enumerator.c: Introduce Enumerator::ArithmeticSequence

This commit introduces new core class Enumerator::ArithmeticSequence.
Enumerator::ArithmeticSequence is a subclass of Enumerator, and
represents a number generator of an arithmetic sequence.

After this commit, Numeric#step and Range#step without blocks
returned an ArithmeticSequence object instead of an Enumerator.

This class introduces the following incompatibilities:

- You can create a zero-step ArithmeticSequence,
  and its size is not ArgumentError, but Infinity.
- You can create a negative-step ArithmeticSequence from a range.

[ruby-core:82816] [Feature #13904]

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@64205 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

11 files changed, 883 insertions, 47 deletions

diff --git a/enumerator.c b/enumerator.c
index 050a9ce58f..66c126d409 100644
--- a/enumerator.c
+++ b/enumerator.c
@@ -15,6 +15,10 @@
 #include "internal.h"
 #include "id.h"
 
+#ifdef HAVE_FLOAT_H
+#include <float.h>
+#endif
+
 /*
  * Document-class: Enumerator
  *
@@ -105,6 +109,7 @@ VALUE rb_cEnumerator;
 static VALUE rb_cLazy;
 static ID id_rewind, id_new, id_yield, id_to_enum;
 static ID id_next, id_result, id_lazy, id_receiver, id_arguments, id_memo, id_method, id_force;
+static ID id_begin, id_end, id_step, id_exclude_end;
 static VALUE sym_each, sym_cycle;
 
 #define id_call idCall
@@ -156,6 +161,8 @@ struct proc_entry {
 static VALUE generator_allocate(VALUE klass);
 static VALUE generator_init(VALUE obj, VALUE proc);
 
+static VALUE rb_cArithSeq;
+
 /*
  * Enumerator
  */
@@ -2375,6 +2382,391 @@ stop_result(VALUE self)
     return rb_attr_get(self, id_result);
 }
 
