What is the precision of highp floats in GLSL ES 2.0 (for iPhone/iPod touch/iPad)?

From the OpenGL ES Shading Language reference:

• highp – 16-bit, floating point range:
  −2⁶² to 2⁶², integer range: −2¹⁶ to 2¹⁶
• mediump – 10 bit, floating
  point range: −2¹⁴ to 2¹⁴, integer
  range: −2¹⁰ to 2¹⁰
• lowp – 8 bit,
  floating point range: −2 to 2,
  integer range: −2⁸ to 2⁸

In OpenGL ES 3 these guarantees have been upgraded, see the GLSL ES 3.00 spec:

• highp – 24-bit, floating point range:
  −2¹²⁶ to 2¹²⁷, signed integer range: −2³¹ to 2³¹−1, unsigned integer range: 0 to 2³²−1
• mediump – 10 bit, floating
  point range: −2¹⁴ to 2¹⁴, signed integer
  range: −2¹⁵ to 2¹⁵−1, unsigned integer range 0 to 2¹⁶−1
• lowp – 8/9 bit (signed/unsigned),
  floating point range: −2 to 2,
  signed integer range: −2⁸ to 2⁸−1, unsigned integer range 0 to 2⁹−1