diff --git a/3d-models.cpp b/3d-models.cpp
index 1917f6eb..86b0af10 100644
--- a/3d-models.cpp
+++ b/3d-models.cpp
@@ -606,7 +606,7 @@ void geometry_information::animate_bird(hpcshape& orig, hpcshape_animated& anima
   for(int i=0; i<=WINGS; i++) {
     auto& tgt = animated[i];
     clone_shape(orig, tgt);
-    ld alpha = cos(180. * degree * i / WINGS) * 30 * degree;
+    ld alpha = cos(M_PI * i / WINGS) * 30 * degree;
     for(int i=tgt.s; i<tgt.e; i++) {
       if(abs(hpc[i][1]) > body) {
         ld off = hpc[i][1] > 0 ? body : -body;
@@ -787,17 +787,17 @@ void geometry_information::shift_last_straight(ld z) {
 
 EX void queueball(const shiftmatrix& V, ld rad, color_t col, eItem what) {
   if(what == itOrbSpeed) {
-    shiftmatrix V1 = V * cspin(1, 2, M_PI/2);
+    shiftmatrix V1 = V * cspin90(1, 2);
     ld tt = ptick(100);
     for(int t=0; t<5; t++) {
       for(int a=-50; a<50; a++)
-        curvepoint(cspin(0, 2, a * M_PI/100.) * cspin(0, 1, t * 72 * degree + tt + a*2*M_PI/50.) * xpush0(rad));
+        curvepoint(cspin(0, 2, a * M_PI/100.) * cspin(0, 1, t * 72._deg + tt + a*TAU/50.) * xpush0(rad));
       queuecurve(V1, col, 0, PPR::LINE);
       }
     return;
     }
   ld z = 63.43 * degree;
-  shiftmatrix V1 = V * cspin(0, 2, M_PI/2);
+  shiftmatrix V1 = V * cspin90(0, 2);
   if(what == itOrbShield) V1 = V * cspin(0, 1, ptick(500));
   if(what == itOrbFlash) V1 = V * cspin(0, 1, ptick(1500));
   if(what == itOrbShield) V1 = V * cspin(1, 2, ptick(1000));
@@ -821,7 +821,7 @@ EX void queueball(const shiftmatrix& V, ld rad, color_t col, eItem what) {
     line(a, c);
     line(a, d);
     line(d, c);
-    line(c, spin(M_PI));
+    line(c, spin180());
     }
   }
 
@@ -1256,7 +1256,7 @@ hpcshape& geometry_information::generate_pipe(ld length, ld width, ePipeEnd endt
   const int MAX_R = 20;
   auto at = [&] (ld i, ld a, ld z = 1, ld s = 1) {
     a += 0.5;
-    ld alpha = 360 * degree * a / MAX_R;
+    ld alpha = TAU * a / MAX_R;
     hpcpush(xpush(i * length / MAX_X) * cspin(1, 2, alpha) * ypush0(width*z));
     #if CAP_GL
     if(floor_textures) utt.tvertices.push_back(glhr::makevertex(0, pers ? 0.549 - s * 0.45 * sin(alpha) : 0.999, 0));
@@ -1282,10 +1282,10 @@ hpcshape& geometry_information::generate_pipe(ld length, ld width, ePipeEnd endt
   if(endtype == ePipeEnd::ball) for(int a=0; a<MAX_R; a++) for(int x=-MAX_R; x<MAX_R; x++) {
     ld xb = x < 0 ? 0 : MAX_X;
     ld mul = MAX_X * width/length * .9; // .9 to prevent Z-fighting
-    ld x0 = xb + mul * sin(x * 90 * degree / MAX_R);
-    ld x1 = xb + mul * sin((x+1) * 90 * degree / MAX_R);
-    ld z0 = cos(x * 90 * degree / MAX_R);
-    ld z1 = cos((x+1) * 90 * degree / MAX_R);
+    ld x0 = xb + mul * sin(x * 90._deg / MAX_R);
+    ld x1 = xb + mul * sin((x+1) * 90._deg / MAX_R);
+    ld z0 = cos(x * 90._deg / MAX_R);
+    ld z1 = cos((x+1) * 90._deg / MAX_R);
     at(x0, a, z0, z0);
     at(x0, a+1, z0, z0);
     at(x1, a, z1, z1);
diff --git a/arbitrile.cpp b/arbitrile.cpp
index e2991f05..462b7fe1 100644
--- a/arbitrile.cpp
+++ b/arbitrile.cpp
@@ -610,8 +610,8 @@ EX bool compute_vertex_valence_flat(arb::arbi_tiling& ac) {
         if(at.sid == at1.sid && (at.eid-at1.eid) % ac.shapes[at.sid].cycle_length == 0) pqty = 0;
         if(qty && pqty == 0 && !total) break;
         ld a = ac.shapes[at.sid].angles[at.eid];
-        while(a < 0) a += 360 * degree;
-        while(a > 360 * degree) a -= 360 * degree;
+        while(a < 0) a += TAU;
+        while(a > TAU) a -= TAU;
         total += a;
         anglelist.push_back(a);
         qty++;
@@ -622,9 +622,9 @@ EX bool compute_vertex_valence_flat(arb::arbi_tiling& ac) {
 
         at = ac.shapes[at.sid].connections[at.eid];
         }
-      while(total < 360*degree - 1e-6);
+      while(total < TAU - 1e-6);
       if(total == 0) qty = OINF;
-      if(total > 360*degree + 1e-6) throw hr_parse_exception("improper total in compute_stats");
+      if(total > TAU + 1e-6) throw hr_parse_exception("improper total in compute_stats");
       if(at.sid != i) throw hr_parse_exception("ended at wrong type determining vertex_valence");
       if((at.eid - k) % ac.shapes[i].cycle_length) {
         reduce_gcd(ac.shapes[i].cycle_length, at.eid - k);
@@ -1997,8 +1997,7 @@ EX void convert() {
       v0 = T * v0;
       v2 = T * v2;
       ld alpha = atan2(v0) - atan2(v2);
-      while(alpha > M_PI) alpha -= 360*degree;
-      while(alpha < -M_PI) alpha += 360*degree;
+      cyclefix(alpha, 0);
       sh.angles.push_back(alpha);
       }
     if(debugflags & DF_GEOM) {
@@ -2117,7 +2116,7 @@ EX void choose() {
   }
 
 EX pair<ld, ld> rep_ideal(ld e, ld u IS(1)) {
-  ld alpha = 2 * M_PI / e;
+  ld alpha = TAU / e;
   hyperpoint h1 = point3(cos(alpha)*u, -sin(alpha)*u, 1);
   hyperpoint h2 = point3(u, 0, 1);
   hyperpoint h3 = point3(cos(alpha)*u, sin(alpha)*u, 1);
@@ -2129,7 +2128,7 @@ EX pair<ld, ld> rep_ideal(ld e, ld u IS(1)) {
   auto Th23 = T * h23;
   ld beta = atan2(T0);
   ld gamma = atan2(Th23);
-  return {len, 90 * degree - (gamma - beta)};
+  return {len, 90._deg - (gamma - beta)};
   }
 
 EX void swap_vertices() {
diff --git a/archimedean.cpp b/archimedean.cpp
index 2e6f840e..145efa34 100644
--- a/archimedean.cpp
+++ b/archimedean.cpp
@@ -447,22 +447,22 @@ void archimedean_tiling::compute_geometry() {
   
   if(real_faces == 2) {
     /* standard methods fail for dihedra, but the answer is easy */
-    edgelength = 2 * M_PI / faces[0];
+    edgelength = TAU / faces[0];
     for(int i=0; i<N; i++)
       if(faces[i] == 2)
         alphas[i] = 0,
         circumradius[i] = M_PI / real_face_type,
         inradius[i] = 0;
       else
-        alphas[i] = M_PI/2,
-        circumradius[i] = inradius[i] = M_PI/2;
+        alphas[i] = 90._deg,
+        circumradius[i] = inradius[i] = 90._deg;
     }
   else if(real_faces == 0) {
     // these are called hosohedra
     edgelength = M_PI;
     for(int i=0; i<N; i++)
       alphas[i] = M_PI / N,
-      circumradius[i] = M_PI/2,
+      circumradius[i] = 90._deg,
       inradius[i] = 0;
     }
   else for(int p=0; p<100; p++) {
@@ -504,7 +504,7 @@ void archimedean_tiling::compute_geometry() {
   triangles.resize(2*N+2);
   for(int i=0; i<N; i++) for(int j=0; j<2; j++) 
     for(int k=0; k<faces[i]; k++) 
-      triangles[2*i+j].emplace_back(2*M_PI/faces[i], circumradius[i]);
+      triangles[2*i+j].emplace_back(TAU/faces[i], circumradius[i]);
   
   for(int k=0; k<N; k++) {
     triangles[2*N].emplace_back(alphas[k], circumradius[k]);
@@ -529,9 +529,9 @@ void archimedean_tiling::compute_geometry() {
   }
 
 ld archimedean_tiling::scale() {
-  if(real_faces == 0 && N == 2) return M_PI / 2;
-  if(real_faces == 2) return M_PI / 2;
-  if(real_faces == 0) return 2 * M_PI / N;
+  if(real_faces == 0 && N == 2) return 90._deg;
+  if(real_faces == 2) return 90._deg;
+  if(real_faces == 0) return TAU / N;
   return edgelength;
   }
 
diff --git a/basegraph.cpp b/basegraph.cpp
index d749285b..0b4ba2ae 100644
--- a/basegraph.cpp
+++ b/basegraph.cpp
@@ -1024,7 +1024,7 @@ EX void drawCircle(int x, int y, int size, color_t color, color_t fillcolor IS(0
     if(pts > 1500) pts = 1500;
     if(ISMOBILE && pts > 72) pts = 72;
     for(int r=0; r<pts; r++) {
-      float rr = (M_PI * 2 * r) / pts;
+      float rr = (TAU * r) / pts;
       glcoords.push_back(glhr::makevertex(x + size * sin(rr), y + size * pconf.stretch * cos(rr), 0));
       }
     current_display->set_all(0, lband_shift);
diff --git a/binary-tiling.cpp b/binary-tiling.cpp
index 16013d21..33bc95ed 100644
--- a/binary-tiling.cpp
+++ b/binary-tiling.cpp
@@ -478,7 +478,7 @@ EX namespace bt {
         }
       if(d == NODIR) return 0;
       if(d == c->type-1) d++;
-      return -(d+2)*M_PI/4;
+      return -(d+2) * 45._deg;
       }
 
     transmatrix adj(heptagon *h, int dir) override {
@@ -726,20 +726,20 @@ EX namespace bt {
       }
     if(geometry == gHoroTris) {
       ld r3 = sqrt(3);
-      direct_tmatrix[0] = xpush(-log(2)) * cspin(1,2, M_PI);
+      direct_tmatrix[0] = xpush(-log(2)) * cspin180(1,2);
       direct_tmatrix[1] = parabolic3(0, +r3/3) * xpush(-log(2));
       direct_tmatrix[2] = parabolic3(-0.5, -r3/6) * xpush(-log(2));
       direct_tmatrix[3] = parabolic3(+0.5, -r3/6) * xpush(-log(2));
-      direct_tmatrix[4] = parabolic3(0, -r3*2/3) * cspin(1,2, M_PI);
-      direct_tmatrix[5] = parabolic3(1, r3/3) * cspin(1,2,M_PI);
-      direct_tmatrix[6] = parabolic3(-1, r3/3) * cspin(1,2,M_PI);
+      direct_tmatrix[4] = parabolic3(0, -r3*2/3) * cspin180(1,2);
+      direct_tmatrix[5] = parabolic3(1, r3/3) * cspin180(1,2);
+      direct_tmatrix[6] = parabolic3(-1, r3/3) * cspin180(1,2);
       }
     if(geometry == gHoroRec) {
       ld r2 = sqrt(2);
       ld l = -log(2)/2;
       ld z = hororec_scale;
-      direct_tmatrix[0] = parabolic3(0, -z) * xpush(l) * cspin(2,1,M_PI/2);
-      direct_tmatrix[1] = parabolic3(0, +z) * xpush(l) * cspin(2,1,M_PI/2);
+      direct_tmatrix[0] = parabolic3(0, -z) * xpush(l) * cspin90(2,1);
+      direct_tmatrix[1] = parabolic3(0, +z) * xpush(l) * cspin90(2,1);
       direct_tmatrix[2] = parabolic3(+2*r2*z, 0);
       direct_tmatrix[3] = parabolic3(0, +4*z);
       direct_tmatrix[4] = parabolic3(-2*r2*z, 0);
@@ -749,9 +749,9 @@ EX namespace bt {
       // also generated with the help of hexb.cpp
       ld l = log(3)/2;
       auto& t = direct_tmatrix;
-      t[0] = parabolic3(horohex_scale, 0) * xpush(-l) * cspin(1, 2, M_PI/2);
-      t[1] = cspin(1, 2, 2*M_PI/3) * t[0];
-      t[2] = cspin(1, 2, 4*M_PI/3) * t[0];
+      t[0] = parabolic3(horohex_scale, 0) * xpush(-l) * cspin(1, 2, 90._deg);
+      t[1] = cspin(1, 2, 120*degree) * t[0];
+      t[2] = cspin(1, 2, 240*degree) * t[0];
       auto it = iso_inverse(t[0]);
 
       t[5] = it * t[1] * t[1];
@@ -978,7 +978,7 @@ EX int celldistance3_hex(heptagon *c1, heptagon *c2) {
   while(isize(d1)) {
     xsteps -= 2;
 
-    T = euscalezoom(hpxy(0,sqrt(3))) * eupush(1,0) * spin(-d2.back() * 2 * M_PI/3) * T * spin(d1.back() * 2 * M_PI/3) * eupush(-1,0) * euscalezoom(hpxy(0,-1/sqrt(3)));
+    T = euscalezoom(hpxy(0,sqrt(3))) * eupush(1,0) * spin(-d2.back() * 120._deg) * T * spin(d1.back() * 2 * M_PI/3) * eupush(-1,0) * euscalezoom(hpxy(0,-1/sqrt(3)));
     
     d1.pop_back(); d2.pop_back();
     
@@ -1166,7 +1166,7 @@ EX void create_faces() {
     hyperpoint down = point3(0,0,2*z);
 
     for(int j=0; j<4; j++) for(int i=0; i<3; i++) {
-      transmatrix T = cspin(0, 1, 2*M_PI*i/3);
+      transmatrix T = cspin(0, 1, 120._deg * i);
 
       hyperpoint hcenter = point3(0,0,-z);
       hyperpoint hu0 = T*point3(+h,  +r3,-z);
diff --git a/blizzard.cpp b/blizzard.cpp
index 9273c035..d7bb393f 100644
--- a/blizzard.cpp
+++ b/blizzard.cpp
@@ -241,7 +241,7 @@ EX void drawArrowTraps() {
           hyperpoint trel = inverse_shift(tu, tC0(tv));
           shiftmatrix tpartial = tu * rspintox(trel) * xpush(hdist0(trel) * tt / 401.0);
           tpartial = tpartial * ypush(.05);
-          if(GDIM == 3) tpartial = tpartial * cspin(1, 2, M_PI/2);
+          if(GDIM == 3) tpartial = tpartial * cspin90(1, 2);
           queuepoly(tpartial, cgi.shTrapArrow, 0xFFFFFFFF);
           }
         }
diff --git a/cell.cpp b/cell.cpp
index 57b94d08..be1d92d5 100644
--- a/cell.cpp
+++ b/cell.cpp
@@ -1071,7 +1071,7 @@ int ld_to_int(ld x) {
 #if CAP_ARCM
 EX gp::loc pseudocoords(cell *c) {
   transmatrix T = arcm::archimedean_gmatrix[c->master].second;
-  return {ld_to_int(T[0][LDIM]), ld_to_int((spin(60*degree) * T)[0][LDIM])};
+  return {ld_to_int(T[0][LDIM]), ld_to_int((spin(60._deg) * T)[0][LDIM])};
   }
 
 EX cdata *arcmCdata(cell *c) {
diff --git a/celldrawer.cpp b/celldrawer.cpp
index 1b33117d..b5eb0d38 100644
--- a/celldrawer.cpp
+++ b/celldrawer.cpp
@@ -88,7 +88,9 @@ void celldrawer::addaura() {
 void eclectic_red(color_t& col) {
   part(col, 0) = part(col, 2) * 3 / 4;
   }
-  
+
+constexpr ld spinspeed = .75 / M_PI;
+
 void celldrawer::setcolors() {
 
   wcol = fcol = winf[c->wall].color;
@@ -105,7 +107,7 @@ void celldrawer::setcolors() {
           0x90 + 8 * sintick(1000, windmap::windcodes[windmap::getId(c)] / 256.)
           ) : 
         #endif
-        0x1010C0 + int(32 * sintick(500, (ls::any_chaos() ? c->CHAOSPARAM : c->landparam)*.75/M_PI));
+        0x1010C0 + int(32 * sintick(500, (ls::any_chaos() ? c->CHAOSPARAM : c->landparam)*spinspeed));
     else if(c->land == laOceanWall)
       fcol = 0x2020FF;
     else if(c->land == laVariant)
@@ -118,7 +120,7 @@ void celldrawer::setcolors() {
         if(c->move(i)->wall != waSea && c->move(i)->wall != waBoat)
           nearshore = true;
       if(nearshore) mafcol += 30; */
-      fcol = fcol + mafcol * (4+sintick(500, ((eubinary||c->master->alt) ? celldistAlt(c) : 0)*.75/M_PI))/5;
+      fcol = fcol + mafcol * (4+sintick(500, ((eubinary||c->master->alt) ? celldistAlt(c) : 0)*spinspeed))/5;
       }
     else if(c->land == laDocks) {
       fcol = 0x0000A0;
@@ -126,7 +128,7 @@ void celldrawer::setcolors() {
     else if(c->land == laAlchemist)
       fcol = 0x900090;
     else if(c->land == laWhirlpool)
-      fcol = 0x0000C0 + int(32 * sintick(200, ((eubinary||c->master->alt) ? celldistAlt(c) : 0)*.75/M_PI));
+      fcol = 0x0000C0 + int(32 * sintick(200, ((eubinary||c->master->alt) ? celldistAlt(c) : 0)*spinspeed));
     else if(c->land == laLivefjord)
       fcol = 0x000080;
     else if(isWarpedType(c->land))
@@ -638,7 +640,7 @@ void celldrawer::tune_colors() {
       celldist(c);
 
     int dc = 
-      0x10101 * (127 + int(127 * sintick(200, d*.75/M_PI)));
+      0x10101 * (127 + int(127 * sintick(200, d*spinspeed)));
     wcol = gradient(wcol, dc, 0, .3, 1);
     fcol = gradient(fcol, dc, 0, .3, 1);
     }
@@ -686,7 +688,7 @@ void celldrawer::draw_wall() {
       int hdir = 0;
       for(int i=0; i<c->type; i++) if(c->move(i)->wall == waClosedGate)
         hdir = i;
-      queuepolyat(V * ddspin(c, hdir, M_PI), cgi.shPalaceGate, darkena(wcol, 0, 0xFF), wmspatial?PPR::WALL3A:PPR::WALL);
+      queuepolyat(V * ddspin180(c, hdir), cgi.shPalaceGate, darkena(wcol, 0, 0xFF), wmspatial?PPR::WALL3A:PPR::WALL);
       return;
       }
     color_t wcol0 = wcol;
@@ -712,7 +714,7 @@ void celldrawer::draw_wall() {
     int hdir = 0;
     for(int i=0; i<c->type; i++) if(c->move(i) && c->move(i)->wall == waClosedGate)
       hdir = i;
-    shiftmatrix V2 = mscale(V, wmspatial?cgi.WALL:1) * ddspin(c, hdir, M_PI);
+    shiftmatrix V2 = mscale(V, wmspatial?cgi.WALL:1) * ddspin180(c, hdir);
     queuepolyat(V2, cgi.shPalaceGate, darkena(wcol, 0, 0xFF), wmspatial?PPR::WALL3A:PPR::WALL);
     starcol = 0;
     }
@@ -787,7 +789,7 @@ void celldrawer::draw_boat() {
     Vboat = V;
     nospin = c->wall == waBoat && applyAnimation(c, Vboat, footphase, LAYER_BOAT);
     if(!nospin) Vboat = face_the_player(V);
-    else Vboat = Vboat * cspin(0, 2, M_PI);
+    else Vboat = Vboat * cspin180(0, 2);
     queuepolyat(mscale(Vboat, cgi.scalefactor/2), cgi.shBoatOuter, outcol, PPR::BOATLEV2);
     queuepolyat(mscale(Vboat, cgi.scalefactor/2-0.01), cgi.shBoatInner, incol, PPR::BOATLEV2);
     return;
@@ -795,7 +797,7 @@ void celldrawer::draw_boat() {
 
   if(wmspatial && c->wall == waBoat) {
     nospin = c->wall == waBoat && applyAnimation(c, Vboat, footphase, LAYER_BOAT);
-    if(!nospin && c->mondir != NODIR) Vboat = Vboat * ddspin(c, c->mondir, M_PI);
+    if(!nospin && c->mondir != NODIR) Vboat = Vboat * ddspin180(c, c->mondir);
     queuepolyat(Vboat, cgi.shBoatOuter, outcol, PPR::BOATLEV);
     Vboat = V;
     }
@@ -803,7 +805,7 @@ void celldrawer::draw_boat() {
     nospin = applyAnimation(c, Vboat, footphase, LAYER_BOAT);
     }
   if(!nospin && c->mondir != NODIR) 
-    Vboat = Vboat * ddspin(c, c->mondir, M_PI);
+    Vboat = Vboat * ddspin180(c, c->mondir);
   else {
     shiftmatrix Vx;
     if(applyAnimation(c, Vx, footphase, LAYER_SMALL))
@@ -964,7 +966,7 @@ void celldrawer::draw_halfvine() {
     queuepolyat(GDIM == 2 ? Vdepth : V2, cgi.shSemiFloor[0], darkena(vcol, fd, 0xFF), PPR::WALL3A);
     if(!noshadow) {
       dynamicval<color_t> p(poly_outline, OUTLINE_TRANS);
-      queuepolyat(V2 * spin(M_PI*2/3), cgi.shSemiFloorShadow, SHADOW_WALL, GDIM == 2 ? PPR::WALLSHADOW : PPR::TRANSPARENT_SHADOW);
+      queuepolyat(V2 * spin(120._deg), cgi.shSemiFloorShadow, SHADOW_WALL, GDIM == 2 ? PPR::WALLSHADOW : PPR::TRANSPARENT_SHADOW);
       }
     #if MAXMDIM >= 4
     if(GDIM == 3 && qfi.fshape) {
@@ -1032,7 +1034,7 @@ void celldrawer::draw_mirrorwall() {
       queuepolyat(V2, cgi.shHalfMirror[2], 0xC0C0C080, PPR::WALL3);
     }
   else {
-    qfi.spin = ddspin(c, d, M_PI);
+    qfi.spin = ddspin180(c, d);
     shiftmatrix V2 = V * qfi.spin;
     if(!wmblack) {
       inmirrorcount++;
@@ -1526,7 +1528,7 @@ void celldrawer::draw_features() {
       queuepoly(V, cgi.shThorns, 0xC080C0FF);
 
       for(int u=0; u<4; u+=2)
-        queuepoly(V * spin(2*M_PI / 3 / 4 * u), cgi.shRose, darkena(wcol, 0, 0xC0));
+        queuepoly(V * spin(30._deg * u), cgi.shRose, darkena(wcol, 0, 0xC0));
       break;
       }
 
@@ -1712,7 +1714,7 @@ void celldrawer::draw_features() {
             ld rad = cgi.hexf * (.3 * (u + ds));
             int tcol = darkena(gradient(forecolor, backcolor, 0, rad, 1.5 * cgi.hexf), 0, 0xFF);
             PRING(a)
-              curvepoint(xspinpush0(a * M_PI / cgi.S42, rad));
+              curvepoint(xspinpush0(a * cgi.S_step, rad));
             queuecurve(V, tcol, 0, PPR::LINE);
             }
           }  
@@ -1904,7 +1906,7 @@ void celldrawer::check_rotations() {
       ds.point = normalize_flat(ds.total);
       if(prod) ds.point = zshift(ds.point, ds.depth / ds.qty);
       if(side == 2) for(int i=0; i<3; i++) ds.point[i] = -ds.point[i];
-      if(side == 1) ds.point = spin(-M_PI/2) * ds.point;
+      if(side == 1) ds.point = spin(-90._deg) * ds.point;
       }
     };
   
@@ -2535,7 +2537,7 @@ void celldrawer::add_map_effects() {
         cell *c2 = c->move(i); 
         if(airdist(c2) < airdist(c)) {
           ld airdir = calcAirdir(c2); // printf("airdir = %d\n", airdir);
-          transmatrix V0 = ddspin(c, i, M_PI);
+          transmatrix V0 = ddspin180(c, i);
           
           double ph = ptick(PURE?150:75) + airdir;
           
@@ -2570,7 +2572,7 @@ void celldrawer::add_map_effects() {
     for(int t=0; t<c->type; t++) if(c->move(t)) {
       if(c->move(t)->ligon) {
         int lcol = darkena(gradient(iinf[itOrbLightning].color, 0, 0, tim, 1100), 0, 0xFF);
-        queueline(V*chei(xspinpush((vid.flasheffects ? ticks : ptick(8)) * M_PI / cgi.S42, cgi.hexf/2), rand() % 1000, 1000) * C0, V*chei(currentmap->adj(c, t), rand() % 1000, 1000) * C0, lcol, 2 + vid.linequality);
+        queueline(V*chei(xspinpush((vid.flasheffects ? ticks : ptick(8)) * cgi.S_step, cgi.hexf/2), rand() % 1000, 1000) * C0, V*chei(currentmap->adj(c, t), rand() % 1000, 1000) * C0, lcol, 2 + vid.linequality);
         }
       for(int u: {-1, 1}) {
         cellwalker cw = cellwalker(c, t) + wstep + u;
@@ -2578,7 +2580,7 @@ void celldrawer::add_map_effects() {
         cell *c2 = cw.peek();
         if(c2 && c2->ligon) {
           int lcol = darkena(gradient(iinf[itOrbLightning].color, 0, 0, tim, 1100), 0, 0xFF);
-          queueline(V*chei(xspinpush((vid.flasheffects ? ticks : ptick(8)) * M_PI / cgi.S42, cgi.hexf/2), rand() % 1000, 1000) * C0, V*chei(currentmap->adj(c, t)*currentmap->adj(cw.at, cw.spin), rand() % 1000, 1000) * C0, lcol, 2 + vid.linequality);
+          queueline(V*chei(xspinpush((vid.flasheffects ? ticks : ptick(8)) * cgi.S_step, cgi.hexf/2), rand() % 1000, 1000) * C0, V*chei(currentmap->adj(c, t)*currentmap->adj(cw.at, cw.spin), rand() % 1000, 1000) * C0, lcol, 2 + vid.linequality);
           }
         }
       }
@@ -2596,8 +2598,7 @@ void celldrawer::add_map_effects() {
       
       int aircol = 0xC0C0FF40;
       
-      if(hdir1 < hdir0-M_PI) hdir1 += 2 * M_PI;
-      if(hdir1 >= hdir0+M_PI) hdir1 -= 2 * M_PI;
+      cyclefix(hdir1, hdir0);
       
       ld hdir = (hdir1*ph1+hdir0*(1-ph1));
   
@@ -2733,7 +2734,7 @@ void celldrawer::draw() {
       inmirrorcount += cmc;
       draw_grid();
       if(cw2.mirrored != cw.mirrored) V = V * Mirror;
-      if(cw2.spin) V = V * spin(2*M_PI*cw2.spin/cw2.at->type);
+      if(cw2.spin) V = V * spin(TAU*cw2.spin/cw2.at->type);
       cw2.spin = 0;
       dynamicval<shiftmatrix> dc(cwtV, cwtV);
       cwtV = V * inverse_shift(ggmatrix(cw2.at), cwtV);
diff --git a/colors.cpp b/colors.cpp
index 1dc89683..cc0e4917 100644
--- a/colors.cpp
+++ b/colors.cpp
@@ -247,13 +247,15 @@ EX int cloakcolor(int rtr) {
 EX int firegradient(double p) {
   return gradient(0xFFFF00, 0xFF0000, 0, p, 1);
   }
-  
+
+constexpr ld PI1000 = 0.001 / A_PI;
+
 EX int firecolor(int phase IS(0), int mul IS(1)) {
-  return gradient(0xFFFF00, 0xFF0000, -1, sintick(100*mul, phase/200./M_PI), 1);
+  return gradient(0xFFFF00, 0xFF0000, -1, sintick(100*mul, phase * 5 * PI1000), 1);
   }
 
 EX int watercolor(int phase) {
-  return 0x0080C0FF + 256 * int(63 * sintick(50, phase/100./M_PI));
+  return 0x0080C0FF + 256 * int(63 * sintick(50, phase * 10 * PI1000));
   }
 
 EX int aircolor(int phase) {
@@ -270,7 +272,7 @@ EX int fghostcolor(cell *c) {
   }
 
 EX int weakfirecolor(int phase) {
-  return gradient(0xFF8000, 0xFF0000, -1, sintick(500, phase/1000./M_PI), 1);
+  return gradient(0xFF8000, 0xFF0000, -1, sintick(500, phase * PI1000), 1);
   }
 
 /* HTML color names */
diff --git a/commandline.cpp b/commandline.cpp
index c6b9815b..d181e5d1 100644
--- a/commandline.cpp
+++ b/commandline.cpp
@@ -256,31 +256,31 @@ int arg::readCommon() {
     PHASE(3);  start_game();
     shift(); ld a = argf();
     shift(); ld b = argf();
-    View = View * spin(M_PI * 2 * a / b);
+    View = View * spin(TAU * a / b);
     playermoved = false;
     }
   else if(argis("-rotate-up")) {
     start_game();
     shiftmatrix S = ggmatrix(cwt.at->master->move(0)->c7);
-    View = spin(90*degree) * spintox(S.T*C0) * View;
+    View = spin90() * spintox(S.T*C0) * View;
     playermoved = false;
     }
   else if(argis("-rotate3")) {
     PHASE(3);  start_game();
     shift(); ld a = argf();
     shift(); ld b = argf();
-    View = View * cspin(1, 2, M_PI * 2 * a / b);
+    View = View * cspin(1, 2, TAU * a / b);
     playermoved = false;
     }
   else if(argis("-face-vertex")) {
     PHASE(3);  start_game();
     auto &ss = currentmap->get_cellshape(cwt.at);
-    View = cspin(0, 2, M_PI/2) * spintox(ss.vertices_only_local[0]);
+    View = cspin90(0, 2) * spintox(ss.vertices_only_local[0]);
     playermoved = false;
     }
   else if(argis("-face-face")) {
     PHASE(3);  start_game();
-    View = cspin(0, 2, M_PI/2);
+    View = cspin90(0, 2);
     }
   else if(argis("-grotate")) {
     PHASE(3);  start_game();
diff --git a/complex2.cpp b/complex2.cpp
index 1f2836a5..b803e10c 100644
--- a/complex2.cpp
+++ b/complex2.cpp
@@ -1239,7 +1239,7 @@ EX namespace dice {
         }
       }
     
-    shiftmatrix V1 = V * ddspin(c, dir) * spin(M_PI);
+    shiftmatrix V1 = V * ddspin(c, dir + M_PI);
     if(dd.mirrored) V1 = V1 * MirrorY;
     
     // loop:
@@ -1260,8 +1260,8 @@ EX namespace dice {
     
     if(1) {
       dynamicval<eGeometry> g(geometry, gSphere);
-      ld alpha = 360 * degree / dw->order;
-      ld beta = 180 * degree / dw->facesides;
+      ld alpha = TAU / dw->order;
+      ld beta = M_PI / dw->facesides;
       inradius  = edge_of_triangle_with_angles(alpha, beta, beta);
       outradius = edge_of_triangle_with_angles(beta, alpha, beta);
       }
@@ -1320,7 +1320,7 @@ EX namespace dice {
       
       for(int d=0; d<si; d++) {
         dynamicval<eGeometry> g(geometry, highdim);
-        add_to_queue(T * cspin(0, 1, 2*M_PI*d/si) * cspin(2, 0, inradius) * cspin(0, 1, M_PI-2*M_PI*dw->spins[ws][d]/si), dw->sides[ws][d]);
+        add_to_queue(T * cspin(0, 1, TAU*d/si) * cspin(2, 0, inradius) * cspin(0, 1, M_PI-TAU*dw->spins[ws][d]/si), dw->sides[ws][d]);
         }
       
       if(1) {
@@ -1363,7 +1363,7 @@ EX namespace dice {
         hyperpoint h, hs;
         if(1) {
           dynamicval<eGeometry> g(geometry, highdim);
-          h = zpush(base_to_base) * T * cspin(0, 1, 2*M_PI*(d+.5)/si) * cspin(2, 0, outradius) * zpush0(dieradius);
+          h = zpush(base_to_base) * T * cspin(0, 1, TAU*(d+.5)/si) * cspin(2, 0, outradius) * zpush0(dieradius);
           if(d < si) face[d] = h;
           hs = sphere_to_space(h);
           }
diff --git a/config.cpp b/config.cpp
index 84cd88e7..fe93a677 100644
--- a/config.cpp
+++ b/config.cpp
@@ -1005,7 +1005,7 @@ EX void initConfig() {
     if(ginf[i].flags & qELLIPTIC)
       sightranges[i] = M_PI;
     else if(ginf[i].cclass == gcSphere)
-      sightranges[i] = 2 * M_PI;
+      sightranges[i] = TAU;
     else if(ginf[i].cclass == gcEuclid)
       sightranges[i] = 10;
     else if(ginf[i].cclass == gcSL2)
@@ -1028,21 +1028,21 @@ EX void initConfig() {
 
   addsaver(sightranges[gBinary3], "sight-binary3", 3.1 + bonus);
   addsaver(sightranges[gCubeTiling], "sight-cubes", 10);
-  addsaver(sightranges[gCell120], "sight-120cell", 2 * M_PI);
+  addsaver(sightranges[gCell120], "sight-120cell", TAU);
   addsaver(sightranges[gECell120], "sight-120cell-elliptic", M_PI);
   addsaver(sightranges[gRhombic3], "sight-rhombic", 10.5 * emul);
   addsaver(sightranges[gBitrunc3], "sight-bitrunc", 12 * emul);
   addsaver(sightranges[gSpace534], "sight-534", 4 + bonus);
   addsaver(sightranges[gSpace435], "sight-435", 3.8 + bonus);
 
-  addsaver(sightranges[gCell5], "sight-5cell", 2 * M_PI);
-  addsaver(sightranges[gCell8], "sight-8cell", 2 * M_PI);
+  addsaver(sightranges[gCell5], "sight-5cell", TAU);
+  addsaver(sightranges[gCell8], "sight-8cell", TAU);
   addsaver(sightranges[gECell8], "sight-8cell-elliptic", M_PI);
-  addsaver(sightranges[gCell16], "sight-16cell", 2 * M_PI);
+  addsaver(sightranges[gCell16], "sight-16cell", TAU);
   addsaver(sightranges[gECell16], "sight-16cell-elliptic", M_PI);
-  addsaver(sightranges[gCell24], "sight-24cell", 2 * M_PI);
+  addsaver(sightranges[gCell24], "sight-24cell", TAU);
   addsaver(sightranges[gECell24], "sight-24cell-elliptic", M_PI);
-  addsaver(sightranges[gCell600], "sight-600cell", 2 * M_PI);
+  addsaver(sightranges[gCell600], "sight-600cell", TAU);
   addsaver(sightranges[gECell600], "sight-600cell-elliptic", M_PI);
   addsaver(sightranges[gHoroTris], "sight-horotris", 2.9 + bonus);
   addsaver(sightranges[gHoroRec], "sight-hororec", 2.2 + bonus);
@@ -1402,14 +1402,14 @@ EX void edit_sightrange() {
       if(GDIM == 3) {
         dialog::addSelItem(XLAT("3D sight range for the fog effect"), fts(sightranges[geometry]), 'r');
         dialog::add_action([] {
-          dialog::editNumber(sightranges[geometry], 0, 2 * M_PI, 0.5, M_PI, XLAT("fog effect"), "");
+          dialog::editNumber(sightranges[geometry], 0, TAU, 0.5, M_PI, XLAT("fog effect"), "");
           });
         }
       }
     if(WDIM == 3) {
       dialog::addSelItem(XLAT("3D sight range"), fts(sightranges[geometry]), 'r');
       dialog::add_action([] {
-      dialog::editNumber(sightranges[geometry], 0, 2 * M_PI, 0.5, M_PI, XLAT("3D sight range"),
+      dialog::editNumber(sightranges[geometry], 0, TAU, 0.5, M_PI, XLAT("3D sight range"),
         XLAT(
           "Sight range for 3D geometries is specified in the absolute units. This value also affects the fog effect.\n\n"
           "In spherical geometries, the sight range of 2π will let you see things behind you as if they were in front of you, "
@@ -2403,7 +2403,7 @@ EX int config3 = addHook(hooks_configfile, 100, [] {
   param_f(linepatterns::parallel_count, "parallel_count")
     ->editable(0, 24, 1, "number of parallels drawn", "", 'n');
   param_f(linepatterns::parallel_max, "parallel_max")
-    ->editable(0, 360*degree, 15*degree, "last parallel drawn", "", 'n');
+    ->editable(0, TAU, 15*degree, "last parallel drawn", "", 'n');
   param_f(vid.depth_bonus, "depth_bonus", 0)
     ->editable(-5, 5, .1, "depth bonus in pseudohedral", "", 'b');
   param_b(vid.pseudohedral, "pseudohedral", false)
@@ -2588,7 +2588,7 @@ EX void showCustomizeChar() {
   initquickqueue();
   transmatrix V = atscreenpos(vid.xres/2, firsty, scale);
   
