_f_slash_z]
Z*I*F(f: z f -- z*if )=>"EXTENSIONS"-
primitive code = [p4_z_star_i_star_f]
-I*Z/F(f: z f -- z/[if] )=>"EXTENSIONS"-
primitive code = [p4_minus_i_star_z_slash_f]
I*F*Z(f: f z -- if*z )=>"EXTENSIONS"-
primitive code = [p4_i_star_f_star_z]
I*F/Z(f: f z -- [0+if]/z )=>"EXTENSIONS"Kahan algorithm *without* due attention to spurious over/underflows and zeros and infinities.
primitive code = [p4_i_star_f_slash_z]
Z*>REAL(f: z1 z2 -- Re[z1*z2] )=>"EXTENSIONS"Compute the real part of the complex product without computing the imaginary part. Recommended by Kahan to avoid gratuitous overflow or underflow signals from the unnecessary part.
primitive code = [p4_z_star_to_real]
Z*>IMAG(f: z1 z2 -- Im[z1*z2] )=>"EXTENSIONS"Compute the imaginary part of the complex product without computing the real part.
primitive code = [p4_z_star_to_imag]
|Z|(f: x y -- |z| )=>"EXTENSIONS"-
primitive code = [p4_z_abs]
ZBOX(f: z -- box[z] )=>"EXTENSIONS"Defined *only* for zero and infinite arguments. This difffers from Kahan's
CBOX[p. 198] by conserving signs when only one of x or y is infinite, consistent with the other cases, and with its use in hisARG[p. 199].primitive code = [p4_z_box]
ARG(f: z -- principal.arg[z] )=>"EXTENSIONS"-
primitive code = [p4_arg]
>POLAR(f: x y -- r theta )=>"EXTENSIONS"Convert the complex number z to its polar representation, where theta is the principal argument.
primitive code = [p4_to_polar]
POLAR>(f: r theta -- x y )=>"EXTENSIONS"-
primitive code = [p4_polar_from]
ZSSQS(f: z -- rho s: k )=>"EXTENSIONS"Compute rho = |(x+iy)/2^k|^2, scaled to avoid overflow or underflow, and leave the scaling integer k. Kahan, p. 200.
primitive code = [p4_z_ssqs]
ZSQRT(f: z -- sqrt[z] )=>"EXTENSIONS"Compute the principal branch of the square root, with Re sqrt[z] >= 0. Kahan, p. 201.
primitive code = [p4_z_sqrt]
ZLN(f: z -- ln|z|+i*theta )=>"EXTENSIONS"Compute the principal branch of the complex natural logarithm. The angle theta is the principal argument. This code uses Kahan's algorithm for the scaled logarithm
CLOGS(z,J)= ln(z*2^J), with J=0 and blind choices of the threshholds T0, T1, and T2. Namely, T0 = 1/sqrt(2), T1 = 5/4, and T2 = 3;primitive code = [p4_z_ln]
ZEXP(f: z -- exp[z] )=>"EXTENSIONS"-
primitive code = [p4_z_exp]
Z^(f: x y u v -- [x+iy]^[u+iv] )=>"EXTENSIONS"Compute in terms of the principal argument of x+iy.
primitive code = [p4_z_hat]
ZCOSH(f: z -- cosh[z] )=>"EXTENSIONS"-
primitive code = [p4_z_cosh]
ZSINH(f: z -- sinh[z] )=>"EXTENSIONS"-
primitive code = [p4_z_sinh]
ZTANH(f: z -- tanh[z] )=>"EXTENSIONS"Kahan, p. 204, including his divide by zero signal suppression for infinite values of
tan(). To quote the very informative "=>'man math'" on our Darwin system about IEEE 754: "Divide-by-Zero is signaled only when a function takes exactly infinite values at finite operands."primitive code = [p4_z_tanh]
ZCOTH(f: z -- 1/tanh[z] )=>"EXTENSIONS"-
primitive code = [p4_z_coth]
ZCOS(f: z -- cosh[i*z] )=>"EXTENSIONS"-
primitive code = [p4_z_cos]
ZSIN(f: z -- -i*sinh[i*z] )=>"EXTENSIONS"-
primitive code = [p4_z_sin]
ZTAN(f: z -- -i*tanh[i*z] )=>"EXTENSIONS"-
primitive code = [p4_z_tan]
ZCOT(f: z -- -i*coth[-i*z] )=>"EXTENSIONS"-
primitive code = [p4_z_cot]
ZACOS(f: z -- u+iv=acos[z] )=>"EXTENSIONS"Kahan, p.202.
primitive code = [p4_z_acos]
ZACOSH(f: z -- u+iv=acosh[z] )=>"EXTENSIONS"Kahan, p.203.
primitive code = [p4_z_acosh]
ZASIN(f: z -- u+iv=asin[z] )=>"EXTENSIONS"Kahan, p.203.
primitive code = [p4_z_asin]
ZASINH(f: z -- -i*asin[i*z] )=>"EXTENSIONS"Kahan, p. 203, couth.
primitive code = [p4_z_asinh]
ZATANH(f: z -- u+iv=atanh[z] )=>"EXTENSIONS"Kahan, p. 203.
primitive code = [p4_z_atanh]
ZATAN(f: z -- -i*atanh[i*z] )=>"EXTENSIONS"Kahan, p. 204, couth.
primitive code = [p4_z_atan]
ZLITERAL=>"EXTENSIONS"(no description)
compiling word = [p4_z_literal]