+VALUE
+rb_arith_seq_new(VALUE obj, VALUE meth, int argc, VALUE const *argv,
+                 rb_enumerator_size_func *size_fn,
+                 VALUE beg, VALUE end, VALUE step, int excl)
+{
+    VALUE aseq = enumerator_init(enumerator_allocate(rb_cArithSeq),
+                                 obj, meth, argc, argv, size_fn, Qnil);
+    rb_ivar_set(aseq, id_begin, beg);
+    rb_ivar_set(aseq, id_end, end);
+    rb_ivar_set(aseq, id_step, step);
+    rb_ivar_set(aseq, id_exclude_end, excl ? Qtrue : Qfalse);
+    return aseq;
+}
+
+static inline VALUE
+arith_seq_begin(VALUE self)
+{
+    return rb_ivar_get(self, id_begin);
+}
+
+static inline VALUE
+arith_seq_end(VALUE self)
+{
+    return rb_ivar_get(self, id_end);
+}
+
+static inline VALUE
+arith_seq_step(VALUE self)
+{
+    return rb_ivar_get(self, id_step);
+}
+
+static inline VALUE
+arith_seq_exclude_end(VALUE self)
+{
+    return rb_ivar_get(self, id_exclude_end);
+}
+
+static inline int
+arith_seq_exclude_end_p(VALUE self)
+{
+    return RTEST(arith_seq_exclude_end(self));
+}
+
+static VALUE
+arith_seq_first(int argc, VALUE *argv, VALUE self)
+{
+    VALUE b, e, s, len_1;
+
+    b = arith_seq_begin(self);
+    e = arith_seq_end(self);
+    s = arith_seq_step(self);
+
+    if (!NIL_P(e)) {
+        len_1 = rb_int_idiv(rb_int_minus(e, b), s);
+        if (rb_num_negative_int_p(len_1)) {
+            if (argc == 0) {
+                return Qnil;
+            }
+            return rb_ary_new_capa(0);
+        }
+    }
+
+    if (argc == 0) {
+        return b;
+    }
+
+    /* TODO: optimization */
+
+    return rb_call_super(argc, argv);
+}
+
+static VALUE
+arith_seq_last(int argc, VALUE *argv, VALUE self)
+{
+    VALUE b, e, s, len_1, len, last, nv, ary;
+    int last_is_adjusted;
+    long n;
+
+    e = arith_seq_end(self);
+    if (NIL_P(e)) {
+        rb_raise(rb_eRangeError,
+                 "cannot get the last element of endless arithmetic sequence");
+    }
+
+    b = arith_seq_begin(self);
+    s = arith_seq_step(self);
+
+    len_1 = rb_int_idiv(rb_int_minus(e, b), s);
+    if (rb_num_negative_int_p(len_1)) {
+        if (argc == 0) {
+            return Qnil;
+        }
+        return rb_ary_new_capa(0);
+    }
+
+    last = rb_int_plus(b, rb_int_mul(s, len_1));
+    if ((last_is_adjusted = arith_seq_exclude_end_p(self) && rb_equal(last, e))) {
+        last = rb_int_minus(last, s);
+    }
+
+    if (argc == 0) {
+        return last;
+    }
+
+    if (last_is_adjusted) {
+        len = len_1;
+    }
+    else {
+        len = rb_int_plus(len_1, INT2FIX(1));
+    }
+
+    rb_scan_args(argc, argv, "1", &nv);
+    if (RTEST(rb_int_gt(nv, len))) {
+        nv = len;
+    }
+    n = NUM2LONG(nv);
+    if (n < 0) {
+        rb_raise(rb_eArgError, "negative array size");
+    }
+
+    ary = rb_ary_new_capa(n);
+    b = rb_int_minus(last, rb_int_mul(s, nv));
+    while (n) {
+        b = rb_int_plus(b, s);
+        rb_ary_push(ary, b);
+        --n;
+    }
+
+    return ary;
+}
+
+static VALUE
+arith_seq_inspect(VALUE self)
+{
+    struct enumerator *e;
+    VALUE eobj, str, eargs;
+    int range_p;
+
+    TypedData_Get_Struct(self, struct enumerator, &enumerator_data_type, e);
+
+    eobj = rb_attr_get(self, id_receiver);
+    if (NIL_P(eobj)) {
+        eobj = e->obj;
+    }
+
+    range_p = RTEST(rb_obj_is_kind_of(eobj, rb_cRange));
+    str = rb_sprintf("(%s%"PRIsVALUE"%s.", range_p ? "(" : "", eobj, range_p ? ")" : "");
+
+    rb_str_buf_append(str, rb_id2str(e->meth));
+
+    eargs = rb_attr_get(eobj, id_arguments);
+    if (NIL_P(eargs)) {
+        eargs = e->args;
+    }
+    if (eargs != Qfalse) {
+        long argc = RARRAY_LEN(eargs);
+        const VALUE *argv = RARRAY_CONST_PTR(eargs); /* WB: no new reference */
+
+        if (argc > 0) {
+            VALUE kwds = Qnil;
+
+            rb_str_buf_cat2(str, "(");
+
+            if (RB_TYPE_P(argv[argc-1], T_HASH)) {
+                int all_key = TRUE;
+                rb_hash_foreach(argv[argc-1], key_symbol_p, (VALUE)&all_key);
+                if (all_key) kwds = argv[--argc];
+            }
+
+            while (argc--) {
+                VALUE arg = *argv++;
+
+                rb_str_append(str, rb_inspect(arg));
+                rb_str_buf_cat2(str, ", ");
+                OBJ_INFECT(str, arg);
+            }
+            if (!NIL_P(kwds)) {
+                rb_hash_foreach(kwds, kwd_append, str);
+            }
+            rb_str_set_len(str, RSTRING_LEN(str)-2); /* drop the last ", " */
+            rb_str_buf_cat2(str, ")");
+        }
+    }
+
+    rb_str_buf_cat2(str, ")");
+
+    return str;
+}
+
+static VALUE
+arith_seq_eq(VALUE self, VALUE other)
+{
+    if (!RTEST(rb_obj_is_kind_of(other, rb_cArithSeq))) {
+        return Qfalse;
+    }
+
+    if (!rb_equal(arith_seq_begin(self), arith_seq_begin(other))) {
+        return Qfalse;
+    }
+
+    if (!rb_equal(arith_seq_end(self), arith_seq_end(other))) {
+        return Qfalse;
+    }
+
+    if (!rb_equal(arith_seq_step(self), arith_seq_step(other))) {
+        return Qfalse;
+    }
+
+    if (arith_seq_exclude_end_p(self) != arith_seq_exclude_end_p(other)) {
+        return Qfalse;
+    }
+
+    return Qtrue;
+}
+
+static VALUE
+arith_seq_hash(VALUE self)
+{
+    st_index_t hash;
+    VALUE v;
+
+    hash = rb_hash_start(arith_seq_exclude_end_p(self));
+    v = rb_hash(arith_seq_begin(self));
+    hash = rb_hash_uint(hash, NUM2LONG(v));
+    v = rb_hash(arith_seq_end(self));
+    hash = rb_hash_uint(hash, NUM2LONG(v));
+    v = rb_hash(arith_seq_step(self));
+    hash = rb_hash_uint(hash, NUM2LONG(v));
+    hash = rb_hash_end(hash);
+
+    return LONG2FIX(hash);
+}
+
+struct arith_seq_gen {
+    VALUE current;
+    VALUE end;
+    VALUE step;
+    int excl;
+};
+
+static VALUE
+arith_seq_each(VALUE self)
+{
+    VALUE c, e, s, len_1, last;
+    int x;
+
+    if (!rb_block_given_p()) return self;
+
+    c = arith_seq_begin(self);
+    e = arith_seq_end(self);
+    s = arith_seq_step(self);
+    x = arith_seq_exclude_end_p(self);
+
+    if (ruby_float_step(c, e, s, x, TRUE)) {
+        return self;
+    }
+
+    if (NIL_P(e)) {
+        while (1) {
+            rb_yield(c);
+            c = rb_int_plus(c, s);
+        }
+
+        return self;
+    }
+
+    if (rb_equal(s, INT2FIX(0))) {
+        while (1) {
+            rb_yield(c);
+        }
+
+        return self;
+    }
+
+    len_1 = rb_int_idiv(rb_int_minus(e, c), s);
+    last = rb_int_plus(c, rb_int_mul(s, len_1));
+    if (x && rb_equal(last, e)) {
+        last = rb_int_minus(last, s);
+    }
+
+    if (rb_num_negative_int_p(s)) {
+        while (RTEST(rb_int_ge(c, last))) {
+            rb_yield(c);
+            c = rb_int_plus(c, s);
+        }
+    }
+    else {
+        while (RTEST(rb_int_ge(last, c))) {
+            rb_yield(c);
+            c = rb_int_plus(c, s);
+        }
+    }
+
+    return self;
+}
+
+static double
+arith_seq_float_step_size(double beg, double end, double step, int excl)
+{
+    double const epsilon = DBL_EPSILON;
+    double n = (end - beg) / step;
+    double err = (fabs(beg) + fabs(end) + fabs(end - beg)) / fabs(step) * epsilon;
+
+    if (isinf(step)) {
+        return step > 0 ? beg <= end : beg >= end;
+    }
+    if (step == 0) {
+        return HUGE_VAL;
+    }
+    if (err > 0.5) err = 0.5;
+    if (excl) {
+        if (n <= 0) return 0;
+        if (n < 1)
+            n = 0;
+        else
+            n = floor(n - err);
+    }
+    else {
+        if (n < 0) return 0;
+        n = floor(n + err);
+    }
+    return n + 1;
+}
+
+static VALUE
+arith_seq_size(VALUE self)
+{
+    VALUE b, e, s, len_1, len, last;
+    int x;
+
+    b = arith_seq_begin(self);
+    e = arith_seq_end(self);
+    s = arith_seq_step(self);
+    x = arith_seq_exclude_end_p(self);
+
+    if (RB_FLOAT_TYPE_P(b) || RB_FLOAT_TYPE_P(e) || RB_FLOAT_TYPE_P(s)) {
+        double ee, n;
+
+        if (NIL_P(e)) {
+            if (rb_num_negative_int_p(s)) {
+                ee = -HUGE_VAL;
+            }
+            else {
+                ee = HUGE_VAL;
+            }
+        }
+        else {
+            ee = NUM2DBL(e);
+        }
+
+        n = arith_seq_float_step_size(NUM2DBL(b), ee, NUM2DBL(s), x);
+        if (isinf(n)) return DBL2NUM(n);
+        if (POSFIXABLE(n)) return LONG2FIX(n);
+        return rb_dbl2big(n);
+    }
+
+    if (NIL_P(e)) {
+        return DBL2NUM(HUGE_VAL);
+    }
+
+    if (!rb_obj_is_kind_of(s, rb_cNumeric)) {
+        s = rb_to_int(s);
+    }
+
+    if (rb_equal(s, INT2FIX(0))) {
+        return DBL2NUM(HUGE_VAL);
+    }
+
+    len_1 = rb_int_idiv(rb_int_minus(e, b), s);
+    if (rb_num_negative_int_p(len_1)) {
+        return INT2FIX(0);
+    }
+
+    last = rb_int_plus(b, rb_int_mul(s, len_1));
+    if (x && rb_equal(last, e)) {
+        len = len_1;
+    }
+    else {
+        len = rb_int_plus(len_1, INT2FIX(1));
+    }
+
+    return len;
+}
+
 void
 InitVM_Enumerator(void)
 {
@@ -2450,6 +2842,22 @@ InitVM_Enumerator(void)
     rb_define_method(rb_cYielder, "yield", yielder_yield, -2);
     rb_define_method(rb_cYielder, "<<", yielder_yield_push, -2);
 