-  double alpha = atan2(mousex - vid.xres/2, mousey - firsty) - M_PI/2;
+  double alpha = atan2(mousex - vid.xres/2, mousey - firsty) - 90._deg;
   V = V * spin(alpha);
   drawMonsterType(moPlayer, NULL, shiftless(V), 0, cc_footphase / scale, NOCOLOR);
   quickqueue();
diff --git a/control.cpp b/control.cpp
index d15f7105..fceb5647 100644
--- a/control.cpp
+++ b/control.cpp
@@ -99,7 +99,6 @@ EX movedir vectodir(hyperpoint P) {
     ld d1 = geo_dist(U * T * C0, Centered * P);
     ld d2 = geo_dist(U * T * C0, Centered * C0);
     dirdist[i] = d1 - d2;
-    //xspinpush0(-i * 2 * M_PI /cwt.at->type, .5), P);
     }
     
   movedir res;
@@ -122,11 +121,9 @@ EX void remission() {
  }
 
 EX hyperpoint move_destination_vec(int d) {
-  if(WDIM == 2) return spin(-d * M_PI/4) * smalltangent();
-  // else if(WDIM == 2 && pmodel == mdPerspective) return cspin(0, 2, d * M_PI/4) * tC0(pushone());
-  // else if(WDIM == 2) return spin(-d * M_PI/4) * tC0(pushone());
-  else if(d&1) return cspin(0, 1, d > 4 ? M_PI/2 : -M_PI/2) * smalltangent();
-  else return cspin(0, 2, d * M_PI/4) * smalltangent();
+  if(WDIM == 2) return spin(-d * 45._deg) * smalltangent();
+  else if(d&1) return cspin(0, 1, d > 4 ? 45._deg : -45._deg) * smalltangent();
+  else return cspin(0, 2, d * 45._deg) * smalltangent();
   }
 
 EX void movepckeydir(int d) {
@@ -401,7 +398,7 @@ EX void full_rotate_camera(int dir, ld val) {
   else if(GDIM == 3) {
     val *= camera_rot_speed;
     if(third_person_rotation) shift_view(ctangent(2, -third_person_rotation)), didsomething = true, playermoved = false;
-    ld max_angle = quarter_circle - 1e-4;
+    ld max_angle = 90._deg - 1e-4;
     if(walking::on && dir == 1) {
       max_angle /= degree;
       walking::eye_angle += val * walking::eye_angle_scale / degree;
@@ -461,8 +458,8 @@ EX void handlePanning(int sym, int uni) {
     }
 #endif
   if(!smooth_scrolling) {
-    if(sym == SDLK_PAGEUP) full_rotate_view(1, M_PI/cgi.S21/2*shiftmul);
-    if(sym == SDLK_PAGEDOWN) full_rotate_view(-1, -M_PI/cgi.S21/2*shiftmul);
+    if(sym == SDLK_PAGEUP) full_rotate_view(1, cgi.S_step*shiftmul);
+    if(sym == SDLK_PAGEDOWN) full_rotate_view(-1, -cgi.S_step*shiftmul);
     if(sym == SDLK_PAGEUP || sym == SDLK_PAGEDOWN) 
       if(isGravityLand(cwt.at->land) && !rug::rug_control()) playermoved = false;
     }
@@ -925,8 +922,8 @@ EX void mainloopiter() {
     if(keystate[SDL_SCANCODE_LEFT] && DEFAULTNOR(SDL_SCANCODE_LEFT)) full_rotate_camera(0, t);
     if(keystate[SDL_SCANCODE_UP] && DEFAULTNOR(SDL_SCANCODE_UP)) full_rotate_camera(1, t);
     if(keystate[SDL_SCANCODE_DOWN] && DEFAULTNOR(SDL_SCANCODE_DOWN)) full_rotate_camera(1, -t);
-    if(keystate[SDL_SCANCODE_PAGEUP] && DEFAULTNOR(SDL_SCANCODE_PAGEUP)) full_rotate_view(t * 180 / M_PI, t);
-    if(keystate[SDL_SCANCODE_PAGEDOWN] && DEFAULTNOR(SDL_SCANCODE_PAGEDOWN)) full_rotate_view(-t * 180 / M_PI, -t);
+    if(keystate[SDL_SCANCODE_PAGEUP] && DEFAULTNOR(SDL_SCANCODE_PAGEUP)) full_rotate_view(t / degree, t);
+    if(keystate[SDL_SCANCODE_PAGEDOWN] && DEFAULTNOR(SDL_SCANCODE_PAGEDOWN)) full_rotate_view(-t / degree, -t);
 
     #else
 
@@ -936,8 +933,8 @@ EX void mainloopiter() {
     if(keystate[SDLK_LEFT] && DEFAULTNOR(SDLK_LEFT)) full_rotate_camera(0, t);
     if(keystate[SDLK_UP] && DEFAULTNOR(SDLK_UP)) full_rotate_camera(1, t);
     if(keystate[SDLK_DOWN] && DEFAULTNOR(SDLK_DOWN)) full_rotate_camera(1, -t);
-    if(keystate[SDLK_PAGEUP] && DEFAULTNOR(SDLK_PAGEUP)) full_rotate_view(t * 180 / M_PI, t);
-    if(keystate[SDLK_PAGEDOWN] && DEFAULTNOR(SDLK_PAGEDOWN)) full_rotate_view(-t * 180 / M_PI, -t);
+    if(keystate[SDLK_PAGEUP] && DEFAULTNOR(SDLK_PAGEUP)) full_rotate_view(t / degree, t);
+    if(keystate[SDLK_PAGEDOWN] && DEFAULTNOR(SDLK_PAGEDOWN)) full_rotate_view(-t / degree, -t);
     #endif
     }
   else sc_ticks = ticks;
@@ -952,8 +949,8 @@ EX void mainloopiter() {
     if(keystate['a'] && DEFAULTNOR('a')) full_rotate_camera(0, t);
     if(keystate['w'] && DEFAULTNOR('w')) full_rotate_camera(1, t);
     if(keystate['s'] && DEFAULTNOR('s')) full_rotate_camera(1, -t);
-    if(keystate['q'] && DEFAULTNOR('q')) full_rotate_view(t * 180 / M_PI, t);
-    if(keystate['e'] && DEFAULTNOR('e')) full_rotate_view(-t * 180 / M_PI, -t);
+    if(keystate['q'] && DEFAULTNOR('q')) full_rotate_view(t / degree, t);
+    if(keystate['e'] && DEFAULTNOR('e')) full_rotate_view(-t / degree, -t);
 
     if(keystate['i'] && GDIM == 3 && DEFAULTNOR('i')) full_forward_camera(-t);
     if(keystate['k'] && GDIM == 3 && DEFAULTNOR('k')) full_forward_camera(t);
diff --git a/crystal.cpp b/crystal.cpp
index 88bc526e..7ed57b4e 100644
--- a/crystal.cpp
+++ b/crystal.cpp
@@ -801,7 +801,7 @@ EX colortable coordcolors = {0xD04040, 0x40D040, 0x4040D0, 0xFFD500, 0xF000F0, 0
 
 EX ld compass_angle() {
   bool bitr = ginf[gCrystal].vertex == 3;
-  return (bitr ? M_PI/8 : 0) - master_to_c7_angle();
+  return (bitr ? 22.5_deg : 0) - master_to_c7_angle();
   }
       
 EX bool crystal_cell(cell *c, shiftmatrix V) {
@@ -822,7 +822,7 @@ EX bool crystal_cell(cell *c, shiftmatrix V) {
       ld dist = cellgfxdist(c, 0);
 
       for(int i=0; i<S7; i++)  {
-        shiftmatrix T = V * spin(compass_angle() - 2 * M_PI * i / S7) * xpush(dist*.3);
+        shiftmatrix T = V * spin(compass_angle() - TAU * i / S7) * xpush(dist*.3);
         
         auto co = m->hcoords[c->master];
         auto lw = m->makewalker(co, i);
@@ -1118,8 +1118,9 @@ EX void init_rotation() {
 
   if(ho & 1) {
     for(int i=(draw_cut ? 2 : cs.dim-1); i>=1; i--) {
-      ld c = cos(M_PI / 2 / (i+1));
-      ld s = sin(M_PI / 2 / (i+1));
+      ld alpha = 90._deg / (i+1);
+      ld c = cos(alpha);
+      ld s = sin(alpha);
       for(int j=0; j<cs.dim; j++)
         tie(crug_rotation[j][0], crug_rotation[j][i]) =
           make_pair(
@@ -1724,8 +1725,8 @@ void transform_crystal_to_euclid () {
   
   clearAnimations();
   cwt.spin = neighborId(cwt.at, infront);
-  View = iddspin(cwt.at, cwt.spin, M_PI/2);
-  if(!flipplayer) View = cspin(0, 2, M_PI) * View;
+  View = iddspin(cwt.at, cwt.spin, 90._deg);
+  if(!flipplayer) View = cspin180(0, 2) * View;
   
   if(pmodel == mdDisk) pmodel = mdPerspective;
   }
diff --git a/debug.cpp b/debug.cpp
index 1a925ab6..99810c99 100644
--- a/debug.cpp
+++ b/debug.cpp
@@ -738,7 +738,7 @@ int read_cheat_args() {
     showstartmenu = false;
     }
   else if(argis("-top")) {
-    PHASE(3); View = View * spin(-M_PI/2);
+    PHASE(3); View = View * spin(-90._deg);
     }
   else if(argis("-idv")) {
     PHASE(3); View = Id;
diff --git a/dialogs.cpp b/dialogs.cpp
index 3e077847..f27cf173 100644
--- a/dialogs.cpp
+++ b/dialogs.cpp
@@ -471,9 +471,9 @@ EX namespace dialog {
 
     curvepoint(hyperpoint(x-si, yt, 1, 1));
     for(int i=0; i<=a/2; i++)
-      curvepoint(hyperpoint(x - si * cos(i*2*M_PI/a), yb + si * sin(i*2*M_PI/a), 1, 1));
+      curvepoint(hyperpoint(x - si * cos(i*TAU/a), yb + si * sin(i*TAU/a), 1, 1));
     for(int i=(a+1)/2; i<=a; i++)
-      curvepoint(hyperpoint(x - si * cos(i*2*M_PI/a), yt + si * sin(i*2*M_PI/a), 1, 1));
+      curvepoint(hyperpoint(x - si * cos(i*TAU/a), yt + si * sin(i*TAU/a), 1, 1));
     queuecurve(V, col, 0x80, PPR::LINE);
 
     int yt1 = yt + (list_actual_size * list_skip) / list_full_size;
@@ -481,9 +481,9 @@ EX namespace dialog {
 
     curvepoint(hyperpoint(x-siz, yt1, 1, 1));
     for(int i=0; i<=a/2; i++)
-      curvepoint(hyperpoint(x - siz * cos(i*2*M_PI/a), yb1 + siz * sin(i*2*M_PI/a), 1, 1));
+      curvepoint(hyperpoint(x - siz * cos(i*TAU/a), yb1 + siz * sin(i*TAU/a), 1, 1));
     for(int i=(a+1)/2; i<=a; i++)
-      curvepoint(hyperpoint(x - siz * cos(i*2*M_PI/a), yt1 + siz * sin(i*2*M_PI/a), 1, 1));
+      curvepoint(hyperpoint(x - siz * cos(i*TAU/a), yt1 + siz * sin(i*TAU/a), 1, 1));
     queuecurve(V, col, 0x80, PPR::LINE);
 
     quickqueue();
@@ -516,9 +516,9 @@ EX namespace dialog {
 
       curvepoint(hyperpoint(sl, y-si, 1, 1));
       for(int i=0; i<=a/2; i++)
-        curvepoint(hyperpoint(sr + si * sin(i*2*M_PI/a), y - si * cos(i*2*M_PI/a), 1, 1));
+        curvepoint(hyperpoint(sr + si * sin(i*TAU/a), y - si * cos(i*TAU/a), 1, 1));
       for(int i=(a+1)/2; i<=a; i++)
-        curvepoint(hyperpoint(sl + si * sin(i*2*M_PI/a), y - si * cos(i*2*M_PI/a), 1, 1));
+        curvepoint(hyperpoint(sl + si * sin(i*TAU/a), y - si * cos(i*TAU/a), 1, 1));
       queuecurve(V, col, 0x80, PPR::LINE);
       quickqueue();
 
@@ -535,7 +535,7 @@ EX namespace dialog {
         queuecurve(V, col, 0x80, PPR::LINE);
         quickqueue();
         }
-      for(int i=0; i<=a; i++) curvepoint(hyperpoint(x + siz * sin(i*2*M_PI/a), y - siz * cos(i*2*M_PI/a), 1, 1));
+      for(int i=0; i<=a; i++) curvepoint(hyperpoint(x + siz * sin(i*TAU/a), y - siz * cos(i*TAU/a), 1, 1));
       queuecurve(V, col, col, PPR::LINE);
       quickqueue();
       }
@@ -629,7 +629,7 @@ EX namespace dialog {
             int bx = (c == 1 || c == 3 || c == 5) ? x+1 : x;
             int by = (c == 2 || c == 4 || c == 5) ? vid.yres : 0;
             int cx = bx == 0 ? 0 : bx == 16 ?vid.xres :
-              vid.xres - dwidth + width * tan((bx-8)/8. * 90 * degree);
+              vid.xres - dwidth + width * tan((bx-8)/8. * 90._deg);
             part(col, 0) = lerp(0, full, bx / 16.);
             if(c == 0) println(hlog, "bx = ", bx, " -> cx = ", cx, " darken = ", part(col, 0));
             auravertices.emplace_back(hyperpoint(cx - current_display->xcenter, by - current_display->ycenter, 0, 1), col);
@@ -754,7 +754,7 @@ EX namespace dialog {
             color_t col = addalpha(I.color);
             ld sizf = dfsize * I.scale / 150;
             ld siz = sizf * sqrt(0.15+0.85*I.param/255.);
-            for(int i=0; i<=a; i++) curvepoint(hyperpoint(siz * sin(i*2*M_PI/a), -siz * cos(i*2*M_PI/a), 1, 1));
+            for(int i=0; i<=a; i++) curvepoint(hyperpoint(siz * sin(i*TAU/a), -siz * cos(i*TAU/a), 1, 1));
             shiftmatrix V = shiftless(atscreenpos(valuex + sizf, mid, pix));
             queuecurve(V, col, (I.colorv << 8) | 0xFF, PPR::LINE);
             quickqueue();
diff --git a/drawing.cpp b/drawing.cpp
index fbc58626..84081eb5 100644
--- a/drawing.cpp
+++ b/drawing.cpp
@@ -439,10 +439,10 @@ void addpoint(const shiftpoint& H) {
     if(sphere && pmodel == mdSpiral) {
       if(isize(glcoords)) {
         hyperpoint Hscr1;
-        shiftpoint H1 = H; H1.shift += 2 * M_PI;
+        shiftpoint H1 = H; H1.shift += TAU;
         applymodel(H1, Hscr1);
         if(hypot_d(2, Hlast-Hscr1) < hypot_d(2, Hlast-Hscr)) { Hscr = Hscr1; }
-        H1.shift -= 4 * M_PI;
+        H1.shift -= 2 * TAU;
         applymodel(H1, Hscr1);
         if(hypot_d(2, Hlast-Hscr1) < hypot_d(2, Hlast-Hscr)) { Hscr = Hscr1; }
         }
@@ -1108,7 +1108,7 @@ EX namespace s2xe {
     }
   
   void add2(pt h, int gen) {
-    glcoords.push_back(glhr::pointtogl(point31(sin(h[0]) * (h[1] + 2 * M_PI * gen), cos(h[0]) * (h[1] + 2 * M_PI * gen), h[2])));
+    glcoords.push_back(glhr::pointtogl(point31(sin(h[0]) * (h[1] + TAU * gen), cos(h[0]) * (h[1] + TAU * gen), h[2])));
     stinf.tvertices.push_back(glhr::makevertex(h[3], h[4], 0));
     }
 
@@ -1125,13 +1125,13 @@ EX namespace s2xe {
   bool to_right(const pt& h2, const pt& h1) {
     ld x2 = h2[0];
     ld x1 = h1[0];
-    if(x2 < x1) x2 += 2 * M_PI;
+    if(x2 < x1) x2 += TAU;
     return x2 >= x2 && x2 <= x1 + M_PI;
     }
   
   EX int qrings = 32;
   
-  ld seg() { return 2 * M_PI / qrings; }
+  ld seg() { return TAU / qrings; }
   
   void add_ortho_triangle(pt bl, pt tl, pt br, pt tr) {
     
@@ -1164,12 +1164,12 @@ EX namespace s2xe {
     }
   
   void add_ordered_triangle(array<pt, 3> v) {
-    if(v[1][0] < v[0][0]) v[1][0] += 2 * M_PI;
-    if(v[2][0] < v[1][0]) v[2][0] += 2 * M_PI;
+    if(v[1][0] < v[0][0]) v[1][0] += TAU;
+    if(v[2][0] < v[1][0]) v[2][0] += TAU;
     if(v[2][0] - v[0][0] < 1e-6) return;
     ld x = (v[1][0] - v[0][0]) / (v[2][0] - v[0][0]);
     
-    if(v[2][0] < v[0][0] + M_PI / 4 && maxy < M_PI - M_PI/4 && sightranges[geometry] <= 5) {
+    if(v[2][0] < v[0][0] + 45._deg && maxy < 135._deg && sightranges[geometry] <= 5) {
       addall(v[0], v[1], v[2]);
       return;
       }
@@ -1195,16 +1195,16 @@ EX namespace s2xe {
     }
 
   void add_triangle_around(array<pt, 3> v) {
-    ld baseheight = (v[0][1] > M_PI/2) ? M_PI : 0;
+    ld baseheight = (v[0][1] > 90._deg) ? M_PI : 0;
     ld tu = (v[0][3] + v[1][3] + v[2][3]) / 3;
     ld tv = (v[0][4] + v[1][4] + v[2][4]) / 3;
     array<pt, 3> vhigh;
     for(int i=0; i<3; i++) { vhigh[i] = v[i]; vhigh[i][1] = baseheight; vhigh[i][3] = tu; vhigh[i][4] = tv; }
-    if(v[1][0] < v[0][0]) v[1][0] = v[1][0] + 2 * M_PI, vhigh[1][0] = vhigh[1][0] + 2 * M_PI;
+    if(v[1][0] < v[0][0]) v[1][0] = v[1][0] + TAU, vhigh[1][0] = vhigh[1][0] + TAU;
     add_ortho_triangle(v[0], vhigh[0], v[1], vhigh[1]);
-    if(v[2][0] < v[1][0]) v[2][0] = v[2][0] + 2 * M_PI, vhigh[2][0] = vhigh[2][0] + 2 * M_PI;
+    if(v[2][0] < v[1][0]) v[2][0] = v[2][0] + TAU, vhigh[2][0] = vhigh[2][0] + TAU;
     add_ortho_triangle(v[1], vhigh[1], v[2], vhigh[2]);
-    if(v[0][0] < v[2][0]) v[0][0] = v[0][0] + 2 * M_PI, vhigh[0][0] = vhigh[0][0] + 2 * M_PI;
+    if(v[0][0] < v[2][0]) v[0][0] = v[0][0] + TAU, vhigh[0][0] = vhigh[0][0] + TAU;
     add_ortho_triangle(v[2], vhigh[2], v[0], vhigh[0]);
     }
 
@@ -1215,12 +1215,12 @@ EX namespace s2xe {
     
     minz = min(abs(v[0][2]), max(abs(v[1][2]), abs(v[2][2])));
     auto& s = sightranges[geometry];
-    maxgen = sqrt(s * s - minz * minz) / (2 * M_PI) + 1;
+    maxgen = sqrt(s * s - minz * minz) / TAU + 1;
     
     maxy = max(v[0][1], max(v[1][1], v[2][1]));
     miny = min(v[0][1], min(v[1][1], v[2][1]));
     with_zero = true;
-    if(maxy < M_PI / 4) {
+    if(maxy < 45._deg) {
       add2(v[0], 0);
       add2(v[1], 0);
       add2(v[2], 0);
@@ -1310,7 +1310,7 @@ void draw_s2xe0(dqi_poly *p) {
   set_width(1);
   glcoords.clear();
 
-  int maxgen = sightranges[geometry] / (2 * M_PI) + 1;
+  int maxgen = sightranges[geometry] / TAU + 1;
   
   auto crossdot = [&] (const hyperpoint h1, const hyperpoint h2) { return make_pair(h1[0] * h2[1] - h1[1] * h2[0], h1[0] * h2[0] + h1[1] * h2[1]); };
   vector<point_data> pd;
@@ -1342,7 +1342,7 @@ void draw_s2xe0(dqi_poly *p) {
   for(int i=0; i<p->cnt; i++) {
     auto &c1 = pd[i];
     auto &c0 = pd[i==0?p->cnt-1 : i-1];
-    if(c1.distance > M_PI/2 && c0.distance > M_PI/2 && crossdot(c0.direction, c1.direction).second < 0) return;
+    if(c1.distance > 90._deg && c0.distance > 90._deg && crossdot(c0.direction, c1.direction).second < 0) return;
     if(c1.bad == 2) return;
     if(c1.bad == 1) no_gens = true;
     }
@@ -1354,12 +1354,12 @@ void draw_s2xe0(dqi_poly *p) {
       angles[i] = atan2(pd[i].direction[1], pd[i].direction[0]);
       }
     sort(angles.begin(), angles.end());
-    angles.push_back(angles[0] + 2 * M_PI);
+    angles.push_back(angles[0] + TAU);
     bool ok = false;
     for(int i=1; i<isize(angles); i++)
       if(angles[i] >= angles[i-1] + M_PI) ok = true;
     if(!ok) {
-      for(auto &c: pd) if(c.distance > M_PI/2) return;
+      for(auto &c: pd) if(c.distance > 90._deg) return;
       no_gens = true;
       }
     }
@@ -1369,7 +1369,7 @@ void draw_s2xe0(dqi_poly *p) {
   for(int gen=-g; gen<=g; gen++) {
     for(int i=0; i<p->cnt; i++) {
       auto& cur = pd[i];
-      ld d = cur.distance + 2 * M_PI * gen;
+      ld d = cur.distance + TAU * gen;
       hyperpoint h;
       h[0] = cur.direction[0] * d;
       h[1] = cur.direction[1] * d;
@@ -1572,9 +1572,9 @@ EX namespace ods {
       
       for(int j=0; j<6; j++) {
         // let Delta be from 0 to 2PI
-        if(h[j][2]<0) h[j][2] += 2 * M_PI;
+        if(h[j][2]<0) h[j][2] += TAU;
         // Theta is from -PI/2 to PI/2. Let it be from 0 to PI
-        h[j][1] += global_projection * M_PI/2;
+        h[j][1] += global_projection * 90._deg;
         h[j][3] = 1;
         }
 
@@ -1591,8 +1591,8 @@ EX namespace ods {
       cyclefix(h[4][0], h[3][0]);
       cyclefix(h[5][0], h[3][0]);
 
-      if(abs(h[1][1] - h[0][1]) > M_PI/2) goto next_i;
-      if(abs(h[2][1] - h[0][1]) > M_PI/2) goto next_i;
+      if(abs(h[1][1] - h[0][1]) > 90._deg) goto next_i;
+      if(abs(h[2][1] - h[0][1]) > 90._deg) goto next_i;
       
       if(h[0][0] < -M_PI || h[0][0] > M_PI) println(hlog, h[0][0]);
 
@@ -1601,7 +1601,7 @@ EX namespace ods {
         if(h[1][0] < -M_PI || h[2][0] < -M_PI) lst++;
         if(h[1][0] > +M_PI || h[2][0] > +M_PI) fst--;
         for(int x=fst; x<=lst; x++) for(int j=0; j<3; j++) {
-          glcoords.push_back(glhr::makevertex(h[j][0] + 2 * M_PI * x, h[j][1], h[j][2]));
+          glcoords.push_back(glhr::makevertex(h[j][0] + TAU * x, h[j][1], h[j][2]));
           if(npoly.tinf) stinf.tvertices.push_back(p->tinf->tvertices[p->offset_texture+i+j]);
           }
         }
diff --git a/fake.cpp b/fake.cpp
index 23bea690..4c2069e7 100644
--- a/fake.cpp
+++ b/fake.cpp
@@ -237,19 +237,17 @@ EX namespace fake {
         auto h1 = V * befake(FPIU(get_corner_position(c, (i+1) % c->type)));
         ld b0 = atan2(unshift(h0));
         ld b1 = atan2(unshift(h1));
-        while(b1 < b0) b1 += 2 * M_PI;
+        while(b1 < b0) b1 += TAU;
         if(a0 == -1) {
           draw_recursive(c->move(i), optimized_shift(V * adj(c, i)), b0, b1, c, depth+1);
           }
         else {
           if(b1 - b0 > M_PI) continue;
           
-          if(b0 < a0 - M_PI) b0 += 2 * M_PI;
-          if(b0 > a0 + M_PI) b0 -= 2 * M_PI;
+          cyclefix(b0, a0);
           if(b0 < a0) b0 = a0;
           
-          if(b1 > a1 + M_PI) b1 -= 2 * M_PI;
-          if(b1 < a1 - M_PI) b1 += 2 * M_PI;
+          cyclefix(b1, a1);
           if(b1 > a1) b1 = a1;
           
           if(b0 > b1) continue;
diff --git a/floorshapes.cpp b/floorshapes.cpp
index 6806141c..cc321c0c 100644
--- a/floorshapes.cpp
+++ b/floorshapes.cpp
@@ -106,17 +106,17 @@ mesher msh(eGeometry g, int sym, ld main, ld v0, ld v1, ld bspi, ld scale) {
   dynamicval<eGeometry> dg(geometry, g);
 
   hyperpoint rot = xpush(v0) * xspinpush0(M_PI - M_PI/sym, main);
-  hyperpoint bnlfar = xpush(v0) * spin(M_PI) * rspintox(rot) * rspintox(rot) * rspintox(rot) * xpush0(hdist0(rot));
-  hyperpoint bnrfar = xpush(v0) * spin(M_PI) * spintox(rot) * spintox(rot) * spintox(rot) * xpush0(hdist0(rot));
+  hyperpoint bnlfar = xpush(v0) * spin180() * rspintox(rot) * rspintox(rot) * rspintox(rot) * xpush0(hdist0(rot));
+  hyperpoint bnrfar = xpush(v0) * spin180() * spintox(rot) * spintox(rot) * spintox(rot) * xpush0(hdist0(rot));
 
-  m.lcorner = xspinpush0 (bspi-M_PI/sym, main);
-  m.rcorner = xspinpush0 (bspi+M_PI/sym, main);
+  m.lcorner = xspinpush0 (bspi - M_PI/sym, main);
+  m.rcorner = xspinpush0 (bspi + M_PI/sym, main);
   m.mfar[0] = xspinpush0 (bspi, v0);
   m.mfar[1] = xspinpush0 (bspi, v1);
   m.vfar[0] = spin(bspi) * bnlfar;
   m.vfar[2] = spin(bspi) * bnrfar;
-  m.vfar[1] = spin(-2*M_PI/sym) * m.vfar[2];
-  m.vfar[3] = spin(+2*M_PI/sym) * m.vfar[0];
+  m.vfar[1] = spin(-TAU/sym) * m.vfar[2];
+  m.vfar[3] = spin(+TAU/sym) * m.vfar[0];
   
   return m;
   }
@@ -131,7 +131,7 @@ matrixitem genitem(const transmatrix& m1, const transmatrix& m2, int nsym) {
   mi.first = m1;
   mi.second.resize(nsym);
   for(int i=0; i<nsym; i++)
-    mi.second[i] = spin(2*M_PI*i/nsym) * m2;
+    mi.second[i] = spin(TAU*i/nsym) * m2;
   return mi;
   }
 
@@ -149,7 +149,7 @@ EX hyperpoint may_kleinize(hyperpoint h) {
 
 void addmatrix(matrixlist& matrices, hyperpoint o0, hyperpoint o1, hyperpoint o2, hyperpoint n0, hyperpoint n1, hyperpoint n2, int d, int osym, int nsym) {
   if(do_kleinize()) o0 = kleinize(o0), o1 = kleinize(o1), o2 = kleinize(o2), n0 = kleinize(n0), n1 = kleinize(n1), n2 = kleinize(n2);
-  matrices.v.push_back(genitem(inverse(spin(2*M_PI*d/osym)*build_matrix(o0, o1, o2,C02)), spin(2*M_PI*d/nsym)*build_matrix(n0, n1, n2,C02), nsym));
+  matrices.v.push_back(genitem(inverse(spin(TAU*d/osym)*build_matrix(o0, o1, o2,C02)), spin(TAU*d/nsym)*build_matrix(n0, n1, n2,C02), nsym));
   }
 
 matrixlist hex_matrices, hept_matrices;
@@ -225,10 +225,10 @@ void geometry_information::bshape2(hpcshape& sh, PPR prio, int shapeid, matrixli
   hyperpoint lstmid = hpxyz(0,0,0);
   for(auto pp: lst) lstmid += pp;
   transmatrix T = spin(-m.o.bspi);
-  while((spin(2*M_PI / rots) * T* lstmid)[0] < (T*lstmid)[0])
-    T = spin(2*M_PI / rots) * T;
-  while((spin(-2*M_PI / rots) * T* lstmid)[0] < (T*lstmid)[0])
-    T = spin(-2*M_PI / rots) * T;
+  while((spin(TAU / rots) * T* lstmid)[0] < (T*lstmid)[0])
+    T = spin(TAU / rots) * T;
+  while((spin(-TAU / rots) * T* lstmid)[0] < (T*lstmid)[0])
+    T = spin(-TAU / rots) * T;
   T = spin(m.o.bspi) * T;
   for(auto &pp: lst) pp = T * pp;
   
@@ -238,7 +238,7 @@ void geometry_information::bshape2(hpcshape& sh, PPR prio, int shapeid, matrixli
     int rep = rots / osym;
     int s = lst.size();
     for(int i=0; i<s*(rep-1); i++)
-      lst.push_back(spin(2*M_PI/rots) * lst[i]);
+      lst.push_back(spin(TAU/rots) * lst[i]);
     rots /= rep;
     }
   
@@ -333,11 +333,11 @@ void geometry_information::bshape_regular(floorshape &fsh, int id, int sides, ld
   
   bshape(fsh.b[id], fsh.prio);
   for(int t=0; t<=sides; t++)
-    hpcpush(xspinpush0(t*2 * M_PI / sides + shift * M_PI / S42, size));
+    hpcpush(xspinpush0(t * TAU / sides + shift * S_step, size));
 
   bshape(fsh.shadow[id], fsh.prio);
   for(int t=0; t<=sides; t++)
-    hpcpush(xspinpush0(t*2 * M_PI / sides + shift * M_PI / S42, size * SHADMUL));
+    hpcpush(xspinpush0(t * TAU / sides + shift * S_step, size * SHADMUL));
 
   for(int k=0; k<SIDEPARS; k++) {
     fsh.side[k].resize(2);
@@ -1218,7 +1218,7 @@ void draw_shape_for_texture(floorshape* sh) {
     queuepoly(shiftless(eupush(gx+a, gy+b)), sh->b[0], 0xFFFFFFFF);
 
   if(sh == &cgi.shCrossFloor) {
-    queuepoly(shiftless(eupush(gx, gy) * spin(M_PI/4)), cgi.shCross, 0x808080FF);
+    queuepoly(shiftless(eupush(gx, gy) * spin(45._deg)), cgi.shCross, 0x808080FF);
     }
 
   if(1) {
@@ -1237,8 +1237,8 @@ void draw_shape_for_texture(floorshape* sh) {
     ld d = hdist(h1, h2);
     hyperpoint h3 = h1 + (h2-h1) /d * min(d, .1);
     for(int a=0; a<4; a++) {
-      curvepoint(eupush(gx,gy) * eupush(spin(90*degree*a) * h1) * C0);
-      curvepoint(eupush(gx,gy) * eupush(spin(90*degree*a) * h3) * C0);
+      curvepoint(eupush(gx,gy) * eupush(spin(90._deg*a) * h1) * C0);
+      curvepoint(eupush(gx,gy) * eupush(spin(90._deg*a) * h3) * C0);
       queuecurve(shiftless(Id), 0x10101010, 0, PPR::LINE);
       }
     }
diff --git a/geom-exp.cpp b/geom-exp.cpp
index 350a96ba..3d5c615e 100644
--- a/geom-exp.cpp
+++ b/geom-exp.cpp
@@ -901,7 +901,7 @@ EX geometry_data compute_geometry_data() {
   gd.size_str =
     disksize ? its(isize(currentmap->allcells())) :
     #if CAP_BT
-    bt::in() ? fts(8 * M_PI * sqrt(2) * log(2) / pow(vid.binary_width, WDIM-1), 4) + " exp(∞)" :
+    bt::in() ? fts(1440._deg * sqrt(2) * log(2) / pow(vid.binary_width, WDIM-1), 4) + " exp(∞)" :
     #endif
     #if CAP_ARCM
     arcm::in() && (WDIM == 2) ? arcm::current.world_size() :
diff --git a/geometry.cpp b/geometry.cpp
index ade445ff..60021ea8 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -410,6 +410,7 @@ hpcshape
   hpcshape shFullCross[2];
 
   int SD3, SD6, SD7, S12, S14, S21, S28, S42, S36, S84;
+  ld S_step;
   
   vector<pair<int, cell*>> walloffsets;
   
@@ -582,7 +583,7 @@ void geometry_information::prepare_basics() {
   
   hexshift = 0;
 
-  ld ALPHA = 2 * M_PI / S7;
+  ld ALPHA = TAU / S7;
   
   ld fmin, fmax;  
   
@@ -612,7 +613,7 @@ void geometry_information::prepare_basics() {
       t->hcrossf = cgi.crossf / d;
       t->tessf = cgi.tessf / d;
       t->hexvdist = cgi.hexvdist / d;
-      t->hexhexdist = hdist(xpush0(cgi.hcrossf), xspinpush0(M_PI*2/S7, cgi.hcrossf)) / d;
+      t->hexhexdist = hdist(xpush0(cgi.hcrossf), xspinpush0(TAU/S7, cgi.hcrossf)) / d;
       t->base_distlimit = cgi.base_distlimit-1;
       });
     goto hybrid_finish;
@@ -629,13 +630,13 @@ void geometry_information::prepare_basics() {
   s3 = S3;
   if(fake::in() && !arcm::in()) s3 = fake::around;
   
-  beta = (S3 >= OINF && !fake::in()) ? 0 : 2*M_PI/s3;
+  beta = (S3 >= OINF && !fake::in()) ? 0 : TAU/s3;
 
   tessf = euclid ? 1 : edge_of_triangle_with_angles(beta, M_PI/S7, M_PI/S7);
   
-  if(elliptic && S7 == 4 && !fake::in()) tessf = M_PI/2;
+  if(elliptic && S7 == 4 && !fake::in()) tessf = 90._deg;
   
-  hcrossf = euclid ? tessf / 2 / sin(M_PI/s3) : edge_of_triangle_with_angles(M_PI/2, M_PI/S7, beta/2);
+  hcrossf = euclid ? tessf / 2 / sin(M_PI/s3) : edge_of_triangle_with_angles(90._deg, M_PI/S7, beta/2);
   
   if(S3 >= OINF) hcrossf = 10;
 
@@ -645,15 +646,15 @@ void geometry_information::prepare_basics() {
   for(int p=0; p<100; p++) {
     ld f =  (fmin+fmax) / 2;
     hyperpoint H = xpush0(f);
-    hyperpoint H1 = spin(2*M_PI/S7) * H;
+    hyperpoint H1 = spin(TAU/S7) * H;
     hyperpoint H2 = xpush0(tessf-f);
     ld v1 = intval(H, H1), v2 = intval(H, H2);
 
     if(fake::in() && WDIM == 2) {
       hexvdist = hdist(xpush0(f), xspinpush0(ALPHA/2, hcrossf));
       v2 = hdist(
-        spin(M_PI/2/S3) * xpush0(hexvdist),
-        spin(-M_PI/2/S3) * xpush0(hexvdist)
+        spin(90._deg/S3) * xpush0(hexvdist),
+        spin(-90._deg/S3) * xpush0(hexvdist)
         );
       
       v1 = hdist(
@@ -667,7 +668,7 @@ void geometry_information::prepare_basics() {
   hexf = fmin;
   
   rhexf = BITRUNCATED ? hexf : hcrossf;
-  edgelen = hdist(xpush0(rhexf), xspinpush0(M_PI*2/S7, rhexf));
+  edgelen = hdist(xpush0(rhexf), xspinpush0(TAU/S7, rhexf));
   
   if(BITRUNCATED && !(S7&1))
     hexshift = ALPHA/2 + ALPHA * ((S7-1)/2) + M_PI;
@@ -690,7 +691,7 @@ void geometry_information::prepare_basics() {
 
   hexhexdist = fake::in() ?
     2 * hdist0(mid(xspinpush0(M_PI/S6, hexvdist), xspinpush0(-M_PI/S6, hexvdist)))
-    : hdist(xpush0(crossf), xspinpush0(M_PI*2/S7, crossf));
+    : hdist(xpush0(crossf), xspinpush0(TAU/S7, crossf));
   
