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/* SPDX-License-Identifier: MIT
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use, copy,
* modify, merge, publish, distribute, sublicense, and/or sell copies
* of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
* Copyright:
* 2020 Evan Nemerson <evan@nemerson.com>
* 2021 Zhi An Ng <zhin@google.com> (Copyright owned by Google, LLC)
*/
#if !defined(SIMDE_ARM_NEON_RSQRTE_H)
#define SIMDE_ARM_NEON_RSQRTE_H
#include "types.h"
HEDLEY_DIAGNOSTIC_PUSH
SIMDE_DISABLE_UNWANTED_DIAGNOSTICS
SIMDE_BEGIN_DECLS_
SIMDE_FUNCTION_ATTRIBUTES
simde_float32_t
simde_vrsqrtes_f32(simde_float32_t a) {
#if defined(SIMDE_ARM_NEON_A64V8_NATIVE)
return vrsqrtes_f32(a);
#else
#if defined(SIMDE_IEEE754_STORAGE)
/* https://basesandframes.files.wordpress.com/2020/04/even_faster_math_functions_green_2020.pdf
Pages 100 - 103 */
#if SIMDE_ACCURACY_PREFERENCE <= 0
return (INT32_C(0x5F37624F) - (a >> 1));
#else
simde_float32 x = a;
simde_float32 xhalf = SIMDE_FLOAT32_C(0.5) * x;
int32_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
#if SIMDE_ACCURACY_PREFERENCE == 1
ix = INT32_C(0x5F375A82) - (ix >> 1);
#else
ix = INT32_C(0x5F37599E) - (ix >> 1);
#endif
simde_memcpy(&x, &ix, sizeof(x));
#if SIMDE_ACCURACY_PREFERENCE >= 2
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
#endif
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
return x;
#endif
#elif defined(simde_math_sqrtf)
return 1.0f / simde_math_sqrtf(a);
#else
HEDLEY_UNREACHABLE();
#endif
#endif
}
#if defined(SIMDE_ARM_NEON_A64V8_ENABLE_NATIVE_ALIASES)
#undef vrsqrtes_f32
#define vrsqrtes_f32(a) simde_vrsqrtes_f32((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_float64_t
simde_vrsqrted_f64(simde_float64_t a) {
#if defined(SIMDE_ARM_NEON_A64V8_NATIVE)
return vrsqrted_f64(a);
#else
#if defined(SIMDE_IEEE754_STORAGE)
//https://www.mdpi.com/1099-4300/23/1/86/htm
simde_float64_t x = a;
simde_float64_t xhalf = SIMDE_FLOAT64_C(0.5) * x;
int64_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
ix = INT64_C(0x5FE6ED2102DCBFDA) - (ix >> 1);
simde_memcpy(&x, &ix, sizeof(x));
x = x * (SIMDE_FLOAT64_C(1.50087895511633457) - xhalf * x * x);
x = x * (SIMDE_FLOAT64_C(1.50000057967625766) - xhalf * x * x);
return x;
#elif defined(simde_math_sqrtf)
return SIMDE_FLOAT64_C(1.0) / simde_math_sqrt(a_.values[i]);
#else
HEDLEY_UNREACHABLE();
#endif
#endif
}
#if defined(SIMDE_ARM_NEON_A64V8_ENABLE_NATIVE_ALIASES)
#undef vrsqrted_f64
#define vrsqrted_f64(a) simde_vrsqrted_f64((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_uint32x2_t
simde_vrsqrte_u32(simde_uint32x2_t a) {
#if defined(SIMDE_ARM_NEON_A32V7_NATIVE)
return vrsqrte_u32(a);
#else
simde_uint32x2_private
a_ = simde_uint32x2_to_private(a),
r_;
for(size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[i])) ; i++) {
if(a_.values[i] < 0x3FFFFFFF) {
r_.values[i] = UINT32_MAX;
} else {
uint32_t a_temp = (a_.values[i] >> 23) & 511;
if(a_temp < 256) {
a_temp = a_temp * 2 + 1;
} else {
a_temp = (a_temp >> 1) << 1;
a_temp = (a_temp + 1) * 2;
}
uint32_t b = 512;
while((a_temp * (b + 1) * (b + 1)) < (1 << 28))
b = b + 1;
r_.values[i] = (b + 1) / 2;
r_.values[i] = r_.values[i] << 23;
}
}