+    /* ArithmeticSequence */
+    rb_cArithSeq = rb_define_class_under(rb_cEnumerator, "ArithmeticSequence", rb_cEnumerator);
+    rb_define_method(rb_cArithSeq, "begin", arith_seq_begin, 0);
+    rb_define_method(rb_cArithSeq, "end", arith_seq_end, 0);
+    rb_define_method(rb_cArithSeq, "exclude_end?", arith_seq_exclude_end, 0);
+    rb_define_method(rb_cArithSeq, "step", arith_seq_step, 0);
+    rb_define_method(rb_cArithSeq, "first", arith_seq_first, -1);
+    rb_define_method(rb_cArithSeq, "last", arith_seq_last, -1);
+    rb_define_method(rb_cArithSeq, "inspect", arith_seq_inspect, 0);
+    rb_define_method(rb_cArithSeq, "==", arith_seq_eq, 1);
+    rb_define_method(rb_cArithSeq, "===", arith_seq_eq, 1);
+    rb_define_method(rb_cArithSeq, "eql?", arith_seq_eq, 1);
+    rb_define_method(rb_cArithSeq, "hash", arith_seq_hash, 0);
+    rb_define_method(rb_cArithSeq, "each", arith_seq_each, 0);
+    rb_define_method(rb_cArithSeq, "size", arith_seq_size, 0);
+
     rb_provide("enumerator.so");	/* for backward compatibility */
 }
 
@@ -2469,6 +2877,10 @@ Init_Enumerator(void)
     id_method = rb_intern("method");
     id_force = rb_intern("force");
     id_to_enum = rb_intern("to_enum");
+    id_begin = rb_intern("begin");
+    id_end = rb_intern("end");
+    id_step = rb_intern("step");
+    id_exclude_end = rb_intern("exclude_end");
     sym_each = ID2SYM(id_each);
     sym_cycle = ID2SYM(rb_intern("cycle"));
 
diff --git a/internal.h b/internal.h
index 7047eb4c3d..81c556c0be 100644
--- a/internal.h
+++ b/internal.h
@@ -1995,6 +1995,11 @@ enum rb_int_parse_flags {
 };
 VALUE rb_int_parse_cstr(const char *str, ssize_t len, char **endp, size_t *ndigits, int base, int flags);
 
+/* enumerator.c (export) */
+VALUE rb_arith_seq_new(VALUE obj, VALUE meth, int argc, VALUE const *argv,
+                       rb_enumerator_size_func *size_fn,
+                       VALUE beg, VALUE end, VALUE step, int excl);
+
 /* error.c (export) */
 int rb_bug_reporter_add(void (*func)(FILE *, void *), void *data);
 NORETURN(void rb_unexpected_type(VALUE,int));
diff --git a/numeric.c b/numeric.c
index 090b5e57ba..b05b8f36e2 100644
--- a/numeric.c
+++ b/numeric.c
@@ -2581,10 +2581,9 @@ num_step_negative_p(VALUE num)
 }
 
 static int
-num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step)
+num_step_extract_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, VALUE *by)
 {
     VALUE hash;
-    int desc;
 