   DEBB(DF_GEOM | DF_POLY,
     (format("S7=%d S6=%d hexf = " LDF" hcross = " LDF" tessf = " LDF" hexshift = " LDF " hexhex = " LDF " hexv = " LDF "\n", S7, S6, hexf, hcrossf, tessf, hexshift, 
@@ -968,7 +969,7 @@ EX namespace geom3 {
       BIRD = 1.20;
       }
     else {
-      INFDEEP = GDIM == 3 ? (sphere ? M_PI/2 : +5) : (euclid || sphere) ? 0.01 : lev_to_projection(0) * tanh(vid.camera);
+      INFDEEP = GDIM == 3 ? (sphere ? 90._deg : +5) : (euclid || sphere) ? 0.01 : lev_to_projection(0) * tanh(vid.camera);
       ld wh = actual_wall_height();
       WALL = lev_to_factor(wh);
       FLOOR = lev_to_factor(0);
@@ -1091,8 +1092,8 @@ EX void switch_always3() {
       ld ms = min<ld>(cgi.scalefactor, 1);
       vid.wall_height = 1.5 * ms;
       if(sphere) {
-        vid.depth = M_PI / 6;
-        vid.wall_height = M_PI / 3;
+        vid.depth = 30 * degree;
+        vid.wall_height = 60 * degree;
         }
       vid.human_wall_ratio = 0.8;
       if(euclid && allowIncreasedSight() && vid.use_smart_range == 0) {
diff --git a/geometry2.cpp b/geometry2.cpp
index 76f4b2af..ece327bf 100644
--- a/geometry2.cpp
+++ b/geometry2.cpp
@@ -57,7 +57,7 @@ transmatrix hrmap_standard::master_relative(cell *c, bool get_inverse) {
   #if CAP_IRR  
   else if(IRREGULAR) {
     int id = irr::cellindex[c];
-    ld alpha = 2 * M_PI / S7 * irr::periodmap[c->master].base.spin;
+    ld alpha = TAU / S7 * irr::periodmap[c->master].base.spin;
     return get_inverse ? irr::cells[id].rpusher * spin(-alpha-master_to_c7_angle()): spin(alpha + master_to_c7_angle()) * irr::cells[id].pusher;
     }
   #endif
@@ -100,12 +100,12 @@ transmatrix hrmap_standard::adj(heptagon *h, int d) {
     int t0 = h->type;
     int t1 = h->cmove(d)->type;
     int sp = h->c.spin(d);
-    return spin(-d * 2 * M_PI / t0) * xpush(spacedist(h->c7, d)) * spin(M_PI + 2*M_PI*sp/t1);
+    return spin(-d * TAU / t0) * xpush(spacedist(h->c7, d)) * spin(M_PI + TAU * sp / t1);
     }
   transmatrix T = cgi.heptmove[d];
   if(h->c.mirror(d)) T = T * Mirror;
   int sp = h->c.spin(d);
-  if(sp) T = T * spin(2*M_PI*sp/S7);
+  if(sp) T = T * spin(TAU*sp/S7);
   return T;
   }
 
@@ -443,7 +443,7 @@ EX bool no_easy_spin() {
 ld hrmap_standard::spin_angle(cell *c, int d) {
   if(WDIM == 3) return SPIN_NOT_AVAILABLE;
   ld hexshift = 0;
-  if(c == c->master->c7 && (S7 % 2 == 0) && BITRUNCATED) hexshift = cgi.hexshift + 2*M_PI/c->type;
+  if(c == c->master->c7 && (S7 % 2 == 0) && BITRUNCATED) hexshift = cgi.hexshift + TAU/c->type;
   else if(cgi.hexshift && c == c->master->c7) hexshift = cgi.hexshift;
   #if CAP_IRR
   if(IRREGULAR) {
@@ -454,7 +454,7 @@ ld hrmap_standard::spin_angle(cell *c, int d) {
     return -atan2(p[1], p[0]) - hexshift;
     }
   #endif
-  return M_PI - d * 2 * M_PI / c->type - hexshift;
+  return M_PI - d * TAU / c->type - hexshift;
   }
 
 EX transmatrix ddspin(cell *c, int d, ld bonus IS(0)) { return currentmap->spin_to(c, d, bonus); }
@@ -543,14 +543,14 @@ EX hyperpoint randomPointIn(int t) {
   if(NONSTDVAR || arcm::in() || kite::in()) {
     // Let these geometries be less confusing.
     // Also easier to implement ;)
-    return xspinpush0(2 * M_PI * randd(), asinh(randd() / 20));
+    return xspinpush0(TAU * randd(), asinh(randd() / 20));
     }
   while(true) {
-    hyperpoint h = xspinpush0(2*M_PI*(randd()-.5)/t, asinh(randd()));
+    hyperpoint h = xspinpush0(TAU * (randd()-.5)/t, asinh(randd()));
     double d =
       PURE ? cgi.tessf : t == 6 ? cgi.hexhexdist : cgi.crossf;
     if(hdist0(h) < hdist0(xpush(-d) * h))
-      return spin(2*M_PI/t * (rand() % t)) * h;
+      return spin(TAU / t * (rand() % t)) * h;
     }
   }
 
@@ -612,7 +612,7 @@ EX hyperpoint nearcorner(cell *c, int i) {
       auto& t = ac.get_triangle(c->master, i-1);
       int id = arcm::id_of(c->master);
       int id1 = ac.get_adj(ac.get_adj(c->master, i-1), -2).first;
-      return xspinpush0(-t.first - M_PI / c->type, ac.inradius[id/2] + ac.inradius[id1/2] + (ac.real_faces == 0 ? 2 * M_PI / (ac.N == 2 ? 2.1 : ac.N) : 0));
+      return xspinpush0(-t.first - M_PI / c->type, ac.inradius[id/2] + ac.inradius[id1/2] + (ac.real_faces == 0 ? TAU / (ac.N == 2 ? 2.1 : ac.N) : 0));
       }
     if(BITRUNCATED) {
       auto &ac = arcm::current;
diff --git a/goldberg.cpp b/goldberg.cpp
index 0c2fea88..336d7a37 100644
--- a/goldberg.cpp
+++ b/goldberg.cpp
@@ -646,12 +646,12 @@ EX namespace gp {
       }
     if(sp>SG3) sp -= SG6;
 
-    return normalize(spin(2*M_PI*sp/S7) * cornmul(T, corner));
+    return normalize(spin(TAU*sp/S7) * cornmul(T, corner));
     }
   
   transmatrix dir_matrix(int i) {
     auto ddspin = [] (int d) -> transmatrix { 
-      return spin(M_PI - d * 2 * M_PI / S7 - cgi.hexshift);
+      return spin(M_PI - d * TAU / S7 - cgi.hexshift);
       };
     return spin(-cgi.gpdata->alpha) * build_matrix(
       C0, 
@@ -678,7 +678,7 @@ EX namespace gp {
         
         hyperpoint h = atz(T, cgi.gpdata->corners, at, 6);
         hyperpoint hl = atz(T, cgi.gpdata->corners, at + eudir(d), 6);
-        cgi.gpdata->Tf[i][x&GOLDBERG_MASK][y&GOLDBERG_MASK][d] = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin(M_PI);
+        cgi.gpdata->Tf[i][x&GOLDBERG_MASK][y&GOLDBERG_MASK][d] = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin180();
         }
       }       
     }
diff --git a/graph.cpp b/graph.cpp
index 725c6270..9db5f0c8 100644
--- a/graph.cpp
+++ b/graph.cpp
@@ -45,6 +45,9 @@ EX bool hide_player() {
      ;
   }
 
+EX transmatrix ddspin180(cell *c, int dir) { return ddspin(c, dir, M_PI); }
+EX transmatrix iddspin180(cell *c, int dir) { return iddspin(c, dir, M_PI); }
+
 #if HDR
 template<class T>
 class span {
@@ -74,11 +77,11 @@ EX int animation_lcm = 0;
 
 EX ld ptick(int period, ld phase IS(0)) {
   if(animation_lcm) animation_lcm = animation_lcm * (period / gcd(animation_lcm, period));
-  return (ticks * animation_factor * vid.ispeed) / period + phase * 2 * M_PI;
+  return (ticks * animation_factor * vid.ispeed) / period + phase * TAU;
   }
 
 EX ld fractick(int period, ld phase IS(0)) {
-  ld t = ptick(period, phase) / 2 / M_PI;
+  ld t = ptick(period, phase) / TAU;
   t -= floor(t);
   if(t<0) t++;
   return t;
@@ -137,7 +140,7 @@ EX bool doHighlight() {
 int dlit;
 
 ld spina(cell *c, int dir) {
-  return 2 * M_PI * dir / c->type;
+  return TAU * dir / c->type;
   }
 
 /** @brief used to alternate colors depending on distance to something. In chessboard-patterned geometries, also use a third step */
@@ -186,7 +189,7 @@ EX void drawShield(const shiftmatrix& V, eItem it) {
 #endif  
   else {
     for(ld a=0; a<=cgi.S84*mt+1e-6; a+=pow(.5, vid.linequality))
-      curvepoint(xspinpush0(a * M_PI/cgi.S42, d + sin(ds + M_PI*2*a/4/mt)*.1));
+      curvepoint(xspinpush0(a * cgi.S_step, d + sin(ds + 90._deg*a/mt)*.1));
     queuecurve(V, darkena(col, 0, 0xFF), 0x8080808, PPR::LINE);
     }
 #endif
@@ -202,7 +205,7 @@ void drawSpeed(const shiftmatrix& V, ld scale=1) {
 #endif
   for(int b=0; b<cgi.S84; b+=cgi.S14) {
     PRING(a)
-      curvepoint(xspinpush0((ds+b+a) * M_PI/cgi.S42, cgi.hexf*a/cgi.S84*scale));
+      curvepoint(xspinpush0((ds+b+a) * cgi.S_step, cgi.hexf*a/cgi.S84*scale));
     queuecurve(V, col, 0x8080808, PPR::LINE);
     }
 #endif
@@ -219,7 +222,7 @@ void drawSafety(const shiftmatrix& V, int ct) {
     }
   #endif
   for(int a=0; a<ct; a++)
-    queueline(V*xspinpush0((ds+a*cgi.S84/ct) * M_PI/cgi.S42, 2*cgi.hexf), V*xspinpush0((ds+(a+(ct-1)/2)*cgi.S84/ct) * M_PI / cgi.S42, 2*cgi.hexf), col, vid.linequality);
+    queueline(V*xspinpush0((ds+a*cgi.S84/ct) * cgi.S_step, 2*cgi.hexf), V*xspinpush0((ds+(a+(ct-1)/2)*cgi.S84/ct) * cgi.S_step, 2*cgi.hexf), col, vid.linequality);
 #endif
   }
 
@@ -238,7 +241,7 @@ void drawFlash(const shiftmatrix& V) {
     if(1) ;
     #endif
     else {
-      PRING(a) curvepoint(xspinpush0(a * M_PI / cgi.S42, rad));
+      PRING(a) curvepoint(xspinpush0(a * cgi.S_step, rad));
       queuecurve(V, col, 0x8080808, PPR::LINE);
       }
     }
@@ -275,12 +278,12 @@ void drawLove(const shiftmatrix& V, int hdir) {
   for(int u=0; u<5; u++) {
     shiftmatrix V1 = chei(V, u, 5);
     PRING(a) {
-      double d = (1 + cos(a * M_PI/cgi.S42)) / 2;
+      double d = (1 + cos(a * cgi.S_step)) / 2;
       double z = a; if(z>cgi.S42) z = cgi.S84-z;
       if(z <= 10) d += (10-z) * (10-z) * (10-z) / 3000.;
 
       ld rad = cgi.hexf * (2.5 + .5 * sin(ds+u*.3)) * d;
-      curvepoint(xspinpush0((cgi.S42+hdir+a-1) * M_PI/cgi.S42, rad));
+      curvepoint(xspinpush0((cgi.S42+hdir+a-1) * cgi.S_step, rad));
       }
     queuecurve(V1, col, 0x8080808, PPR::LINE);
     }
@@ -292,7 +295,7 @@ void drawWinter(const shiftmatrix& V, ld hdir, color_t col) {
   float ds = ptick(300);
   col = darkena(col, 0, 0xFF);
   for(int u=0; u<20; u++) {
-    ld rad = sin(ds+u * 2 * M_PI / 20) * M_PI / S7;
+    ld rad = sin(ds+u * TAU / 20) * M_PI / S7;
     shiftmatrix V1 = chei(V, u, 20);
     queueline(V1*xspinpush0(M_PI+hdir+rad, cgi.hexf*.5), V1*xspinpush0(M_PI+hdir+rad, cgi.hexf*3), col, 2 + vid.linequality);
     }
@@ -312,7 +315,7 @@ void drawLightning(const shiftmatrix& V) {
     else {
       if(u % 5) leng = 1.25 + sintick(200, ld(u) * 1.25) * 0.25;
       else leng = 2 + sintick(200, ld(u) * 1.25);
-      rad = (u + ds) * (M_PI / 10);
+      rad = (u + ds) * TAU / 20;
       }
     shiftmatrix V1 = chei(V, u, 20);
     queueline(V1*xspinpush0(rad, cgi.hexf*0.3), V1*xspinpush0(rad, cgi.hexf*leng), col, 2 + vid.linequality);
@@ -332,7 +335,7 @@ void drawCurse(const shiftmatrix& V, eItem it) {
       }
     else {
       leng = 0.85 + sintick(150, ld(u) * 1.25) * 0.15;
-      rad = (u + ds) * (M_PI / 10);
+      rad = (u + ds) * TAU / 20;
       }
     shiftmatrix V1 = chei(V, u, 20);
     queueline(V1*xspinpush0(rad, cgi.hexf*0.3), V1*xspinpush0(rad, cgi.hexf*leng), col, 2 + vid.linequality);
@@ -368,7 +371,7 @@ EX void drawPlayerEffects(const shiftmatrix& V, const shiftmatrix& Vparam, cell
     else if(SWORDDIM == 3) {
 #if CAP_SHAPES
       shiftmatrix Vsword = 
-        shmup::on ? V * shmup::swordmatrix[multi::cpid] * cspin(2, 0, M_PI/2) 
+        shmup::on ? V * shmup::swordmatrix[multi::cpid] * cspin90(2, 0)
                   : Vparam * rgpushxto0(inverse_shift(gmatrix[c], tC0(V))) * sword::dir[multi::cpid].T;
 
       if(items[itOrbSword])
@@ -384,7 +387,7 @@ EX void drawPlayerEffects(const shiftmatrix& V, const shiftmatrix& Vparam, cell
       ang %= sword::sword_angles;
 
 #if CAP_QUEUE || CAP_SHAPES
-      shiftmatrix Vnow = Vparam * rgpushxto0(inverse_shift(Vparam, tC0(V))) * ddspin(c,0,M_PI);
+      shiftmatrix Vnow = Vparam * rgpushxto0(inverse_shift(Vparam, tC0(V))) * ddspin180(c,0);
 #endif
 
       int adj = 1 - ((sword_angles/cwt.at->type)&1);
@@ -444,7 +447,7 @@ EX void drawPlayerEffects(const shiftmatrix& V, const shiftmatrix& Vparam, cell
       ld rad = cgi.hexf * u / 250;
       color_t col = darkena(iinf[itOrbSafety].color, 0, 0xFF);
       PRING(a)
-        curvepoint(xspinpush0(a * M_PI / cgi.S42, rad));
+        curvepoint(xspinpush0(a * cgi.S_step, rad));
       queuecurve(V, col, 0, PPR::LINE);
       }
     }
@@ -453,7 +456,7 @@ EX void drawPlayerEffects(const shiftmatrix& V, const shiftmatrix& Vparam, cell
 void drawStunStars(const shiftmatrix& V, int t) {
 #if CAP_SHAPES
   for(int i=0; i<3*t; i++) {
-    shiftmatrix V2 = V * spin(M_PI * 2 * i / (3*t) + ptick(200));
+    shiftmatrix V2 = V * spin(TAU * i / (3*t) + ptick(200));
 #if MAXMDIM >= 4
     if(GDIM == 3) V2 = V2 * zpush(cgi.HEAD);
 #endif
@@ -519,7 +522,7 @@ EX namespace tortoise {
     if(d > 0) mcol = 0xFFFFFF;
     else if(d < 0) mcol = 0;
     
-      int dd = 0xFF * (atan(fabs(d)/2) / (M_PI/2));
+      int dd = 0xFF * (atan(fabs(d)/2) / 90._deg);
       
     return gradient(0x487830, mcol, 0, dd, 0xFF);
     }
@@ -754,7 +757,7 @@ EX shiftmatrix face_the_player(const shiftmatrix V) {
   if(vrhr::enabled) {
     shiftpoint h = tC0(V);    
     hyperpoint uh = unshift(h);
-    return shiftless(cspin(1, 2, 90*degree) * rspintox(cspin(2, 1, 90*degree) * uh) * xpush(hdist0(uh)) * cspin(0, 2, 90*degree) * cspin(1, 0, 90*degree));
+    return shiftless(cspin90(1, 2) * rspintox(cspin90(2, 1) * uh) * xpush(hdist0(uh)) * cspin90(0, 2) * spin270());
     }
   #endif
   return rgpushxto0(tC0(V));
@@ -853,7 +856,7 @@ EX bool drawItemType(eItem it, cell *c, const shiftmatrix& V, color_t icol, int
     
 #if CAP_SHAPES
   auto sinptick = [c, pticks] (int period) { return c ? sintick(period) : sin(animation_factor * vid.ispeed * pticks / period);};
-  auto spinptick = [c, pticks] (int period, ld phase) { return c ? spintick(period, phase) : spin((animation_factor * vid.ispeed * pticks) / period + phase * 2 * M_PI); };
+  auto spinptick = [c, pticks] (int period, ld phase) { return c ? spintick(period, phase) : spin((animation_factor * vid.ispeed * pticks) / period + phase * TAU); };
   int ct6 = c ? ctof(c) : 1;
   hpcshape *xsh = 
     (it == itPirate || it == itKraken) ? &cgi.shPirateX :
@@ -1005,16 +1008,14 @@ EX bool drawItemType(eItem it, cell *c, const shiftmatrix& V, color_t icol, int
   
   else if(it == itRose) {
     for(int u=0; u<4; u++)
-      queuepoly(Vit * spinptick(1500, 0) * spin(2*M_PI / 3 / 4 * u), cgi.shRoseItem, darkena(icol, 0, hidden ? 0x30 : 0xA0));
+      queuepoly(Vit * spinptick(1500, 0) * spin(30._deg * u), cgi.shRoseItem, darkena(icol, 0, hidden ? 0x30 : 0xA0));
     }
 
   else if(it == itBarrow && c) {
     for(int i = 0; i<c->landparam; i++)
-      queuepolyat(Vit * spin(2 * M_PI * i / c->landparam) * xpush(.15) * spinptick(1500, 0), *xsh, darkena(icol, 0, hidden ? 0x40 : 
+      queuepolyat(Vit * spin(TAU * i / c->landparam) * xpush(.15) * spinptick(1500, 0), *xsh, darkena(icol, 0, hidden ? 0x40 : 
         (highwall(c) && wmspatial) ? 0x60 : 0xFF),
         PPR::HIDDEN);
-
-//      queuepoly(Vit*spin(M_PI+(1-2*ang)*2*M_PI/cgi.S84), cgi.shMagicSword, darkena(0xC00000, 0, 0x80 + 0x70 * sin(ticks / 200.0)));
     }
     
   else if(xsh) {
@@ -1072,12 +1073,12 @@ EX bool drawItemType(eItem it, cell *c, const shiftmatrix& V, color_t icol, int
       auto dark = darkena(icol1, 0, inice ? 0x80 : hidden ? 0x20 : (it == itOrbBeauty) ? 0xA0 : 0xC0);
       auto dark1 = darkena(icol1, 0, inice ? 0x40 : hidden ? 0x10 : (it == itOrbBeauty) ? 0x50 : 0x60);
       if(c && GDIM == 2) Vit = rgpushxto0(tC0(Vit));
-      auto Vit1 = Vit * spin(90 * degree);
+      auto Vit1 = Vit * spin90();
 
       if (it == itOrbBeauty) {
         queuepolyat(Vit, cgi.shDisk, dark1, prio);
         for(int u=0; u<3; u++)
-          queuepolyat(Vit1 * spin(2*M_PI / 3 / 3 * u), cgi.shSmallRose, dark, prio);
+          queuepolyat(Vit1 * spin(40._deg * u), cgi.shSmallRose, dark, prio);
         }
       else if (it == itOrbLife) {
         queuepolyat(Vit, cgi.shDisk, dark1, prio);
@@ -1113,7 +1114,7 @@ EX bool drawItemType(eItem it, cell *c, const shiftmatrix& V, color_t icol, int
         queuepolyat(Vit, cgi.shDisk, dark1, prio);
         queuepolyat(Vit, cgi.shDiskM, dark, prio);
         for (int i=0; i<5; i++) {
-          shiftmatrix V2 = Vit * spin(2*M_PI * i / 5 + ptick(300));
+          shiftmatrix V2 = Vit * spin(TAU * i / 5 + ptick(300));
           queuepolyat(V2, cgi.shSmallFlailBall, dark, prio);
           }
         }
@@ -1189,7 +1190,7 @@ EX bool drawItemType(eItem it, cell *c, const shiftmatrix& V, color_t icol, int
         bool reversed = (shape == &cgi.shTreeIcon || shape == &cgi.shHumanoid || it == itOrbSword2);
         bool left90 = (shape == &cgi.shLeafIcon || shape == &cgi.shLightningBolt);
         if (shape)
-          queuepolyat(reversed ? Vit1 * MirrorX : left90 ? Vit1 * spin(-90*degree) : Vit1, *shape, (it == itOrbInvis || it == itOrbTeleport) ? 0x20 : 0x80, prio);
+          queuepolyat(reversed ? Vit1 * MirrorX : left90 ? Vit1 * spin270() : Vit1, *shape, (it == itOrbInvis || it == itOrbTeleport) ? 0x20 : 0x80, prio);
         if (it == itOrbSide1 || (shape == &cgi.shEccentricDisk && it != itOrbDiscord))
           queuepolyat(Vit1*Mirror, *shape, 0x80, prio);
         if (jump || it == itOrbEnergy)
@@ -1381,7 +1382,7 @@ EX void drawPlayer(eMonster m, cell *where, const shiftmatrix& V, color_t col, d
         }
   
       if(items[itOrbSide1] && !shmup::on)
-        queuepoly(VBODY * VBS * spin(-M_PI/24), cs.charid >= 2 ? cgi.shSabre : cgi.shPSword, fc(314, cs.swordcolor, 3)); // 3 not colored
+        queuepoly(VBODY * VBS * spin(-15._deg), cs.charid >= 2 ? cgi.shSabre : cgi.shPSword, fc(314, cs.swordcolor, 3)); // 3 not colored
       
       shiftmatrix VWPN = cs.lefthanded ? VBODY * VBS * Mirror : VBODY * VBS;
       
@@ -1451,7 +1452,7 @@ EX int wingphase(int period, int phase IS(0)) {
   }
 
 transmatrix wingmatrix(int period, int phase = 0) {
-  ld t = fractick(period, phase) * 2 * M_PI;
+  ld t = fractick(period, phase) * TAU;
   transmatrix Vwing = Id;
   Vwing[1][1] = .85 + .15 * sin(t);
   return Vwing;
@@ -1508,7 +1509,7 @@ void drawMimic(eMonster m, cell *where, const shiftmatrix& V, color_t col, doubl
       if(items[itOrbThorns] && emp)
         queuepoly(VBODY * VBS, cgi.shHedgehogBladePlayer, darkena(col, 0, 0x40));
       if(items[itOrbSide1] && !shmup::on)
-        queuepoly(VBODY * VBS * spin(-M_PI/24), cs.charid >= 2 ? cgi.shSabre : cgi.shPSword, darkena(col, 0, 0x40));      
+        queuepoly(VBODY * VBS * spin(-15._deg), cs.charid >= 2 ? cgi.shSabre : cgi.shPSword, darkena(col, 0, 0x40));
       if(items[itOrbSide3] && emp)
         queuepoly(VBODY * VBS, (cs.charid&1) ? cgi.shFerocityF : cgi.shFerocityM, darkena(col, 0, 0x40));
 
@@ -1547,7 +1548,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const shiftmatrix& V1, color_t
   char xch = minf[m].glyph;
   
   shiftmatrix V = V1;
-  if(WDIM == 3 && (classflag(m) & CF_FACE_UP) && where && !hybri) V = V1 * cspin(0, 2, M_PI/2);
+  if(WDIM == 3 && (classflag(m) & CF_FACE_UP) && where && !hybri) V = V1 * cspin90(0, 2);
   
   #if CAP_SHAPES
   if(among(m, moTortoise, moWorldTurtle) && where && where->stuntime >= 3)
@@ -1590,7 +1591,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const shiftmatrix& V1, color_t
     
     case moBullet:
       ShadowV(V, cgi.shKnife);
-      queuepoly(VBODY * spin(-M_PI/4), cgi.shKnife, getcs().swordcolor);
+      queuepoly(VBODY * spin270(), cgi.shKnife, getcs().swordcolor);
       return true;
     
     case moKnight: case moKnightMoved: {
@@ -2109,7 +2110,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const shiftmatrix& V1, color_t
     
     case moJiangshi: {
       ShadowV(V, cgi.shJiangShi);
-      auto z2 = WDIM == 3 ? 0 : GDIM == 3 ? -abs(sin(footphase * M_PI * 2)) * cgi.human_height/3 : geom3::lev_to_factor(abs(sin(footphase * M_PI * 2)) * cgi.human_height);
+      auto z2 = WDIM == 3 ? 0 : GDIM == 3 ? -abs(sin(footphase * TAU)) * cgi.human_height/3 : geom3::lev_to_factor(abs(sin(footphase * TAU)) * cgi.human_height);
       auto V0 = V;
       auto V = mmscale(V0, z2);
       otherbodyparts(V, darkena(col, 0, 0xFF), m, m == moJiangshi ? 0 : footphase);
@@ -2328,7 +2329,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const shiftmatrix& V1, color_t
     case moLancer: case moFlailer: case moMiner: {
       shiftmatrix V2 = V;
       if(m == moLancer)
-        V2 = V * spin((where && where->type == 6) ? -M_PI/3 : -M_PI/2 );
+        V2 = V * spin((where && where->type == 6) ? -60._deg : -90._deg );
       shiftmatrix Vh = mmscale(V2, cgi.HEAD);
       shiftmatrix Vb = mmscale(V2, cgi.BODY);
       Vb = Vb * otherbodyparts(V2, darkena(col, 1, 0xFF), m, footphase);
@@ -2512,7 +2513,7 @@ EX bool drawMonsterType(eMonster m, cell *where, const shiftmatrix& V1, color_t
     }
   else if(isMagneticPole(m)) {
     if(m == moNorthPole)
-      queuepolyat(VBODY * spin(M_PI), cgi.shTentacle, 0x000000C0, PPR::TENTACLE1);
+      queuepolyat(VBODY * spin180(), cgi.shTentacle, 0x000000C0, PPR::TENTACLE1);
     queuepolyat(VBODY, cgi.shDisk, darkena(col, 0, 0xFF), PPR::MONSTER_BODY);
     }
   else if(isMetalBeast(m) || m == moBrownBug) {
@@ -2660,7 +2661,6 @@ EX bool applyAnimation(cell *c, shiftmatrix& V, double& footphase, int layer) {
     V = V * a.wherenow;
     if(a.mirrored) V = V * Mirror;
     if(a.attacking == 2) V = V * pispin;
-    // if(GDIM == 3) V = V * cspin(0, 2, M_PI/2);
     a.ltick = ticks;
     return true;
     }
@@ -2874,7 +2874,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
               if(doHighlight())
                 poly_outline = outline;
               shiftmatrix Vbx = Vb;
-              if(WDIM == 2) Vbx = Vbx * spin(sin(M_PI * i / 6.) * wav / (i+.1));
+              if(WDIM == 2) Vbx = Vbx * spin(sin(TAU * i / 12) * wav / (i+.1));
               Vbx = Vbx * xpush(length * (i) / 12.0);
               // shiftmatrix Vbx2 = Vnext * xpush(length2 * i / 6.0);
               // Vbx = Vbx * rspintox(inverse(Vbx) * Vbx2 * C0) * pispin;
@@ -2889,7 +2889,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
         shiftmatrix T = Vparam * ddspin(c, c->mondir);
         color_t col = darkena(0x606020, 0, 0xFF);
         for(int u=-1; u<=1; u++)
-          queueline(T*xspinpush0(M_PI/2, u*cgi.crossf/5), T*xspinpush(0, cgi.crossf)*xspinpush0(M_PI/2, u*cgi.crossf/5), col, 2 + vid.linequality);
+          queueline(T*xspinpush0(90._deg, u*cgi.crossf/5), T*xspinpush(0, cgi.crossf)*xspinpush0(90._deg, u*cgi.crossf/5), col, 2 + vid.linequality);
         }
       }
 
@@ -2898,7 +2898,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
         if(hybri) {
           queuepoly(Vb, cgi.shILeaf[ctof(c)], darkena(col, 0, 0xFF));
           for(int a=0; a<c->type-2; a++)
-            queuepoly(Vb * spin(a * 2 * M_PI / (c->type-2)), cgi.shILeaf[2], darkena(col, 0, 0xFF));
+            queuepoly(Vb * spin(a * TAU / (c->type-2)), cgi.shILeaf[2], darkena(col, 0, 0xFF));
           }
         else if(GDIM == 3) {
           queuepoly(face_the_player(Vb), cgi.shILeaf[1], darkena(col, 0, 0xFF));
@@ -2949,7 +2949,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
             Vb = Vb * pispin;
             }
           else {
-            Vb = Vb0 * ddspin(c, nd, M_PI);
+            Vb = Vb0 * ddspin180(c, nd);
             }
           if(c->monmirror) Vb = Vb * Mirror;
           shiftmatrix Vbb = mmscale(Vb, cgi.ABODY);
@@ -2969,8 +2969,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
             /* todo what if no spin_angle */
             ld hdir0 = currentmap->spin_angle(c, nd) + M_PI;
             ld hdir1 = currentmap->spin_angle(c, c->mondir);
-            while(hdir1 > hdir0 + M_PI) hdir1 -= 2*M_PI;
-            while(hdir1 < hdir0 - M_PI) hdir1 += 2*M_PI;
+            cyclefix(hdir1, hdir0);
             Vb = Vb0 * spin((hdir0 + hdir1)/2 + M_PI);
             }
           if(c->monmirror) Vb = Vb * Mirror;
@@ -2999,7 +2998,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
             Vb = Vb * pispin;
             }
           else {
-            Vb = Vb0 * ddspin(c, nd, M_PI);
+            Vb = Vb0 * ddspin180(c, nd);
             }
           if(c->monmirror) Vb = Vb * Mirror;
           shiftmatrix Vbb = mmscale(Vb, cgi.ABODY) * pispin;
@@ -3087,7 +3086,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
       Vb = Vb * T * rspintox(tC0(iso_inverse(T))) * xpush(cgi.tentacle_length);
       }
     else {
-      Vb = Vb * ddspin(c, c->mondir, M_PI);
+      Vb = Vb * ddspin180(c, c->mondir);
       Vb = Vb * xpush(cgi.tentacle_length - cellgfxdist(c, c->mondir));
       }
     if(c->monmirror) Vb = Vb * Mirror;
@@ -3109,7 +3108,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
     
   else if((hasFacing(c) && c->mondir != NODIR) || history::on || quotient || dont_face_pc) {
     if(c->monst == moKrakenH) Vs = Vb, nospins = nospinb;
-    if(!nospins && c->mondir < c->type) Vs = Vs * ddspin(c, c->mondir, M_PI);
+    if(!nospins && c->mondir < c->type) Vs = Vs * ddspin180(c, c->mondir);
     if(c->monst == moPair) Vs = Vs * xpush(-.12);
     if(c->monmirror) Vs = Vs * Mirror;
     if(isFriendly(c)) drawPlayerEffects(Vs, Vparam, c, c->monst);
@@ -3141,7 +3140,7 @@ EX bool drawMonster(const shiftmatrix& Vparam, int ct, cell *c, color_t col, col
         // cwtV * rgpushxto0(inverse(cwtV) * tC0(Vs));
         }
       if(c->monst == moHunterChanging)  
-        Vs = Vs * (hybri ? spin(M_PI) : cspin(WDIM-2, WDIM-1, M_PI));
+        Vs = Vs * (hybri ? spin180() : cspin180(WDIM-2, WDIM-1));
       }
     if(c->monmirror) Vs = Vs * Mirror;
     
@@ -3240,7 +3239,7 @@ void apply_joukowsky_aura(shiftpoint& h) {
 EX void addauraspecial(shiftpoint h, color_t col, int dir) {
   if(!haveaura_cached) return;
   apply_joukowsky_aura(h);
-  int r = int(2*AURA + dir + atan2(h[1], h[0]) * AURA / 2 / M_PI) % AURA; 
+  int r = int(2*AURA + dir + atan2(h[1], h[0]) * AURA / TAU) % AURA;
   auraspecials.emplace_back(r, col);
   }
 
@@ -3248,7 +3247,7 @@ EX void addaura(shiftpoint h, color_t col, int fd) {
   if(!haveaura_cached) return;
   apply_joukowsky_aura(h);
 
-  int r = gmod(atan2(h[1], h[0]) * AURA / 2 / M_PI, AURA);
+  int r = gmod(atan2(h[1], h[0]) * AURA / TAU, AURA);
   aurac[r][3] += auramemo << fd;
   col = darkened(col);
   aurac[r][0] += (col>>16)&255;
@@ -3322,7 +3321,7 @@ EX void drawaura() {
       if(cmul>1) cmul=1;
       if(cmul<0) cmul=0;
       
-      ld alpha = AURA * atan2(hx,hy) / (2 * M_PI);
+      ld alpha = AURA * atan2(hx,hy) / TAU;
       if(alpha<0) alpha += AURA;
       if(alpha >= AURA) alpha -= AURA;
       
@@ -3363,7 +3362,7 @@ EX void drawaura() {
   bool joukowsky = among(pmodel, mdJoukowskyInverted, mdJoukowsky) && hyperbolic && pconf.model_transition < 1;
 
   for(int r=0; r<=AURA; r++) for(int z=0; z<11; z++) {
-    float rr = (M_PI * 2 * r) / AURA;
+    float rr = (TAU * r) / AURA;
     float rad0 = inversion ? rad / facs[z] : rad * facs[z];
     int rm = r % AURA;
     ld c = cos(rr);
@@ -3467,14 +3466,14 @@ EX int countMinesAround(cell *c) {
 
 EX transmatrix applyPatterndir(cell *c, const patterns::patterninfo& si) {
   if(NONSTDVAR || bt::in()) return Id;
-  transmatrix V = ddspin(c, si.dir, M_PI);
+  transmatrix V = ddspin180(c, si.dir);
   if(si.reflect) V = V * Mirror;
   if(euclid) return V;
-  return V * iddspin(c, 0, M_PI);
+  return V * iddspin180(c, 0);
   }
 
 EX transmatrix applyDowndir(cell *c, const cellfunction& cf) {
-  return ddspin(c, patterns::downdir(c, cf), M_PI);
+  return ddspin180(c, patterns::downdir(c, cf));
   }
 
 void draw_movement_arrows(cell *c, const transmatrix& V, int df) {
@@ -3488,7 +3487,7 @@ void draw_movement_arrows(cell *c, const transmatrix& V, int df) {
 
   for(int d=0; d<8; d++) {
   
-    movedir md = vectodir(spin(-d * M_PI/4) * smalltangent());
+    movedir md = vectodir(spin(-d * 45._deg) * smalltangent());
     cellwalker xc = cwt + md.d;
     if(xc.spin != df) continue;
     xc += wstep;
@@ -3504,7 +3503,7 @@ void draw_movement_arrows(cell *c, const transmatrix& V, int df) {
       
       if(vid.axes >= 5) keylist += key;
       else
-        queuepoly(shiftless(fixrot * spin(-d * M_PI/4)), cgi.shArrow, col);
+        queuepoly(shiftless(fixrot * spin(-d * 45._deg)), cgi.shArrow, col);
 
       if((c->type & 1) && (isStunnable(c->monst) || isPushable(c->wall))) {
         transmatrix Centered = rgpushxto0(unshift(tC0(cwtV)));
@@ -3552,7 +3551,7 @@ EX color_t reptilecolor(cell *c) {
 
 ld wavefun(ld x) { 
   return sin(x);
-  /* x /= (2*M_PI);
+  /* x /= TAU;
   x -= (int) x;
   if(x > .5) return (x-.5) * 2;
   else return 0; */
@@ -4490,7 +4489,7 @@ EX void drawDirectionalParticle(cell *c, int dir, color_t col, int maxspeed IS(1
     int speed = 1 + rand() % maxspeed;
     auto fd = flashdata(ticks, rand() % 16, c, col, speed);
     fd.angle = -atan2(tC0(currentmap->adj(c, dir)));
-    fd.angle += 2 * M_PI * (rand() % 100 - rand() % 100) / 100 / c->type;
+    fd.angle += TAU * (rand() % 100 - rand() % 100) / 100 / c->type;
     flashes.push_back(fd); 
     }
   }
@@ -4914,7 +4913,7 @@ EX void draw_flash(struct flashdata& f, const shiftmatrix& V, bool& kill) {
       ld rad[25];
       for(int a=0; a<24; a++) rad[a] = (0.5 + randd() * .3 + 0.5 * (a&1)) / (2.8 + celldistance(f.where, cwt.at) * .2);
       rad[24] = rad[0];
-      for(int a=0; a<24; a++) curvepoint(xspinpush0(15 * degree * a, rad[a]));
+      for(int a=0; a<24; a++) curvepoint(xspinpush0(TAU * a / 24, rad[a]));
       queuecurve(V, 0xFF, 0xFF0000FF, PPR::SUPERLINE);
       }
     }
@@ -4948,7 +4947,7 @@ EX void draw_flash(struct flashdata& f, const shiftmatrix& V, bool& kill) {
       else 
 #endif
       {
-        PRING(a) curvepoint(xspinpush0(a * M_PI / cgi.S42, rad));
+        PRING(a) curvepoint(xspinpush0(a * cgi.S_step, rad));
         queuecurve(V, flashcol, 0x8080808, PPR::LINE);
         }
       }
@@ -4969,7 +4968,7 @@ EX void draw_flash(struct flashdata& f, const shiftmatrix& V, bool& kill) {
       else 
 #endif
       {
-        PRING(a) curvepoint(xspinpush0(a * M_PI / cgi.S42, rad));
+        PRING(a) curvepoint(xspinpush0(a * cgi.S_step, rad));
         queuecurve(V, flashcol, 0x8080808, PPR::LINE);
         }
       }
@@ -5387,7 +5386,7 @@ EX void drawmovestar(double dx, double dy) {
     if(rightclick && (d == 2 || d == 6 || d == 3 || d == 5)) col &= 0xFFFFFF3F;
     if(!leftclick && !rightclick && (d&1)) col &= 0xFFFFFF3F;
 #endif
-    queueline(tC0(Centered), Centered * xspinpush0(d * M_PI / 4, cgi.scalefactor/2), col, 3 + vid.linequality);
+    queueline(tC0(Centered), Centered * xspinpush0(d * 45._deg, cgi.scalefactor/2), col, 3 + vid.linequality);
 #endif
     }
   }
@@ -5877,7 +5876,7 @@ EX void restartGraph() {
   if(!autocheat) linepatterns::clearAll();
   if(currentmap) {
     resetview();
-    if(sphere) View = spin(-M_PI/2);
+    if(sphere) View = spin(-90._deg);
     }
   }
 
