The popcount example does compile, if you drop the "assume" form,

    (import (chicken bitwise) (chicken fixnum))
    (define (popcount32 x) ; From "Hacker's Delight"                                                                                                                                       
    ;  (assume                                                                                                                                                                             
       (let ((x (fx- x (bitwise-and (arithmetic-shift x -1) #x55555555))))
         (let ((x (fx+ (bitwise-and x #x33333333)
                       (bitwise-and (arithmetic-shift x -2) #x33333333))))
           (let ((x (bitwise-and (fx+ x (arithmetic-shift x -4)) #x0F0F0F0F)))
             (let ((x (fx+ x (arithmetic-shift x -8))))
               (let ((x (fx+ x (arithmetic-shift x -16))))
                 (bitwise-and x #x0000003F)))))))

Turns into somewhat redundant C, looks much like transliterated bytecode, e.g.

    long v17 = 0;
    // ...
    // popcnt.scm:7                                                                                                                                                                            
    v17 = 0;
    // ...
    // popcnt.scm:7                                                                                                                                                                            
    v17 = (t37 & 252645135);
    // popcount32                                                                                                                                                                              
    // popcnt.scm:8                                                                                                                                                                            
    t40 = crunch_arithmetic_shift(v17, -8);

Interesting find in the (small) crunch.h is

    #ifdef CRUNCH_FREESTANDING
    #include <inttypes.h>
    #include <stdarg.h>
    #include <complex.h>
    #include "crunch-environment.h"
    #else
    // loads of stuff

though I haven't found crunch-environment.h in the source yet

The nice thing is that you can emit pretty sloppy C and the C compiler will optimize it pretty well.