return simde_uint32x2_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A32V7_ENABLE_NATIVE_ALIASES)
#undef vrsqrte_u32
#define vrsqrte_u32(a) simde_vrsqrte_u32((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_float32x2_t
simde_vrsqrte_f32(simde_float32x2_t a) {
#if defined(SIMDE_ARM_NEON_A32V7_NATIVE)
return vrsqrte_f32(a);
#else
simde_float32x2_private
r_,
a_ = simde_float32x2_to_private(a);
#if defined(SIMDE_IEEE754_STORAGE)
/* https://basesandframes.files.wordpress.com/2020/04/even_faster_math_functions_green_2020.pdf
Pages 100 - 103 */
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[0])) ; i++) {
#if SIMDE_ACCURACY_PREFERENCE <= 0
r_.i32[i] = INT32_C(0x5F37624F) - (a_.i32[i] >> 1);
#else
simde_float32 x = a_.values[i];
simde_float32 xhalf = SIMDE_FLOAT32_C(0.5) * x;
int32_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
#if SIMDE_ACCURACY_PREFERENCE == 1
ix = INT32_C(0x5F375A82) - (ix >> 1);
#else
ix = INT32_C(0x5F37599E) - (ix >> 1);
#endif
simde_memcpy(&x, &ix, sizeof(x));
#if SIMDE_ACCURACY_PREFERENCE >= 2
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
#endif
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
r_.values[i] = x;
#endif
}
#elif defined(simde_math_sqrtf)
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.f32) / sizeof(r_.f32[0])) ; i++) {
r_.f32[i] = 1.0f / simde_math_sqrtf(a_.f32[i]);
}
#else
HEDLEY_UNREACHABLE();
#endif
return simde_float32x2_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A32V7_ENABLE_NATIVE_ALIASES)
#undef vrsqrte_f32
#define vrsqrte_f32(a) simde_vrsqrte_f32((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_float64x1_t
simde_vrsqrte_f64(simde_float64x1_t a) {
#if defined(SIMDE_ARM_NEON_A64V8_NATIVE)
return vrsqrte_f64(a);
#else
simde_float64x1_private
r_,
a_ = simde_float64x1_to_private(a);
#if defined(SIMDE_IEEE754_STORAGE)
//https://www.mdpi.com/1099-4300/23/1/86/htm
SIMDE_VECTORIZE
for(size_t i = 0 ; i < (sizeof(r_.values)/sizeof(r_.values[0])) ; i++) {
simde_float64_t x = a_.values[i];
simde_float64_t xhalf = SIMDE_FLOAT64_C(0.5) * x;
int64_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
ix = INT64_C(0x5FE6ED2102DCBFDA) - (ix >> 1);
simde_memcpy(&x, &ix, sizeof(x));
x = x * (SIMDE_FLOAT64_C(1.50087895511633457) - xhalf * x * x);
x = x * (SIMDE_FLOAT64_C(1.50000057967625766) - xhalf * x * x);
r_.values[i] = x;
}
#elif defined(simde_math_sqrtf)
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[0])) ; i++) {
r_.values[i] = SIMDE_FLOAT64_C(1.0) / simde_math_sqrt(a_.values[i]);
}
#else
HEDLEY_UNREACHABLE();
#endif
return simde_float64x1_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A64V8_ENABLE_NATIVE_ALIASES)
#undef vrsqrte_f64
#define vrsqrte_f64(a) simde_vrsqrte_f64((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_uint32x4_t
simde_vrsqrteq_u32(simde_uint32x4_t a) {
#if defined(SIMDE_ARM_NEON_A32V7_NATIVE)
return vrsqrteq_u32(a);
#else
simde_uint32x4_private
a_ = simde_uint32x4_to_private(a),
r_;
for(size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[i])) ; i++) {
if(a_.values[i] < 0x3FFFFFFF) {
r_.values[i] = UINT32_MAX;
} else {
uint32_t a_temp = (a_.values[i] >> 23) & 511;
if(a_temp < 256) {
a_temp = a_temp * 2 + 1;
} else {
a_temp = (a_temp >> 1) << 1;