@@ -6037,7 +6036,7 @@ EX void drawBug(const cellwalker& cw, color_t col) {
 #if CAP_SHAPES
   initquickqueue();
   shiftmatrix V = ggmatrix(cw.at);
-  if(cw.spin) V = V * ddspin(cw.at, cw.spin, M_PI);
+  if(cw.spin) V = V * ddspin180(cw.at, cw.spin);
   queuepoly(V, cgi.shBugBody, col);
   quickqueue();
 #endif
diff --git a/history.cpp b/history.cpp
index 238d8d9f..44353b9e 100644
--- a/history.cpp
+++ b/history.cpp
@@ -40,12 +40,12 @@ namespace spiral {
     CY = band[0]->h;
     SX = out->w;
     SY = out->h;
+    
+    ld prec = 2*M_PI*M_PI;
 
-    ld k = -2*M_PI*M_PI / log(2.6180339);
+    ld k = -prec / log(2.6180339);
 
-//   cxld mnoznik = cxld(0, M_PI) / cxld(k, M_PI);
-
-    cxld factor = cxld(0, -CY/2/M_PI/M_PI) * cxld(k, M_PI);
+    cxld factor = cxld(0, -CY/prec) * cxld(k, M_PI);
     
     Yshift = CY * k / M_PI;
     
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index a7becfcc..4d26e39b 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -13,11 +13,18 @@
 namespace hr {
 
 #if HDR
-static const ld full_circle = 2 * M_PI;
-static const ld quarter_circle = M_PI / 2;
-static const ld degree = M_PI / 180;
+
+#ifndef M_PI
+#define M_PI 3.14159265358979
+#endif
+
+static constexpr ld A_PI = M_PI;
+static const ld TAU = 2 * A_PI;
+static const ld degree = A_PI / 180;
 static const ld golden_phi = (sqrt(5)+1)/2;
 static const ld log_golden_phi = log(golden_phi);
+
+constexpr ld operator"" _deg(long double deg) { return deg * A_PI / 180; }
 #endif
 
 eGeometry geometry;
@@ -231,10 +238,6 @@ constexpr hyperpoint C03 = hyperpoint(0,0,0,1);
 // basic functions and types
 //===========================
 
-#ifndef M_PI
-#define M_PI 3.14159265358979
-#endif
-
 EX ld squar(ld x) { return x*x; }
 
 EX int sig(int z) { return ginf[geometry].g.sig[z]; }
@@ -284,7 +287,7 @@ EX ld acos_auto(ld x) {
 /** \brief volume of a three-dimensional ball of radius r in the current isotropic geometry */
 EX ld volume_auto(ld r) {
   switch(cgclass) {
-    case gcEuclid: return 4 * r * r * r / 3 * M_PI;
+    case gcEuclid: return r * r * r * 240._deg;
     case gcHyperbolic: return M_PI * (sinh(2*r) - 2 * r);
     case gcSphere: return M_PI * (2 * r - sin(2*r));
     default: return 0;
@@ -295,8 +298,8 @@ EX ld volume_auto(ld r) {
 EX ld area_auto(ld r) {
   switch(cgclass) {
     case gcEuclid: return r * r * M_PI;
-    case gcHyperbolic: return 2 * M_PI * (cosh(r) - 1);
-    case gcSphere: return 2 * M_PI * (1 - cos(r));
+    case gcHyperbolic: return TAU * (cosh(r) - 1);
+    case gcSphere: return TAU * (1 - cos(r));
     default: return 0;
     }
   }
@@ -307,7 +310,7 @@ EX ld wvolarea_auto(ld r) {
   else return area_auto(r);
   }
 
-EX ld asin_clamp(ld x) { return x>1 ? M_PI/2 : x<-1 ? -M_PI/2 : std::isnan(x) ? 0 : asin(x); }
+EX ld asin_clamp(ld x) { return x>1 ? 90._deg : x<-1 ? -90._deg : std::isnan(x) ? 0 : asin(x); }
 
 EX ld acos_clamp(ld x) { return x>1 ? 0 : x<-1 ? M_PI : std::isnan(x) ? 0 : acos(x); }
 
@@ -589,18 +592,42 @@ EX transmatrix cspin(int a, int b, ld alpha) {
   return T;
   }
 
+/** rotate by 90 degrees in the coordinates a, b */
+EX transmatrix cspin90(int a, int b) {
+  transmatrix T = Id;
+  T[a][a] = 0; T[a][b] = 1;
+  T[b][a] = -1; T[b][b] = 0;
+  return T;
+  }
+
+/** rotate by 180 degrees in the coordinates a, b */
+EX transmatrix cspin180(int a, int b) {
+  transmatrix T = Id;
+  T[a][a] = T[b][b] = -1;
+  return T;
+  }
+
 /** rotate by alpha degrees in the XY plane */
 EX transmatrix spin(ld alpha) { return cspin(0, 1, alpha); }
 
+/** rotate by 90 degrees in the XY plane */
+EX transmatrix spin90() { return cspin90(0, 1); }
+
+/** rotate by 180 degrees in the XY plane */
+EX transmatrix spin180() { return cspin180(0, 1); }
+
+/** rotate by 270 degrees in the XY plane */
+EX transmatrix spin270() { return cspin90(1, 0); }
+
 EX transmatrix random_spin3() {
   ld alpha2 = asin(randd() * 2 - 1);
-  ld alpha = randd() * 2 * M_PI;
-  ld alpha3 = randd() * 2 * M_PI;
+  ld alpha = randd() * TAU;
+  ld alpha3 = randd() * TAU;
   return cspin(0, 1, alpha) * cspin(0, 2, alpha2) * cspin(1, 2, alpha3);
   }
 
 EX transmatrix random_spin() {
-  if(WDIM == 2) return spin(randd() * 2 * M_PI);
+  if(WDIM == 2) return spin(randd() * TAU);
   else return random_spin3();
   }
 
@@ -1181,13 +1208,13 @@ EX ld hdist0(const shiftpoint& mh) {
 EX ld circlelength(ld r) {
   switch(cgclass) {
     case gcEuclid:
-      return 2 * M_PI * r;
+      return TAU * r;
     case gcHyperbolic:
-      return 2 * M_PI * sinh(r);
+      return TAU * sinh(r);
     case gcSphere:
-      return 2 * M_PI * sin(r);
+      return TAU * sin(r);
     default:
-      return 2 * M_PI * r;
+      return TAU * r;
     }
   }
 
@@ -1378,12 +1405,12 @@ EX transmatrix spin_towards(const transmatrix Position, transmatrix& ori, const
       }
     T = rspintox(U);
     }
-  if(back < 0) T = T * spin(M_PI), alpha = -alpha;
+  if(back < 0) T = T * spin180(), alpha = -alpha;
   if(prod) {
     if(dir == 0) ori = cspin(2, 0, alpha);
-    if(dir == 2) ori = cspin(2, 0, alpha - M_PI/2), dir = 0;
+    if(dir == 2) ori = cspin(2, 0, alpha - 90._deg), dir = 0;
     }
-  if(dir) T = T * cspin(dir, 0, -M_PI/2);
+  if(dir) T = T * cspin(dir, 0, -90._deg);
   T = Position * T;
   return T;
   }
@@ -1536,7 +1563,7 @@ EX ld geo_dist(const shiftpoint h1, const shiftpoint h2, flagtype prec IS(pNORMA
 
 EX ld geo_dist_q(const hyperpoint h1, const hyperpoint h2, flagtype prec IS(pNORMAL)) {
   auto d = geo_dist(h1, h2, prec);
-  if(elliptic && d > M_PI/2) return M_PI - d;
+  if(elliptic && d > 90._deg) return M_PI - d;
   return d;
   }
 
@@ -1551,15 +1578,15 @@ EX hyperpoint lp_apply(const hyperpoint h) {
 EX hyperpoint smalltangent() { return xtangent(.1); }
 
 EX void cyclefix(ld& a, ld b) {
-  while(a > b + M_PI) a -= 2 * M_PI;
-  while(a < b - M_PI) a += 2 * M_PI;
+  while(a > b + M_PI) a -= TAU;
+  while(a < b - M_PI) a += TAU;
   }
 
 EX ld raddif(ld a, ld b) {
   ld d = a-b;
   if(d < 0) d = -d;
-  if(d > 2*M_PI) d -= 2*M_PI;
-  if(d > M_PI) d = 2 * M_PI-d;
+  if(d > TAU) d -= TAU;
+  if(d > M_PI) d = TAU-d;
   return d;
   }
 
diff --git a/hypgraph.cpp b/hypgraph.cpp
index ce594abe..b961c405 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -105,13 +105,13 @@ EX shiftmatrix minimize_point_value(shiftmatrix T, function<ld(const shiftmatrix
       ld dist = value(T1);
       if(dist < best) best = dist, T = T1;
       if(mdBandAny()) {
-        T1.shift += 2 * M_PI;
+        T1.shift += TAU;
         dist = value(T1);
         if(dist < best) best = dist, T = T1;
-        T1.shift -= 4 * M_PI;
+        T1.shift -= 720._deg;
         dist = value(T1);
         if(dist < best) best = dist, T = T1;
-        T1.shift += 2 * M_PI;
+        T1.shift += TAU;
         }
       }
   
@@ -306,14 +306,14 @@ void make_twopoint(ld& x, ld& y) {
   if(sphere) {
     int tss = twopoint_sphere_flips;
     if(tss&1) { tss--; 
-      dleft = 2*M_PI - 2*p - dleft;
-      dright = 2*M_PI - 2*p - dright;
+      dleft = TAU - 2*p - dleft;
+      dright = TAU - 2*p - dright;
       swap(dleft, dright);
       y = -y;
       }
     while(tss) { tss -= 2;
-      dleft = 2*M_PI - 4*p + dleft;
-      dright = 2*M_PI - 4*p + dright;
+      dleft = TAU - 4*p + dleft;
+      dright = TAU - 4*p + dright;
       }
     }
   x = (dright*dright-dleft*dleft) / 4 / p;
@@ -453,7 +453,7 @@ EX void threepoint_projection(const hyperpoint& H, hyperpoint& ret) {
 
   ld dist[3];
   for(int i=0; i<3; i++) {
-    hyperpoint h1 = xspinpush0(2*M_PI*i/3, p);    
+    hyperpoint h1 = xspinpush0(TAU*i/3, p);
     dist[i] = geo_dist(h1, H1);
     }
   
@@ -471,7 +471,7 @@ EX void threepoint_projection(const hyperpoint& H, hyperpoint& ret) {
   transmatrix T = Id;
   hyperpoint v = C0;
   for(int i=0; i<3; i++) {
-    hyperpoint pp = xspinpush0(2*M_PI*i/3, p);
+    hyperpoint pp = xspinpush0(TAU*i/3, p);
     v[i] = dist[i]*dist[i] - p*p;
     T[i][0] = -2 * pp[0];
     T[i][1] = -2 * pp[1];
@@ -1105,8 +1105,8 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ret[2] = 0;
         
         ret[0] -= pow(0.5, 1-mt);
-        ret[0] /= -(1-mt) * M_PI / 2;
-        ret[1] /= (1-mt) * M_PI / 2;
+        ret[0] /= -(1-mt) * 90._deg;
+        ret[1] /= (1-mt) * 90._deg;
         
         models::apply_orientation(ret[1], ret[0]);
         }
@@ -1153,17 +1153,17 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ld theta = 
           hyperbolic ? min(y / 2 + 0.572365, y * 0.78509) :
           euclid ? y :
-          y > 0 ? max(y * 0.012/0.015, M_PI/2 - (M_PI/2-y) * 0.066262/0.015708) :
-          min(y * 0.012/0.015, -M_PI/2 + (M_PI/2+y) * 0.066262/0.015708);
+          y > 0 ? max(y * 0.012/0.015, 90._deg - (90._deg-y) * 0.066262/0.015708) :
+          min(y * 0.012/0.015, -90._deg + (90._deg+y) * 0.066262/0.015708);
           
-        if(sphere && abs(theta) >= M_PI/2 - 1e-6) ;
+        if(sphere && abs(theta) >= 90._deg - 1e-6) ;
         else {
           for(int it=0; it<4; it++) {
             auto a = (sin_auto(2*theta) +2*theta - M_PI * sin_auto(y));
             auto b = (2 + 2 * cos_auto(2*theta));
             theta = theta - a / b;
           } }
-        y = M_PI * sin_auto(theta) / 2;
+        y = 90._deg * sin_auto(theta);
         x = x * cos_auto(theta); 
         });
       break;
@@ -1192,7 +1192,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ld d0 = hypot(x0, z0);
         
         if(md == mdAitoff || md == mdWinkelTripel) ;
-        else if(sphere) d = sqrt(2*(1 - cos(d))) * M_PI / 2;
+        else if(sphere) d = sqrt(2*(1 - cos(d))) * 90._deg;
         else d = sqrt(2*(cosh(d) - 1)) / 1.5;
 
         x = x0 * d / d0 / pconf.aitoff_parameter, y = z0 * d / d0;
@@ -1270,13 +1270,10 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ld df, zf;
       hypot_zlev(zlev, d, df, zf);
       
-      // 4 pi / 2pi = M_PI 
-      
       if(md == mdEquivolume)
-        d = pow(volume_auto(d), 1/3.) * pow(M_PI / 2, 1/3.);
+        d = pow(volume_auto(d), 1/3.) * pow(90._deg, 1/3.);
       else if(md == mdEquiarea && sphere) {
-        d = sqrt(2*(1 - cos(d))) * M_PI / 2;
-        //d = sin((d+90*degree)/2);
+        d = sqrt(2*(1 - cos(d))) * 90._deg;
         }
       else if(pmodel == mdEquiarea && hyperbolic)
         d = sqrt(2*(cosh(d) - 1)) / 1.5;
@@ -1572,7 +1569,7 @@ EX transmatrix actualV(const heptspin& hs, const transmatrix& V) {
   if(WDIM == 3) return V;
   #if CAP_IRR
   if(IRREGULAR)
-    return V * spin(M_PI + 2 * M_PI / S7 * (hs.spin + irr::periodmap[hs.at].base.spin));
+    return V * spin(M_PI + TAU / S7 * (hs.spin + irr::periodmap[hs.at].base.spin));
   #endif
   #if CAP_ARCM
   if(arcm::in()) return V * spin(-arcm::current.triangles[arcm::id_of(hs.at)][hs.spin].first);
@@ -1581,7 +1578,7 @@ EX transmatrix actualV(const heptspin& hs, const transmatrix& V) {
   if(bt::in()) return V;
   #endif
   if(kite::in()) return V;
-  return (hs.spin || !BITRUNCATED) ? V * spin(hs.spin*2*M_PI/hs.at->type + master_to_c7_angle()) : V;
+  return (hs.spin || !BITRUNCATED) ? V * spin(hs.spin*TAU/hs.at->type + master_to_c7_angle()) : V;
   }
 
 EX shiftmatrix actualV(const heptspin& hs, const shiftmatrix& V) {
@@ -1800,14 +1797,14 @@ void hrmap::draw_all() {
       int qty = ceil(1. / pconf.sphere_spiral_multiplier);
       if(qty > 100) qty = 100;
       for(int i=-qty; i < qty; i++)
-        draw_at(centerover, cview(2 * M_PI * i));
+        draw_at(centerover, cview(TAU * i));
       }
     else {
       draw_at(centerover, cview());
       if(vid.use_smart_range) for(int i=1;; i++) {
         int drawn = cells_drawn;
-        draw_at(centerover, cview(2 * M_PI * i));
-        draw_at(centerover, cview(-2 * M_PI * i));
+        draw_at(centerover, cview(TAU * i));
+        draw_at(centerover, cview(-TAU * i));
         if(drawn == cells_drawn) break;
         }
       }
@@ -1879,7 +1876,7 @@ void hrmap_standard::draw_at(cell *at, const shiftmatrix& where) {
       shiftmatrix Vd;
       if(inforder::mixed()) {
         int d1 = gmod(hs.spin+d, c->type);
-        Vd = V * spin(-2*M_PI*d/c->type) * xpush(spacedist(c, d1)) * spin(M_PI);
+        Vd = V * spin(-TAU*d/c->type) * xpush(spacedist(c, d1)) * spin180();
         }
       else
         Vd = V * cgi.heptmove[d];
@@ -1925,7 +1922,7 @@ EX void spinEdge(ld aspd) {
     
     int dir = down_is_forward ? 0 : 1;
 
-    V = cspin(2, dir, 90 * degree) * V;
+    V = cspin90(2, dir) * V;
 
     if(1) {
       dynamicval<eGeometry> g(geometry, gSphere);
@@ -1942,7 +1939,7 @@ EX void spinEdge(ld aspd) {
     
     vrhr::be_33(V);
 
-    V = cspin(dir, 2, 90 * degree) * V;
+    V = cspin90(dir, 2) * V;
     V = inverse(T) * V;
     if(!prod) V = V * gpushxto0(h);
     get_view_orientation() = V;
@@ -2038,7 +2035,7 @@ EX void centerpc(ld aspd) {
     else
       View = iso_inverse(T);
     if(prod) NLP = ortho_inverse(pc->ori);
-    if(WDIM == 2) rotate_view( cspin(0, 1, M_PI) * cspin(2, 1, M_PI/2 + shmup::playerturny[id]) * spin(-M_PI/2) );
+    if(WDIM == 2) rotate_view( cspin180(0, 1) * cspin(2, 1, 90._deg + shmup::playerturny[id]) * spin270() );
     return;
     }
   #endif
@@ -2160,7 +2157,7 @@ void addball(ld a, ld b, ld c) {
 void ballgeometry() {
   queuereset(mdPixel, PPR::CIRCLE);
   for(int i=0; i<60; i++)
-    addball(i * M_PI/30, 10, 0);
+    addball(TAU * i / 60, 10, 0);
   for(double d=10; d>=-10; d-=.2)
     addball(0, d, 0);
   for(double d=-10; d<=10; d+=.2)
@@ -2198,15 +2195,15 @@ EX void resetview() {
       }
 
     if(GDIM == 2) View = spin(M_PI + vid.fixed_facing_dir * degree) * View;
-    if(GDIM == 3 && !prod) View = cspin(0, 2, M_PI/2) * View;
-    if(prod) NLP = cspin(0, 2, M_PI/2);
+    if(GDIM == 3 && !prod) View = cspin90(0, 2) * View;
+    if(prod) NLP = cspin90(0, 2);
     if(cheater && eqmatrix(View, lView) && !centering) {
       View = Id;
       static ld cyc = 0;
-      cyc += 90 * degree;
+      cyc += 90._deg;
       View = spin(cyc) * View;
       if(GDIM == 2) View = spin(M_PI + vid.fixed_facing_dir * degree) * View;
-      if(GDIM == 3 && !prod) View = cspin(0, 2, M_PI/2) * View;
+      if(GDIM == 3 && !prod) View = cspin90(0, 2) * View;
       }
     }
   else if(currentmap) {
@@ -2435,7 +2432,7 @@ EX void draw_model_elements() {
     case mdThreePoint: {
       vid.linewidth *= 5;
       for(int i=0; i<=3; i++) {
-        hyperpoint h = xspinpush0(2*M_PI*i/3, pconf.twopoint_param);
+        hyperpoint h = xspinpush0(120._deg*i, pconf.twopoint_param);
         models::apply_orientation(h[1], h[0]);
         models::apply_orientation_yz(h[2], h[1]);
         curvepoint(h);
@@ -2519,11 +2516,11 @@ void queuestraight(hyperpoint X, int style, color_t lc, color_t fc, PPR p) {
   ld mul1 = hypot(vid.xres, vid.yres) / hypot_d(2, H1);
   
   queuereset(mdPixel, p);
-  curvepoint(H0 + spin(M_PI/2) * H0 * mul0);
-  curvepoint(H0 - spin(M_PI/2) * H0 * mul0);
-  curvepoint(H1 + spin(M_PI/2) * H1 * mul1);
-  curvepoint(H1 - spin(M_PI/2) * H1 * mul1);
-  curvepoint(H0 + spin(M_PI/2) * H0 * mul0);
+  curvepoint(H0 + spin90() * H0 * mul0);
+  curvepoint(H0 - spin90() * H0 * mul0);
+  curvepoint(H1 + spin90() * H1 * mul1);
+  curvepoint(H1 - spin90() * H1 * mul1);
+  curvepoint(H0 + spin90() * H0 * mul0);
   
   queuecurve(shiftless(Id), lc, fc, p).flags |= POLY_ALWAYS_IN | POLY_FORCEWIDE;
   queuereset(pmodel, p);
@@ -2562,7 +2559,7 @@ EX void draw_boundary(int w) {
   #endif
 
   if(elliptic && !among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdMollweide, mdCollignon))
-    circle_around_center(M_PI/2, periodcolor, 0, PPR::CIRCLE);
+    circle_around_center(90._deg, periodcolor, 0, PPR::CIRCLE);
   
   int broken_coord = models::get_broken_coord(pmodel);
   if(broken_coord) {
@@ -2617,7 +2614,7 @@ EX void draw_boundary(int w) {
       if(pmodel == mdBand && pconf.model_transition != 1) return;
       bool bndband = (among(pmodel, mdBand, mdMiller, mdGallStereographic, mdCentralCyl) ? hyperbolic : sphere);
       transmatrix T = spin(-pconf.model_orientation * degree);
-      ld right = M_PI/2 - 1e-5;
+      ld right = 90._deg - 1e-5;
       if(bndband) 
         queuestraight(T * ypush0(hyperbolic ? 10 : right), 2, lc, fc, p);
       ld xperiod = elliptic ? fakeinf/2 : fakeinf;
@@ -2640,7 +2637,7 @@ EX void draw_boundary(int w) {
     
     case mdHalfplane: 
       if(hyperbolic && GDIM == 2) {
-        queuestraight(xspinpush0(-pconf.model_orientation * degree - M_PI/2, fakeinf), 1, lc, fc, p);
+        queuestraight(xspinpush0(-pconf.model_orientation * degree - 90._deg, fakeinf), 1, lc, fc, p);
         return;
         }
       break;
@@ -2708,13 +2705,13 @@ EX void draw_boundary(int w) {
             ld alpha = M_PI - atan2(a[0], -a[1]);
             
             for(ld t=-1; t<=1; t += step)
-              curvepoint(xspinpush0(-M_PI/2 - t * alpha, mz));
+              curvepoint(xspinpush0(-90._deg - t * alpha, mz));
             }
           else {
             ld alpha = - atan2(a[0], -a[1]);
             
             for(ld t=-1; t<=1; t += step)
-              curvepoint(xspinpush0(+M_PI/2 - t * alpha, mz));
+              curvepoint(xspinpush0(+90._deg - t * alpha, mz));
             }
           
           queuecurve(shiftless(Id), lc, fc, p);
@@ -3100,7 +3097,7 @@ EX hyperpoint lie_exp(hyperpoint h) {
 EX hyperpoint rel_log(shiftpoint h) {
   if(sl2) {
     optimize_shift(h);
-    ld cycles = floor(h.shift / (2*M_PI) + .5);
+    ld cycles = floor(h.shift / TAU + .5);
     hyperpoint h1 = unshift(h);
     ld choice = h1[2] * h1[2] - h1[0] * h1[0] - h1[1] * h1[1];
     ld r, z;
@@ -3108,7 +3105,7 @@ EX hyperpoint rel_log(shiftpoint h) {
       ld r = sqrt(choice);
       ld z = asin_clamp(r);
       if(h1[3] < 0) z = M_PI - z;
-      z += cycles * 2 * M_PI;
+      z += cycles * TAU;
       }
     else if(cycles || h1[3] < -1 || choice == 0) {
       /* impossible, or light-like */
@@ -3238,7 +3235,7 @@ EX void shift_view_towards(shiftpoint H, ld l) {
 EX void set_view(hyperpoint camera, hyperpoint forward, hyperpoint upward) {
   if(GDIM == 2) {
     View = gpushxto0(camera);
-    View = spin(90*degree) * spintox(View * upward) * View;
+    View = spin90() * spintox(View * upward) * View;
     return;
     }
   
diff --git a/intra.cpp b/intra.cpp
index 6424454c..33ffd89c 100644
--- a/intra.cpp
+++ b/intra.cpp
@@ -187,8 +187,8 @@ EX portal_data make_portal(cellwalker cw, int spin) {
     for(auto p: fac) id.v0 += p;
     id.v0 = normalize_flat(id.v0);
     hyperpoint h = normalize_flat(fac[0]);
-    id.T = cspin(0, 1, -90*degree) * spintox(gpushxto0(id.v0) * h) * gpushxto0(id.v0);
-    if((id.T * C0)[0] > 0) id.T = cspin(0, 1, 180*degree) * id.T;
+    id.T = cspin90(1, 0) * spintox(gpushxto0(id.v0) * h) * gpushxto0(id.v0);
+    if((id.T * C0)[0] > 0) id.T = spin180() * id.T;
     for(int i=0; i<3; i++) id.T[3][i] = id.T[i][3] = i==3;
     if(debug_portal & 128)
     for(int a=0; a<4; a++) {
@@ -233,13 +233,13 @@ EX portal_data make_portal(cellwalker cw, int spin) {
     id.T = gpushxto0(id.v0);
     for(auto p: fac1) {
       if(abs((id.T * p)[2]) > 1e-3 && abs((id.T * p)[0]) < 1e-3)
-        id.T = cspin(2, 0, 90*degree) * id.T;
+        id.T = cspin90(2, 0) * id.T;
       if(abs((id.T * p)[2]) > 1e-3 && abs((id.T * p)[1]) < 1e-3)
-        id.T = cspin(2, 1, 90*degree) * id.T;
+        id.T = cspin90(2, 1) * id.T;
       }
-    if((id.T * C03)[2] > 0) id.T = cspin(2, 0, 180*degree) * id.T;
-    if(abs((id.T * removed)[0]) > 1e-2) id.T = cspin(0, 1, 90*degree) * id.T;
-    if((id.T * removed)[1] < -1e-2) id.T = cspin(0, 1, 180*degree) * id.T;
+    if((id.T * C03)[2] > 0) id.T = cspin180(2, 0) * id.T;
+    if(abs((id.T * removed)[0]) > 1e-2) id.T = cspin90(0, 1) * id.T;
+    if((id.T * removed)[1] < -1e-2) id.T = cspin180(0, 1) * id.T;
     vector<hyperpoint> v;
     geometry = gg;
     for(auto f: fac) v.push_back(id.to_poco(f));
@@ -254,7 +254,7 @@ EX portal_data make_portal(cellwalker cw, int spin) {
   else {
     id.kind = 0;
     id.v0 = project_on_triangle(fac[0], fac[1], fac[2]);
-    id.T = cpush(2, -hdist0(id.v0)) * cspin(2, 0, 90*degree) * spintox(id.v0);
+    id.T = cpush(2, -hdist0(id.v0)) * cspin90(2, 0) * spintox(id.v0);
     hyperpoint ctr = Hypc;
     for(auto p: fac) ctr += id.T*p;
     ctr = normalize(ctr);
diff --git a/irregular.cpp b/irregular.cpp
index c79aa879..108ab329 100644
--- a/irregular.cpp
+++ b/irregular.cpp
@@ -460,7 +460,7 @@ bool step(int delta) {
         ld dist = cgi.hcrossf / 2;
         ld dists[8];
         for(int i=0; i<S7; i++) {
-          dists[i] = hdist(s.p, xspinpush0(cgi.hexshift - i * 2 * M_PI / S7, -cgi.hcrossf));
+          dists[i] = hdist(s.p, xspinpush0(cgi.hexshift - i * TAU / S7, -cgi.hcrossf));
           if(dists[i] < dist)
             d = i, dist = dists[i];
           }
diff --git a/kite.cpp b/kite.cpp
index 3bb9f305..b9acff9b 100644
--- a/kite.cpp
+++ b/kite.cpp
@@ -53,8 +53,8 @@ hyperpoint mhpxy(ld x, ld y) {
 const ld phi = golden_phi;
 const ld rphi = 1 / phi;
 
-const ld down = 1 / tan(36 * degree);
-const ld up = 1 / tan(72 * degree);
+const ld down = 1 / tan(36._deg);
+const ld up = 1 / tan(72._deg);
 
 const ld dart_center = (down + 2 * up) / 3;
 const ld kite_center = up;
@@ -82,8 +82,8 @@ EX pair<vector<vector<hyperpoint>>, vector<vector<ld>>> make_walls() {
     hyperpoint dtop    = meupush( 0, shf+t*up) * meuscale(rphi) * C0;
     hyperpoint dbottom = meupush( 0, shf-down) * meuscale(rphi) * C0;
     
-    hyperpoint dleftmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(-1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(-36 * degree) * meupush(0, down - up) * C0;
-    hyperpoint drightmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(36 * degree) * meupush(0, down - up) * C0;
+    hyperpoint dleftmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(-1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(-36._deg) * meupush(0, down - up) * C0;
+    hyperpoint drightmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(36._deg) * meupush(0, down - up) * C0;
     
     hyperpoint dcenter = meupush( 0, shf-up) * meuscale(rphi) * C0;
     
@@ -247,12 +247,12 @@ struct hrmap_kite : hrmap {
     }
 
   void make_graphrules() {
-    pKite1 = meupush(-1, kite_center + 0) * mspin(108 * degree) * meuscale(rphi) * meupush(0, down - kite_center);
-    pKite2 = meupush(1, kite_center + 0) * mspin(-108 * degree) * meuscale(rphi) * meupush(0, down - kite_center);
-    pKite3 = meupush(0, kite_center - down) * mspin(36 * degree) * meuscale(rphi) * meupush(0, down - dart_center);
+    pKite1 = meupush(-1, kite_center + 0) * mspin(108._deg) * meuscale(rphi) * meupush(0, down - kite_center);
+    pKite2 = meupush(1, kite_center + 0) * mspin(-108._deg) * meuscale(rphi) * meupush(0, down - kite_center);
+    pKite3 = meupush(0, kite_center - down) * mspin(36._deg) * meuscale(rphi) * meupush(0, down - dart_center);
     
     pDart1 = meupush(0, dart_center-down) * meuscale(rphi) * meupush(0, down - kite_center);
-    pDart2 = meupush(-1, dart_center+0) * mspin((54 + 90) * degree) * meuscale(rphi) * meupush(0, down - dart_center);
+    pDart2 = meupush(-1, dart_center+0) * mspin(144._deg) * meuscale(rphi) * meupush(0, down - dart_center);
     
     ipKite1 = inverse(pKite1);
     ipKite2 = inverse(pKite2);
diff --git a/mapeditor.cpp b/mapeditor.cpp
index a161a216..b5add395 100644
--- a/mapeditor.cpp
+++ b/mapeditor.cpp
@@ -89,7 +89,7 @@ EX namespace mapeditor {
       int ll = ceil(360 * len);
       shiftmatrix W = V * rgpushxto0(s);
       for(int i=0; i<=ll; i++)
-        curvepoint(xspinpush0(360*degree*i/ll, radius));
+        curvepoint(xspinpush0(TAU*i/ll, radius));
       queuecurve(W, col, fill, PPR::LINE);
       }
 
@@ -1979,18 +1979,18 @@ EX namespace mapeditor {
         }
       transmatrix T;
       if(front_config == eFront::equidistants) T = Id;
-      else if(front_config == eFront::const_x) T = cspin(2, 0, M_PI/2);
-      else if(front_config == eFront::const_y) T = cspin(2, 1, M_PI/2);
+      else if(front_config == eFront::const_x) T = cspin90(2, 0);
+      else if(front_config == eFront::const_y) T = cspin90(2, 1);
       else return;
       for(int i=0; i<4; i+=2) {
         for(int u=2; u<=20; u++) {
           PRING(d) {
-            curvepoint(T * xspinpush(M_PI*d/cgi.S42, u/20.) * zpush0(front_edit));
+            curvepoint(T * xspinpush(d*cgi.S_step, u/20.) * zpush0(front_edit));
             }
           queuecurve(d2, cols[i + (u%5 != 0)], 0, i < 2 ? PPR::LINE : PPR::SUPERLINE);
           }
         for(int d=0; d<cgi.S84; d++) {
-          for(int u=0; u<=20; u++) curvepoint(T * xspinpush(M_PI*d/cgi.S42, u/20.) * zpush(front_edit) * C0);
+          for(int u=0; u<=20; u++) curvepoint(T * xspinpush(d*cgi.S_step, u/20.) * zpush(front_edit) * C0);
           queuecurve(d2, cols[i + (d % (cgi.S84/drawcell->type) != 0)], 0, i < 2 ? PPR::LINE : PPR::SUPERLINE);
           }
         }
@@ -1999,11 +1999,11 @@ EX namespace mapeditor {
 
     for(int d=0; d<cgi.S84; d++) {
       unsigned col = (d % (cgi.S84/drawcell->type) == 0) ? gridcolor : lightgrid;
-      queueline(d2 * C0, d2 * xspinpush0(M_PI*d/cgi.S42, 1), col, 4 + vid.linequality);
+      queueline(d2 * C0, d2 * xspinpush0(d*cgi.S_step, 1), col, 4 + vid.linequality);
       }
     for(int u=2; u<=20; u++) {
       PRING(d) {
-        curvepoint(xspinpush0(M_PI*d/cgi.S42, u/20.));
+        curvepoint(xspinpush0(d*cgi.S_step, u/20.));
         }
       queuecurve(d2, (u%5==0) ? gridcolor : lightgrid, 0, PPR::LINE);
       }
@@ -2057,8 +2057,7 @@ EX namespace mapeditor {
         // total: rh2 - rh1
         // ld z = degree;
         ld x = b2 - b1 + M_PI;
-        while(x > M_PI) x -= 2 * M_PI;
-        while(x < -M_PI) x += 2 * M_PI;
+        cyclefix(x, 0);
         area += x;
         }
       }
@@ -2440,7 +2439,7 @@ EX namespace mapeditor {
       }
     
     if(uni == 'a' && haveshape) {
-      mh = spin(2*M_PI*-ew.rotid/dsCur->rots) * mh;
+      mh = spin(TAU*-ew.rotid/dsCur->rots) * mh;
       if(ew.symid) mh = Mirror * mh;
     
       if(ew.pointid < 0 || ew.pointid >= isize(dsCur->list)) 
@@ -2462,7 +2461,7 @@ EX namespace mapeditor {
 
       if(i < 0 || i >= isize(dsCur->list)) return;
 
