2 #define _MOVIT_FP16_H 1
8 // Code for converting to and from fp16 (from fp64), without any particular
9 // machine support, with proper IEEE round-to-even behavior (and correct
10 // handling of NaNs and infinities). This is needed because some OpenGL
11 // drivers don't properly round off when asked to convert data themselves.
13 // These routines are originally written by Fabian Giesen, and released by
14 // him into the public domain;
15 // see https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/.
16 // They are quite fast, and can be vectorized if need be; of course, using
17 // the f16c instructions (see below) will be faster still.
21 // structs instead of ints, so that they are not implicitly convertible.
31 // Use the f16c instructions from Haswell if available (and we know that they
32 // are at compile time).
33 static inline float fp16_to_fp32(fp16_int_t x)
35 return _cvtsh_ss(x.val);
38 static inline fp16_int_t fp32_to_fp16(float x)
41 ret.val = _cvtss_sh(x, 0);
52 static inline float fp16_to_fp32(fp16_int_t h)
54 fp32 magic; magic.u = 113 << 23;
55 unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
59 unsigned int shifted = (h.val & 0x7fff) << 13;
60 unsigned int exponent = shifted & shifted_exp;
64 if (exponent == 0) { // Zero / Denormal
67 } else if (exponent == shifted_exp) { // Inf/NaN
68 o.u += (255 - 31) << 23;
70 o.u += (127 - 15) << 23;
73 o.u |= (h.val & 0x8000) << 16; // copy sign bit
77 static inline fp16_int_t fp32_to_fp16(float x)
80 unsigned int f32infty = 255 << 23;
81 unsigned int f16max = (127 + 16) << 23;
82 fp32 denorm_magic; denorm_magic.u = ((127 - 15) + (23 - 10) + 1) << 23;
83 unsigned int sign_mask = 0x80000000u;
86 unsigned int sign = f.u & sign_mask;
89 // NOTE all the integer compares in this function can be safely
90 // compiled into signed compares since all operands are below
91 // 0x80000000. Important if you want fast straight SSE2 code
92 // (since there's no unsigned PCMPGTD).
94 if (f.u >= f16max) { // result is Inf or NaN (all exponent bits set)
95 o.val = (f.u > f32infty) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
96 } else { // (De)normalized number or zero
97 if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero
98 // use a magic value to align our 10 mantissa bits at the bottom of
99 // the float. as long as FP addition is round-to-nearest-even this
101 f.f += denorm_magic.f;
103 // and one integer subtract of the bias later, we have our final float!
104 o.val = f.u - denorm_magic.u;
106 unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
108 // update exponent, rounding bias part 1
109 f.u += (unsigned(15 - 127) << 23) + 0xfff;
110 // rounding bias part 2
123 // Overloads for use in templates.
124 static inline float to_fp32(double x) { return x; }
125 static inline float to_fp32(float x) { return x; }
126 static inline float to_fp32(fp16_int_t x) { return fp16_to_fp32(x); }
128 template<class T> inline T from_fp32(float x);
129 template<> inline double from_fp32<double>(float x) { return x; }
130 template<> inline float from_fp32<float>(float x) { return x; }
131 template<> inline fp16_int_t from_fp32<fp16_int_t>(float x) { return fp32_to_fp16(x); }
133 template<class From, class To>
134 inline To convert_float(From x) { return from_fp32<To>(to_fp32(x)); }
137 inline Same convert_float(Same x) { return x; }
141 #endif // _MOVIT_FP16_H