a_temp = (a_temp + 1) * 2;
}
uint32_t b = 512;
while((a_temp * (b + 1) * (b + 1)) < (1 << 28))
b = b + 1;
r_.values[i] = (b + 1) / 2;
r_.values[i] = r_.values[i] << 23;
}
}
return simde_uint32x4_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A32V7_ENABLE_NATIVE_ALIASES)
#undef vrsqrteq_u32
#define vrsqrteq_u32(a) simde_vrsqrteq_u32((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_float32x4_t
simde_vrsqrteq_f32(simde_float32x4_t a) {
#if defined(SIMDE_ARM_NEON_A32V7_NATIVE)
return vrsqrteq_f32(a);
#elif defined(SIMDE_POWER_ALTIVEC_P6_NATIVE)
return vec_rsqrte(a);
#else
simde_float32x4_private
r_,
a_ = simde_float32x4_to_private(a);
#if defined(SIMDE_X86_SSE_NATIVE)
r_.m128 = _mm_rsqrt_ps(a_.m128);
#elif defined(SIMDE_IEEE754_STORAGE)
/* https://basesandframes.files.wordpress.com/2020/04/even_faster_math_functions_green_2020.pdf
Pages 100 - 103 */
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[0])) ; i++) {
#if SIMDE_ACCURACY_PREFERENCE <= 0
r_.i32[i] = INT32_C(0x5F37624F) - (a_.i32[i] >> 1);
#else
simde_float32 x = a_.values[i];
simde_float32 xhalf = SIMDE_FLOAT32_C(0.5) * x;
int32_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
#if SIMDE_ACCURACY_PREFERENCE == 1
ix = INT32_C(0x5F375A82) - (ix >> 1);
#else
ix = INT32_C(0x5F37599E) - (ix >> 1);
#endif
simde_memcpy(&x, &ix, sizeof(x));
#if SIMDE_ACCURACY_PREFERENCE >= 2
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
#endif
x = x * (SIMDE_FLOAT32_C(1.5008909) - xhalf * x * x);
r_.values[i] = x;
#endif
}
#elif defined(simde_math_sqrtf)
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.f32) / sizeof(r_.f32[0])) ; i++) {
r_.f32[i] = 1.0f / simde_math_sqrtf(a_.f32[i]);
}
#else
HEDLEY_UNREACHABLE();
#endif
return simde_float32x4_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A32V7_ENABLE_NATIVE_ALIASES)
#undef vrsqrteq_f32
#define vrsqrteq_f32(a) simde_vrsqrteq_f32((a))
#endif
SIMDE_FUNCTION_ATTRIBUTES
simde_float64x2_t
simde_vrsqrteq_f64(simde_float64x2_t a) {
#if defined(SIMDE_ARM_NEON_A64V8_NATIVE)
return vrsqrteq_f64(a);
#else
simde_float64x2_private
r_,
a_ = simde_float64x2_to_private(a);
#if defined(SIMDE_IEEE754_STORAGE)
//https://www.mdpi.com/1099-4300/23/1/86/htm
SIMDE_VECTORIZE
for(size_t i = 0 ; i < (sizeof(r_.values)/sizeof(r_.values[0])) ; i++) {
simde_float64_t x = a_.values[i];
simde_float64_t xhalf = SIMDE_FLOAT64_C(0.5) * x;
int64_t ix;
simde_memcpy(&ix, &x, sizeof(ix));
ix = INT64_C(0x5FE6ED2102DCBFDA) - (ix >> 1);
simde_memcpy(&x, &ix, sizeof(x));
x = x * (SIMDE_FLOAT64_C(1.50087895511633457) - xhalf * x * x);
x = x * (SIMDE_FLOAT64_C(1.50000057967625766) - xhalf * x * x);
r_.values[i] = x;
}
#elif defined(simde_math_sqrtf)
SIMDE_VECTORIZE
for (size_t i = 0 ; i < (sizeof(r_.values) / sizeof(r_.values[0])) ; i++) {
r_.values[i] = SIMDE_FLOAT64_C(1.0) / simde_math_sqrt(a_.values[i]);
}
#else
HEDLEY_UNREACHABLE();
#endif
return simde_float64x2_from_private(r_);
#endif
}
#if defined(SIMDE_ARM_NEON_A64V8_ENABLE_NATIVE_ALIASES)
#undef vrsqrteq_f64
#define vrsqrteq_f64(a) simde_vrsqrteq_f64((a))
#endif
SIMDE_END_DECLS_
HEDLEY_DIAGNOSTIC_POP
#endif /* !defined(SIMDE_ARM_NEON_RSQRTE_H) */
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