-      mh = spin(2*M_PI*-ew.rotid/dsCur->rots) * mh;
+      mh = spin(TAU*-ew.rotid/dsCur->rots) * mh;
       if(ew.symid) mh = Mirror * mh;
 
       if(uni == 'm' || uni == 'M') 
@@ -2839,7 +2838,7 @@ EX namespace mapeditor {
           shiftmatrix T = rgpushxto0(lstart);
           texture::where = lstartcell;
           for(int i=0; i<circp; i++)
-            texture::drawPixel(T * xspinpush0(2 * M_PI * i / circp, rad), tcolor);
+            texture::drawPixel(T * xspinpush0(TAU * i / circp, rad), tcolor);
           lstartcell = NULL;
           }
 #endif          
@@ -2936,13 +2935,13 @@ EX namespace mapeditor {
             for(int r=0; r<us->d[l].rots; r++) {
               for(int i=0; i<isize(us->d[l].list); i++) {
                 hyperpoint h = us->d[l].list[i];
-                h = spin(360 * degree * r / us->d[l].rots) * h;
+                h = spin(TAU * r / us->d[l].rots) * h;
                 for(int d=0; d<GDIM; d++) print(hlog, fts(h[d]), ", ");
                 }
               if(us->d[l].sym) for(int i=isize(us->d[l].list)-1; i>=0; i--) {
                 hyperpoint h = us->d[l].list[i];
                 h[1] = -h[1];
-                h = spin(360 * degree * r / us->d[l].rots) * h;
+                h = spin(TAU * r / us->d[l].rots) * h;
                 for(int d=0; d<GDIM; d++) print(hlog, fts(h[d]), ", ");
                 }
               }
@@ -3022,7 +3021,7 @@ EX namespace mapeditor {
     if(radius > .1) circp *= 2; 
     
     for(int j=0; j<circp; j++)
-      pts.push_back(xspinpush0(M_PI*j*2/circp, radius));
+      pts.push_back(xspinpush0(TAU * j / circp, radius));
     for(int j=0; j<circp; j++) curvepoint(pts[j]);
     curvepoint(pts[0]);
     queuecurve(Ctr, dtcolor, 0, PPR::LINE);
@@ -3057,7 +3056,7 @@ EX namespace mapeditor {
 
       for(int j=0; j<=texture::texturesym; j++)
       for(int i=0; i<c->type; i += sih.symmetries) {
-        shiftmatrix M2 = V * applyPatterndir(c, sih) * spin(2*M_PI*i/c->type);
+        shiftmatrix M2 = V * applyPatterndir(c, sih) * spin(TAU * i / c->type);
         if(j) M2 = M2 * Mirror;
         switch(holdmouse ? mousekey : 'd') {
           case 'c':
@@ -3141,14 +3140,14 @@ EX namespace mapeditor {
     
           if(mouseout()) break;
     
-          shiftpoint P2 = V * spin(2*M_PI*a/ds.rots) * (b?Mirror*mh:mh);
+          shiftpoint P2 = V * spin(TAU * a / ds.rots) * (b?Mirror*mh:mh);
         
           queuestr(P2, 10, "x", 0xFF00FF);
           }
         
         if(isize(ds.list) == 0) return us;
         
-        shiftpoint Plast = V * spin(-2*M_PI/ds.rots) * (ds.sym?Mirror*ds.list[0]:ds.list[isize(ds.list)-1]);
+        shiftpoint Plast = V * spin(-TAU / ds.rots) * (ds.sym?Mirror*ds.list[0]:ds.list[isize(ds.list)-1]);
         int state = 0;
         int gstate = 0;
         double dist2 = 0;
@@ -3157,14 +3156,14 @@ EX namespace mapeditor {
         for(int a=0; a<ds.rots; a++) 
         for(int b=0; b<(ds.sym?2:1); b++) {
         
-          hyperpoint mh2 = spin(2*M_PI*-ew.rotid/ds.rots) * mh;
+          hyperpoint mh2 = spin(TAU * -ew.rotid/ds.rots) * mh;
           if(ew.symid) mh2 = Mirror * mh2;
-          shiftpoint pseudomouse = V * spin(2*M_PI*a/ds.rots) * mirrorif(mh2, b);      
+          shiftpoint pseudomouse = V * spin(TAU * a / ds.rots) * mirrorif(mh2, b);
         
           for(int t=0; t<isize(ds.list); t++) {
             int ti = b ? isize(ds.list)-1-t : t;
   
-            shiftpoint P2 = V * spin(2*M_PI*a/ds.rots) * mirrorif(ds.list[ti], b);
+            shiftpoint P2 = V * spin(TAU * a / ds.rots) * mirrorif(ds.list[ti], b);
             
             if(!mouseout()) {
               double d = hdist(moh, P2);
diff --git a/menus.cpp b/menus.cpp
index 145c6ad2..77da41f2 100644
--- a/menus.cpp
+++ b/menus.cpp
@@ -884,17 +884,6 @@ EX void showStartMenu() {
 
   timerstart = time(NULL);
   
-  /*
-  initquickqueue();
-  int siz = min(vid.xres, vid.yres) / 8;
-  drawMonsterType(moPrincess, NULL, atscreenpos(siz,siz,siz) * spin(-M_PI/4), 0, 0);
-  drawMonsterType(moKnight, NULL, atscreenpos(vid.xres-siz,siz,siz) * spin(-3*M_PI/4), 0, 0);
-  drawItemType(itOrbYendor, NULL, atscreenpos(siz,vid.yres-siz,siz) * spin(M_PI/4), iinf[itOrbYendor].color, 0, false);
-  drawItemType(itKey, NULL, atscreenpos(siz,vid.yres-siz,siz) * spin(M_PI/4), iinf[itKey].color, 0, false);
-  drawItemType(itHyperstone, NULL, atscreenpos(vid.xres-siz,vid.yres-siz,siz) * spin(3*M_PI/4), iinf[itHyperstone].color, 0, false);
-  quickqueue();
-  */
-
   keyhandler = [] (int sym, int uni) {
     dialog::handleNavigation(sym, uni);
     if(uni == 'o') uni = 'i';
diff --git a/models.cpp b/models.cpp
index 3208ebad..6acbb661 100644
--- a/models.cpp
+++ b/models.cpp
@@ -176,7 +176,7 @@ EX namespace models {
       euclidean_spin = pispin * iso_inverse(cview().T * currentmap->master_relative(centerover, true));
       euclidean_spin = gpushxto0(euclidean_spin * C0) * euclidean_spin;
       hyperpoint h = inverse(euclidean_spin) * (C0 + (euc::eumove(gp::loc{1,0})*C0 - C0) * vpconf.spiral_x + (euc::eumove(gp::loc{0,1})*C0 - C0) * vpconf.spiral_y);
-      spiral_multiplier = cld(0, 2 * M_PI) / cld(h[0], h[1]);
+      spiral_multiplier = cld(0, TAU) / cld(h[0], h[1]);
       }
     
     if(centerover && !history::on)
@@ -323,11 +323,11 @@ EX namespace models {
       initquickqueue();
       queuereset(mdPixel, PPR::LINE);              
       for(int a=-1; a<=1; a++) {
-        curvepoint(point2(-M_PI/2 * current_display->radius, a*current_display->radius));
-        curvepoint(point2(+M_PI/2 * current_display->radius, a*current_display->radius));
+        curvepoint(point2(-90._deg * current_display->radius, a*current_display->radius));
+        curvepoint(point2(+90._deg * current_display->radius, a*current_display->radius));
         queuecurve(shiftless(Id), forecolor, 0, PPR::LINE);
-        curvepoint(point2(a*current_display->radius, -M_PI/2*current_display->radius));
-        curvepoint(point2(a*current_display->radius, +M_PI/2*current_display->radius));
+        curvepoint(point2(a*current_display->radius, -90._deg * current_display->radius));
+        curvepoint(point2(a*current_display->radius, +90._deg * current_display->radius));
         queuecurve(shiftless(Id), forecolor, 0, PPR::LINE);
         }
       queuereset(vpconf.model, PPR::LINE);
@@ -1035,7 +1035,7 @@ EX namespace models {
           "Here you can change this parameter.", 'b');
       param_f(p.miller_parameter, sp+"miller");
       param_f(p.loximuthal_parameter, sp+"loximuthal")
-      -> editable(-M_PI/2, M_PI/2, .1, "loximuthal parameter", 
+      -> editable(-90._deg, 90._deg, .1, "loximuthal parameter",
           "Loximuthal is similar to azimuthal equidistant, but based on loxodromes (lines of constant geographic direction) rather than geodesics. "
           "The loximuthal projection maps (the shortest) loxodromes to straight lines of the same length, going through the starting point. "
           "This setting changes the latitude of the starting point.\n\n"
diff --git a/netgen.cpp b/netgen.cpp
index b51fa664..46276879 100644
--- a/netgen.cpp
+++ b/netgen.cpp
@@ -366,8 +366,8 @@ EX namespace netgen {
       printf("faza %d cell %d\n", faza, i);
   
       for(int e=0; e<t; e++) {
-        vec v1 = center[i] * nscale + raylen[i] * ang(rot[i] + 2*M_PI*e/t);
-        vec v2 = center[i] * nscale + raylen[i] * ang(rot[i] + 2*M_PI*(e+1)/t);
+        vec v1 = center[i] * nscale + raylen[i] * ang(rot[i] + TAU * e/t);
+        vec v2 = center[i] * nscale + raylen[i] * ang(rot[i] + TAU * (e+1)/t);
         vec v3 = (v1+v2)/2;
   
         if(faza == 1) blackline(v1, v2);
@@ -486,10 +486,10 @@ EX namespace netgen {
     for(int e=0; e<it; e++) if(nei[i][e] == j) ie = e;
     for(int e=0; e<jt; e++) if(nei[j][e] == i) je = e;
     
-    rot[i] = rot[j] + 2*M_PI*(je+.5)/jt - 2*M_PI*(ie+.5)/it + M_PI;
+    rot[i] = rot[j] + TAU*(je+.5)/jt - TAU*(ie+.5)/it + M_PI;
     center[i] = 
       center[j] +
-        (edgist[i]+edgist[j]) * ang(rot[j] + 2*M_PI*(je+.5)/jt);
+        (edgist[i]+edgist[j]) * ang(rot[j] + TAU*(je+.5)/jt);
     }
 
   shiftpoint vec_to_p(vec v) {
@@ -555,8 +555,8 @@ EX namespace netgen {
         applyGlue(i);
   
       for(int e=0; e<t; e++) {
-        vec v1 = center[i] + raylen[i] * ang(rot[i] + 2*M_PI*e/t);
-        vec v2 = center[i] + raylen[i] * ang(rot[i] + 2*M_PI*(e+1)/t);
+        vec v1 = center[i] + raylen[i] * ang(rot[i] + TAU*e/t);
+        vec v2 = center[i] + raylen[i] * ang(rot[i] + TAU*(e+1)/t);
         vec v3 = (v1+v2)/2;
   
         if(nei[i][e] >= 0 && !dragging) {
@@ -756,7 +756,7 @@ EX namespace netgen {
         }
       if(uni == 's') {
         View = Id;
-        if(ctof(centerover)) View = spin(2 * M_PI * (rand() % 7) / 7) * View;
+        if(ctof(centerover)) View = spin(TAU * (rand() % 7) / 7) * View;
         playermoved = false;
         }
       else if(uni == 'c') {
diff --git a/nonisotropic.cpp b/nonisotropic.cpp
index bed84f9e..3646152f 100644
--- a/nonisotropic.cpp
+++ b/nonisotropic.cpp
@@ -784,14 +784,14 @@ EX namespace nilv {
     
     if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
     else if(side > 1e-6) {
-      wmin = 0, wmax = 2 * M_PI;
+      wmin = 0, wmax = TAU;
       }
     else if(side < -1e-6) {
-      wmin = - 2 * M_PI, wmax = 0;
+      wmin = - TAU, wmax = 0;
       }
     else return point3(h[0], h[1], 0);
     
-    ld alpha_total = h[0] ? atan(h[1] / h[0]) : M_PI/2;
+    ld alpha_total = h[0] ? atan(h[1] / h[0]) : 90._deg;
   
     ld b;
     if(abs(h[0]) > abs(h[1]))
@@ -1578,14 +1578,14 @@ EX namespace product {
       if(twisted && i == c->type-1 && where[c].second == hybrid::csteps-1) {
         auto b = spins[where[c].first].first;
         transmatrix T = mscale(Id, cgi.plevel);
-        T = T * spin(2 * M_PI * b.spin / b.at->type);
+        T = T * spin(TAU * b.spin / b.at->type);
         if(b.mirrored) T = T * Mirror;
         return T;
         }
       if(twisted && i == c->type-2 && where[c].second == 0) {
         auto b = spins[where[c].first].second;
         transmatrix T = mscale(Id, -cgi.plevel);
-        T = T * spin(2 * M_PI * b.spin / b.at->type);
+        T = T * spin(TAU * b.spin / b.at->type);
         if(b.mirrored) T = T * Mirror;
         return T;
         }
@@ -1799,7 +1799,7 @@ EX namespace slr {
   
       ld z = cr * (K - 1/SV/SV);
   
-      ld k = M_PI/2;
+      ld k = 90._deg;
       ld a = k / K;
       ld zw = xy * cr / sr;
       ld u = z * a;
@@ -2572,7 +2572,7 @@ EX namespace stretch {
       
       res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
       
-      a = a - 2 * M_PI;
+      a = a - TAU;
 
       res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
       
@@ -2583,7 +2583,7 @@ EX namespace stretch {
       ld a = atan2(h[2], h[3]);
       
       for(int it=-generations; it<generations; it++) {
-        res.push_back(point31(0, 0, (a + 2 * M_PI * it) * SV));
+        res.push_back(point31(0, 0, (a + TAU * it) * SV));
         }
       
       return res;
@@ -2594,16 +2594,13 @@ EX namespace stretch {
     ld base_min_a = asin(xy);
     ld base_max_a = M_PI - base_min_a;
   
-    ld seek = M_PI/2-atan2(h[3], h[2]);
+    ld seek = 90._deg - atan2(h[3], h[2]);
   
     auto ang = [&] (ld a) {
       ld rp = xy / sin(a);
       ld co = abs(rp) >= 1 ? 0 : sqrt(1-rp*rp);
       
       return atan2(co * sin(a), cos(a)) - co * (1 - 1/SV/SV) * a;
-      
-      // while(a0 > M_PI) a0 -= 2 * M_PI;
-      // while(a0 < -M_PI) a0 += 2 * M_PI;
       };
     
     for(int shift=-generations; shift<generations; shift++) {
@@ -2637,10 +2634,10 @@ EX namespace stretch {
           
           // println(hlog, "*** ", mi, t, " ** ", tie(min_a, ang_min), tie(extreme, ang_extreme), tie(max_a, ang_max), " -> ", vmin, " to ", vmax);
           
-          int cmin = ceil((vmin - seek) / 2 / M_PI);
-          int cmax = floor((vmax - seek) / 2 / M_PI);
+          int cmin = ceil((vmin - seek) / TAU);
+          int cmax = floor((vmax - seek) / TAU);
           for(int c = cmin; c <= cmax; c++) {
-            ld cseek = seek + c * 2 * M_PI;
+            ld cseek = seek + c * TAU;
   
             for(int it=0; it<40; it++) {
             
diff --git a/passable.cpp b/passable.cpp
index dfe6ef89..42d8a463 100644
--- a/passable.cpp
+++ b/passable.cpp
@@ -304,7 +304,7 @@ EX ld calcAirdir(cell *c) {
   for(int i=0; i<c->type; i++) {
     cell *c2 = c->move(i);
     if(c2 && c2->monst == moAirElemental) {
-      return c->c.spin(i) * 2 * M_PI / c2->type;
+      return c->c.spin(i) * TAU / c2->type;
       }
     }
   for(int i=0; i<c->type; i++) {
@@ -315,7 +315,7 @@ EX ld calcAirdir(cell *c) {
     for(int i=0; i<c2->type; i++) {
       cell *c3 = c2->move(i);
       if(c3 && c3->monst == moAirElemental) {
-        return c2->c.spin(i) * 2 * M_PI / c3->type;
+        return c2->c.spin(i) * TAU / c3->type;
         }
       }
     }
diff --git a/pattern2.cpp b/pattern2.cpp
index 19009354..7ce5a26d 100644
--- a/pattern2.cpp
+++ b/pattern2.cpp
@@ -2717,7 +2717,7 @@ EX namespace linepatterns {
     ALLCELLS(
        if(is_master(c) && !euclid) for(int i=0; i<S7; i++) 
           if(c->master->move(i) && c->master->move(i) < c->master) {
-            gridlinef(V, C0, xspinpush0(-2*M_PI*i/S7 - master_to_c7_angle(), cgi.tessf), col, 2 + vid.linequality);
+            gridlinef(V, C0, xspinpush0(-TAU*i/S7 - master_to_c7_angle(), cgi.tessf), col, 2 + vid.linequality);
             }
        )
     );
@@ -2726,7 +2726,7 @@ EX namespace linepatterns {
     ALLCELLS(
       if(is_master(c) && !euclid) for(int i=0; i<S7; i++) 
         if(c->master->move(i) && way(c->master, i) && c->master->move(i)->dm4 == c->master->dm4)
-          gridlinef(V, C0, xspinpush0(-2*M_PI*i/S7 - master_to_c7_angle(), cgi.tessf), col, 2 + vid.linequality);
+          gridlinef(V, C0, xspinpush0(-TAU*i/S7 - master_to_c7_angle(), cgi.tessf), col, 2 + vid.linequality);
       )
     );
 
@@ -2821,15 +2821,15 @@ EX namespace linepatterns {
       if(pseudohept(c) && (p/4 == 10 || p/4 == 8))
       for(int i=0; i<S7; i++) if(c->move(i) && emeraldval(c->move(i)) == p-4) {
         gridlinef(V, C0, tC0(cgi.heptmove[i]), col, 2 + vid.linequality);
-        gridlinef(V, C0, xspinpush0(-i * 2 * M_PI / S7, -hdist/2), col, 2 + vid.linequality);
+        gridlinef(V, C0, xspinpush0(-i * TAU / S7, -hdist/2), col, 2 + vid.linequality);
         }
       )
     );
   linepattern patPalacelike("firewall lines", 0xFF400000, stdhyp_only, 
     ALLCELLS(
       if(pseudohept(c)) for(int i=0; i<7; i++) 
-        gridlinef(V, ddspin(c,i,M_PI*5/7) * xpush0(cgi.tessf/2),
-                     ddspin(c,i,M_PI*9/7) * xpush0(cgi.tessf/2),
+        gridlinef(V, ddspin(c,i,A_PI*5/7) * xpush0(cgi.tessf/2),
+                     ddspin(c,i,A_PI*9/7) * xpush0(cgi.tessf/2),
                             col, 1 + vid.linequality);
       )
     );
@@ -2840,8 +2840,8 @@ EX namespace linepatterns {
           cell *c1 = createMov(c, (i+3) % 7);
           cell *c2 = createMov(c, (i+4) % 7);
           if(polarb50(c1) != a && polarb50(c2) != a)
-              gridlinef(V, ddspin(c,i,M_PI*5/7) * xpush0(cgi.tessf/2),
-                        ddspin(c,i,M_PI*9/7) * xpush0(cgi.tessf/2),
+              gridlinef(V, ddspin(c,i,A_PI*5/7) * xpush0(cgi.tessf/2),
+                        ddspin(c,i,A_PI*9/7) * xpush0(cgi.tessf/2),
                                   col, 1 + vid.linequality);
           }
       )
@@ -2871,8 +2871,8 @@ EX namespace linepatterns {
           heptagon *h2 = c->master->modmove(i-1);
           if(!h1 || !h2) continue;
           if(emeraldval(h1->c7)/4 == 8 && emeraldval(h2->c7)/4 == 8)
-              gridlinef(V, ddspin(c,i,M_PI*5/7) * xpush0(cgi.tessf/2),
-                        ddspin(c,i,M_PI*9/7) * xpush0(cgi.tessf/2),
+              gridlinef(V, ddspin(c,i,A_PI*5/7) * xpush0(cgi.tessf/2),
+                        ddspin(c,i,A_PI*9/7) * xpush0(cgi.tessf/2),
                                   col, 1 + vid.linequality);
           }
       )
@@ -2951,9 +2951,9 @@ EX namespace linepatterns {
       )
     );
   EX ld parallel_count = 6;
-  EX ld parallel_max = 90 * degree;
-  EX ld parallel_length = 180 * degree;
-  linepattern patParallels("parallels", 0xFFFFFF00, always_available, 
+  EX ld parallel_max = 90._deg;
+  EX ld parallel_length = M_PI;
+  linepattern patParallels("parallels", 0xFFFFFF00, always_available,
     ATCENTER(
       for(int i=-int(parallel_count); i<=parallel_count; i ++) {
         ld phi = i * parallel_max / parallel_count;
diff --git a/polygons.cpp b/polygons.cpp
index 0133dc5b..f127cea1 100644
--- a/polygons.cpp
+++ b/polygons.cpp
@@ -18,8 +18,7 @@ static constexpr ld WOLF = (-15.5);
 void geometry_information::hpc_connect_ideal(hyperpoint a, hyperpoint b) {
   ld left = -atan2(a);
   ld right = -atan2(b);
-  if(right > left + 180*degree) right -= 360*degree;
-  if(right < left - 180*degree) right += 360*degree;
+  cyclefix(right, left);
   /* call hpc.push_back directly to avoid adding points */
   ld qty = ceil(abs(right-left) / ideal_each);
   for(int i=0; i<=qty; i++) hpc.push_back(xspinpush0(lerp(left, right, i/qty), ideal_limit));
@@ -149,7 +148,7 @@ void geometry_information::extra_vertices() {
 #endif
   }
 
-transmatrix geometry_information::ddi(int a, ld x) { return xspinpush(a * M_PI / S42, x); }
+transmatrix geometry_information::ddi(int a, ld x) { return xspinpush(a * S_step, x); }
 
 void geometry_information::drawTentacle(hpcshape &h, ld rad, ld var, ld divby) {
   double tlength = max(crossf, hexhexdist);
@@ -319,7 +318,7 @@ void geometry_information::bshape(hpcshape& sh, PPR prio, double shzoom, int sha
       }
     }
   else shzoomx *= bscale7, shzoomy *= bscale7;
-  double bonusf = /* sphere ? M_PI*4/35 : */ (rots-rots2+.0) / rots2;
+  double bonusf = (rots-rots2+.0) / rots2;
 
   auto ipoint = [&] (int i, int mul) {
     hyperpoint h = hpxy(polydata[whereis+2*i] * shzoomx, polydata[whereis+2*i+1] * shzoomy * mul);
@@ -330,10 +329,10 @@ void geometry_information::bshape(hpcshape& sh, PPR prio, double shzoom, int sha
 
   for(int r=0; r<rots2; r++) {
     for(int i=0; i<qty; i++)
-      hpcpush(spin(2*M_PI*r/rots2) * ipoint(i, 1));
+      hpcpush(spin(TAU*r/rots2) * ipoint(i, 1));
     if(sym == 2)
     for(int i=qty-1; i>=0; i--)
-      hpcpush(spin(2*M_PI*r/rots2) * ipoint(i, -1));
+      hpcpush(spin(TAU*r/rots2) * ipoint(i, -1));
     }
   hpcpush(ipoint(0, 1));
   finishshape();
@@ -412,8 +411,8 @@ void geometry_information::make_sidewalls() {
 void geometry_information::procedural_shapes() {
   bshape(shMovestar, PPR::MOVESTAR);
   for(int i=0; i<=8; i++) {
-    hpcpush(xspinpush0(M_PI * i/4, crossf));
-    if(i != 8) hpcpush(xspinpush0(M_PI * i/4 + M_PI/8, crossf/4));
+    hpcpush(xspinpush0(90._deg * i, crossf));
+    if(i != 8) hpcpush(xspinpush0(90._deg * i + 45._deg, crossf/4));
     }
 
   // procedural floors
@@ -525,7 +524,7 @@ void geometry_information::procedural_shapes() {
 
   bshape(shCross, PPR::WALL);
   for(int i=0; i<=84; i+=7)
-    hpcpush(xspinpush0(2*M_PI*i/84, zhexf * (i%3 ? 0.8 : 0.3)));
+    hpcpush(xspinpush0(TAU*i/84, zhexf * (i%3 ? 0.8 : 0.3)));
 
 // items
 
@@ -634,8 +633,8 @@ void geometry_information::procedural_shapes() {
 
   bshape(shEccentricDisk, PPR::ITEM);
   for(int i=0; i<=S84; i+=SD3) {
-    hpcpush(hpxy(sin(i*2*M_PI/S84)*orbsize*.075,
-                 cos(i*2*M_PI/S84)*orbsize*.075 + .07));
+    hpcpush(hpxy(sin(i*S_step)*orbsize*.075,
+                 cos(i*S_step)*orbsize*.075 + .07));
     }
 
   bshape(shDiskSq, PPR::ITEM);
@@ -645,11 +644,11 @@ void geometry_information::procedural_shapes() {
 
   bshape(shEgg, PPR::ITEM);
   RING(i)
-    hpcpush(hpxy(sin(i*2*M_PI/S84)*0.242 * orbsize, cos(i*2*M_PI/S84)*0.177*orbsize));
+    hpcpush(hpxy(sin(i*S_step)*0.242 * orbsize, cos(i*S_step)*0.177*orbsize));
 
   bshape(shSmallEgg, PPR::ITEM);
   RING(i)
-    hpcpush(hpxy(sin(i*2*M_PI/S84)*0.242 * orbsize/2, cos(i*2*M_PI/S84)*0.177*orbsize/2));
+    hpcpush(hpxy(sin(i*S_step)*0.242 * orbsize/2, cos(i*S_step)*0.177*orbsize/2));
   
   auto make_ring = [this] (hpcshape& sh, reaction_t f) {
     bshape(sh, PPR::ITEM);
@@ -812,11 +811,11 @@ void geometry_information::procedural_shapes() {
 
   bshape(shSlime, PPR::MONSTER_BODY);
   PRING(i)
-    hpcpush(ddi(i, scalefactor * hcrossf7 * (0.7 + .2 * sin(i * M_PI * 2 / S84 * 9))) * C0);
+    hpcpush(ddi(i, scalefactor * hcrossf7 * (0.7 + .2 * sin(i * S_step * 9))) * C0);
 
   bshape(shJelly, PPR::MONSTER_BODY);
   PRING(i)
-    hpcpush(ddi(i, scalefactor * hcrossf7 * (0.4 + .03 * sin(i * M_PI * 2 / S84 * 7))) * C0);
+    hpcpush(ddi(i, scalefactor * hcrossf7 * (0.4 + .03 * sin(i * S_step * 7))) * C0);
 
   bshape(shHeptaMarker, PPR::HEPTAMARK);
   for(int t=0; t<=SD7; t++) hpcpush(ddi(t*S12, zhexf*.2) * C0);
@@ -826,25 +825,25 @@ void geometry_information::procedural_shapes() {
 
   bshape(shRose, PPR::ITEM);
   PRING(t)
-    hpcpush(xspinpush0(M_PI * t / (S42+.0), scalefactor * hcrossf7 * (0.2 + .15 * sin(M_PI * t / (S42+.0) * 3))));
+    hpcpush(xspinpush0(S_step * t, scalefactor * hcrossf7 * (0.2 + .15 * sin(S_step * t * 3))));
   finishshape();
 
   shRoseItem = shRose;
 
   bshape(shSmallRose, PPR::ITEM);
   PRING(t)
-    hpcpush(xspinpush0(M_PI * t / (S42+.0), scalefactor/2 * hcrossf7 * (0.2 + .15 * sin(M_PI * t / (S42+.0) * 3))));
+    hpcpush(xspinpush0(S_step * t, scalefactor/2 * hcrossf7 * (0.2 + .15 * sin(S_step * t * 3))));
   finishshape();
 
   bshape(shThorns, PPR::THORNS);
   for(int t=0; t<=60; t++)
-    hpcpush(xspinpush0(M_PI * t / 30.0, scalefactor * hcrossf7 * ((t&1) ? 0.3 : 0.6)));
+    hpcpush(xspinpush0(TAU * t / 60, scalefactor * hcrossf7 * ((t&1) ? 0.3 : 0.6)));
 
   for(int i=0; i<16; i++) {
     bshape(shParticle[i], PPR::PARTICLE);
     for(int t=0; t<6; t++)
 //    hpcpush(xspinpush0(M_PI * t * 2 / 6 + M_PI * 2/6 * hrand(100) / 150., (0.03 + hrand(100) * 0.0003) * scalefactor));
-      hpcpush(xspinpush0(M_PI * t * 2 / 6 + M_PI * 2/6 * randd() / 1.5, (0.03 + randd() * 0.03) * scalefactor));
+      hpcpush(xspinpush0(TAU * t / 6 + 60._deg * randd() / 1.5, (0.03 + randd() * 0.03) * scalefactor));
     hpc.push_back(hpc[last->s]);
     }
 
@@ -853,7 +852,7 @@ void geometry_information::procedural_shapes() {
     if(GDIM == 3) asteroid_size[i] *= 7;
     bshape(shAsteroid[i], PPR::PARTICLE);
     for(int t=0; t<12; t++)
-      hpcpush(xspinpush0(M_PI * t / 6, asteroid_size[i] * (1 - randd() * .2)));
+      hpcpush(xspinpush0(TAU * t / 12, asteroid_size[i] * (1 - randd() * .2)));
     hpc.push_back(hpc[last->s]);
     }
 
@@ -1100,7 +1099,7 @@ void geometry_information::configure_floorshapes() {
   if(!BITRUNCATED) {
     ld hedge = hdist(xspinpush0(M_PI/S7, rhexf), xspinpush0(-M_PI/S7, rhexf));
 
-    trihepta1 = hdist0(xpush(tessf) * xspinpush0(2*M_PI*2/S7, tessf)) / 2 * .98;
+    trihepta1 = hdist0(xpush(tessf) * xspinpush0(TAU*2/S7, tessf)) / 2 * .98;
     trihepta0 = hdist0(xpush(-tessf) * xspinpush0(M_PI/S7, rhexf+hedge/2)) * .98;
     }
 
@@ -1150,6 +1149,7 @@ void geometry_information::prepare_shapes() {
   S28 = SD7 * 4;
   S36 = SD6 * 6;
   S84 = S42 * 2;
+  S_step = A_PI / S42;
 
   // printf("crossf = %f euclid = %d sphere = %d\n", float(crossf), euclid, sphere);
   hpc.clear(); ext.clear();
@@ -1179,11 +1179,11 @@ void geometry_information::prepare_shapes() {
     dynamicval<int> d(vid.texture_step, max(vid.texture_step, 4));
     ld len6 = hdist0(mid(xpush0(hexvdist), spin(M_PI/S3) * xpush0(hexvdist)));
 
-    ld len7 = hdist0(mid(xpush0(hexf), spin(M_PI*2/S7) * xpush0(hexf)));
-    ld hlen7 = hdist0(mid(xpush0(hcrossf), spin(M_PI*2/S7) * xpush0(hcrossf)));
+    ld len7 = hdist0(mid(xpush0(hexf), spin(TAU/S7) * xpush0(hexf)));
+    ld hlen7 = hdist0(mid(xpush0(hcrossf), spin(TAU/S7) * xpush0(hcrossf)));
 
     ld lenx = hdist(xpush0(hexvdist), spin(M_PI/S3) * xpush0(hexvdist));
-    ld hlenx = hdist(xpush0(hcrossf), spin(2*M_PI/S7) * xpush0(hcrossf));
+    ld hlenx = hdist(xpush0(hcrossf), spin(TAU/S7) * xpush0(hcrossf));
 
     bshape(shHalfMirror[2], PPR::WALL);
     hpcpush(C0); hpcpush(xpush0(-len6*scalefactor));  chasmifyPoly(FLOOR, WALL, 0);
diff --git a/racing.cpp b/racing.cpp
index a32de41b..78109d48 100644
--- a/racing.cpp
+++ b/racing.cpp
@@ -54,10 +54,10 @@ EX int race_start_tick, race_finish_tick[MAXPLAYER];
 typedef unsigned char uchar;
 
 uchar frac_to_uchar(ld x) { return uchar(x * 256); }
-uchar angle_to_uchar(ld x) { return frac_to_uchar(x / 2 / M_PI); }
+uchar angle_to_uchar(ld x) { return frac_to_uchar(x / TAU); }
 
 ld uchar_to_frac(uchar x) { return x / 256.; }
-transmatrix spin_uchar(uchar x) { return spin(uchar_to_frac(x) * 2 * M_PI); }
+transmatrix spin_uchar(uchar x) { return spin(uchar_to_frac(x) * TAU); }
 
 static const ld distance_multiplier = 4;
 
@@ -763,7 +763,7 @@ EX bool set_view() {
       }
     at /= multi::players;
     at = normalize(at);
-    atm = rgpushxto0(at) * spin(-90*degree) * rspintox(gpushxto0(at) * first);
+    atm = rgpushxto0(at) * spin270() * rspintox(gpushxto0(at) * first);
     }
   
   if(racing::player_relative || quotient || (kite::in() && GDIM == 3)) {
@@ -788,11 +788,11 @@ EX bool set_view() {
 
     View = xpush(-x) * T * iT1 * ypush(vid.yshift) * View;
 
-    if(GDIM == 3) View = cspin(2, 0, M_PI/2) * View;
+    if(GDIM == 3) View = cspin(2, 0, 90._deg) * View;
     fixmatrix(View);
     }
   if(GDIM == 3 && WDIM == 2)
-    View = cspin(0, 1, M_PI) * cspin(2, 1, M_PI/2 + shmup::playerturny[multi::cpid]) * spin(-M_PI/2) * View;
+    View = spin180() * cspin(2, 1, 90._deg + shmup::playerturny[multi::cpid]) * spin270() * View;
   else if(GDIM == 2) View = spin(race_angle * degree) * View;
   return true;
   }
@@ -1348,7 +1348,7 @@ void draw_ghost(ghost& ghost) {
 
 shiftmatrix racerel(ld rel) {
   int bsize = vid.fsize * 2;
-  return shiftless(atscreenpos(bsize, vid.yres - bsize - rel * (vid.yres - bsize*2) / 100, bsize) * spin(M_PI/2));
+  return shiftless(atscreenpos(bsize, vid.yres - bsize - rel * (vid.yres - bsize*2) / 100, bsize) * spin90());
   }
 
 EX int get_percentage(cell *c) {
diff --git a/radar.cpp b/radar.cpp
index 19ea1b11..d18913ad 100644
--- a/radar.cpp
+++ b/radar.cpp
@@ -110,7 +110,7 @@ EX void draw_radar(bool cornermode) {
     curvepoint(atscreenpos(cx-cos(i * degree)*rad, cy-sin(i*degree)*rad, 1) * C0);
   queuecurve(sId, 0xFFFFFFFF, 0x000000FF, PPR::ZERO);      
 
-  ld alpha = 15 * degree;
+  ld alpha = 15._deg;
   ld co = cos(alpha);
   ld si = sin(alpha);
   
diff --git a/raycaster.cpp b/raycaster.cpp
index dd2b6764..5524d8b0 100644
--- a/raycaster.cpp
+++ b/raycaster.cpp
@@ -2634,9 +2634,9 @@ EX void cast() {
     glUniformMatrix4fv(o->uStraighten, 1, 0, glhr::tmtogl_transpose(asonov::straighten).as_array());
     }
   if(o->uReflectX != -1) {
-    auto h = glhr::pointtogl(tangent_length(spin(90*degree) * asonov::ty, 2));
+    auto h = glhr::pointtogl(tangent_length(spin90() * asonov::ty, 2));
     glUniform4fv(o->uReflectX, 1, &h[0]);
-    h = glhr::pointtogl(tangent_length(spin(90*degree) * asonov::tx, 2));
+    h = glhr::pointtogl(tangent_length(spin90() * asonov::tx, 2));
     glUniform4fv(o->uReflectY, 1, &h[0]);
     }
   #endif
diff --git a/reg3.cpp b/reg3.cpp
index b34e510f..c08c61bb 100644
--- a/reg3.cpp
+++ b/reg3.cpp
@@ -216,14 +216,14 @@ EX namespace reg3 {
         
     if(1) {
       dynamicval<eGeometry> dg(geometry, gSphere);
-      angle_between_faces = edge_of_triangle_with_angles(2*M_PI/mid, M_PI/face, M_PI/face);
+      angle_between_faces = edge_of_triangle_with_angles(TAU/mid, M_PI/face, M_PI/face);
       
       h0 = xtangent(1);
       h1 = cspin(0, 1, angle_between_faces) * h0;
-      h2 = cspin(1, 2, 2*M_PI/face) * h1;
-      h3 = cspin(1, 2, -2*M_PI/face) * h1;
+      h2 = cspin(1, 2, TAU/face) * h1;
+      h3 = cspin(1, 2, -TAU/face) * h1;
 