     argc = rb_scan_args(argc, argv, "02:", to, step, &hash);
     if (!NIL_P(hash)) {
@@ -2599,28 +2598,47 @@ num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step)
 	}
 	if (values[1] != Qundef) {
 	    if (argc > 1) rb_raise(rb_eArgError, "step is given twice");
-	    *step = values[1];
+	    *by = values[1];
 	}
     }
+
+    return argc;
+}
+
+static int
+num_step_check_fix_args(int argc, VALUE *to, VALUE *step, VALUE by, int fix_nil, int allow_zero_step)
+{
+    int desc;
+    if (by != Qundef) {
+        *step = by;
+    }
     else {
-	/* compatibility */
-	if (argc > 1 && NIL_P(*step)) {
-	    rb_raise(rb_eTypeError, "step must be numeric");
-	}
-	if (rb_equal(*step, INT2FIX(0))) {
-	    rb_raise(rb_eArgError, "step can't be 0");
-	}
+        /* compatibility */
+        if (argc > 1 && NIL_P(*step)) {
+            rb_raise(rb_eTypeError, "step must be numeric");
+        }
+        if (!allow_zero_step && rb_equal(*step, INT2FIX(0))) {
+            rb_raise(rb_eArgError, "step can't be 0");
+        }
     }
     if (NIL_P(*step)) {
 	*step = INT2FIX(1);
     }
     desc = num_step_negative_p(*step);
-    if (NIL_P(*to)) {
-	*to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
+    if (fix_nil && NIL_P(*to)) {
+        *to = desc ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
     }
     return desc;
 }
 
+static int
+num_step_scan_args(int argc, const VALUE *argv, VALUE *to, VALUE *step, int fix_nil, int allow_zero_step)
+{
+    VALUE by = Qundef;
+    argc = num_step_extract_args(argc, argv, to, step, &by);
+    return num_step_check_fix_args(argc, to, step, by, fix_nil, allow_zero_step);
+}
+
 static VALUE
 num_step_size(VALUE from, VALUE args, VALUE eobj)
 {
@@ -2628,7 +2646,7 @@ num_step_size(VALUE from, VALUE args, VALUE eobj)
     int argc = args ? RARRAY_LENINT(args) : 0;
     const VALUE *argv = args ? RARRAY_CONST_PTR(args) : 0;
 
-    num_step_scan_args(argc, argv, &to, &step);
+    num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
 
     return ruby_num_interval_step_size(from, to, step, FALSE);
 }
@@ -2691,9 +2709,28 @@ num_step(int argc, VALUE *argv, VALUE from)
     VALUE to, step;
     int desc, inf;
 
-    RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);
+    /* RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size); */
+
+    if (!rb_block_given_p()) {
+        VALUE by = Qundef;
+
+        num_step_extract_args(argc, argv, &to, &step, &by);
+        if (by != Qundef) {
+            step = by;
+        }
+        if (NIL_P(step)) {
+            step = INT2FIX(1);
+        }
+        if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) &&
+            rb_obj_is_kind_of(step, rb_cNumeric)) {
+            return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv,
+                                    num_step_size, from, to, step, FALSE);
+        }
+
+        RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);
+    }
 
-    desc = num_step_scan_args(argc, argv, &to, &step);
+    desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
     if (rb_equal(step, INT2FIX(0))) {
 	inf = 1;
     }
diff --git a/range.c b/range.c
index bcc8d1a8f4..56c1ee253b 100644
--- a/range.c
+++ b/range.c
@@ -388,18 +388,26 @@ range_step(int argc, VALUE *argv, VALUE range)
 {
     VALUE b, e, step, tmp;
 
-    RETURN_SIZED_ENUMERATOR(range, argc, argv, range_step_size);
-
     b = RANGE_BEG(range);
     e = RANGE_END(range);
     if (argc == 0) {
-	step = INT2FIX(1);
+        step = INT2FIX(1);
     }
     else {
-	rb_scan_args(argc, argv, "01", &step);
-	step = check_step_domain(step);
+        rb_scan_args(argc, argv, "01", &step);
+    }
+
+    if (!rb_block_given_p()) {
+        if (rb_obj_is_kind_of(b, rb_cNumeric) && (NIL_P(e) || rb_obj_is_kind_of(e, rb_cNumeric))) {
+            return rb_arith_seq_new(range, ID2SYM(rb_frame_this_func()), argc, argv,
+                    range_step_size, b, e, step, EXCL(range));
+        }
+
+        RETURN_SIZED_ENUMERATOR(range, argc, argv, range_step_size);
     }
 
+    step = check_step_domain(step);
+
     if (FIXNUM_P(b) && NIL_P(e) && FIXNUM_P(step)) {
 	long i = FIX2LONG(b), unit = FIX2LONG(step);
 	do {
diff --git a/spec/ruby/core/numeric/shared/step.rb b/spec/ruby/core/numeric/shared/step.rb
index fa703b7554..f058c64a50 100644
--- a/spec/ruby/core/numeric/shared/step.rb
+++ b/spec/ruby/core/numeric/shared/step.rb
@@ -259,15 +259,15 @@ describe :numeric_step, :shared => true do
 
   describe "when no block is given" do
     it "returns an Enumerator when step is 0" do
-      1.send(@method, *@step_args.call(2, 0)).should be_an_instance_of(Enumerator)
+      1.send(@method, *@step_args.call(2, 0)).should be_an_instance_of(Enumerator::ArithmeticSequence)
     end
 
     it "returns an Enumerator when not passed a block and self > stop" do
-      1.send(@method, *@step_args.call(0, 2)).should be_an_instance_of(Enumerator)
+      1.send(@method, *@step_args.call(0, 2)).should be_an_instance_of(Enumerator::ArithmeticSequence)
     end
 
     it "returns an Enumerator when not passed a block and self < stop" do
-      1.send(@method, *@step_args.call(2, 3)).should be_an_instance_of(Enumerator)
+      1.send(@method, *@step_args.call(2, 3)).should be_an_instance_of(Enumerator::ArithmeticSequence)
     end
 
