/* SPDX-FileCopyrightText: 2024 Blender Authors * * SPDX-License-Identifier: GPL-2.0-or-later */ /** \file * \ingroup bli */ #include "BLI_math_half.hh" #if defined(__ARM_NEON) /* Use ARM FP16 conversion instructions */ # define USE_HARDWARE_FP16_NEON # include #endif #if (defined(__x86_64__) || defined(_M_X64)) /* All AVX2 CPUs have F16C instructions, so use those if we're compiling for AVX2. * Otherwise use "manual" SSE2 4x-wide conversion. */ # if defined(__AVX2__) # define USE_HARDWARE_FP16_F16C # else # define USE_SSE2_FP16 # endif # include #endif uint16_t blender::math::float_to_half(float v) { #if defined(USE_HARDWARE_FP16_NEON) float16x4_t h4 = vcvt_f16_f32(vdupq_n_f32(v)); float16_t h = vget_lane_f16(h4, 0); return *(uint16_t *)&h; #else /* Based on float_to_half_fast3_rtne from public domain https://gist.github.com/rygorous/2156668 * see corresponding blog post https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/ */ union FP32 { uint32_t u; float f; }; FP32 f; f.f = v; FP32 f32infty = {255 << 23}; FP32 f16max = {(127 + 16) << 23}; FP32 denorm_magic = {((127 - 15) + (23 - 10) + 1) << 23}; uint32_t sign_mask = 0x80000000u; uint16_t o = {0}; uint32_t sign = f.u & sign_mask; f.u ^= sign; /* * NOTE all the integer compares in this function can be safely * compiled into signed compares since all operands are below * 0x80000000. Important if you want fast straight SSE2 code * (since there's no unsigned PCMPGTD). */ if (f.u >= f16max.u) { /* result is Inf or NaN (all exponent bits set) */ o = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; /* NaN->qNaN and Inf->Inf */ } else { /* (De)normalized number or zero */ if (f.u < (113 << 23)) { /* Resulting FP16 is subnormal or zero. * Use a magic value to align our 10 mantissa bits at the bottom of * the float. as long as FP addition is round-to-nearest-even this * just works. */ f.f += denorm_magic.f; /* and one integer subtract of the bias later, we have our final float! */ o = f.u - denorm_magic.u; } else { uint32_t mant_odd = (f.u >> 13) & 1; /* resulting mantissa is odd */ /* update exponent, rounding bias part 1 */ f.u += (uint32_t(15 - 127) << 23) + 0xfff; /* rounding bias part 2 */ f.u += mant_odd; /* take the bits! */ o = f.u >> 13; } } o |= sign >> 16; return o; #endif } float blender::math::half_to_float(uint16_t v) { #if defined(USE_HARDWARE_FP16_NEON) uint16x4_t v4 = vdup_n_u16(v); float16x4_t h4 = vreinterpret_f16_u16(v4); float32x4_t f4 = vcvt_f32_f16(h4); return vgetq_lane_f32(f4, 0); #else /* Based on half_to_float_fast4 from public domain https://gist.github.com/rygorous/2144712 * see corresponding blog post https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/ */ union FP32 { uint32_t u; float f; }; constexpr FP32 magic = {113 << 23}; constexpr uint32_t shifted_exp = 0x7c00 << 13; /* exponent mask after shift */ FP32 o; o.u = (v & 0x7fff) << 13; /* exponent/mantissa bits */ uint32_t exp = shifted_exp & o.u; /* just the exponent */ o.u += (127 - 15) << 23; /* exponent adjust */ /* handle exponent special cases */ if (exp == shifted_exp) { /* Inf/NaN? */ o.u += (128 - 16) << 23; /* extra exp adjust */ } else if (exp == 0) { /* Zero/Denormal? */ o.u += 1 << 23; /* extra exp adjust */ o.f -= magic.f; /* renormalize */ } o.u |= (v & 0x8000) << 16; /* sign bit */ return o.f; #endif } #ifdef USE_SSE2_FP16 /* 4x wide float<->half conversion using SSE2 code, based on * https://gist.github.com/rygorous/4d9e9e88cab13c703773dc767a23575f */ /* Float->half conversion with round-to-nearest-even, SSE2+. * leaves half-floats in 32-bit lanes (sign extended). */ static inline __m128i F32_to_F16_4x(const __m128 &f) { const __m128 mask_sign = _mm_set1_ps(-0.0f); /* all FP32 values >=this round to +inf */ const __m128i c_f16max = _mm_set1_epi32((127 + 16) << 23); const __m128i c_nanbit = _mm_set1_epi32(0x200); const __m128i c_nanlobits = _mm_set1_epi32(0x1ff); const __m128i c_infty_as_fp16 = _mm_set1_epi32(0x7c00); /* smallest FP32 that yields a normalized FP16 */ const __m128i c_min_normal = _mm_set1_epi32((127 - 14) << 23); const __m128i c_subnorm_magic = _mm_set1_epi32(((127 - 15) + (23 - 10) + 1) << 23); /* adjust exponent and add mantissa rounding */ const __m128i c_normal_bias = _mm_set1_epi32(0xfff - ((127 - 15) << 23)); __m128 justsign = _mm_and_ps(f, mask_sign); __m128 absf = _mm_andnot_ps(mask_sign, f); /* f & ~mask_sign */ /* the cast is "free" (extra bypass latency, but no throughput hit) */ __m128i absf_int = _mm_castps_si128(absf); __m128 b_isnan = _mm_cmpunord_ps(absf, absf); /* is this a NaN? */ __m128i b_isregular = _mm_cmpgt_epi32(c_f16max, absf_int); /* (sub)normalized or special? */ __m128i nan_payload = _mm_and_si128(_mm_srli_epi32(absf_int, 13), c_nanlobits); /* payload bits for NaNs */ __m128i nan_quiet = _mm_or_si128(nan_payload, c_nanbit); /* and set quiet bit */ __m128i nanfinal = _mm_and_si128(_mm_castps_si128(b_isnan), nan_quiet); __m128i inf_or_nan = _mm_or_si128(nanfinal, c_infty_as_fp16); /* output for specials */ /* subnormal? */ __m128i b_issub = _mm_cmpgt_epi32(c_min_normal, absf_int); /* "result is subnormal" path */ __m128 subnorm1 = _mm_add_ps( absf, _mm_castsi128_ps(c_subnorm_magic)); /* magic value to round output mantissa */ __m128i subnorm2 = _mm_sub_epi32(_mm_castps_si128(subnorm1), c_subnorm_magic); /* subtract out bias */ /* "result is normal" path */ __m128i mantoddbit = _mm_slli_epi32(absf_int, 31 - 13); /* shift bit 13 (mantissa LSB) to sign */ __m128i mantodd = _mm_srai_epi32(mantoddbit, 31); /* -1 if FP16 mantissa odd, else 0 */ __m128i round1 = _mm_add_epi32(absf_int, c_normal_bias); /* if mantissa LSB odd, bias towards rounding up (RTNE) */ __m128i round2 = _mm_sub_epi32(round1, mantodd); __m128i normal = _mm_srli_epi32(round2, 13); /* rounded result */ /* combine the two non-specials */ __m128i nonspecial = _mm_or_si128(_mm_and_si128(subnorm2, b_issub), _mm_andnot_si128(b_issub, normal)); /* merge in specials as well */ __m128i joined = _mm_or_si128(_mm_and_si128(nonspecial, b_isregular), _mm_andnot_si128(b_isregular, inf_or_nan)); __m128i sign_shift = _mm_srai_epi32(_mm_castps_si128(justsign), 16); __m128i result = _mm_or_si128(joined, sign_shift); return result; } /* Half->float conversion, SSE2+. Input in 32-bit lanes. */ static inline __m128 F16_to_F32_4x(const __m128i &h) { const __m128i mask_nosign = _mm_set1_epi32(0x7fff); const __m128 magic_mult = _mm_castsi128_ps(_mm_set1_epi32((254 - 15) << 23)); const __m128i was_infnan = _mm_set1_epi32(0x7bff); const __m128 exp_infnan = _mm_castsi128_ps(_mm_set1_epi32(255 << 23)); const __m128i was_nan = _mm_set1_epi32(0x7c00); const __m128i nan_quiet = _mm_set1_epi32(1 << 22); __m128i expmant = _mm_and_si128(mask_nosign, h); __m128i justsign = _mm_xor_si128(h, expmant); __m128i shifted = _mm_slli_epi32(expmant, 13); __m128 scaled = _mm_mul_ps(_mm_castsi128_ps(shifted), magic_mult); __m128i b_wasinfnan = _mm_cmpgt_epi32(expmant, was_infnan); __m128i sign = _mm_slli_epi32(justsign, 16); __m128 infnanexp = _mm_and_ps(_mm_castsi128_ps(b_wasinfnan), exp_infnan); __m128i b_wasnan = _mm_cmpgt_epi32(expmant, was_nan); __m128i nanquiet = _mm_and_si128(b_wasnan, nan_quiet); __m128 infnandone = _mm_or_ps(infnanexp, _mm_castsi128_ps(nanquiet)); __m128 sign_inf = _mm_or_ps(_mm_castsi128_ps(sign), infnandone); __m128 result = _mm_or_ps(scaled, sign_inf); return result; } #endif // USE_SSE2_FP16 void blender::math::float_to_half_array(const float *src, uint16_t *dst, size_t length) { size_t i = 0; #if defined(USE_HARDWARE_FP16_F16C) /* 8-wide loop using AVX2 F16C */ for (; i + 7 < length; i += 8) { __m256 src8 = _mm256_loadu_ps(src); __m128i h8 = _mm256_cvtps_ph(src8, _MM_FROUND_TO_NEAREST_INT); _mm_storeu_epi32(dst, h8); src += 8; dst += 8; } #elif defined(USE_SSE2_FP16) /* 4-wide loop using SSE2 */ for (; i + 3 < length; i += 4) { __m128 src4 = _mm_loadu_ps(src); __m128i h4 = F32_to_F16_4x(src4); __m128i h4_packed = _mm_packs_epi32(h4, h4); _mm_storeu_si64(dst, h4_packed); src += 4; dst += 4; } #elif defined(USE_HARDWARE_FP16_NEON) /* 4-wide loop using NEON */ for (; i + 3 < length; i += 4) { float32x4_t src4 = vld1q_f32(src); float16x4_t h4 = vcvt_f16_f32(src4); vst1_f16((float16_t *)dst, h4); src += 4; dst += 4; } #endif /* Use scalar path to convert the tail of array (or whole array if none of * wider paths above were used). */ for (; i < length; i++) { *dst++ = float_to_half(*src++); } } void blender::math::half_to_float_array(const uint16_t *src, float *dst, size_t length) { size_t i = 0; #if defined(USE_HARDWARE_FP16_F16C) /* 8-wide loop using AVX2 F16C */ for (; i + 7 < length; i += 8) { __m128i src8 = _mm_loadu_epi32(src); __m256 f8 = _mm256_cvtph_ps(src8); _mm256_storeu_ps(dst, f8); src += 8; dst += 8; } #elif defined(USE_SSE2_FP16) /* 4-wide loop using SSE2 */ for (; i + 3 < length; i += 4) { __m128i src4 = _mm_loadu_si64(src); src4 = _mm_unpacklo_epi16(src4, src4); __m128 f4 = F16_to_F32_4x(src4); _mm_storeu_ps(dst, f4); src += 4; dst += 4; } #elif defined(USE_HARDWARE_FP16_NEON) /* 4-wide loop using NEON */ for (; i + 3 < length; i += 4) { float16x4_t src4 = vld1_f16((const float16_t *)src); float32x4_t f4 = vcvt_f32_f16(src4); vst1q_f32(dst, f4); src += 4; dst += 4; } #endif /* Use scalar path to convert the tail of array (or whole array if none of * wider paths above were used). */ for (; i < length; i++) { *dst++ = half_to_float(*src++); } } #ifdef USE_HARDWARE_FP16_NEON # undef USE_HARDWARE_FP16_NEON #endif