-      hcrossf = edge_of_triangle_with_angles(M_PI/2, M_PI/mid, M_PI/face);
+      hcrossf = edge_of_triangle_with_angles(90._deg, M_PI/mid, M_PI/face);
 
       h012 = cspin(1, 2, M_PI/face) * cspin(0, 1, hcrossf) * h0;
       h013 = cspin(1, 2, -M_PI/face) * cspin(0, 1, hcrossf) * h0;
@@ -245,7 +245,7 @@ EX namespace reg3 {
       u = normalize(u);
 
       hyperpoint h = C0 * face;
-      for(int i=0; i<face; i++) h += d * (cspin(1, 2, M_PI*2*i/face) * h012);
+      for(int i=0; i<face; i++) h += d * (cspin(1, 2, TAU*i/face) * h012);
       h = normalize(h);
 
       hyperpoint h2 = rspintox(h) * xpush0(2 * hdist0(h));
@@ -276,25 +276,25 @@ EX namespace reg3 {
     hyperpoint v2 = C0 + klein_scale * h012;
 
     hyperpoint midface = Hypc;
-    for(int i=0; i<face; i++) midface += cspin(1, 2, 2*i*M_PI/face) * v2;
+    for(int i=0; i<face; i++) midface += cspin(1, 2, TAU * i/face) * v2;
     midface = normalize(midface);
     ld between_centers = 2 * hdist0(midface);
     DEBB(DF_GEOM, ("between_centers = ", between_centers));
     
     if(S7 == 20) {
       spins[0] = Id;
-      spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
-      spins[2] = spins[1] * cspin(1, 2, -2 * M_PI/face) * spins[1];
-      spins[3] = spins[1] * cspin(1, 2, +2 * M_PI/face) * spins[1];
-      for(int a=4; a<10; a++) spins[a] = cspin(1, 2, 2*M_PI/face) * spins[a-3];
-      for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * cspin(0, 1, M_PI);
+      spins[1] = cspin(0, 1, angle_between_faces) * cspin180(1, 2);
+      spins[2] = spins[1] * cspin(1, 2, -TAU/face) * spins[1];
+      spins[3] = spins[1] * cspin(1, 2, +TAU/face) * spins[1];
+      for(int a=4; a<10; a++) spins[a] = cspin(1, 2, TAU/face) * spins[a-3];
+      for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * spin180();
       }
 
     if(S7 == 12 || S7 == 8) {
       spins[0] = Id;
-      spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
-      for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];      
-      for(int a=S7/2; a<S7; a++) spins[a] = cspin(0, 1, M_PI) * spins[a-S7/2];
+      spins[1] = cspin(0, 1, angle_between_faces) * cspin180(1, 2);
+      for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, TAU*(a-1)/face) * spins[1];
+      for(int a=S7/2; a<S7; a++) spins[a] = cspin180(0, 1) * spins[a-S7/2];
       if(S7 == 8) swap(spins[6], spins[7]);
       if(S7 == 12) swap(spins[8], spins[11]);
       if(S7 == 12) swap(spins[9], spins[10]);
@@ -302,25 +302,25 @@ EX namespace reg3 {
     
     if(S7 == 6) {
       spins[0] = Id;
-      spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
-      spins[2] = cspin(1, 2, M_PI/2) * spins[1];
-      for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * cspin(0, 1, M_PI);
+      spins[1] = cspin(0, 1, angle_between_faces) * cspin180(1, 2);
+      spins[2] = cspin90(1, 2) * spins[1];
+      for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * cspin180(0, 1);
       }
     
     if(S7 == 4) {
       spins[0] = Id;
-      spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
-      for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];      
+      spins[1] = cspin(0, 1, angle_between_faces) * cspin180(1, 2);
+      for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, TAU*(a-1)/face) * spins[1];      
       }
     
     cellshape.clear();
     cellshape.resize(S7);
     for(int a=0; a<S7; a++) {
       for(int b=0; b<face; b++)
-        cellshape[a].push_back(spins[a] * cspin(1, 2, 2*M_PI*b/face) * v2);
+        cellshape[a].push_back(spins[a] * cspin(1, 2, TAU*b/face) * v2);
       }
     
-    cgi.adjmoves[0] = cpush(0, between_centers) * cspin(0, 2, M_PI);
+    cgi.adjmoves[0] = cpush(0, between_centers) * cspin180(0, 2);
     for(int i=1; i<S7; i++) cgi.adjmoves[i] = spins[i] * cgi.adjmoves[0];
 
     for(int a=0; a<S7; a++)
@@ -334,7 +334,7 @@ EX namespace reg3 {
     else cgi.strafedist = hdist(cgi.adjmoves[0] * C0, cgi.adjmoves[1] * C0);
     
     if(stretch::applicable()) {
-      transmatrix T = cspin(0, 2, 90 * degree);
+      transmatrix T = cspin90(0, 2);
       transmatrix iT = inverse(T);
       for(auto& v: cgi.adjmoves) v = T * v * iT;
       for(auto& vv: cellshape) for(auto& v: vv) v = T * v;
@@ -1294,7 +1294,7 @@ EX namespace reg3 {
             allh[a]->c.connect(b, allh[a1], flip(b), false);
             transmatrix T = cgi.adjmoves[b];
             hyperpoint p = tC0(T);
-            tmatrices[a][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, 108 * degree) * spintox(p);
+            tmatrices[a][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, 108._deg) * spintox(p);
             }
           }      
         make_subconnections();
@@ -1310,7 +1310,7 @@ EX namespace reg3 {
   hrmap_quotient3 *gen_quotient_map(bool minimized, fieldpattern::fpattern &fp) {
     #if CAP_FIELD
     if(geometry == gSpace535 && minimized) {
-      return new seifert_weber::hrmap_singlecell(108*degree);
+      return new seifert_weber::hrmap_singlecell(108._deg);
       }
     else if(geometry == gSpace535)
       return new seifert_weber::hrmap_seifert_cover;
@@ -2527,8 +2527,8 @@ EX const vector<int>& rule_get_childpos() {
 
 EX hrmap* new_map() {
   if(geometry == gSeifertCover) return new seifert_weber::hrmap_seifert_cover;
-  if(geometry == gSeifertWeber) return new seifert_weber::hrmap_singlecell(108*degree);
-  if(geometry == gHomologySphere) return new seifert_weber::hrmap_singlecell(36*degree);
+  if(geometry == gSeifertWeber) return new seifert_weber::hrmap_singlecell(108._deg);
+  if(geometry == gHomologySphere) return new seifert_weber::hrmap_singlecell(36._deg);
   if(quotient && !sphere) return new hrmap_field3(&currfp);
   if(variation_rule_available()) return new hrmap_h3_subrule;
   if(pure_rule_available()) return new hrmap_h3_rule;
@@ -2633,7 +2633,7 @@ EX bool pseudohept(cell *c) {
     auto m = currentmap;
     hyperpoint h = tC0(m->relative_matrix(c->master, m->getOrigin(), C0));
     if(S7 == 12) {
-      hyperpoint h1 = cspin(0, 1, atan2(16, 69) + M_PI/4) * h;
+      hyperpoint h1 = cspin(0, 1, atan2(16, 69) + 45._deg) * h;
       for(int i=0; i<4; i++) if(abs(abs(h1[i]) - .5) > .01) return false;
       return true;
       }
diff --git a/rogueviz/ads/display.cpp b/rogueviz/ads/display.cpp
index 5c6326ad..647952db 100644
--- a/rogueviz/ads/display.cpp
+++ b/rogueviz/ads/display.cpp
@@ -23,8 +23,8 @@ void apply_duality(shiftmatrix& S) {
     S.T = Duality * S.T * Duality;
     };
   if(use_duality == 2) {
-    S = ads_matrix(Id, -90*degree) * S * ads_matrix(Id, +90*degree);
-    S.T = spin(90*degree) * S.T;
+    S = ads_matrix(Id, -90._deg) * S * ads_matrix(Id, +90._deg);
+    S.T = spin(90._deg) * S.T;
     }
   }
 
@@ -278,7 +278,7 @@ void view_ads_game() {
     for(int u=0; u<30; u++) {
       auto bcurrent = current;
       
-      transmatrix T = rgpushxto0( spin(12*degree*u) * xpush0(0.5) );
+      transmatrix T = rgpushxto0( spin(TAU*u/30) * xpush0(0.5) );
   
       current.T = current.T * T;
       auto base1 = findflat(ads_point(C0, 0));
diff --git a/rogueviz/ads/ds-game.cpp b/rogueviz/ads/ds-game.cpp
index 26fb0f97..56cf24bf 100644
--- a/rogueviz/ads/ds-game.cpp
+++ b/rogueviz/ads/ds-game.cpp
@@ -140,7 +140,7 @@ struct rock_generator {
     for(int i=0; i<qty; i++) {
       cshift ++;
       for(ld j=-3; j<=3; j++) {
-        add(spin(alpha + i * spinv) * cspin(0, 2, j * step) * spin(90*degree) * lorentz(0, 3, rapidity));
+        add(spin(alpha + i * spinv) * cspin(0, 2, j * step) * spin90() * lorentz(0, 3, rapidity));
         }
       }
     }
@@ -197,7 +197,7 @@ struct rock_generator {
       ld step = rand_range(.2, .5);
       ld alpha = rand_range(0, TAU);
       cshift += rand_range(0.5, 1) * (1 + cshift / 10);
-      auto r = add(spin(alpha) * cspin(0, 2, step) * spin(90*degree) * lorentz(0, 3, rapidity));
+      auto r = add(spin(alpha) * cspin(0, 2, step) * spin90() * lorentz(0, 3, rapidity));
       eResourceType rt = eResourceType(2 + rand() % 4);
       if(rt == rtGold) rt = rtHull;
       r->type = oResource;
diff --git a/rogueviz/ads/ds-texture.cpp b/rogueviz/ads/ds-texture.cpp
index f6fdfb08..f159fbec 100644
--- a/rogueviz/ads/ds-texture.cpp
+++ b/rogueviz/ads/ds-texture.cpp
@@ -98,10 +98,10 @@ void draw_texture(texture_to_use& tu) {
   int pts_id = 0;
 
   auto add = [&] (int x, int y) {
-    ld x0 = (y-(YSCALE/2.)) / YSCALE * M_PI * 4;
+    ld x0 = (y-(YSCALE/2.)) / YSCALE * 720._deg;
     ld mercator_y0 = (x-(XSCALE/2.)) / (XSCALE/2.) * M_PI * MWIDTH;
     ld y0 = asin(tanh(2 * mercator_y0));
-    ld y1 = y0 - 90 * degree;
+    ld y1 = y0 - 90._deg;
     
     et.tinf.tvertices.push_back(glhr::makevertex(x * 1. / XSCALE, .5 + (y-0.5) / MWIDTH / YSCALE, 0));
 
@@ -111,7 +111,7 @@ void draw_texture(texture_to_use& tu) {
       ld s = current.shift - tu.ctr;
 
       // We actually want to compute this, but this is not precise enough:
-      // cr = ds_cross0(current.T * lorentz(2, 3, -current.shift) * cspin(0, 1, x0) * cspin(0, 2, y0 - 90*degree));
+      // cr = ds_cross0(current.T * lorentz(2, 3, -current.shift) * cspin(0, 1, x0) * cspin(0, 2, y0 - 90._deg));
       
       // Here is what we get for current.T == Id: (computed with sympy)      
       hyperpoint now;
diff --git a/rogueviz/ads/map.cpp b/rogueviz/ads/map.cpp
index b2d28417..83428c2f 100644
--- a/rogueviz/ads/map.cpp
+++ b/rogueviz/ads/map.cpp
@@ -66,7 +66,7 @@ void compute_life(cell *c, transmatrix S1, const worldline_visitor& wv) {
   int iter = 0;
   cell *cur_c = c;
   auto cur_w = hybrid::get_where(c);
-  while(t < 2 * M_PI) {
+  while(t < TAU) {
     iter++;
     auto last_w = cur_w;
     auto next_w = cur_w;
@@ -74,7 +74,7 @@ void compute_life(cell *c, transmatrix S1, const worldline_visitor& wv) {
     ld next_t;
     ld last_time = t;
     cell *next_c = nullptr;
-    binsearch(t, t+M_PI/2, [&] (ld t1) { 
+    binsearch(t, t+90._deg, [&] (ld t1) {
       S1 = S1 * chg_shift(t1 - last_time);
       last_time = t1;
       virtualRebase(cur_c, S1);
diff --git a/rogueviz/antidesitter.cpp b/rogueviz/antidesitter.cpp
index f530ddb8..0fcbdb56 100644
--- a/rogueviz/antidesitter.cpp
+++ b/rogueviz/antidesitter.cpp
@@ -228,7 +228,7 @@ bool handleKey(int sym, int uni) {
   }
 
 void auto_shift() {
-   current.T = spin(30*degree) * lorentz(0, 3, 1) * spin(-30*degree) * current.T;
+   current.T = spin(30._deg) * lorentz(0, 3, 1) * spin(-30._deg) * current.T;
    }
 
 /* in our cellular automaton, each tile is affected by its own history, and the spatial neighbors of its ms-step history */
@@ -509,7 +509,7 @@ void ads_ca_check() {
   }
 
 ld get_shift_cycles(ld shift) {
-  return floor(shift / 2 / M_PI + .5) * 2 * M_PI;
+  return floor(shift / TAU + .5) * TAU;
   }
 
 shiftpoint shift_perfect_mul(shiftmatrix T, shiftpoint h) {
@@ -524,8 +524,7 @@ shiftpoint shift_perfect_mul(shiftmatrix T, shiftpoint h) {
     optimize_shift(cand);
     
     if(i > 0) {
-      while(cand.shift > res.shift + M_PI) cand.shift -= 2 * M_PI;
-      while(cand.shift < res.shift - M_PI) cand.shift += 2 * M_PI;
+      cyclefix(cand.shift, res.shift);
       }
     res = cand;    
     }
@@ -567,7 +566,7 @@ flatresult findflat(shiftpoint h) {
 
 /*
   hyperpoint h = unshift(S0);
-  transmatrix deg90 = cspin(2, 3, 90*degree) * cspin(0, 1, 90*degree);
+  transmatrix deg90 = cspin(2, 3, 90._deg) * cspin(0, 1, 90._deg);
   hyperpoint h0 = unshift(current) * h;
   hyperpoint h90 = unshift(current) * deg90 * h;
 
@@ -586,7 +585,7 @@ flatresult findflat(shiftpoint h) {
   else {
     cost = 0;
     sint = 1;
-    t = 90*degree;
+    t = 90._deg;
     }
   
   hyperpoint h2 = h0 * cost + h90 * sint;
diff --git a/rogueviz/ascending-descending.cpp b/rogueviz/ascending-descending.cpp
index c82ea919..7933d099 100644
--- a/rogueviz/ascending-descending.cpp
+++ b/rogueviz/ascending-descending.cpp
@@ -85,7 +85,7 @@ pair<hyperpoint, hyperpoint> trace_path(ld v) {
   hyperpoint lctr = A;
   ld angle = 0;
   
-  ld arclen = radius * M_PI/2;
+  ld arclen = radius * 90._deg;
   
   auto change_angle = [&] (ld x) {
     if(v == 0) return;
@@ -109,7 +109,7 @@ pair<hyperpoint, hyperpoint> trace_path(ld v) {
   change_angle(4);
   shift_to(E, true);
   
-  angle *= M_PI/2;
+  angle *= 90._deg;
   
   if(v > 0) vperiod = vorig - v;
   
@@ -197,7 +197,7 @@ void prepare_nilform() {
   println(hlog, "scale = ", scale);
   println(hlog, nilize(E).second);  
   
-  vperiod = radius * 2 * M_PI + hypot_d(3, B-A) + hypot_d(3, C-B) + hypot_d(3, D-C) + hypot_d(3, E-D);
+  vperiod = radius * TAU + hypot_d(3, B-A) + hypot_d(3, C-B) + hypot_d(3, D-C) + hypot_d(3, E-D);
   println(hlog, "vperiod = ", vperiod);
   
   make_routes();
diff --git a/rogueviz/backhead.cpp b/rogueviz/backhead.cpp
index e0fed8a7..2c93f44f 100644
--- a/rogueviz/backhead.cpp
+++ b/rogueviz/backhead.cpp
@@ -116,17 +116,17 @@ void face_animation() {
   if(tf == 0) {
     View = cspin(0, 2, 360 * degree * smoothen(t)) * View;
     View = zpush(-0.1) * View;
-    View = cspin(0, 2, M_PI) * View;
+    View = cspin180(0, 2) * View;
     back = 0;
     }
   else if(tf == 1) {
     View = zpush(-0.1 * (1-smoothen(t))) * View;
     if(t > .9)
     back = -0.1 * smoothen(10*t-9);
-    View = cspin(0, 2, M_PI) * View;
+    View = cspin180(0, 2) * View;
     }
   else if(tf == 2) {
-    View = cspin(0, 2, 75*degree*sin(2*M_PI*smoothen(t))) * View;
+    View = cspin(0, 2, 75._deg*sin(TAU*smoothen(t))) * View;
     }
   else if(tf == 3) {
     View = cspin(1, 2, up*degree*smoothen(t)) * View;
diff --git a/rogueviz/balls.cpp b/rogueviz/balls.cpp
index 3341216b..5881c682 100644
--- a/rogueviz/balls.cpp
+++ b/rogueviz/balls.cpp
@@ -35,7 +35,7 @@ void initialize(int max_ball) {
   shShell.flags |= POLY_TRIANGLES;
 
   auto pt = [] (int i, int j) {
-    cgi.hpcpush(direct_exp(/* cspin(0, 2, -30*degree) **/ cspin(2, 1, 90*degree) * cspin(0, 1, j * degree) * cspin(0, 2, i * M_PI / 2 / 16) * ztangent(r_big_ball)));
+    cgi.hpcpush(direct_exp(/* cspin(0, 2, -30._deg) **/ cspin90(2, 1) * cspin(0, 1, j * degree) * cspin(0, 2, i * 90._deg / 16) * ztangent(r_big_ball)));
     };
 
   for(int i=0; i<16; i++)
@@ -176,7 +176,7 @@ int args() {
     cgi.require_shapes();
     shift();
     initialize(argi());
-    View = cspin(1, 2, M_PI/2);
+    View = cspin90(1, 2);
     }
 
   else return 1;
diff --git a/rogueviz/bringris.cpp b/rogueviz/bringris.cpp
index f3076a90..823c233b 100644
--- a/rogueviz/bringris.cpp
+++ b/rogueviz/bringris.cpp
@@ -889,16 +889,16 @@ void set_view() {
     dist -= 1e-4;
     move_dist = PIU(hdist(get_corner_position(currentmap->gamestart(), 0), get_corner_position(currentmap->gamestart(), 1)));
     tView = xpush(-dist) * tView;
-    tView = spin(135*degree) * tView;
+    tView = spin(135._deg) * tView;
     }  
   if(in_h2xe() && UNRECTIFIED)
-    tView = spin(135*degree) * tView;
+    tView = spin(135._deg) * tView;
   if(in_h2xe() && S7 == 4)
-    tView = spin(90*degree) * tView;
+    tView = spin90() * tView;
   if(in_s2xe())
-    tView = spin(90*degree) * tView;
+    tView = spin90() * tView;
   if(in_e2xe())
-    tView = spin(90*degree) * tView;
+    tView = spin90() * tView;
   }
 
 void set_tview(transmatrix T) {
@@ -913,12 +913,12 @@ void set_tview(transmatrix T) {
   ncenter = centerover;
   // tView = View;
   if(bgeom == 4)
-    tView = spin(72*degree*at.spin);
+    tView = spin(72._deg*at.spin);
   else
-    tView = spin(90*degree*at.spin);
+    tView = spin(90._deg*at.spin);
   if(at.mirrored)
     tView = MirrorY * tView;
-  // tView = spin(90*degree*at.spin);
+  // tView = spin(90._deg*at.spin);
   set_view();  
 
   pView = rel * tView;
@@ -934,7 +934,7 @@ void rotate_block(int d, bool camera_only) {
   cellwalker at1 = flatspin(at, d);
   if(camera_only || !shape_conflict(at1)) {
     at = at1;
-    set_tview(spin(d*90*degree));
+    set_tview(spin(d*90._deg));
     }
   else playSound(cwt.at, "hit-crush3");
   if(!camera_only) draw_shape();
@@ -1169,7 +1169,7 @@ void draw_screen(int xstart, bool show_next) {
   #if CAP_VR
   if(!explore) {
     E4;
-    vrhr::hmd_at_ui = vrhr::hmd_ref_at * cspin(0, 2, 30*degree);
+    vrhr::hmd_at_ui = vrhr::hmd_ref_at * cspin(0, 2, 30._deg);
     }
   #endif
     
@@ -1190,16 +1190,16 @@ void draw_screen(int xstart, bool show_next) {
     View = pView;
     if(nil) {
       centerover = at.at;
-      rotate_view(cspin(1, 2, -90*degree));
+      rotate_view(cspin90(2, 1));
       shift_view(ztangent(3 * nilv::nilwidth));
-      rotate_view(cspin(0, 1, -90*degree));
+      rotate_view(cspin90(1, 0));
       anims::moved();
       }
     else if(sol) {
       centerover = at.at;
-      rotate_view(cspin(1, 2, 180*degree));
+      rotate_view(cspin180(1, 2));
       shift_view(ztangent(1));
-      rotate_view(cspin(0, 1, -90*degree));
+      rotate_view(cspin90(1, 0));
       anims::moved();
       }
     else {
diff --git a/rogueviz/dhrg/gridmapping.cpp b/rogueviz/dhrg/gridmapping.cpp
index b4407ea4..bdbd7aeb 100644
--- a/rogueviz/dhrg/gridmapping.cpp
+++ b/rogueviz/dhrg/gridmapping.cpp
@@ -35,11 +35,8 @@ void do_analyze_grid(int maxv) {
         alpha[qalpha++] = atan2(h1[0], h1[1]);
         }
       if(qalpha != 2) printf("Error: qalpha = %d\n", qalpha);
-      ld df = alpha[0] - alpha[1];
-      if(df<0) df = -df;
-      while(df > 2*M_PI) df -= 2*M_PI;
-      while(df > M_PI) df = 2*M_PI - df;
-      df /= 4*M_PI;
+      ld df = raddif(alpha[0], alpha[1]);
+      df /= 720._deg;
       wstats[d][0] += df;
       if(d==2) printf("df == %" PLDF " dd = %" PLDF "\n", df, dd);
       wstats[d][1] += df*dd;
diff --git a/rogueviz/dhrg/loglik.cpp b/rogueviz/dhrg/loglik.cpp
index 0d990f60..235eefa0 100644
--- a/rogueviz/dhrg/loglik.cpp
+++ b/rogueviz/dhrg/loglik.cpp
@@ -114,7 +114,7 @@ void origcoords() {
   using namespace rogueviz;
   vertexcoords.resize(N);
   for(int i=0; i<N; i++) 
-    vertexcoords[i] = spin(coords[i].second * 2 * M_PI / 360) * xpush(coords[i].first) * C0;
+    vertexcoords[i] = spin(coords[i].second * degree) * xpush(coords[i].first) * C0;
   }
 
 // compute vertexcoords from the RogueViz representation
diff --git a/rogueviz/extra-projections.cpp b/rogueviz/extra-projections.cpp
index ab77d739..7a69397f 100644
--- a/rogueviz/extra-projections.cpp
+++ b/rogueviz/extra-projections.cpp
@@ -100,8 +100,8 @@ void add_extra_projections() {
     ld sy = y > 0 ? 1 : -1;
     y /= sy;
     ld z = 4. - 3. * (hyperbolic ? -sinh(y) : sin(y));
-    x = 2. * x * sqrt(z / 6. / M_PI);
-    y = sy * sqrt(2*M_PI/3) * (2. - sqrt(z));
+    x = 2. * x * sqrt(z / 1080._deg);
+    y = sy * sqrt(120._deg) * (2. - sqrt(z));
     });
   
   // https://en.wikipedia.org/wiki/Eckert_IV_projection
@@ -109,7 +109,7 @@ void add_extra_projections() {
     cld theta = newton_inverse(
       [] (cld th) { return th + sin(th) * cos(th) + 2. * sin(th); }, 
       [] (cld th) { return 1. + cos(th) * cos(th) - sin(th) * sin(th) + 2. * cos(th); }, 
-      (2+M_PI/2) * sin(y), y);
+      (2+90._deg) * sin(y), y);
     static ld cox = 2 / sqrt(4*M_PI+M_PI*M_PI);
     static ld coy = 2 * sqrt(M_PI/(4+M_PI));
     x = cox * x * (1. + cos(theta));
@@ -120,12 +120,12 @@ void add_extra_projections() {
   add_complex("Ortelius", 0, [] (cld& x, cld& y) {
     cld sx = (real(x)+imag(x)) > 0 ? 1 : -1;
     x /= sx;
-    if(abs(real(x)) < 90*degree) {
+    if(abs(real(x)) < 90._deg) {
       cld F = M_PI*M_PI / 8. / x + x / 2.;
       x = (x - F + sqrt(F*F-y*y));
       }
     else {
-      x = sqrt(M_PI*M_PI/4 - y*y) + x - M_PI/2;
+      x = sqrt(M_PI*M_PI/4 - y*y) + x - 90._deg;
       }
     x *= sx;
     });
diff --git a/rogueviz/fifteen.cpp b/rogueviz/fifteen.cpp
index 8d2de859..5d804d0f 100644
--- a/rogueviz/fifteen.cpp
+++ b/rogueviz/fifteen.cpp
@@ -64,7 +64,7 @@ void compute_triangle_markers() {
   println(hlog, triangle_markers);
 
   for(int i=0; i<isize(fif); i++) {
-    turns.push_back(triangle_markers[i+1] == 0 ? 90*degree : 0);
+    turns.push_back(triangle_markers[i+1] == 0 ? 90._deg : 0);
     }
   }
 
@@ -480,7 +480,7 @@ auto fifteen_hook =
                 popScreenAll();
                 fullcenter();
                 if(lev == "coiled" || lev == "mobiusband")
-                  View = spin(90*degree) * View;
+                  View = spin90() * View;
                 if(lev == "mobiusband")
                   View = MirrorX * View;
                 }
diff --git a/rogueviz/flocking.cpp b/rogueviz/flocking.cpp
index b38710b8..ad0a34f5 100644
--- a/rogueviz/flocking.cpp
+++ b/rogueviz/flocking.cpp
@@ -237,7 +237,7 @@ namespace flocking {
         if(prod) {
           NLP = inverse(vdata[0].m->ori);
           
-          NLP = hr::cspin(1, 2, 90 * degree) * spin(90 * degree) * NLP;
+          NLP = hr::cspin90(1, 2) * spin90() * NLP;
 
           if(NLP[0][2]) {
             auto downspin = -atan2(NLP[0][2], NLP[1][2]);
@@ -245,9 +245,9 @@ namespace flocking {
             }
           }          
         else {
-          View =spin(90 * degree) * View;
+          View =spin90() * View;
           if(GDIM == 3) {
-            View = hr::cspin(1, 2, 90 * degree) * View;
+            View = hr::cspin90(1, 2) * View;
             }
           shift_view(ztangent(follow_dist));
           }        
diff --git a/rogueviz/functions.cpp b/rogueviz/functions.cpp
index 4d07c66b..fa7ab75d 100644
--- a/rogueviz/functions.cpp
+++ b/rogueviz/functions.cpp
@@ -22,7 +22,7 @@ hyperpoint find_point(ld t) {
   exp_parser ep;
   auto &dict = ep.extra_params;
   dict["t"] = t;
-  dict["phi"] = t * 2 * M_PI;
+  dict["phi"] = t * TAU;
   dict["x"] = tan(t * M_PI - M_PI/2);
   for(auto& ff: formula) {
     ep.s = ff;
diff --git a/rogueviz/fundamental.cpp b/rogueviz/fundamental.cpp
index 8edc4e9e..3a3dc1cf 100644
--- a/rogueviz/fundamental.cpp
+++ b/rogueviz/fundamental.cpp
@@ -52,7 +52,7 @@ shiftmatrix labelpos(shiftpoint h1, shiftpoint h2) {
   shiftmatrix T = rgpushxto0(h);
   hyperpoint hx = inverse_shift(T, h2);
   ld alpha = atan2(-hx[1], hx[0]);
-  return T * xspinpush(alpha + M_PI/2, label_dist);
+  return T * xspinpush(alpha + 90._deg, label_dist);
   }
  
 ld widthfactor = 5;
diff --git a/rogueviz/horo63.cpp b/rogueviz/horo63.cpp
index 8eee4e8b..cd36b819 100644
--- a/rogueviz/horo63.cpp
+++ b/rogueviz/horo63.cpp
@@ -23,7 +23,7 @@ bool draw_horo63(cell *c, const shiftmatrix& V) {
     array<hyperpoint, 6> c;
     hyperpoint ctr;
     for(int i=0; i<6; i++) {
-      hyperpoint h = spin(60*degree*i) * point31(1,0,0);
+      hyperpoint h = spin(TAU*i/6) * point31(1,0,0);
       h[0] += x;
       h[0] += y/2.;
       h[1] += sqrt(3)/2. * y;
diff --git a/rogueviz/hypcity.cpp b/rogueviz/hypcity.cpp
index dc4ac19f..6d170da9 100644
--- a/rogueviz/hypcity.cpp
+++ b/rogueviz/hypcity.cpp
@@ -55,7 +55,7 @@ void prepare_tf() {
       hx[1] = h[1] * t * 2;
       hx[2] = 0;
       hx[3] = 1;
-      if(hyperbolic) hx = spin(45 * degree) * hx;
+      if(hyperbolic) hx = spin(45._deg) * hx;
       hx = normalize(hx);
       hx = zshift(hx, h[2]*(t*(sphere ? 3 : 7)));
 
diff --git a/rogueviz/hyperbolic-analogs.cpp b/rogueviz/hyperbolic-analogs.cpp
index 052c7368..8c3afc44 100644
--- a/rogueviz/hyperbolic-analogs.cpp
+++ b/rogueviz/hyperbolic-analogs.cpp
@@ -29,7 +29,7 @@ vector<reaction_t> models_to_use = {
       pmodel = mdDisk;
       pconf.alpha = 1000;
       pconf.scale *= pconf.alpha;
-      View = cspin(1, 2, 20 * degree) * View;
+      View = cspin(1, 2, 20._deg) * View;
       }
     else {
       pmodel = mdHyperboloid;
@@ -112,7 +112,7 @@ vector<reaction_t> models_to_use = {
     pconf.scale = .5;
     if(sphere) pconf.scale *= 2;
     spherename = "loximuthal projection";
-    pconf.loximuthal_parameter = 15 * degree;
+    pconf.loximuthal_parameter = 15._deg;
     },
   [] {
     pmodel = mdSinusoidal;
@@ -276,13 +276,13 @@ EX void compare() {
   if(at4 == 0)
     earthpart = lerp(255, earthpart, t4);
   else if(at4 == 1)
-    View = spin(t4 * 180 * degree) * View;
+    View = spin(t4 * M_PI) * View;
   else if(at4 == 2)
-    View = xpush(t4 * M_PI) * spin(M_PI) * View;
+    View = xpush(t4 * M_PI) * spin180() * View;
   else if(at4 == 3)
-    View = ypush(t4 * M_PI) * xpush(M_PI) * spin(M_PI) * View;
+    View = ypush(t4 * M_PI) * xpush(M_PI) * spin180() * View;
   else if(at4 == 4) {
-    View = ypush(M_PI) * xpush(M_PI) * spin(M_PI) * View;
+    View = ypush(M_PI) * xpush(M_PI) * spin180() * View;
     earthpart = lerp(255, earthpart, 1-t4);
     }
   anims::moved();
diff --git a/rogueviz/hyperbolic-minesweeper-pres.cpp b/rogueviz/hyperbolic-minesweeper-pres.cpp
index 4f05ffec..4eb2dba8 100644
--- a/rogueviz/hyperbolic-minesweeper-pres.cpp
+++ b/rogueviz/hyperbolic-minesweeper-pres.cpp
@@ -76,7 +76,7 @@ vector<cell*> cl_sphere() {
   vector<cell*> lst;
   auto all = currentmap->allcells();
   for(cell *c: all) {
-    hyperpoint h = spin(45*degree) * currentmap->relative_matrix(c, cs.at, C0) * C0;
+    hyperpoint h = spin(45._deg) * currentmap->relative_matrix(c, cs.at, C0) * C0;
     if(-h[2] < max(abs(h[0]), abs(h[1]))) {
       lst.push_back(c);
       }
@@ -266,9 +266,9 @@ void mine_slide(tour::presmode mode, reaction_t set_geom, function<vector<cell*>
     cwt.at = centerover = starter;
     View = Id;
     if(hyperbolic)
-      View = spin(45*degree) * View;
+      View = spin(45._deg) * View;
     if(sphere) {
-      View = spin(45*degree) * View;
+      View = spin(45._deg) * View;
       slide_backup(pconf.scale, 1000);
       slide_backup(pconf.alpha, 1000);
       slide_backup(modelcolor, 0xFF);
@@ -343,7 +343,7 @@ void enable_earth() {
   texture::config.color_alpha = 255;
   mapeditor::drawplayer = false;
   fullcenter();
-  View = spin(4 * M_PI / 5 + M_PI / 2) * View;
+  View = spin(234._deg) * View;
   }
 
 slide sweeper_slides[] = {
@@ -515,10 +515,10 @@ slide sweeper_slides[] = {
         enable_earth();
       
         View = Id;
-        View = spin(3 * M_PI / 5) * View;
-        View = spin(90*degree) * View;
-        View = cspin(2, 0, 45 * degree) * View;
-        View = cspin(1, 2, 30 * degree) * View;
+        View = spin(108._deg) * View;
+        View = spin(90._deg) * View;
+        View = cspin(2, 0, 45._deg) * View;
+        View = cspin(1, 2, 30._deg) * View;
         playermoved = false;
         tour::slide_backup(vid.axes, 0);
         tour::slide_backup(vid.drawmousecircle, false);
@@ -569,7 +569,7 @@ slide sweeper_slides[] = {
         start_game();
         tour::slide_backup(vid.use_smart_range, 2);
         tour::slide_backup(vid.smart_range_detail, 1);
-        View = spin(90*degree);
+        View = spin90();
         using linepatterns::patTree;
         tour::slide_backup(patTree.color, 0);
         }        
@@ -847,7 +847,7 @@ slide sweeper_slides[] = {
         start_game();
         tour::slide_backup(vid.use_smart_range, 2);
         tour::slide_backup(vid.smart_range_detail, 1);
-        View = spin(90*degree);
+        View = spin90();
         using linepatterns::patTree;
         tour::slide_backup(patTree.color, 0);
         }        
diff --git a/rogueviz/hypocycloid.cpp b/rogueviz/hypocycloid.cpp
index fe19fbf2..16f37518 100644
--- a/rogueviz/hypocycloid.cpp
+++ b/rogueviz/hypocycloid.cpp
@@ -72,9 +72,9 @@ void circ_frame() {
   
   shiftmatrix at = ggmatrix(cwt.at) * xpush(xdist);
   
-  ld kdegree = 2 * M_PI / prec;
+  ld kdegree = TAU / prec;
 
-  ld cs = 2*M_PI*cshift;
+  ld cs = TAU * cshift;
 
   if(shape) {
     auto shapefun = [&] (ld x) {
diff --git a/rogueviz/impossible-ring.cpp b/rogueviz/impossible-ring.cpp
index 19c0c8d2..3d86110d 100644
--- a/rogueviz/impossible-ring.cpp
+++ b/rogueviz/impossible-ring.cpp
@@ -61,12 +61,12 @@ struct iring {
   
     ld delta = 0.004;
     
-    transmatrix T = cspin(1, 2, 45*degree);
+    transmatrix T = cspin(1, 2, 45._deg);
     
     int switchat = nil ? 1024 : 2048;
     
     auto step = [&] (int id) {
-      ld alpha = id * 1. / steps * 2 * M_PI;
+      ld alpha = id * 1. / steps * TAU;
       if(id < switchat)
         return T * point3(cos(alpha) * delta, sin(alpha) * delta, 0);
       else
@@ -113,7 +113,7 @@ struct iring {
 
       hyperpoint uds[3];  
 
-      ld alpha = a * 1. / steps * 2 * M_PI;
+      ld alpha = a * 1. / steps * TAU;
       if(a < switchat) {
         uds[0] = T * point31(sin(alpha) * cscale, -cos(alpha) * cscale, 0) - C0;
         uds[1] = T * point31(0, 0, cscale) - C0;
diff --git a/rogueviz/intra-demos.cpp b/rogueviz/intra-demos.cpp
index 1f4b7386..11c1d74b 100644
--- a/rogueviz/intra-demos.cpp
+++ b/rogueviz/intra-demos.cpp
@@ -237,7 +237,7 @@ void create_intra_120() {
     hyperpoint h = currentmap->get_corner(s, 1);
     for(cell *c: currentmap->allcells()) {
       hyperpoint j = currentmap->relative_matrix(c, s, C0) * C0;
-      if(hdist(h, j) > M_PI/2) c->wall = waPalace;
+      if(hdist(h, j) > 90._deg) c->wall = waPalace;
       }
     for(cell *c: currentmap->allcells()) if(c->wall == waPalace) {
       int nei = 0;
@@ -277,7 +277,7 @@ void create_intra_1440() {
   for(cell *c: currentmap->allcells()) {
     hyperpoint j = currentmap->relative_matrix(c, s, C0) * C0;
     // hyperpoint j = inverse(currentmap->relative_matrix(cwt.at, c, C0)) * C0;
-    if(hdist(h, j) > M_PI/2) 
+    if(hdist(h, j) > 90._deg)
       set_wall(c, (celldistance(c, s)&1) ? 0xFF80FF : 0xFF00FF);
     }
   }
diff --git a/rogueviz/magmahep.cpp b/rogueviz/magmahep.cpp
index 6b45175d..b5a7eee0 100644
--- a/rogueviz/magmahep.cpp
+++ b/rogueviz/magmahep.cpp
@@ -58,7 +58,7 @@ void make() {
   /* compute the vertices */
   vertices.resize(magmav+1);
   for(int i=0; i<=magmav; i++)
-    vertices[i] = spin(2*M_PI*(i+(v-7)/4.)/v) * xpush0(1);
+    vertices[i] = spin(TAU*(i+(v-7)/4.)/v) * xpush0(1);
   ld xx = vertices[2][0];
   
   int down = v/2 + 2;
@@ -196,7 +196,7 @@ void draw_at(transmatrix T, color_t col, int id) {
   if(magmadebug) {
     for(int i=0; i<magmav; i++) {
       hyperpoint h = mid(vertices[i], vertices[i+1]);
-      h += spin(M_PI/2) * (vertices[i+1] - vertices[i]) * .05;
+      h += spin90() * (vertices[i+1] - vertices[i]) * .05;
       queuestr(T * rgpushxto0(h), 0.4, its(i), 0x80);
       }
     queuestr(T * rgpushxto0(hcenter), 0.4, "#"+its(id), 0x80);
diff --git a/rogueviz/newconf.cpp b/rogueviz/newconf.cpp
index ce24db37..c7f3a1f7 100644
--- a/rogueviz/newconf.cpp
+++ b/rogueviz/newconf.cpp
@@ -489,7 +489,7 @@ int redraws;
 
 void redraw_texture() {
   View = Id;
-  if(arcm::in()) View = View * spin(45 * degree);
+  if(arcm::in()) View = View * spin(45._deg);
   dynamicval<int> cgl(vid.cells_generated_limit, 9999999);
   dynamicval<int> cdl(vid.cells_drawn_limit, 9999999);
   dynamicval<bool> r(mousing, false);
@@ -629,7 +629,7 @@ void draw_ncee() {
     period = 2 * hdist0(tC0(currentmap->adj(cwt.at, 0)));
     }
 