     it "returns an Enumerator that uses the given step" do
diff --git a/spec/ruby/core/numeric/step_spec.rb b/spec/ruby/core/numeric/step_spec.rb
index a932b4df73..54133f8810 100644
--- a/spec/ruby/core/numeric/step_spec.rb
+++ b/spec/ruby/core/numeric/step_spec.rb
@@ -23,23 +23,23 @@ describe "Numeric#step" do
 
     describe "when no block is given" do
       it "returns an Enumerator when step is 0" do
-        1.step(5, 0).should be_an_instance_of(Enumerator)
+        1.step(5, 0).should be_an_instance_of(Enumerator::ArithmeticSequence)
       end
 
       it "returns an Enumerator when step is 0.0" do
-        1.step(2, 0.0).should be_an_instance_of(Enumerator)
+        1.step(2, 0.0).should be_an_instance_of(Enumerator::ArithmeticSequence)
       end
 
       describe "returned Enumerator" do
         describe "size" do
           it "raises an ArgumentError when step is 0" do
             enum = 1.step(5, 0)
-            lambda { enum.size }.should raise_error(ArgumentError)
+            enum.size.should == Float::INFINITY
           end
 
           it "raises an ArgumentError when step is 0.0" do
             enum = 1.step(2, 0.0)
-            lambda { enum.size }.should raise_error(ArgumentError)
+            enum.size.should == Float::INFINITY
           end
         end
       end
diff --git a/spec/ruby/core/range/step_spec.rb b/spec/ruby/core/range/step_spec.rb
index 3d5e75b033..c364600fb0 100644
--- a/spec/ruby/core/range/step_spec.rb
+++ b/spec/ruby/core/range/step_spec.rb
@@ -5,9 +5,9 @@ describe "Range#step" do
     ScratchPad.record []
   end
 
-  it "returns an enumerator when no block is given" do
+  it "returns an arithmetic sequence when no block is given" do
     enum = (1..10).step(4)
-    enum.should be_an_instance_of(Enumerator)
+    enum.should be_an_instance_of(Enumerator::ArithmeticSequence)
     enum.to_a.should eql([1, 5, 9])
   end
 
@@ -263,7 +263,7 @@ describe "Range#step" do
   end
 
   describe "when no block is given" do
-    describe "returned Enumerator" do
+    describe "returned Enumerator::ArithmeticSequence" do
       describe "size" do
         it "raises a TypeError if step does not respond to #to_int" do
           obj = mock("Range#step non-integer")
@@ -279,19 +279,9 @@ describe "Range#step" do
           lambda { enum.size }.should raise_error(TypeError)
         end
 
-        it "raises an ArgumentError if step is 0" do
-          enum = (-1..1).step(0)
-          lambda { enum.size }.should raise_error(ArgumentError)
-        end
-
-        it "raises an ArgumentError if step is 0.0" do
-          enum = (-1..1).step(0.0)
-          lambda { enum.size }.should raise_error(ArgumentError)
-        end
-
-        it "raises an ArgumentError if step is negative" do
-          enum = (-1..1).step(-2)
-          lambda {  enum.size }.should raise_error(ArgumentError)
+        it "returns Float::INFINITY for zero step" do
+          (-1..1).step(0).size.should == Float::INFINITY
+          (-1..1).step(0.0).size.should == Float::INFINITY
         end
 
         it "returns the ceil of range size divided by the number of steps" do
@@ -307,6 +297,11 @@ describe "Range#step" do
           (-5...5).step(2).size.should == 5
         end
 
