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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include "../imf.h"
#pragma OPENCL FP_CONTRACT OFF
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c11 = {0xbc8917bfu};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c10 = {0x3c0afad8u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c9 = {0x3cf6afd7u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c8 = {0xbd1e9009u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c7 = {0xbc0e2ce0u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c6 = {0x3d8ee88fu};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c5 = {0xbd84d3d8u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c4 = {0xbd3a0aceu};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c3 = {0x3e34898cu};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c2 = {0xbe05f565u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c1l = {0x31b69212u};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c1 = {0xbe8259aeu};
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_c0 = {0xbd94e63fu};
// 2.0^32
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_two32 = {0x4f800000u};
// 2.0^64
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_two64 = {0x5f800000u};
// 2.0^(-64)
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_twom64 = {0x1f800000u};
// 0
static __constant union {
unsigned int w;
float f;
int i;
} __satan2_ha_zero = {0x00000000u};
__attribute__((always_inline)) inline int
__ocl_svml_internal_satan2_ha(float *pa, float *pb, float *pres) {
int nRet = 0;
float xin = *pb, yin = *pa;
// float atan2f_ha(float yin, float xin)
{
volatile union {
unsigned int w;
float f;
int i;
} y, x;
union {
unsigned int w;
float f;
int i;
} ya, xa, hcorr, lcorr, fx, fy, hcorr2, lcorr2, sres, Q00;
unsigned sgn_x, sgn_y, sgn_r, sgn_c;
int sgnx_mask, smask;
float frcp_x, f_eps, fQl, R, poly;
volatile float fQ0;
y.f = yin;
x.f = xin;
// absolute values
xa.w = x.w & 0x7fffffff;
ya.w = y.w & 0x7fffffff;
// input signs
sgn_x = x.w ^ xa.w;
sgn_y = y.w ^ ya.w;
// initialize result correction (0, pi, or pi/2)
sgnx_mask = ((int)sgn_x) >> 31;
hcorr.w = sgnx_mask & 0x40490FDB;
lcorr.w = sgnx_mask & 0xB3BBBD2E;
// initialize sign correction
// sgn_r = sgn_x;
// now switch y, x if |y|>|x|
fy.w = (((xa.w) < (ya.w)) ? (xa.w) : (ya.w));
fx.w = (((xa.w) >= (ya.w)) ? (xa.w) : (ya.w));
// set correction term to pi/2 if xa<ya
smask = ((int)(xa.w - ya.w)) >> 31;
hcorr2.w = smask & 0x3fc90FDB;
lcorr2.w = smask & 0xB33BBD2E;
hcorr.f = hcorr2.f - hcorr.f;
lcorr.f = lcorr2.f - lcorr.f;
sgn_c = (smask & 0x80000000);
hcorr.w ^= sgn_c;
lcorr.w ^= sgn_c;
// also apply sign correction
sgn_r = sgn_c ^ (sgn_x ^ sgn_y);
// reciprocal: rcp_x ~ 1/x
frcp_x = 1.0f / (fx.f);
// refine reciprocal
f_eps = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )((-frcp_x), fx.f, 1.0f);
// quotient estimate
Q00.f = fQ0 = fy.f * frcp_x;
// redirect special inputs: NaN/Inf/zero, |x|>2^126
// testing done on ordered inputs
if (((unsigned)(fx.w - 0x00800000) > 0x7e000000) ||
(fy.f == __satan2_ha_zero.f) || (Q00.w < 0x0d800000))
goto SPECIAL_ATAN2F;
ATAN2F_MAIN:
// low part of quotient
fQl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fy.f, frcp_x, (-fQ0));
fQl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fQ0, f_eps, fQl);
// reduced argument
R = fQ0 - 0.5f;
R = R + fQl;
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(__satan2_ha_c11.f, R,
__satan2_ha_c10.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c9.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c8.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c7.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c6.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c5.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c3.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c1l.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __satan2_ha_c0.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(__satan2_ha_c1.f, R, poly);
// fQl + fQl*poly
sres.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, fQl, fQl);
// (R+ R*poly)+lcorr
sres.f = sres.f + lcorr.f;
// ((R+ R*poly)+lcorr)+Q0*poly
sres.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fQ0, poly, sres.f);
// ((R+ R*poly)+lcorr)+Q0*poly + Q0
sres.f = sres.f + fQ0;
// ((R+ R*poly)+lcorr)+Q0*poly + Q0 + hcorr
sres.f = sres.f + hcorr.f;
sres.w = sres.w ^ sgn_r;
*pres = sres.f;
return nRet;
SPECIAL_ATAN2F:
// NaN input
if (fx.w > 0x7f800000u) {
if (xa.w > 0x7f800000u)
sres.w = x.w | 0x00400000u;
else
sres.w = y.w | 0x00400000u;
*pres = sres.f;
return nRet;
}
// zero input?
if (fy.f == __satan2_ha_zero.f) {
sres.w = sgn_y ^ (hcorr.w & 0x7fffffff);
*pres = sres.f;
return nRet;
}
// Inf input?
if (fx.w == 0x7f800000) {
if (fy.w < 0x7f800000u) {
if (ya.w == 0x7f800000u)
sres.w = sgn_y ^ 0x3fc90FDB;
else
sres.w = sgn_r ^ sgn_c ^ hcorr.w;
*pres = sres.f;
return nRet;
}
// both inputs are +/-Inf
if (x.w == 0xff800000u)
sres.w = 0x4016CBE4;
else // +Inf
sres.w = 0x3f490FDB;
sres.w ^= sgn_y;
*pres = sres.f;
return nRet;
}
// very small |x|, |y|?
if (fx.w < 0x00800000u) {
// scale inputs
fx.f *= __satan2_ha_two32.f;
fy.f *= __satan2_ha_two32.f;
} else if (fx.w > 0x7e800000u) {
// large |x|
fx.f *= 0.25f;
fy.f *= 0.25f;
}
// reciprocal: rcp_x ~ 1/x
frcp_x = 1.0f / (fx.f);
// refine reciprocal
f_eps = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )((-frcp_x), fx.f, 1.0f);
// quotient estimate
Q00.f = fQ0 = fy.f * frcp_x;
if (Q00.w < 0x0d800000) {
fy.f *= __satan2_ha_two64.f;
// reciprocal: rcp_x ~ 1/x
frcp_x = 1.0f / (fx.f);
// refine reciprocal
f_eps = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )((-frcp_x), fx.f, 1.0f);
// quotient estimate
fQ0 = fy.f * frcp_x;
// low part of quotient
fQl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fy.f, frcp_x, (-fQ0));
fQl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fQ0, f_eps, fQl);
sres.f = fQ0 + fQl;
sres.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(
sres.f, __satan2_ha_twom64.f, hcorr.f);
sres.w = sres.w ^ sgn_r;
*pres = sres.f;
return nRet;
}
// return to main path
goto ATAN2F_MAIN;
}
return nRet;
}
float __ocl_svml_atan2f_ha(float x, float y) {
float r;
__ocl_svml_internal_satan2_ha(&x, &y, &r);
return r;
}
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