-  period *= 2 / M_PI;
+  period /= 90._deg;
   
   dynamicval<eModel> pm(pmodel, mdPixel);
   dynamicval<eGeometry> pg(geometry, gEuclid);
@@ -919,7 +919,7 @@ void ncee() {
     if(uni == 'X') {
       int D = 100;
   
-      fmap = genellipse(D, -10 * degree), reset_vxy();
+      fmap = genellipse(D, -10._deg), reset_vxy();
       #if CAP_NCONF
       nconf_solve(); 
       #endif
diff --git a/rogueviz/nilrider/level.cpp b/rogueviz/nilrider/level.cpp
index f6513256..8ca09f66 100644
--- a/rogueviz/nilrider/level.cpp
+++ b/rogueviz/nilrider/level.cpp
@@ -219,8 +219,8 @@ void level::init_shapes() {
       if(bmch == 'f' && (x&1) && (y&1)) {
         for(int s=0; s<4; s++) {
           hyperpoint st = point3(x+.1, y+.1, 0);
-          hyperpoint a = spin(90*degree*s) * point3(.1, .1, 0);
-          hyperpoint b = spin(90*degree*(s+1)) * point3(.1, .1, 0);
+          hyperpoint a = spin(90._deg*s) * point3(.1, .1, 0);
+          hyperpoint b = spin(90._deg*(s+1)) * point3(.1, .1, 0);
           hyperpoint hi = point3(0, 0, 1);
           for(int z=0; z<3; z++) {
             ld z1 = (3-z) / 3.;
@@ -252,8 +252,8 @@ void level::init_shapes() {
           ld need = safe_alt(ctr, -1) / scale / scale;
           int max_y = need * 2 + 1;
 
-          hyperpoint a = spin(90*degree*s) * point3(1, 0, 0);
-          hyperpoint b = spin(90*degree*s) * point3(0, 1, 0);
+          hyperpoint a = spin(90._deg*s) * point3(1, 0, 0);
+          hyperpoint b = spin(90._deg*s) * point3(0, 1, 0);
           
           auto pt = [&] (ld af, ld bf, ld yf) {
             hyperpoint ha = a * af * scale; ha[3] = 1;
@@ -402,12 +402,12 @@ void level::init() {
     dynamicval<bool> lop1(loaded_or_planned, true);
     dynamicval<bool> lop2(planning_mode, false);
     if(c.tick(this) == b) break;
-    start.heading_angle -= 1 * degree;
+    start.heading_angle -= degree;
     }
 
   if(flags & nrlOrder) {
     sort(triangles.begin(), triangles.end(), [this] (triangledata a, triangledata b) {
-      return atan2(spin(120*degree)*(a.where - start.where)) < atan2(spin(120*degree)*(b.where - start.where));
+      return atan2(spin(120._deg)*(a.where - start.where)) < atan2(spin(120._deg)*(b.where - start.where));
       });
     for(auto t: triangles) println(hlog, t.where);
     }
@@ -419,8 +419,7 @@ xy_float level::get_xy_f(hyperpoint h) {
   if(flags & nrlPolar) {
     tie(h[0], h[1]) = make_pair(atan2(h[0], h[1]), hypot(h[0], h[1]));
     ld bar = (minx + maxx) / 2;
-    while(h[0] < bar - M_PI) h[0] += 2 * M_PI;
-    while(h[0] > bar + M_PI) h[0] -= 2 * M_PI;
+    cyclefix(h[0], bar);
     }
   int tY = isize(map_tiles);
   int tX = isize(map_tiles[0]);
@@ -455,7 +454,7 @@ hyperpoint level::mappt(ld x, ld y, int s) {
   };
 
 void level::init_plan() {
-  plan.emplace_back(start.where, hpxy(cos(start.heading_angle + 90*degree) * 2, sin(start.heading_angle + 90*degree) * 2));
+  plan.emplace_back(start.where, hpxy(cos(start.heading_angle + 90._deg) * 2, sin(start.heading_angle + 90._deg) * 2));
   current = start;
   }
 
diff --git a/rogueviz/nilrider/levels.cpp b/rogueviz/nilrider/levels.cpp
index 9b569322..9b443915 100644
--- a/rogueviz/nilrider/levels.cpp
+++ b/rogueviz/nilrider/levels.cpp
@@ -62,7 +62,7 @@ ld geodesics_0(hyperpoint h) {
   ld r = hypot_d(2, h);
   ld phi = atan2(h[1], h[0]);
   
-  ld z = (phi / 2 / M_PI) * (M_PI * r * r + 2 * M_PI);
+  ld z = (phi / TAU) * (M_PI * r * r + TAU);
   return z + rot_plane(h);
   }
 
@@ -70,7 +70,7 @@ ld geodesics_at_4(hyperpoint h) {
   ld r = 4;
   ld phi = atan2(h[1], h[0]);
   
-  ld z = (phi / 2 / M_PI) * (M_PI * r * r + 2 * M_PI);
+  ld z = (phi / TAU) * (M_PI * r * r + TAU);
   return z + rot_plane(h);
   }
 
@@ -381,7 +381,7 @@ level geodesical(
   "light rays are assumed to be geodesics.\n\n"
   "Geodesics in Nil are horizontal, vertical, and helical. "
   "In this level, all the roads are (fragments of) helical geodesics.",
-  -45*degree, 3*dft_block, 225*degree, 0,
+  -45._deg, 3*dft_block, 225._deg, 0,
   // -8*dft_block, +8*dft_block, +8*dft_block, 0, 
   {
   "ffffffffffffffff",
@@ -404,7 +404,7 @@ level geodesical(
 level geodesical4(
   "Helical Geodesic", 's', nrlPolar,
   "The main road here is a helical geodesic. Orthogonal lines are horizontal.",  
-  -80*degree, 8.5*dft_block, 260*degree, 0.5*dft_block,
+  -80._deg, 8.5*dft_block, 260._deg, 0.5*dft_block,
   // -8*dft_block, +8*dft_block, +8*dft_block, 0, 
   {
   "!!!!!!!!!!!!!!!!",
@@ -560,10 +560,9 @@ struct complex_surface {
     auto d = hypot_d(2, h1);
     ld r = 2;
     h1 = h1 * (r / d);
-    ld phi = atan2(h1[1], h1[0]) + 90*degree;
-    ld phis = atan2((start-ctr)[1], (start-ctr)[0]) + 90 * degree;
-    if(phi < phis-M_PI) phi += 2 * M_PI;
-    if(phi > phis+M_PI) phi -= 2 * M_PI;
+    ld phi = atan2(h1[1], h1[0]) + 90._deg;
+    ld phis = atan2((start-ctr)[1], (start-ctr)[0]) + 90._deg;
+    cyclefix(phi, phis);
     h1 += ctr;
     auto z = [&] (ld a) { return point31(r*sin(a), -r*cos(a), (r * r / 2) * (a-sin(a)*cos(a))); };
 
@@ -577,11 +576,11 @@ struct complex_surface {
     hyperpoint h2 = h; if(start[0] == ctr[0]) h2[1] = start[1]; else h2[0] = start[0];
     hyperpoint pre = rgpushxto0(start) * flatpush(h2-start) * flatpush(h-h2) * C0;
 
-    hyperpoint last = rgpushxto0(start) * gpushxto0(z(phis)) * rgpushxto0(z(phis + dir * 90*degree)) * C0;
+    hyperpoint last = rgpushxto0(start) * gpushxto0(z(phis)) * rgpushxto0(z(phis + dir * 90._deg)) * C0;
     hyperpoint h3 = h; if(start[0] != ctr[0]) h3[1] = last[1]; else h3[0] = last[0];
     hyperpoint post = rgpushxto0(last) * flatpush(h3-last) * flatpush(h-h3) * C0;
 
-    ld p = (1+sin((phi-phis)*2 - 90*degree)) / 2.;
+    ld p = (1+sin((phi-phis)*2 - 90._deg)) / 2.;
 
     pre[2] = pre[2] + (post[2] - pre[2]) * p;
 
diff --git a/rogueviz/nilrider/nilrider.cpp b/rogueviz/nilrider/nilrider.cpp
index ceec52a5..13403d95 100644
--- a/rogueviz/nilrider/nilrider.cpp
+++ b/rogueviz/nilrider/nilrider.cpp
@@ -104,8 +104,8 @@ bool turn(int delta) {
     }
   #endif
 
-  if(min_gfx_slope < -90*degree) min_gfx_slope = -90*degree;
-  if(min_gfx_slope > +90*degree) min_gfx_slope = +90*degree;
+  if(min_gfx_slope < -90._deg) min_gfx_slope = -90._deg;
+  if(min_gfx_slope > +90._deg) min_gfx_slope = +90._deg;
   
   backing = false;
 
@@ -659,7 +659,7 @@ auto celldemo = arg::add3("-unilcycle", initialize) + arg::add3("-unilplan", []
     ->editable(0, 5, 0.05, "camera distance", "how far is the unicycle from the camera", 'd')
     ->set_reaction([] { curlev->current.centerview(curlev); });
     param_f(min_gfx_slope, "min_gfx_slope")
-    ->editable(-90*degree, 90*degree, degree, "min camera slope", "affected by up/down", 'm');
+    ->editable(-90._deg, 90._deg, degree, "min camera slope", "affected by up/down", 'm');
     })
   + arg::add3("-fullsim", [] {
     /* for animations */
diff --git a/rogueviz/nilrider/nilrider.h b/rogueviz/nilrider/nilrider.h
index 867f7389..d0c96cb7 100644
--- a/rogueviz/nilrider/nilrider.h
+++ b/rogueviz/nilrider/nilrider.h
@@ -200,7 +200,7 @@ inline ld gravity = 1 / 16.;
 inline ld whdist = 0.5;
 
 /** minimum slope for rendering */
-inline ld min_gfx_slope = +M_PI/2;
+inline ld min_gfx_slope = +90._deg;
 
 /** current slope for rendering */
 inline ld gfx_slope = 0;
diff --git a/rogueviz/nilrider/statues.cpp b/rogueviz/nilrider/statues.cpp
index 47a01eba..c0a5b513 100644
--- a/rogueviz/nilrider/statues.cpp
+++ b/rogueviz/nilrider/statues.cpp
@@ -95,8 +95,8 @@ bool closed_grid(int x, int y) {
 
 template<class T1, class T2> void add_statue(const T1& grid, const T2& f) {
   auto pt = [&] (int x, int y) {
-    ld x1 = x * M_PI / 16.;
-    ld y1 = y * M_PI / 32.;
+    ld x1 = x * TAU / 32;
+    ld y1 = y * TAU / 64;
     cgi.hpcpush(f(x1,y1));
     };
   for(int y=-16; y<16; y++)
@@ -130,7 +130,7 @@ void init_statues() {
   for(int i=0; i<8; i++) {
     hyperpoint z = point31(0, 1e-6, 8);
     hyperpoint ih = inverse_exp(shiftless(z));
-    ih = spin(i * 45 * degree) * ih;
+    ih = spin(i * TAU / 8) * ih;
     add_statue(closed_grid, [&] (ld lon, ld lat) {
       lat = lat * .75;
       hyperpoint h = direct_exp(ih * (.5 + lat / M_PI));
@@ -141,7 +141,7 @@ void init_statues() {
   cgi.extra_vertices();
   cgi.add_texture(shGeostatue);
 
-  for(ld z: vector<ld> {M_PI/2+1e-2, M_PI+1e-2, M_PI*2+1e-2, 7, 10})
+  for(ld z: vector<ld> {90._deg+1e-2, M_PI+1e-2, TAU+1e-2, 7, 10})
   for(hyperpoint h: {point31(0, 0, z), point31(1e-3, 0, z), point31(1e-6, 0, z), point31(0, 1e-6, z)}) {
     hyperpoint i = inverse_exp(shiftless(h));
     println(hlog, i, " @ ", hypot_d(3, i));
diff --git a/rogueviz/nilrider/timestamp.cpp b/rogueviz/nilrider/timestamp.cpp
index b8fb06ee..d18f0be0 100644
--- a/rogueviz/nilrider/timestamp.cpp
+++ b/rogueviz/nilrider/timestamp.cpp
@@ -25,7 +25,7 @@ void timestamp::draw_unilcycle(const shiftmatrix& V) {
   hyperpoint base = Ta * Tb * point31(0, 0, whrad);
   
   for(int a=0; a<points; a++) {
-    ld beta = 360 * degree * a / points + circpos;
+    ld beta = TAU * a / points + circpos;
     whpoint[a] = base + Ta * point3(whrad*sin(beta),0,whrad*cos(beta));
     }
   whpoint[points] = whpoint[0];
@@ -116,7 +116,7 @@ bool timestamp::collect(level *lev) {
 /* convert heading to integral units, to make saved replays consistent */
 
 constexpr ld h_units = 360 * 60 * 60;
-constexpr ld h_mul = h_units / 2 / M_PI;
+constexpr ld h_mul = h_units / TAU;
 
 int heading_to_int(ld a) {
   a = a * h_mul;
@@ -252,7 +252,7 @@ void timestamp::draw_instruments(level* l) {
   curvepoint(hpxy(0, rad));
   curvepoint(hpxy(-rad/4, 0));  
   curvepoint(hpxy(rad/4, 0));
-  queuecurve(sId * atscreenpos(cx, cy, pix) * spin(90 * degree + slope), 0xFF, 0x40C040FF, PPR::ZERO);
+  queuecurve(sId * atscreenpos(cx, cy, pix) * spin(90._deg + slope), 0xFF, 0x40C040FF, PPR::ZERO);
 
   // compass
   
diff --git a/rogueviz/pentagonal.cpp b/rogueviz/pentagonal.cpp
index 0219685a..c7263fc7 100644
--- a/rogueviz/pentagonal.cpp
+++ b/rogueviz/pentagonal.cpp
@@ -156,7 +156,7 @@ void run_snub(int v, int w) {
   for(cell *c: currentmap->allcells()) {
     int id = arcm::id_of(c->master);
     if(among(id, 0, 1)) for(int d=0; d<v; d++) {
-      transmatrix T = rel * ggmatrix(c).T * spin(2*M_PI*d/v);
+      transmatrix T = rel * ggmatrix(c).T * spin(TAU*d/v);
       array<hyperpoint,3> hts;
       for(int i=0; i<3; i++) 
         hts[i] = T * ts[i] * C0;
@@ -213,12 +213,12 @@ void create_model() {
   hyperpoint chk = ts[0] * xspinpush0(alpha, h);
 
   mts[0] = chk;
-  mts[1] = spin(-2*M_PI/v) * chk;
+  mts[1] = spin(-TAU/v) * chk;
   mts[2] = matrix2 * chk;
 
   hyperpoint c[5];
   for(int i=0; i<5; i++)
-    c[i] = hpxy(sin(2 * i * M_PI/5), cos(2 * i * M_PI/5));
+    c[i] = hpxy(sin(i * TAU/5), cos(i * TAU/5));
     
   hyperpoint tria[5];
   tria[0] = mts[0];
@@ -256,7 +256,7 @@ void create_model() {
   
   // printf("createmodel with ticks = %d\n", ticks);
 
-  transmatrix t = hyperbolic ? hr::cspin(0, 2, M_PI) * xpush(sin(ticks * M_PI * 2 / anims::period)) : hr::cspin(0, 2, ticks * M_PI * 2 / anims::period);
+  transmatrix t = hyperbolic ? hr::cspin180(0, 2) * xpush(sin(ticks * TAU / anims::period)) : hr::cspin(0, 2, ticks * TAU / anims::period);
   
   hyperpoint hs = hyperbolic ? hpxyz(0,0,-1) : hpxyz(0,0,0);
   
diff --git a/rogueviz/pentaroll.cpp b/rogueviz/pentaroll.cpp
index 6375c899..d0791c17 100644
--- a/rogueviz/pentaroll.cpp
+++ b/rogueviz/pentaroll.cpp
@@ -112,7 +112,7 @@ void animate() {
   
   /* set_view does not orient correctly, so we rotate it */
   
-  View = cspin(2, 0, M_PI/2) * View;
+  View = cspin90(2, 0) * View;
   
   /* we move the camera backward */
 
diff --git a/rogueviz/plane-immersion.cpp b/rogueviz/plane-immersion.cpp
index 3d142308..9da6dfdd 100644
--- a/rogueviz/plane-immersion.cpp
+++ b/rogueviz/plane-immersion.cpp
@@ -19,8 +19,8 @@ color_t gridcol = 0xFFFFFFFF;
 hyperpoint fp(ld x, ld y) {
   x *= scale;
   y *= scale;
-  x *= M_PI/10 * sqrt(2)/2;
-  y *= M_PI/10 * sqrt(2)/2;
+  x *= A_PI/10 * sqrt(2)/2;
+  y *= A_PI/10 * sqrt(2)/2;
   if(euclid)
     return hyperpoint(x, y, 0, 1);
   
@@ -28,12 +28,12 @@ hyperpoint fp(ld x, ld y) {
     ld a = sqrt(2)/2;
     x /= a;
     y /= a;
-    hyperpoint h = cspin(2, 3, -M_PI/4) * hyperpoint(sin(x)*a, sin(y)*a, cos(x)*a, cos(y)*a);
+    hyperpoint h = cspin(2, 3, -45._deg) * hyperpoint(sin(x)*a, sin(y)*a, cos(x)*a, cos(y)*a);
     return h;
     }
 
   if(hyperbolic)
-    return cspin(0, 2, -M_PI/2) * tC0(parabolic13(x, y));
+    return cspin90(2, 0) * tC0(parabolic13(x, y));
   
   if(nil)
     return hyperpoint(0, y, x, 1);
@@ -45,7 +45,7 @@ hyperpoint fp(ld x, ld y) {
     ld a = sqrt(2)/2;
     x /= a;
     y /= a;
-    hyperpoint h = cspin(2, 3, -M_PI/4) * hyperpoint(sinh(x)*a, sinh(y)*a, cosh(x)*a, cosh(y)*a);
+    hyperpoint h = cspin(2, 3, -45._deg) * hyperpoint(sinh(x)*a, sinh(y)*a, cosh(x)*a, cosh(y)*a);
     return h;
     }
 
@@ -90,16 +90,16 @@ void relocate() {
   
   vid.fixed_yz = false;
   
-  if(nil) rotate_view(cspin(2, 0, M_PI/2));
-  if(prod) rotate_view(cspin(1, 2, M_PI/2));
+  if(nil) rotate_view(cspin90(2, 0));
+  if(prod) rotate_view(cspin90(1, 2));
 
   if(emba == 1) {  
-    rotate_view(cspin(0, 1, M_PI/4));
-    rotate_view(cspin(1, 2, M_PI/6));
+    rotate_view(cspin(0, 1, 45._deg));
+    rotate_view(cspin(1, 2, 30._deg));
     }
   
   if(emba == 2) {
-    rotate_view(cspin(1, 2, M_PI/2 * .9));
+    rotate_view(cspin(1, 2, 81._deg));
     }
   
   for(int a=0; a<100; a++) 
diff --git a/rogueviz/planets.cpp b/rogueviz/planets.cpp
index ddf20f9c..49ce418d 100644
--- a/rogueviz/planets.cpp
+++ b/rogueviz/planets.cpp
@@ -239,7 +239,7 @@ ld prec = 5;
 void draw_earth() {
   load_planets();
 
-  shiftmatrix S = ggmatrix(currentmap->gamestart()) * spin(90*degree);
+  shiftmatrix S = ggmatrix(currentmap->gamestart()) * spin90();
 
   ld mte = radius[src_planet] / radius[tgt_planet];
   
@@ -425,7 +425,7 @@ EX void compare() {
       dark = dark * dark * (3-2*dark);
       }
     alpha = dark * max_alpha;
-    View = cspin(0, 2, (rot - lrot) * 2 * M_PI) * View;
+    View = cspin(0, 2, (rot - lrot) * TAU) * View;
     lrot = rot;
     anims::moved();
     }
diff --git a/rogueviz/platformer.cpp b/rogueviz/platformer.cpp
index 2ad0c33c..a567eb99 100644
--- a/rogueviz/platformer.cpp
+++ b/rogueviz/platformer.cpp
@@ -85,12 +85,12 @@ hyperpoint to_hyper(ld x, ld y) {
   y -= 1;
   hyperpoint h;
   h[0] = -x; h[1] = y; h[2] = 1;
-  h = spin(-90*degree) * h;
+  h = spin270() * h;
   return perspective_to_space(h, 1, gcHyperbolic);
   }
 
 pair<ld, ld> from_hyper(hyperpoint h) {
-  h = spin(+90*degree) * h; h[0] = -h[0];
+  h = spin90() * h; h[0] = -h[0];
   h[2] += 1;
   h /= h[2];
 
diff --git a/rogueviz/playing-with-impossibility.cpp b/rogueviz/playing-with-impossibility.cpp
index 94c48a07..b38bebf1 100644
--- a/rogueviz/playing-with-impossibility.cpp
+++ b/rogueviz/playing-with-impossibility.cpp
@@ -120,7 +120,7 @@ void nil_screen(presmode mode, int id) {
       else t = floor(t) + 2 * (t - floor(t));
       t -= floor(t/4)*4;
       
-      ld t2 = 90 * degree * t;
+      ld t2 = 90._deg * t;
       
       curvepoint(p2(0,0));
       curvepoint(p2(5,5));
@@ -144,7 +144,7 @@ void nil_screen(presmode mode, int id) {
     if(id < 3) {
 
       if(id == 2) {
-        drawMonsterType(moEagle, nullptr, g.pos(5,5,1.5) * spin(-t * 90 * degree) * xyzscale(1.5), 0x40C040, ticks / 1000., 0);
+        drawMonsterType(moEagle, nullptr, g.pos(5,5,1.5) * spin(-t * 90._deg) * xyzscale(1.5), 0x40C040, ticks / 1000., 0);
         }
     
       color_t dark = 0xFF;
@@ -305,7 +305,7 @@ void geodesic_screen(presmode mode, int id) {
     // flat_model_enabler fme;
     initquickqueue();
 
-    dmv_grapher g(MirrorZ * cspin(1, 2, .3 * angle / (M_PI/2)) * spin(angle/2));
+    dmv_grapher g(MirrorZ * cspin(1, 2, .3 * angle / 90._deg) * spin(angle/2));
     
     ld val = 25;
     
@@ -320,7 +320,7 @@ void geodesic_screen(presmode mode, int id) {
     ld rrh = radh * sqrt(1/2.);
     
     ld zmove = val - M_PI * radh * radh;
-    ld len = hypot(2 * M_PI * radh, zmove);
+    ld len = hypot(TAU * radh, zmove);
     
     ld t = inHighQual ? ticks / 1000. : (ticks - geo_zero) / 500;
 
@@ -334,7 +334,7 @@ void geodesic_screen(presmode mode, int id) {
       queuecurve(g.T, col, 0, PPR::LINE);
       
       auto be_shadow = [&] (hyperpoint& h) {
-        // ld part = 1 - angle / (M_PI / 2);
+        // ld part = 1 - angle / 90._deg;
         // h[0] += h[2] * part / 10;
         h[2] = 0;
         };
@@ -396,8 +396,8 @@ void geodesic_screen(presmode mode, int id) {
 
     if(id >= 2) 
       draw_path([&] (ld t) { 
-        ld tx = min(t, 2 * M_PI * rad);
-        ld ta = tx / rad - 135 * degree;
+        ld tx = min(t, TAU * rad);
+        ld ta = tx / rad - 135._deg;
         ld x = rr + rad * cos(ta);
         ld y = rr + rad * sin(ta);
         ld z = rad * tx / 2 - ((rr * x) - (rr * y)) / 2;
@@ -407,10 +407,10 @@ void geodesic_screen(presmode mode, int id) {
     if(id >= 3)
       draw_path([&] (ld t) { 
         ld tx = min(t, len);
-        ld ta = tx / len * 2 * M_PI - 135 * degree;
+        ld ta = tx / len * TAU - 135._deg;
         ld x = rrh + radh * cos(ta);
         ld y = rrh + radh * sin(ta);
-        ld z = radh * radh * (tx/len*2*M_PI) / 2 - ((rrh * x) - (rrh * y)) / 2 + zmove * tx / len;
+        ld z = radh * radh * (tx/len*TAU) / 2 - ((rrh * x) - (rrh * y)) / 2 + zmove * tx / len;
         
         return point31(x, y, z);
         }, helix);
@@ -447,7 +447,7 @@ void geodesic_screen(presmode mode, int id) {
     if(id >= 2) {
       dialog::addBreak(100);
       dialog_may_latex("\\textsf{circle}", "circle", circle >> 8);
-      dialog_may_latex("$"+fts(2 * M_PI * rad)+"$", fts(2 * M_PI * rad), circle >> 8);
+      dialog_may_latex("$"+fts(TAU * rad)+"$", fts(TAU * rad), circle >> 8);
       }
     else dialog::addBreak(300);
 
@@ -553,7 +553,7 @@ void impossible_ring_slide(tour::presmode mode) {
     for(int id=0; id<2; id++) {
       shiftmatrix T = ggmatrix(currentmap->gamestart());
       println(hlog, "angle = ", angle);
-      if(id == 1) T = T * spin(180*degree) * xpush(1.5) * cspin(0, 2, angle) * xpush(-1.5);
+      if(id == 1) T = T * spin180() * xpush(1.5) * cspin(0, 2, angle) * xpush(-1.5);
       
       for(ld z: {+.5, -.5}) {
         for(ld d=0; d<=180; d++)
@@ -599,7 +599,7 @@ void enable_earth() {
   texture::config.color_alpha = 255;
   mapeditor::drawplayer = false;
   fullcenter();
-  View = spin(4 * M_PI / 5 + M_PI / 2) * View;
+  View = spin(234._deg) * View;
   }
 
 slide dmv_slides[] = {
@@ -647,8 +647,8 @@ slide dmv_slides[] = {
         shiftmatrix T = ggmatrix(currentmap->gamestart());
         vid.linewidth *= 4;
         shiftpoint h1 = T * xspinpush0(0, 2);
-        shiftpoint h2 = T * xspinpush0(120*degree, 2);
-        shiftpoint h3 = T * xspinpush0(240*degree, 2);
+        shiftpoint h2 = T * xspinpush0(120._deg, 2);
+        shiftpoint h3 = T * xspinpush0(240._deg, 2);
         queueline(h1, h2, 0xFF0000FF, 4);
         queueline(h2, h3, 0xFF0000FF, 4);
         queueline(h3, h1, 0xFF0000FF, 4);
@@ -669,21 +669,21 @@ slide dmv_slides[] = {
         enable_earth();
       
         View = Id;
-        View = spin(3 * M_PI / 5) * View;
-        View = spin(90*degree) * View;
-        View = cspin(2, 0, 45 * degree) * View;
-        View = cspin(1, 2, 30 * degree) * View;
+        View = spin(108._deg) * View;
+        View = spin(90._deg) * View;
+        View = cspin(2, 0, 45._deg) * View;
+        View = cspin(1, 2, 30._deg) * View;
         playermoved = false;
         tour::slide_backup(vid.axes, 0);
         tour::slide_backup(vid.drawmousecircle, false);
         tour::slide_backup(draw_centerover, false);
         }
       add_temporary_hook(mode, hooks_frame, 200, [] {
-        shiftmatrix T = ggmatrix(currentmap->gamestart()) * spin(-3 * M_PI / 5);
+        shiftmatrix T = ggmatrix(currentmap->gamestart()) * spin(-108._deg);
         vid.linewidth *= 4;
         shiftpoint h1 = T * C0;
-        shiftpoint h2 = T * xpush0(M_PI/2);
-        shiftpoint h3 = T * ypush0(M_PI/2);
+        shiftpoint h2 = T * xpush0(90._deg);
+        shiftpoint h3 = T * ypush0(90._deg);
         queueline(h1, h2, 0xFF0000FF, 3);
         queueline(h2, h3, 0xFF0000FF, 3);
         queueline(h3, h1, 0xFF0000FF, 3);
@@ -734,8 +734,8 @@ slide dmv_slides[] = {
         shiftmatrix T = ggmatrix(currentmap->gamestart());
         vid.linewidth *= 16;
         shiftpoint h1 = T * xspinpush0(0, 2);
-        shiftpoint h2 = T * xspinpush0(120*degree, 2);
-        shiftpoint h3 = T * xspinpush0(240*degree, 2);
+        shiftpoint h2 = T * xspinpush0(120._deg, 2);
+        shiftpoint h3 = T * xspinpush0(240._deg, 2);
         queueline(h1, h2, 0xFF0000FF, 4);
         queueline(h2, h3, 0xFF0000FF, 4);
         queueline(h3, h1, 0xFF0000FF, 4);
@@ -1270,7 +1270,7 @@ slide dmv_slides[] = {
         rogueviz::balls::initialize(1);
         rogueviz::balls::balls.resize(3);
         pmodel = mdEquidistant;
-        View = cspin(1, 2, M_PI/2);
+        View = cspin90(1, 2);
         }
       non_game_slide_scroll(mode);
       }
diff --git a/rogueviz/presentation.cpp b/rogueviz/presentation.cpp
index 8da015a4..3a1f1248 100644
--- a/rogueviz/presentation.cpp
+++ b/rogueviz/presentation.cpp
@@ -46,8 +46,8 @@ void grapher::arrow(hyperpoint h1, hyperpoint h2, ld sca, color_t col) {
   ld siz = hypot_d(2, h);
   h *= sca / siz;
   curvepoint(h2);
-  curvepoint(h2 - spin(15*degree) * h);
-  curvepoint(h2 - spin(-15*degree) * h);
+  curvepoint(h2 - spin(15._deg) * h);
+  curvepoint(h2 - spin(-15._deg) * h);
   curvepoint(h2);
   queuecurve(T, col, col, PPR::LINE);
   }
@@ -429,7 +429,7 @@ void use_angledir(presmode mode, bool reset) {
     angle = 0, dir = -1;
   add_temporary_hook(mode, shmup::hooks_turn, 200, [] (int i) {
     angle += dir * i / 500.;
-    if(angle > M_PI/2) angle = M_PI/2;
+    if(angle > 90._deg) angle = 90._deg;
     if(angle < 0) angle = 0;
     return false;
     });
diff --git a/rogueviz/qtm.cpp b/rogueviz/qtm.cpp
index a3b6d5f0..670c2b2c 100644
--- a/rogueviz/qtm.cpp
+++ b/rogueviz/qtm.cpp
@@ -25,7 +25,7 @@ int qmode;
 
 color_t rainbow_color_at(hyperpoint h) {
   ld sat = 1 - 1 / h[2];
-  ld hue = atan2(h[0], h[1]) / (2 * M_PI);
+  ld hue = atan2(h[0], h[1]) / TAU;
   return rainbow_color(sat, hue);
   }
   
diff --git a/rogueviz/random-walk.cpp b/rogueviz/random-walk.cpp
index 7636eb95..4b57635d 100644
--- a/rogueviz/random-walk.cpp
+++ b/rogueviz/random-walk.cpp
@@ -71,7 +71,7 @@ bool advance_walkers(int delta) {
       auto& w = walkers[i];
       hyperpoint h = tC0(w.T);
       if(WDIM == 2) {
-        w.T = w.T * xspinpush(randd() * 2 * M_PI, step_size);
+        w.T = w.T * xspinpush(randd() * TAU, step_size);
         }
       else {
         hyperpoint dir = random_spin() * xtangent(step_size);
diff --git a/rogueviz/reverb.cpp b/rogueviz/reverb.cpp
index 4b5e1eba..b5d1364c 100644
--- a/rogueviz/reverb.cpp
+++ b/rogueviz/reverb.cpp
@@ -204,7 +204,7 @@ bool draw_bird(cell *c, const transmatrix& V) {
       id++; if(id == isize(orig)) id = 0;
       }
     id = tot * WINGS / maxvol / 2;
-    queuepoly(rgpushxto0(tC0(V)) * cspin(0, 2, M_PI/2) * cspin(1, 2, 90 * degree) * cspin(0, 2, 45 * degree),
+    queuepoly(rgpushxto0(tC0(V)) * cspin90(0, 2) * cspin90(1, 2) * cspin(0, 2, 45._deg),
        GDIM == 3 ? cgi.shAnimatedTinyEagle[id] : cgi.shTinyBird, 0xFFFFFFFF
        ); 
     }
@@ -312,9 +312,9 @@ auto hchook = addHook(hooks_drawcell, 100, draw_bird)
   hyperpoint h = all[int(id)] * (1-id+int(id)) + all[int(id+1)] * (id-int(id));
   h = normalize(h);
   centerover = currentmap->gamestart();
-  View = /* cspin(2, 0, M_PI/2) * rspintox(gpushxto0(h) * C0) * */ gpushxto0(h);
+  View = /* cspin90(2, 0) * rspintox(gpushxto0(h) * C0) * */ gpushxto0(h);
   View = spintox(View * C0) * View;
-  View = cspin(2, 0, M_PI/2) * View;
+  View = cspin90(2, 0) * View;
 
   shift_view(point3(0, 0, -1e-2));
 
diff --git a/rogueviz/sample.cpp b/rogueviz/sample.cpp
index 02b544c1..3dca503d 100644
--- a/rogueviz/sample.cpp
+++ b/rogueviz/sample.cpp
@@ -16,8 +16,8 @@ bool draw_simple_scene() {
   shiftmatrix Where = ggmatrix(currentmap->gamestart());
 
   curvepoint(xpush0(0.2));
-  curvepoint(spin(120*degree) * xpush0(0.2));
-  curvepoint(spin(240*degree) * xpush0(0.2));
+  curvepoint(spin(120._deg) * xpush0(0.2));
+  curvepoint(spin(240._deg) * xpush0(0.2));
   curvepoint(xpush0(0.2));
   
   queuecurve(Where, 0xFF0000FF, 0x00FF00FF, PPR::LINE);
diff --git a/rogueviz/simple-impossible.cpp b/rogueviz/simple-impossible.cpp
index 57c908de..95640e52 100644
--- a/rogueviz/simple-impossible.cpp
+++ b/rogueviz/simple-impossible.cpp
@@ -180,7 +180,7 @@ void draw_ro() {
 vector<hyperpoint> path;
 
 void build(bool in_pair) {
-  to_iso = cspin(1, 2, atan(1/sqrt(2))) * cspin(0, 2, M_PI/4);
+  to_iso = cspin(1, 2, atan(1/sqrt(2))) * cspin(0, 2, 45._deg);
   from_iso = inverse(to_iso);
   
   last_co = euc::coord(0, 0, 3);
@@ -242,7 +242,7 @@ void build(bool in_pair) {
   }
 
 void build_net() {
-  to_iso = cspin(1, 2, atan(1/sqrt(2))) * cspin(0, 2, M_PI/4);
+  to_iso = cspin(1, 2, atan(1/sqrt(2))) * cspin(0, 2, 45._deg);
   from_iso = inverse(to_iso);
   
   last_co = euc::coord(0, 0, 0);
@@ -315,22 +315,22 @@ void build_stair() {
           hs[3] = point31(+xx, -xx, -hei);
           }
         else if(dix == 3 || (dix == 2 && step == 0) || (dix == 1 && step > 0)) {
-          transmatrix T = spin(90*degree*diy);
+          transmatrix T = spin(90._deg*diy);
           hs[0] = T * point31(+xx, -xx, -hei);
           hs[1] = T * point31(+xx, +xx, -hei);
           hs[2] = T * point31(+xx, +xx, +hei);
           hs[3] = T * point31(+xx, -xx, +hei);
           }
         else if(dix == 0) {
-          transmatrix T = spin(90*degree*diy);
+          transmatrix T = spin(90._deg*diy);
           hs[0] = T * point31(+xx, -xx, -hei);
           hs[1] = T * point31(+xx, +xx, -hei);
           hs[2] = to_rot(eupush(C0 + shift) * to_heis(T * point31(-xx, +xx, -hei)));
           hs[3] = to_rot(eupush(C0 + shift) * to_heis(T * point31(-xx, -xx, -hei)));
           }
         else {
-          transmatrix T = spin(90*degree*diy);
-          hyperpoint lshift = step ? shift : spin(-90*degree) * shift;
+          transmatrix T = spin(90._deg*diy);
+          hyperpoint lshift = step ? shift : spin270() * shift;
           hs[0] = to_rot(eupush(C0 - lshift) * to_heis(T * point31(-xx, +xx, hei)));
           hs[1] = to_rot(eupush(C0 - lshift) * to_heis(T * point31(-xx, -xx, hei)));
           hs[2] = T * point31(+xx, -xx, hei);
@@ -343,7 +343,7 @@ void build_stair() {
       at = eupush(at) * (C0 + shift);
       }
     