+        it "returns the ceil of range size divided by the number of steps even if step is negative" do
+          (-1..1).step(-1).size.should == 0
+          (1..-1).step(-1).size.should == 3
+        end
+
         it "returns the correct number of steps when one of the arguments is a float" do
           (-1..1.0).step(0.5).size.should == 5
           (-1.0...1.0).step(0.5).size.should == 4
diff --git a/test/ruby/test_arithmetic_sequence.rb b/test/ruby/test_arithmetic_sequence.rb
new file mode 100644
index 0000000000..fe1af362f4
--- /dev/null
+++ b/test/ruby/test_arithmetic_sequence.rb
@@ -0,0 +1,367 @@
+# frozen_string_literal: false
+require 'test/unit'
+
+class TestArithmeticSequence < Test::Unit::TestCase
+  def test_begin
+    assert_equal(1, 1.step.begin)
+    assert_equal(1, 1.step(10).begin)
+    assert_equal(1, 1.step(to: 10).begin)
+    assert_equal(1, 1.step(nil).begin)
+    assert_equal(1, 1.step(to: nil).begin)
+    assert_equal(1, 1.step(by: 2).begin)
+    assert_equal(1, 1.step(by: -1).begin)
+    assert_equal(1, 1.step(by: nil).begin)
+    assert_equal(1, 1.step(10, 2).begin)
+    assert_equal(1, 1.step(10, by: 2).begin)
+    assert_equal(1, 1.step(to: 10, by: 2).begin)
+    assert_equal(10, 10.step(to: 1, by: -1).begin)
+    assert_equal(10, 10.step(to: 1, by: -2).begin)
+    assert_equal(10, 10.step(to: -1, by: -2).begin)
+    assert_equal(10.0, 10.0.step(to: -1.0, by: -2.0).begin)
+  end
+
+  def test_end
+    assert_equal(nil, 1.step.end)
+    assert_equal(10, 1.step(10).end)
+    assert_equal(10, 1.step(to: 10).end)
+    assert_equal(nil, 1.step(nil).end)
+    assert_equal(nil, 1.step(to: nil).end)
+    assert_equal(nil, 1.step(by: 2).end)
+    assert_equal(nil, 1.step(by: -1).end)
+    assert_equal(nil, 1.step(by: nil).end)
+    assert_equal(10, 1.step(10, 2).end)
+    assert_equal(10, 1.step(10, by: 2).end)
+    assert_equal(10, 1.step(to: 10, by: 2).end)
+    assert_equal(1, 10.step(to: 1, by: -1).end)
+    assert_equal(1, 10.step(to: 1, by: -2).end)
+    assert_equal(-1, 10.step(to: -1, by: -2).end)
+    assert_equal(-1.0, 10.0.step(to: -1.0, by: -2.0).end)
+  end
+
+  def test_exclude_end_p
+    assert_equal(false, 1.step.exclude_end?)
+    assert_equal(false, 1.step(10).exclude_end?)
+    assert_equal(false, 1.step(to: 10).exclude_end?)
+    assert_equal(false, 1.step(nil).exclude_end?)
+    assert_equal(false, 1.step(to: nil).exclude_end?)
+    assert_equal(false, 1.step(by: 2).exclude_end?)
+    assert_equal(false, 1.step(by: -1).exclude_end?)
+    assert_equal(false, 1.step(by: nil).exclude_end?)
+    assert_equal(false, 1.step(10, 2).exclude_end?)
+    assert_equal(false, 1.step(10, by: 2).exclude_end?)
+    assert_equal(false, 1.step(to: 10, by: 2).exclude_end?)
+    assert_equal(false, 10.step(to: 1, by: -1).exclude_end?)
+    assert_equal(false, 10.step(to: 1, by: -2).exclude_end?)
+    assert_equal(false, 10.step(to: -1, by: -2).exclude_end?)
+  end
+
+  def test_step
+    assert_equal(1, 1.step.step)
+    assert_equal(1, 1.step(10).step)
+    assert_equal(1, 1.step(to: 10).step)
+    assert_equal(1, 1.step(nil).step)
+    assert_equal(1, 1.step(to: nil).step)
+    assert_equal(2, 1.step(by: 2).step)
+    assert_equal(-1, 1.step(by: -1).step)
+    assert_equal(1, 1.step(by: nil).step)
+    assert_equal(2, 1.step(10, 2).step)
+    assert_equal(2, 1.step(10, by: 2).step)
+    assert_equal(2, 1.step(to: 10, by: 2).step)
+    assert_equal(-1, 10.step(to: 1, by: -1).step)
+    assert_equal(-2, 10.step(to: 1, by: -2).step)
+    assert_equal(-2, 10.step(to: -1, by: -2).step)
+    assert_equal(-2.0, 10.0.step(to: -1.0, by: -2.0).step)
+  end
+
+  def test_eq
+    seq = 1.step
+    assert_equal(seq, seq)
+    assert_equal(seq, 1.step)
+    assert_equal(seq, 1.step(nil))
+  end
+
+  def test_eqq
+    seq = 1.step
+    assert_operator(seq, :===, seq)
+    assert_operator(seq, :===, 1.step)
+    assert_operator(seq, :===, 1.step(nil))
+  end
+
+  def test_eql_p
+    seq = 1.step
+    assert_operator(seq, :eql?, seq)
+    assert_operator(seq, :eql?, 1.step)
+    assert_operator(seq, :eql?, 1.step(nil))
+  end
+
+  def test_hash
+    seq = 1.step
+    assert_equal(seq.hash, seq.hash)
+    assert_equal(seq.hash, 1.step.hash)
+    assert_equal(seq.hash, 1.step(nil).hash)
+  end
+
+  def test_first
+    seq = 1.step
+    assert_equal(1, seq.first)
+    assert_equal([1], seq.first(1))
+    assert_equal([1, 2, 3], seq.first(3))
+
+    seq = 1.step(by: 2)
+    assert_equal(1, seq.first)
+    assert_equal([1], seq.first(1))
+    assert_equal([1, 3, 5], seq.first(3))
+
+    seq = 10.step(by: -2)
+    assert_equal(10, seq.first)
+    assert_equal([10], seq.first(1))
+    assert_equal([10, 8, 6], seq.first(3))
+
+    seq = 1.step(by: 4)
+    assert_equal([1, 5, 9], seq.first(3))
+
+    seq = 1.step(10, by: 4)
+    assert_equal([1, 5, 9], seq.first(5))
+
+    seq = 1.step(0)
+    assert_equal(nil, seq.first)
+    assert_equal([], seq.first(1))
+    assert_equal([], seq.first(3))
+
+    seq = 1.step(10, by: -1)
+    assert_equal(nil, seq.first)
+    assert_equal([], seq.first(1))
+    assert_equal([], seq.first(3))
+
+    seq = 10.0.step(-1.0, by: -2.0)
+    assert_equal(10.0, seq.first)
+    assert_equal([10.0], seq.first(1))
+    assert_equal([10.0, 8.0, 6.0], seq.first(3))
+  end
+
+  def test_last
+    seq = 1.step(10)
+    assert_equal(10, seq.last)
+    assert_equal([10], seq.last(1))
+    assert_equal([8, 9, 10], seq.last(3))
+
+    seq = 1.step(10, 2)
+    assert_equal(9, seq.last)
+    assert_equal([9], seq.last(1))
+    assert_equal([5, 7, 9], seq.last(3))
+
+    seq = 10.step(1, -2)
+    assert_equal(2, seq.last)
+    assert_equal([2], seq.last(1))
+    assert_equal([6, 4, 2], seq.last(3))
+
+    seq = 10.step(-1, -2)
+    assert_equal(0, seq.last)
+
+    seq = 1.step(10, 4)
+    assert_equal([1, 5, 9], seq.last(5))
+
+    seq = 10.step(1)
+    assert_equal(nil, seq.last)
+    assert_equal([], seq.last(1))
+    assert_equal([], seq.last(5))
+
+    seq = 1.step(10, -1)
+    assert_equal(nil, seq.last)
+    assert_equal([], seq.last(1))
+    assert_equal([], seq.last(5))
+
+    seq = (1..10).step
+    assert_equal(10, seq.last)
+    assert_equal([10], seq.last(1))
+    assert_equal([8, 9, 10], seq.last(3))
+
+    seq = (1...10).step
+    assert_equal(9, seq.last)
+    assert_equal([9], seq.last(1))
+    assert_equal([7, 8, 9], seq.last(3))
+
+    seq = 10.0.step(-3.0, by: -2.0)
+    assert_equal(-2.0, seq.last)
+    assert_equal([-2.0], seq.last(1))
+    assert_equal([2.0, 0.0, -2.0], seq.last(3))
+  end
+
+  def test_to_a
+    assert_equal([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 1.step(10).to_a)
+    assert_equal([1, 3, 5, 7, 9], 1.step(10, 2).to_a)
+    assert_equal([1, 3, 5, 7, 9], (1..10).step(2).to_a)
+    assert_equal([10, 8, 6, 4, 2], 10.step(1, by: -2).to_a)
+    assert_equal([10, 8, 6, 4, 2], (10..1).step(-2).to_a)
+    assert_equal([10.0, 8.0, 6.0, 4.0, 2.0], (10.0..1.0).step(-2.0).to_a)
+  end
+
+  def test_slice
+    seq = 1.step(10, 2)
+    assert_equal([[1, 3, 5], [7, 9]], seq.each_slice(3).to_a)
+
+    seq = 10.step(1, -2)
+    assert_equal([[10, 8, 6], [4, 2]], seq.each_slice(3).to_a)
+  end
+
+  def test_cons
+    seq = 1.step(10, 2)
+    assert_equal([[1, 3, 5], [3, 5, 7], [5, 7, 9]], seq.each_cons(3).to_a)
+
+    seq = 10.step(1, -2)
+    assert_equal([[10, 8, 6], [8, 6, 4], [6, 4, 2]], seq.each_cons(3).to_a)
+  end
+
+  def test_with_index
+    seq = 1.step(6, 2)
+    assert_equal([[1, 0], [3, 1], [5, 2]], seq.with_index.to_a)
+    assert_equal([[1, 10], [3, 11], [5, 12]], seq.with_index(10).to_a)
+
+    seq = 10.step(5, -2)
+    assert_equal([[10, 0], [8, 1], [6, 2]], seq.with_index.to_a)
+    assert_equal([[10, 10], [8, 11], [6, 12]], seq.with_index(10).to_a)
+  end
+
+  def test_with_object
+    obj = [0, 1]
+    seq = 1.step(10, 2)
+    ret = seq.each_with_object(obj) do |i, memo|
+      memo[0] += i
+      memo[1] *= i
+    end
+    assert_same(obj, ret)
+    assert_equal([25, 945], ret)
+
+    obj = [0, 1]
+    seq = 10.step(1, -2)
+    ret = seq.each_with_object(obj) do |i, memo|
+      memo[0] += i
+      memo[1] *= i
+    end
+    assert_same(obj, ret)
+    assert_equal([30, 3840], ret)
+  end
+
+  def test_next
+    seq = 1.step(10, 2)
+    [1, 3, 5, 7, 9].each do |i|
+      assert_equal(i, seq.next)
+    end
+
+    seq = 10.step(1, -2)
+    [10, 8, 6, 4, 2].each do |i|
+      assert_equal(i, seq.next)
+    end
+  end
+
+  def test_next_rewind
+    seq = 1.step(6, 2)
+    assert_equal(1, seq.next)
+    assert_equal(3, seq.next)
+    seq.rewind
+    assert_equal(1, seq.next)
+    assert_equal(3, seq.next)
+    assert_equal(5, seq.next)
+    assert_raise(StopIteration) { seq.next }
+
+    seq = 10.step(5, -2)
+    assert_equal(10, seq.next)
+    assert_equal(8, seq.next)
+    seq.rewind
+    assert_equal(10, seq.next)
+    assert_equal(8, seq.next)
+    assert_equal(6, seq.next)
+    assert_raise(StopIteration) { seq.next }
+  end
+
+  def test_next_after_stopiteration
+    seq = 1.step(2, 2)
+    assert_equal(1, seq.next)
+    assert_raise(StopIteration) { seq.next }
+    assert_raise(StopIteration) { seq.next }
+    seq.rewind
+    assert_equal(1, seq.next)
+    assert_raise(StopIteration) { seq.next }
+    assert_raise(StopIteration) { seq.next }
+  end
+
+  def test_stop_result
+    seq = 1.step(2, 2)
+    res = seq.each {}
+    assert_equal(1, seq.next)
+    exc = assert_raise(StopIteration) { seq.next }
+    assert_equal(res, exc.result)
+  end
+
+  def test_peek
+    seq = 1.step(2, 2)
+    assert_equal(1, seq.peek)
+    assert_equal(1, seq.peek)
+    assert_equal(1, seq.next)
+    assert_raise(StopIteration) { seq.peek }
+    assert_raise(StopIteration) { seq.peek }
+
+    seq = 10.step(9, -2)
+    assert_equal(10, seq.peek)
+    assert_equal(10, seq.peek)
+    assert_equal(10, seq.next)
+    assert_raise(StopIteration) { seq.peek }
+    assert_raise(StopIteration) { seq.peek }
+  end
+
+  def test_next_values
+    seq = 1.step(2, 2)
+    assert_equal([1], seq.next_values)
+  end
+
+  def test_peek_values
+    seq = 1.step(2, 2)
+    assert_equal([1], seq.peek_values)
+  end
+
+  def test_num_step_inspect
+    assert_equal('(1.step)', 1.step.inspect)
+    assert_equal('(1.step(10))', 1.step(10).inspect)
+    assert_equal('(1.step(10, 2))', 1.step(10, 2).inspect)
+    assert_equal('(1.step(10, by: 2))', 1.step(10, by: 2).inspect)
+    assert_equal('(1.step(by: 2))', 1.step(by: 2).inspect)
+  end
+
+  def test_range_step_inspect
+    assert_equal('((1..).step)', (1..).step.inspect)
+    assert_equal('((1..10).step)', (1..10).step.inspect)
+    assert_equal('((1..10).step(2))', (1..10).step(2).inspect)
+  end
+
+  def test_num_step_size
+    assert_equal(10, 1.step(10).size)
+    assert_equal(5, 1.step(10, 2).size)
+    assert_equal(4, 1.step(10, 3).size)
+    assert_equal(1, 1.step(10, 10).size)
+    assert_equal(0, 1.step(0).size)
+    assert_equal(Float::INFINITY, 1.step.size)
+
+    assert_equal(10, 10.step(1, -1).size)
+    assert_equal(5, 10.step(1, -2).size)
+    assert_equal(4, 10.step(1, -3).size)
+    assert_equal(1, 10.step(1, -10).size)
+    assert_equal(0, 1.step(2, -1).size)
+    assert_equal(Float::INFINITY, 1.step(by: -1).size)
+  end
+
+  def test_range_step_size
+    assert_equal(10, (1..10).step.size)
+    assert_equal(9, (1...10).step.size)
+    assert_equal(5, (1..10).step(2).size)
+    assert_equal(5, (1...10).step(2).size)
+    assert_equal(4, (1...9).step(2).size)
+    assert_equal(Float::INFINITY, (1..).step.size)
+
+    assert_equal(10, (10..1).step(-1).size)
+    assert_equal(9, (10...1).step(-1).size)
+    assert_equal(5, (10..1).step(-2).size)
+    assert_equal(5, (10...1).step(-2).size)
+    assert_equal(4, (10...2).step(-2).size)
+    assert_equal(Float::INFINITY, (1..).step(-1).size)
+  end
+end
diff --git a/test/ruby/test_enumerator.rb b/test/ruby/test_enumerator.rb
index 6568cbff18..22ec62e252 100644
--- a/test/ruby/test_enumerator.rb
+++ b/test/ruby/test_enumerator.rb
@@ -632,7 +632,7 @@ class TestEnumerator < Test::Unit::TestCase
     assert_equal 4, (1..10).step(3).size
     assert_equal 3, (1...10).step(3).size
     assert_equal Float::INFINITY, (42..Float::INFINITY).step(2).size
-    assert_raise(ArgumentError){ (1..10).step(-2).size }
+    assert_equal 0, (1..10).step(-2).size
   end
 