-    shift = spin(90*degree) * shift;
+    shift = spin90() * shift;
     }
   
   println(hlog, "path = ", path);
diff --git a/rogueviz/smoothcam.cpp b/rogueviz/smoothcam.cpp
index 05c665ad..ad42df72 100644
--- a/rogueviz/smoothcam.cpp
+++ b/rogueviz/smoothcam.cpp
@@ -281,22 +281,22 @@ void snap_to_center() {
 
   dialog::addItem("mouse up", 'w');
   dialog::add_action([] {
-    View = spin(90*degree) * spintox(unshift(mapeditor::mouse_snap())) * View;
+    View = spin90() * spintox(unshift(mapeditor::mouse_snap())) * View;
     });
 
   dialog::addItem("mouse down", 's');
   dialog::add_action([] {
-    View = spin(-90*degree) * spintox(unshift(mapeditor::mouse_snap())) * View;
+    View = spin270() * spintox(unshift(mapeditor::mouse_snap())) * View;
     });
 
   dialog::addItem("mouse left", 'a');
   dialog::add_action([] {
-    View = spin(180*degree) * spintox(unshift(mapeditor::mouse_snap())) * View;
+    View = spin180() * spintox(unshift(mapeditor::mouse_snap())) * View;
     });
 
   dialog::addItem("mouse left", 'd');
   dialog::add_action([] {
-    View = spin(0*degree) * spintox(unshift(mapeditor::mouse_snap())) * View;
+    View = Id * spintox(unshift(mapeditor::mouse_snap())) * View;
     });
 
   dialog::addBack();
diff --git a/rogueviz/som/embeddings.cpp b/rogueviz/som/embeddings.cpp
index cc266d0c..38fd8d6e 100644
--- a/rogueviz/som/embeddings.cpp
+++ b/rogueviz/som/embeddings.cpp
@@ -93,7 +93,7 @@ ld hrandd() {
 ld gaussian_random() {
   ld u1 = hrandd();
   ld u2 = hrandd();
-  return sqrt(-2*log(u1)) * cos(2*M_PI*u2);
+  return sqrt(-2*log(u1)) * cos(TAU*u2);
   }
 
 void apply_delta(cellwalker cw, kohvec& v) {
@@ -226,9 +226,9 @@ void get_coordinates(kohvec& v, cell *c, cell *c0) {
         alloc(v);
         int s = T0[0][0];
         for(int i=0; i<3; i++) {
-          hyperpoint h1 = spin(120*degree*i) * h;
+          hyperpoint h1 = spin(120._deg*i) * h;
           ld x = h1[1];
-          ld alpha = 2 * M_PI * x / s / (sqrt(3) / 2);
+          ld alpha = TAU * x / s / (sqrt(3) / 2);
           // println(hlog, kz(x), " -> ", kz(alpha));
           v[2*i] = cos(alpha);
           v[2*i+1] = sin(alpha);
@@ -250,7 +250,7 @@ void get_coordinates(kohvec& v, cell *c, cell *c0) {
         auto& T0 = eu_input.user_axes;
         for(int i=0; i<3; i++) {
           int s = T0[i][i];
-          ld alpha = 2 * M_PI * h[i] / s;
+          ld alpha = TAU * h[i] / s;
           v[2*i] = cos(alpha) * s;
           v[2*i+1] = sin(alpha) * s;
           }
diff --git a/rogueviz/som/kohonen.cpp b/rogueviz/som/kohonen.cpp
index 2f33710c..e0f48d6b 100644
--- a/rogueviz/som/kohonen.cpp
+++ b/rogueviz/som/kohonen.cpp
@@ -358,7 +358,7 @@ void distribute_neurons() {
     
     if(!triangulate(data[s].val, w, find, vdata[id].m->at))
       vdata[id].m->at = 
-        spin(2*M_PI*w.csample / w.drawn_samples) * xpush(rad * (w.drawn_samples-1) / w.drawn_samples);
+        spin(TAU*w.csample / w.drawn_samples) * xpush(rad * (w.drawn_samples-1) / w.drawn_samples);
     w.csample++;
     for(auto& e: vdata[id].edges) e.second->orig = nullptr;
     }
diff --git a/rogueviz/som/tests.cpp b/rogueviz/som/tests.cpp
index eadf9f7c..e6c834bf 100644
--- a/rogueviz/som/tests.cpp
+++ b/rogueviz/som/tests.cpp
@@ -735,7 +735,7 @@ void shot_settings() {
   brm_limit = GDIM == 2 ? 1000 : 0;
   
   if(GDIM == 3)
-    View = cspin(0, 2, 30 * degree) * cspin(1, 2, 30*degree) * View;
+    View = cspin(0, 2, 30 * degree) * cspin(1, 2, 30._deg) * View;
   
   shift_view(ctangent(2, -0.5));
 
diff --git a/rogueviz/spiral.cpp b/rogueviz/spiral.cpp
index d5f11e88..0b9ff650 100644
--- a/rogueviz/spiral.cpp
+++ b/rogueviz/spiral.cpp
@@ -13,7 +13,7 @@ namespace spiral {
   ld mul;
   
   transmatrix at(double d) {
-    return spin(log(d) * 2 * M_PI / log(mul)) * xpush(log(d));
+    return spin(log(d) * TAU / log(mul)) * xpush(log(d));
     }
 
   void place(int N, ld _mul) {
diff --git a/rogueviz/staircase.cpp b/rogueviz/staircase.cpp
index 96b15a3f..16ec930f 100644
--- a/rogueviz/staircase.cpp
+++ b/rogueviz/staircase.cpp
@@ -19,7 +19,7 @@ basic_textureinfo tinf;
 
 hyperpoint spcoord(hyperpoint h) {
   ld phi = h[0], y = h[1], z = h[2], r = global_r;
-  ld aphi = (r+phi + floor(progress))*M_PI/6;
+  ld aphi = (r+phi + floor(progress))*30._deg;
   return zpush(acurvature*(y + r - frac(progress))/szoom) * xspinpush0(aphi, acurvature * z);
   }
 
@@ -106,7 +106,7 @@ void make_texture() {
     pix(2,x,y) = 0xFF400000 + 0x10000 * (y * 63 / fw);
     pix(8,x,y) = 0xFF101010;
     pix(10,x,y) = 0xFF000000 + gradient(0, 0xFFD500, 0, x*(fw-x), fw*fw/4);
-    pix(5,x,y) = 0xFF000000 + gradient(0, 0x804000, -1, sin(2*M_PI*8*y/fw), 1);
+    pix(5,x,y) = 0xFF000000 + gradient(0, 0x804000, -1, sin(TAU*8*y/fw), 1);
     pix(7,x,y) = 0xFF000000 + gradient(0, 0x808080, 0, x*ll(fw-x)*y*(fw-y), ll(fw/2)*(fw/2)*(fw-fw/2)*(fw-fw/2));
     }
 
diff --git a/rogueviz/sunflower.cpp b/rogueviz/sunflower.cpp
index 80ca7f06..64c31f7f 100644
--- a/rogueviz/sunflower.cpp
+++ b/rogueviz/sunflower.cpp
@@ -74,8 +74,8 @@ bool sunflower_cell(cell *c, shiftmatrix V) {
   
   if(sphere) {
     if(infer == 'r') 
-      range = qty * density * M_PI/2;
-    else qd = range * 2/M_PI;
+      range = qty * density * 90._deg;
+    else qd = range / 90._deg;
     }
   else if(euclid) {
     if(infer == 'r')
@@ -108,7 +108,7 @@ bool sunflower_cell(cell *c, shiftmatrix V) {
     ld best_error = 1;
     vector<int> sgns;
     for(int i=1; i<iqty; i++) {
-      ld v = i * step_angle / (2*M_PI);
+      ld v = i * step_angle / TAU;
       v = frac(v);
       auto sgn = v > .5;
       if(sgn) v = 1-v;
@@ -263,7 +263,7 @@ void show() {
   dialog::addSelItem("radius", fts(range), 'q');
   dialog::add_action([] {
     if(infer == 'r') infer = 'd';
-    dialog::editNumber(range, 0, 10, .1, 2*M_PI, "range", "range");
+    dialog::editNumber(range, 0, 10, .1, TAU, "range", "range");
     dialog::scaleLog();
     });
   
diff --git a/rug.cpp b/rug.cpp
index c7af552f..a2bc2cef 100644
--- a/rug.cpp
+++ b/rug.cpp
@@ -191,16 +191,14 @@ EX rugpoint *addRugpoint(shiftpoint h, double dist) {
     ld d = h1[0] * h[1] - h1[1] * h[0]; 
     ld a = h[0] * h1[0] + h[1] * h1[1];
 
-    // m->flat = modelscale * hpxyz(d * 2 * M_PI, sin(a * 2 * M_PI), cos(a * 2 * M_PI));
-
     USING_NATIVE_GEOMETRY;
-    hyperpoint hpoint = ypush(modelscale) * xpush0(modelscale * d * 2 * M_PI);
+    hyperpoint hpoint = ypush(modelscale) * xpush0(modelscale * d * TAU);
     ld hpdist = hdist0(hpoint);
     ld z = hypot_d(2, hpoint);
     if(z==0) z = 1;
     hpoint = hpoint * hpdist / z;
     
-    m->native = point31(hpoint[0], hpoint[1] * sin(a*2*M_PI), hpoint[1]*cos(a*2*M_PI));
+    m->native = point31(hpoint[0], hpoint[1] * sin(a*TAU), hpoint[1]*cos(a*TAU));
     }
   else if(sphere) {
     m->valid = good_shape = true;
@@ -216,7 +214,7 @@ EX rugpoint *addRugpoint(shiftpoint h, double dist) {
     else if(sphere) {
       if(modelscale >= 1) 
         // do as good as we can...
-        scale = M_PI / 2 - 1e-3, good_shape = false, m->valid = false;
+        scale = 90._deg - 1e-3, good_shape = false, m->valid = false;
       else scale = asin(modelscale);
       }
     else
@@ -374,15 +372,15 @@ struct clifford_torus {
     }
   clifford_torus();
   ld get_modelscale() {
-    return hypot_d(2, xh) * xfactor * 2 * M_PI;
+    return hypot_d(2, xh) * xfactor * TAU;
     }
   ld compute_mx();  
   };
 #endif
 
 struct hyperpoint clifford_torus::torus_to_s4(hyperpoint t) {
-  double alpha = -t[0] * 2 * M_PI;
-  double beta = t[1] * 2 * M_PI;
+  double alpha = -t[0] * TAU;
+  double beta = t[1] * TAU;
   
   ld ax = alpha + 1.124651, bx = beta + 1.214893;
   return hyperpoint(
@@ -1085,7 +1083,7 @@ EX void prepareTexture() {
     shiftmatrix V = rgpushxto0(finger_center->h);
     queuestr(V, 0.5, "X", 0xFFFFFFFF, 2);
     for(int i=0; i<72; i++)
-      queueline(V * xspinpush0(i*M_PI/32, finger_range), V * xspinpush0((i+1)*M_PI/32, finger_range), 0xFFFFFFFF, vid.linequality);
+      queueline(V * xspinpush0(i*A_PI/32, finger_range), V * xspinpush0((i+1)*A_PI/32, finger_range), 0xFFFFFFFF, vid.linequality);
     }
   drawqueue();
   calcparam();
@@ -1286,7 +1284,7 @@ EX bool handlekeys(int sym, int uni) {
       crystal::switch_z_coordinate();
     else
     #endif
-      rotate_view(cspin(0, 2, M_PI));
+      rotate_view(cspin180(0, 2));
     return true;
     }
   else if(NUMBERKEY == '4') {
@@ -1295,7 +1293,7 @@ EX bool handlekeys(int sym, int uni) {
       crystal::flip_z();
     else
     #endif
-      rotate_view(cspin(0, 2, M_PI/2));
+      rotate_view(cspin90(0, 2));
     return true;
     }
   #if CAP_CRYSTAL
@@ -1573,7 +1571,7 @@ EX void show() {
   if(rug::rugged)
     dialog::addSelItem(XLAT("model iterations"), its(queueiter), 0);
   dialog::addItem(XLAT("stereo vision config"), 'f');
-  // dialog::addSelItem(XLAT("protractor"), fts(protractor * 180 / M_PI) + "°", 'f');
+  // dialog::addSelItem(XLAT("protractor"), fts(protractor / degree) + "°", 'f');
   if(!good_shape) {
     dialog::addSelItem(XLAT("maximum error"), fts(err_zero), 'e');
     if(rug::rugged)
diff --git a/screenshot.cpp b/screenshot.cpp
index 02320100..ce4dfc9c 100644
--- a/screenshot.cpp
+++ b/screenshot.cpp
@@ -1125,7 +1125,7 @@ EX ld shift_angle, movement_angle, movement_angle_2;
 EX ld normal_angle = 90;
 EX ld period = 10000;
 EX int noframes = 30;
-EX ld cycle_length = 2 * M_PI;
+EX ld cycle_length = TAU;
 EX ld parabolic_length = 1;
 EX ld skiprope_rotation;
 
@@ -1282,7 +1282,7 @@ EX void apply() {
         rotate_view(cspin(1, 2, normal_angle * degree));
         rotate_view(spin(-movement_angle_2 * degree));
         }
-      rotate_view(spin(2 * M_PI * t / period));
+      rotate_view(spin(TAU * t / period));
       if(GDIM == 3) {
         rotate_view(spin(movement_angle_2 * degree));
         rotate_view(cspin(2, 1, normal_angle * degree));
@@ -1297,7 +1297,7 @@ EX void apply() {
         cspin(0, GDIM-1, movement_angle * degree) * spin(shift_angle * degree) * xtangent(cycle_length * t / period)
         );
       moved();
-      rotate_view(cspin(0, GDIM-1, 2 * M_PI * t / period));
+      rotate_view(cspin(0, GDIM-1, TAU * t / period));
       if(clearup) {
         centerover->wall = waNone;
         }
@@ -1317,7 +1317,7 @@ EX void apply() {
     #endif
     case maCircle: {
       centerover = rotation_center;
-      ld alpha = circle_spins * 2 * M_PI * ticks / period;
+      ld alpha = circle_spins * TAU * ticks / period;
       View = spin(-cos_auto(circle_radius)*alpha) * xpush(circle_radius) * spin(alpha) * rotation_center_View;
       moved();
       break;
@@ -1341,17 +1341,17 @@ EX void apply() {
   if(rug::rugged) {
     if(rug_rotation1) {
       rug::using_rugview rv;
-      rotate_view(cspin(1, 2, -rug_angle * degree) * cspin(0, 2, rug_rotation1 * 2 * M_PI * t / period) * cspin(1, 2, rug_angle * degree));
+      rotate_view(cspin(1, 2, -rug_angle * degree) * cspin(0, 2, rug_rotation1 * TAU * t / period) * cspin(1, 2, rug_angle * degree));
       }
     if(rug_rotation2) {
       rug::using_rugview rv;
-      View = View * cspin(0, 1, rug_rotation2 * 2 * M_PI * t / period);
+      View = View * cspin(0, 1, rug_rotation2 * TAU * t / period);
       }
     if(rug_forward) 
       animate_rug_movement(rug_forward * t / period);
     }
   #endif
-  pconf.skiprope += skiprope_rotation * t * 2 * M_PI / period;
+  pconf.skiprope += skiprope_rotation * t * TAU / period;
 
   if(ballangle_rotation) {
     if(models::has_orientation(vpconf.model))
@@ -1485,12 +1485,12 @@ void display_animation() {
   if(ma == maCircle && (circle_display_color & 0xFF)) {
     for(int s=0; s<10; s++) {
       if(s == 0) curvepoint(xpush0(circle_radius - .1));
-      for(int z=0; z<100; z++) curvepoint(xspinpush0((z+s*100) * 2 * M_PI / 1000., circle_radius));
+      for(int z=0; z<100; z++) curvepoint(xspinpush0((z+s*100) * 2 * A_PI / 1000., circle_radius));
       queuecurve(ggmatrix(rotation_center), circle_display_color, 0, PPR::LINE);
       }
     if(sphere) for(int s=0; s<10; s++) {
       if(s == 0) curvepoint(xpush0(circle_radius - .1));
-      for(int z=0; z<100; z++) curvepoint(xspinpush0((z+s*100) * 2 * M_PI / 1000., circle_radius));
+      for(int z=0; z<100; z++) curvepoint(xspinpush0((z+s*100) * 2 * A_PI / 1000., circle_radius));
       queuecurve(ggmatrix(rotation_center) * centralsym, circle_display_color, 0, PPR::LINE);
       }
     }
@@ -1534,7 +1534,7 @@ EX void show() {
   cmode = sm::SIDE; needs_highqual = false;
   animation_lcm = 1;
   gamescreen();
-  animation_period = 2 * M_PI * animation_lcm / animation_factor;
+  animation_period = TAU * animation_lcm / animation_factor;
   dialog::init(XLAT("animations"), iinf[itPalace].color, 150, 100);
   dialog::addSelItem(XLAT("period"), fts(period)+ " ms", 'p');
   dialog::add_action([] () { dialog::editNumber(period, 0, 10000, 1000, 200, XLAT("period"), 
@@ -1547,7 +1547,7 @@ EX void show() {
       dialog::editNumber(animation_period, 0, 10000, 1000, 1000, XLAT("game animation period"), 
         XLAT("Least common multiple of the animation periods of all the game objects on screen, such as rotating items.")
         );
-      dialog::reaction = [] () { animation_factor = 2 * M_PI * animation_lcm / animation_period; };
+      dialog::reaction = [] () { animation_factor = TAU * animation_lcm / animation_period; };
       dialog::extra_options = [] () {
         dialog::addItem("default", 'D');
         dialog::add_action([] () {
@@ -1614,10 +1614,10 @@ EX void show() {
       else if(ma == maTranslation) {
         dialog::addSelItem(XLAT("cycle length"), fts(cycle_length), 'c');
         dialog::add_action([] () { 
-          dialog::editNumber(cycle_length, 0, 10, 0.1, 2*M_PI, "shift", ""); 
+          dialog::editNumber(cycle_length, 0, 10, 0.1, TAU, "shift", ""); 
           dialog::extra_options = [] () {
-            dialog::addSelItem(XLAT("full circle"), fts(2 * M_PI), 'A');
-            dialog::add_action([] () { cycle_length = 2 * M_PI; });
+            dialog::addSelItem(XLAT("full circle"), fts(TAU), 'A');
+            dialog::add_action([] () { cycle_length = TAU; });
             dialog::addSelItem(XLAT("Zebra period"), fts(2.898149445355172), 'B');
             dialog::add_action([] () { cycle_length = 2.898149445355172; });
             dialog::addSelItem(XLAT("Bolza period"), fts(2 * 1.528571), 'C');
@@ -1690,7 +1690,7 @@ EX void show() {
       dialog::extra_options = [] () {
         if(among(rug::gwhere, gSphere, gElliptic))  {
           dialog::addItem(XLAT("synchronize"), 'S');
-          dialog::add_action([] () { rug_forward = 2 * M_PI; popScreen(); });
+          dialog::add_action([] () { rug_forward = TAU; popScreen(); });
           }
         rug_angle_options();
         };
@@ -1967,7 +1967,7 @@ startanim rug { "Hypersian Rug", [] {
 startanim spin_around { "spinning around", no_init,  [] {
   dynamicval<ld> da(pconf.alpha, 999);
   dynamicval<ld> ds(pconf.scale, 500);
-  ld alpha = 2 * M_PI * ticks / 10000.;
+  ld alpha = TAU * ticks / 10000.;
   ld circle_radius = acosh(2.);
   dynamicval<transmatrix> dv(View, spin(-cos_auto(circle_radius)*alpha) * xpush(circle_radius) * spin(alpha) * View);
   gamescreen();
@@ -1996,7 +1996,7 @@ startanim row_of_ghosts { "row of ghosts", no_init, [] {
     for(int x=-25; x<=25; x++)
       for(int y=-25; y<=25; y++) {
         ld ay = (y + mod)/5.;
-        draw_ghost(xpush(x/5.) * spin(M_PI/2) * xpush(ay), int(y-t));
+        draw_ghost(xpush(x/5.) * spin90() * xpush(ay), int(y-t));
         }
     });
   dynamicval<bool> rd(mapeditor::drawplayer, false);
@@ -2011,15 +2011,15 @@ startanim army_of_ghosts { "army of ghosts", no_init, [] {
     ld mod = (tt-t*400)/400.;
     for(int x=-12; x<=12; x++) {
       ld ax = x/4.;
-      transmatrix T = spin(-M_PI/2) * xpush(ax) * spin(M_PI/2);
+      transmatrix T = spin270() * xpush(ax) * spin90();
       for(int y=0;; y++) {
         ld ay = (mod - y)/4.;
-        transmatrix U = spin(M_PI/2) * xpush(ay / cosh(ax)) * T;
+        transmatrix U = spin90() * xpush(ay / cosh(ax)) * T;
         if(!in_smart_range(shiftless(U))) break;
         draw_ghost(U, (-y - t));
         if(y) {
           ay = (mod + y)/4.;
-          transmatrix U = spin(M_PI/2) * xpush(ay / cosh(ax)) * T;
+          transmatrix U = spin90() * xpush(ay / cosh(ax)) * T;
           draw_ghost(U, (y - t));
           }
         }
@@ -2032,7 +2032,7 @@ startanim ghost_spiral { "ghost spiral", no_init, [] {
   dynamicval<reaction_t> r(add_to_frame, [] {
     ld t = (ticks - ticks_start - 2000) / 150000.;
     for(ld i=3; i<=40; i++) {
-      draw_ghost(spin(t * i * 2 * M_PI) * xpush(asinh(15. / i)) * spin(M_PI/2), 1);
+      draw_ghost(spin(t * i * TAU) * xpush(asinh(15. / i)) * spin90(), 1);
       }
     });
   gamescreen();
@@ -2043,12 +2043,12 @@ startanim fib_ghosts { "Fibonacci ghosts", no_init, [] {
   dynamicval<reaction_t> r(add_to_frame, [] {
     ld phase = (ticks - ticks_start - 2000) / 1000.;
     for(int i=0; i<=500; i++) {
-      ld step = M_PI * (3 - sqrt(5));
+      ld step = A_PI * (3 - sqrt(5));
       ld density = 0.01;
       ld area = 1 + (i+.5) * density;
       ld r = acosh(area);
       ld length = sinh(r);
-      transmatrix T = spin(i * step + phase / length) * xpush(r) * spin(M_PI/2);
+      transmatrix T = spin(i * step + phase / length) * xpush(r) * spin90();
       draw_ghost(T, i);
       }
     });
diff --git a/shaders.cpp b/shaders.cpp
index a8f753a7..22456701 100644
--- a/shaders.cpp
+++ b/shaders.cpp
@@ -798,7 +798,7 @@ void display_data::set_projection(int ed, ld shift) {
     glhr::projection_multiply(model_orientation_gl());
 
   if(selected->shader_flags & SF_BAND)
-    glhr::projection_multiply(glhr::scale(2 / M_PI, 2 / M_PI, GDIM == 3 ? 2/M_PI : 1));
+    glhr::projection_multiply(glhr::scale(1 / 90._deg, 1 / 90._deg, GDIM == 3 ? 1/90._deg : 1));
 
   if(selected->shader_flags & SF_BAND) {
     glhr::projection_multiply(glhr::translate(shift, 0, 0));
diff --git a/shmup.cpp b/shmup.cpp
index 2f53a72d..f2f07527 100644
--- a/shmup.cpp
+++ b/shmup.cpp
@@ -440,7 +440,7 @@ void shootBullet(monster *m) {
   for(int i=1; i<8; i++) if(markOrb(orbdir[i])) {
     monster* bullet = new monster;
     bullet->base = m->base;
-    bullet->at = m->at * cspin(0, WDIM-1, M_PI/4*i);
+    bullet->at = m->at * cspin(0, WDIM-1, TAU * i/8);
     if(prod) bullet->ori = m->ori;
     if(WDIM == 3) bullet->at = bullet->at * cpush(2, 0.15 * SCALE);
     bullet->type = moBullet;
@@ -448,7 +448,7 @@ void shootBullet(monster *m) {
     bullet->pid = m->pid;
     bullet->hitpoints = 0;
     bullet->fragoff = ticks + bullet_time;
-    bullet->inertia = cspin(0, WDIM-1, -M_PI/4 * i) * m->inertia;
+    bullet->inertia = cspin(0, WDIM-1, -TAU * i/8) * m->inertia;
     bullet->inertia[frontdir()] += bullet_velocity(m->type) * SCALE;
     additional.push_back(bullet);
     }
@@ -635,10 +635,10 @@ shiftpoint hornpos(int id) {
 #define IGO 9
 
 double igospan[IGO+1] = { 0, 
-  M_PI/6, -M_PI/6, 
-  M_PI/4, -M_PI/4,
-  M_PI/3, -M_PI/3,
-  M_PI/2.1, -M_PI/2.1,
+  A_PI/6, -A_PI/6,
+  A_PI/4, -A_PI/4,
+  A_PI/3, -A_PI/3,
+  A_PI/2.1, -A_PI/2.1,
   0
   };
 
@@ -1527,7 +1527,7 @@ void destroyMimics() {
 EX void teleported() {
   monster *m = pc[cpid];
   m->base = cwt.at;
-  m->at = rgpushxto0(inverse_shift(gmatrix[cwt.at], mouseh)) * spin(rand() % 1000 * M_PI / 2000);
+  m->at = rgpushxto0(inverse_shift(gmatrix[cwt.at], mouseh)) * random_spin();
   m->findpat();
   destroyMimics();
   }
@@ -2161,9 +2161,9 @@ void moveMonster(monster *m, int delta) {
     if(m->type == moHedge) {
       hyperpoint h = inverse_shift(m->pat, tC0(goal));
       if(h[1] < 0)
-        nat = nat * spin(M_PI * delta / 3000 / speedfactor());
+        nat = nat * spin(A_PI * delta / 3000 / speedfactor());
       else
-        nat = nat * spin(M_PI * -delta / 3000 / speedfactor());
+        nat = nat * spin(A_PI * -delta / 3000 / speedfactor());
       m->rebasePat(nat, m->base);
       // at most 45 degrees
       if(h[0] < fabsl(h[1])) return;
@@ -2832,7 +2832,7 @@ EX void recall() {
     if(players == 1)
       pc[i]->at = Id;
     else
-      pc[i]->at = spin(2*M_PI*i/players) * xpush(firstland == laMotion ? .5 : .3) * Id;
+      pc[i]->at = spin(TAU*i/players) * xpush(firstland == laMotion ? .5 : .3) * Id;
     /* ggmatrix(cwt.at);
     display(gmatrix[cwt.at]);
     pc[i]->findpat(); */
@@ -2851,7 +2851,7 @@ EX void init() {
     if(players == 1)
       pc[i]->at = Id;
     else
-      pc[i]->at = spin(2*M_PI*i/players) * xpush(firstland == laMotion ? .5 : .3) * Id;
+      pc[i]->at = spin(TAU*i/players) * xpush(firstland == laMotion ? .5 : .3) * Id;
     pc[i]->pat = shiftless(pc[i]->at);
     pc[i]->base = cwt.at;
     pc[i]->vel = 0;
@@ -3013,7 +3013,7 @@ bool celldrawer::draw_shmup_monster() {
     if(m->inBoat) {
       view = m->pat;
       if(WDIM == 2) Vboat = view;
-      if(WDIM == 3) Vboat = view * spin(-M_PI/2);
+      if(WDIM == 3) Vboat = view * spin270();
       
       bool magic = m->type == moPlayer && items[itOrbWater];
       color_t outcolor = magic ? watercolor(0) : 0xC06000FF;
@@ -3056,7 +3056,7 @@ bool celldrawer::draw_shmup_monster() {
               view = view * spin(-atan2(h[1], h[0]));
               }
             else {
-              view = view * spin(-M_PI/2) * cspin(0, 2, -M_PI/2);
+              view = view * spin270() * cspin90(2, 0);
               }
             }
           if(m->inBoat) m->footphase = 0;
@@ -3167,12 +3167,7 @@ bool celldrawer::draw_shmup_monster() {
         if(hasHitpoints(m->type))
           c->hitpoints = m->hitpoints;
         if(m->type == moTortoise) tortoise::emap[c] = getBits(m->torigin) & ((1<<tortoise::numbits)-1);
-        /* if(m->type == moMimic && GDIM == 3)
-          drawMonsterType(m->type, c, view * spin(-M_PI/2), col, m->footphase); */
-        /* else if(GDIM == 3)
-          drawMonsterType(m->type, c, view * cspin(0, 2, M_PI/2), col, m->footphase); */
-        /* else */
-          drawMonsterType(m->type, c, view, col, m->footphase, col);
+        drawMonsterType(m->type, c, view, col, m->footphase, col);
         if(m->type == moTortoise) tortoise::emap.erase(c);
         break;
       }
diff --git a/surface.cpp b/surface.cpp
index a29a43a5..3a119700 100644
--- a/surface.cpp
+++ b/surface.cpp
@@ -72,7 +72,7 @@ hyperpoint coord(hyperpoint h) {
       }
     
     case dsDini: {
-      ld t = h[0]; // atan(h[0])/2 + M_PI * 3/ 4;
+      ld t = h[0];
       ld v = h[1];
       
       ld a = sqrt(1-dini_b*dini_b);
@@ -166,11 +166,11 @@ ld compute_curvature(hyperpoint at) {
 hyperpoint shape_origin() {
   switch(sh) {
     case dsDini:
-      return point31(M_PI * .82, 0, 0);
+      return point31(A_PI * .82, 0, 0);
     case dsTractricoid:
       return point31(1, 0, 0);
     case dsKuen:
-      return point31(M_PI * .500001, M_PI * 1, 0);
+      return point31(90._deg * 1.000001, M_PI, 0);
     case dsHyperlike:
       return point31(0,0,0);
     default:
@@ -206,13 +206,13 @@ int surface_branch(hyperpoint p) {
 bool inbound(ld& x, ld& y) {
   switch(sh) {
     case dsDini:
-      return flag_clamp(x, M_PI/2, M_PI);
+      return flag_clamp(x, 90._deg, M_PI);
     
     case dsTractricoid:
       return flag_clamp_min(x, 0) & flag_clamp_sym(y, M_PI);
     
     case dsKuen: 
-      return flag_clamp(x, 0, M_PI) & flag_clamp(y, 0, 2*M_PI);
+      return flag_clamp(x, 0, M_PI) & flag_clamp(y, 0, TAU);
     
     case dsHyperlike:
       return flag_clamp_sym(x, M_PI) & flag_clamp_sym(y, hyperlike_bound());
@@ -351,7 +351,7 @@ ld kuen_hypot(ld v, ld u) {
   }
 
 int kuen_branch(ld v, ld u) {
-  if(v > M_PI/2)
+  if(v > 90._deg)
   return kuen_cross(v, u)[2] > 0 ? 1 : 2;
   else
   return kuen_cross(v, u)[2] < 0 ? 1 : 2;
@@ -380,7 +380,7 @@ void draw_kuen_map() {
     for(int r=0; r<512; r++)
     for(int h=0; h<512; h++) {
       ld v = M_PI * (r+.5) / 512;
-      ld u = 2 * M_PI * (h+.5) / 512;
+      ld u = TAU * (h+.5) / 512;
       auto du = coord_derivative(point3(v,u,0), 0);
       auto dv = coord_derivative(point3(v,u,0), 1);
       auto n = hypot_d(3, du^dv);
@@ -401,7 +401,7 @@ void draw_kuen_map() {
   for(auto p: rug::points) {
     auto hp = p->surface_point.params;
     int x = int(512 * hp[0] / M_PI);
-    int y = int(512 * hp[1] / 2 / M_PI);
+    int y = int(512 * hp[1] / TAU);
     qpixel(kuen_map, x, y) = 0xFF000000 | dexp_colors[p->dexp_id];
     }
 
@@ -431,7 +431,7 @@ void run_hyperlike() {
   int lim = (int) sqrt(rug::vertex_limit);
   for(int r=0; r<lim; r++)
   for(int h=0; h<lim; h++) 
-    rug::addRugpoint(shiftless(xpush(2 * M_PI * hyper_b * (2*r-lim) / lim) * ypush(hyperlike_bound() * (2*h-lim) / lim) * C0), -1);
+    rug::addRugpoint(shiftless(xpush(TAU * hyper_b * (2*r-lim) / lim) * ypush(hyperlike_bound() * (2*h-lim) / lim) * C0), -1);
   for(int r=0; r<lim-1; r++)
   for(int h=0; h<lim-1; h++) {
     addTriangle(rug::points[lim*r+h], rug::points[lim*r+h+1], rug::points[lim*r+h+lim]);
@@ -464,13 +464,13 @@ void run_hyperlike() {
 void run_kuen() {
   full_mesh();
 
-  auto H = Id; // spin(-M_PI / 4) * xpush(2);
+  auto H = Id;
   auto Hi = inverse(H);
   
-  auto frontal_map = at_zero(hpxyz(M_PI * .500001, M_PI * 1, 0), Id);
-  auto back0 = at_zero(hpxyz(M_PI * .500001, .67, 0), H);
-  auto back1 = at_other(back0, Hi * spin(-M_PI/2) * hpxy(0.511, -0.5323));
-  auto back2 = at_other(back0, Hi * spin(-M_PI/2) * hpxy(0.511, 0.5323));
+  auto frontal_map = at_zero(hpxyz(90._deg * 1.000001, M_PI * 1, 0), Id);
+  auto back0 = at_zero(hpxyz(90._deg * 1.000001, .67, 0), H);
+  auto back1 = at_other(back0, Hi * spin(-90._deg) * hpxy(0.511, -0.5323));
+  auto back2 = at_other(back0, Hi * spin(-90._deg) * hpxy(0.511, 0.5323));
   
   frontal_map.H = frontal_map.H * ypush(2.6);
   back0.H = back0.H * ypush(.4);
@@ -566,7 +566,7 @@ template<class T> void run_function(T f) {
 
 void run_other() {
   full_mesh();
-  auto dp = at_zero(shape_origin(),  spin(M_PI/2));
+  auto dp = at_zero(shape_origin(),  spin(90._deg));
 
   int it = 0;
   for(auto p: rug::points) {
diff --git a/textures.cpp b/textures.cpp
index e6be9bdb..d0aba796 100644
--- a/textures.cpp
+++ b/textures.cpp
@@ -756,7 +756,7 @@ struct magic_param {
   void shuffle() {
     do_spin = hrand(2);
     spinangle = hrandf() - hrandf();
-    moveangle = hrandf() * 2 * M_PI;
+    moveangle = hrandf() * TAU;
     shift = hrandf() - hrandf();
     scale = hrandf() - hrandf();
     proj = hrandf() - hrandf();
@@ -1565,7 +1565,7 @@ void splitseg(const shiftmatrix& A, const array<ld, 2>& angles, const array<shif
 void fillcircle(shiftpoint h, color_t col) {
   shiftmatrix A = rgpushxto0(h);
   
-  ld step = M_PI * 2/3;
+  ld step = 120._deg;
   
   array<shiftpoint, 3> mh = make_array(A * xpush0(mapeditor::dtwidth), A * xspinpush0(step, mapeditor::dtwidth), A * xspinpush0(-step, mapeditor::dtwidth));
   auto mp = ptc(mh);
@@ -1588,9 +1588,9 @@ void actDrawPixel(cell *c, shiftpoint h, color_t col) {
     hyperpoint h1 = inverse_shift(M * applyPatterndir(c, si), h);
     auto& tinf = config.texture_map[si.id];
     for(auto& M2: tinf.matrices) for(int i = 0; i<c->type; i += si.symmetries) {
-      fillcircle(M2 * spin(2 * M_PI * i / c->type) * h1, col);
+      fillcircle(M2 * spin(TAU * i / c->type) * h1, col);
       if(texturesym)
-        fillcircle(M2 * spin(2 * M_PI * i / c->type) * Mirror * h1, col);
+        fillcircle(M2 * spin(TAU * i / c->type) * Mirror * h1, col);
       }
     }
   catch(out_of_range&) {}
diff --git a/usershapes.cpp b/usershapes.cpp
index 0aeb2954..a256e9c1 100644
--- a/usershapes.cpp
+++ b/usershapes.cpp
@@ -45,13 +45,13 @@ void geometry_information::pushShape(usershapelayer& ds) {
   
   for(int r=0; r<ds.rots; r++) {
     for(int i=0; i<isize(ds.list)/z*z; i++)
-      hpcpush(T * spin(2*M_PI*r/ds.rots) * ds.list[i]);
+      hpcpush(T * spin(TAU*r/ds.rots) * ds.list[i]);
 
     if(ds.sym) {
   
       transmatrix mirrortrans = Id; mirrortrans[1][1] = -1;
       for(int i=isize(ds.list)-1; i>=0; i--)
-        hpcpush(T * spin(2*M_PI*r/ds.rots) * mirrortrans * ds.list[i]);
+        hpcpush(T * spin(TAU*r/ds.rots) * mirrortrans * ds.list[i]);
       }
     }
   
diff --git a/util.cpp b/util.cpp
index 96947a7b..e88d062f 100644
--- a/util.cpp
+++ b/util.cpp
@@ -230,7 +230,7 @@ cld exp_parser::parse(int prio) {
     force_eat(",");
     ld b = rparse(0);
     force_eat(")");
-    res = edge_of_triangle_with_angles(2*M_PI/a, M_PI/b, M_PI/b);
+    res = edge_of_triangle_with_angles(TAU/a, M_PI/b, M_PI/b);
     }
   else if(eat("edge_angles(")) {
     cld a = rparse(0);
@@ -253,7 +253,7 @@ cld exp_parser::parse(int prio) {
     force_eat(",");
     ld b = rparse(0);
     force_eat(")");
-    res = edge_of_triangle_with_angles(M_PI/2, M_PI/a, M_PI/b);
+    res = edge_of_triangle_with_angles(90._deg, M_PI/a, M_PI/b);
     }
   #if CAP_ARCM
   else if(eat("arcmedge(")) {
@@ -307,8 +307,7 @@ cld exp_parser::parse(int prio) {
       hyperpoint h = xpush(c) * spin(M_PI - 2*alpha) * xpush0(c);
       ld result = 2 * atan2(h);
       if(result < 0) result = -result;
-      while(result > 2 * M_PI) result -= 2 * M_PI;
-      if(result > M_PI) result = 2 * M_PI - result;
+      cyclefix(result, 0);
       res = result;
       }