   def test_size_for_downup_to
diff --git a/test/ruby/test_numeric.rb b/test/ruby/test_numeric.rb
index 2026f3b155..e48c3448e8 100644
--- a/test/ruby/test_numeric.rb
+++ b/test/ruby/test_numeric.rb
@@ -260,11 +260,11 @@ class TestNumeric < Test::Unit::TestCase
     assert_raise(ArgumentError) { 1.step(10, 1, 0) { } }
     assert_raise(ArgumentError) { 1.step(10, 1, 0).size }
     assert_raise(ArgumentError) { 1.step(10, 0) { } }
-    assert_raise(ArgumentError) { 1.step(10, 0).size }
     assert_raise(ArgumentError) { 1.step(10, "1") { } }
     assert_raise(ArgumentError) { 1.step(10, "1").size }
     assert_raise(TypeError) { 1.step(10, nil) { } }
-    assert_raise(TypeError) { 1.step(10, nil).size }
+    assert_nothing_raised { 1.step(10, 0).size }
+    assert_nothing_raised { 1.step(10, nil).size }
     assert_nothing_raised { 1.step(by: 0, to: nil) }
     assert_nothing_raised { 1.step(by: 0, to: nil).size }
     assert_nothing_raised { 1.step(by: 0) }
@@ -272,6 +272,14 @@ class TestNumeric < Test::Unit::TestCase
     assert_nothing_raised { 1.step(by: nil) }
     assert_nothing_raised { 1.step(by: nil).size }
 
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(10))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(10, 2))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(10, by: 2))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(by: 2))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(by: 2, to: nil))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(by: 2, to: 10))
+    assert_kind_of(Enumerator::ArithmeticSequence, 1.step(by: -1))
+
     bug9811 = '[ruby-dev:48177] [Bug #9811]'
     assert_raise(ArgumentError, bug9811) { 1.step(10, foo: nil) {} }
     assert_raise(ArgumentError, bug9811) { 1.step(10, foo: nil).size }
diff --git a/test/ruby/test_range.rb b/test/ruby/test_range.rb
index eada19cfb6..a845dc4929 100644
--- a/test/ruby/test_range.rb
+++ b/test/ruby/test_range.rb
@@ -222,7 +222,11 @@ class TestRange < Test::Unit::TestCase
     (0..).step(2) {|x| a << x; break if a.size == 10 }
     assert_equal([0, 2, 4, 6, 8, 10, 12, 14, 16, 18], a)
 
-    assert_raise(ArgumentError) { (0..10).step(-1) { } }
+    assert_kind_of(Enumerator::ArithmeticSequence, (0..10).step)
+    assert_kind_of(Enumerator::ArithmeticSequence, (0..10).step(2))
+    assert_kind_of(Enumerator::ArithmeticSequence, (0..10).step(0.5))
+    assert_kind_of(Enumerator::ArithmeticSequence, (10..0).step(-1))
+
     assert_raise(ArgumentError) { (0..10).step(0) { } }
     assert_raise(ArgumentError) { (0..).step(-1) { } }
     assert_raise(ArgumentError) { (0..).step(0) { } }